TSTP Solution File: SEU369+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU369+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 07:52:42 EST 2010
% Result : Theorem 1.25s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 14
% Syntax : Number of formulae : 145 ( 21 unt; 0 def)
% Number of atoms : 741 ( 44 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 938 ( 342 ~; 436 |; 125 &)
% ( 8 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 226 ( 9 sgn 115 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',d3_lattice3) ).
fof(3,axiom,
! [X1] :
( rel_str(X1)
=> relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',dt_u1_orders_2) ).
fof(5,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complete_latt_str(boole_lattice(X1)) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',fc1_knaster) ).
fof(6,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',redefinition_m2_relset_1) ).
fof(34,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',d2_lattice3) ).
fof(35,conjecture,
! [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
=> ( related_reflexive(boole_POSet(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',t2_yellow_1) ).
fof(37,axiom,
! [X1] :
( rel_str(X1)
=> ( strict_rel_str(X1)
=> X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',abstractness_v1_orders_2) ).
fof(40,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',dt_k3_lattice3) ).
fof(44,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ! [X3,X4] :
( rel_str_of(X1,X2) = rel_str_of(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',free_g1_orders_2) ).
fof(51,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',redefinition_r3_lattices) ).
fof(83,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',dt_k1_lattice3) ).
fof(90,axiom,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',t2_lattice3) ).
fof(101,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',t7_lattice3) ).
fof(106,axiom,
! [X1] : boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
file('/tmp/tmp72E2iE/sel_SEU369+1.p_1',d2_yellow_1) ).
fof(122,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
=> ( related_reflexive(boole_POSet(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[35]) ).
fof(123,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(125,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complete_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(138,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
inference(fof_simplification,[status(thm)],[34,theory(equality)]) ).
fof(141,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[40,theory(equality)]) ).
fof(145,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( below_refl(X1,X2,X3)
<=> below(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[51,theory(equality)]) ).
fof(175,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[101,theory(equality)]) ).
fof(183,plain,
! [X1] :
( empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
inference(fof_nnf,[status(thm)],[123]) ).
fof(184,plain,
! [X3] :
( empty_carrier(X3)
| ~ lattice(X3)
| ~ latt_str(X3)
| ! [X4] :
( ~ element(X4,the_carrier(X3))
| cast_to_el_of_LattPOSet(X3,X4) = X4 ) ),
inference(variable_rename,[status(thm)],[183]) ).
fof(185,plain,
! [X3,X4] :
( ~ element(X4,the_carrier(X3))
| cast_to_el_of_LattPOSet(X3,X4) = X4
| empty_carrier(X3)
| ~ lattice(X3)
| ~ latt_str(X3) ),
inference(shift_quantors,[status(thm)],[184]) ).
cnf(186,plain,
( empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[185]) ).
fof(198,plain,
! [X1] :
( ~ rel_str(X1)
| relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(199,plain,
! [X2] :
( ~ rel_str(X2)
| relation_of2_as_subset(the_InternalRel(X2),the_carrier(X2),the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[198]) ).
cnf(200,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[199]) ).
fof(206,plain,
! [X2] :
( ~ empty_carrier(boole_lattice(X2))
& strict_latt_str(boole_lattice(X2))
& join_commutative(boole_lattice(X2))
& join_associative(boole_lattice(X2))
& meet_commutative(boole_lattice(X2))
& meet_associative(boole_lattice(X2))
& meet_absorbing(boole_lattice(X2))
& join_absorbing(boole_lattice(X2))
& lattice(boole_lattice(X2))
& distributive_lattstr(boole_lattice(X2))
& modular_lattstr(boole_lattice(X2))
& lower_bounded_semilattstr(boole_lattice(X2))
& upper_bounded_semilattstr(boole_lattice(X2))
& bounded_lattstr(boole_lattice(X2))
& complemented_lattstr(boole_lattice(X2))
& boolean_lattstr(boole_lattice(X2))
& complete_latt_str(boole_lattice(X2)) ),
inference(variable_rename,[status(thm)],[125]) ).
cnf(215,plain,
lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[206]) ).
cnf(216,plain,
join_absorbing(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[206]) ).
cnf(217,plain,
meet_absorbing(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[206]) ).
cnf(219,plain,
meet_commutative(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[206]) ).
cnf(223,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[206]) ).
fof(224,plain,
! [X1,X2,X3] :
( ( ~ relation_of2_as_subset(X3,X1,X2)
| relation_of2(X3,X1,X2) )
& ( ~ relation_of2(X3,X1,X2)
| relation_of2_as_subset(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(225,plain,
! [X4,X5,X6] :
( ( ~ relation_of2_as_subset(X6,X4,X5)
| relation_of2(X6,X4,X5) )
& ( ~ relation_of2(X6,X4,X5)
| relation_of2_as_subset(X6,X4,X5) ) ),
inference(variable_rename,[status(thm)],[224]) ).
cnf(227,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[225]) ).
fof(356,plain,
! [X1] :
( empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
inference(fof_nnf,[status(thm)],[138]) ).
fof(357,plain,
! [X2] :
( empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2)
| poset_of_lattice(X2) = rel_str_of(the_carrier(X2),k2_lattice3(X2)) ),
inference(variable_rename,[status(thm)],[356]) ).
cnf(358,plain,
( poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1))
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[357]) ).
fof(359,negated_conjecture,
? [X1,X2] :
( element(X2,the_carrier(boole_POSet(X1)))
& ? [X3] :
( element(X3,the_carrier(boole_POSet(X1)))
& ( ~ related_reflexive(boole_POSet(X1),X2,X3)
| ~ subset(X2,X3) )
& ( related_reflexive(boole_POSet(X1),X2,X3)
| subset(X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[122]) ).
fof(360,negated_conjecture,
? [X4,X5] :
( element(X5,the_carrier(boole_POSet(X4)))
& ? [X6] :
( element(X6,the_carrier(boole_POSet(X4)))
& ( ~ related_reflexive(boole_POSet(X4),X5,X6)
| ~ subset(X5,X6) )
& ( related_reflexive(boole_POSet(X4),X5,X6)
| subset(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[359]) ).
fof(361,negated_conjecture,
( element(esk10_0,the_carrier(boole_POSet(esk9_0)))
& element(esk11_0,the_carrier(boole_POSet(esk9_0)))
& ( ~ related_reflexive(boole_POSet(esk9_0),esk10_0,esk11_0)
| ~ subset(esk10_0,esk11_0) )
& ( related_reflexive(boole_POSet(esk9_0),esk10_0,esk11_0)
| subset(esk10_0,esk11_0) ) ),
inference(skolemize,[status(esa)],[360]) ).
cnf(362,negated_conjecture,
( subset(esk10_0,esk11_0)
| related_reflexive(boole_POSet(esk9_0),esk10_0,esk11_0) ),
inference(split_conjunct,[status(thm)],[361]) ).
cnf(363,negated_conjecture,
( ~ subset(esk10_0,esk11_0)
| ~ related_reflexive(boole_POSet(esk9_0),esk10_0,esk11_0) ),
inference(split_conjunct,[status(thm)],[361]) ).
cnf(364,negated_conjecture,
element(esk11_0,the_carrier(boole_POSet(esk9_0))),
inference(split_conjunct,[status(thm)],[361]) ).
cnf(365,negated_conjecture,
element(esk10_0,the_carrier(boole_POSet(esk9_0))),
inference(split_conjunct,[status(thm)],[361]) ).
fof(372,plain,
! [X1] :
( ~ rel_str(X1)
| ~ strict_rel_str(X1)
| X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(373,plain,
! [X2] :
( ~ rel_str(X2)
| ~ strict_rel_str(X2)
| X2 = rel_str_of(the_carrier(X2),the_InternalRel(X2)) ),
inference(variable_rename,[status(thm)],[372]) ).
cnf(374,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ strict_rel_str(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[373]) ).
fof(381,plain,
! [X1] :
( empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
inference(fof_nnf,[status(thm)],[141]) ).
fof(382,plain,
! [X2] :
( empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2)
| ( strict_rel_str(poset_of_lattice(X2))
& reflexive_relstr(poset_of_lattice(X2))
& transitive_relstr(poset_of_lattice(X2))
& antisymmetric_relstr(poset_of_lattice(X2))
& rel_str(poset_of_lattice(X2)) ) ),
inference(variable_rename,[status(thm)],[381]) ).
fof(383,plain,
! [X2] :
( ( strict_rel_str(poset_of_lattice(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( reflexive_relstr(poset_of_lattice(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( transitive_relstr(poset_of_lattice(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( antisymmetric_relstr(poset_of_lattice(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( rel_str(poset_of_lattice(X2))
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) ) ),
inference(distribute,[status(thm)],[382]) ).
cnf(384,plain,
( empty_carrier(X1)
| rel_str(poset_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[383]) ).
cnf(388,plain,
( empty_carrier(X1)
| strict_rel_str(poset_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[383]) ).
fof(398,plain,
! [X1,X2] :
( ~ relation_of2(X2,X1,X1)
| ! [X3,X4] :
( rel_str_of(X1,X2) != rel_str_of(X3,X4)
| ( X1 = X3
& X2 = X4 ) ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(399,plain,
! [X5,X6] :
( ~ relation_of2(X6,X5,X5)
| ! [X7,X8] :
( rel_str_of(X5,X6) != rel_str_of(X7,X8)
| ( X5 = X7
& X6 = X8 ) ) ),
inference(variable_rename,[status(thm)],[398]) ).
fof(400,plain,
! [X5,X6,X7,X8] :
( rel_str_of(X5,X6) != rel_str_of(X7,X8)
| ( X5 = X7
& X6 = X8 )
| ~ relation_of2(X6,X5,X5) ),
inference(shift_quantors,[status(thm)],[399]) ).
fof(401,plain,
! [X5,X6,X7,X8] :
( ( X5 = X7
| rel_str_of(X5,X6) != rel_str_of(X7,X8)
| ~ relation_of2(X6,X5,X5) )
& ( X6 = X8
| rel_str_of(X5,X6) != rel_str_of(X7,X8)
| ~ relation_of2(X6,X5,X5) ) ),
inference(distribute,[status(thm)],[400]) ).
cnf(403,plain,
( X2 = X3
| ~ relation_of2(X1,X2,X2)
| rel_str_of(X2,X1) != rel_str_of(X3,X4) ),
inference(split_conjunct,[status(thm)],[401]) ).
fof(437,plain,
! [X1,X2,X3] :
( empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ( ( ~ below_refl(X1,X2,X3)
| below(X1,X2,X3) )
& ( ~ below(X1,X2,X3)
| below_refl(X1,X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[145]) ).
fof(438,plain,
! [X4,X5,X6] :
( empty_carrier(X4)
| ~ meet_commutative(X4)
| ~ meet_absorbing(X4)
| ~ join_absorbing(X4)
| ~ latt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4))
| ( ( ~ below_refl(X4,X5,X6)
| below(X4,X5,X6) )
& ( ~ below(X4,X5,X6)
| below_refl(X4,X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[437]) ).
fof(439,plain,
! [X4,X5,X6] :
( ( ~ below_refl(X4,X5,X6)
| below(X4,X5,X6)
| empty_carrier(X4)
| ~ meet_commutative(X4)
| ~ meet_absorbing(X4)
| ~ join_absorbing(X4)
| ~ latt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4)) )
& ( ~ below(X4,X5,X6)
| below_refl(X4,X5,X6)
| empty_carrier(X4)
| ~ meet_commutative(X4)
| ~ meet_absorbing(X4)
| ~ join_absorbing(X4)
| ~ latt_str(X4)
| ~ element(X5,the_carrier(X4))
| ~ element(X6,the_carrier(X4)) ) ),
inference(distribute,[status(thm)],[438]) ).
cnf(440,plain,
( empty_carrier(X2)
| below_refl(X2,X3,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ latt_str(X2)
| ~ join_absorbing(X2)
| ~ meet_absorbing(X2)
| ~ meet_commutative(X2)
| ~ below(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[439]) ).
cnf(441,plain,
( empty_carrier(X2)
| below(X2,X3,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| ~ latt_str(X2)
| ~ join_absorbing(X2)
| ~ meet_absorbing(X2)
| ~ meet_commutative(X2)
| ~ below_refl(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[439]) ).
fof(618,plain,
! [X2] :
( strict_latt_str(boole_lattice(X2))
& latt_str(boole_lattice(X2)) ),
inference(variable_rename,[status(thm)],[83]) ).
cnf(619,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[618]) ).
fof(666,plain,
! [X1,X2] :
( ~ element(X2,the_carrier(boole_lattice(X1)))
| ! [X3] :
( ~ element(X3,the_carrier(boole_lattice(X1)))
| ( ( ~ below(boole_lattice(X1),X2,X3)
| subset(X2,X3) )
& ( ~ subset(X2,X3)
| below(boole_lattice(X1),X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[90]) ).
fof(667,plain,
! [X4,X5] :
( ~ element(X5,the_carrier(boole_lattice(X4)))
| ! [X6] :
( ~ element(X6,the_carrier(boole_lattice(X4)))
| ( ( ~ below(boole_lattice(X4),X5,X6)
| subset(X5,X6) )
& ( ~ subset(X5,X6)
| below(boole_lattice(X4),X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[666]) ).
fof(668,plain,
! [X4,X5,X6] :
( ~ element(X6,the_carrier(boole_lattice(X4)))
| ( ( ~ below(boole_lattice(X4),X5,X6)
| subset(X5,X6) )
& ( ~ subset(X5,X6)
| below(boole_lattice(X4),X5,X6) ) )
| ~ element(X5,the_carrier(boole_lattice(X4))) ),
inference(shift_quantors,[status(thm)],[667]) ).
fof(669,plain,
! [X4,X5,X6] :
( ( ~ below(boole_lattice(X4),X5,X6)
| subset(X5,X6)
| ~ element(X6,the_carrier(boole_lattice(X4)))
| ~ element(X5,the_carrier(boole_lattice(X4))) )
& ( ~ subset(X5,X6)
| below(boole_lattice(X4),X5,X6)
| ~ element(X6,the_carrier(boole_lattice(X4)))
| ~ element(X5,the_carrier(boole_lattice(X4))) ) ),
inference(distribute,[status(thm)],[668]) ).
cnf(670,plain,
( below(boole_lattice(X2),X1,X3)
| ~ element(X1,the_carrier(boole_lattice(X2)))
| ~ element(X3,the_carrier(boole_lattice(X2)))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[669]) ).
cnf(671,plain,
( subset(X1,X3)
| ~ element(X1,the_carrier(boole_lattice(X2)))
| ~ element(X3,the_carrier(boole_lattice(X2)))
| ~ below(boole_lattice(X2),X1,X3) ),
inference(split_conjunct,[status(thm)],[669]) ).
fof(749,plain,
! [X1] :
( empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ( ( ~ below_refl(X1,X2,X3)
| related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) )
& ( ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| below_refl(X1,X2,X3) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[175]) ).
fof(750,plain,
! [X4] :
( empty_carrier(X4)
| ~ lattice(X4)
| ~ latt_str(X4)
| ! [X5] :
( ~ element(X5,the_carrier(X4))
| ! [X6] :
( ~ element(X6,the_carrier(X4))
| ( ( ~ below_refl(X4,X5,X6)
| related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6)) )
& ( ~ related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6))
| below_refl(X4,X5,X6) ) ) ) ) ),
inference(variable_rename,[status(thm)],[749]) ).
fof(751,plain,
! [X4,X5,X6] :
( ~ element(X6,the_carrier(X4))
| ( ( ~ below_refl(X4,X5,X6)
| related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6)) )
& ( ~ related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6))
| below_refl(X4,X5,X6) ) )
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ lattice(X4)
| ~ latt_str(X4) ),
inference(shift_quantors,[status(thm)],[750]) ).
fof(752,plain,
! [X4,X5,X6] :
( ( ~ below_refl(X4,X5,X6)
| related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6))
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ lattice(X4)
| ~ latt_str(X4) )
& ( ~ related_reflexive(poset_of_lattice(X4),cast_to_el_of_LattPOSet(X4,X5),cast_to_el_of_LattPOSet(X4,X6))
| below_refl(X4,X5,X6)
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ lattice(X4)
| ~ latt_str(X4) ) ),
inference(distribute,[status(thm)],[751]) ).
cnf(753,plain,
( empty_carrier(X1)
| below_refl(X1,X2,X3)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ),
inference(split_conjunct,[status(thm)],[752]) ).
cnf(754,plain,
( empty_carrier(X1)
| related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below_refl(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[752]) ).
fof(771,plain,
! [X2] : boole_POSet(X2) = poset_of_lattice(boole_lattice(X2)),
inference(variable_rename,[status(thm)],[106]) ).
cnf(772,plain,
boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[771]) ).
cnf(853,negated_conjecture,
element(esk10_0,the_carrier(poset_of_lattice(boole_lattice(esk9_0)))),
inference(rw,[status(thm)],[365,772,theory(equality)]),
[unfolding] ).
cnf(854,negated_conjecture,
element(esk11_0,the_carrier(poset_of_lattice(boole_lattice(esk9_0)))),
inference(rw,[status(thm)],[364,772,theory(equality)]),
[unfolding] ).
cnf(855,negated_conjecture,
( subset(esk10_0,esk11_0)
| related_reflexive(poset_of_lattice(boole_lattice(esk9_0)),esk10_0,esk11_0) ),
inference(rw,[status(thm)],[362,772,theory(equality)]),
[unfolding] ).
cnf(858,negated_conjecture,
( ~ subset(esk10_0,esk11_0)
| ~ related_reflexive(poset_of_lattice(boole_lattice(esk9_0)),esk10_0,esk11_0) ),
inference(rw,[status(thm)],[363,772,theory(equality)]),
[unfolding] ).
cnf(972,plain,
( relation_of2(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[227,200,theory(equality)]) ).
cnf(1267,plain,
( related_reflexive(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(spm,[status(thm)],[754,186,theory(equality)]) ).
cnf(1269,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(spm,[status(thm)],[753,186,theory(equality)]) ).
cnf(1272,plain,
( below_refl(boole_lattice(X1),X2,X3)
| empty_carrier(boole_lattice(X1))
| ~ join_absorbing(boole_lattice(X1))
| ~ meet_absorbing(boole_lattice(X1))
| ~ meet_commutative(boole_lattice(X1))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ latt_str(boole_lattice(X1))
| ~ subset(X2,X3) ),
inference(spm,[status(thm)],[440,670,theory(equality)]) ).
cnf(1273,plain,
( below_refl(boole_lattice(X1),X2,X3)
| empty_carrier(boole_lattice(X1))
| $false
| ~ meet_absorbing(boole_lattice(X1))
| ~ meet_commutative(boole_lattice(X1))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ latt_str(boole_lattice(X1))
| ~ subset(X2,X3) ),
inference(rw,[status(thm)],[1272,216,theory(equality)]) ).
cnf(1274,plain,
( below_refl(boole_lattice(X1),X2,X3)
| empty_carrier(boole_lattice(X1))
| $false
| $false
| ~ meet_commutative(boole_lattice(X1))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ latt_str(boole_lattice(X1))
| ~ subset(X2,X3) ),
inference(rw,[status(thm)],[1273,217,theory(equality)]) ).
cnf(1275,plain,
( below_refl(boole_lattice(X1),X2,X3)
| empty_carrier(boole_lattice(X1))
| $false
| $false
| $false
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ latt_str(boole_lattice(X1))
| ~ subset(X2,X3) ),
inference(rw,[status(thm)],[1274,219,theory(equality)]) ).
cnf(1276,plain,
( below_refl(boole_lattice(X1),X2,X3)
| empty_carrier(boole_lattice(X1))
| $false
| $false
| $false
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X3,the_carrier(boole_lattice(X1)))
| $false
| ~ subset(X2,X3) ),
inference(rw,[status(thm)],[1275,619,theory(equality)]) ).
cnf(1277,plain,
( below_refl(boole_lattice(X1),X2,X3)
| empty_carrier(boole_lattice(X1))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ subset(X2,X3) ),
inference(cn,[status(thm)],[1276,theory(equality)]) ).
cnf(1278,plain,
( below_refl(boole_lattice(X1),X2,X3)
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X3,the_carrier(boole_lattice(X1)))
| ~ subset(X2,X3) ),
inference(sr,[status(thm)],[1277,223,theory(equality)]) ).
cnf(1279,plain,
( subset(X1,X2)
| empty_carrier(boole_lattice(X3))
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3)))
| ~ below_refl(boole_lattice(X3),X1,X2)
| ~ join_absorbing(boole_lattice(X3))
| ~ meet_absorbing(boole_lattice(X3))
| ~ meet_commutative(boole_lattice(X3))
| ~ latt_str(boole_lattice(X3)) ),
inference(spm,[status(thm)],[671,441,theory(equality)]) ).
cnf(1281,plain,
( subset(X1,X2)
| empty_carrier(boole_lattice(X3))
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3)))
| ~ below_refl(boole_lattice(X3),X1,X2)
| $false
| ~ meet_absorbing(boole_lattice(X3))
| ~ meet_commutative(boole_lattice(X3))
| ~ latt_str(boole_lattice(X3)) ),
inference(rw,[status(thm)],[1279,216,theory(equality)]) ).
cnf(1282,plain,
( subset(X1,X2)
| empty_carrier(boole_lattice(X3))
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3)))
| ~ below_refl(boole_lattice(X3),X1,X2)
| $false
| $false
| ~ meet_commutative(boole_lattice(X3))
| ~ latt_str(boole_lattice(X3)) ),
inference(rw,[status(thm)],[1281,217,theory(equality)]) ).
cnf(1283,plain,
( subset(X1,X2)
| empty_carrier(boole_lattice(X3))
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3)))
| ~ below_refl(boole_lattice(X3),X1,X2)
| $false
| $false
| $false
| ~ latt_str(boole_lattice(X3)) ),
inference(rw,[status(thm)],[1282,219,theory(equality)]) ).
cnf(1284,plain,
( subset(X1,X2)
| empty_carrier(boole_lattice(X3))
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3)))
| ~ below_refl(boole_lattice(X3),X1,X2)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[1283,619,theory(equality)]) ).
cnf(1285,plain,
( subset(X1,X2)
| empty_carrier(boole_lattice(X3))
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3)))
| ~ below_refl(boole_lattice(X3),X1,X2) ),
inference(cn,[status(thm)],[1284,theory(equality)]) ).
cnf(1286,plain,
( subset(X1,X2)
| ~ element(X2,the_carrier(boole_lattice(X3)))
| ~ element(X1,the_carrier(boole_lattice(X3)))
| ~ below_refl(boole_lattice(X3),X1,X2) ),
inference(sr,[status(thm)],[1285,223,theory(equality)]) ).
cnf(1450,plain,
( the_carrier(X1) = X2
| rel_str_of(the_carrier(X1),the_InternalRel(X1)) != rel_str_of(X2,X3)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[403,972,theory(equality)]) ).
cnf(2712,plain,
( related_reflexive(poset_of_lattice(X1),X2,X3)
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(spm,[status(thm)],[1267,186,theory(equality)]) ).
cnf(2752,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(poset_of_lattice(X1),X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(spm,[status(thm)],[1269,186,theory(equality)]) ).
cnf(2782,plain,
( the_carrier(X1) = X2
| X1 != rel_str_of(X2,X3)
| ~ rel_str(X1)
| ~ strict_rel_str(X1) ),
inference(spm,[status(thm)],[1450,374,theory(equality)]) ).
cnf(2788,plain,
( the_carrier(rel_str_of(X1,X2)) = X1
| ~ strict_rel_str(rel_str_of(X1,X2))
| ~ rel_str(rel_str_of(X1,X2)) ),
inference(er,[status(thm)],[2782,theory(equality)]) ).
cnf(2931,plain,
( the_carrier(poset_of_lattice(X1)) = the_carrier(X1)
| empty_carrier(X1)
| ~ strict_rel_str(poset_of_lattice(X1))
| ~ rel_str(poset_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(spm,[status(thm)],[2788,358,theory(equality)]) ).
cnf(3738,plain,
( the_carrier(poset_of_lattice(X1)) = the_carrier(X1)
| empty_carrier(X1)
| ~ strict_rel_str(poset_of_lattice(X1))
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(csr,[status(thm)],[2931,384]) ).
cnf(3739,plain,
( the_carrier(poset_of_lattice(X1)) = the_carrier(X1)
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(csr,[status(thm)],[3738,388]) ).
cnf(3740,negated_conjecture,
( element(esk10_0,the_carrier(boole_lattice(esk9_0)))
| empty_carrier(boole_lattice(esk9_0))
| ~ latt_str(boole_lattice(esk9_0))
| ~ lattice(boole_lattice(esk9_0)) ),
inference(spm,[status(thm)],[853,3739,theory(equality)]) ).
cnf(3741,negated_conjecture,
( element(esk11_0,the_carrier(boole_lattice(esk9_0)))
| empty_carrier(boole_lattice(esk9_0))
| ~ latt_str(boole_lattice(esk9_0))
| ~ lattice(boole_lattice(esk9_0)) ),
inference(spm,[status(thm)],[854,3739,theory(equality)]) ).
cnf(3792,negated_conjecture,
( element(esk10_0,the_carrier(boole_lattice(esk9_0)))
| empty_carrier(boole_lattice(esk9_0))
| $false
| ~ lattice(boole_lattice(esk9_0)) ),
inference(rw,[status(thm)],[3740,619,theory(equality)]) ).
cnf(3793,negated_conjecture,
( element(esk10_0,the_carrier(boole_lattice(esk9_0)))
| empty_carrier(boole_lattice(esk9_0))
| $false
| $false ),
inference(rw,[status(thm)],[3792,215,theory(equality)]) ).
cnf(3794,negated_conjecture,
( element(esk10_0,the_carrier(boole_lattice(esk9_0)))
| empty_carrier(boole_lattice(esk9_0)) ),
inference(cn,[status(thm)],[3793,theory(equality)]) ).
cnf(3795,negated_conjecture,
element(esk10_0,the_carrier(boole_lattice(esk9_0))),
inference(sr,[status(thm)],[3794,223,theory(equality)]) ).
cnf(3796,negated_conjecture,
( element(esk11_0,the_carrier(boole_lattice(esk9_0)))
| empty_carrier(boole_lattice(esk9_0))
| $false
| ~ lattice(boole_lattice(esk9_0)) ),
inference(rw,[status(thm)],[3741,619,theory(equality)]) ).
cnf(3797,negated_conjecture,
( element(esk11_0,the_carrier(boole_lattice(esk9_0)))
| empty_carrier(boole_lattice(esk9_0))
| $false
| $false ),
inference(rw,[status(thm)],[3796,215,theory(equality)]) ).
cnf(3798,negated_conjecture,
( element(esk11_0,the_carrier(boole_lattice(esk9_0)))
| empty_carrier(boole_lattice(esk9_0)) ),
inference(cn,[status(thm)],[3797,theory(equality)]) ).
cnf(3799,negated_conjecture,
element(esk11_0,the_carrier(boole_lattice(esk9_0))),
inference(sr,[status(thm)],[3798,223,theory(equality)]) ).
cnf(11516,negated_conjecture,
( empty_carrier(boole_lattice(esk9_0))
| ~ subset(esk10_0,esk11_0)
| ~ below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| ~ element(esk11_0,the_carrier(boole_lattice(esk9_0)))
| ~ element(esk10_0,the_carrier(boole_lattice(esk9_0)))
| ~ latt_str(boole_lattice(esk9_0))
| ~ lattice(boole_lattice(esk9_0)) ),
inference(spm,[status(thm)],[858,2712,theory(equality)]) ).
cnf(11520,negated_conjecture,
( empty_carrier(boole_lattice(esk9_0))
| ~ subset(esk10_0,esk11_0)
| ~ below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| $false
| ~ element(esk10_0,the_carrier(boole_lattice(esk9_0)))
| ~ latt_str(boole_lattice(esk9_0))
| ~ lattice(boole_lattice(esk9_0)) ),
inference(rw,[status(thm)],[11516,3799,theory(equality)]) ).
cnf(11521,negated_conjecture,
( empty_carrier(boole_lattice(esk9_0))
| ~ subset(esk10_0,esk11_0)
| ~ below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| $false
| $false
| ~ latt_str(boole_lattice(esk9_0))
| ~ lattice(boole_lattice(esk9_0)) ),
inference(rw,[status(thm)],[11520,3795,theory(equality)]) ).
cnf(11522,negated_conjecture,
( empty_carrier(boole_lattice(esk9_0))
| ~ subset(esk10_0,esk11_0)
| ~ below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| $false
| $false
| $false
| ~ lattice(boole_lattice(esk9_0)) ),
inference(rw,[status(thm)],[11521,619,theory(equality)]) ).
cnf(11523,negated_conjecture,
( empty_carrier(boole_lattice(esk9_0))
| ~ subset(esk10_0,esk11_0)
| ~ below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[11522,215,theory(equality)]) ).
cnf(11524,negated_conjecture,
( empty_carrier(boole_lattice(esk9_0))
| ~ subset(esk10_0,esk11_0)
| ~ below_refl(boole_lattice(esk9_0),esk10_0,esk11_0) ),
inference(cn,[status(thm)],[11523,theory(equality)]) ).
cnf(11525,negated_conjecture,
( ~ subset(esk10_0,esk11_0)
| ~ below_refl(boole_lattice(esk9_0),esk10_0,esk11_0) ),
inference(sr,[status(thm)],[11524,223,theory(equality)]) ).
cnf(11526,negated_conjecture,
( ~ subset(esk10_0,esk11_0)
| ~ element(esk10_0,the_carrier(boole_lattice(esk9_0)))
| ~ element(esk11_0,the_carrier(boole_lattice(esk9_0))) ),
inference(spm,[status(thm)],[11525,1278,theory(equality)]) ).
cnf(11527,negated_conjecture,
( ~ subset(esk10_0,esk11_0)
| $false
| ~ element(esk11_0,the_carrier(boole_lattice(esk9_0))) ),
inference(rw,[status(thm)],[11526,3795,theory(equality)]) ).
cnf(11528,negated_conjecture,
( ~ subset(esk10_0,esk11_0)
| $false
| $false ),
inference(rw,[status(thm)],[11527,3799,theory(equality)]) ).
cnf(11529,negated_conjecture,
~ subset(esk10_0,esk11_0),
inference(cn,[status(thm)],[11528,theory(equality)]) ).
cnf(11693,negated_conjecture,
related_reflexive(poset_of_lattice(boole_lattice(esk9_0)),esk10_0,esk11_0),
inference(sr,[status(thm)],[855,11529,theory(equality)]) ).
cnf(11696,negated_conjecture,
( below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| empty_carrier(boole_lattice(esk9_0))
| ~ element(esk11_0,the_carrier(boole_lattice(esk9_0)))
| ~ element(esk10_0,the_carrier(boole_lattice(esk9_0)))
| ~ latt_str(boole_lattice(esk9_0))
| ~ lattice(boole_lattice(esk9_0)) ),
inference(spm,[status(thm)],[2752,11693,theory(equality)]) ).
cnf(11703,negated_conjecture,
( below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| empty_carrier(boole_lattice(esk9_0))
| $false
| ~ element(esk10_0,the_carrier(boole_lattice(esk9_0)))
| ~ latt_str(boole_lattice(esk9_0))
| ~ lattice(boole_lattice(esk9_0)) ),
inference(rw,[status(thm)],[11696,3799,theory(equality)]) ).
cnf(11704,negated_conjecture,
( below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| empty_carrier(boole_lattice(esk9_0))
| $false
| $false
| ~ latt_str(boole_lattice(esk9_0))
| ~ lattice(boole_lattice(esk9_0)) ),
inference(rw,[status(thm)],[11703,3795,theory(equality)]) ).
cnf(11705,negated_conjecture,
( below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| empty_carrier(boole_lattice(esk9_0))
| $false
| $false
| $false
| ~ lattice(boole_lattice(esk9_0)) ),
inference(rw,[status(thm)],[11704,619,theory(equality)]) ).
cnf(11706,negated_conjecture,
( below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| empty_carrier(boole_lattice(esk9_0))
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[11705,215,theory(equality)]) ).
cnf(11707,negated_conjecture,
( below_refl(boole_lattice(esk9_0),esk10_0,esk11_0)
| empty_carrier(boole_lattice(esk9_0)) ),
inference(cn,[status(thm)],[11706,theory(equality)]) ).
cnf(11708,negated_conjecture,
below_refl(boole_lattice(esk9_0),esk10_0,esk11_0),
inference(sr,[status(thm)],[11707,223,theory(equality)]) ).
cnf(11713,negated_conjecture,
( subset(esk10_0,esk11_0)
| ~ element(esk11_0,the_carrier(boole_lattice(esk9_0)))
| ~ element(esk10_0,the_carrier(boole_lattice(esk9_0))) ),
inference(spm,[status(thm)],[1286,11708,theory(equality)]) ).
cnf(11716,negated_conjecture,
( subset(esk10_0,esk11_0)
| $false
| ~ element(esk10_0,the_carrier(boole_lattice(esk9_0))) ),
inference(rw,[status(thm)],[11713,3799,theory(equality)]) ).
cnf(11717,negated_conjecture,
( subset(esk10_0,esk11_0)
| $false
| $false ),
inference(rw,[status(thm)],[11716,3795,theory(equality)]) ).
cnf(11718,negated_conjecture,
subset(esk10_0,esk11_0),
inference(cn,[status(thm)],[11717,theory(equality)]) ).
cnf(11719,negated_conjecture,
$false,
inference(sr,[status(thm)],[11718,11529,theory(equality)]) ).
cnf(11720,negated_conjecture,
$false,
11719,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU369+1.p
% --creating new selector for []
% -running prover on /tmp/tmp72E2iE/sel_SEU369+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU369+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU369+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU369+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------