%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU391+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:48:41 PM UTC 2026
% Result : Theorem 2.70s 1.30s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 93 ( 9 unt; 3 def)
% Number of atoms : 406 ( 15 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 504 ( 191 ~; 242 |; 54 &)
% ( 8 <=>; 7 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 97 ( 0 sgn 80 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_yellow19) ).
fof(f61,axiom,
! [X0,X1,X2] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ~ empty_carrier(X2)
& net_str(X2,X1) )
=> ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& X0 = X3
& is_eventually_in(X1,X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).
fof(f92,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( in(X2,filter_of_net_str(X0,X1))
<=> ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_yellow19) ).
fof(f93,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( in(X2,filter_of_net_str(X0,X1))
<=> ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f92]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| empty_carrier(X1)
| ~ net_str(X1,X0) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f189]) ).
fof(f221,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& X0 = X3
& is_eventually_in(X1,X2,X3) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f222,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& X0 = X3
& is_eventually_in(X1,X2,X3) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(flattening,[],[f221]) ).
fof(f242,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( in(X2,filter_of_net_str(X0,X1))
<~> ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) ) )
& ~ empty_carrier(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f243,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( in(X2,filter_of_net_str(X0,X1))
<~> ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) ) )
& ~ empty_carrier(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f242]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| X0 != X3
| ~ is_eventually_in(X1,X2,X3) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& X0 = X3
& is_eventually_in(X1,X2,X3) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(nnf_transformation,[],[f222]) ).
fof(f268,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| X0 != X3
| ~ is_eventually_in(X1,X2,X3) ) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X1)))
& X0 = X4
& is_eventually_in(X1,X2,X4) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(rectify,[],[f267]) ).
fof(f269,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_1_yellow19(X1,X2))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| X0 != X3
| ~ is_eventually_in(X1,X2,X3) ) )
& ( ( element(sK8(X0,X1,X2),powerset(the_carrier(X1)))
& sK8(X0,X1,X2) = X0
& is_eventually_in(X1,X2,sK8(X0,X1,X2)) )
| ~ in(X0,a_2_1_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X4,sK8(X0,X1,X2))],[f268]) ).
fof(f297,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_eventually_in(X0,X1,X2)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X2,filter_of_net_str(X0,X1)) )
& ( ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) )
| in(X2,filter_of_net_str(X0,X1)) ) )
& ~ empty_carrier(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(nnf_transformation,[],[f243]) ).
fof(f298,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_eventually_in(X0,X1,X2)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X2,filter_of_net_str(X0,X1)) )
& ( ( is_eventually_in(X0,X1,X2)
& element(X2,powerset(the_carrier(X0))) )
| in(X2,filter_of_net_str(X0,X1)) ) )
& ~ empty_carrier(X1)
& net_str(X1,X0) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f297]) ).
fof(f299,plain,
( ( ~ is_eventually_in(sK35,sK36,sK37)
| ~ element(sK37,powerset(the_carrier(sK35)))
| ~ in(sK37,filter_of_net_str(sK35,sK36)) )
& ( ( is_eventually_in(sK35,sK36,sK37)
& element(sK37,powerset(the_carrier(sK35))) )
| in(sK37,filter_of_net_str(sK35,sK36)) )
& ~ empty_carrier(sK36)
& net_str(sK36,sK35)
& ~ empty_carrier(sK35)
& one_sorted_str(sK35) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35,sK36,sK37]),skolemize(X0,sK35),skolemize(X1,sK36),skolemize(X2,sK37)],[f298]) ).
fof(f354,plain,
! [X0,X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| empty_carrier(X1)
| ~ net_str(X1,X0)
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f441,plain,
! [X2,X0,X1] :
( is_eventually_in(X1,X2,sK8(X0,X1,X2))
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f442,plain,
! [X2,X0,X1] :
( sK8(X0,X1,X2) = X0
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f443,plain,
! [X2,X0,X1] :
( element(sK8(X0,X1,X2),powerset(the_carrier(X1)))
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f444,plain,
! [X2,X3,X0,X1] :
( in(X0,a_2_1_yellow19(X1,X2))
| ~ element(X3,powerset(the_carrier(X1)))
| X0 != X3
| ~ is_eventually_in(X1,X2,X3)
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f559,plain,
one_sorted_str(sK35),
inference(cnf_transformation,[],[f299]) ).
fof(f560,plain,
~ empty_carrier(sK35),
inference(cnf_transformation,[],[f299]) ).
fof(f561,plain,
net_str(sK36,sK35),
inference(cnf_transformation,[],[f299]) ).
fof(f562,plain,
~ empty_carrier(sK36),
inference(cnf_transformation,[],[f299]) ).
fof(f563,plain,
( element(sK37,powerset(the_carrier(sK35)))
| in(sK37,filter_of_net_str(sK35,sK36)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f564,plain,
( is_eventually_in(sK35,sK36,sK37)
| in(sK37,filter_of_net_str(sK35,sK36)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f565,plain,
( ~ is_eventually_in(sK35,sK36,sK37)
| ~ element(sK37,powerset(the_carrier(sK35)))
| ~ in(sK37,filter_of_net_str(sK35,sK36)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f576,plain,
! [X2,X3,X1] :
( ~ net_str(X2,X1)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ is_eventually_in(X1,X2,X3)
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| in(X3,a_2_1_yellow19(X1,X2)) ),
inference(equality_resolution,[],[f444]) ).
fof(f578,definition,
( spl39_1
<=> in(sK37,filter_of_net_str(sK35,sK36)) ),
introduced(definition,[new_symbols(definition,[spl39_1])],[avatar_definition]) ).
fof(f579,plain,
( ~ in(sK37,filter_of_net_str(sK35,sK36))
| spl39_1 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f580,plain,
( in(sK37,filter_of_net_str(sK35,sK36))
| ~ spl39_1 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f582,definition,
( spl39_2
<=> element(sK37,powerset(the_carrier(sK35))) ),
introduced(definition,[new_symbols(definition,[spl39_2])],[avatar_definition]) ).
fof(f583,plain,
( ~ element(sK37,powerset(the_carrier(sK35)))
| spl39_2 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f584,plain,
( element(sK37,powerset(the_carrier(sK35)))
| ~ spl39_2 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f585,plain,
( spl39_1
| spl39_2 ),
inference(avatar_split_clause,[],[f563,f582,f578]) ).
fof(f587,definition,
( spl39_3
<=> is_eventually_in(sK35,sK36,sK37) ),
introduced(definition,[new_symbols(definition,[spl39_3])],[avatar_definition]) ).
fof(f588,plain,
( ~ is_eventually_in(sK35,sK36,sK37)
| spl39_3 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f589,plain,
( is_eventually_in(sK35,sK36,sK37)
| ~ spl39_3 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f590,plain,
( spl39_1
| spl39_3 ),
inference(avatar_split_clause,[],[f564,f587,f578]) ).
fof(f591,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(avatar_split_clause,[],[f565,f587,f582,f578]) ).
fof(f762,plain,
! [X2,X0,X1] :
( is_eventually_in(X1,X2,X0)
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1)
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(superposition,[],[f441,f442]) ).
fof(f763,plain,
! [X2,X0,X1] :
( ~ net_str(X2,X1)
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| is_eventually_in(X1,X2,X0) ),
inference(duplicate_literal_removal,[],[f762]) ).
fof(f765,plain,
! [X2,X0,X1] :
( element(X0,powerset(the_carrier(X1)))
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1)
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| ~ net_str(X2,X1) ),
inference(superposition,[],[f443,f442]) ).
fof(f766,plain,
! [X2,X0,X1] :
( ~ net_str(X2,X1)
| ~ in(X0,a_2_1_yellow19(X1,X2))
| empty_carrier(X1)
| ~ one_sorted_str(X1)
| empty_carrier(X2)
| element(X0,powerset(the_carrier(X1))) ),
inference(duplicate_literal_removal,[],[f765]) ).
fof(f769,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK35)))
| ~ is_eventually_in(sK35,sK36,X0)
| empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| empty_carrier(sK36)
| in(X0,a_2_1_yellow19(sK35,sK36)) ),
inference(resolution,[],[f576,f561]) ).
fof(f772,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK35)))
| ~ is_eventually_in(sK35,sK36,X0)
| ~ one_sorted_str(sK35)
| empty_carrier(sK36)
| in(X0,a_2_1_yellow19(sK35,sK36)) ),
inference(forward_subsumption_resolution,[],[f769,f560]) ).
fof(f773,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK35)))
| ~ is_eventually_in(sK35,sK36,X0)
| empty_carrier(sK36)
| in(X0,a_2_1_yellow19(sK35,sK36)) ),
inference(forward_subsumption_resolution,[],[f772,f559]) ).
fof(f774,plain,
! [X0] :
( ~ is_eventually_in(sK35,sK36,X0)
| ~ element(X0,powerset(the_carrier(sK35)))
| in(X0,a_2_1_yellow19(sK35,sK36)) ),
inference(forward_subsumption_resolution,[],[f773,f562]) ).
fof(f775,plain,
( ~ element(sK37,powerset(the_carrier(sK35)))
| in(sK37,a_2_1_yellow19(sK35,sK36))
| ~ spl39_3 ),
inference(resolution,[],[f774,f589]) ).
fof(f778,plain,
( in(sK37,a_2_1_yellow19(sK35,sK36))
| ~ spl39_2
| ~ spl39_3 ),
inference(forward_subsumption_resolution,[],[f775,f584]) ).
fof(f795,plain,
( in(sK37,filter_of_net_str(sK35,sK36))
| empty_carrier(sK36)
| ~ net_str(sK36,sK35)
| empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| ~ spl39_2
| ~ spl39_3 ),
inference(superposition,[],[f778,f354]) ).
fof(f796,plain,
( empty_carrier(sK36)
| ~ net_str(sK36,sK35)
| empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(forward_subsumption_resolution,[],[f795,f579]) ).
fof(f802,plain,
( ~ net_str(sK36,sK35)
| empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(forward_subsumption_resolution,[],[f796,f562]) ).
fof(f803,plain,
( empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(forward_subsumption_resolution,[],[f802,f561]) ).
fof(f804,plain,
( ~ one_sorted_str(sK35)
| spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(forward_subsumption_resolution,[],[f803,f560]) ).
fof(f805,plain,
( $false
| spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(forward_subsumption_resolution,[],[f804,f559]) ).
fof(f806,plain,
( spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(avatar_contradiction_clause,[],[f805]) ).
fof(f925,plain,
! [X0] :
( ~ in(X0,a_2_1_yellow19(sK35,sK36))
| empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| empty_carrier(sK36)
| is_eventually_in(sK35,sK36,X0) ),
inference(resolution,[],[f763,f561]) ).
fof(f928,plain,
! [X0] :
( ~ in(X0,a_2_1_yellow19(sK35,sK36))
| ~ one_sorted_str(sK35)
| empty_carrier(sK36)
| is_eventually_in(sK35,sK36,X0) ),
inference(forward_subsumption_resolution,[],[f925,f560]) ).
fof(f929,plain,
! [X0] :
( ~ in(X0,a_2_1_yellow19(sK35,sK36))
| empty_carrier(sK36)
| is_eventually_in(sK35,sK36,X0) ),
inference(forward_subsumption_resolution,[],[f928,f559]) ).
fof(f930,plain,
! [X0] :
( is_eventually_in(sK35,sK36,X0)
| ~ in(X0,a_2_1_yellow19(sK35,sK36)) ),
inference(forward_subsumption_resolution,[],[f929,f562]) ).
fof(f932,plain,
( ~ in(sK37,a_2_1_yellow19(sK35,sK36))
| spl39_3 ),
inference(resolution,[],[f930,f588]) ).
fof(f933,plain,
! [X0] :
( ~ in(X0,a_2_1_yellow19(sK35,sK36))
| empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| empty_carrier(sK36)
| element(X0,powerset(the_carrier(sK35))) ),
inference(resolution,[],[f766,f561]) ).
fof(f936,plain,
! [X0] :
( ~ in(X0,a_2_1_yellow19(sK35,sK36))
| ~ one_sorted_str(sK35)
| empty_carrier(sK36)
| element(X0,powerset(the_carrier(sK35))) ),
inference(forward_subsumption_resolution,[],[f933,f560]) ).
fof(f937,plain,
! [X0] :
( ~ in(X0,a_2_1_yellow19(sK35,sK36))
| empty_carrier(sK36)
| element(X0,powerset(the_carrier(sK35))) ),
inference(forward_subsumption_resolution,[],[f936,f559]) ).
fof(f938,plain,
! [X0] :
( ~ in(X0,a_2_1_yellow19(sK35,sK36))
| element(X0,powerset(the_carrier(sK35))) ),
inference(forward_subsumption_resolution,[],[f937,f562]) ).
fof(f940,plain,
( ~ in(sK37,filter_of_net_str(sK35,sK36))
| empty_carrier(sK36)
| ~ net_str(sK36,sK35)
| empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| spl39_3 ),
inference(superposition,[],[f932,f354]) ).
fof(f941,plain,
( empty_carrier(sK36)
| ~ net_str(sK36,sK35)
| empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| ~ spl39_1
| spl39_3 ),
inference(forward_subsumption_resolution,[],[f940,f580]) ).
fof(f951,plain,
( ~ net_str(sK36,sK35)
| empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| ~ spl39_1
| spl39_3 ),
inference(forward_subsumption_resolution,[],[f941,f562]) ).
fof(f952,plain,
( empty_carrier(sK35)
| ~ one_sorted_str(sK35)
| ~ spl39_1
| spl39_3 ),
inference(forward_subsumption_resolution,[],[f951,f561]) ).
fof(f953,plain,
( ~ one_sorted_str(sK35)
| ~ spl39_1
| spl39_3 ),
inference(forward_subsumption_resolution,[],[f952,f560]) ).
fof(f954,plain,
( $false
| ~ spl39_1
| spl39_3 ),
inference(forward_subsumption_resolution,[],[f953,f559]) ).
fof(f955,plain,
( ~ spl39_1
| spl39_3 ),
inference(avatar_contradiction_clause,[],[f954]) ).
fof(f976,plain,
! [X0] :
( ~ in(X0,filter_of_net_str(sK35,sK36))
| element(X0,powerset(the_carrier(sK35)))
| empty_carrier(sK36)
| ~ net_str(sK36,sK35)
| empty_carrier(sK35)
| ~ one_sorted_str(sK35) ),
inference(superposition,[],[f938,f354]) ).
fof(f977,plain,
! [X0] :
( ~ in(X0,filter_of_net_str(sK35,sK36))
| element(X0,powerset(the_carrier(sK35)))
| ~ net_str(sK36,sK35)
| empty_carrier(sK35)
| ~ one_sorted_str(sK35) ),
inference(forward_subsumption_resolution,[],[f976,f562]) ).
fof(f982,plain,
! [X0] :
( ~ in(X0,filter_of_net_str(sK35,sK36))
| element(X0,powerset(the_carrier(sK35)))
| empty_carrier(sK35)
| ~ one_sorted_str(sK35) ),
inference(forward_subsumption_resolution,[],[f977,f561]) ).
fof(f983,plain,
! [X0] :
( ~ in(X0,filter_of_net_str(sK35,sK36))
| element(X0,powerset(the_carrier(sK35)))
| ~ one_sorted_str(sK35) ),
inference(forward_subsumption_resolution,[],[f982,f560]) ).
fof(f984,plain,
! [X0] :
( ~ in(X0,filter_of_net_str(sK35,sK36))
| element(X0,powerset(the_carrier(sK35))) ),
inference(forward_subsumption_resolution,[],[f983,f559]) ).
fof(f1268,plain,
( element(sK37,powerset(the_carrier(sK35)))
| ~ spl39_1 ),
inference(resolution,[],[f984,f580]) ).
fof(f1274,plain,
( $false
| ~ spl39_1
| spl39_2 ),
inference(forward_subsumption_resolution,[],[f1268,f583]) ).
fof(f1275,plain,
( ~ spl39_1
| spl39_2 ),
inference(avatar_contradiction_clause,[],[f1274]) ).
cnf(s1,plain,
( spl39_1
| spl39_2 ),
inference(sat_conversion,[],[f585]) ).
cnf(s2,plain,
( spl39_1
| spl39_3 ),
inference(sat_conversion,[],[f590]) ).
cnf(s3,plain,
( ~ spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(sat_conversion,[],[f591]) ).
cnf(s7,plain,
( spl39_1
| ~ spl39_2
| ~ spl39_3 ),
inference(sat_conversion,[],[f806]) ).
cnf(s17,plain,
( ~ spl39_1
| spl39_3 ),
inference(sat_conversion,[],[f955]) ).
cnf(s34,plain,
( ~ spl39_1
| spl39_2 ),
inference(sat_conversion,[],[f1275]) ).
cnf(s35,plain,
spl39_1,
inference(rat,[],[s7,s1,s2]) ).
cnf(s36,plain,
spl39_2,
inference(rat,[],[s34,s35]) ).
cnf(s38,plain,
spl39_3,
inference(rat,[],[s17,s35]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s3,s36,s38,s35]) ).
fof(f1276,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU391+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 05:02:25 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.70/1.30 % (2035129)Detected formulas, will run a generic FOF schedule.
% 2.70/1.30 % (2035241)dis-21_1_sil=8000:lcm=predicate:random_seed=2159477930: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)
% 2.70/1.30 % (2035241)Instruction limit reached!
% 2.70/1.30 % (2035241)------------------------------
% 2.70/1.30 % (2035241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.30 % (2035241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.30 % (2035241)CaDiCaL version: 2.1.3
% 2.70/1.30 % (2035241)Termination reason: Instruction limit
% 2.70/1.30 % (2035241)Termination phase: Saturation
% 2.70/1.30 % (2035241)Time elapsed: 0.040 s
% 2.70/1.30 % (2035241)Peak memory usage: 93 MB
% 2.70/1.30 % (2035241)Instructions burned: 133 (million)
% 2.70/1.30 % (2035236)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=2229186844:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.30 % (2035237)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=128781527:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.30 % (2035240)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4145588409:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.30 % (2035235)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=3295370899:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.30 % (2035238)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1021456615:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.30 % (2035239)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2831467237:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.30 % (2035238)Refutation not found, incomplete strategy
% 2.70/1.30 % (2035238)------------------------------
% 2.70/1.30 % (2035238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.30 % (2035238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.30 % (2035238)CaDiCaL version: 2.1.3
% 2.70/1.30 % (2035238)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.30 % (2035238)Time elapsed: 0.004 s
% 2.70/1.30 % (2035238)Peak memory usage: 89 MB
% 2.70/1.30 % (2035238)Instructions burned: 4 (million)
% 2.70/1.30 % (2035240)First to succeed.
% 2.70/1.30 % (2035239)Also succeeded, but the first one will report.
% 2.70/1.30 % (2035240)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2035129"
% 2.70/1.30 % (2035249)lrs+10_1_sil=8000:sp=occurrence:random_seed=2380419560:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.70/1.30 % (2035249)Also succeeded, but the first one will report.
% 2.70/1.30 % (2035238)------------------------------
% 2.70/1.30 % (2035238)------------------------------
% 2.70/1.30 % (2035240)Refutation found. Thanks to Tanya!
% 2.70/1.30 % SZS status Theorem for theBenchmark
% 2.70/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.81/1.50 % (2035240)------------------------------
% 3.81/1.50 % (2035240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.50 % (2035240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.50 % (2035240)CaDiCaL version: 2.1.3
% 3.81/1.50 % (2035240)Termination reason: Refutation
% 3.81/1.50 % (2035240)Time elapsed: 0.028 s
% 3.81/1.50 % (2035240)Peak memory usage: 90 MB
% 3.81/1.50 % (2035240)Instructions burned: 37 (million)
% 3.81/1.50 % (2035240)------------------------------
% 3.81/1.50 % (2035240)------------------------------
% 3.81/1.50 % (2035129)Success in time 0.457 s
% 3.81/1.50 % Vampire exiting
%------------------------------------------------------------------------------