%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU413+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 : n011.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 12:48:49 PM UTC 2026
% Result : Theorem 9.27s 2.47s
% Output : Refutation 10.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 92 ( 33 unt; 10 def)
% Number of atoms : 285 ( 2 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 324 ( 131 ~; 126 |; 38 &)
% ( 12 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 64 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f117,axiom,
! [X0,X1] : k4_xboole_0(X0,k4_xboole_0(X0,X1)) = k3_xboole_0(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f3169,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r1_orders_2(X0,X1,X2)
<=> r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_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(f4458,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2,X3] :
( ( v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
& r2_hidden(X3,u1_struct_0(X0)) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_latsum_1) ).
fof(f4460,conjecture,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( ( v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& r2_hidden(X3,u1_struct_0(X0)) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_latsum_1) ).
fof(f4461,negated_conjecture,
~ ! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( ( v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& r2_hidden(X3,u1_struct_0(X0)) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4460]) ).
fof(f4491,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(f4492,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,[],[f4491]) ).
fof(f4536,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ r2_hidden(X3,u1_struct_0(X0)) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f4458]) ).
fof(f4537,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ r2_hidden(X3,u1_struct_0(X0)) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(flattening,[],[f4536]) ).
fof(f4540,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(X0))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& r2_hidden(X3,u1_struct_0(X0))
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
& l1_orders_2(X1) )
& l1_orders_2(X0) ),
inference(ennf_transformation,[],[f4461]) ).
fof(f4541,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(X0))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& r2_hidden(X3,u1_struct_0(X0))
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
& l1_orders_2(X1) )
& l1_orders_2(X0) ),
inference(flattening,[],[f4540]) ).
fof(f4663,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( r1_orders_2(X0,X1,X2)
<=> r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f3169]) ).
fof(f4788,plain,
( ~ r2_hidden(sK5,u1_struct_0(sK3))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),k1_zfmisc_1(u1_struct_0(sK4)))
& r1_orders_2(k1_latsum_1(sK3,sK4),sK5,sK6)
& r2_hidden(sK6,u1_struct_0(sK3))
& m1_subset_1(sK6,u1_struct_0(k1_latsum_1(sK3,sK4)))
& m1_subset_1(sK5,u1_struct_0(k1_latsum_1(sK3,sK4)))
& l1_orders_2(sK4)
& l1_orders_2(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f4541]) ).
fof(f4864,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( r1_orders_2(X0,X1,X2)
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) )
& ( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2) ) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l1_orders_2(X0) ),
inference(nnf_transformation,[],[f4663]) ).
fof(f4938,plain,
! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(cnf_transformation,[],[f4492]) ).
fof(f4996,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f4537]) ).
fof(f5005,plain,
l1_orders_2(sK3),
inference(cnf_transformation,[],[f4788]) ).
fof(f5006,plain,
l1_orders_2(sK4),
inference(cnf_transformation,[],[f4788]) ).
fof(f5007,plain,
m1_subset_1(sK5,u1_struct_0(k1_latsum_1(sK3,sK4))),
inference(cnf_transformation,[],[f4788]) ).
fof(f5008,plain,
m1_subset_1(sK6,u1_struct_0(k1_latsum_1(sK3,sK4))),
inference(cnf_transformation,[],[f4788]) ).
fof(f5009,plain,
r2_hidden(sK6,u1_struct_0(sK3)),
inference(cnf_transformation,[],[f4788]) ).
fof(f5010,plain,
r1_orders_2(k1_latsum_1(sK3,sK4),sK5,sK6),
inference(cnf_transformation,[],[f4788]) ).
fof(f5011,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),k1_zfmisc_1(u1_struct_0(sK4))),
inference(cnf_transformation,[],[f4788]) ).
fof(f5012,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4),
inference(cnf_transformation,[],[f4788]) ).
fof(f5013,plain,
~ r2_hidden(sK5,u1_struct_0(sK3)),
inference(cnf_transformation,[],[f4788]) ).
fof(f5131,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k4_xboole_0(X0,k4_xboole_0(X0,X1)),
inference(cnf_transformation,[],[f117]) ).
fof(f5295,plain,
! [X2,X0,X1] :
( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f4864]) ).
fof(f5506,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(k4_xboole_0(u1_struct_0(X0),k4_xboole_0(u1_struct_0(X0),u1_struct_0(X1))),X1)
| ~ m1_subset_1(k4_xboole_0(u1_struct_0(X0),k4_xboole_0(u1_struct_0(X0),u1_struct_0(X1))),k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(definition_unfolding,[],[f4996,f5131,f5131]) ).
fof(f5515,plain,
v12_waybel_0(k4_xboole_0(u1_struct_0(sK3),k4_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),sK4),
inference(definition_unfolding,[],[f5012,f5131]) ).
fof(f5516,plain,
m1_subset_1(k4_xboole_0(u1_struct_0(sK3),k4_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),k1_zfmisc_1(u1_struct_0(sK4))),
inference(definition_unfolding,[],[f5011,f5131]) ).
fof(f5756,definition,
( spl170_1
<=> r2_hidden(sK5,u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl170_1])],[avatar_definition]) ).
fof(f5758,plain,
( ~ r2_hidden(sK5,u1_struct_0(sK3))
| spl170_1 ),
inference(avatar_component_clause,[],[f5756]) ).
fof(f5759,plain,
~ spl170_1,
inference(avatar_split_clause,[],[f5013,f5756]) ).
fof(f5873,definition,
( spl170_2
<=> l1_orders_2(sK3) ),
introduced(definition,[new_symbols(definition,[spl170_2])],[avatar_definition]) ).
fof(f5875,plain,
( l1_orders_2(sK3)
| ~ spl170_2 ),
inference(avatar_component_clause,[],[f5873]) ).
fof(f5876,plain,
spl170_2,
inference(avatar_split_clause,[],[f5005,f5873]) ).
fof(f5878,definition,
( spl170_3
<=> l1_orders_2(sK4) ),
introduced(definition,[new_symbols(definition,[spl170_3])],[avatar_definition]) ).
fof(f5880,plain,
( l1_orders_2(sK4)
| ~ spl170_3 ),
inference(avatar_component_clause,[],[f5878]) ).
fof(f5881,plain,
spl170_3,
inference(avatar_split_clause,[],[f5006,f5878]) ).
fof(f5883,definition,
( spl170_4
<=> m1_subset_1(sK5,u1_struct_0(k1_latsum_1(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl170_4])],[avatar_definition]) ).
fof(f5885,plain,
( m1_subset_1(sK5,u1_struct_0(k1_latsum_1(sK3,sK4)))
| ~ spl170_4 ),
inference(avatar_component_clause,[],[f5883]) ).
fof(f5886,plain,
spl170_4,
inference(avatar_split_clause,[],[f5007,f5883]) ).
fof(f5888,definition,
( spl170_5
<=> v12_waybel_0(k4_xboole_0(u1_struct_0(sK3),k4_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),sK4) ),
introduced(definition,[new_symbols(definition,[spl170_5])],[avatar_definition]) ).
fof(f5890,plain,
( v12_waybel_0(k4_xboole_0(u1_struct_0(sK3),k4_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),sK4)
| ~ spl170_5 ),
inference(avatar_component_clause,[],[f5888]) ).
fof(f5891,plain,
spl170_5,
inference(avatar_split_clause,[],[f5515,f5888]) ).
fof(f6728,definition,
( spl170_6
<=> r1_orders_2(k1_latsum_1(sK3,sK4),sK5,sK6) ),
introduced(definition,[new_symbols(definition,[spl170_6])],[avatar_definition]) ).
fof(f6730,plain,
( r1_orders_2(k1_latsum_1(sK3,sK4),sK5,sK6)
| ~ spl170_6 ),
inference(avatar_component_clause,[],[f6728]) ).
fof(f6731,plain,
spl170_6,
inference(avatar_split_clause,[],[f5010,f6728]) ).
fof(f6733,definition,
( spl170_7
<=> r2_hidden(sK6,u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl170_7])],[avatar_definition]) ).
fof(f6735,plain,
( r2_hidden(sK6,u1_struct_0(sK3))
| ~ spl170_7 ),
inference(avatar_component_clause,[],[f6733]) ).
fof(f6736,plain,
spl170_7,
inference(avatar_split_clause,[],[f5009,f6733]) ).
fof(f6940,plain,
( r2_hidden(k4_tarski(sK5,sK6),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ m1_subset_1(sK6,u1_struct_0(k1_latsum_1(sK3,sK4)))
| ~ m1_subset_1(sK5,u1_struct_0(k1_latsum_1(sK3,sK4)))
| ~ l1_orders_2(k1_latsum_1(sK3,sK4))
| ~ spl170_6 ),
inference(resolution,[],[f6730,f5295]) ).
fof(f7005,plain,
( r2_hidden(k4_tarski(sK5,sK6),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ m1_subset_1(sK5,u1_struct_0(k1_latsum_1(sK3,sK4)))
| ~ l1_orders_2(k1_latsum_1(sK3,sK4))
| ~ spl170_6 ),
inference(forward_subsumption_resolution,[],[f6940,f5008]) ).
fof(f7045,plain,
( r2_hidden(k4_tarski(sK5,sK6),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ l1_orders_2(k1_latsum_1(sK3,sK4))
| ~ spl170_4
| ~ spl170_6 ),
inference(forward_subsumption_resolution,[],[f7005,f5885]) ).
fof(f7185,plain,
( ! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK3))
| ~ m1_subset_1(k4_xboole_0(u1_struct_0(sK3),k4_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),k1_zfmisc_1(u1_struct_0(sK4)))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ r2_hidden(X1,u1_struct_0(sK3))
| ~ l1_orders_2(sK4)
| ~ l1_orders_2(sK3) )
| ~ spl170_5 ),
inference(resolution,[],[f5890,f5506]) ).
fof(f7229,plain,
( ! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK3))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ r2_hidden(X1,u1_struct_0(sK3))
| ~ l1_orders_2(sK4)
| ~ l1_orders_2(sK3) )
| ~ spl170_5 ),
inference(forward_subsumption_resolution,[],[f7185,f5516]) ).
fof(f7243,plain,
( ! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK3))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ r2_hidden(X1,u1_struct_0(sK3))
| ~ l1_orders_2(sK3) )
| ~ spl170_3
| ~ spl170_5 ),
inference(forward_subsumption_resolution,[],[f7229,f5880]) ).
fof(f7248,plain,
( ! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK3))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ r2_hidden(X1,u1_struct_0(sK3)) )
| ~ spl170_2
| ~ spl170_3
| ~ spl170_5 ),
inference(forward_subsumption_resolution,[],[f7243,f5875]) ).
fof(f7252,definition,
( spl170_12
<=> ! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK3))
| ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ r2_hidden(X1,u1_struct_0(sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl170_12])],[avatar_definition]) ).
fof(f7253,plain,
( ! [X0,X1] :
( ~ r2_hidden(k4_tarski(X0,X1),u1_orders_2(k1_latsum_1(sK3,sK4)))
| r2_hidden(X0,u1_struct_0(sK3))
| ~ r2_hidden(X1,u1_struct_0(sK3)) )
| ~ spl170_12 ),
inference(avatar_component_clause,[],[f7252]) ).
fof(f7254,plain,
( spl170_12
| ~ spl170_2
| ~ spl170_3
| ~ spl170_5 ),
inference(avatar_split_clause,[],[f7248,f5888,f5878,f5873,f7252]) ).
fof(f7544,definition,
( spl170_17
<=> l1_orders_2(k1_latsum_1(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl170_17])],[avatar_definition]) ).
fof(f7546,plain,
( ~ l1_orders_2(k1_latsum_1(sK3,sK4))
| spl170_17 ),
inference(avatar_component_clause,[],[f7544]) ).
fof(f7548,definition,
( spl170_18
<=> r2_hidden(k4_tarski(sK5,sK6),u1_orders_2(k1_latsum_1(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl170_18])],[avatar_definition]) ).
fof(f7550,plain,
( r2_hidden(k4_tarski(sK5,sK6),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ spl170_18 ),
inference(avatar_component_clause,[],[f7548]) ).
fof(f7551,plain,
( ~ spl170_17
| spl170_18
| ~ spl170_4
| ~ spl170_6 ),
inference(avatar_split_clause,[],[f7045,f6728,f5883,f7548,f7544]) ).
fof(f7552,plain,
( ~ l1_orders_2(sK3)
| ~ l1_orders_2(sK4)
| spl170_17 ),
inference(resolution,[],[f7546,f4938]) ).
fof(f7556,plain,
( ~ l1_orders_2(sK4)
| ~ spl170_2
| spl170_17 ),
inference(forward_subsumption_resolution,[],[f7552,f5875]) ).
fof(f7558,plain,
( $false
| ~ spl170_2
| ~ spl170_3
| spl170_17 ),
inference(forward_subsumption_resolution,[],[f7556,f5880]) ).
fof(f7559,plain,
( ~ spl170_2
| ~ spl170_3
| spl170_17 ),
inference(avatar_contradiction_clause,[],[f7558]) ).
fof(f8018,plain,
( r2_hidden(sK5,u1_struct_0(sK3))
| ~ r2_hidden(sK6,u1_struct_0(sK3))
| ~ spl170_12
| ~ spl170_18 ),
inference(resolution,[],[f7550,f7253]) ).
fof(f8156,plain,
( ~ r2_hidden(sK6,u1_struct_0(sK3))
| spl170_1
| ~ spl170_12
| ~ spl170_18 ),
inference(forward_subsumption_resolution,[],[f8018,f5758]) ).
fof(f8179,plain,
( $false
| spl170_1
| ~ spl170_7
| ~ spl170_12
| ~ spl170_18 ),
inference(forward_subsumption_resolution,[],[f8156,f6735]) ).
fof(f8180,plain,
( spl170_1
| ~ spl170_7
| ~ spl170_12
| ~ spl170_18 ),
inference(avatar_contradiction_clause,[],[f8179]) ).
cnf(s1,plain,
~ spl170_1,
inference(sat_conversion,[],[f5759]) ).
cnf(s2,plain,
spl170_2,
inference(sat_conversion,[],[f5876]) ).
cnf(s3,plain,
spl170_3,
inference(sat_conversion,[],[f5881]) ).
cnf(s4,plain,
spl170_4,
inference(sat_conversion,[],[f5886]) ).
cnf(s5,plain,
spl170_5,
inference(sat_conversion,[],[f5891]) ).
cnf(s6,plain,
spl170_6,
inference(sat_conversion,[],[f6731]) ).
cnf(s7,plain,
spl170_7,
inference(sat_conversion,[],[f6736]) ).
cnf(s9,plain,
( ~ spl170_2
| ~ spl170_3
| ~ spl170_5
| spl170_12 ),
inference(sat_conversion,[],[f7254]) ).
cnf(s14,plain,
( ~ spl170_4
| ~ spl170_6
| ~ spl170_17
| spl170_18 ),
inference(sat_conversion,[],[f7551]) ).
cnf(s15,plain,
( ~ spl170_2
| ~ spl170_3
| spl170_17 ),
inference(sat_conversion,[],[f7559]) ).
cnf(s16,plain,
( spl170_1
| ~ spl170_7
| ~ spl170_12
| ~ spl170_18 ),
inference(sat_conversion,[],[f8180]) ).
cnf(s18,plain,
spl170_17,
inference(rat,[],[s15,s3,s2]) ).
cnf(s19,plain,
spl170_12,
inference(rat,[],[s9,s3,s5,s2]) ).
cnf(s20,plain,
spl170_18,
inference(rat,[],[s14,s4,s6,s18]) ).
cnf(s21,plain,
spl170_1,
inference(rat,[],[s16,s20,s7,s19]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s1,s21]) ).
fof(f8199,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU413+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 05:15:06 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 9.27/2.47 % (3040375)Detected formulas, will run a generic FOF schedule.
% 9.27/2.47 % (3040406)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4201927568:i=109:sd=1:ins=1:gsp=on:ss=axioms_2997 on theBenchmark for (2997ds/109Mi)
% 9.27/2.47 % (3040403)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=439874872:i=141193_2997 on theBenchmark for (2997ds/141193Mi)
% 9.27/2.47 % (3040410)dis-21_1_sil=8000:lcm=predicate:random_seed=2924266774:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2997 on theBenchmark for (2997ds/129Mi)
% 9.27/2.47 % (3040404)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=456265908:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2997 on theBenchmark for (2997ds/134677Mi)
% 9.27/2.47 % (3040405)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=1492867614:i=141695:sd=1:nm=32:gsp=on:ss=included_2997 on theBenchmark for (2997ds/141695Mi)
% 9.27/2.47 % (3040406)Instruction limit reached!
% 9.27/2.47 % (3040406)------------------------------
% 9.27/2.47 % (3040406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040406)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040406)Termination reason: Instruction limit
% 9.27/2.47 % (3040406)Termination phase: Saturation
% 9.27/2.47 % (3040406)Time elapsed: 0.078 s
% 9.27/2.47 % (3040406)Peak memory usage: 94 MB
% 9.27/2.47 % (3040406)Instructions burned: 109 (million)
% 9.27/2.47 % (3040408)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1875000804:s2a=on:i=139:gtg=position_2997 on theBenchmark for (2997ds/139Mi)
% 9.27/2.47 % (3040407)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1871371231:i=119:av=off:ss=axioms_2997 on theBenchmark for (2997ds/119Mi)
% 9.27/2.47 % (3040410)Instruction limit reached!
% 9.27/2.47 % (3040410)------------------------------
% 9.27/2.47 % (3040410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040410)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040410)Termination reason: Instruction limit
% 9.27/2.47 % (3040410)Termination phase: Preprocessing 3
% 9.27/2.47 % (3040410)Time elapsed: 0.145 s
% 9.27/2.47 % (3040410)Peak memory usage: 95 MB
% 9.27/2.47 % (3040410)Instructions burned: 129 (million)
% 9.27/2.47 % (3040407)Instruction limit reached!
% 9.27/2.47 % (3040407)------------------------------
% 9.27/2.47 % (3040407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040407)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040407)Termination reason: Instruction limit
% 9.27/2.47 % (3040407)Termination phase: Saturation
% 9.27/2.47 % (3040407)Time elapsed: 0.129 s
% 9.27/2.47 % (3040407)Peak memory usage: 94 MB
% 9.27/2.47 % (3040407)Instructions burned: 119 (million)
% 9.27/2.47 % (3040408)Instruction limit reached!
% 9.27/2.47 % (3040408)------------------------------
% 9.27/2.47 % (3040408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040408)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040408)Termination reason: Instruction limit
% 9.27/2.47 % (3040408)Termination phase: Naming
% 9.27/2.47 % (3040408)Time elapsed: 0.143 s
% 9.27/2.47 % (3040408)Peak memory usage: 94 MB
% 9.27/2.47 % (3040408)Instructions burned: 139 (million)
% 9.27/2.47 % (3040421)lrs+10_1_sil=8000:sp=occurrence:random_seed=1043176392:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 9.27/2.47 % (3040429)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=1191090433:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 9.27/2.47 % (3040426)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1832528614:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 9.27/2.47 % (3040428)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2112220339:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 9.27/2.47 % (3040426)Instruction limit reached!
% 9.27/2.47 % (3040426)------------------------------
% 9.27/2.47 % (3040426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040426)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040426)Termination reason: Instruction limit
% 9.27/2.47 % (3040426)Termination phase: Saturation
% 9.27/2.47 % (3040426)Time elapsed: 0.046 s
% 9.27/2.47 % (3040426)Peak memory usage: 95 MB
% 9.27/2.47 % (3040426)Instructions burned: 158 (million)
% 9.27/2.47 % (3040421)Instruction limit reached!
% 9.27/2.47 % (3040421)------------------------------
% 9.27/2.47 % (3040421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040421)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040421)Termination reason: Instruction limit
% 9.27/2.47 % (3040421)Termination phase: Saturation
% 9.27/2.47 % (3040421)Time elapsed: 0.246 s
% 9.27/2.47 % (3040421)Peak memory usage: 98 MB
% 9.27/2.47 % (3040421)Instructions burned: 285 (million)
% 9.27/2.47 % (3040429)Instruction limit reached!
% 9.27/2.47 % (3040429)------------------------------
% 9.27/2.47 % (3040429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040429)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040429)Termination reason: Instruction limit
% 9.27/2.47 % (3040429)Termination phase: Property scanning
% 9.27/2.47 % (3040429)Time elapsed: 0.160 s
% 9.27/2.47 % (3040429)Peak memory usage: 99 MB
% 9.27/2.47 % (3040429)Instructions burned: 249 (million)
% 9.27/2.47 % (3040428)Instruction limit reached!
% 9.27/2.47 % (3040428)------------------------------
% 9.27/2.47 % (3040428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040428)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040428)Termination reason: Instruction limit
% 9.27/2.47 % (3040428)Termination phase: Saturation
% 9.27/2.47 % (3040428)Time elapsed: 0.214 s
% 9.27/2.47 % (3040428)Peak memory usage: 97 MB
% 9.27/2.47 % (3040428)Instructions burned: 326 (million)
% 9.27/2.47 % (3040436)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1779102357:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 9.27/2.47 % (3040437)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1324230907:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 9.27/2.47 % (3040439)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=92558641:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 9.27/2.47 % (3040436)Instruction limit reached!
% 9.27/2.47 % (3040436)------------------------------
% 9.27/2.47 % (3040436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040436)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040436)Termination reason: Instruction limit
% 9.27/2.47 % (3040436)Termination phase: Saturation
% 9.27/2.47 % (3040436)Time elapsed: 0.132 s
% 9.27/2.47 % (3040436)Peak memory usage: 99 MB
% 9.27/2.47 % (3040436)Instructions burned: 295 (million)
% 9.27/2.47 % (3040441)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=125044609:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 9.27/2.47 % (3040439)Instruction limit reached!
% 9.27/2.47 % (3040439)------------------------------
% 9.27/2.47 % (3040439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040439)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040439)Termination reason: Instruction limit
% 9.27/2.47 % (3040439)Termination phase: Saturation
% 9.27/2.47 % (3040439)Time elapsed: 0.072 s
% 9.27/2.47 % (3040439)Peak memory usage: 95 MB
% 9.27/2.47 % (3040439)Instructions burned: 114 (million)
% 9.27/2.47 % (3040441)Instruction limit reached!
% 9.27/2.47 % (3040441)------------------------------
% 9.27/2.47 % (3040441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040441)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040441)Termination reason: Instruction limit
% 9.27/2.47 % (3040441)Termination phase: Preprocessing 3
% 9.27/2.47 % (3040441)Time elapsed: 0.091 s
% 9.27/2.47 % (3040441)Peak memory usage: 97 MB
% 9.27/2.47 % (3040441)Instructions burned: 128 (million)
% 9.27/2.47 % (3040479)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1116095354:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2988 on theBenchmark for (2988ds/114Mi)
% 9.27/2.47 % (3040479)Instruction limit reached!
% 9.27/2.47 % (3040479)------------------------------
% 9.27/2.47 % (3040479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.27/2.47 % (3040479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.27/2.47 % (3040495)lrs+10_1_sil=8000:sp=occurrence:random_seed=1858158919:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2987 on theBenchmark for (2987ds/907Mi)
% 9.27/2.47 % (3040479)CaDiCaL version: 2.1.3
% 9.27/2.47 % (3040479)Termination reason: Instruction limit
% 9.27/2.47 % (3040479)Termination phase: SInE selection
% 9.27/2.47 % (3040479)Time elapsed: 0.051 s
% 9.27/2.47 % (3040479)Peak memory usage: 89 MB
% 9.27/2.47 % (3040479)Instructions burned: 114 (million)
% 9.27/2.47 % (3040405)First to succeed.
% 9.27/2.47 % (3040405)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3040375"
% 9.27/2.47 % (3040531)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3603761235:i=437:sd=1:aac=none:ss=included_2986 on theBenchmark for (2986ds/437Mi)
% 9.27/2.47 % (3040555)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=872186359:i=5202:ss=axioms:sgt=16_2986 on theBenchmark for (2986ds/5202Mi)
% 9.27/2.47 % (3040405)Refutation found. Thanks to Tanya!
% 9.27/2.47 % SZS status Theorem for theBenchmark
% 9.27/2.47 % SZS output start Proof for theBenchmark
% See solution above
% 10.60/2.66 % (3040405)------------------------------
% 10.60/2.66 % (3040405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.60/2.66 % (3040405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.60/2.66 % (3040405)CaDiCaL version: 2.1.3
% 10.60/2.66 % (3040405)Termination reason: Refutation
% 10.60/2.66 % (3040405)Time elapsed: 0.975 s
% 10.60/2.66 % (3040405)Peak memory usage: 144 MB
% 10.60/2.66 % (3040405)Instructions burned: 1748 (million)
% 10.60/2.66 % (3040405)------------------------------
% 10.60/2.66 % (3040405)------------------------------
% 10.60/2.66 % (3040375)Success in time 1.603 s
% 10.60/2.66 % Vampire exiting
%------------------------------------------------------------------------------