%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU387+2 : 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 : n016.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 12:48:40 PM UTC 2026
% Result : Theorem 17.04s 3.48s
% Output : Refutation 17.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 89 ( 51 unt; 4 def)
% Number of atoms : 311 ( 25 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 411 ( 189 ~; 156 |; 56 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-1 aty)
% Number of variables : 82 ( 76 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f159,axiom,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_1) ).
fof(f274,axiom,
! [X0] :
( strict_rel_str(boole_POSet(X0))
& rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(f440,axiom,
! [X0] :
( ~ empty_carrier(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& complete_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_waybel_1) ).
fof(f544,axiom,
! [X0] : k1_pcomps_1(X0) = powerset(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
fof(f677,axiom,
! [X0] : bottom_of_relstr(boole_POSet(X0)) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_yellow_1) ).
fof(f731,conjecture,
! [X0] :
( ~ empty(X0)
=> ! [X1] :
( ( ~ empty(X1)
& filtered_subset(X1,boole_POSet(X0))
& upper_relstr_subset(X1,boole_POSet(X0))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& element(X1,powerset(the_carrier(boole_POSet(X0)))) )
=> ! [X2] :
~ ( in(X2,X1)
& empty(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yellow19) ).
fof(f732,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ! [X1] :
( ( ~ empty(X1)
& filtered_subset(X1,boole_POSet(X0))
& upper_relstr_subset(X1,boole_POSet(X0))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& element(X1,powerset(the_carrier(boole_POSet(X0)))) )
=> ! [X2] :
~ ( in(X2,X1)
& empty(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f731]) ).
fof(f794,axiom,
! [X0] : the_carrier(boole_POSet(X0)) = powerset(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel_7) ).
fof(f827,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f837,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f849,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& reflexive_relstr(X0)
& transitive_relstr(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( ( ~ empty(X1)
& filtered_subset(X1,X0)
& upper_relstr_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_waybel_7) ).
fof(f1824,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( in(X2,X1)
& empty(X2) )
& ~ empty(X1)
& filtered_subset(X1,boole_POSet(X0))
& upper_relstr_subset(X1,boole_POSet(X0))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& element(X1,powerset(the_carrier(boole_POSet(X0)))) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f732]) ).
fof(f1825,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( in(X2,X1)
& empty(X2) )
& ~ empty(X1)
& filtered_subset(X1,boole_POSet(X0))
& upper_relstr_subset(X1,boole_POSet(X0))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& element(X1,powerset(the_carrier(boole_POSet(X0)))) )
& ~ empty(X0) ),
inference(flattening,[],[f1824]) ).
fof(f1950,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f827]) ).
fof(f1963,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f837]) ).
fof(f1975,plain,
! [X0] :
( ! [X1] :
( ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) )
| empty(X1)
| ~ filtered_subset(X1,X0)
| ~ upper_relstr_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ transitive_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f849]) ).
fof(f1976,plain,
! [X0] :
( ! [X1] :
( ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) )
| empty(X1)
| ~ filtered_subset(X1,X0)
| ~ upper_relstr_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ transitive_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f1975]) ).
fof(f2872,plain,
( in(sK607,sK606)
& empty(sK607)
& ~ empty(sK606)
& filtered_subset(sK606,boole_POSet(sK605))
& upper_relstr_subset(sK606,boole_POSet(sK605))
& proper_element(sK606,powerset(the_carrier(boole_POSet(sK605))))
& element(sK606,powerset(the_carrier(boole_POSet(sK605))))
& ~ empty(sK605) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK605,sK606,sK607]),skolemize(X0,sK605),skolemize(X1,sK606),skolemize(X2,sK607)],[f1825]) ).
fof(f2941,plain,
! [X0] :
( ! [X1] :
( ( ( proper_element(X1,powerset(the_carrier(X0)))
| in(bottom_of_relstr(X0),X1) )
& ( ~ in(bottom_of_relstr(X0),X1)
| ~ proper_element(X1,powerset(the_carrier(X0))) ) )
| empty(X1)
| ~ filtered_subset(X1,X0)
| ~ upper_relstr_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ transitive_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f1976]) ).
fof(f3542,plain,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f159]) ).
fof(f3855,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f274]) ).
fof(f4309,plain,
! [X0] : lower_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f440]) ).
fof(f4313,plain,
! [X0] : antisymmetric_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f440]) ).
fof(f4314,plain,
! [X0] : transitive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f440]) ).
fof(f4315,plain,
! [X0] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f440]) ).
fof(f4317,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f440]) ).
fof(f4782,plain,
! [X0] : powerset(X0) = k1_pcomps_1(X0),
inference(cnf_transformation,[],[f544]) ).
fof(f5428,plain,
! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f677]) ).
fof(f5519,plain,
element(sK606,powerset(the_carrier(boole_POSet(sK605)))),
inference(cnf_transformation,[],[f2872]) ).
fof(f5520,plain,
proper_element(sK606,powerset(the_carrier(boole_POSet(sK605)))),
inference(cnf_transformation,[],[f2872]) ).
fof(f5521,plain,
upper_relstr_subset(sK606,boole_POSet(sK605)),
inference(cnf_transformation,[],[f2872]) ).
fof(f5522,plain,
filtered_subset(sK606,boole_POSet(sK605)),
inference(cnf_transformation,[],[f2872]) ).
fof(f5524,plain,
empty(sK607),
inference(cnf_transformation,[],[f2872]) ).
fof(f5525,plain,
in(sK607,sK606),
inference(cnf_transformation,[],[f2872]) ).
fof(f5643,plain,
! [X0] : powerset(X0) = the_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f794]) ).
fof(f5709,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f1950]) ).
fof(f5725,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f1963]) ).
fof(f5746,plain,
! [X0,X1] :
( ~ in(bottom_of_relstr(X0),X1)
| ~ proper_element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ filtered_subset(X1,X0)
| ~ upper_relstr_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ transitive_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f2941]) ).
fof(f5989,plain,
! [X0] : rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f3855,f3542]) ).
fof(f6153,plain,
! [X0] : ~ empty_carrier(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f4317,f3542]) ).
fof(f6155,plain,
! [X0] : reflexive_relstr(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f4315,f3542]) ).
fof(f6156,plain,
! [X0] : transitive_relstr(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f4314,f3542]) ).
fof(f6157,plain,
! [X0] : antisymmetric_relstr(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f4313,f3542]) ).
fof(f6161,plain,
! [X0] : lower_bounded_relstr(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f4309,f3542]) ).
fof(f6533,plain,
! [X0] : empty_set = bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f5428,f3542]) ).
fof(f6555,plain,
filtered_subset(sK606,poset_of_lattice(boole_lattice(sK605))),
inference(definition_unfolding,[],[f5522,f3542]) ).
fof(f6556,plain,
upper_relstr_subset(sK606,poset_of_lattice(boole_lattice(sK605))),
inference(definition_unfolding,[],[f5521,f3542]) ).
fof(f6557,plain,
proper_element(sK606,k1_pcomps_1(the_carrier(poset_of_lattice(boole_lattice(sK605))))),
inference(definition_unfolding,[],[f5520,f4782,f3542]) ).
fof(f6558,plain,
element(sK606,k1_pcomps_1(the_carrier(poset_of_lattice(boole_lattice(sK605))))),
inference(definition_unfolding,[],[f5519,f4782,f3542]) ).
fof(f6608,plain,
! [X0] : k1_pcomps_1(X0) = the_carrier(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f5643,f4782,f3542]) ).
fof(f6649,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(the_carrier(X0)))
| ~ in(bottom_of_relstr(X0),X1)
| empty(X1)
| ~ filtered_subset(X1,X0)
| ~ upper_relstr_subset(X1,X0)
| ~ element(X1,k1_pcomps_1(the_carrier(X0)))
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ transitive_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f5746,f4782,f4782]) ).
fof(f6950,definition,
sF629 = boole_lattice(sK605),
introduced(definition,[new_symbols(definition,[sF629])],[function_definition]) ).
fof(f6951,plain,
boole_lattice(sK605) = sF629,
inference(reorient_equations,[],[f6950]) ).
fof(f6952,definition,
sF630 = poset_of_lattice(sF629),
introduced(definition,[new_symbols(definition,[sF630])],[function_definition]) ).
fof(f6953,plain,
poset_of_lattice(sF629) = sF630,
inference(reorient_equations,[],[f6952]) ).
fof(f6954,plain,
filtered_subset(sK606,sF630),
inference(definition_folding,[],[f6555,f6953,f6951]) ).
fof(f6955,plain,
upper_relstr_subset(sK606,sF630),
inference(definition_folding,[],[f6556,f6953,f6951]) ).
fof(f6956,definition,
sF631 = the_carrier(sF630),
introduced(definition,[new_symbols(definition,[sF631])],[function_definition]) ).
fof(f6957,plain,
the_carrier(sF630) = sF631,
inference(reorient_equations,[],[f6956]) ).
fof(f6958,definition,
sF632 = k1_pcomps_1(sF631),
introduced(definition,[new_symbols(definition,[sF632])],[function_definition]) ).
fof(f6959,plain,
k1_pcomps_1(sF631) = sF632,
inference(reorient_equations,[],[f6958]) ).
fof(f6960,plain,
proper_element(sK606,sF632),
inference(definition_folding,[],[f6557,f6959,f6957,f6953,f6951]) ).
fof(f6961,plain,
element(sK606,sF632),
inference(definition_folding,[],[f6558,f6959,f6957,f6953,f6951]) ).
fof(f7380,plain,
k1_pcomps_1(sK605) = the_carrier(poset_of_lattice(sF629)),
inference(superposition,[],[f6608,f6951]) ).
fof(f7382,plain,
the_carrier(sF630) = k1_pcomps_1(sK605),
inference(forward_demodulation,[],[f7380,f6953]) ).
fof(f7383,plain,
sF631 = k1_pcomps_1(sK605),
inference(forward_demodulation,[],[f7382,f6957]) ).
fof(f7447,plain,
empty_set = sK607,
inference(resolution,[],[f5709,f5524]) ).
fof(f7449,plain,
in(empty_set,sK606),
inference(superposition,[],[f5525,f7447]) ).
fof(f7452,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),X1)
| empty(X1)
| ~ filtered_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ upper_relstr_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| empty_carrier(poset_of_lattice(boole_lattice(X0)))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ transitive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ lower_bounded_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0))) ),
inference(superposition,[],[f6649,f6608]) ).
fof(f7457,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),X1)
| ~ filtered_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ upper_relstr_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| empty_carrier(poset_of_lattice(boole_lattice(X0)))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ transitive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ lower_bounded_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0))) ),
inference(forward_subsumption_resolution,[],[f7452,f5725]) ).
fof(f7461,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),X1)
| ~ filtered_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ upper_relstr_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ transitive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ lower_bounded_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0))) ),
inference(forward_subsumption_resolution,[],[f7457,f6153]) ).
fof(f7465,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),X1)
| ~ filtered_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ upper_relstr_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ transitive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ lower_bounded_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0))) ),
inference(forward_subsumption_resolution,[],[f7461,f6155]) ).
fof(f7468,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),X1)
| ~ filtered_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ upper_relstr_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ antisymmetric_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ lower_bounded_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0))) ),
inference(forward_subsumption_resolution,[],[f7465,f6156]) ).
fof(f7494,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),X1)
| ~ filtered_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ upper_relstr_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ lower_bounded_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0))) ),
inference(forward_subsumption_resolution,[],[f7468,f6157]) ).
fof(f7496,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),X1)
| ~ filtered_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ upper_relstr_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0))) ),
inference(forward_subsumption_resolution,[],[f7494,f6161]) ).
fof(f7521,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ in(bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),X1)
| ~ filtered_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ upper_relstr_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ element(X1,k1_pcomps_1(k1_pcomps_1(X0))) ),
inference(forward_subsumption_resolution,[],[f7496,f5989]) ).
fof(f7522,plain,
! [X0,X1] :
( ~ proper_element(X1,k1_pcomps_1(k1_pcomps_1(X0)))
| ~ in(empty_set,X1)
| ~ filtered_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ upper_relstr_subset(X1,poset_of_lattice(boole_lattice(X0)))
| ~ element(X1,k1_pcomps_1(k1_pcomps_1(X0))) ),
inference(forward_demodulation,[],[f7521,f6533]) ).
fof(f7528,plain,
! [X0] :
( ~ proper_element(X0,k1_pcomps_1(sF631))
| ~ in(empty_set,X0)
| ~ filtered_subset(X0,poset_of_lattice(boole_lattice(sK605)))
| ~ upper_relstr_subset(X0,poset_of_lattice(boole_lattice(sK605)))
| ~ element(X0,k1_pcomps_1(sF631)) ),
inference(superposition,[],[f7522,f7383]) ).
fof(f7529,plain,
! [X0] :
( ~ proper_element(X0,sF632)
| ~ in(empty_set,X0)
| ~ filtered_subset(X0,poset_of_lattice(boole_lattice(sK605)))
| ~ upper_relstr_subset(X0,poset_of_lattice(boole_lattice(sK605)))
| ~ element(X0,k1_pcomps_1(sF631)) ),
inference(forward_demodulation,[],[f7528,f6959]) ).
fof(f7531,plain,
! [X0] :
( ~ filtered_subset(X0,poset_of_lattice(sF629))
| ~ proper_element(X0,sF632)
| ~ in(empty_set,X0)
| ~ upper_relstr_subset(X0,poset_of_lattice(boole_lattice(sK605)))
| ~ element(X0,k1_pcomps_1(sF631)) ),
inference(forward_demodulation,[],[f7529,f6951]) ).
fof(f7533,plain,
! [X0] :
( ~ filtered_subset(X0,sF630)
| ~ proper_element(X0,sF632)
| ~ in(empty_set,X0)
| ~ upper_relstr_subset(X0,poset_of_lattice(boole_lattice(sK605)))
| ~ element(X0,k1_pcomps_1(sF631)) ),
inference(forward_demodulation,[],[f7531,f6953]) ).
fof(f7534,plain,
! [X0] :
( ~ upper_relstr_subset(X0,poset_of_lattice(sF629))
| ~ filtered_subset(X0,sF630)
| ~ proper_element(X0,sF632)
| ~ in(empty_set,X0)
| ~ element(X0,k1_pcomps_1(sF631)) ),
inference(forward_demodulation,[],[f7533,f6951]) ).
fof(f7535,plain,
! [X0] :
( ~ upper_relstr_subset(X0,sF630)
| ~ filtered_subset(X0,sF630)
| ~ proper_element(X0,sF632)
| ~ in(empty_set,X0)
| ~ element(X0,k1_pcomps_1(sF631)) ),
inference(forward_demodulation,[],[f7534,f6953]) ).
fof(f7536,plain,
! [X0] :
( ~ proper_element(X0,sF632)
| ~ upper_relstr_subset(X0,sF630)
| ~ filtered_subset(X0,sF630)
| ~ element(X0,sF632)
| ~ in(empty_set,X0) ),
inference(forward_demodulation,[],[f7535,f6959]) ).
fof(f7537,plain,
( ~ upper_relstr_subset(sK606,sF630)
| ~ filtered_subset(sK606,sF630)
| ~ element(sK606,sF632)
| ~ in(empty_set,sK606) ),
inference(resolution,[],[f7536,f6960]) ).
fof(f7538,plain,
( ~ filtered_subset(sK606,sF630)
| ~ element(sK606,sF632)
| ~ in(empty_set,sK606) ),
inference(forward_subsumption_resolution,[],[f7537,f6955]) ).
fof(f7539,plain,
( ~ element(sK606,sF632)
| ~ in(empty_set,sK606) ),
inference(forward_subsumption_resolution,[],[f7538,f6954]) ).
fof(f7540,plain,
~ in(empty_set,sK606),
inference(forward_subsumption_resolution,[],[f7539,f6961]) ).
fof(f7541,plain,
$false,
inference(forward_subsumption_resolution,[],[f7540,f7449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU387+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.40 % Computer : n016.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 28 05:08:48 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 17.04/3.48 % (3272910)Detected formulas, will run a generic FOF schedule.
% 17.04/3.48 % (3272915)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=490933111:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 17.04/3.48 % (3272918)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2057714587:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 17.04/3.48 % (3272917)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=2047943672:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 17.04/3.48 % (3272920)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=990216805:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 17.04/3.48 % (3272916)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=577192335:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 17.04/3.48 % (3272921)dis-21_1_sil=8000:lcm=predicate:random_seed=1301346771: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)
% 17.04/3.48 % (3272919)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1236048921:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 17.04/3.48 % (3272918)Instruction limit reached!
% 17.04/3.48 % (3272918)------------------------------
% 17.04/3.48 % (3272918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272918)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272918)Termination reason: Instruction limit
% 17.04/3.48 % (3272918)Termination phase: Blocked clause elimination
% 17.04/3.48 % (3272918)Time elapsed: 0.105 s
% 17.04/3.48 % (3272918)Peak memory usage: 90 MB
% 17.04/3.48 % (3272918)Instructions burned: 109 (million)
% 17.04/3.48 % (3272921)Instruction limit reached!
% 17.04/3.48 % (3272921)------------------------------
% 17.04/3.48 % (3272921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272921)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272921)Termination reason: Instruction limit
% 17.04/3.48 % (3272921)Termination phase: Saturation
% 17.04/3.48 % (3272921)Time elapsed: 0.122 s
% 17.04/3.48 % (3272921)Peak memory usage: 92 MB
% 17.04/3.48 % (3272921)Instructions burned: 129 (million)
% 17.04/3.48 % (3272919)Instruction limit reached!
% 17.04/3.48 % (3272919)------------------------------
% 17.04/3.48 % (3272919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272919)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272919)Termination reason: Instruction limit
% 17.04/3.48 % (3272919)Termination phase: Saturation
% 17.04/3.48 % (3272919)Time elapsed: 0.127 s
% 17.04/3.48 % (3272919)Peak memory usage: 91 MB
% 17.04/3.48 % (3272919)Instructions burned: 119 (million)
% 17.04/3.48 % (3272920)Instruction limit reached!
% 17.04/3.48 % (3272920)------------------------------
% 17.04/3.48 % (3272920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272920)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272920)Termination reason: Instruction limit
% 17.04/3.48 % (3272920)Termination phase: Saturation
% 17.04/3.48 % (3272920)Time elapsed: 0.142 s
% 17.04/3.48 % (3272920)Peak memory usage: 92 MB
% 17.04/3.48 % (3272920)Instructions burned: 141 (million)
% 17.04/3.48 % (3272929)lrs+10_1_sil=8000:sp=occurrence:random_seed=3758819429:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 17.04/3.48 % (3272931)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1298517216:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 17.04/3.48 % (3272930)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2482993815:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 17.04/3.48 % (3272932)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=935107647:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 17.04/3.48 % (3272929)Instruction limit reached!
% 17.04/3.48 % (3272929)------------------------------
% 17.04/3.48 % (3272929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272929)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272929)Termination reason: Instruction limit
% 17.04/3.48 % (3272929)Termination phase: Saturation
% 17.04/3.48 % (3272929)Time elapsed: 0.157 s
% 17.04/3.48 % (3272929)Peak memory usage: 95 MB
% 17.04/3.48 % (3272929)Instructions burned: 286 (million)
% 17.04/3.48 % (3272930)Instruction limit reached!
% 17.04/3.48 % (3272930)------------------------------
% 17.04/3.48 % (3272930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272930)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272930)Termination reason: Instruction limit
% 17.04/3.48 % (3272930)Termination phase: Saturation
% 17.04/3.48 % (3272930)Time elapsed: 0.158 s
% 17.04/3.48 % (3272930)Peak memory usage: 90 MB
% 17.04/3.48 % (3272930)Instructions burned: 157 (million)
% 17.04/3.48 % (3272932)Instruction limit reached!
% 17.04/3.48 % (3272932)------------------------------
% 17.04/3.48 % (3272932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272932)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272932)Termination reason: Instruction limit
% 17.04/3.48 % (3272932)Termination phase: Saturation
% 17.04/3.48 % (3272932)Time elapsed: 0.242 s
% 17.04/3.48 % (3272932)Peak memory usage: 94 MB
% 17.04/3.48 % (3272932)Instructions burned: 248 (million)
% 17.04/3.48 % (3272937)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3413822755:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 17.04/3.48 % (3272931)Instruction limit reached!
% 17.04/3.48 % (3272931)------------------------------
% 17.04/3.48 % (3272931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272931)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272931)Termination reason: Instruction limit
% 17.04/3.48 % (3272931)Termination phase: Saturation
% 17.04/3.48 % (3272931)Time elapsed: 0.348 s
% 17.04/3.48 % (3272931)Peak memory usage: 95 MB
% 17.04/3.48 % (3272931)Instructions burned: 325 (million)
% 17.04/3.48 % (3272938)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3747315597:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 17.04/3.48 % (3272937)Instruction limit reached!
% 17.04/3.48 % (3272937)------------------------------
% 17.04/3.48 % (3272937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272937)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272937)Termination reason: Instruction limit
% 17.04/3.48 % (3272937)Termination phase: Saturation
% 17.04/3.48 % (3272937)Time elapsed: 0.162 s
% 17.04/3.48 % (3272937)Peak memory usage: 94 MB
% 17.04/3.48 % (3272937)Instructions burned: 295 (million)
% 17.04/3.48 % (3272939)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=770581720:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 17.04/3.48 % (3272941)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3539793311:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 17.04/3.48 % (3272943)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3554704505:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2988 on theBenchmark for (2988ds/114Mi)
% 17.04/3.48 % (3272939)Instruction limit reached!
% 17.04/3.48 % (3272939)------------------------------
% 17.04/3.48 % (3272939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272939)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272939)Termination reason: Instruction limit
% 17.04/3.48 % (3272939)Termination phase: Saturation
% 17.04/3.48 % (3272939)Time elapsed: 0.113 s
% 17.04/3.48 % (3272939)Peak memory usage: 92 MB
% 17.04/3.48 % (3272939)Instructions burned: 113 (million)
% 17.04/3.48 % (3272941)Instruction limit reached!
% 17.04/3.48 % (3272941)------------------------------
% 17.04/3.48 % (3272941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272941)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272941)Termination reason: Instruction limit
% 17.04/3.48 % (3272941)Termination phase: Blocked clause elimination
% 17.04/3.48 % (3272941)Time elapsed: 0.125 s
% 17.04/3.48 % (3272941)Peak memory usage: 91 MB
% 17.04/3.48 % (3272941)Instructions burned: 128 (million)
% 17.04/3.48 % (3272943)Instruction limit reached!
% 17.04/3.48 % (3272943)------------------------------
% 17.04/3.48 % (3272943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272943)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272943)Termination reason: Instruction limit
% 17.04/3.48 % (3272943)Termination phase: Saturation
% 17.04/3.48 % (3272943)Time elapsed: 0.063 s
% 17.04/3.48 % (3272943)Peak memory usage: 90 MB
% 17.04/3.48 % (3272943)Instructions burned: 115 (million)
% 17.04/3.48 % (3272949)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2778179143:i=5202:ss=axioms:sgt=16_2985 on theBenchmark for (2985ds/5202Mi)
% 17.04/3.48 % (3272947)lrs+10_1_sil=8000:sp=occurrence:random_seed=3305596437:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2986 on theBenchmark for (2986ds/907Mi)
% 17.04/3.48 % (3272948)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2066609163:i=437:sd=1:aac=none:ss=included_2985 on theBenchmark for (2985ds/437Mi)
% 17.04/3.48 % (3272915)First to succeed.
% 17.04/3.48 % (3272915)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3272910"
% 17.04/3.48 % (3272948)Instruction limit reached!
% 17.04/3.48 % (3272948)------------------------------
% 17.04/3.48 % (3272948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.04/3.48 % (3272948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/3.48 % (3272948)CaDiCaL version: 2.1.3
% 17.04/3.48 % (3272948)Termination reason: Instruction limit
% 17.04/3.48 % (3272948)Termination phase: Saturation
% 17.04/3.48 % (3272948)Time elapsed: 0.437 s
% 17.04/3.48 % (3272948)Peak memory usage: 96 MB
% 17.04/3.48 % (3272948)Instructions burned: 437 (million)
% 17.04/3.48 % (3272916)Also succeeded, but the first one will report.
% 17.04/3.48 % (3272953)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3521641293:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2978 on theBenchmark for (2978ds/134Mi)
% 17.04/3.48 % (3272915)Refutation found. Thanks to Tanya!
% 17.04/3.48 % SZS status Theorem for theBenchmark
% 17.04/3.48 % SZS output start Proof for theBenchmark
% See solution above
% 17.99/3.76 % (3272915)------------------------------
% 17.99/3.76 % (3272915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.99/3.76 % (3272915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.99/3.76 % (3272915)CaDiCaL version: 2.1.3
% 17.99/3.76 % (3272915)Termination reason: Refutation
% 17.99/3.76 % (3272915)Time elapsed: 1.757 s
% 17.99/3.76 % (3272915)Peak memory usage: 172 MB
% 17.99/3.76 % (3272915)Instructions burned: 1887 (million)
% 17.99/3.76 % (3272915)------------------------------
% 17.99/3.76 % (3272915)------------------------------
% 17.99/3.76 % (3272910)Success in time 2.469 s
% 17.99/3.76 % Vampire exiting
%------------------------------------------------------------------------------