TSTP Solution File: SEU349+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU349+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:06:20 EDT 2023
% Result : Theorem 125.91s 17.78s
% Output : CNFRefutation 125.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 26
% Syntax : Number of formulae : 218 ( 15 unt; 0 def)
% Number of atoms : 1080 ( 92 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1447 ( 585 ~; 668 |; 140 &)
% ( 18 <=>; 34 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 361 ( 1 sgn; 204 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f3,axiom,
! [X0] :
( latt_str(X0)
=> ( ( lattice(X0)
& ~ empty_carrier(X0) )
=> ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(f6,axiom,
! [X0] :
( ( latt_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( latt_element_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X2)
=> below(X0,X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_lattice3) ).
fof(f7,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
fof(f8,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(f10,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
fof(f16,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(f17,axiom,
! [X0,X1] :
( ( element(X1,the_carrier(X0))
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
fof(f28,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f44,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice3) ).
fof(f46,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f56,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f57,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& latt_str(X0)
& join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(f58,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& rel_str(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( related_reflexive(X0,X1,X2)
<=> related(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
fof(f64,conjecture,
! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice3) ).
fof(f65,negated_conjecture,
~ ! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
inference(negated_conjecture,[],[f64]) ).
fof(f71,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
fof(f78,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f79,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f78]) ).
fof(f81,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f82,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f81]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( latt_element_smaller(X0,X1,X2)
<=> ! [X3] :
( below(X0,X3,X1)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( latt_element_smaller(X0,X1,X2)
<=> ! [X3] :
( below(X0,X3,X1)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f88,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f89]) ).
fof(f93,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f94,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f93]) ).
fof(f98,plain,
! [X0] :
( ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f99,plain,
! [X0] :
( ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f101,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f100]) ).
fof(f109,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f118,plain,
! [X0] :
( ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f119,plain,
! [X0] :
( ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f118]) ).
fof(f122,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X1 = X3
& X0 = X2 )
| rel_str_of(X0,X1) != rel_str_of(X2,X3) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ( related_reflexive(X0,X1,X2)
<=> related(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ( related_reflexive(X0,X1,X2)
<=> related(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f130]) ).
fof(f139,plain,
? [X0,X1] :
( ? [X2] :
( ( latt_element_smaller(X1,X2,X0)
<~> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
& element(X2,the_carrier(X1)) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f140,plain,
? [X0,X1] :
( ? [X2] :
( ( latt_element_smaller(X1,X2,X0)
<~> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
& element(X2,the_carrier(X1)) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) ),
inference(flattening,[],[f139]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f147]) ).
fof(f150,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ below(X0,X3,X1)
& in(X3,X2)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( below(X0,X3,X1)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0)) )
| ~ latt_element_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f86]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ below(X0,X3,X1)
& in(X3,X2)
& element(X3,the_carrier(X0)) ) )
& ( ! [X4] :
( below(X0,X4,X1)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0)) )
| ~ latt_element_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(rectify,[],[f150]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ below(X0,X3,X1)
& in(X3,X2)
& element(X3,the_carrier(X0)) )
=> ( ~ below(X0,sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X2)
& element(sK0(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f153,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_element_smaller(X0,X1,X2)
| ( ~ below(X0,sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X2)
& element(sK0(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X4] :
( below(X0,X4,X1)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0)) )
| ~ latt_element_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f151,f152]) ).
fof(f154,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f94]) ).
fof(f155,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X4,X2)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(rectify,[],[f154]) ).
fof(f156,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ related(X0,X3,X2)
& in(X3,X1)
& element(X3,the_carrier(X0)) )
=> ( ~ related(X0,sK1(X0,X1,X2),X2)
& in(sK1(X0,X1,X2),X1)
& element(sK1(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ( ~ related(X0,sK1(X0,X1,X2),X2)
& in(sK1(X0,X1,X2),X1)
& element(sK1(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X4,X2)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f155,f156]) ).
fof(f190,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ( ( below_refl(X0,X1,X2)
| ~ below(X0,X1,X2) )
& ( below(X0,X1,X2)
| ~ below_refl(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f129]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ( ( related_reflexive(X0,X1,X2)
| ~ related(X0,X1,X2) )
& ( related(X0,X1,X2)
| ~ related_reflexive(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f131]) ).
fof(f193,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0) )
& ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| latt_element_smaller(X1,X2,X0) )
& element(X2,the_carrier(X1)) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) ),
inference(nnf_transformation,[],[f140]) ).
fof(f194,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0) )
& ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| latt_element_smaller(X1,X2,X0) )
& element(X2,the_carrier(X1)) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) ),
inference(flattening,[],[f193]) ).
fof(f195,plain,
( ? [X0,X1] :
( ? [X2] :
( ( ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0) )
& ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| latt_element_smaller(X1,X2,X0) )
& element(X2,the_carrier(X1)) )
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ( ? [X2] :
( ( ~ relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,X2))
| ~ latt_element_smaller(sK19,X2,sK18) )
& ( relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,X2))
| latt_element_smaller(sK19,X2,sK18) )
& element(X2,the_carrier(sK19)) )
& latt_str(sK19)
& lattice(sK19)
& ~ empty_carrier(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f196,plain,
( ? [X2] :
( ( ~ relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,X2))
| ~ latt_element_smaller(sK19,X2,sK18) )
& ( relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,X2))
| latt_element_smaller(sK19,X2,sK18) )
& element(X2,the_carrier(sK19)) )
=> ( ( ~ relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| ~ latt_element_smaller(sK19,sK20,sK18) )
& ( relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| latt_element_smaller(sK19,sK20,sK18) )
& element(sK20,the_carrier(sK19)) ) ),
introduced(choice_axiom,[]) ).
fof(f197,plain,
( ( ~ relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| ~ latt_element_smaller(sK19,sK20,sK18) )
& ( relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| latt_element_smaller(sK19,sK20,sK18) )
& element(sK20,the_carrier(sK19))
& latt_str(sK19)
& lattice(sK19)
& ~ empty_carrier(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f194,f196,f195]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( below_refl(X0,X1,X2)
| ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
& ( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ below_refl(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f199,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f204,plain,
! [X0] :
( meet_commutative(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f206,plain,
! [X0] :
( meet_absorbing(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f207,plain,
! [X0] :
( join_absorbing(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f210,plain,
! [X2,X0,X1,X4] :
( below(X0,X4,X1)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0))
| ~ latt_element_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f211,plain,
! [X2,X0,X1] :
( latt_element_smaller(X0,X1,X2)
| element(sK0(X0,X1,X2),the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f212,plain,
! [X2,X0,X1] :
( latt_element_smaller(X0,X1,X2)
| in(sK0(X0,X1,X2),X2)
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f213,plain,
! [X2,X0,X1] :
( latt_element_smaller(X0,X1,X2)
| ~ below(X0,sK0(X0,X1,X2),X1)
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f214,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f215,plain,
! [X0,X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f217,plain,
! [X2,X0,X1,X4] :
( related(X0,X4,X2)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f218,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X0,X1,X2)
| element(sK1(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f219,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X0,X1,X2)
| in(sK1(X0,X1,X2),X1)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f220,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X0,X1,X2)
| ~ related(X0,sK1(X0,X1,X2),X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f232,plain,
! [X0] :
( rel_str(poset_of_lattice(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f233,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f241,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f263,plain,
! [X0] :
( ~ empty_carrier(poset_of_lattice(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f264,plain,
! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f265,plain,
! [X0] :
( reflexive_relstr(poset_of_lattice(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f269,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f290,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f292,plain,
! [X2,X0,X1] :
( below(X0,X1,X2)
| ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f293,plain,
! [X2,X0,X1] :
( below_refl(X0,X1,X2)
| ~ below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f294,plain,
! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ related_reflexive(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f295,plain,
! [X2,X0,X1] :
( related_reflexive(X0,X1,X2)
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f301,plain,
~ empty_carrier(sK19),
inference(cnf_transformation,[],[f197]) ).
fof(f302,plain,
lattice(sK19),
inference(cnf_transformation,[],[f197]) ).
fof(f303,plain,
latt_str(sK19),
inference(cnf_transformation,[],[f197]) ).
fof(f304,plain,
element(sK20,the_carrier(sK19)),
inference(cnf_transformation,[],[f197]) ).
fof(f305,plain,
( relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| latt_element_smaller(sK19,sK20,sK18) ),
inference(cnf_transformation,[],[f197]) ).
fof(f306,plain,
( ~ relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| ~ latt_element_smaller(sK19,sK20,sK18) ),
inference(cnf_transformation,[],[f197]) ).
fof(f312,plain,
! [X2,X0,X1] :
( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f313,plain,
! [X2,X0,X1] :
( below_refl(X0,X1,X2)
| ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_49,plain,
( ~ strict_rel_str(X0)
| ~ rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_51,plain,
( ~ lattice(X0)
| ~ latt_str(X0)
| join_absorbing(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_52,plain,
( ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| meet_absorbing(X0) ),
inference(cnf_transformation,[],[f206]) ).
cnf(c_54,plain,
( ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| meet_commutative(X0) ),
inference(cnf_transformation,[],[f204]) ).
cnf(c_58,plain,
( ~ below(X0,sK0(X0,X1,X2),X1)
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| latt_element_smaller(X0,X1,X2)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f213]) ).
cnf(c_59,plain,
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| in(sK0(X1,X0,X2),X2)
| latt_element_smaller(X1,X0,X2)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f212]) ).
cnf(c_60,plain,
( ~ element(X0,the_carrier(X1))
| ~ latt_str(X1)
| element(sK0(X1,X0,X2),the_carrier(X1))
| latt_element_smaller(X1,X0,X2)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_61,plain,
( ~ latt_element_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X3,the_carrier(X0))
| ~ in(X3,X2)
| ~ latt_str(X0)
| below(X0,X3,X1)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f210]) ).
cnf(c_62,plain,
( ~ lattice(X0)
| ~ latt_str(X0)
| rel_str_of(the_carrier(X0),k2_lattice3(X0)) = poset_of_lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f214]) ).
cnf(c_63,plain,
( ~ element(X0,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| cast_to_el_of_LattPOSet(X1,X0) = X0
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f215]) ).
cnf(c_65,plain,
( ~ related(X0,sK1(X0,X1,X2),X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| relstr_set_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f220]) ).
cnf(c_66,plain,
( ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| in(sK1(X1,X2,X0),X2)
| relstr_set_smaller(X1,X2,X0) ),
inference(cnf_transformation,[],[f219]) ).
cnf(c_67,plain,
( ~ element(X0,the_carrier(X1))
| ~ rel_str(X1)
| element(sK1(X1,X2,X0),the_carrier(X1))
| relstr_set_smaller(X1,X2,X0) ),
inference(cnf_transformation,[],[f218]) ).
cnf(c_68,plain,
( ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| ~ rel_str(X0)
| related(X0,X3,X2) ),
inference(cnf_transformation,[],[f217]) ).
cnf(c_76,plain,
( ~ lattice(X0)
| ~ latt_str(X0)
| rel_str(poset_of_lattice(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f232]) ).
cnf(c_81,plain,
( ~ element(X0,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| element(cast_to_el_of_LattPOSet(X1,X0),the_carrier(poset_of_lattice(X1)))
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_89,plain,
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f241]) ).
cnf(c_113,plain,
( ~ lattice(X0)
| ~ latt_str(X0)
| reflexive_relstr(poset_of_lattice(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f265]) ).
cnf(c_114,plain,
( ~ lattice(X0)
| ~ latt_str(X0)
| strict_rel_str(poset_of_lattice(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f264]) ).
cnf(c_115,plain,
( ~ empty_carrier(poset_of_lattice(X0))
| ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f263]) ).
cnf(c_118,plain,
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f269]) ).
cnf(c_139,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f290]) ).
cnf(c_140,plain,
( ~ below(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_absorbing(X0)
| ~ latt_str(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| below_refl(X0,X1,X2)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f293]) ).
cnf(c_141,plain,
( ~ below_refl(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_absorbing(X0)
| ~ latt_str(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| below(X0,X1,X2)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f292]) ).
cnf(c_142,plain,
( ~ related(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| related_reflexive(X0,X1,X2)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f295]) ).
cnf(c_143,plain,
( ~ related_reflexive(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| related(X0,X1,X2)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f294]) ).
cnf(c_149,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| ~ latt_element_smaller(sK19,sK20,sK18) ),
inference(cnf_transformation,[],[f306]) ).
cnf(c_150,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| latt_element_smaller(sK19,sK20,sK18) ),
inference(cnf_transformation,[],[f305]) ).
cnf(c_151,negated_conjecture,
element(sK20,the_carrier(sK19)),
inference(cnf_transformation,[],[f304]) ).
cnf(c_152,negated_conjecture,
latt_str(sK19),
inference(cnf_transformation,[],[f303]) ).
cnf(c_153,negated_conjecture,
lattice(sK19),
inference(cnf_transformation,[],[f302]) ).
cnf(c_154,negated_conjecture,
~ empty_carrier(sK19),
inference(cnf_transformation,[],[f301]) ).
cnf(c_160,plain,
( ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ lattice(X0)
| ~ latt_str(X0)
| below_refl(X0,X1,X2)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f313]) ).
cnf(c_161,plain,
( ~ below_refl(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ lattice(X0)
| ~ latt_str(X0)
| related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f312]) ).
cnf(c_194,plain,
( ~ lattice(sK19)
| ~ latt_str(sK19)
| empty_carrier(sK19)
| meet_commutative(sK19) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_196,plain,
( ~ lattice(sK19)
| ~ latt_str(sK19)
| empty_carrier(sK19)
| meet_absorbing(sK19) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_197,plain,
( ~ lattice(sK19)
| ~ latt_str(sK19)
| join_absorbing(sK19)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_199,plain,
( ~ lattice(sK19)
| ~ latt_str(sK19)
| strict_rel_str(poset_of_lattice(sK19))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_114]) ).
cnf(c_200,plain,
( ~ lattice(sK19)
| ~ latt_str(sK19)
| reflexive_relstr(poset_of_lattice(sK19))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_113]) ).
cnf(c_204,plain,
( ~ lattice(sK19)
| ~ latt_str(sK19)
| rel_str(poset_of_lattice(sK19))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_208,plain,
( ~ empty_carrier(poset_of_lattice(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_115]) ).
cnf(c_217,plain,
( ~ lattice(sK19)
| ~ latt_str(sK19)
| rel_str_of(the_carrier(sK19),k2_lattice3(sK19)) = poset_of_lattice(sK19)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_309,plain,
X0 = X0,
theory(equality) ).
cnf(c_311,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_312,plain,
( X0 != X1
| the_carrier(X0) = the_carrier(X1) ),
theory(equality) ).
cnf(c_316,plain,
( X0 != X1
| ~ in(X1,X2)
| in(X0,X2) ),
theory(equality) ).
cnf(c_322,plain,
( X0 != X1
| X2 != X3
| ~ element(X1,X3)
| element(X0,X2) ),
theory(equality) ).
cnf(c_326,plain,
( X0 != X1
| ~ related(X2,X1,X3)
| related(X2,X0,X3) ),
theory(equality) ).
cnf(c_342,plain,
( sK19 != sK19
| the_carrier(sK19) = the_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_312]) ).
cnf(c_347,plain,
sK19 = sK19,
inference(instantiation,[status(thm)],[c_309]) ).
cnf(c_351,plain,
( ~ rel_str(poset_of_lattice(X0))
| relation_of2_as_subset(the_InternalRel(poset_of_lattice(X0)),the_carrier(poset_of_lattice(X0)),the_carrier(poset_of_lattice(X0))) ),
inference(instantiation,[status(thm)],[c_89]) ).
cnf(c_352,plain,
( ~ rel_str(poset_of_lattice(sK19))
| relation_of2_as_subset(the_InternalRel(poset_of_lattice(sK19)),the_carrier(poset_of_lattice(sK19)),the_carrier(poset_of_lattice(sK19))) ),
inference(instantiation,[status(thm)],[c_351]) ).
cnf(c_354,plain,
( ~ strict_rel_str(poset_of_lattice(X0))
| ~ rel_str(poset_of_lattice(X0))
| rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0))) = poset_of_lattice(X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_355,plain,
( ~ strict_rel_str(poset_of_lattice(sK19))
| ~ rel_str(poset_of_lattice(sK19))
| rel_str_of(the_carrier(poset_of_lattice(sK19)),the_InternalRel(poset_of_lattice(sK19))) = poset_of_lattice(sK19) ),
inference(instantiation,[status(thm)],[c_354]) ).
cnf(c_380,plain,
( ~ element(sK20,the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_408,plain,
( ~ element(sK20,the_carrier(sK19))
| ~ latt_str(sK19)
| in(sK0(sK19,sK20,X0),X0)
| latt_element_smaller(sK19,sK20,X0)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_412,plain,
( ~ element(sK20,the_carrier(sK19))
| ~ latt_str(sK19)
| element(sK0(sK19,sK20,X0),the_carrier(sK19))
| latt_element_smaller(sK19,sK20,X0)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_521,plain,
( ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| ~ rel_str(poset_of_lattice(sK19))
| element(sK1(poset_of_lattice(sK19),X0,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
| relstr_set_smaller(poset_of_lattice(sK19),X0,cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_522,plain,
( ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| ~ rel_str(poset_of_lattice(sK19))
| in(sK1(poset_of_lattice(sK19),X0,cast_to_el_of_LattPOSet(sK19,sK20)),X0)
| relstr_set_smaller(poset_of_lattice(sK19),X0,cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_552,plain,
( ~ element(sK20,the_carrier(sK19))
| ~ latt_str(sK19)
| element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| latt_element_smaller(sK19,sK20,sK18)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_412]) ).
cnf(c_557,plain,
( ~ element(sK20,the_carrier(sK19))
| ~ latt_str(sK19)
| in(sK0(sK19,sK20,sK18),sK18)
| latt_element_smaller(sK19,sK20,sK18)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_408]) ).
cnf(c_674,plain,
( ~ relation_of2_as_subset(the_InternalRel(poset_of_lattice(X0)),the_carrier(poset_of_lattice(X0)),the_carrier(poset_of_lattice(X0)))
| relation_of2(the_InternalRel(poset_of_lattice(X0)),the_carrier(poset_of_lattice(X0)),the_carrier(poset_of_lattice(X0))) ),
inference(instantiation,[status(thm)],[c_139]) ).
cnf(c_677,plain,
( ~ relation_of2_as_subset(the_InternalRel(poset_of_lattice(sK19)),the_carrier(poset_of_lattice(sK19)),the_carrier(poset_of_lattice(sK19)))
| relation_of2(the_InternalRel(poset_of_lattice(sK19)),the_carrier(poset_of_lattice(sK19)),the_carrier(poset_of_lattice(sK19))) ),
inference(instantiation,[status(thm)],[c_674]) ).
cnf(c_1468,plain,
( ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| ~ rel_str(poset_of_lattice(sK19))
| element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
| relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_521]) ).
cnf(c_1496,plain,
( ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| ~ rel_str(poset_of_lattice(sK19))
| in(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK18)
| relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_522]) ).
cnf(c_1539,plain,
( the_carrier(sK19) != X0
| X1 != X0
| the_carrier(sK19) = X1 ),
inference(instantiation,[status(thm)],[c_311]) ).
cnf(c_1861,plain,
( ~ strict_rel_str(poset_of_lattice(X0))
| ~ lattice(X0)
| ~ latt_str(X0)
| rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0))) = poset_of_lattice(X0)
| empty_carrier(X0) ),
inference(superposition,[status(thm)],[c_76,c_49]) ).
cnf(c_1863,plain,
( ~ lattice(X0)
| ~ latt_str(X0)
| rel_str_of(the_carrier(poset_of_lattice(X0)),the_InternalRel(poset_of_lattice(X0))) = poset_of_lattice(X0)
| empty_carrier(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1861,c_114,c_1861]) ).
cnf(c_2141,plain,
( ~ lattice(sK19)
| rel_str_of(the_carrier(poset_of_lattice(sK19)),the_InternalRel(poset_of_lattice(sK19))) = poset_of_lattice(sK19)
| empty_carrier(sK19) ),
inference(superposition,[status(thm)],[c_152,c_1863]) ).
cnf(c_2142,plain,
rel_str_of(the_carrier(poset_of_lattice(sK19)),the_InternalRel(poset_of_lattice(sK19))) = poset_of_lattice(sK19),
inference(global_subsumption_just,[status(thm)],[c_2141,c_153,c_152,c_154,c_199,c_204,c_355]) ).
cnf(c_2852,plain,
( ~ element(sK0(sK19,sK20,X0),the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| element(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,X0)),the_carrier(poset_of_lattice(sK19)))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_2853,plain,
( ~ element(sK0(sK19,sK20,X0),the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,X0)) = sK0(sK19,sK20,X0)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_2890,plain,
( X0 != sK0(sK19,sK20,X1)
| ~ in(sK0(sK19,sK20,X1),X1)
| in(X0,X1) ),
inference(instantiation,[status(thm)],[c_316]) ).
cnf(c_4191,plain,
( X0 != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| X1 != the_carrier(poset_of_lattice(sK19))
| ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
| element(X0,X1) ),
inference(instantiation,[status(thm)],[c_322]) ).
cnf(c_5060,plain,
( the_carrier(sK19) != the_carrier(sK19)
| X0 != the_carrier(sK19)
| the_carrier(sK19) = X0 ),
inference(instantiation,[status(thm)],[c_1539]) ).
cnf(c_8832,plain,
( ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)) = sK0(sK19,sK20,sK18)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_2853]) ).
cnf(c_8835,plain,
( ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| element(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),the_carrier(poset_of_lattice(sK19)))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_2852]) ).
cnf(c_8859,plain,
( X0 != sK0(sK19,sK20,sK18)
| ~ in(sK0(sK19,sK20,sK18),sK18)
| in(X0,sK18) ),
inference(instantiation,[status(thm)],[c_2890]) ).
cnf(c_9524,plain,
( the_carrier(X0) != the_carrier(sK19)
| the_carrier(sK19) != the_carrier(sK19)
| the_carrier(sK19) = the_carrier(X0) ),
inference(instantiation,[status(thm)],[c_5060]) ).
cnf(c_11683,plain,
( ~ lattice(sK19)
| rel_str_of(the_carrier(sK19),k2_lattice3(sK19)) = poset_of_lattice(sK19)
| empty_carrier(sK19) ),
inference(superposition,[status(thm)],[c_152,c_62]) ).
cnf(c_11684,plain,
rel_str_of(the_carrier(sK19),k2_lattice3(sK19)) = poset_of_lattice(sK19),
inference(global_subsumption_just,[status(thm)],[c_11683,c_153,c_152,c_154,c_217]) ).
cnf(c_13460,plain,
( rel_str_of(X0,X1) != poset_of_lattice(sK19)
| ~ relation_of2(X1,X0,X0)
| the_carrier(sK19) = X0 ),
inference(superposition,[status(thm)],[c_11684,c_118]) ).
cnf(c_13606,plain,
( ~ related(poset_of_lattice(sK19),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| ~ rel_str(poset_of_lattice(sK19))
| relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_13701,plain,
( ~ relation_of2(the_InternalRel(poset_of_lattice(sK19)),the_carrier(poset_of_lattice(sK19)),the_carrier(poset_of_lattice(sK19)))
| the_carrier(poset_of_lattice(sK19)) = the_carrier(sK19) ),
inference(superposition,[status(thm)],[c_2142,c_13460]) ).
cnf(c_14321,plain,
( cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)) != sK0(sK19,sK20,sK18)
| ~ in(sK0(sK19,sK20,sK18),sK18)
| in(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),sK18) ),
inference(instantiation,[status(thm)],[c_8859]) ).
cnf(c_14617,plain,
( the_carrier(poset_of_lattice(sK19)) != the_carrier(sK19)
| the_carrier(sK19) != the_carrier(sK19)
| the_carrier(sK19) = the_carrier(poset_of_lattice(sK19)) ),
inference(instantiation,[status(thm)],[c_9524]) ).
cnf(c_14618,plain,
( the_carrier(sK19) != the_carrier(poset_of_lattice(sK19))
| X0 != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
| element(X0,the_carrier(sK19)) ),
inference(instantiation,[status(thm)],[c_4191]) ).
cnf(c_14981,plain,
sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) = sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),
inference(instantiation,[status(thm)],[c_309]) ).
cnf(c_15743,plain,
( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(X0))
| ~ lattice(X0)
| ~ latt_str(X0)
| cast_to_el_of_LattPOSet(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) = sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| empty_carrier(X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_15746,plain,
( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) = sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_15743]) ).
cnf(c_17496,plain,
( ~ below_refl(X0,sK0(X0,X1,X2),X1)
| ~ element(sK0(X0,X1,X2),the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_absorbing(X0)
| ~ latt_str(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| below(X0,sK0(X0,X1,X2),X1)
| empty_carrier(X0) ),
inference(instantiation,[status(thm)],[c_141]) ).
cnf(c_21018,plain,
( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| the_carrier(sK19) != the_carrier(poset_of_lattice(sK19))
| ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(poset_of_lattice(sK19)))
| element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19)) ),
inference(instantiation,[status(thm)],[c_14618]) ).
cnf(c_22896,plain,
( ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ below_refl(sK19,sK0(sK19,sK20,sK18),sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ meet_absorbing(sK19)
| ~ meet_commutative(sK19)
| below(sK19,sK0(sK19,sK20,sK18),sK20)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_17496]) ).
cnf(c_28551,plain,
( ~ below(sK19,sK0(sK19,sK20,sK18),sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ latt_str(sK19)
| latt_element_smaller(sK19,sK20,sK18)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_30638,plain,
( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| below_refl(sK19,sK0(sK19,sK20,sK18),sK20)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_160]) ).
cnf(c_37921,plain,
( ~ element(X0,the_carrier(sK19))
| ~ below_refl(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),cast_to_el_of_LattPOSet(sK19,sK20))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_161]) ).
cnf(c_39859,plain,
( ~ below(sK19,X0,sK20)
| ~ element(X0,the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ meet_absorbing(sK19)
| ~ meet_commutative(sK19)
| below_refl(sK19,X0,sK20)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_44475,plain,
( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(X0))
| ~ in(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK18)
| ~ latt_element_smaller(X0,X1,sK18)
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| below(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),X1)
| empty_carrier(X0) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_53710,plain,
( ~ below(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK20)
| ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ meet_absorbing(sK19)
| ~ meet_commutative(sK19)
| below_refl(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK20)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_39859]) ).
cnf(c_53711,plain,
( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19))
| ~ in(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK18)
| ~ latt_element_smaller(sK19,sK20,sK18)
| ~ element(sK20,the_carrier(sK19))
| ~ latt_str(sK19)
| below(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK20)
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_44475]) ).
cnf(c_54739,plain,
( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19))
| ~ below_refl(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),cast_to_el_of_LattPOSet(sK19,sK20))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_37921]) ).
cnf(c_55523,plain,
( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != X0
| X1 != X0
| sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) = X1 ),
inference(instantiation,[status(thm)],[c_311]) ).
cnf(c_72688,plain,
( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(X0))
| ~ lattice(X0)
| ~ latt_str(X0)
| element(cast_to_el_of_LattPOSet(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),the_carrier(poset_of_lattice(X0)))
| empty_carrier(X0) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_72689,plain,
( ~ element(sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| element(cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),the_carrier(poset_of_lattice(sK19)))
| empty_carrier(sK19) ),
inference(instantiation,[status(thm)],[c_72688]) ).
cnf(c_73995,plain,
( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| X0 != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) = X0 ),
inference(instantiation,[status(thm)],[c_55523]) ).
cnf(c_80095,plain,
( cast_to_el_of_LattPOSet(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) = cast_to_el_of_LattPOSet(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
inference(instantiation,[status(thm)],[c_73995]) ).
cnf(c_80096,plain,
( cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) = cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))) ),
inference(instantiation,[status(thm)],[c_80095]) ).
cnf(c_102970,plain,
( ~ related(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(cast_to_el_of_LattPOSet(X0,X2),the_carrier(poset_of_lattice(X0)))
| ~ rel_str(poset_of_lattice(X0))
| ~ reflexive_relstr(poset_of_lattice(X0))
| related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| empty_carrier(poset_of_lattice(X0)) ),
inference(instantiation,[status(thm)],[c_142]) ).
cnf(c_104247,plain,
( X0 != X1
| ~ related(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3))
| related(poset_of_lattice(X2),X0,cast_to_el_of_LattPOSet(X2,X3)) ),
inference(instantiation,[status(thm)],[c_326]) ).
cnf(c_104293,plain,
( ~ related_reflexive(poset_of_lattice(X0),X1,X2)
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ element(X2,the_carrier(poset_of_lattice(X0)))
| ~ rel_str(poset_of_lattice(X0))
| ~ reflexive_relstr(poset_of_lattice(X0))
| related(poset_of_lattice(X0),X1,X2)
| empty_carrier(poset_of_lattice(X0)) ),
inference(instantiation,[status(thm)],[c_143]) ).
cnf(c_110115,plain,
( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != X0
| ~ related(poset_of_lattice(sK19),X0,cast_to_el_of_LattPOSet(sK19,sK20))
| related(poset_of_lattice(sK19),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_104247]) ).
cnf(c_135706,plain,
( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != cast_to_el_of_LattPOSet(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)))
| ~ related(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),cast_to_el_of_LattPOSet(sK19,sK20))
| related(poset_of_lattice(sK19),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_110115]) ).
cnf(c_135708,plain,
( sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) != cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)))
| ~ related(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),cast_to_el_of_LattPOSet(sK19,sK20))
| related(poset_of_lattice(sK19),sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)),cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_135706]) ).
cnf(c_137385,plain,
( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(cast_to_el_of_LattPOSet(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),the_carrier(poset_of_lattice(sK19)))
| ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| ~ rel_str(poset_of_lattice(sK19))
| ~ reflexive_relstr(poset_of_lattice(sK19))
| related(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(X0,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),cast_to_el_of_LattPOSet(sK19,sK20))
| empty_carrier(poset_of_lattice(sK19)) ),
inference(instantiation,[status(thm)],[c_104293]) ).
cnf(c_137386,plain,
( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),the_carrier(poset_of_lattice(sK19)))
| ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| ~ rel_str(poset_of_lattice(sK19))
| ~ reflexive_relstr(poset_of_lattice(sK19))
| related(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))),cast_to_el_of_LattPOSet(sK19,sK20))
| empty_carrier(poset_of_lattice(sK19)) ),
inference(instantiation,[status(thm)],[c_137385]) ).
cnf(c_138553,negated_conjecture,
~ latt_element_smaller(sK19,sK20,sK18),
inference(global_subsumption_just,[status(thm)],[c_149,c_153,c_152,c_154,c_151,c_194,c_196,c_197,c_200,c_204,c_208,c_149,c_342,c_347,c_352,c_380,c_677,c_1468,c_1496,c_13606,c_13701,c_14617,c_14981,c_15746,c_21018,c_53710,c_53711,c_54739,c_72689,c_80096,c_135708,c_137386]) ).
cnf(c_159227,plain,
( ~ related(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),the_carrier(poset_of_lattice(sK19)))
| ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| ~ rel_str(poset_of_lattice(sK19))
| ~ reflexive_relstr(poset_of_lattice(sK19))
| related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),cast_to_el_of_LattPOSet(sK19,sK20))
| empty_carrier(poset_of_lattice(sK19)) ),
inference(instantiation,[status(thm)],[c_102970]) ).
cnf(c_284853,plain,
( ~ element(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),the_carrier(poset_of_lattice(sK19)))
| ~ in(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),X0)
| ~ relstr_set_smaller(poset_of_lattice(sK19),X0,cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(cast_to_el_of_LattPOSet(sK19,sK20),the_carrier(poset_of_lattice(sK19)))
| ~ rel_str(poset_of_lattice(sK19))
| related(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_68]) ).
cnf(c_290311,plain,
( ~ relstr_set_smaller(poset_of_lattice(sK19),X0,cast_to_el_of_LattPOSet(sK19,sK20))
| ~ in(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_284853,c_153,c_152,c_154,c_151,c_194,c_196,c_197,c_200,c_204,c_208,c_380,c_552,c_8835,c_22896,c_28551,c_30638,c_138553,c_159227,c_284853]) ).
cnf(c_290312,plain,
( ~ in(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),X0)
| ~ relstr_set_smaller(poset_of_lattice(sK19),X0,cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(renaming,[status(thm)],[c_290311]) ).
cnf(c_290322,plain,
( ~ in(cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18)),sK18)
| ~ relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20)) ),
inference(instantiation,[status(thm)],[c_290312]) ).
cnf(c_290324,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_290322,c_138553,c_14321,c_8832,c_557,c_552,c_150,c_151,c_154,c_152,c_153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU349+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 22:47:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 125.91/17.78 % SZS status Started for theBenchmark.p
% 125.91/17.78 % SZS status Theorem for theBenchmark.p
% 125.91/17.78
% 125.91/17.78 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 125.91/17.78
% 125.91/17.78 ------ iProver source info
% 125.91/17.78
% 125.91/17.78 git: date: 2023-05-31 18:12:56 +0000
% 125.91/17.78 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 125.91/17.78 git: non_committed_changes: false
% 125.91/17.78 git: last_make_outside_of_git: false
% 125.91/17.78
% 125.91/17.78 ------ Parsing...
% 125.91/17.78 ------ Clausification by vclausify_rel & Parsing by iProver...
% 125.91/17.78
% 125.91/17.78 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e
% 125.91/17.78
% 125.91/17.78 ------ Preprocessing...
% 125.91/17.78
% 125.91/17.78 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 125.91/17.78 ------ Proving...
% 125.91/17.78 ------ Problem Properties
% 125.91/17.78
% 125.91/17.78
% 125.91/17.78 clauses 108
% 125.91/17.78 conjectures 6
% 125.91/17.78 EPR 42
% 125.91/17.78 Horn 66
% 125.91/17.78 unary 29
% 125.91/17.78 binary 20
% 125.91/17.78 lits 348
% 125.91/17.78 lits eq 11
% 125.91/17.78 fd_pure 0
% 125.91/17.78 fd_pseudo 0
% 125.91/17.78 fd_cond 1
% 125.91/17.78 fd_pseudo_cond 3
% 125.91/17.78 AC symbols 0
% 125.91/17.78
% 125.91/17.78 ------ Input Options Time Limit: Unbounded
% 125.91/17.78
% 125.91/17.78
% 125.91/17.78 ------
% 125.91/17.78 Current options:
% 125.91/17.78 ------
% 125.91/17.78
% 125.91/17.78
% 125.91/17.78
% 125.91/17.78
% 125.91/17.78 ------ Proving...
% 125.91/17.78
% 125.91/17.78
% 125.91/17.78 % SZS status Theorem for theBenchmark.p
% 125.91/17.78
% 125.91/17.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 125.91/17.79
% 125.91/17.79
%------------------------------------------------------------------------------