%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU387+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:57:18 PM UTC 2026
% Result : Theorem 1.38s 1.34s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 88 ( 40 unt; 1 def)
% Number of atoms : 428 ( 10 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 506 ( 166 ~; 111 |; 213 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 30 ( 28 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-1 aty)
% Number of variables : 86 ( 0 sgn 80 !; 6 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( rel_str(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(f44,axiom,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& boolean_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_waybel_7) ).
fof(f49,axiom,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& directed_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_yellow_6) ).
fof(f75,axiom,
! [X0] : bottom_of_relstr(boole_POSet(X0)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).
fof(f78,conjecture,
! [X0] :
( ~ empty(X0)
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(X0))))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& upper_relstr_subset(X1,boole_POSet(X0))
& filtered_subset(X1,boole_POSet(X0))
& ~ empty(X1) )
=> ! [X2] :
~ ( empty(X2)
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow19) ).
fof(f79,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(X0))))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& upper_relstr_subset(X1,boole_POSet(X0))
& filtered_subset(X1,boole_POSet(X0))
& ~ empty(X1) )
=> ! [X2] :
~ ( empty(X2)
& in(X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f78]) ).
fof(f83,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f84,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f86,axiom,
! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(X0)))
& upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1) )
=> ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_7) ).
fof(f90,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f49]) ).
fof(f93,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f44]) ).
fof(f95,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f93]) ).
fof(f99,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f95]) ).
fof(f101,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f99]) ).
fof(f103,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f101]) ).
fof(f104,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f90]) ).
fof(f160,plain,
! [X0] :
( empty(X0)
| ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f177,plain,
? [X0] :
( ~ empty(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(boole_POSet(X0))))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& upper_relstr_subset(X1,boole_POSet(X0))
& filtered_subset(X1,boole_POSet(X0))
& ~ empty(X1)
& ? [X2] :
( empty(X2)
& in(X2,X1) ) ) ),
inference(ennf_transformation,[],[f79]) ).
fof(f178,plain,
? [X0] :
( ~ empty(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(boole_POSet(X0))))
& proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
& upper_relstr_subset(X1,boole_POSet(X0))
& filtered_subset(X1,boole_POSet(X0))
& ~ empty(X1)
& ? [X2] :
( empty(X2)
& in(X2,X1) ) ) ),
inference(flattening,[],[f177]) ).
fof(f183,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f83]) ).
fof(f184,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f84]) ).
fof(f186,plain,
! [X0] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1)
| ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) ) ) ),
inference(ennf_transformation,[],[f86]) ).
fof(f187,plain,
! [X0] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1)
| ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) ) ) ),
inference(flattening,[],[f186]) ).
fof(f221,plain,
( ~ empty(sK28)
& element(sK29,powerset(the_carrier(boole_POSet(sK28))))
& proper_element(sK29,powerset(the_carrier(boole_POSet(sK28))))
& upper_relstr_subset(sK29,boole_POSet(sK28))
& filtered_subset(sK29,boole_POSet(sK28))
& ~ empty(sK29)
& empty(sK30)
& in(sK30,sK29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30]),skolemize(X0,sK28),skolemize(X1,sK29),skolemize(X2,sK30)],[f178]) ).
fof(f222,plain,
! [X0] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(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))) ) ) ) ),
inference(nnf_transformation,[],[f187]) ).
fof(f278,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f345,plain,
! [X0] : lower_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f346,plain,
! [X0] : antisymmetric_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f347,plain,
! [X0] : transitive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f348,plain,
! [X0] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f350,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f461,plain,
! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f75]) ).
fof(f465,plain,
element(sK29,powerset(the_carrier(boole_POSet(sK28)))),
inference(cnf_transformation,[],[f221]) ).
fof(f466,plain,
proper_element(sK29,powerset(the_carrier(boole_POSet(sK28)))),
inference(cnf_transformation,[],[f221]) ).
fof(f467,plain,
upper_relstr_subset(sK29,boole_POSet(sK28)),
inference(cnf_transformation,[],[f221]) ).
fof(f468,plain,
filtered_subset(sK29,boole_POSet(sK28)),
inference(cnf_transformation,[],[f221]) ).
fof(f470,plain,
empty(sK30),
inference(cnf_transformation,[],[f221]) ).
fof(f471,plain,
in(sK30,sK29),
inference(cnf_transformation,[],[f221]) ).
fof(f475,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f183]) ).
fof(f476,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
fof(f478,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ filtered_subset(X1,X0)
| empty(X1)
| ~ proper_element(X1,powerset(the_carrier(X0)))
| ~ in(bottom_of_relstr(X0),X1) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_86,plain,
! [X0: $i] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f278]) ).
tcf(c_145,plain,
! [X0: $i] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f350]) ).
tcf(c_147,plain,
! [X0: $i] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f348]) ).
tcf(c_148,plain,
! [X0: $i] : transitive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f347]) ).
tcf(c_149,plain,
! [X0: $i] : antisymmetric_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f346]) ).
tcf(c_150,plain,
! [X0: $i] : lower_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f345]) ).
tcf(c_268,plain,
! [X0: $i] : bottom_of_relstr(boole_POSet(X0)) = empty_set,
inference(cnf_transformation,[],[f461]) ).
tcf(c_271,negated_conjecture,
in(sK30,sK29),
inference(cnf_transformation,[],[f471]) ).
tcf(c_272,negated_conjecture,
empty(sK30),
inference(cnf_transformation,[],[f470]) ).
tcf(c_274,negated_conjecture,
filtered_subset(sK29,boole_POSet(sK28)),
inference(cnf_transformation,[],[f468]) ).
tcf(c_275,negated_conjecture,
upper_relstr_subset(sK29,boole_POSet(sK28)),
inference(cnf_transformation,[],[f467]) ).
tcf(c_276,negated_conjecture,
proper_element(sK29,powerset(the_carrier(boole_POSet(sK28)))),
inference(cnf_transformation,[],[f466]) ).
tcf(c_277,negated_conjecture,
element(sK29,powerset(the_carrier(boole_POSet(sK28)))),
inference(cnf_transformation,[],[f465]) ).
tcf(c_282,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f475]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f476]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| empty_carrier(X1)
| ~ antisymmetric_relstr(X1)
| ~ transitive_relstr(X1)
| ~ lower_bounded_relstr(X1)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ upper_relstr_subset(X0,X1)
| ~ filtered_subset(X0,X1)
| ~ in(bottom_of_relstr(X1),X0)
| ~ proper_element(X0,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f478]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_283]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ~ antisymmetric_relstr(X1)
| ~ transitive_relstr(X1)
| ~ lower_bounded_relstr(X1)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ upper_relstr_subset(X0,X1)
| ~ filtered_subset(X0,X1)
| ~ in(bottom_of_relstr(X1),X0)
| ~ proper_element(X0,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_286,c_407]) ).
tcf(c_3116,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0)
| ~ upper_relstr_subset(X1,X0)
| ~ in(bottom_of_relstr(X0),X1)
| ~ proper_element(X1,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X1 != sK29 )
| ( boole_POSet(sK28) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_274,c_1070]) ).
tcf(c_3117,plain,
( empty_carrier(boole_POSet(sK28))
| ~ antisymmetric_relstr(boole_POSet(sK28))
| ~ transitive_relstr(boole_POSet(sK28))
| ~ lower_bounded_relstr(boole_POSet(sK28))
| ~ reflexive_relstr(boole_POSet(sK28))
| ~ rel_str(boole_POSet(sK28))
| ~ upper_relstr_subset(sK29,boole_POSet(sK28))
| ~ in(bottom_of_relstr(boole_POSet(sK28)),sK29)
| ~ proper_element(sK29,powerset(the_carrier(boole_POSet(sK28))))
| ~ element(sK29,powerset(the_carrier(boole_POSet(sK28)))) ),
inference(unflattening,[status(thm)],[c_3116]) ).
tcf(c_3118,plain,
( empty_carrier(boole_POSet(sK28))
| ~ antisymmetric_relstr(boole_POSet(sK28))
| ~ transitive_relstr(boole_POSet(sK28))
| ~ lower_bounded_relstr(boole_POSet(sK28))
| ~ reflexive_relstr(boole_POSet(sK28))
| ~ rel_str(boole_POSet(sK28))
| ~ in(bottom_of_relstr(boole_POSet(sK28)),sK29) ),
inference(global_subsumption_just,[status(thm)],[c_3117,c_275,c_277,c_276,c_3117]) ).
tcf(c_13908,negated_conjecture,
empty(sK30),
inference(demodulation,[status(thm)],[c_272]) ).
tcf(c_13909,negated_conjecture,
in(sK30,sK29),
inference(demodulation,[status(thm)],[c_271]) ).
tcf(c_16869,plain,
empty_set = sK30,
inference(superposition,[status(thm)],[c_13908,c_282]) ).
tcf(c_16874,plain,
in(empty_set,sK29),
inference(demodulation,[status(thm)],[c_13909,c_16869]) ).
fof(f190,definition,
! [X0] :
( ~ sP1(X0)
| ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f191,plain,
! [X0] :
( empty(X0)
| sP1(X0) ),
inference(definition_folding,[],[f160,f190]) ).
fof(f198,plain,
! [X0] :
( ~ sP1(X0)
| ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(nnf_transformation,[],[f190]) ).
fof(f312,plain,
! [X0] :
( ~ sP1(X0)
| lower_bounded_relstr(boole_POSet(X0)) ),
inference(cnf_transformation,[],[f198]) ).
fof(f313,plain,
! [X0] :
( ~ sP1(X0)
| antisymmetric_relstr(boole_POSet(X0)) ),
inference(cnf_transformation,[],[f198]) ).
fof(f314,plain,
! [X0] :
( ~ sP1(X0)
| transitive_relstr(boole_POSet(X0)) ),
inference(cnf_transformation,[],[f198]) ).
fof(f315,plain,
! [X0] :
( ~ sP1(X0)
| reflexive_relstr(boole_POSet(X0)) ),
inference(cnf_transformation,[],[f198]) ).
fof(f318,plain,
! [X0] :
( ~ sP1(X0)
| ~ empty_carrier(boole_POSet(X0)) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_112,plain,
! [X0: $i] :
( ~ sP1(X0)
| ~ empty_carrier(boole_POSet(X0)) ),
inference(cnf_transformation,[],[f318]) ).
tcf(c_115,plain,
! [X0: $i] :
( reflexive_relstr(boole_POSet(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f315]) ).
tcf(c_116,plain,
! [X0: $i] :
( transitive_relstr(boole_POSet(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_117,plain,
! [X0: $i] :
( antisymmetric_relstr(boole_POSet(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_118,plain,
! [X0: $i] :
( lower_bounded_relstr(boole_POSet(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_374,plain,
! [X0: $i] : lower_bounded_relstr(boole_POSet(X0)),
inference(global_subsumption_just,[status(thm)],[c_118,c_150]) ).
tcf(c_376,plain,
! [X0: $i] : antisymmetric_relstr(boole_POSet(X0)),
inference(global_subsumption_just,[status(thm)],[c_117,c_149]) ).
tcf(c_378,plain,
! [X0: $i] : transitive_relstr(boole_POSet(X0)),
inference(global_subsumption_just,[status(thm)],[c_116,c_148]) ).
tcf(c_380,plain,
! [X0: $i] : reflexive_relstr(boole_POSet(X0)),
inference(global_subsumption_just,[status(thm)],[c_115,c_147]) ).
tcf(c_384,plain,
! [X0: $i] : ~ empty_carrier(boole_POSet(X0)),
inference(global_subsumption_just,[status(thm)],[c_112,c_145]) ).
tcf(c_3134,plain,
~ in(bottom_of_relstr(boole_POSet(sK28)),sK29),
inference(forward_subsumption_resolution,[status(thm)],[c_3118,c_384,c_376,c_378,c_374,c_380,c_86]) ).
tcf(c_9659,plain,
~ in(empty_set,sK29),
inference(demodulation,[status(thm)],[c_3134,c_268]) ).
tcf(c_13903,plain,
~ in(empty_set,sK29),
inference(demodulation,[status(thm)],[c_9659]) ).
tcf(c_16876,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16874,c_13903]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU387+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 % Computer : n003.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.40 % DateTime : Thu Sep 24 13:58:06 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46
% 0.14/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.46
% 0.14/0.46 % Detected problem language: tptp
% 0.14/0.48 % Proving...
% 1.38/1.34 % SZS status Started for theBenchmark.p
% 1.38/1.34 % SZS status Theorem for theBenchmark.p
% 1.38/1.34
% 1.38/1.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.38/1.34
% 1.38/1.34 % ------ iProver source info
% 1.38/1.34
% 1.38/1.34 % git: date: 2026-07-19 20:42:38 +0200
% 1.38/1.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.38/1.34 % git: non_committed_changes: false
% 1.38/1.34
% 1.38/1.34 % ------ Parsing...
% 1.38/1.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.38/1.34
% 1.38/1.34 % ------ Preprocessing... sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 4 sf_s rm: 18 0s sf_e pe_s pe_e %
% 1.38/1.34
% 1.38/1.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.38/1.34
% 1.38/1.34 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.38/1.34 % ------ Proving...
% 1.38/1.34 % ------ Problem Properties
% 1.38/1.34
% 1.38/1.34 %
% 1.38/1.34 % clauses 207
% 1.38/1.34 % conjectures 6
% 1.38/1.34 % EPR 34
% 1.38/1.34 % Horn 184
% 1.38/1.34 % unary 98
% 1.38/1.34 % binary 99
% 1.38/1.34 % lits 326
% 1.38/1.34 % lits eq 57
% 1.38/1.34 % fd_pure 0
% 1.38/1.34 % fd_pseudo 0
% 1.38/1.34 % fd_cond 1
% 1.38/1.34 % fd_pseudo_cond 3
% 1.38/1.34 % AC symbols 0
% 1.38/1.34
% 1.38/1.34 % ------ Schedule dynamic 5 is on
% 1.38/1.34
% 1.38/1.34 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.38/1.34
% 1.38/1.34
% 1.38/1.34 % ------
% 1.38/1.34 % Current options:
% 1.38/1.34 % ------
% 1.38/1.34
% 1.38/1.34
% 1.38/1.34 %
% 1.38/1.34
% 1.38/1.34 % ------ Proving...
% 1.38/1.34 %
% 1.38/1.34
% 1.38/1.34 % SZS status Theorem for theBenchmark.p
% 1.38/1.34
% 1.38/1.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.38/1.35
% 1.38/1.35
%------------------------------------------------------------------------------