TSTP Solution File: SEU345+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU345+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 07:35:07 EST 2010
% Result : Theorem 7.36s
% Output : CNFRefutation 7.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 114 ( 22 unt; 0 def)
% Number of atoms : 582 ( 180 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 749 ( 281 ~; 327 |; 115 &)
% ( 5 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 2 con; 0-3 aty)
% Number of variables : 211 ( 11 sgn 106 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ) ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',d16_lattices) ).
fof(6,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',dt_l3_lattices) ).
fof(14,axiom,
! [X1,X2] :
( ( strict_latt_str(X2)
& latt_str(X2) )
=> ( X2 = boole_lattice(X1)
<=> ( the_carrier(X2) = powerset(X1)
& ! [X3] :
( element(X3,powerset(X1))
=> ! [X4] :
( element(X4,powerset(X1))
=> ( apply_binary(the_L_join(X2),X3,X4) = subset_union2(X1,X3,X4)
& apply_binary(the_L_meet(X2),X3,X4) = subset_intersection2(X1,X3,X4) ) ) ) ) ) ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',d1_lattice3) ).
fof(17,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( element(X2,the_carrier(X1))
& ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',d13_lattices) ).
fof(33,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',dt_k5_lattices) ).
fof(50,axiom,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',t1_lattice3) ).
fof(53,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',t2_boole) ).
fof(71,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)) ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',fc2_lattice3) ).
fof(74,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',dt_k1_lattice3) ).
fof(75,conjecture,
! [X1] :
( lower_bounded_semilattstr(boole_lattice(X1))
& bottom_of_semilattstr(boole_lattice(X1)) = empty_set ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',t3_lattice3) ).
fof(76,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',rc2_subset_1) ).
fof(97,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',commutativity_k3_xboole_0) ).
fof(101,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/tmp/tmpAHuU3f/sel_SEU345+1.p_1',t6_boole) ).
fof(103,negated_conjecture,
~ ! [X1] :
( lower_bounded_semilattstr(boole_lattice(X1))
& bottom_of_semilattstr(boole_lattice(X1)) = empty_set ),
inference(assume_negation,[status(cth)],[75]) ).
fof(104,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( X2 = bottom_of_semilattstr(X1)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(111,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ( lower_bounded_semilattstr(X1)
<=> ? [X2] :
( element(X2,the_carrier(X1))
& ! [X3] :
( element(X3,the_carrier(X1))
=> ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[17,theory(equality)]) ).
fof(115,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[33,theory(equality)]) ).
fof(127,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)) ),
inference(fof_simplification,[status(thm)],[71,theory(equality)]) ).
fof(139,plain,
! [X1] :
( empty_carrier(X1)
| ~ meet_semilatt_str(X1)
| ~ lower_bounded_semilattstr(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ( ( X2 != bottom_of_semilattstr(X1)
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) )
& ( ? [X3] :
( element(X3,the_carrier(X1))
& ( meet(X1,X2,X3) != X2
| meet(X1,X3,X2) != X2 ) )
| X2 = bottom_of_semilattstr(X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[104]) ).
fof(140,plain,
! [X4] :
( empty_carrier(X4)
| ~ meet_semilatt_str(X4)
| ~ lower_bounded_semilattstr(X4)
| ! [X5] :
( ~ element(X5,the_carrier(X4))
| ( ( X5 != bottom_of_semilattstr(X4)
| ! [X6] :
( ~ element(X6,the_carrier(X4))
| ( meet(X4,X5,X6) = X5
& meet(X4,X6,X5) = X5 ) ) )
& ( ? [X7] :
( element(X7,the_carrier(X4))
& ( meet(X4,X5,X7) != X5
| meet(X4,X7,X5) != X5 ) )
| X5 = bottom_of_semilattstr(X4) ) ) ) ),
inference(variable_rename,[status(thm)],[139]) ).
fof(141,plain,
! [X4] :
( empty_carrier(X4)
| ~ meet_semilatt_str(X4)
| ~ lower_bounded_semilattstr(X4)
| ! [X5] :
( ~ element(X5,the_carrier(X4))
| ( ( X5 != bottom_of_semilattstr(X4)
| ! [X6] :
( ~ element(X6,the_carrier(X4))
| ( meet(X4,X5,X6) = X5
& meet(X4,X6,X5) = X5 ) ) )
& ( ( element(esk1_2(X4,X5),the_carrier(X4))
& ( meet(X4,X5,esk1_2(X4,X5)) != X5
| meet(X4,esk1_2(X4,X5),X5) != X5 ) )
| X5 = bottom_of_semilattstr(X4) ) ) ) ),
inference(skolemize,[status(esa)],[140]) ).
fof(142,plain,
! [X4,X5,X6] :
( ( ( ~ element(X6,the_carrier(X4))
| ( meet(X4,X5,X6) = X5
& meet(X4,X6,X5) = X5 )
| X5 != bottom_of_semilattstr(X4) )
& ( ( element(esk1_2(X4,X5),the_carrier(X4))
& ( meet(X4,X5,esk1_2(X4,X5)) != X5
| meet(X4,esk1_2(X4,X5),X5) != X5 ) )
| X5 = bottom_of_semilattstr(X4) ) )
| ~ element(X5,the_carrier(X4))
| ~ lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) ),
inference(shift_quantors,[status(thm)],[141]) ).
fof(143,plain,
! [X4,X5,X6] :
( ( meet(X4,X5,X6) = X5
| ~ element(X6,the_carrier(X4))
| X5 != bottom_of_semilattstr(X4)
| ~ element(X5,the_carrier(X4))
| ~ lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) )
& ( meet(X4,X6,X5) = X5
| ~ element(X6,the_carrier(X4))
| X5 != bottom_of_semilattstr(X4)
| ~ element(X5,the_carrier(X4))
| ~ lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) )
& ( element(esk1_2(X4,X5),the_carrier(X4))
| X5 = bottom_of_semilattstr(X4)
| ~ element(X5,the_carrier(X4))
| ~ lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) )
& ( meet(X4,X5,esk1_2(X4,X5)) != X5
| meet(X4,esk1_2(X4,X5),X5) != X5
| X5 = bottom_of_semilattstr(X4)
| ~ element(X5,the_carrier(X4))
| ~ lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) ) ),
inference(distribute,[status(thm)],[142]) ).
cnf(146,plain,
( empty_carrier(X1)
| meet(X1,X3,X2) = X2
| ~ meet_semilatt_str(X1)
| ~ lower_bounded_semilattstr(X1)
| ~ element(X2,the_carrier(X1))
| X2 != bottom_of_semilattstr(X1)
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[143]) ).
fof(161,plain,
! [X1] :
( ~ latt_str(X1)
| ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(162,plain,
! [X2] :
( ~ latt_str(X2)
| ( meet_semilatt_str(X2)
& join_semilatt_str(X2) ) ),
inference(variable_rename,[status(thm)],[161]) ).
fof(163,plain,
! [X2] :
( ( meet_semilatt_str(X2)
| ~ latt_str(X2) )
& ( join_semilatt_str(X2)
| ~ latt_str(X2) ) ),
inference(distribute,[status(thm)],[162]) ).
cnf(165,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[163]) ).
fof(184,plain,
! [X1,X2] :
( ~ strict_latt_str(X2)
| ~ latt_str(X2)
| ( ( X2 != boole_lattice(X1)
| ( the_carrier(X2) = powerset(X1)
& ! [X3] :
( ~ element(X3,powerset(X1))
| ! [X4] :
( ~ element(X4,powerset(X1))
| ( apply_binary(the_L_join(X2),X3,X4) = subset_union2(X1,X3,X4)
& apply_binary(the_L_meet(X2),X3,X4) = subset_intersection2(X1,X3,X4) ) ) ) ) )
& ( the_carrier(X2) != powerset(X1)
| ? [X3] :
( element(X3,powerset(X1))
& ? [X4] :
( element(X4,powerset(X1))
& ( apply_binary(the_L_join(X2),X3,X4) != subset_union2(X1,X3,X4)
| apply_binary(the_L_meet(X2),X3,X4) != subset_intersection2(X1,X3,X4) ) ) )
| X2 = boole_lattice(X1) ) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(185,plain,
! [X5,X6] :
( ~ strict_latt_str(X6)
| ~ latt_str(X6)
| ( ( X6 != boole_lattice(X5)
| ( the_carrier(X6) = powerset(X5)
& ! [X7] :
( ~ element(X7,powerset(X5))
| ! [X8] :
( ~ element(X8,powerset(X5))
| ( apply_binary(the_L_join(X6),X7,X8) = subset_union2(X5,X7,X8)
& apply_binary(the_L_meet(X6),X7,X8) = subset_intersection2(X5,X7,X8) ) ) ) ) )
& ( the_carrier(X6) != powerset(X5)
| ? [X9] :
( element(X9,powerset(X5))
& ? [X10] :
( element(X10,powerset(X5))
& ( apply_binary(the_L_join(X6),X9,X10) != subset_union2(X5,X9,X10)
| apply_binary(the_L_meet(X6),X9,X10) != subset_intersection2(X5,X9,X10) ) ) )
| X6 = boole_lattice(X5) ) ) ),
inference(variable_rename,[status(thm)],[184]) ).
fof(186,plain,
! [X5,X6] :
( ~ strict_latt_str(X6)
| ~ latt_str(X6)
| ( ( X6 != boole_lattice(X5)
| ( the_carrier(X6) = powerset(X5)
& ! [X7] :
( ~ element(X7,powerset(X5))
| ! [X8] :
( ~ element(X8,powerset(X5))
| ( apply_binary(the_L_join(X6),X7,X8) = subset_union2(X5,X7,X8)
& apply_binary(the_L_meet(X6),X7,X8) = subset_intersection2(X5,X7,X8) ) ) ) ) )
& ( the_carrier(X6) != powerset(X5)
| ( element(esk3_2(X5,X6),powerset(X5))
& element(esk4_2(X5,X6),powerset(X5))
& ( apply_binary(the_L_join(X6),esk3_2(X5,X6),esk4_2(X5,X6)) != subset_union2(X5,esk3_2(X5,X6),esk4_2(X5,X6))
| apply_binary(the_L_meet(X6),esk3_2(X5,X6),esk4_2(X5,X6)) != subset_intersection2(X5,esk3_2(X5,X6),esk4_2(X5,X6)) ) )
| X6 = boole_lattice(X5) ) ) ),
inference(skolemize,[status(esa)],[185]) ).
fof(187,plain,
! [X5,X6,X7,X8] :
( ( ( ( ( ~ element(X8,powerset(X5))
| ( apply_binary(the_L_join(X6),X7,X8) = subset_union2(X5,X7,X8)
& apply_binary(the_L_meet(X6),X7,X8) = subset_intersection2(X5,X7,X8) )
| ~ element(X7,powerset(X5)) )
& the_carrier(X6) = powerset(X5) )
| X6 != boole_lattice(X5) )
& ( the_carrier(X6) != powerset(X5)
| ( element(esk3_2(X5,X6),powerset(X5))
& element(esk4_2(X5,X6),powerset(X5))
& ( apply_binary(the_L_join(X6),esk3_2(X5,X6),esk4_2(X5,X6)) != subset_union2(X5,esk3_2(X5,X6),esk4_2(X5,X6))
| apply_binary(the_L_meet(X6),esk3_2(X5,X6),esk4_2(X5,X6)) != subset_intersection2(X5,esk3_2(X5,X6),esk4_2(X5,X6)) ) )
| X6 = boole_lattice(X5) ) )
| ~ strict_latt_str(X6)
| ~ latt_str(X6) ),
inference(shift_quantors,[status(thm)],[186]) ).
fof(188,plain,
! [X5,X6,X7,X8] :
( ( apply_binary(the_L_join(X6),X7,X8) = subset_union2(X5,X7,X8)
| ~ element(X8,powerset(X5))
| ~ element(X7,powerset(X5))
| X6 != boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( apply_binary(the_L_meet(X6),X7,X8) = subset_intersection2(X5,X7,X8)
| ~ element(X8,powerset(X5))
| ~ element(X7,powerset(X5))
| X6 != boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( the_carrier(X6) = powerset(X5)
| X6 != boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( element(esk3_2(X5,X6),powerset(X5))
| the_carrier(X6) != powerset(X5)
| X6 = boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( element(esk4_2(X5,X6),powerset(X5))
| the_carrier(X6) != powerset(X5)
| X6 = boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) )
& ( apply_binary(the_L_join(X6),esk3_2(X5,X6),esk4_2(X5,X6)) != subset_union2(X5,esk3_2(X5,X6),esk4_2(X5,X6))
| apply_binary(the_L_meet(X6),esk3_2(X5,X6),esk4_2(X5,X6)) != subset_intersection2(X5,esk3_2(X5,X6),esk4_2(X5,X6))
| the_carrier(X6) != powerset(X5)
| X6 = boole_lattice(X5)
| ~ strict_latt_str(X6)
| ~ latt_str(X6) ) ),
inference(distribute,[status(thm)],[187]) ).
cnf(192,plain,
( the_carrier(X1) = powerset(X2)
| ~ latt_str(X1)
| ~ strict_latt_str(X1)
| X1 != boole_lattice(X2) ),
inference(split_conjunct,[status(thm)],[188]) ).
fof(199,plain,
! [X1] :
( empty_carrier(X1)
| ~ meet_semilatt_str(X1)
| ( ( ~ lower_bounded_semilattstr(X1)
| ? [X2] :
( element(X2,the_carrier(X1))
& ! [X3] :
( ~ element(X3,the_carrier(X1))
| ( meet(X1,X2,X3) = X2
& meet(X1,X3,X2) = X2 ) ) ) )
& ( ! [X2] :
( ~ element(X2,the_carrier(X1))
| ? [X3] :
( element(X3,the_carrier(X1))
& ( meet(X1,X2,X3) != X2
| meet(X1,X3,X2) != X2 ) ) )
| lower_bounded_semilattstr(X1) ) ) ),
inference(fof_nnf,[status(thm)],[111]) ).
fof(200,plain,
! [X4] :
( empty_carrier(X4)
| ~ meet_semilatt_str(X4)
| ( ( ~ lower_bounded_semilattstr(X4)
| ? [X5] :
( element(X5,the_carrier(X4))
& ! [X6] :
( ~ element(X6,the_carrier(X4))
| ( meet(X4,X5,X6) = X5
& meet(X4,X6,X5) = X5 ) ) ) )
& ( ! [X7] :
( ~ element(X7,the_carrier(X4))
| ? [X8] :
( element(X8,the_carrier(X4))
& ( meet(X4,X7,X8) != X7
| meet(X4,X8,X7) != X7 ) ) )
| lower_bounded_semilattstr(X4) ) ) ),
inference(variable_rename,[status(thm)],[199]) ).
fof(201,plain,
! [X4] :
( empty_carrier(X4)
| ~ meet_semilatt_str(X4)
| ( ( ~ lower_bounded_semilattstr(X4)
| ( element(esk5_1(X4),the_carrier(X4))
& ! [X6] :
( ~ element(X6,the_carrier(X4))
| ( meet(X4,esk5_1(X4),X6) = esk5_1(X4)
& meet(X4,X6,esk5_1(X4)) = esk5_1(X4) ) ) ) )
& ( ! [X7] :
( ~ element(X7,the_carrier(X4))
| ( element(esk6_2(X4,X7),the_carrier(X4))
& ( meet(X4,X7,esk6_2(X4,X7)) != X7
| meet(X4,esk6_2(X4,X7),X7) != X7 ) ) )
| lower_bounded_semilattstr(X4) ) ) ),
inference(skolemize,[status(esa)],[200]) ).
fof(202,plain,
! [X4,X6,X7] :
( ( ( ~ element(X7,the_carrier(X4))
| ( element(esk6_2(X4,X7),the_carrier(X4))
& ( meet(X4,X7,esk6_2(X4,X7)) != X7
| meet(X4,esk6_2(X4,X7),X7) != X7 ) )
| lower_bounded_semilattstr(X4) )
& ( ( ( ~ element(X6,the_carrier(X4))
| ( meet(X4,esk5_1(X4),X6) = esk5_1(X4)
& meet(X4,X6,esk5_1(X4)) = esk5_1(X4) ) )
& element(esk5_1(X4),the_carrier(X4)) )
| ~ lower_bounded_semilattstr(X4) ) )
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) ),
inference(shift_quantors,[status(thm)],[201]) ).
fof(203,plain,
! [X4,X6,X7] :
( ( element(esk6_2(X4,X7),the_carrier(X4))
| ~ element(X7,the_carrier(X4))
| lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) )
& ( meet(X4,X7,esk6_2(X4,X7)) != X7
| meet(X4,esk6_2(X4,X7),X7) != X7
| ~ element(X7,the_carrier(X4))
| lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) )
& ( meet(X4,esk5_1(X4),X6) = esk5_1(X4)
| ~ element(X6,the_carrier(X4))
| ~ lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) )
& ( meet(X4,X6,esk5_1(X4)) = esk5_1(X4)
| ~ element(X6,the_carrier(X4))
| ~ lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) )
& ( element(esk5_1(X4),the_carrier(X4))
| ~ lower_bounded_semilattstr(X4)
| empty_carrier(X4)
| ~ meet_semilatt_str(X4) ) ),
inference(distribute,[status(thm)],[202]) ).
cnf(207,plain,
( empty_carrier(X1)
| lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| meet(X1,esk6_2(X1,X2),X2) != X2
| meet(X1,X2,esk6_2(X1,X2)) != X2 ),
inference(split_conjunct,[status(thm)],[203]) ).
cnf(208,plain,
( empty_carrier(X1)
| lower_bounded_semilattstr(X1)
| element(esk6_2(X1,X2),the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[203]) ).
fof(257,plain,
! [X1] :
( empty_carrier(X1)
| ~ meet_semilatt_str(X1)
| element(bottom_of_semilattstr(X1),the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[115]) ).
fof(258,plain,
! [X2] :
( empty_carrier(X2)
| ~ meet_semilatt_str(X2)
| element(bottom_of_semilattstr(X2),the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[257]) ).
cnf(259,plain,
( element(bottom_of_semilattstr(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[258]) ).
fof(308,plain,
! [X1,X2] :
( ~ element(X2,the_carrier(boole_lattice(X1)))
| ! [X3] :
( ~ element(X3,the_carrier(boole_lattice(X1)))
| ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[50]) ).
fof(309,plain,
! [X4,X5] :
( ~ element(X5,the_carrier(boole_lattice(X4)))
| ! [X6] :
( ~ element(X6,the_carrier(boole_lattice(X4)))
| ( join(boole_lattice(X4),X5,X6) = set_union2(X5,X6)
& meet(boole_lattice(X4),X5,X6) = set_intersection2(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[308]) ).
fof(310,plain,
! [X4,X5,X6] :
( ~ element(X6,the_carrier(boole_lattice(X4)))
| ( join(boole_lattice(X4),X5,X6) = set_union2(X5,X6)
& meet(boole_lattice(X4),X5,X6) = set_intersection2(X5,X6) )
| ~ element(X5,the_carrier(boole_lattice(X4))) ),
inference(shift_quantors,[status(thm)],[309]) ).
fof(311,plain,
! [X4,X5,X6] :
( ( join(boole_lattice(X4),X5,X6) = set_union2(X5,X6)
| ~ element(X6,the_carrier(boole_lattice(X4)))
| ~ element(X5,the_carrier(boole_lattice(X4))) )
& ( meet(boole_lattice(X4),X5,X6) = set_intersection2(X5,X6)
| ~ element(X6,the_carrier(boole_lattice(X4)))
| ~ element(X5,the_carrier(boole_lattice(X4))) ) ),
inference(distribute,[status(thm)],[310]) ).
cnf(312,plain,
( meet(boole_lattice(X2),X1,X3) = set_intersection2(X1,X3)
| ~ element(X1,the_carrier(boole_lattice(X2)))
| ~ element(X3,the_carrier(boole_lattice(X2))) ),
inference(split_conjunct,[status(thm)],[311]) ).
fof(317,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[53]) ).
cnf(318,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[317]) ).
fof(379,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)) ),
inference(variable_rename,[status(thm)],[127]) ).
cnf(387,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[379]) ).
cnf(388,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[379]) ).
fof(395,plain,
! [X2] :
( strict_latt_str(boole_lattice(X2))
& latt_str(boole_lattice(X2)) ),
inference(variable_rename,[status(thm)],[74]) ).
cnf(396,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[395]) ).
fof(398,negated_conjecture,
? [X1] :
( ~ lower_bounded_semilattstr(boole_lattice(X1))
| bottom_of_semilattstr(boole_lattice(X1)) != empty_set ),
inference(fof_nnf,[status(thm)],[103]) ).
fof(399,negated_conjecture,
? [X2] :
( ~ lower_bounded_semilattstr(boole_lattice(X2))
| bottom_of_semilattstr(boole_lattice(X2)) != empty_set ),
inference(variable_rename,[status(thm)],[398]) ).
fof(400,negated_conjecture,
( ~ lower_bounded_semilattstr(boole_lattice(esk13_0))
| bottom_of_semilattstr(boole_lattice(esk13_0)) != empty_set ),
inference(skolemize,[status(esa)],[399]) ).
cnf(401,negated_conjecture,
( bottom_of_semilattstr(boole_lattice(esk13_0)) != empty_set
| ~ lower_bounded_semilattstr(boole_lattice(esk13_0)) ),
inference(split_conjunct,[status(thm)],[400]) ).
fof(402,plain,
! [X3] :
? [X4] :
( element(X4,powerset(X3))
& empty(X4) ),
inference(variable_rename,[status(thm)],[76]) ).
fof(403,plain,
! [X3] :
( element(esk14_1(X3),powerset(X3))
& empty(esk14_1(X3)) ),
inference(skolemize,[status(esa)],[402]) ).
cnf(404,plain,
empty(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[403]) ).
cnf(405,plain,
element(esk14_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[403]) ).
fof(488,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[97]) ).
cnf(489,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[488]) ).
fof(496,plain,
! [X1] :
( ~ empty(X1)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[101]) ).
fof(497,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[496]) ).
cnf(498,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[497]) ).
cnf(508,plain,
empty_set = esk14_1(X1),
inference(spm,[status(thm)],[498,404,theory(equality)]) ).
cnf(513,plain,
meet_semilatt_str(boole_lattice(X1)),
inference(spm,[status(thm)],[165,396,theory(equality)]) ).
cnf(517,plain,
set_intersection2(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[318,489,theory(equality)]) ).
cnf(606,plain,
( powerset(X1) = the_carrier(boole_lattice(X1))
| ~ strict_latt_str(boole_lattice(X1))
| ~ latt_str(boole_lattice(X1)) ),
inference(er,[status(thm)],[192,theory(equality)]) ).
cnf(607,plain,
( powerset(X1) = the_carrier(boole_lattice(X1))
| $false
| ~ latt_str(boole_lattice(X1)) ),
inference(rw,[status(thm)],[606,387,theory(equality)]) ).
cnf(608,plain,
( powerset(X1) = the_carrier(boole_lattice(X1))
| $false
| $false ),
inference(rw,[status(thm)],[607,396,theory(equality)]) ).
cnf(609,plain,
powerset(X1) = the_carrier(boole_lattice(X1)),
inference(cn,[status(thm)],[608,theory(equality)]) ).
cnf(698,plain,
( meet(X1,X2,bottom_of_semilattstr(X1)) = bottom_of_semilattstr(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(bottom_of_semilattstr(X1),the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(er,[status(thm)],[146,theory(equality)]) ).
cnf(741,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[405,508,theory(equality)]) ).
cnf(759,plain,
( element(bottom_of_semilattstr(boole_lattice(X1)),powerset(X1))
| empty_carrier(boole_lattice(X1))
| ~ meet_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[259,609,theory(equality)]) ).
cnf(771,plain,
( element(esk6_2(boole_lattice(X1),X2),powerset(X1))
| lower_bounded_semilattstr(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| ~ element(X2,powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[208,609,theory(equality)]) ).
cnf(784,plain,
( meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,the_carrier(boole_lattice(X1))) ),
inference(rw,[status(thm)],[312,609,theory(equality)]) ).
cnf(785,plain,
( meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(rw,[status(thm)],[784,609,theory(equality)]) ).
cnf(786,plain,
( element(bottom_of_semilattstr(boole_lattice(X1)),powerset(X1))
| empty_carrier(boole_lattice(X1))
| $false ),
inference(rw,[status(thm)],[759,513,theory(equality)]) ).
cnf(787,plain,
( element(bottom_of_semilattstr(boole_lattice(X1)),powerset(X1))
| empty_carrier(boole_lattice(X1)) ),
inference(cn,[status(thm)],[786,theory(equality)]) ).
cnf(788,plain,
element(bottom_of_semilattstr(boole_lattice(X1)),powerset(X1)),
inference(sr,[status(thm)],[787,388,theory(equality)]) ).
cnf(814,plain,
( element(esk6_2(boole_lattice(X1),X2),powerset(X1))
| lower_bounded_semilattstr(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| ~ element(X2,powerset(X1))
| $false ),
inference(rw,[status(thm)],[771,513,theory(equality)]) ).
cnf(815,plain,
( element(esk6_2(boole_lattice(X1),X2),powerset(X1))
| lower_bounded_semilattstr(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| ~ element(X2,powerset(X1)) ),
inference(cn,[status(thm)],[814,theory(equality)]) ).
cnf(816,plain,
( element(esk6_2(boole_lattice(X1),X2),powerset(X1))
| lower_bounded_semilattstr(boole_lattice(X1))
| ~ element(X2,powerset(X1)) ),
inference(sr,[status(thm)],[815,388,theory(equality)]) ).
cnf(878,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| meet(boole_lattice(X1),X2,esk6_2(boole_lattice(X1),X2)) != X2
| set_intersection2(esk6_2(boole_lattice(X1),X2),X2) != X2
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ meet_semilatt_str(boole_lattice(X1))
| ~ element(X2,powerset(X1))
| ~ element(esk6_2(boole_lattice(X1),X2),powerset(X1)) ),
inference(spm,[status(thm)],[207,785,theory(equality)]) ).
cnf(894,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| meet(boole_lattice(X1),X2,esk6_2(boole_lattice(X1),X2)) != X2
| set_intersection2(X2,esk6_2(boole_lattice(X1),X2)) != X2
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ meet_semilatt_str(boole_lattice(X1))
| ~ element(X2,powerset(X1))
| ~ element(esk6_2(boole_lattice(X1),X2),powerset(X1)) ),
inference(rw,[status(thm)],[878,489,theory(equality)]) ).
cnf(895,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| meet(boole_lattice(X1),X2,esk6_2(boole_lattice(X1),X2)) != X2
| set_intersection2(X2,esk6_2(boole_lattice(X1),X2)) != X2
| ~ element(X2,powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1))
| ~ element(X2,powerset(X1))
| ~ element(esk6_2(boole_lattice(X1),X2),powerset(X1)) ),
inference(rw,[status(thm)],[894,609,theory(equality)]) ).
cnf(896,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| meet(boole_lattice(X1),X2,esk6_2(boole_lattice(X1),X2)) != X2
| set_intersection2(X2,esk6_2(boole_lattice(X1),X2)) != X2
| ~ element(X2,powerset(X1))
| $false
| ~ element(X2,powerset(X1))
| ~ element(esk6_2(boole_lattice(X1),X2),powerset(X1)) ),
inference(rw,[status(thm)],[895,513,theory(equality)]) ).
cnf(897,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| empty_carrier(boole_lattice(X1))
| meet(boole_lattice(X1),X2,esk6_2(boole_lattice(X1),X2)) != X2
| set_intersection2(X2,esk6_2(boole_lattice(X1),X2)) != X2
| ~ element(X2,powerset(X1))
| ~ element(esk6_2(boole_lattice(X1),X2),powerset(X1)) ),
inference(cn,[status(thm)],[896,theory(equality)]) ).
cnf(898,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| meet(boole_lattice(X1),X2,esk6_2(boole_lattice(X1),X2)) != X2
| set_intersection2(X2,esk6_2(boole_lattice(X1),X2)) != X2
| ~ element(X2,powerset(X1))
| ~ element(esk6_2(boole_lattice(X1),X2),powerset(X1)) ),
inference(sr,[status(thm)],[897,388,theory(equality)]) ).
cnf(2503,plain,
( meet(X1,X2,bottom_of_semilattstr(X1)) = bottom_of_semilattstr(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ lower_bounded_semilattstr(X1)
| ~ meet_semilatt_str(X1) ),
inference(csr,[status(thm)],[698,259]) ).
cnf(2507,plain,
( bottom_of_semilattstr(boole_lattice(X1)) = set_intersection2(X2,bottom_of_semilattstr(boole_lattice(X1)))
| empty_carrier(boole_lattice(X1))
| ~ element(bottom_of_semilattstr(boole_lattice(X1)),powerset(X1))
| ~ element(X2,powerset(X1))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ lower_bounded_semilattstr(boole_lattice(X1))
| ~ meet_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[785,2503,theory(equality)]) ).
cnf(2514,plain,
( bottom_of_semilattstr(boole_lattice(X1)) = set_intersection2(X2,bottom_of_semilattstr(boole_lattice(X1)))
| empty_carrier(boole_lattice(X1))
| $false
| ~ element(X2,powerset(X1))
| ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ lower_bounded_semilattstr(boole_lattice(X1))
| ~ meet_semilatt_str(boole_lattice(X1)) ),
inference(rw,[status(thm)],[2507,788,theory(equality)]) ).
cnf(2515,plain,
( bottom_of_semilattstr(boole_lattice(X1)) = set_intersection2(X2,bottom_of_semilattstr(boole_lattice(X1)))
| empty_carrier(boole_lattice(X1))
| $false
| ~ element(X2,powerset(X1))
| ~ element(X2,powerset(X1))
| ~ lower_bounded_semilattstr(boole_lattice(X1))
| ~ meet_semilatt_str(boole_lattice(X1)) ),
inference(rw,[status(thm)],[2514,609,theory(equality)]) ).
cnf(2516,plain,
( bottom_of_semilattstr(boole_lattice(X1)) = set_intersection2(X2,bottom_of_semilattstr(boole_lattice(X1)))
| empty_carrier(boole_lattice(X1))
| $false
| ~ element(X2,powerset(X1))
| ~ element(X2,powerset(X1))
| ~ lower_bounded_semilattstr(boole_lattice(X1))
| $false ),
inference(rw,[status(thm)],[2515,513,theory(equality)]) ).
cnf(2517,plain,
( bottom_of_semilattstr(boole_lattice(X1)) = set_intersection2(X2,bottom_of_semilattstr(boole_lattice(X1)))
| empty_carrier(boole_lattice(X1))
| ~ element(X2,powerset(X1))
| ~ lower_bounded_semilattstr(boole_lattice(X1)) ),
inference(cn,[status(thm)],[2516,theory(equality)]) ).
cnf(2518,plain,
( set_intersection2(X2,bottom_of_semilattstr(boole_lattice(X1))) = bottom_of_semilattstr(boole_lattice(X1))
| ~ element(X2,powerset(X1))
| ~ lower_bounded_semilattstr(boole_lattice(X1)) ),
inference(sr,[status(thm)],[2517,388,theory(equality)]) ).
cnf(2543,plain,
( bottom_of_semilattstr(boole_lattice(X1)) = empty_set
| ~ element(empty_set,powerset(X1))
| ~ lower_bounded_semilattstr(boole_lattice(X1)) ),
inference(spm,[status(thm)],[517,2518,theory(equality)]) ).
cnf(2555,plain,
( bottom_of_semilattstr(boole_lattice(X1)) = empty_set
| $false
| ~ lower_bounded_semilattstr(boole_lattice(X1)) ),
inference(rw,[status(thm)],[2543,741,theory(equality)]) ).
cnf(2556,plain,
( bottom_of_semilattstr(boole_lattice(X1)) = empty_set
| ~ lower_bounded_semilattstr(boole_lattice(X1)) ),
inference(cn,[status(thm)],[2555,theory(equality)]) ).
cnf(2560,negated_conjecture,
~ lower_bounded_semilattstr(boole_lattice(esk13_0)),
inference(spm,[status(thm)],[401,2556,theory(equality)]) ).
cnf(4623,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| meet(boole_lattice(X1),X2,esk6_2(boole_lattice(X1),X2)) != X2
| set_intersection2(X2,esk6_2(boole_lattice(X1),X2)) != X2
| ~ element(X2,powerset(X1)) ),
inference(csr,[status(thm)],[898,816]) ).
cnf(4625,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| set_intersection2(X2,esk6_2(boole_lattice(X1),X2)) != X2
| ~ element(X2,powerset(X1))
| ~ element(esk6_2(boole_lattice(X1),X2),powerset(X1)) ),
inference(spm,[status(thm)],[4623,785,theory(equality)]) ).
cnf(88177,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| set_intersection2(X2,esk6_2(boole_lattice(X1),X2)) != X2
| ~ element(X2,powerset(X1)) ),
inference(csr,[status(thm)],[4625,816]) ).
cnf(88178,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| ~ element(empty_set,powerset(X1)) ),
inference(spm,[status(thm)],[88177,517,theory(equality)]) ).
cnf(88243,plain,
( lower_bounded_semilattstr(boole_lattice(X1))
| $false ),
inference(rw,[status(thm)],[88178,741,theory(equality)]) ).
cnf(88244,plain,
lower_bounded_semilattstr(boole_lattice(X1)),
inference(cn,[status(thm)],[88243,theory(equality)]) ).
cnf(88245,negated_conjecture,
$false,
inference(rw,[status(thm)],[2560,88244,theory(equality)]) ).
cnf(88246,negated_conjecture,
$false,
inference(cn,[status(thm)],[88245,theory(equality)]) ).
cnf(88247,negated_conjecture,
$false,
88246,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU345+1.p
% --creating new selector for []
% -running prover on /tmp/tmpAHuU3f/sel_SEU345+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU345+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU345+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU345+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
%
%------------------------------------------------------------------------------