%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU413+3 : 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 : 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 8.08s 3.09s
% Output : Refutation 9.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 93 ( 34 unt; 10 def)
% Number of atoms : 298 ( 2 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 348 ( 143 ~; 138 |; 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 : 60 ( 0 sgn 52 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f117,axiom,
! [X0,X1] : k4_xboole_0(X0,k4_xboole_0(X0,X1)) = k3_xboole_0(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f7711,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/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
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/sandbox2/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(f19047,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/sandbox2/benchmark/theBenchmark.p',t21_latsum_1) ).
fof(f19049,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/sandbox2/benchmark/theBenchmark.p',t23_latsum_1) ).
fof(f19050,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)],[f19049]) ).
fof(f19077,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(f19078,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,[],[f19077]) ).
fof(f19122,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,[],[f19047]) ).
fof(f19123,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,[],[f19122]) ).
fof(f19126,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,[],[f19050]) ).
fof(f19127,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,[],[f19126]) ).
fof(f19290,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,[],[f7711]) ).
fof(f19437,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)],[f19127]) ).
fof(f19540,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,[],[f19290]) ).
fof(f19612,plain,
! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1) ),
inference(cnf_transformation,[],[f19078]) ).
fof(f19670,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,[],[f19123]) ).
fof(f19679,plain,
l1_orders_2(sK3),
inference(cnf_transformation,[],[f19437]) ).
fof(f19680,plain,
l1_orders_2(sK4),
inference(cnf_transformation,[],[f19437]) ).
fof(f19681,plain,
m1_subset_1(sK5,u1_struct_0(k1_latsum_1(sK3,sK4))),
inference(cnf_transformation,[],[f19437]) ).
fof(f19682,plain,
m1_subset_1(sK6,u1_struct_0(k1_latsum_1(sK3,sK4))),
inference(cnf_transformation,[],[f19437]) ).
fof(f19683,plain,
r2_hidden(sK6,u1_struct_0(sK3)),
inference(cnf_transformation,[],[f19437]) ).
fof(f19684,plain,
r1_orders_2(k1_latsum_1(sK3,sK4),sK5,sK6),
inference(cnf_transformation,[],[f19437]) ).
fof(f19685,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,[],[f19437]) ).
fof(f19686,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4),
inference(cnf_transformation,[],[f19437]) ).
fof(f19687,plain,
~ r2_hidden(sK5,u1_struct_0(sK3)),
inference(cnf_transformation,[],[f19437]) ).
fof(f19848,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k4_xboole_0(X0,k4_xboole_0(X0,X1)),
inference(cnf_transformation,[],[f117]) ).
fof(f20062,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,[],[f19540]) ).
fof(f20289,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,[],[f19670,f19848,f19848]) ).
fof(f20298,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,[],[f19686,f19848]) ).
fof(f20299,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,[],[f19685,f19848]) ).
fof(f20552,definition,
( spl194_1
<=> r2_hidden(sK5,u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl194_1])],[avatar_definition]) ).
fof(f20554,plain,
( ~ r2_hidden(sK5,u1_struct_0(sK3))
| spl194_1 ),
inference(avatar_component_clause,[],[f20552]) ).
fof(f20555,plain,
~ spl194_1,
inference(avatar_split_clause,[],[f19687,f20552]) ).
fof(f20673,definition,
( spl194_2
<=> 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,[spl194_2])],[avatar_definition]) ).
fof(f20675,plain,
( v12_waybel_0(k4_xboole_0(u1_struct_0(sK3),k4_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),sK4)
| ~ spl194_2 ),
inference(avatar_component_clause,[],[f20673]) ).
fof(f20676,plain,
spl194_2,
inference(avatar_split_clause,[],[f20298,f20673]) ).
fof(f20678,definition,
( spl194_3
<=> l1_orders_2(sK3) ),
introduced(definition,[new_symbols(definition,[spl194_3])],[avatar_definition]) ).
fof(f20680,plain,
( l1_orders_2(sK3)
| ~ spl194_3 ),
inference(avatar_component_clause,[],[f20678]) ).
fof(f20681,plain,
spl194_3,
inference(avatar_split_clause,[],[f19679,f20678]) ).
fof(f20683,definition,
( spl194_4
<=> m1_subset_1(sK5,u1_struct_0(k1_latsum_1(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl194_4])],[avatar_definition]) ).
fof(f20685,plain,
( m1_subset_1(sK5,u1_struct_0(k1_latsum_1(sK3,sK4)))
| ~ spl194_4 ),
inference(avatar_component_clause,[],[f20683]) ).
fof(f20686,plain,
spl194_4,
inference(avatar_split_clause,[],[f19681,f20683]) ).
fof(f20688,definition,
( spl194_5
<=> l1_orders_2(sK4) ),
introduced(definition,[new_symbols(definition,[spl194_5])],[avatar_definition]) ).
fof(f20690,plain,
( l1_orders_2(sK4)
| ~ spl194_5 ),
inference(avatar_component_clause,[],[f20688]) ).
fof(f20691,plain,
spl194_5,
inference(avatar_split_clause,[],[f19680,f20688]) ).
fof(f21616,definition,
( spl194_6
<=> r1_orders_2(k1_latsum_1(sK3,sK4),sK5,sK6) ),
introduced(definition,[new_symbols(definition,[spl194_6])],[avatar_definition]) ).
fof(f21618,plain,
( r1_orders_2(k1_latsum_1(sK3,sK4),sK5,sK6)
| ~ spl194_6 ),
inference(avatar_component_clause,[],[f21616]) ).
fof(f21619,plain,
spl194_6,
inference(avatar_split_clause,[],[f19684,f21616]) ).
fof(f21621,definition,
( spl194_7
<=> r2_hidden(sK6,u1_struct_0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl194_7])],[avatar_definition]) ).
fof(f21623,plain,
( r2_hidden(sK6,u1_struct_0(sK3))
| ~ spl194_7 ),
inference(avatar_component_clause,[],[f21621]) ).
fof(f21624,plain,
spl194_7,
inference(avatar_split_clause,[],[f19683,f21621]) ).
fof(f21835,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))
| ~ spl194_6 ),
inference(resolution,[],[f21618,f20062]) ).
fof(f21904,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))
| ~ spl194_6 ),
inference(forward_subsumption_resolution,[],[f21835,f19682]) ).
fof(f21946,plain,
( r2_hidden(k4_tarski(sK5,sK6),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ l1_orders_2(k1_latsum_1(sK3,sK4))
| ~ spl194_4
| ~ spl194_6 ),
inference(forward_subsumption_resolution,[],[f21904,f20685]) ).
fof(f22072,definition,
( spl194_8
<=> 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))) ),
introduced(definition,[new_symbols(definition,[spl194_8])],[avatar_definition]) ).
fof(f22074,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)))
| ~ spl194_8 ),
inference(avatar_component_clause,[],[f22072]) ).
fof(f22075,plain,
spl194_8,
inference(avatar_split_clause,[],[f20299,f22072]) ).
fof(f22724,definition,
( spl194_15
<=> l1_orders_2(k1_latsum_1(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl194_15])],[avatar_definition]) ).
fof(f22725,plain,
( l1_orders_2(k1_latsum_1(sK3,sK4))
| ~ spl194_15 ),
inference(avatar_component_clause,[],[f22724]) ).
fof(f22726,plain,
( ~ l1_orders_2(k1_latsum_1(sK3,sK4))
| spl194_15 ),
inference(avatar_component_clause,[],[f22724]) ).
fof(f22735,plain,
( ~ l1_orders_2(sK3)
| ~ l1_orders_2(sK4)
| spl194_15 ),
inference(resolution,[],[f22726,f19612]) ).
fof(f22739,plain,
( ~ l1_orders_2(sK4)
| ~ spl194_3
| spl194_15 ),
inference(forward_subsumption_resolution,[],[f22735,f20680]) ).
fof(f22741,plain,
( $false
| ~ spl194_3
| ~ spl194_5
| spl194_15 ),
inference(forward_subsumption_resolution,[],[f22739,f20690]) ).
fof(f22742,plain,
( ~ spl194_3
| ~ spl194_5
| spl194_15 ),
inference(avatar_contradiction_clause,[],[f22741]) ).
fof(f22914,plain,
( r2_hidden(k4_tarski(sK5,sK6),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ spl194_4
| ~ spl194_6
| ~ spl194_15 ),
inference(backward_subsumption_resolution,[],[f21946,f22725]) ).
fof(f23397,definition,
( spl194_18
<=> r2_hidden(k4_tarski(sK5,sK6),u1_orders_2(k1_latsum_1(sK3,sK4))) ),
introduced(definition,[new_symbols(definition,[spl194_18])],[avatar_definition]) ).
fof(f23399,plain,
( r2_hidden(k4_tarski(sK5,sK6),u1_orders_2(k1_latsum_1(sK3,sK4)))
| ~ spl194_18 ),
inference(avatar_component_clause,[],[f23397]) ).
fof(f23400,plain,
( spl194_18
| ~ spl194_4
| ~ spl194_6
| ~ spl194_15 ),
inference(avatar_split_clause,[],[f22914,f22724,f21616,f20683,f23397]) ).
fof(f23413,plain,
( r2_hidden(sK5,u1_struct_0(sK3))
| ~ v12_waybel_0(k4_xboole_0(u1_struct_0(sK3),k4_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),sK4)
| ~ 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(sK6,u1_struct_0(sK3))
| ~ l1_orders_2(sK4)
| ~ l1_orders_2(sK3)
| ~ spl194_18 ),
inference(resolution,[],[f23399,f20289]) ).
fof(f23556,plain,
( ~ v12_waybel_0(k4_xboole_0(u1_struct_0(sK3),k4_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),sK4)
| ~ 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(sK6,u1_struct_0(sK3))
| ~ l1_orders_2(sK4)
| ~ l1_orders_2(sK3)
| spl194_1
| ~ spl194_18 ),
inference(forward_subsumption_resolution,[],[f23413,f20554]) ).
fof(f23647,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)))
| ~ r2_hidden(sK6,u1_struct_0(sK3))
| ~ l1_orders_2(sK4)
| ~ l1_orders_2(sK3)
| spl194_1
| ~ spl194_2
| ~ spl194_18 ),
inference(forward_subsumption_resolution,[],[f23556,f20675]) ).
fof(f23655,plain,
( ~ r2_hidden(sK6,u1_struct_0(sK3))
| ~ l1_orders_2(sK4)
| ~ l1_orders_2(sK3)
| spl194_1
| ~ spl194_2
| ~ spl194_8
| ~ spl194_18 ),
inference(forward_subsumption_resolution,[],[f23647,f22074]) ).
fof(f23661,plain,
( ~ l1_orders_2(sK4)
| ~ l1_orders_2(sK3)
| spl194_1
| ~ spl194_2
| ~ spl194_7
| ~ spl194_8
| ~ spl194_18 ),
inference(forward_subsumption_resolution,[],[f23655,f21623]) ).
fof(f23665,plain,
( ~ l1_orders_2(sK3)
| spl194_1
| ~ spl194_2
| ~ spl194_5
| ~ spl194_7
| ~ spl194_8
| ~ spl194_18 ),
inference(forward_subsumption_resolution,[],[f23661,f20690]) ).
fof(f23666,plain,
( $false
| spl194_1
| ~ spl194_2
| ~ spl194_3
| ~ spl194_5
| ~ spl194_7
| ~ spl194_8
| ~ spl194_18 ),
inference(forward_subsumption_resolution,[],[f23665,f20680]) ).
fof(f23667,plain,
( spl194_1
| ~ spl194_2
| ~ spl194_3
| ~ spl194_5
| ~ spl194_7
| ~ spl194_8
| ~ spl194_18 ),
inference(avatar_contradiction_clause,[],[f23666]) ).
cnf(s1,plain,
~ spl194_1,
inference(sat_conversion,[],[f20555]) ).
cnf(s2,plain,
spl194_2,
inference(sat_conversion,[],[f20676]) ).
cnf(s3,plain,
spl194_3,
inference(sat_conversion,[],[f20681]) ).
cnf(s4,plain,
spl194_4,
inference(sat_conversion,[],[f20686]) ).
cnf(s5,plain,
spl194_5,
inference(sat_conversion,[],[f20691]) ).
cnf(s6,plain,
spl194_6,
inference(sat_conversion,[],[f21619]) ).
cnf(s7,plain,
spl194_7,
inference(sat_conversion,[],[f21624]) ).
cnf(s8,plain,
spl194_8,
inference(sat_conversion,[],[f22075]) ).
cnf(s13,plain,
( ~ spl194_3
| ~ spl194_5
| spl194_15 ),
inference(sat_conversion,[],[f22742]) ).
cnf(s14,plain,
( ~ spl194_4
| ~ spl194_6
| ~ spl194_15
| spl194_18 ),
inference(sat_conversion,[],[f23400]) ).
cnf(s18,plain,
( spl194_1
| ~ spl194_2
| ~ spl194_3
| ~ spl194_5
| ~ spl194_7
| ~ spl194_8
| ~ spl194_18 ),
inference(sat_conversion,[],[f23667]) ).
cnf(s19,plain,
spl194_15,
inference(rat,[],[s13,s5,s3]) ).
cnf(s20,plain,
spl194_18,
inference(rat,[],[s14,s4,s6,s19]) ).
cnf(s21,plain,
spl194_1,
inference(rat,[],[s18,s20,s8,s7,s5,s3,s2]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s1,s21]) ).
fof(f23668,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU413+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.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 05:15:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 8.08/3.09 % (3040034)Detected formulas, will run a generic FOF schedule.
% 8.08/3.09 % (3040381)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=3078771233:i=141695:sd=1:nm=32:gsp=on:ss=included_2988 on theBenchmark for (2988ds/141695Mi)
% 8.08/3.09 % (3040383)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=219069710:i=119:av=off:ss=axioms_2988 on theBenchmark for (2988ds/119Mi)
% 8.08/3.09 % (3040384)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=523238269:s2a=on:i=139:gtg=position_2988 on theBenchmark for (2988ds/139Mi)
% 8.08/3.09 % (3040382)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2711714600:i=109:sd=1:ins=1:gsp=on:ss=axioms_2988 on theBenchmark for (2988ds/109Mi)
% 8.08/3.09 % (3040379)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=200261829:i=141193_2988 on theBenchmark for (2988ds/141193Mi)
% 8.08/3.09 % (3040380)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=3560883191:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2988 on theBenchmark for (2988ds/134677Mi)
% 8.08/3.09 % (3040385)dis-21_1_sil=8000:lcm=predicate:random_seed=4101191499:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2988 on theBenchmark for (2988ds/129Mi)
% 8.08/3.09 % (3040384)Instruction limit reached!
% 8.08/3.09 % (3040384)------------------------------
% 8.08/3.09 % (3040384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040384)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040384)Termination reason: Instruction limit
% 8.08/3.09 % (3040384)Termination phase: Property scanning
% 8.08/3.09 % (3040384)Time elapsed: 0.059 s
% 8.08/3.09 % (3040384)Peak memory usage: 112 MB
% 8.08/3.09 % (3040384)Instructions burned: 140 (million)
% 8.08/3.09 % (3040382)Instruction limit reached!
% 8.08/3.09 % (3040382)------------------------------
% 8.08/3.09 % (3040382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040382)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040382)Termination reason: Instruction limit
% 8.08/3.09 % (3040382)Termination phase: SInE selection
% 8.08/3.09 % (3040382)Time elapsed: 0.082 s
% 8.08/3.09 % (3040382)Peak memory usage: 112 MB
% 8.08/3.09 % (3040382)Instructions burned: 109 (million)
% 8.08/3.09 % (3040383)Instruction limit reached!
% 8.08/3.09 % (3040383)------------------------------
% 8.08/3.09 % (3040383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040383)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040383)Termination reason: Instruction limit
% 8.08/3.09 % (3040383)Termination phase: Unused predicate definition removal
% 8.08/3.09 % (3040383)Time elapsed: 0.100 s
% 8.08/3.09 % (3040383)Peak memory usage: 113 MB
% 8.08/3.09 % (3040383)Instructions burned: 119 (million)
% 8.08/3.09 % (3040385)Instruction limit reached!
% 8.08/3.09 % (3040385)------------------------------
% 8.08/3.09 % (3040385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040385)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040385)Termination reason: Instruction limit
% 8.08/3.09 % (3040385)Termination phase: SInE selection
% 8.08/3.09 % (3040385)Time elapsed: 0.088 s
% 8.08/3.09 % (3040385)Peak memory usage: 113 MB
% 8.08/3.09 % (3040385)Instructions burned: 130 (million)
% 8.08/3.09 % (3040393)lrs+10_1_sil=8000:sp=occurrence:random_seed=3252011213:i=285:sd=3:ss=axioms:sgt=8_2986 on theBenchmark for (2986ds/285Mi)
% 8.08/3.09 % (3040394)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2555972700:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2986 on theBenchmark for (2986ds/157Mi)
% 8.08/3.09 % (3040395)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3596894292:i=325:sd=1:ss=axioms:sgt=32_2986 on theBenchmark for (2986ds/325Mi)
% 8.08/3.09 % (3040396)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=1270278205:s2a=on:i=248:s2at=1.23:gtg=position_2986 on theBenchmark for (2986ds/248Mi)
% 8.08/3.09 % (3040394)Instruction limit reached!
% 8.08/3.09 % (3040394)------------------------------
% 8.08/3.09 % (3040394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040394)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040394)Termination reason: Instruction limit
% 8.08/3.09 % (3040394)Termination phase: Property scanning
% 8.08/3.09 % (3040394)Time elapsed: 0.067 s
% 8.08/3.09 % (3040394)Peak memory usage: 112 MB
% 8.08/3.09 % (3040394)Instructions burned: 157 (million)
% 8.08/3.09 % (3040393)Instruction limit reached!
% 8.08/3.09 % (3040393)------------------------------
% 8.08/3.09 % (3040393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040393)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040393)Termination reason: Instruction limit
% 8.08/3.09 % (3040393)Termination phase: Saturation
% 8.08/3.09 % (3040393)Time elapsed: 0.207 s
% 8.08/3.09 % (3040393)Peak memory usage: 120 MB
% 8.08/3.09 % (3040393)Instructions burned: 285 (million)
% 8.08/3.09 % (3040396)Instruction limit reached!
% 8.08/3.09 % (3040396)------------------------------
% 8.08/3.09 % (3040396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040396)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040396)Termination reason: Instruction limit
% 8.08/3.09 % (3040396)Termination phase: Property scanning
% 8.08/3.09 % (3040396)Time elapsed: 0.137 s
% 8.08/3.09 % (3040396)Peak memory usage: 112 MB
% 8.08/3.09 % (3040396)Instructions burned: 248 (million)
% 8.08/3.09 % (3040402)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1286045554:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2984 on theBenchmark for (2984ds/294Mi)
% 8.08/3.09 % (3040395)Instruction limit reached!
% 8.08/3.09 % (3040395)------------------------------
% 8.08/3.09 % (3040395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040395)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040395)Termination reason: Instruction limit
% 8.08/3.09 % (3040395)Termination phase: Saturation
% 8.08/3.09 % (3040395)Time elapsed: 0.284 s
% 8.08/3.09 % (3040395)Peak memory usage: 120 MB
% 8.08/3.09 % (3040395)Instructions burned: 325 (million)
% 8.08/3.09 % (3040409)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2869646061:i=2350_2983 on theBenchmark for (2983ds/2350Mi)
% 8.08/3.09 % (3040411)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2575525346:cts=off:i=113:fsr=off:ss=included:sgt=4_2983 on theBenchmark for (2983ds/113Mi)
% 8.08/3.09 % (3040413)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2226406326:i=127:av=off:fsr=off:sup=off_2982 on theBenchmark for (2982ds/127Mi)
% 8.08/3.09 % (3040411)Instruction limit reached!
% 8.08/3.09 % (3040411)------------------------------
% 8.08/3.09 % (3040411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040411)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040411)Termination reason: Instruction limit
% 8.08/3.09 % (3040411)Termination phase: SInE selection
% 8.08/3.09 % (3040411)Time elapsed: 0.125 s
% 8.08/3.09 % (3040411)Peak memory usage: 112 MB
% 8.08/3.09 % (3040411)Instructions burned: 113 (million)
% 8.08/3.09 % (3040381)First to succeed.
% 8.08/3.09 % (3040381)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3040034"
% 8.08/3.09 % (3040402)Instruction limit reached!
% 8.08/3.09 % (3040402)------------------------------
% 8.08/3.09 % (3040402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040402)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040402)Termination reason: Instruction limit
% 8.08/3.09 % (3040402)Termination phase: Property scanning
% 8.08/3.09 % (3040402)Time elapsed: 0.330 s
% 8.08/3.09 % (3040402)Peak memory usage: 120 MB
% 8.08/3.09 % (3040402)Instructions burned: 295 (million)
% 8.08/3.09 % (3040413)Instruction limit reached!
% 8.08/3.09 % (3040413)------------------------------
% 8.08/3.09 % (3040413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.08/3.09 % (3040413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.08/3.09 % (3040413)CaDiCaL version: 2.1.3
% 8.08/3.09 % (3040413)Termination reason: Instruction limit
% 8.08/3.09 % (3040413)Termination phase: Preprocessing 1
% 8.08/3.09 % (3040413)Time elapsed: 0.150 s
% 8.08/3.09 % (3040413)Peak memory usage: 113 MB
% 8.08/3.09 % (3040413)Instructions burned: 130 (million)
% 8.08/3.09 % (3040425)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=898040619:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2979 on theBenchmark for (2979ds/114Mi)
% 8.08/3.09 % (3040381)Refutation found. Thanks to Tanya!
% 8.08/3.09 % SZS status Theorem for theBenchmark
% 8.08/3.09 % SZS output start Proof for theBenchmark
% See solution above
% 9.53/3.25 % (3040381)------------------------------
% 9.53/3.25 % (3040381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.53/3.25 % (3040381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.53/3.25 % (3040381)CaDiCaL version: 2.1.3
% 9.53/3.25 % (3040381)Termination reason: Refutation
% 9.53/3.25 % (3040381)Time elapsed: 0.804 s
% 9.53/3.25 % (3040381)Peak memory usage: 177 MB
% 9.53/3.25 % (3040381)Instructions burned: 2199 (million)
% 9.53/3.25 % (3040381)------------------------------
% 9.53/3.25 % (3040381)------------------------------
% 9.53/3.25 % (3040034)Success in time 2.234 s
% 9.53/3.25 % Vampire exiting
%------------------------------------------------------------------------------