%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU407+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:48:45 PM UTC 2026
% Result : Theorem 4.11s 1.58s
% Output : Refutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 88 ( 20 unt; 4 def)
% Number of atoms : 314 ( 41 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 383 ( 157 ~; 143 |; 60 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-6 aty)
% Number of variables : 109 ( 0 sgn 100 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_orders_2(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( r2_hidden(X2,u1_struct_0(X0))
| r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_latsum_1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& l1_orders_2(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( r2_hidden(X2,u1_struct_0(X0))
| r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',d2_latsum_1) ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(f18,axiom,
! [X0] :
( l1_orders_2(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f30,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/sandbox2/benchmark/theBenchmark.p',fc1_latsum_1) ).
fof(f31,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f47,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( v1_xboole_0(X1)
| r2_hidden(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f48,axiom,
! [X0,X1] : k2_xboole_0(X0,k4_xboole_0(X1,X0)) = k2_xboole_0(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f59,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r2_hidden(X2,u1_struct_0(X0))
& ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
& ~ v3_struct_0(X1)
& l1_orders_2(X1) )
& ~ v3_struct_0(X0)
& l1_orders_2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f60,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r2_hidden(X2,u1_struct_0(X0))
& ~ r2_hidden(X2,k4_xboole_0(u1_struct_0(X1),u1_struct_0(X0)))
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
& ~ v3_struct_0(X1)
& l1_orders_2(X1) )
& ~ v3_struct_0(X0)
& l1_orders_2(X0) ),
inference(flattening,[],[f59]) ).
fof(f63,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,[],[f30]) ).
fof(f64,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,[],[f63]) ).
fof(f65,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,[],[f10]) ).
fof(f66,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,[],[f65]) ).
fof(f67,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,[],[f7]) ).
fof(f68,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,[],[f67]) ).
fof(f71,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f72,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f71]) ).
fof(f76,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f80,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f81,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f80]) ).
fof(f86,plain,
( ~ r2_hidden(sK2,u1_struct_0(sK0))
& ~ r2_hidden(sK2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)))
& m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
& ~ v3_struct_0(sK1)
& l1_orders_2(sK1)
& ~ v3_struct_0(sK0)
& l1_orders_2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f60]) ).
fof(f87,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,[],[f68]) ).
fof(f88,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,[],[f87]) ).
fof(f93,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,[],[f8]) ).
fof(f94,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,[],[f93]) ).
fof(f95,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,[],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( X2 = k2_xboole_0(X0,X1)
| ( ( ( ~ r2_hidden(sK7(X0,X1,X2),X0)
& ~ r2_hidden(sK7(X0,X1,X2),X1) )
| ~ r2_hidden(sK7(X0,X1,X2),X2) )
& ( r2_hidden(sK7(X0,X1,X2),X0)
| r2_hidden(sK7(X0,X1,X2),X1)
| r2_hidden(sK7(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,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f95]) ).
fof(f97,plain,
l1_orders_2(sK0),
inference(cnf_transformation,[],[f86]) ).
fof(f99,plain,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f86]) ).
fof(f100,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f86]) ).
fof(f101,plain,
m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f86]) ).
fof(f102,plain,
~ r2_hidden(sK2,k4_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0))),
inference(cnf_transformation,[],[f86]) ).
fof(f103,plain,
~ r2_hidden(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f86]) ).
fof(f107,plain,
! [X0,X1] :
( ~ v3_struct_0(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| v3_struct_0(X1)
| ~ l1_orders_2(X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f108,plain,
! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f109,plain,
! [X0,X1] :
( v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f111,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,[],[f88]) ).
fof(f117,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f121,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f124,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f127,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f132,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X0)
| r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2)
| k2_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f96]) ).
fof(f139,plain,
! [X0,X1] :
( ~ v1_orders_2(k1_latsum_1(X0,X1))
| u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(equality_resolution,[],[f111]) ).
fof(f143,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k2_xboole_0(X0,X1))
| r2_hidden(X4,X1)
| r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f132]) ).
fof(f144,plain,
( r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1))) ),
inference(resolution,[],[f127,f101]) ).
fof(f147,definition,
( spl8_1
<=> v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f149,plain,
( v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f151,definition,
( spl8_2
<=> r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f153,plain,
( r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f144,f151,f147]) ).
fof(f202,plain,
! [X2,X0,X1] :
( r2_hidden(X2,k4_xboole_0(X1,X0))
| ~ r2_hidden(X2,k2_xboole_0(X0,X1))
| r2_hidden(X2,X0) ),
inference(superposition,[],[f143,f124]) ).
fof(f208,plain,
! [X0,X1] :
( u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(resolution,[],[f139,f109]) ).
fof(f209,plain,
! [X0,X1] :
( u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(duplicate_literal_removal,[],[f208]) ).
fof(f210,plain,
! [X0,X1] :
( ~ l1_orders_2(X1)
| u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1))
| ~ l1_orders_2(X0) ),
inference(forward_subsumption_resolution,[],[f209,f108]) ).
fof(f250,plain,
( ~ r2_hidden(sK2,k2_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| r2_hidden(sK2,u1_struct_0(sK0)) ),
inference(resolution,[],[f202,f102]) ).
fof(f255,plain,
~ r2_hidden(sK2,k2_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),
inference(forward_subsumption_resolution,[],[f250,f103]) ).
fof(f267,plain,
! [X0] :
( ~ l1_orders_2(X0)
| u1_struct_0(k1_latsum_1(X0,sK1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(sK1)) ),
inference(resolution,[],[f210,f99]) ).
fof(f305,plain,
u1_struct_0(k1_latsum_1(sK0,sK1)) = k2_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),
inference(resolution,[],[f267,f97]) ).
fof(f321,plain,
~ r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(superposition,[],[f255,f305]) ).
fof(f323,plain,
( $false
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f321,f153]) ).
fof(f324,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[],[f323]) ).
fof(f325,plain,
( v3_struct_0(k1_latsum_1(sK0,sK1))
| ~ l1_struct_0(k1_latsum_1(sK0,sK1))
| ~ spl8_1 ),
inference(resolution,[],[f149,f117]) ).
fof(f329,definition,
( spl8_3
<=> l1_struct_0(k1_latsum_1(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f331,plain,
( ~ l1_struct_0(k1_latsum_1(sK0,sK1))
| spl8_3 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f333,definition,
( spl8_4
<=> v3_struct_0(k1_latsum_1(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f335,plain,
( v3_struct_0(k1_latsum_1(sK0,sK1))
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f336,plain,
( ~ spl8_3
| spl8_4
| ~ spl8_1 ),
inference(avatar_split_clause,[],[f325,f147,f333,f329]) ).
fof(f337,plain,
( ~ l1_orders_2(k1_latsum_1(sK0,sK1))
| spl8_3 ),
inference(resolution,[],[f331,f121]) ).
fof(f338,plain,
( ~ l1_orders_2(sK0)
| ~ l1_orders_2(sK1)
| spl8_3 ),
inference(resolution,[],[f337,f108]) ).
fof(f339,plain,
( ~ l1_orders_2(sK1)
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f338,f97]) ).
fof(f340,plain,
( $false
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f339,f99]) ).
fof(f341,plain,
spl8_3,
inference(avatar_contradiction_clause,[],[f340]) ).
fof(f358,plain,
( ~ l1_orders_2(sK0)
| v3_struct_0(sK1)
| ~ l1_orders_2(sK1)
| ~ spl8_4 ),
inference(resolution,[],[f335,f107]) ).
fof(f361,plain,
( v3_struct_0(sK1)
| ~ l1_orders_2(sK1)
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f358,f97]) ).
fof(f363,plain,
( ~ l1_orders_2(sK1)
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f361,f100]) ).
fof(f366,plain,
( $false
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f363,f99]) ).
fof(f367,plain,
~ spl8_4,
inference(avatar_contradiction_clause,[],[f366]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f154]) ).
cnf(s2,plain,
~ spl8_2,
inference(sat_conversion,[],[f324]) ).
cnf(s3,plain,
( ~ spl8_1
| ~ spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f336]) ).
cnf(s4,plain,
spl8_3,
inference(sat_conversion,[],[f341]) ).
cnf(s6,plain,
~ spl8_4,
inference(sat_conversion,[],[f367]) ).
cnf(s7,plain,
~ spl8_1,
inference(rat,[],[s3,s6,s4]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s2,s7]) ).
fof(f368,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU407+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n003.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 05:12:12 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 4.11/1.58 % (1201548)Detected formulas, will run a generic FOF schedule.
% 4.11/1.58 % (1201559)dis-21_1_sil=8000:lcm=predicate:random_seed=2531513645: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)
% 4.11/1.58 % (1201559)Instruction limit reached!
% 4.11/1.58 % (1201559)------------------------------
% 4.11/1.58 % (1201559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.58 % (1201559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.58 % (1201559)CaDiCaL version: 2.1.3
% 4.11/1.58 % (1201559)Termination reason: Instruction limit
% 4.11/1.58 % (1201559)Termination phase: Saturation
% 4.11/1.58 % (1201559)Time elapsed: 0.040 s
% 4.11/1.58 % (1201559)Peak memory usage: 89 MB
% 4.11/1.58 % (1201559)Instructions burned: 133 (million)
% 4.11/1.58 % (1201553)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=1282148714:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.11/1.58 % (1201555)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=3071969047:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.11/1.58 % (1201556)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1463172289:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.11/1.58 % (1201557)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2721406080:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.11/1.58 % (1201554)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=4058061926:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.11/1.58 % (1201558)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4053415930:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.11/1.58 % (1201556)Refutation not found, incomplete strategy
% 4.11/1.58 % (1201556)------------------------------
% 4.11/1.58 % (1201556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.58 % (1201556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.58 % (1201556)CaDiCaL version: 2.1.3
% 4.11/1.58 % (1201556)Termination reason: Refutation not found, incomplete strategy
% 4.11/1.58 % (1201556)Time elapsed: 0.002 s
% 4.11/1.58 % (1201556)Peak memory usage: 88 MB
% 4.11/1.58 % (1201556)Instructions burned: 2 (million)
% 4.11/1.58 % (1201557)Instruction limit reached!
% 4.11/1.58 % (1201557)------------------------------
% 4.11/1.58 % (1201557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.58 % (1201557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.58 % (1201557)CaDiCaL version: 2.1.3
% 4.11/1.58 % (1201557)Termination reason: Instruction limit
% 4.11/1.58 % (1201557)Termination phase: Saturation
% 4.11/1.58 % (1201557)Time elapsed: 0.074 s
% 4.11/1.58 % (1201557)Peak memory usage: 88 MB
% 4.11/1.58 % (1201557)Instructions burned: 120 (million)
% 4.11/1.58 % (1201558)Instruction limit reached!
% 4.11/1.58 % (1201558)------------------------------
% 4.11/1.58 % (1201558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.58 % (1201558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.58 % (1201558)CaDiCaL version: 2.1.3
% 4.11/1.58 % (1201558)Termination reason: Instruction limit
% 4.11/1.58 % (1201558)Termination phase: Saturation
% 4.11/1.58 % (1201558)Time elapsed: 0.092 s
% 4.11/1.58 % (1201558)Peak memory usage: 90 MB
% 4.11/1.58 % (1201558)Instructions burned: 140 (million)
% 4.11/1.58 % (1201567)lrs+10_1_sil=8000:sp=occurrence:random_seed=1825392146:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.11/1.58 % (1201567)Instruction limit reached!
% 4.11/1.58 % (1201567)------------------------------
% 4.11/1.58 % (1201567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.58 % (1201567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.58 % (1201567)CaDiCaL version: 2.1.3
% 4.11/1.58 % (1201567)Termination reason: Instruction limit
% 4.11/1.58 % (1201567)Termination phase: Saturation
% 4.11/1.58 % (1201567)Time elapsed: 0.094 s
% 4.11/1.58 % (1201567)Peak memory usage: 91 MB
% 4.11/1.58 % (1201567)Instructions burned: 287 (million)
% 4.11/1.58 % (1201568)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1673959561:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.11/1.58 % (1201556)------------------------------
% 4.11/1.58 % (1201556)------------------------------
% 4.11/1.58 % (1201569)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1478480059:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.11/1.58 % (1201569)First to succeed.
% 4.11/1.58 % (1201569)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1201548"
% 4.11/1.58 % (1201568)Instruction limit reached!
% 4.11/1.58 % (1201568)------------------------------
% 4.11/1.58 % (1201568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.58 % (1201568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.58 % (1201568)CaDiCaL version: 2.1.3
% 4.11/1.58 % (1201568)Termination reason: Instruction limit
% 4.11/1.58 % (1201568)Termination phase: Saturation
% 4.11/1.58 % (1201568)Time elapsed: 0.078 s
% 4.11/1.58 % (1201568)Peak memory usage: 91 MB
% 4.11/1.58 % (1201568)Instructions burned: 157 (million)
% 4.11/1.58 % (1201571)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=2619537401:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.11/1.58 % (1201571)Instruction limit reached!
% 4.11/1.58 % (1201571)------------------------------
% 4.11/1.58 % (1201571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.58 % (1201571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.58 % (1201571)CaDiCaL version: 2.1.3
% 4.11/1.58 % (1201571)Termination reason: Instruction limit
% 4.11/1.58 % (1201571)Termination phase: Saturation
% 4.11/1.58 % (1201571)Time elapsed: 0.071 s
% 4.11/1.58 % (1201571)Peak memory usage: 93 MB
% 4.11/1.58 % (1201571)Instructions burned: 248 (million)
% 4.11/1.58 % (1201574)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2886604066:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.11/1.58 % (1201574)Refutation not found, incomplete strategy
% 4.11/1.58 % (1201574)------------------------------
% 4.11/1.58 % (1201574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.58 % (1201574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.58 % (1201574)CaDiCaL version: 2.1.3
% 4.11/1.58 % (1201574)Termination reason: Refutation not found, incomplete strategy
% 4.11/1.58 % (1201574)Time elapsed: 0.004 s
% 4.11/1.58 % (1201574)Peak memory usage: 89 MB
% 4.11/1.58 % (1201574)Instructions burned: 4 (million)
% 4.11/1.58 % (1201575)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2599522272:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.11/1.58 % (1201569)Refutation found. Thanks to Tanya!
% 4.11/1.58 % SZS status Theorem for theBenchmark
% 4.11/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 5.53/1.77 % (1201569)------------------------------
% 5.53/1.77 % (1201569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.77 % (1201569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.77 % (1201569)CaDiCaL version: 2.1.3
% 5.53/1.77 % (1201569)Termination reason: Refutation
% 5.53/1.77 % (1201569)Time elapsed: 0.014 s
% 5.53/1.77 % (1201569)Peak memory usage: 89 MB
% 5.53/1.77 % (1201569)Instructions burned: 17 (million)
% 5.53/1.77 % (1201569)------------------------------
% 5.53/1.77 % (1201569)------------------------------
% 5.53/1.77 % (1201548)Success in time 0.708 s
% 5.53/1.77 % Vampire exiting
%------------------------------------------------------------------------------