%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU342+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 07:36:13 EST 2010
% Result : Theorem 1.16s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 10
% Syntax : Number of formulae : 127 ( 17 unt; 0 def)
% Number of atoms : 570 ( 78 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 682 ( 239 ~; 344 |; 74 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 200 ( 9 sgn 88 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',t33_zfmisc_1) ).
fof(6,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',redefinition_k1_domain_1) ).
fof(9,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',dt_l3_lattices) ).
fof(11,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',fc1_struct_0) ).
fof(14,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',t32_filter_1) ).
fof(15,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',commutativity_k2_tarski) ).
fof(27,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ( in(X1,a_1_0_filter_1(X2))
<=> ? [X3,X4] :
( element(X3,the_carrier(X2))
& element(X4,the_carrier(X2))
& X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
& below_refl(X2,X3,X4) ) ) ),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',fraenkel_a_1_0_filter_1) ).
fof(31,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',dt_l1_lattices) ).
fof(33,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation_of_lattice(X1) = a_1_0_filter_1(X1) ),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',d8_filter_1) ).
fof(36,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpzFlwtE/sel_SEU342+1.p_1',d5_tarski) ).
fof(45,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[14]) ).
fof(47,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).
fof(49,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(51,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[45,theory(equality)]) ).
fof(55,plain,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ( in(X1,a_1_0_filter_1(X2))
<=> ? [X3,X4] :
( element(X3,the_carrier(X2))
& element(X4,the_carrier(X2))
& X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
& below_refl(X2,X3,X4) ) ) ),
inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).
fof(58,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation_of_lattice(X1) = a_1_0_filter_1(X1) ),
inference(fof_simplification,[status(thm)],[33,theory(equality)]) ).
fof(73,plain,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) != ordered_pair(X3,X4)
| ( X1 = X3
& X2 = X4 ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(74,plain,
! [X5,X6,X7,X8] :
( ordered_pair(X5,X6) != ordered_pair(X7,X8)
| ( X5 = X7
& X6 = X8 ) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,plain,
! [X5,X6,X7,X8] :
( ( X5 = X7
| ordered_pair(X5,X6) != ordered_pair(X7,X8) )
& ( X6 = X8
| ordered_pair(X5,X6) != ordered_pair(X7,X8) ) ),
inference(distribute,[status(thm)],[74]) ).
cnf(76,plain,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(77,plain,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(78,plain,
! [X1,X2,X3,X4] :
( empty(X1)
| empty(X2)
| ~ element(X3,X1)
| ~ element(X4,X2)
| ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(79,plain,
! [X5,X6,X7,X8] :
( empty(X5)
| empty(X6)
| ~ element(X7,X5)
| ~ element(X8,X6)
| ordered_pair_as_product_element(X5,X6,X7,X8) = ordered_pair(X7,X8) ),
inference(variable_rename,[status(thm)],[78]) ).
cnf(80,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4)
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[79]) ).
fof(85,plain,
! [X1] :
( ~ latt_str(X1)
| ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(86,plain,
! [X2] :
( ~ latt_str(X2)
| ( meet_semilatt_str(X2)
& join_semilatt_str(X2) ) ),
inference(variable_rename,[status(thm)],[85]) ).
fof(87,plain,
! [X2] :
( ( meet_semilatt_str(X2)
| ~ latt_str(X2) )
& ( join_semilatt_str(X2)
| ~ latt_str(X2) ) ),
inference(distribute,[status(thm)],[86]) ).
cnf(89,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[87]) ).
fof(93,plain,
! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[49]) ).
fof(94,plain,
! [X2] :
( empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ empty(the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[93]) ).
cnf(95,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[94]) ).
fof(104,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& ? [X2] :
( element(X2,the_carrier(X1))
& ? [X3] :
( element(X3,the_carrier(X1))
& ( ~ in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| ~ below_refl(X1,X2,X3) )
& ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| below_refl(X1,X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[51]) ).
fof(105,negated_conjecture,
? [X4] :
( ~ empty_carrier(X4)
& lattice(X4)
& latt_str(X4)
& ? [X5] :
( element(X5,the_carrier(X4))
& ? [X6] :
( element(X6,the_carrier(X4))
& ( ~ in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4))
| ~ below_refl(X4,X5,X6) )
& ( in(ordered_pair_as_product_element(the_carrier(X4),the_carrier(X4),X5,X6),relation_of_lattice(X4))
| below_refl(X4,X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[104]) ).
fof(106,negated_conjecture,
( ~ empty_carrier(esk4_0)
& lattice(esk4_0)
& latt_str(esk4_0)
& element(esk5_0,the_carrier(esk4_0))
& element(esk6_0,the_carrier(esk4_0))
& ( ~ in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),relation_of_lattice(esk4_0))
| ~ below_refl(esk4_0,esk5_0,esk6_0) )
& ( in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),relation_of_lattice(esk4_0))
| below_refl(esk4_0,esk5_0,esk6_0) ) ),
inference(skolemize,[status(esa)],[105]) ).
cnf(107,negated_conjecture,
( below_refl(esk4_0,esk5_0,esk6_0)
| in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),relation_of_lattice(esk4_0)) ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(108,negated_conjecture,
( ~ below_refl(esk4_0,esk5_0,esk6_0)
| ~ in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),relation_of_lattice(esk4_0)) ),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(109,negated_conjecture,
element(esk6_0,the_carrier(esk4_0)),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(110,negated_conjecture,
element(esk5_0,the_carrier(esk4_0)),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(111,negated_conjecture,
latt_str(esk4_0),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(112,negated_conjecture,
lattice(esk4_0),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(113,negated_conjecture,
~ empty_carrier(esk4_0),
inference(split_conjunct,[status(thm)],[106]) ).
fof(114,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[15]) ).
cnf(115,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[114]) ).
fof(143,plain,
! [X1,X2] :
( empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2)
| ( ( ~ in(X1,a_1_0_filter_1(X2))
| ? [X3,X4] :
( element(X3,the_carrier(X2))
& element(X4,the_carrier(X2))
& X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
& below_refl(X2,X3,X4) ) )
& ( ! [X3,X4] :
( ~ element(X3,the_carrier(X2))
| ~ element(X4,the_carrier(X2))
| X1 != ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
| ~ below_refl(X2,X3,X4) )
| in(X1,a_1_0_filter_1(X2)) ) ) ),
inference(fof_nnf,[status(thm)],[55]) ).
fof(144,plain,
! [X5,X6] :
( empty_carrier(X6)
| ~ lattice(X6)
| ~ latt_str(X6)
| ( ( ~ in(X5,a_1_0_filter_1(X6))
| ? [X7,X8] :
( element(X7,the_carrier(X6))
& element(X8,the_carrier(X6))
& X5 = ordered_pair_as_product_element(the_carrier(X6),the_carrier(X6),X7,X8)
& below_refl(X6,X7,X8) ) )
& ( ! [X9,X10] :
( ~ element(X9,the_carrier(X6))
| ~ element(X10,the_carrier(X6))
| X5 != ordered_pair_as_product_element(the_carrier(X6),the_carrier(X6),X9,X10)
| ~ below_refl(X6,X9,X10) )
| in(X5,a_1_0_filter_1(X6)) ) ) ),
inference(variable_rename,[status(thm)],[143]) ).
fof(145,plain,
! [X5,X6] :
( empty_carrier(X6)
| ~ lattice(X6)
| ~ latt_str(X6)
| ( ( ~ in(X5,a_1_0_filter_1(X6))
| ( element(esk10_2(X5,X6),the_carrier(X6))
& element(esk11_2(X5,X6),the_carrier(X6))
& X5 = ordered_pair_as_product_element(the_carrier(X6),the_carrier(X6),esk10_2(X5,X6),esk11_2(X5,X6))
& below_refl(X6,esk10_2(X5,X6),esk11_2(X5,X6)) ) )
& ( ! [X9,X10] :
( ~ element(X9,the_carrier(X6))
| ~ element(X10,the_carrier(X6))
| X5 != ordered_pair_as_product_element(the_carrier(X6),the_carrier(X6),X9,X10)
| ~ below_refl(X6,X9,X10) )
| in(X5,a_1_0_filter_1(X6)) ) ) ),
inference(skolemize,[status(esa)],[144]) ).
fof(146,plain,
! [X5,X6,X9,X10] :
( ( ( ~ element(X9,the_carrier(X6))
| ~ element(X10,the_carrier(X6))
| X5 != ordered_pair_as_product_element(the_carrier(X6),the_carrier(X6),X9,X10)
| ~ below_refl(X6,X9,X10)
| in(X5,a_1_0_filter_1(X6)) )
& ( ~ in(X5,a_1_0_filter_1(X6))
| ( element(esk10_2(X5,X6),the_carrier(X6))
& element(esk11_2(X5,X6),the_carrier(X6))
& X5 = ordered_pair_as_product_element(the_carrier(X6),the_carrier(X6),esk10_2(X5,X6),esk11_2(X5,X6))
& below_refl(X6,esk10_2(X5,X6),esk11_2(X5,X6)) ) ) )
| empty_carrier(X6)
| ~ lattice(X6)
| ~ latt_str(X6) ),
inference(shift_quantors,[status(thm)],[145]) ).
fof(147,plain,
! [X5,X6,X9,X10] :
( ( ~ element(X9,the_carrier(X6))
| ~ element(X10,the_carrier(X6))
| X5 != ordered_pair_as_product_element(the_carrier(X6),the_carrier(X6),X9,X10)
| ~ below_refl(X6,X9,X10)
| in(X5,a_1_0_filter_1(X6))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ latt_str(X6) )
& ( element(esk10_2(X5,X6),the_carrier(X6))
| ~ in(X5,a_1_0_filter_1(X6))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ latt_str(X6) )
& ( element(esk11_2(X5,X6),the_carrier(X6))
| ~ in(X5,a_1_0_filter_1(X6))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ latt_str(X6) )
& ( X5 = ordered_pair_as_product_element(the_carrier(X6),the_carrier(X6),esk10_2(X5,X6),esk11_2(X5,X6))
| ~ in(X5,a_1_0_filter_1(X6))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ latt_str(X6) )
& ( below_refl(X6,esk10_2(X5,X6),esk11_2(X5,X6))
| ~ in(X5,a_1_0_filter_1(X6))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ latt_str(X6) ) ),
inference(distribute,[status(thm)],[146]) ).
cnf(148,plain,
( empty_carrier(X1)
| below_refl(X1,esk10_2(X2,X1),esk11_2(X2,X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_1_0_filter_1(X1)) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(149,plain,
( empty_carrier(X1)
| X2 = ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),esk10_2(X2,X1),esk11_2(X2,X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_1_0_filter_1(X1)) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(150,plain,
( empty_carrier(X1)
| element(esk11_2(X2,X1),the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_1_0_filter_1(X1)) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(151,plain,
( empty_carrier(X1)
| element(esk10_2(X2,X1),the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_1_0_filter_1(X1)) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(152,plain,
( empty_carrier(X1)
| in(X2,a_1_0_filter_1(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ below_refl(X1,X3,X4)
| X2 != ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X3,X4)
| ~ element(X4,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[147]) ).
fof(160,plain,
! [X1] :
( ~ meet_semilatt_str(X1)
| one_sorted_str(X1) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(161,plain,
! [X2] :
( ~ meet_semilatt_str(X2)
| one_sorted_str(X2) ),
inference(variable_rename,[status(thm)],[160]) ).
cnf(162,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[161]) ).
fof(165,plain,
! [X1] :
( empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| relation_of_lattice(X1) = a_1_0_filter_1(X1) ),
inference(fof_nnf,[status(thm)],[58]) ).
fof(166,plain,
! [X2] :
( empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2)
| relation_of_lattice(X2) = a_1_0_filter_1(X2) ),
inference(variable_rename,[status(thm)],[165]) ).
cnf(167,plain,
( relation_of_lattice(X1) = a_1_0_filter_1(X1)
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[166]) ).
fof(170,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[36]) ).
cnf(171,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[170]) ).
cnf(206,plain,
( X2 = X4
| unordered_pair(unordered_pair(X1,X2),singleton(X1)) != unordered_pair(unordered_pair(X3,X4),singleton(X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[76,171,theory(equality)]),171,theory(equality)]),
[unfolding] ).
cnf(207,plain,
( X1 = X3
| unordered_pair(unordered_pair(X1,X2),singleton(X1)) != unordered_pair(unordered_pair(X3,X4),singleton(X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[77,171,theory(equality)]),171,theory(equality)]),
[unfolding] ).
cnf(208,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3))
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(rw,[status(thm)],[80,171,theory(equality)]),
[unfolding] ).
cnf(211,plain,
( one_sorted_str(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[162,89,theory(equality)]) ).
cnf(244,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0)
| ~ in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),a_1_0_filter_1(esk4_0))
| ~ lattice(esk4_0)
| ~ latt_str(esk4_0) ),
inference(spm,[status(thm)],[108,167,theory(equality)]) ).
cnf(246,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0)
| ~ in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),a_1_0_filter_1(esk4_0))
| $false
| ~ latt_str(esk4_0) ),
inference(rw,[status(thm)],[244,112,theory(equality)]) ).
cnf(247,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0)
| ~ in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),a_1_0_filter_1(esk4_0))
| $false
| $false ),
inference(rw,[status(thm)],[246,111,theory(equality)]) ).
cnf(248,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0)
| ~ in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),a_1_0_filter_1(esk4_0)) ),
inference(cn,[status(thm)],[247,theory(equality)]) ).
cnf(249,negated_conjecture,
( ~ below_refl(esk4_0,esk5_0,esk6_0)
| ~ in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),a_1_0_filter_1(esk4_0)) ),
inference(sr,[status(thm)],[248,113,theory(equality)]) ).
cnf(253,plain,
( X1 = X2
| unordered_pair(singleton(X3),unordered_pair(X3,X1)) != unordered_pair(unordered_pair(X4,X2),singleton(X4)) ),
inference(spm,[status(thm)],[206,115,theory(equality)]) ).
cnf(262,plain,
( X1 = X2
| unordered_pair(singleton(X1),unordered_pair(X1,X3)) != unordered_pair(unordered_pair(X2,X4),singleton(X2)) ),
inference(spm,[status(thm)],[207,115,theory(equality)]) ).
cnf(281,plain,
( empty_carrier(X1)
| in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),a_1_0_filter_1(X1))
| ~ lattice(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(er,[status(thm)],[152,theory(equality)]) ).
cnf(298,plain,
( unordered_pair(unordered_pair(esk10_2(X2,X1),esk11_2(X2,X1)),singleton(esk10_2(X2,X1))) = X2
| empty_carrier(X1)
| empty(the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_1_0_filter_1(X1))
| ~ element(esk11_2(X2,X1),the_carrier(X1))
| ~ element(esk10_2(X2,X1),the_carrier(X1)) ),
inference(spm,[status(thm)],[149,208,theory(equality)]) ).
cnf(301,plain,
( ordered_pair_as_product_element(X5,X6,X1,X2) = ordered_pair_as_product_element(X3,X4,X1,X2)
| empty(X3)
| empty(X4)
| empty(X5)
| empty(X6)
| ~ element(X2,X4)
| ~ element(X1,X3)
| ~ element(X2,X6)
| ~ element(X1,X5) ),
inference(spm,[status(thm)],[208,208,theory(equality)]) ).
cnf(303,plain,
( unordered_pair(singleton(esk10_2(X2,X1)),unordered_pair(esk10_2(X2,X1),esk11_2(X2,X1))) = X2
| empty_carrier(X1)
| empty(the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_1_0_filter_1(X1))
| ~ element(esk11_2(X2,X1),the_carrier(X1))
| ~ element(esk10_2(X2,X1),the_carrier(X1)) ),
inference(rw,[status(thm)],[298,115,theory(equality)]) ).
cnf(313,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[95,211,theory(equality)]) ).
cnf(474,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0)
| ~ lattice(esk4_0)
| ~ element(esk6_0,the_carrier(esk4_0))
| ~ element(esk5_0,the_carrier(esk4_0))
| ~ latt_str(esk4_0) ),
inference(spm,[status(thm)],[249,281,theory(equality)]) ).
cnf(475,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0)
| $false
| ~ element(esk6_0,the_carrier(esk4_0))
| ~ element(esk5_0,the_carrier(esk4_0))
| ~ latt_str(esk4_0) ),
inference(rw,[status(thm)],[474,112,theory(equality)]) ).
cnf(476,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0)
| $false
| $false
| ~ element(esk5_0,the_carrier(esk4_0))
| ~ latt_str(esk4_0) ),
inference(rw,[status(thm)],[475,109,theory(equality)]) ).
cnf(477,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0)
| $false
| $false
| $false
| ~ latt_str(esk4_0) ),
inference(rw,[status(thm)],[476,110,theory(equality)]) ).
cnf(478,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[477,111,theory(equality)]) ).
cnf(479,negated_conjecture,
( empty_carrier(esk4_0)
| ~ below_refl(esk4_0,esk5_0,esk6_0) ),
inference(cn,[status(thm)],[478,theory(equality)]) ).
cnf(480,negated_conjecture,
~ below_refl(esk4_0,esk5_0,esk6_0),
inference(sr,[status(thm)],[479,113,theory(equality)]) ).
cnf(507,negated_conjecture,
in(ordered_pair_as_product_element(the_carrier(esk4_0),the_carrier(esk4_0),esk5_0,esk6_0),relation_of_lattice(esk4_0)),
inference(sr,[status(thm)],[107,480,theory(equality)]) ).
cnf(1084,plain,
( unordered_pair(singleton(esk10_2(X2,X1)),unordered_pair(esk10_2(X2,X1),esk11_2(X2,X1))) = X2
| empty_carrier(X1)
| empty(the_carrier(X1))
| ~ lattice(X1)
| ~ element(esk11_2(X2,X1),the_carrier(X1))
| ~ latt_str(X1)
| ~ in(X2,a_1_0_filter_1(X1)) ),
inference(csr,[status(thm)],[303,151]) ).
cnf(1085,plain,
( unordered_pair(singleton(esk10_2(X2,X1)),unordered_pair(esk10_2(X2,X1),esk11_2(X2,X1))) = X2
| empty_carrier(X1)
| empty(the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_1_0_filter_1(X1)) ),
inference(csr,[status(thm)],[1084,150]) ).
cnf(1086,plain,
( unordered_pair(singleton(esk10_2(X2,X1)),unordered_pair(esk10_2(X2,X1),esk11_2(X2,X1))) = X2
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ in(X2,a_1_0_filter_1(X1)) ),
inference(csr,[status(thm)],[1085,313]) ).
cnf(1096,plain,
( esk11_2(X1,X2) = X3
| empty_carrier(X2)
| X1 != unordered_pair(unordered_pair(X4,X3),singleton(X4))
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ in(X1,a_1_0_filter_1(X2)) ),
inference(spm,[status(thm)],[253,1086,theory(equality)]) ).
cnf(1101,plain,
( esk10_2(X1,X2) = X3
| empty_carrier(X2)
| X1 != unordered_pair(unordered_pair(X3,X4),singleton(X3))
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ in(X1,a_1_0_filter_1(X2)) ),
inference(spm,[status(thm)],[262,1086,theory(equality)]) ).
cnf(1388,negated_conjecture,
( in(ordered_pair_as_product_element(X1,X2,esk5_0,esk6_0),relation_of_lattice(esk4_0))
| empty(the_carrier(esk4_0))
| empty(X2)
| empty(X1)
| ~ element(esk6_0,X2)
| ~ element(esk5_0,X1)
| ~ element(esk6_0,the_carrier(esk4_0))
| ~ element(esk5_0,the_carrier(esk4_0)) ),
inference(spm,[status(thm)],[507,301,theory(equality)]) ).
cnf(1452,negated_conjecture,
( in(ordered_pair_as_product_element(X1,X2,esk5_0,esk6_0),relation_of_lattice(esk4_0))
| empty(the_carrier(esk4_0))
| empty(X2)
| empty(X1)
| ~ element(esk6_0,X2)
| ~ element(esk5_0,X1)
| $false
| ~ element(esk5_0,the_carrier(esk4_0)) ),
inference(rw,[status(thm)],[1388,109,theory(equality)]) ).
cnf(1453,negated_conjecture,
( in(ordered_pair_as_product_element(X1,X2,esk5_0,esk6_0),relation_of_lattice(esk4_0))
| empty(the_carrier(esk4_0))
| empty(X2)
| empty(X1)
| ~ element(esk6_0,X2)
| ~ element(esk5_0,X1)
| $false
| $false ),
inference(rw,[status(thm)],[1452,110,theory(equality)]) ).
cnf(1454,negated_conjecture,
( in(ordered_pair_as_product_element(X1,X2,esk5_0,esk6_0),relation_of_lattice(esk4_0))
| empty(the_carrier(esk4_0))
| empty(X2)
| empty(X1)
| ~ element(esk6_0,X2)
| ~ element(esk5_0,X1) ),
inference(cn,[status(thm)],[1453,theory(equality)]) ).
cnf(1528,negated_conjecture,
( empty(the_carrier(esk4_0))
| empty(X1)
| empty(X2)
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),relation_of_lattice(esk4_0))
| ~ element(esk6_0,X2)
| ~ element(esk5_0,X1) ),
inference(spm,[status(thm)],[1454,208,theory(equality)]) ).
cnf(1750,negated_conjecture,
( empty(the_carrier(esk4_0))
| empty(X1)
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),relation_of_lattice(esk4_0))
| ~ element(esk5_0,X1) ),
inference(spm,[status(thm)],[1528,109,theory(equality)]) ).
cnf(1752,negated_conjecture,
( empty(the_carrier(esk4_0))
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),relation_of_lattice(esk4_0)) ),
inference(spm,[status(thm)],[1750,110,theory(equality)]) ).
cnf(1757,negated_conjecture,
( empty(the_carrier(esk4_0))
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0))
| empty_carrier(esk4_0)
| ~ lattice(esk4_0)
| ~ latt_str(esk4_0) ),
inference(spm,[status(thm)],[1752,167,theory(equality)]) ).
cnf(1760,negated_conjecture,
( empty(the_carrier(esk4_0))
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0))
| empty_carrier(esk4_0)
| $false
| ~ latt_str(esk4_0) ),
inference(rw,[status(thm)],[1757,112,theory(equality)]) ).
cnf(1761,negated_conjecture,
( empty(the_carrier(esk4_0))
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0))
| empty_carrier(esk4_0)
| $false
| $false ),
inference(rw,[status(thm)],[1760,111,theory(equality)]) ).
cnf(1762,negated_conjecture,
( empty(the_carrier(esk4_0))
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0))
| empty_carrier(esk4_0) ),
inference(cn,[status(thm)],[1761,theory(equality)]) ).
cnf(1763,negated_conjecture,
( empty(the_carrier(esk4_0))
| in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0)) ),
inference(sr,[status(thm)],[1762,113,theory(equality)]) ).
cnf(3549,plain,
( esk11_2(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) = X2
| empty_carrier(X3)
| ~ lattice(X3)
| ~ latt_str(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),a_1_0_filter_1(X3)) ),
inference(er,[status(thm)],[1096,theory(equality)]) ).
cnf(3565,plain,
( esk10_2(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) = X1
| empty_carrier(X3)
| ~ lattice(X3)
| ~ latt_str(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),a_1_0_filter_1(X3)) ),
inference(er,[status(thm)],[1101,theory(equality)]) ).
cnf(8496,negated_conjecture,
( esk11_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk6_0
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| ~ lattice(esk4_0)
| ~ latt_str(esk4_0) ),
inference(spm,[status(thm)],[3549,1763,theory(equality)]) ).
cnf(8506,negated_conjecture,
( esk11_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk6_0
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| $false
| ~ latt_str(esk4_0) ),
inference(rw,[status(thm)],[8496,112,theory(equality)]) ).
cnf(8507,negated_conjecture,
( esk11_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk6_0
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| $false
| $false ),
inference(rw,[status(thm)],[8506,111,theory(equality)]) ).
cnf(8508,negated_conjecture,
( esk11_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk6_0
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0)) ),
inference(cn,[status(thm)],[8507,theory(equality)]) ).
cnf(8509,negated_conjecture,
( esk11_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk6_0
| empty(the_carrier(esk4_0)) ),
inference(sr,[status(thm)],[8508,113,theory(equality)]) ).
cnf(8517,negated_conjecture,
( below_refl(esk4_0,esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0),esk6_0)
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| ~ lattice(esk4_0)
| ~ latt_str(esk4_0)
| ~ in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0)) ),
inference(spm,[status(thm)],[148,8509,theory(equality)]) ).
cnf(8533,negated_conjecture,
( below_refl(esk4_0,esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0),esk6_0)
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| $false
| ~ latt_str(esk4_0)
| ~ in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0)) ),
inference(rw,[status(thm)],[8517,112,theory(equality)]) ).
cnf(8534,negated_conjecture,
( below_refl(esk4_0,esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0),esk6_0)
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| $false
| $false
| ~ in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0)) ),
inference(rw,[status(thm)],[8533,111,theory(equality)]) ).
cnf(8535,negated_conjecture,
( below_refl(esk4_0,esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0),esk6_0)
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| ~ in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0)) ),
inference(cn,[status(thm)],[8534,theory(equality)]) ).
cnf(8536,negated_conjecture,
( below_refl(esk4_0,esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0),esk6_0)
| empty(the_carrier(esk4_0))
| ~ in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),a_1_0_filter_1(esk4_0)) ),
inference(sr,[status(thm)],[8535,113,theory(equality)]) ).
cnf(10135,negated_conjecture,
( below_refl(esk4_0,esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0),esk6_0)
| empty(the_carrier(esk4_0)) ),
inference(csr,[status(thm)],[8536,1763]) ).
cnf(11250,negated_conjecture,
( esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk5_0
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| ~ lattice(esk4_0)
| ~ latt_str(esk4_0) ),
inference(spm,[status(thm)],[3565,1763,theory(equality)]) ).
cnf(11260,negated_conjecture,
( esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk5_0
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| $false
| ~ latt_str(esk4_0) ),
inference(rw,[status(thm)],[11250,112,theory(equality)]) ).
cnf(11261,negated_conjecture,
( esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk5_0
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0))
| $false
| $false ),
inference(rw,[status(thm)],[11260,111,theory(equality)]) ).
cnf(11262,negated_conjecture,
( esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk5_0
| empty_carrier(esk4_0)
| empty(the_carrier(esk4_0)) ),
inference(cn,[status(thm)],[11261,theory(equality)]) ).
cnf(11263,negated_conjecture,
( esk10_2(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) = esk5_0
| empty(the_carrier(esk4_0)) ),
inference(sr,[status(thm)],[11262,113,theory(equality)]) ).
cnf(11322,negated_conjecture,
( below_refl(esk4_0,esk5_0,esk6_0)
| empty(the_carrier(esk4_0)) ),
inference(spm,[status(thm)],[10135,11263,theory(equality)]) ).
cnf(11352,negated_conjecture,
empty(the_carrier(esk4_0)),
inference(sr,[status(thm)],[11322,480,theory(equality)]) ).
cnf(11355,negated_conjecture,
( empty_carrier(esk4_0)
| ~ latt_str(esk4_0) ),
inference(spm,[status(thm)],[313,11352,theory(equality)]) ).
cnf(11440,negated_conjecture,
( empty_carrier(esk4_0)
| $false ),
inference(rw,[status(thm)],[11355,111,theory(equality)]) ).
cnf(11441,negated_conjecture,
empty_carrier(esk4_0),
inference(cn,[status(thm)],[11440,theory(equality)]) ).
cnf(11442,negated_conjecture,
$false,
inference(sr,[status(thm)],[11441,113,theory(equality)]) ).
cnf(11443,negated_conjecture,
$false,
11442,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU342+1.p
% --creating new selector for []
% -running prover on /tmp/tmpzFlwtE/sel_SEU342+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU342+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU342+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU342+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
%
%------------------------------------------------------------------------------