%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU408+3 : 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 : n003.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 7.30s 3.02s
% Output : Refutation 9.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 18 unt; 2 def)
% Number of atoms : 319 ( 42 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 : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-6 aty)
% Number of variables : 101 ( 0 sgn 92 !; 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(f418,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(f675,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f19022,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(f19025,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(f19026,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(f19037,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(f19038,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)],[f19037]) ).
fof(f19095,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,[],[f19038]) ).
fof(f19096,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,[],[f19095]) ).
fof(f19118,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f675]) ).
fof(f19164,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,[],[f19026]) ).
fof(f19165,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,[],[f19164]) ).
fof(f19166,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,[],[f19025]) ).
fof(f19167,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,[],[f19166]) ).
fof(f19168,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,[],[f19022]) ).
fof(f19169,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,[],[f19168]) ).
fof(f19943,plain,
( ~ m1_subset_1(sK21,u1_struct_0(k1_latsum_1(sK19,sK20)))
& r2_hidden(sK21,u1_struct_0(sK20))
& ~ v3_struct_0(sK20)
& v2_orders_2(sK20)
& v3_orders_2(sK20)
& v4_orders_2(sK20)
& v1_lattice3(sK20)
& l1_orders_2(sK20)
& ~ v3_struct_0(sK19)
& v2_orders_2(sK19)
& v3_orders_2(sK19)
& v4_orders_2(sK19)
& v1_lattice3(sK19)
& l1_orders_2(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X0,sK19),skolemize(X1,sK20),skolemize(X2,sK21)],[f19096]) ).
fof(f19977,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,[],[f19167]) ).
fof(f19978,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,[],[f19977]) ).
fof(f20256,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(f20257,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,[],[f20256]) ).
fof(f20258,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,[],[f20257]) ).
fof(f20259,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ( ( ( ~ r2_hidden(sK235(X0,X1,X2),X0)
& ~ r2_hidden(sK235(X0,X1,X2),X1) )
| ~ r2_hidden(sK235(X0,X1,X2),X2) )
& ( r2_hidden(sK235(X0,X1,X2),X0)
| r2_hidden(sK235(X0,X1,X2),X1)
| r2_hidden(sK235(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,[sK235]),skolemize(X3,sK235(X0,X1,X2))],[f20258]) ).
fof(f20263,plain,
l1_orders_2(sK19),
inference(cnf_transformation,[],[f19943]) ).
fof(f20269,plain,
l1_orders_2(sK20),
inference(cnf_transformation,[],[f19943]) ).
fof(f20274,plain,
~ v3_struct_0(sK20),
inference(cnf_transformation,[],[f19943]) ).
fof(f20275,plain,
r2_hidden(sK21,u1_struct_0(sK20)),
inference(cnf_transformation,[],[f19943]) ).
fof(f20276,plain,
~ m1_subset_1(sK21,u1_struct_0(k1_latsum_1(sK19,sK20))),
inference(cnf_transformation,[],[f19943]) ).
fof(f20297,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f19118]) ).
fof(f20360,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,[],[f19165]) ).
fof(f20363,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,[],[f19978]) ).
fof(f20365,plain,
! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(cnf_transformation,[],[f19169]) ).
fof(f21613,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k3_tarski(k2_tarski(X0,X1)),
inference(cnf_transformation,[],[f418]) ).
fof(f21654,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f54]) ).
fof(f21661,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X0)
| k2_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f20259]) ).
fof(f21685,plain,
! [X2,X0,X1] :
( u1_struct_0(X2) = k3_tarski(k2_tarski(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,[],[f20363,f21613]) ).
fof(f22029,plain,
! [X0,X1] : k3_tarski(k2_tarski(X0,X1)) = k3_tarski(k2_tarski(X1,X0)),
inference(definition_unfolding,[],[f21654,f21613,f21613]) ).
fof(f22037,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X0)
| k3_tarski(k2_tarski(X0,X1)) != X2 ),
inference(definition_unfolding,[],[f21661,f21613]) ).
fof(f22057,plain,
! [X0,X1] :
( u1_struct_0(k1_latsum_1(X0,X1)) = k3_tarski(k2_tarski(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,[],[f21685]) ).
fof(f22180,plain,
! [X0,X1,X4] :
( r2_hidden(X4,k3_tarski(k2_tarski(X0,X1)))
| ~ r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f22037]) ).
fof(f22211,plain,
~ r2_hidden(sK21,u1_struct_0(k1_latsum_1(sK19,sK20))),
inference(resolution,[],[f20276,f20297]) ).
fof(f22229,definition,
( spl237_3
<=> l1_orders_2(k1_latsum_1(sK19,sK20)) ),
introduced(definition,[new_symbols(definition,[spl237_3])],[avatar_definition]) ).
fof(f22230,plain,
( l1_orders_2(k1_latsum_1(sK19,sK20))
| ~ spl237_3 ),
inference(avatar_component_clause,[],[f22229]) ).
fof(f22231,plain,
( ~ l1_orders_2(k1_latsum_1(sK19,sK20))
| spl237_3 ),
inference(avatar_component_clause,[],[f22229]) ).
fof(f22233,definition,
( spl237_4
<=> v1_orders_2(k1_latsum_1(sK19,sK20)) ),
introduced(definition,[new_symbols(definition,[spl237_4])],[avatar_definition]) ).
fof(f22234,plain,
( v1_orders_2(k1_latsum_1(sK19,sK20))
| ~ spl237_4 ),
inference(avatar_component_clause,[],[f22233]) ).
fof(f22235,plain,
( ~ v1_orders_2(k1_latsum_1(sK19,sK20))
| spl237_4 ),
inference(avatar_component_clause,[],[f22233]) ).
fof(f22250,plain,
( ~ l1_orders_2(sK19)
| ~ l1_orders_2(sK20)
| spl237_3 ),
inference(resolution,[],[f22231,f20365]) ).
fof(f22251,plain,
( ~ l1_orders_2(sK20)
| spl237_3 ),
inference(forward_subsumption_resolution,[],[f22250,f20263]) ).
fof(f22252,plain,
( $false
| spl237_3 ),
inference(forward_subsumption_resolution,[],[f22251,f20269]) ).
fof(f22253,plain,
spl237_3,
inference(avatar_contradiction_clause,[],[f22252]) ).
fof(f22255,plain,
( ~ l1_orders_2(sK19)
| v3_struct_0(sK20)
| ~ l1_orders_2(sK20)
| spl237_4 ),
inference(resolution,[],[f22235,f20360]) ).
fof(f22258,plain,
( v3_struct_0(sK20)
| ~ l1_orders_2(sK20)
| spl237_4 ),
inference(forward_subsumption_resolution,[],[f22255,f20263]) ).
fof(f22261,plain,
( ~ l1_orders_2(sK20)
| spl237_4 ),
inference(forward_subsumption_resolution,[],[f22258,f20274]) ).
fof(f22266,plain,
( $false
| spl237_4 ),
inference(forward_subsumption_resolution,[],[f22261,f20269]) ).
fof(f22267,plain,
spl237_4,
inference(avatar_contradiction_clause,[],[f22266]) ).
fof(f22274,plain,
( ~ r2_hidden(sK21,k3_tarski(k2_tarski(u1_struct_0(sK19),u1_struct_0(sK20))))
| ~ v1_orders_2(k1_latsum_1(sK19,sK20))
| ~ l1_orders_2(k1_latsum_1(sK19,sK20))
| ~ l1_orders_2(sK20)
| ~ l1_orders_2(sK19) ),
inference(superposition,[],[f22211,f22057]) ).
fof(f22275,plain,
( ~ r2_hidden(sK21,k3_tarski(k2_tarski(u1_struct_0(sK19),u1_struct_0(sK20))))
| ~ l1_orders_2(k1_latsum_1(sK19,sK20))
| ~ l1_orders_2(sK20)
| ~ l1_orders_2(sK19)
| ~ spl237_4 ),
inference(forward_subsumption_resolution,[],[f22274,f22234]) ).
fof(f22276,plain,
( ~ r2_hidden(sK21,k3_tarski(k2_tarski(u1_struct_0(sK19),u1_struct_0(sK20))))
| ~ l1_orders_2(sK20)
| ~ l1_orders_2(sK19)
| ~ spl237_3
| ~ spl237_4 ),
inference(forward_subsumption_resolution,[],[f22275,f22230]) ).
fof(f22277,plain,
( ~ r2_hidden(sK21,k3_tarski(k2_tarski(u1_struct_0(sK19),u1_struct_0(sK20))))
| ~ l1_orders_2(sK19)
| ~ spl237_3
| ~ spl237_4 ),
inference(forward_subsumption_resolution,[],[f22276,f20269]) ).
fof(f22278,plain,
( ~ r2_hidden(sK21,k3_tarski(k2_tarski(u1_struct_0(sK19),u1_struct_0(sK20))))
| ~ spl237_3
| ~ spl237_4 ),
inference(forward_subsumption_resolution,[],[f22277,f20263]) ).
fof(f22279,plain,
( ~ r2_hidden(sK21,k3_tarski(k2_tarski(u1_struct_0(sK20),u1_struct_0(sK19))))
| ~ spl237_3
| ~ spl237_4 ),
inference(forward_demodulation,[],[f22278,f22029]) ).
fof(f22358,plain,
( ~ r2_hidden(sK21,u1_struct_0(sK20))
| ~ spl237_3
| ~ spl237_4 ),
inference(resolution,[],[f22279,f22180]) ).
fof(f22360,plain,
( $false
| ~ spl237_3
| ~ spl237_4 ),
inference(forward_subsumption_resolution,[],[f22358,f20275]) ).
fof(f22361,plain,
( ~ spl237_3
| ~ spl237_4 ),
inference(avatar_contradiction_clause,[],[f22360]) ).
cnf(s3,plain,
spl237_3,
inference(sat_conversion,[],[f22253]) ).
cnf(s6,plain,
spl237_4,
inference(sat_conversion,[],[f22267]) ).
cnf(s8,plain,
( ~ spl237_3
| ~ spl237_4 ),
inference(sat_conversion,[],[f22361]) ).
cnf(s9,plain,
~ spl237_3,
inference(rat,[],[s8,s6]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s3,s9]) ).
fof(f22362,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU408+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 05:12:44 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 7.30/3.02 % (1208610)Detected formulas, will run a generic FOF schedule.
% 7.30/3.02 % (1208615)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=132937047:i=141193_2989 on theBenchmark for (2989ds/141193Mi)
% 7.30/3.02 % (1208617)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=940508083:i=141695:sd=1:nm=32:gsp=on:ss=included_2989 on theBenchmark for (2989ds/141695Mi)
% 7.30/3.02 % (1208619)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=835848826:i=119:av=off:ss=axioms_2989 on theBenchmark for (2989ds/119Mi)
% 7.30/3.02 % (1208616)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=3514455905:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2989 on theBenchmark for (2989ds/134677Mi)
% 7.30/3.02 % (1208621)dis-21_1_sil=8000:lcm=predicate:random_seed=1531701468:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2989 on theBenchmark for (2989ds/129Mi)
% 7.30/3.02 % (1208620)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1957449424:s2a=on:i=139:gtg=position_2989 on theBenchmark for (2989ds/139Mi)
% 7.30/3.02 % (1208618)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2718987637:i=109:sd=1:ins=1:gsp=on:ss=axioms_2989 on theBenchmark for (2989ds/109Mi)
% 7.30/3.02 % (1208620)Instruction limit reached!
% 7.30/3.02 % (1208620)------------------------------
% 7.30/3.02 % (1208620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208620)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208620)Termination reason: Instruction limit
% 7.30/3.02 % (1208620)Termination phase: Property scanning
% 7.30/3.02 % (1208620)Time elapsed: 0.060 s
% 7.30/3.02 % (1208620)Peak memory usage: 112 MB
% 7.30/3.02 % (1208620)Instructions burned: 141 (million)
% 7.30/3.02 % (1208619)Instruction limit reached!
% 7.30/3.02 % (1208619)------------------------------
% 7.30/3.02 % (1208619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208619)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208619)Termination reason: Instruction limit
% 7.30/3.02 % (1208619)Termination phase: Preprocessing 2
% 7.30/3.02 % (1208619)Time elapsed: 0.099 s
% 7.30/3.02 % (1208619)Peak memory usage: 114 MB
% 7.30/3.02 % (1208619)Instructions burned: 119 (million)
% 7.30/3.02 % (1208621)Instruction limit reached!
% 7.30/3.02 % (1208621)------------------------------
% 7.30/3.02 % (1208621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208621)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208621)Termination reason: Instruction limit
% 7.30/3.02 % (1208621)Termination phase: SInE selection
% 7.30/3.02 % (1208621)Time elapsed: 0.087 s
% 7.30/3.02 % (1208621)Peak memory usage: 112 MB
% 7.30/3.02 % (1208621)Instructions burned: 130 (million)
% 7.30/3.02 % (1208618)Instruction limit reached!
% 7.30/3.02 % (1208618)------------------------------
% 7.30/3.02 % (1208618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208618)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208618)Termination reason: Instruction limit
% 7.30/3.02 % (1208618)Termination phase: SInE selection
% 7.30/3.02 % (1208618)Time elapsed: 0.088 s
% 7.30/3.02 % (1208618)Peak memory usage: 112 MB
% 7.30/3.02 % (1208618)Instructions burned: 109 (million)
% 7.30/3.02 % (1208629)lrs+10_1_sil=8000:sp=occurrence:random_seed=1673650661:i=285:sd=3:ss=axioms:sgt=8_2986 on theBenchmark for (2986ds/285Mi)
% 7.30/3.02 % (1208630)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3086425841:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2986 on theBenchmark for (2986ds/157Mi)
% 7.30/3.02 % (1208631)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3703201859:i=325:sd=1:ss=axioms:sgt=32_2986 on theBenchmark for (2986ds/325Mi)
% 7.30/3.02 % (1208632)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=4285454755:s2a=on:i=248:s2at=1.23:gtg=position_2986 on theBenchmark for (2986ds/248Mi)
% 7.30/3.02 % (1208630)Instruction limit reached!
% 7.30/3.02 % (1208630)------------------------------
% 7.30/3.02 % (1208630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208630)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208630)Termination reason: Instruction limit
% 7.30/3.02 % (1208630)Termination phase: Property scanning
% 7.30/3.02 % (1208630)Time elapsed: 0.067 s
% 7.30/3.02 % (1208630)Peak memory usage: 112 MB
% 7.30/3.02 % (1208630)Instructions burned: 158 (million)
% 7.30/3.02 % (1208632)Instruction limit reached!
% 7.30/3.02 % (1208632)------------------------------
% 7.30/3.02 % (1208632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208632)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208632)Termination reason: Instruction limit
% 7.30/3.02 % (1208632)Termination phase: Property scanning
% 7.30/3.02 % (1208632)Time elapsed: 0.104 s
% 7.30/3.02 % (1208632)Peak memory usage: 112 MB
% 7.30/3.02 % (1208632)Instructions burned: 249 (million)
% 7.30/3.02 % (1208629)Instruction limit reached!
% 7.30/3.02 % (1208629)------------------------------
% 7.30/3.02 % (1208629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208629)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208629)Termination reason: Instruction limit
% 7.30/3.02 % (1208629)Termination phase: Saturation
% 7.30/3.02 % (1208629)Time elapsed: 0.215 s
% 7.30/3.02 % (1208629)Peak memory usage: 119 MB
% 7.30/3.02 % (1208629)Instructions burned: 285 (million)
% 7.30/3.02 % (1208637)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4159369072:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2984 on theBenchmark for (2984ds/294Mi)
% 7.30/3.02 % (1208631)Instruction limit reached!
% 7.30/3.02 % (1208631)------------------------------
% 7.30/3.02 % (1208631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208631)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208631)Termination reason: Instruction limit
% 7.30/3.02 % (1208631)Termination phase: Saturation
% 7.30/3.02 % (1208631)Time elapsed: 0.238 s
% 7.30/3.02 % (1208631)Peak memory usage: 119 MB
% 7.30/3.02 % (1208631)Instructions burned: 325 (million)
% 7.30/3.02 % (1208638)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1857872231:i=2350_2983 on theBenchmark for (2983ds/2350Mi)
% 7.30/3.02 % (1208639)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2517808877:cts=off:i=113:fsr=off:ss=included:sgt=4_2983 on theBenchmark for (2983ds/113Mi)
% 7.30/3.02 % (1208637)First to succeed.
% 7.30/3.02 % (1208637)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1208610"
% 7.30/3.02 % (1208641)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=242176112:i=127:av=off:fsr=off:sup=off_2982 on theBenchmark for (2982ds/127Mi)
% 7.30/3.02 % (1208639)Instruction limit reached!
% 7.30/3.02 % (1208639)------------------------------
% 7.30/3.02 % (1208639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208639)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208639)Termination reason: Instruction limit
% 7.30/3.02 % (1208639)Termination phase: SInE selection
% 7.30/3.02 % (1208639)Time elapsed: 0.089 s
% 7.30/3.02 % (1208639)Peak memory usage: 112 MB
% 7.30/3.02 % (1208639)Instructions burned: 113 (million)
% 7.30/3.02 % (1208641)Instruction limit reached!
% 7.30/3.02 % (1208641)------------------------------
% 7.30/3.02 % (1208641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.30/3.02 % (1208641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.30/3.02 % (1208641)CaDiCaL version: 2.1.3
% 7.30/3.02 % (1208641)Termination reason: Instruction limit
% 7.30/3.02 % (1208641)Termination phase: Preprocessing 1
% 7.30/3.02 % (1208641)Time elapsed: 0.092 s
% 7.30/3.02 % (1208641)Peak memory usage: 113 MB
% 7.30/3.02 % (1208641)Instructions burned: 128 (million)
% 7.30/3.02 % (1208645)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1775769018:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2980 on theBenchmark for (2980ds/114Mi)
% 7.30/3.02 % (1208637)Refutation found. Thanks to Tanya!
% 7.30/3.02 % SZS status Theorem for theBenchmark
% 7.30/3.02 % SZS output start Proof for theBenchmark
% See solution above
% 9.24/3.16 % (1208637)------------------------------
% 9.24/3.16 % (1208637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.24/3.16 % (1208637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.24/3.16 % (1208637)CaDiCaL version: 2.1.3
% 9.24/3.16 % (1208637)Termination reason: Refutation
% 9.24/3.16 % (1208637)Time elapsed: 0.189 s
% 9.24/3.16 % (1208637)Peak memory usage: 120 MB
% 9.24/3.16 % (1208637)Instructions burned: 279 (million)
% 9.24/3.16 % (1208637)------------------------------
% 9.24/3.16 % (1208637)------------------------------
% 9.24/3.16 % (1208610)Success in time 2.16 s
% 9.24/3.16 % Vampire exiting
%------------------------------------------------------------------------------