TSTP Solution File: SEU351+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU351+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 07:44:44 EST 2010
% Result : Theorem 9.08s
% Output : CNFRefutation 9.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 11
% Syntax : Number of formulae : 312 ( 12 unt; 0 def)
% Number of atoms : 2077 ( 243 equ)
% Maximal formula atoms : 50 ( 6 avg)
% Number of connectives : 2792 (1027 ~;1474 |; 222 &)
% ( 16 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 557 ( 1 sgn 202 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X4,X2) ) ) ) ) ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',d17_lattice3) ).
fof(10,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& latt_str(X2) )
=> ( in(X1,a_2_2_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',fraenkel_a_2_2_lattice3) ).
fof(12,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( latt_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) ) ) ) ) ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',t34_lattice3) ).
fof(14,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',t2_tarski) ).
fof(16,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( X3 = join_of_latt_set(X1,X2)
<=> ( latt_element_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_element_smaller(X1,X4,X2)
=> below(X1,X3,X4) ) ) ) ) ) ) ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',d21_lattice3) ).
fof(18,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X2,X4) ) ) ) ) ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',d16_lattice3) ).
fof(22,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& complete_latt_str(X2)
& latt_str(X2) )
=> ( in(X1,a_2_3_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',fraenkel_a_2_3_lattice3) ).
fof(23,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/tmpE44kEP/sel_SEU351+1.p_1',redefinition_r3_lattices) ).
fof(34,axiom,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',cc1_lattices) ).
fof(36,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] : meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2)) ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',d22_lattice3) ).
fof(37,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
file('/tmp/tmpE44kEP/sel_SEU351+1.p_1',dt_k15_lattice3) ).
fof(38,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( latt_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(39,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_element_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X4,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(42,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& latt_str(X2) )
=> ( in(X1,a_2_2_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(44,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( X2 = meet_of_latt_set(X1,X3)
<=> ( latt_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_set_smaller(X1,X4,X3)
=> below_refl(X1,X4,X2) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[38,theory(equality)]) ).
fof(47,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( X3 = join_of_latt_set(X1,X2)
<=> ( latt_element_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( latt_element_smaller(X1,X4,X2)
=> below(X1,X3,X4) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).
fof(48,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( latt_set_smaller(X1,X2,X3)
<=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( in(X4,X3)
=> below(X1,X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[18,theory(equality)]) ).
fof(49,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& complete_latt_str(X2)
& latt_str(X2) )
=> ( in(X1,a_2_3_lattice3(X2,X3))
<=> ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) ) ),
inference(fof_simplification,[status(thm)],[22,theory(equality)]) ).
fof(50,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)],[23,theory(equality)]) ).
fof(53,plain,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
inference(fof_simplification,[status(thm)],[34,theory(equality)]) ).
fof(54,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ! [X2] : meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2)) ),
inference(fof_simplification,[status(thm)],[36,theory(equality)]) ).
fof(55,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[37,theory(equality)]) ).
fof(57,plain,
! [X1] :
( empty_carrier(X1)
| ~ latt_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ( ~ latt_element_smaller(X1,X2,X3)
| ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ in(X4,X3)
| below(X1,X4,X2) ) )
& ( ? [X4] :
( element(X4,the_carrier(X1))
& in(X4,X3)
& ~ below(X1,X4,X2) )
| latt_element_smaller(X1,X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(58,plain,
! [X5] :
( empty_carrier(X5)
| ~ latt_str(X5)
| ! [X6] :
( ~ element(X6,the_carrier(X5))
| ! [X7] :
( ( ~ latt_element_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X8,X6) ) )
& ( ? [X9] :
( element(X9,the_carrier(X5))
& in(X9,X7)
& ~ below(X5,X9,X6) )
| latt_element_smaller(X5,X6,X7) ) ) ) ),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,plain,
! [X5] :
( empty_carrier(X5)
| ~ latt_str(X5)
| ! [X6] :
( ~ element(X6,the_carrier(X5))
| ! [X7] :
( ( ~ latt_element_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X8,X6) ) )
& ( ( element(esk1_3(X5,X6,X7),the_carrier(X5))
& in(esk1_3(X5,X6,X7),X7)
& ~ below(X5,esk1_3(X5,X6,X7),X6) )
| latt_element_smaller(X5,X6,X7) ) ) ) ),
inference(skolemize,[status(esa)],[58]) ).
fof(60,plain,
! [X5,X6,X7,X8] :
( ( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X8,X6)
| ~ latt_element_smaller(X5,X6,X7) )
& ( ( element(esk1_3(X5,X6,X7),the_carrier(X5))
& in(esk1_3(X5,X6,X7),X7)
& ~ below(X5,esk1_3(X5,X6,X7),X6) )
| latt_element_smaller(X5,X6,X7) ) )
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) ),
inference(shift_quantors,[status(thm)],[59]) ).
fof(61,plain,
! [X5,X6,X7,X8] :
( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X8,X6)
| ~ latt_element_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( element(esk1_3(X5,X6,X7),the_carrier(X5))
| latt_element_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( in(esk1_3(X5,X6,X7),X7)
| latt_element_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( ~ below(X5,esk1_3(X5,X6,X7),X6)
| latt_element_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) ) ),
inference(distribute,[status(thm)],[60]) ).
cnf(62,plain,
( empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,esk1_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(63,plain,
( empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| in(esk1_3(X1,X2,X3),X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(64,plain,
( empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| element(esk1_3(X1,X2,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(65,plain,
( empty_carrier(X1)
| below(X1,X4,X2)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3)
| ~ in(X4,X3)
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[61]) ).
fof(87,plain,
! [X1,X2,X3] :
( empty_carrier(X2)
| ~ latt_str(X2)
| ( ( ~ in(X1,a_2_2_lattice3(X2,X3))
| ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) )
& ( ! [X4] :
( ~ element(X4,the_carrier(X2))
| X1 != X4
| ~ latt_set_smaller(X2,X4,X3) )
| in(X1,a_2_2_lattice3(X2,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(88,plain,
! [X5,X6,X7] :
( empty_carrier(X6)
| ~ latt_str(X6)
| ( ( ~ in(X5,a_2_2_lattice3(X6,X7))
| ? [X8] :
( element(X8,the_carrier(X6))
& X5 = X8
& latt_set_smaller(X6,X8,X7) ) )
& ( ! [X9] :
( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7) )
| in(X5,a_2_2_lattice3(X6,X7)) ) ) ),
inference(variable_rename,[status(thm)],[87]) ).
fof(89,plain,
! [X5,X6,X7] :
( empty_carrier(X6)
| ~ latt_str(X6)
| ( ( ~ in(X5,a_2_2_lattice3(X6,X7))
| ( element(esk4_3(X5,X6,X7),the_carrier(X6))
& X5 = esk4_3(X5,X6,X7)
& latt_set_smaller(X6,esk4_3(X5,X6,X7),X7) ) )
& ( ! [X9] :
( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7) )
| in(X5,a_2_2_lattice3(X6,X7)) ) ) ),
inference(skolemize,[status(esa)],[88]) ).
fof(90,plain,
! [X5,X6,X7,X9] :
( ( ( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7)
| in(X5,a_2_2_lattice3(X6,X7)) )
& ( ~ in(X5,a_2_2_lattice3(X6,X7))
| ( element(esk4_3(X5,X6,X7),the_carrier(X6))
& X5 = esk4_3(X5,X6,X7)
& latt_set_smaller(X6,esk4_3(X5,X6,X7),X7) ) ) )
| empty_carrier(X6)
| ~ latt_str(X6) ),
inference(shift_quantors,[status(thm)],[89]) ).
fof(91,plain,
! [X5,X6,X7,X9] :
( ( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7)
| in(X5,a_2_2_lattice3(X6,X7))
| empty_carrier(X6)
| ~ latt_str(X6) )
& ( element(esk4_3(X5,X6,X7),the_carrier(X6))
| ~ in(X5,a_2_2_lattice3(X6,X7))
| empty_carrier(X6)
| ~ latt_str(X6) )
& ( X5 = esk4_3(X5,X6,X7)
| ~ in(X5,a_2_2_lattice3(X6,X7))
| empty_carrier(X6)
| ~ latt_str(X6) )
& ( latt_set_smaller(X6,esk4_3(X5,X6,X7),X7)
| ~ in(X5,a_2_2_lattice3(X6,X7))
| empty_carrier(X6)
| ~ latt_str(X6) ) ),
inference(distribute,[status(thm)],[90]) ).
cnf(92,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,esk4_3(X2,X1,X3),X3)
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[91]) ).
cnf(93,plain,
( empty_carrier(X1)
| X2 = esk4_3(X2,X1,X3)
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[91]) ).
cnf(94,plain,
( empty_carrier(X1)
| element(esk4_3(X2,X1,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ in(X2,a_2_2_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[91]) ).
cnf(95,plain,
( empty_carrier(X1)
| in(X2,a_2_2_lattice3(X1,X3))
| ~ latt_str(X1)
| ~ latt_set_smaller(X1,X4,X3)
| X2 != X4
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[91]) ).
fof(99,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1)
& ? [X2] :
( element(X2,the_carrier(X1))
& ? [X3] :
( ( X2 != meet_of_latt_set(X1,X3)
| ~ latt_set_smaller(X1,X2,X3)
| ? [X4] :
( element(X4,the_carrier(X1))
& latt_set_smaller(X1,X4,X3)
& ~ below_refl(X1,X4,X2) ) )
& ( X2 = meet_of_latt_set(X1,X3)
| ( latt_set_smaller(X1,X2,X3)
& ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ latt_set_smaller(X1,X4,X3)
| below_refl(X1,X4,X2) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(100,negated_conjecture,
? [X5] :
( ~ empty_carrier(X5)
& lattice(X5)
& complete_latt_str(X5)
& latt_str(X5)
& ? [X6] :
( element(X6,the_carrier(X5))
& ? [X7] :
( ( X6 != meet_of_latt_set(X5,X7)
| ~ latt_set_smaller(X5,X6,X7)
| ? [X8] :
( element(X8,the_carrier(X5))
& latt_set_smaller(X5,X8,X7)
& ~ below_refl(X5,X8,X6) ) )
& ( X6 = meet_of_latt_set(X5,X7)
| ( latt_set_smaller(X5,X6,X7)
& ! [X9] :
( ~ element(X9,the_carrier(X5))
| ~ latt_set_smaller(X5,X9,X7)
| below_refl(X5,X9,X6) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,negated_conjecture,
( ~ empty_carrier(esk5_0)
& lattice(esk5_0)
& complete_latt_str(esk5_0)
& latt_str(esk5_0)
& element(esk6_0,the_carrier(esk5_0))
& ( esk6_0 != meet_of_latt_set(esk5_0,esk7_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ( element(esk8_0,the_carrier(esk5_0))
& latt_set_smaller(esk5_0,esk8_0,esk7_0)
& ~ below_refl(esk5_0,esk8_0,esk6_0) ) )
& ( esk6_0 = meet_of_latt_set(esk5_0,esk7_0)
| ( latt_set_smaller(esk5_0,esk6_0,esk7_0)
& ! [X9] :
( ~ element(X9,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,X9,esk7_0)
| below_refl(esk5_0,X9,esk6_0) ) ) ) ),
inference(skolemize,[status(esa)],[100]) ).
fof(102,negated_conjecture,
! [X9] :
( ( ( ( ~ element(X9,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,X9,esk7_0)
| below_refl(esk5_0,X9,esk6_0) )
& latt_set_smaller(esk5_0,esk6_0,esk7_0) )
| esk6_0 = meet_of_latt_set(esk5_0,esk7_0) )
& ( esk6_0 != meet_of_latt_set(esk5_0,esk7_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ( element(esk8_0,the_carrier(esk5_0))
& latt_set_smaller(esk5_0,esk8_0,esk7_0)
& ~ below_refl(esk5_0,esk8_0,esk6_0) ) )
& element(esk6_0,the_carrier(esk5_0))
& ~ empty_carrier(esk5_0)
& lattice(esk5_0)
& complete_latt_str(esk5_0)
& latt_str(esk5_0) ),
inference(shift_quantors,[status(thm)],[101]) ).
fof(103,negated_conjecture,
! [X9] :
( ( ~ element(X9,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,X9,esk7_0)
| below_refl(esk5_0,X9,esk6_0)
| esk6_0 = meet_of_latt_set(esk5_0,esk7_0) )
& ( latt_set_smaller(esk5_0,esk6_0,esk7_0)
| esk6_0 = meet_of_latt_set(esk5_0,esk7_0) )
& ( element(esk8_0,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| esk6_0 != meet_of_latt_set(esk5_0,esk7_0) )
& ( latt_set_smaller(esk5_0,esk8_0,esk7_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| esk6_0 != meet_of_latt_set(esk5_0,esk7_0) )
& ( ~ below_refl(esk5_0,esk8_0,esk6_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| esk6_0 != meet_of_latt_set(esk5_0,esk7_0) )
& element(esk6_0,the_carrier(esk5_0))
& ~ empty_carrier(esk5_0)
& lattice(esk5_0)
& complete_latt_str(esk5_0)
& latt_str(esk5_0) ),
inference(distribute,[status(thm)],[102]) ).
cnf(104,negated_conjecture,
latt_str(esk5_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(105,negated_conjecture,
complete_latt_str(esk5_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(106,negated_conjecture,
lattice(esk5_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(107,negated_conjecture,
~ empty_carrier(esk5_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(108,negated_conjecture,
element(esk6_0,the_carrier(esk5_0)),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(109,negated_conjecture,
( esk6_0 != meet_of_latt_set(esk5_0,esk7_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below_refl(esk5_0,esk8_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(110,negated_conjecture,
( latt_set_smaller(esk5_0,esk8_0,esk7_0)
| esk6_0 != meet_of_latt_set(esk5_0,esk7_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(111,negated_conjecture,
( element(esk8_0,the_carrier(esk5_0))
| esk6_0 != meet_of_latt_set(esk5_0,esk7_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(112,negated_conjecture,
( esk6_0 = meet_of_latt_set(esk5_0,esk7_0)
| latt_set_smaller(esk5_0,esk6_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(113,negated_conjecture,
( esk6_0 = meet_of_latt_set(esk5_0,esk7_0)
| below_refl(esk5_0,X1,esk6_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(split_conjunct,[status(thm)],[103]) ).
fof(117,plain,
! [X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X2) ) )
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(118,plain,
! [X4,X5] :
( ? [X6] :
( ( ~ in(X6,X4)
| ~ in(X6,X5) )
& ( in(X6,X4)
| in(X6,X5) ) )
| X4 = X5 ),
inference(variable_rename,[status(thm)],[117]) ).
fof(119,plain,
! [X4,X5] :
( ( ( ~ in(esk9_2(X4,X5),X4)
| ~ in(esk9_2(X4,X5),X5) )
& ( in(esk9_2(X4,X5),X4)
| in(esk9_2(X4,X5),X5) ) )
| X4 = X5 ),
inference(skolemize,[status(esa)],[118]) ).
fof(120,plain,
! [X4,X5] :
( ( ~ in(esk9_2(X4,X5),X4)
| ~ in(esk9_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk9_2(X4,X5),X4)
| in(esk9_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[119]) ).
cnf(121,plain,
( X1 = X2
| in(esk9_2(X1,X2),X2)
| in(esk9_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[120]) ).
cnf(122,plain,
( X1 = X2
| ~ in(esk9_2(X1,X2),X2)
| ~ in(esk9_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[120]) ).
fof(126,plain,
! [X1] :
( empty_carrier(X1)
| ~ latt_str(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ! [X2,X3] :
( ~ element(X3,the_carrier(X1))
| ( ( X3 != join_of_latt_set(X1,X2)
| ( latt_element_smaller(X1,X3,X2)
& ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ latt_element_smaller(X1,X4,X2)
| below(X1,X3,X4) ) ) )
& ( ~ latt_element_smaller(X1,X3,X2)
| ? [X4] :
( element(X4,the_carrier(X1))
& latt_element_smaller(X1,X4,X2)
& ~ below(X1,X3,X4) )
| X3 = join_of_latt_set(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(127,plain,
! [X5] :
( empty_carrier(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| ! [X6,X7] :
( ~ element(X7,the_carrier(X5))
| ( ( X7 != join_of_latt_set(X5,X6)
| ( latt_element_smaller(X5,X7,X6)
& ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ latt_element_smaller(X5,X8,X6)
| below(X5,X7,X8) ) ) )
& ( ~ latt_element_smaller(X5,X7,X6)
| ? [X9] :
( element(X9,the_carrier(X5))
& latt_element_smaller(X5,X9,X6)
& ~ below(X5,X7,X9) )
| X7 = join_of_latt_set(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[126]) ).
fof(128,plain,
! [X5] :
( empty_carrier(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| ! [X6,X7] :
( ~ element(X7,the_carrier(X5))
| ( ( X7 != join_of_latt_set(X5,X6)
| ( latt_element_smaller(X5,X7,X6)
& ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ latt_element_smaller(X5,X8,X6)
| below(X5,X7,X8) ) ) )
& ( ~ latt_element_smaller(X5,X7,X6)
| ( element(esk10_3(X5,X6,X7),the_carrier(X5))
& latt_element_smaller(X5,esk10_3(X5,X6,X7),X6)
& ~ below(X5,X7,esk10_3(X5,X6,X7)) )
| X7 = join_of_latt_set(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[127]) ).
fof(129,plain,
! [X5,X6,X7,X8] :
( ( ( ( ( ~ element(X8,the_carrier(X5))
| ~ latt_element_smaller(X5,X8,X6)
| below(X5,X7,X8) )
& latt_element_smaller(X5,X7,X6) )
| X7 != join_of_latt_set(X5,X6) )
& ( ~ latt_element_smaller(X5,X7,X6)
| ( element(esk10_3(X5,X6,X7),the_carrier(X5))
& latt_element_smaller(X5,esk10_3(X5,X6,X7),X6)
& ~ below(X5,X7,esk10_3(X5,X6,X7)) )
| X7 = join_of_latt_set(X5,X6) ) )
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) ),
inference(shift_quantors,[status(thm)],[128]) ).
fof(130,plain,
! [X5,X6,X7,X8] :
( ( ~ element(X8,the_carrier(X5))
| ~ latt_element_smaller(X5,X8,X6)
| below(X5,X7,X8)
| X7 != join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( latt_element_smaller(X5,X7,X6)
| X7 != join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( element(esk10_3(X5,X6,X7),the_carrier(X5))
| ~ latt_element_smaller(X5,X7,X6)
| X7 = join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( latt_element_smaller(X5,esk10_3(X5,X6,X7),X6)
| ~ latt_element_smaller(X5,X7,X6)
| X7 = join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( ~ below(X5,X7,esk10_3(X5,X6,X7))
| ~ latt_element_smaller(X5,X7,X6)
| X7 = join_of_latt_set(X5,X6)
| ~ element(X7,the_carrier(X5))
| empty_carrier(X5)
| ~ lattice(X5)
| ~ complete_latt_str(X5)
| ~ latt_str(X5)
| empty_carrier(X5)
| ~ latt_str(X5) ) ),
inference(distribute,[status(thm)],[129]) ).
cnf(131,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| X2 = join_of_latt_set(X1,X3)
| ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3)
| ~ below(X1,X2,esk10_3(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(132,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| X2 = join_of_latt_set(X1,X3)
| latt_element_smaller(X1,esk10_3(X1,X3,X2),X3)
| ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(133,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| X2 = join_of_latt_set(X1,X3)
| element(esk10_3(X1,X3,X2),the_carrier(X1))
| ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(134,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| X2 != join_of_latt_set(X1,X3) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(135,plain,
( empty_carrier(X1)
| empty_carrier(X1)
| below(X1,X2,X4)
| ~ latt_str(X1)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| X2 != join_of_latt_set(X1,X3)
| ~ latt_element_smaller(X1,X4,X3)
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[130]) ).
fof(137,plain,
! [X1] :
( empty_carrier(X1)
| ~ latt_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ( ~ latt_set_smaller(X1,X2,X3)
| ! [X4] :
( ~ element(X4,the_carrier(X1))
| ~ in(X4,X3)
| below(X1,X2,X4) ) )
& ( ? [X4] :
( element(X4,the_carrier(X1))
& in(X4,X3)
& ~ below(X1,X2,X4) )
| latt_set_smaller(X1,X2,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[48]) ).
fof(138,plain,
! [X5] :
( empty_carrier(X5)
| ~ latt_str(X5)
| ! [X6] :
( ~ element(X6,the_carrier(X5))
| ! [X7] :
( ( ~ latt_set_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X6,X8) ) )
& ( ? [X9] :
( element(X9,the_carrier(X5))
& in(X9,X7)
& ~ below(X5,X6,X9) )
| latt_set_smaller(X5,X6,X7) ) ) ) ),
inference(variable_rename,[status(thm)],[137]) ).
fof(139,plain,
! [X5] :
( empty_carrier(X5)
| ~ latt_str(X5)
| ! [X6] :
( ~ element(X6,the_carrier(X5))
| ! [X7] :
( ( ~ latt_set_smaller(X5,X6,X7)
| ! [X8] :
( ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X6,X8) ) )
& ( ( element(esk11_3(X5,X6,X7),the_carrier(X5))
& in(esk11_3(X5,X6,X7),X7)
& ~ below(X5,X6,esk11_3(X5,X6,X7)) )
| latt_set_smaller(X5,X6,X7) ) ) ) ),
inference(skolemize,[status(esa)],[138]) ).
fof(140,plain,
! [X5,X6,X7,X8] :
( ( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X6,X8)
| ~ latt_set_smaller(X5,X6,X7) )
& ( ( element(esk11_3(X5,X6,X7),the_carrier(X5))
& in(esk11_3(X5,X6,X7),X7)
& ~ below(X5,X6,esk11_3(X5,X6,X7)) )
| latt_set_smaller(X5,X6,X7) ) )
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) ),
inference(shift_quantors,[status(thm)],[139]) ).
fof(141,plain,
! [X5,X6,X7,X8] :
( ( ~ element(X8,the_carrier(X5))
| ~ in(X8,X7)
| below(X5,X6,X8)
| ~ latt_set_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( element(esk11_3(X5,X6,X7),the_carrier(X5))
| latt_set_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( in(esk11_3(X5,X6,X7),X7)
| latt_set_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) )
& ( ~ below(X5,X6,esk11_3(X5,X6,X7))
| latt_set_smaller(X5,X6,X7)
| ~ element(X6,the_carrier(X5))
| empty_carrier(X5)
| ~ latt_str(X5) ) ),
inference(distribute,[status(thm)],[140]) ).
cnf(142,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,X2,X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,X2,esk11_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[141]) ).
cnf(143,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,X2,X3)
| in(esk11_3(X1,X2,X3),X3)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[141]) ).
cnf(144,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,X2,X3)
| element(esk11_3(X1,X2,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[141]) ).
cnf(145,plain,
( empty_carrier(X1)
| below(X1,X2,X4)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_set_smaller(X1,X2,X3)
| ~ in(X4,X3)
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[141]) ).
fof(155,plain,
! [X1,X2,X3] :
( empty_carrier(X2)
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2)
| ( ( ~ in(X1,a_2_3_lattice3(X2,X3))
| ? [X4] :
( element(X4,the_carrier(X2))
& X1 = X4
& latt_set_smaller(X2,X4,X3) ) )
& ( ! [X4] :
( ~ element(X4,the_carrier(X2))
| X1 != X4
| ~ latt_set_smaller(X2,X4,X3) )
| in(X1,a_2_3_lattice3(X2,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[49]) ).
fof(156,plain,
! [X5,X6,X7] :
( empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6)
| ( ( ~ in(X5,a_2_3_lattice3(X6,X7))
| ? [X8] :
( element(X8,the_carrier(X6))
& X5 = X8
& latt_set_smaller(X6,X8,X7) ) )
& ( ! [X9] :
( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7) )
| in(X5,a_2_3_lattice3(X6,X7)) ) ) ),
inference(variable_rename,[status(thm)],[155]) ).
fof(157,plain,
! [X5,X6,X7] :
( empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6)
| ( ( ~ in(X5,a_2_3_lattice3(X6,X7))
| ( element(esk15_3(X5,X6,X7),the_carrier(X6))
& X5 = esk15_3(X5,X6,X7)
& latt_set_smaller(X6,esk15_3(X5,X6,X7),X7) ) )
& ( ! [X9] :
( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7) )
| in(X5,a_2_3_lattice3(X6,X7)) ) ) ),
inference(skolemize,[status(esa)],[156]) ).
fof(158,plain,
! [X5,X6,X7,X9] :
( ( ( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7)
| in(X5,a_2_3_lattice3(X6,X7)) )
& ( ~ in(X5,a_2_3_lattice3(X6,X7))
| ( element(esk15_3(X5,X6,X7),the_carrier(X6))
& X5 = esk15_3(X5,X6,X7)
& latt_set_smaller(X6,esk15_3(X5,X6,X7),X7) ) ) )
| empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6) ),
inference(shift_quantors,[status(thm)],[157]) ).
fof(159,plain,
! [X5,X6,X7,X9] :
( ( ~ element(X9,the_carrier(X6))
| X5 != X9
| ~ latt_set_smaller(X6,X9,X7)
| in(X5,a_2_3_lattice3(X6,X7))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6) )
& ( element(esk15_3(X5,X6,X7),the_carrier(X6))
| ~ in(X5,a_2_3_lattice3(X6,X7))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6) )
& ( X5 = esk15_3(X5,X6,X7)
| ~ in(X5,a_2_3_lattice3(X6,X7))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6) )
& ( latt_set_smaller(X6,esk15_3(X5,X6,X7),X7)
| ~ in(X5,a_2_3_lattice3(X6,X7))
| empty_carrier(X6)
| ~ lattice(X6)
| ~ complete_latt_str(X6)
| ~ latt_str(X6) ) ),
inference(distribute,[status(thm)],[158]) ).
cnf(160,plain,
( empty_carrier(X1)
| latt_set_smaller(X1,esk15_3(X2,X1,X3),X3)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[159]) ).
cnf(161,plain,
( empty_carrier(X1)
| X2 = esk15_3(X2,X1,X3)
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[159]) ).
cnf(162,plain,
( empty_carrier(X1)
| element(esk15_3(X2,X1,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3)) ),
inference(split_conjunct,[status(thm)],[159]) ).
cnf(163,plain,
( empty_carrier(X1)
| in(X2,a_2_3_lattice3(X1,X3))
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_set_smaller(X1,X4,X3)
| X2 != X4
| ~ element(X4,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[159]) ).
fof(164,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)],[50]) ).
fof(165,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)],[164]) ).
fof(166,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)],[165]) ).
cnf(167,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)],[166]) ).
cnf(168,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)],[166]) ).
fof(198,plain,
! [X1] :
( ~ latt_str(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ),
inference(fof_nnf,[status(thm)],[53]) ).
fof(199,plain,
! [X2] :
( ~ latt_str(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ( ~ empty_carrier(X2)
& join_commutative(X2)
& join_associative(X2)
& meet_commutative(X2)
& meet_associative(X2)
& meet_absorbing(X2)
& join_absorbing(X2) ) ),
inference(variable_rename,[status(thm)],[198]) ).
fof(200,plain,
! [X2] :
( ( ~ empty_carrier(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( join_commutative(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( join_associative(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( meet_commutative(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( meet_associative(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( meet_absorbing(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) )
& ( join_absorbing(X2)
| empty_carrier(X2)
| ~ lattice(X2)
| ~ latt_str(X2) ) ),
inference(distribute,[status(thm)],[199]) ).
cnf(201,plain,
( empty_carrier(X1)
| join_absorbing(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[200]) ).
cnf(202,plain,
( empty_carrier(X1)
| meet_absorbing(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[200]) ).
cnf(204,plain,
( empty_carrier(X1)
| meet_commutative(X1)
| ~ latt_str(X1)
| ~ lattice(X1) ),
inference(split_conjunct,[status(thm)],[200]) ).
fof(211,plain,
! [X1] :
( empty_carrier(X1)
| ~ latt_str(X1)
| ! [X2] : meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2)) ),
inference(fof_nnf,[status(thm)],[54]) ).
fof(212,plain,
! [X3] :
( empty_carrier(X3)
| ~ latt_str(X3)
| ! [X4] : meet_of_latt_set(X3,X4) = join_of_latt_set(X3,a_2_2_lattice3(X3,X4)) ),
inference(variable_rename,[status(thm)],[211]) ).
fof(213,plain,
! [X3,X4] :
( meet_of_latt_set(X3,X4) = join_of_latt_set(X3,a_2_2_lattice3(X3,X4))
| empty_carrier(X3)
| ~ latt_str(X3) ),
inference(shift_quantors,[status(thm)],[212]) ).
cnf(214,plain,
( empty_carrier(X1)
| meet_of_latt_set(X1,X2) = join_of_latt_set(X1,a_2_2_lattice3(X1,X2))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[213]) ).
fof(215,plain,
! [X1,X2] :
( empty_carrier(X1)
| ~ latt_str(X1)
| element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[55]) ).
fof(216,plain,
! [X3,X4] :
( empty_carrier(X3)
| ~ latt_str(X3)
| element(join_of_latt_set(X3,X4),the_carrier(X3)) ),
inference(variable_rename,[status(thm)],[215]) ).
cnf(217,plain,
( element(join_of_latt_set(X1,X2),the_carrier(X1))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[216]) ).
cnf(249,plain,
( esk4_3(esk9_2(X1,a_2_2_lattice3(X2,X3)),X2,X3) = esk9_2(X1,a_2_2_lattice3(X2,X3))
| empty_carrier(X2)
| X1 = a_2_2_lattice3(X2,X3)
| in(esk9_2(X1,a_2_2_lattice3(X2,X3)),X1)
| ~ latt_str(X2) ),
inference(spm,[status(thm)],[93,121,theory(equality)]) ).
cnf(253,plain,
( esk15_3(esk9_2(a_2_3_lattice3(X1,X2),X3),X1,X2) = esk9_2(a_2_3_lattice3(X1,X2),X3)
| empty_carrier(X1)
| a_2_3_lattice3(X1,X2) = X3
| in(esk9_2(a_2_3_lattice3(X1,X2),X3),X3)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[161,121,theory(equality)]) ).
cnf(258,plain,
( esk4_3(esk1_3(X1,X2,a_2_2_lattice3(X3,X4)),X3,X4) = esk1_3(X1,X2,a_2_2_lattice3(X3,X4))
| empty_carrier(X3)
| latt_element_smaller(X1,X2,a_2_2_lattice3(X3,X4))
| empty_carrier(X1)
| ~ latt_str(X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[93,63,theory(equality)]) ).
cnf(259,plain,
( esk15_3(esk1_3(X1,X2,a_2_3_lattice3(X3,X4)),X3,X4) = esk1_3(X1,X2,a_2_3_lattice3(X3,X4))
| empty_carrier(X3)
| latt_element_smaller(X1,X2,a_2_3_lattice3(X3,X4))
| empty_carrier(X1)
| ~ complete_latt_str(X3)
| ~ lattice(X3)
| ~ latt_str(X3)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[161,63,theory(equality)]) ).
cnf(267,plain,
( in(X1,a_2_2_lattice3(X2,X3))
| empty_carrier(X2)
| ~ latt_set_smaller(X2,X1,X3)
| ~ element(X1,the_carrier(X2))
| ~ latt_str(X2) ),
inference(er,[status(thm)],[95,theory(equality)]) ).
cnf(268,plain,
( latt_element_smaller(X1,join_of_latt_set(X1,X2),X2)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ element(join_of_latt_set(X1,X2),the_carrier(X1))
| ~ latt_str(X1) ),
inference(er,[status(thm)],[134,theory(equality)]) ).
cnf(271,plain,
( in(X1,a_2_3_lattice3(X2,X3))
| empty_carrier(X2)
| ~ complete_latt_str(X2)
| ~ lattice(X2)
| ~ latt_set_smaller(X2,X1,X3)
| ~ element(X1,the_carrier(X2))
| ~ latt_str(X2) ),
inference(er,[status(thm)],[163,theory(equality)]) ).
cnf(284,plain,
( below(X1,esk15_3(X2,X1,X3),X4)
| empty_carrier(X1)
| ~ in(X4,X3)
| ~ element(X4,the_carrier(X1))
| ~ element(esk15_3(X2,X1,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3)) ),
inference(spm,[status(thm)],[145,160,theory(equality)]) ).
cnf(287,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0) ),
inference(spm,[status(thm)],[168,113,theory(equality)]) ).
cnf(288,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ element(X1,the_carrier(esk5_0))
| $false
| ~ latt_str(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0) ),
inference(rw,[status(thm)],[287,108,theory(equality)]) ).
cnf(289,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ element(X1,the_carrier(esk5_0))
| $false
| $false
| ~ latt_set_smaller(esk5_0,X1,esk7_0) ),
inference(rw,[status(thm)],[288,104,theory(equality)]) ).
cnf(290,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,X1,esk7_0) ),
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(291,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,X1,esk7_0) ),
inference(sr,[status(thm)],[290,107,theory(equality)]) ).
cnf(292,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| ~ element(esk8_0,the_carrier(esk5_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[109,167,theory(equality)]) ).
cnf(294,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| ~ element(esk8_0,the_carrier(esk5_0))
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[292,108,theory(equality)]) ).
cnf(295,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| ~ element(esk8_0,the_carrier(esk5_0))
| $false
| $false ),
inference(rw,[status(thm)],[294,104,theory(equality)]) ).
cnf(296,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| ~ element(esk8_0,the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[295,theory(equality)]) ).
cnf(297,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| ~ element(esk8_0,the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[296,107,theory(equality)]) ).
cnf(298,plain,
( below(X1,X2,esk10_3(X1,X3,X4))
| empty_carrier(X1)
| join_of_latt_set(X1,X3) = X4
| ~ in(X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ element(esk10_3(X1,X3,X4),the_carrier(X1))
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_element_smaller(X1,X4,X3)
| ~ element(X4,the_carrier(X1)) ),
inference(spm,[status(thm)],[65,132,theory(equality)]) ).
cnf(413,negated_conjecture,
( esk4_3(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),esk5_0,X2) = esk9_2(X1,a_2_2_lattice3(esk5_0,X2))
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| empty_carrier(esk5_0) ),
inference(spm,[status(thm)],[249,104,theory(equality)]) ).
cnf(414,negated_conjecture,
( esk4_3(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),esk5_0,X2) = esk9_2(X1,a_2_2_lattice3(esk5_0,X2))
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1) ),
inference(sr,[status(thm)],[413,107,theory(equality)]) ).
cnf(424,plain,
( X1 = a_2_2_lattice3(X2,X3)
| empty_carrier(X2)
| ~ in(esk9_2(X1,a_2_2_lattice3(X2,X3)),X1)
| ~ latt_set_smaller(X2,esk9_2(X1,a_2_2_lattice3(X2,X3)),X3)
| ~ element(esk9_2(X1,a_2_2_lattice3(X2,X3)),the_carrier(X2))
| ~ latt_str(X2) ),
inference(spm,[status(thm)],[122,267,theory(equality)]) ).
cnf(445,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ lattice(esk5_0)
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[291,201,theory(equality)]) ).
cnf(446,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0))
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[445,106,theory(equality)]) ).
cnf(447,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0))
| $false
| $false ),
inference(rw,[status(thm)],[446,104,theory(equality)]) ).
cnf(448,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[447,theory(equality)]) ).
cnf(449,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[448,107,theory(equality)]) ).
cnf(450,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ lattice(esk5_0)
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[449,202,theory(equality)]) ).
cnf(451,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0))
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[450,106,theory(equality)]) ).
cnf(452,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0))
| $false
| $false ),
inference(rw,[status(thm)],[451,104,theory(equality)]) ).
cnf(453,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[452,theory(equality)]) ).
cnf(454,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[453,107,theory(equality)]) ).
cnf(456,negated_conjecture,
( esk15_3(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),esk5_0,X1) = esk9_2(a_2_3_lattice3(esk5_0,X1),X2)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| empty_carrier(esk5_0)
| ~ lattice(esk5_0)
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[253,105,theory(equality)]) ).
cnf(457,negated_conjecture,
( esk15_3(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),esk5_0,X1) = esk9_2(a_2_3_lattice3(esk5_0,X1),X2)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| empty_carrier(esk5_0)
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[456,106,theory(equality)]) ).
cnf(458,negated_conjecture,
( esk15_3(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),esk5_0,X1) = esk9_2(a_2_3_lattice3(esk5_0,X1),X2)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| empty_carrier(esk5_0)
| $false
| $false ),
inference(rw,[status(thm)],[457,104,theory(equality)]) ).
cnf(459,negated_conjecture,
( esk15_3(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),esk5_0,X1) = esk9_2(a_2_3_lattice3(esk5_0,X1),X2)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| empty_carrier(esk5_0) ),
inference(cn,[status(thm)],[458,theory(equality)]) ).
cnf(460,negated_conjecture,
( esk15_3(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),esk5_0,X1) = esk9_2(a_2_3_lattice3(esk5_0,X1),X2)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2) ),
inference(sr,[status(thm)],[459,107,theory(equality)]) ).
cnf(506,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X2)
| empty_carrier(esk5_0)
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| ~ in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),a_2_2_lattice3(esk5_0,X2))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[92,414,theory(equality)]) ).
cnf(507,negated_conjecture,
( element(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),the_carrier(esk5_0))
| empty_carrier(esk5_0)
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| ~ in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),a_2_2_lattice3(esk5_0,X2))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[94,414,theory(equality)]) ).
cnf(511,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X2)
| empty_carrier(esk5_0)
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| ~ in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),a_2_2_lattice3(esk5_0,X2))
| $false ),
inference(rw,[status(thm)],[506,104,theory(equality)]) ).
cnf(512,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X2)
| empty_carrier(esk5_0)
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| ~ in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),a_2_2_lattice3(esk5_0,X2)) ),
inference(cn,[status(thm)],[511,theory(equality)]) ).
cnf(513,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X2)
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| ~ in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),a_2_2_lattice3(esk5_0,X2)) ),
inference(sr,[status(thm)],[512,107,theory(equality)]) ).
cnf(514,negated_conjecture,
( element(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),the_carrier(esk5_0))
| empty_carrier(esk5_0)
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| ~ in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),a_2_2_lattice3(esk5_0,X2))
| $false ),
inference(rw,[status(thm)],[507,104,theory(equality)]) ).
cnf(515,negated_conjecture,
( element(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),the_carrier(esk5_0))
| empty_carrier(esk5_0)
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| ~ in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),a_2_2_lattice3(esk5_0,X2)) ),
inference(cn,[status(thm)],[514,theory(equality)]) ).
cnf(516,negated_conjecture,
( element(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),the_carrier(esk5_0))
| X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| ~ in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),a_2_2_lattice3(esk5_0,X2)) ),
inference(sr,[status(thm)],[515,107,theory(equality)]) ).
cnf(523,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ lattice(esk5_0)
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[454,204,theory(equality)]) ).
cnf(524,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0))
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[523,106,theory(equality)]) ).
cnf(525,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0))
| $false
| $false ),
inference(rw,[status(thm)],[524,104,theory(equality)]) ).
cnf(526,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[525,theory(equality)]) ).
cnf(527,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,X1,esk6_0)
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[526,107,theory(equality)]) ).
cnf(528,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,esk4_3(X1,esk5_0,esk7_0),esk6_0)
| empty_carrier(esk5_0)
| ~ element(esk4_3(X1,esk5_0,esk7_0),the_carrier(esk5_0))
| ~ in(X1,a_2_2_lattice3(esk5_0,esk7_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[527,92,theory(equality)]) ).
cnf(530,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,esk4_3(X1,esk5_0,esk7_0),esk6_0)
| empty_carrier(esk5_0)
| ~ element(esk4_3(X1,esk5_0,esk7_0),the_carrier(esk5_0))
| ~ in(X1,a_2_2_lattice3(esk5_0,esk7_0))
| $false ),
inference(rw,[status(thm)],[528,104,theory(equality)]) ).
cnf(531,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,esk4_3(X1,esk5_0,esk7_0),esk6_0)
| empty_carrier(esk5_0)
| ~ element(esk4_3(X1,esk5_0,esk7_0),the_carrier(esk5_0))
| ~ in(X1,a_2_2_lattice3(esk5_0,esk7_0)) ),
inference(cn,[status(thm)],[530,theory(equality)]) ).
cnf(532,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,esk4_3(X1,esk5_0,esk7_0),esk6_0)
| ~ element(esk4_3(X1,esk5_0,esk7_0),the_carrier(esk5_0))
| ~ in(X1,a_2_2_lattice3(esk5_0,esk7_0)) ),
inference(sr,[status(thm)],[531,107,theory(equality)]) ).
cnf(575,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X1)
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| ~ complete_latt_str(esk5_0)
| ~ lattice(esk5_0)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[160,460,theory(equality)]) ).
cnf(576,negated_conjecture,
( element(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),the_carrier(esk5_0))
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| ~ complete_latt_str(esk5_0)
| ~ lattice(esk5_0)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[162,460,theory(equality)]) ).
cnf(577,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X1)
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| $false
| ~ lattice(esk5_0)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[575,105,theory(equality)]) ).
cnf(578,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X1)
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| $false
| $false
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[577,106,theory(equality)]) ).
cnf(579,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X1)
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| $false
| $false
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1))
| $false ),
inference(rw,[status(thm)],[578,104,theory(equality)]) ).
cnf(580,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X1)
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1)) ),
inference(cn,[status(thm)],[579,theory(equality)]) ).
cnf(581,negated_conjecture,
( latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X1)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1)) ),
inference(sr,[status(thm)],[580,107,theory(equality)]) ).
cnf(582,negated_conjecture,
( element(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),the_carrier(esk5_0))
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| $false
| ~ lattice(esk5_0)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[576,105,theory(equality)]) ).
cnf(583,negated_conjecture,
( element(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),the_carrier(esk5_0))
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| $false
| $false
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[582,106,theory(equality)]) ).
cnf(584,negated_conjecture,
( element(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),the_carrier(esk5_0))
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| $false
| $false
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1))
| $false ),
inference(rw,[status(thm)],[583,104,theory(equality)]) ).
cnf(585,negated_conjecture,
( element(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),the_carrier(esk5_0))
| empty_carrier(esk5_0)
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1)) ),
inference(cn,[status(thm)],[584,theory(equality)]) ).
cnf(586,negated_conjecture,
( element(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),the_carrier(esk5_0))
| a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1)) ),
inference(sr,[status(thm)],[585,107,theory(equality)]) ).
cnf(638,plain,
( latt_element_smaller(X1,join_of_latt_set(X1,X2),X2)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[268,217]) ).
cnf(639,plain,
( latt_element_smaller(X1,meet_of_latt_set(X1,X2),a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[638,214,theory(equality)]) ).
cnf(646,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),esk6_0)
| latt_element_smaller(X1,X2,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(X1)
| empty_carrier(esk5_0)
| ~ in(esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(esk5_0)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[532,258,theory(equality)]) ).
cnf(647,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),esk6_0)
| latt_element_smaller(X1,X2,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(X1)
| empty_carrier(esk5_0)
| ~ in(esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0))
| ~ element(X2,the_carrier(X1))
| $false
| ~ latt_str(X1) ),
inference(rw,[status(thm)],[646,104,theory(equality)]) ).
cnf(648,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),esk6_0)
| latt_element_smaller(X1,X2,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(X1)
| empty_carrier(esk5_0)
| ~ in(esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(cn,[status(thm)],[647,theory(equality)]) ).
cnf(649,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),esk6_0)
| latt_element_smaller(X1,X2,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(X1)
| ~ in(esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(sr,[status(thm)],[648,107,theory(equality)]) ).
cnf(1018,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ join_absorbing(esk5_0)
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0) ),
inference(csr,[status(thm)],[297,111]) ).
cnf(1019,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| ~ lattice(esk5_0)
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[1018,201,theory(equality)]) ).
cnf(1020,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[1019,106,theory(equality)]) ).
cnf(1021,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| $false
| $false ),
inference(rw,[status(thm)],[1020,104,theory(equality)]) ).
cnf(1022,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0) ),
inference(cn,[status(thm)],[1021,theory(equality)]) ).
cnf(1023,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_absorbing(esk5_0)
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0) ),
inference(sr,[status(thm)],[1022,107,theory(equality)]) ).
cnf(1057,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| ~ lattice(esk5_0)
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[1023,202,theory(equality)]) ).
cnf(1058,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[1057,106,theory(equality)]) ).
cnf(1059,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| $false
| $false ),
inference(rw,[status(thm)],[1058,104,theory(equality)]) ).
cnf(1060,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0) ),
inference(cn,[status(thm)],[1059,theory(equality)]) ).
cnf(1061,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ meet_commutative(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0) ),
inference(sr,[status(thm)],[1060,107,theory(equality)]) ).
cnf(1062,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| ~ lattice(esk5_0)
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[1061,204,theory(equality)]) ).
cnf(1063,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[1062,106,theory(equality)]) ).
cnf(1064,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0)
| $false
| $false ),
inference(rw,[status(thm)],[1063,104,theory(equality)]) ).
cnf(1065,negated_conjecture,
( empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0) ),
inference(cn,[status(thm)],[1064,theory(equality)]) ).
cnf(1066,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) != esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0) ),
inference(sr,[status(thm)],[1065,107,theory(equality)]) ).
cnf(1081,plain,
( below(X1,esk15_3(X2,X1,X3),X4)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,a_2_3_lattice3(X1,X3))
| ~ in(X4,X3)
| ~ element(X4,the_carrier(X1))
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[284,162]) ).
cnf(1088,plain,
( below(X1,esk1_3(X2,X3,a_2_3_lattice3(X1,X4)),X5)
| empty_carrier(X1)
| latt_element_smaller(X2,X3,a_2_3_lattice3(X1,X4))
| empty_carrier(X2)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(esk1_3(X2,X3,a_2_3_lattice3(X1,X4)),a_2_3_lattice3(X1,X4))
| ~ in(X5,X4)
| ~ element(X5,the_carrier(X1))
| ~ latt_str(X1)
| ~ element(X3,the_carrier(X2))
| ~ latt_str(X2) ),
inference(spm,[status(thm)],[1081,259,theory(equality)]) ).
cnf(1165,plain,
( join_of_latt_set(X1,X3) = X4
| below(X1,X2,esk10_3(X1,X3,X4))
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,X3)
| ~ latt_element_smaller(X1,X4,X3)
| ~ element(X4,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[298,133]) ).
cnf(1167,plain,
( join_of_latt_set(X1,X2) = X3
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ latt_str(X1)
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[131,1165,theory(equality)]) ).
cnf(3694,negated_conjecture,
( X1 = a_2_2_lattice3(esk5_0,X2)
| latt_set_smaller(esk5_0,esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1) ),
inference(csr,[status(thm)],[513,121]) ).
cnf(3785,negated_conjecture,
( X1 = a_2_2_lattice3(esk5_0,X2)
| in(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),X1)
| element(esk9_2(X1,a_2_2_lattice3(esk5_0,X2)),the_carrier(esk5_0)) ),
inference(csr,[status(thm)],[516,121]) ).
cnf(4280,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = X2
| latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X1)
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2) ),
inference(csr,[status(thm)],[581,121]) ).
cnf(4284,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = X2
| latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X1)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1)) ),
inference(spm,[status(thm)],[122,4280,theory(equality)]) ).
cnf(4310,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = X2
| in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),X2)
| element(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),the_carrier(esk5_0)) ),
inference(csr,[status(thm)],[586,121]) ).
cnf(4315,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = X2
| element(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),the_carrier(esk5_0))
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),X2),a_2_3_lattice3(esk5_0,X1)) ),
inference(spm,[status(thm)],[122,4310,theory(equality)]) ).
cnf(5381,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| below(esk5_0,esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),esk6_0)
| latt_element_smaller(X1,X2,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(X1)
| ~ element(esk1_3(X1,X2,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0))
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[649,63]) ).
cnf(5382,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0)
| ~ element(esk1_3(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0)) ),
inference(spm,[status(thm)],[62,5381,theory(equality)]) ).
cnf(5383,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| $false
| ~ latt_str(esk5_0)
| ~ element(esk1_3(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0)) ),
inference(rw,[status(thm)],[5382,108,theory(equality)]) ).
cnf(5384,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| $false
| $false
| ~ element(esk1_3(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0)) ),
inference(rw,[status(thm)],[5383,104,theory(equality)]) ).
cnf(5385,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ element(esk1_3(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[5384,theory(equality)]) ).
cnf(5386,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ element(esk1_3(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0)),the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[5385,107,theory(equality)]) ).
cnf(5484,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[5386,64,theory(equality)]) ).
cnf(5486,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[5484,108,theory(equality)]) ).
cnf(5487,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| $false
| $false ),
inference(rw,[status(thm)],[5486,104,theory(equality)]) ).
cnf(5488,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0) ),
inference(cn,[status(thm)],[5487,theory(equality)]) ).
cnf(5489,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0)) ),
inference(sr,[status(thm)],[5488,107,theory(equality)]) ).
cnf(5496,negated_conjecture,
( join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,esk7_0)) = esk6_0
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ complete_latt_str(esk5_0)
| ~ lattice(esk5_0)
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[1167,5489,theory(equality)]) ).
cnf(5507,negated_conjecture,
( join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,esk7_0)) = esk6_0
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| $false
| ~ lattice(esk5_0)
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[5496,105,theory(equality)]) ).
cnf(5508,negated_conjecture,
( join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,esk7_0)) = esk6_0
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| $false
| $false
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[5507,106,theory(equality)]) ).
cnf(5509,negated_conjecture,
( join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,esk7_0)) = esk6_0
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| $false
| $false
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[5508,108,theory(equality)]) ).
cnf(5510,negated_conjecture,
( join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,esk7_0)) = esk6_0
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| $false
| $false
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| $false
| $false ),
inference(rw,[status(thm)],[5509,104,theory(equality)]) ).
cnf(5511,negated_conjecture,
( join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,esk7_0)) = esk6_0
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0)) ),
inference(cn,[status(thm)],[5510,theory(equality)]) ).
cnf(5512,negated_conjecture,
( join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,esk7_0)) = esk6_0
| meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0)) ),
inference(sr,[status(thm)],[5511,107,theory(equality)]) ).
cnf(5514,negated_conjecture,
( esk6_0 = meet_of_latt_set(esk5_0,esk7_0)
| empty_carrier(esk5_0)
| ~ latt_str(esk5_0)
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0)) ),
inference(spm,[status(thm)],[214,5512,theory(equality)]) ).
cnf(5530,negated_conjecture,
( esk6_0 = meet_of_latt_set(esk5_0,esk7_0)
| empty_carrier(esk5_0)
| $false
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0)) ),
inference(rw,[status(thm)],[5514,104,theory(equality)]) ).
cnf(5531,negated_conjecture,
( esk6_0 = meet_of_latt_set(esk5_0,esk7_0)
| empty_carrier(esk5_0)
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0)) ),
inference(cn,[status(thm)],[5530,theory(equality)]) ).
cnf(5532,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ in(esk6_0,a_2_2_lattice3(esk5_0,esk7_0)) ),
inference(sr,[status(thm)],[5531,107,theory(equality)]) ).
cnf(5566,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| empty_carrier(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[5532,267,theory(equality)]) ).
cnf(5567,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| empty_carrier(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[5566,108,theory(equality)]) ).
cnf(5568,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| empty_carrier(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| $false
| $false ),
inference(rw,[status(thm)],[5567,104,theory(equality)]) ).
cnf(5569,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| empty_carrier(esk5_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0) ),
inference(cn,[status(thm)],[5568,theory(equality)]) ).
cnf(5570,negated_conjecture,
( meet_of_latt_set(esk5_0,esk7_0) = esk6_0
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0) ),
inference(sr,[status(thm)],[5569,107,theory(equality)]) ).
cnf(5571,negated_conjecture,
meet_of_latt_set(esk5_0,esk7_0) = esk6_0,
inference(csr,[status(thm)],[5570,112]) ).
cnf(5575,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| ~ complete_latt_str(esk5_0)
| ~ lattice(esk5_0)
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[639,5571,theory(equality)]) ).
cnf(5589,negated_conjecture,
( $false
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0) ),
inference(rw,[status(thm)],[1066,5571,theory(equality)]) ).
cnf(5590,negated_conjecture,
( ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ below(esk5_0,esk8_0,esk6_0) ),
inference(cn,[status(thm)],[5589,theory(equality)]) ).
cnf(5604,negated_conjecture,
( latt_set_smaller(esk5_0,esk8_0,esk7_0)
| $false
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0) ),
inference(rw,[status(thm)],[110,5571,theory(equality)]) ).
cnf(5605,negated_conjecture,
( latt_set_smaller(esk5_0,esk8_0,esk7_0)
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0) ),
inference(cn,[status(thm)],[5604,theory(equality)]) ).
cnf(5606,negated_conjecture,
( element(esk8_0,the_carrier(esk5_0))
| $false
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0) ),
inference(rw,[status(thm)],[111,5571,theory(equality)]) ).
cnf(5607,negated_conjecture,
( element(esk8_0,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,esk6_0,esk7_0) ),
inference(cn,[status(thm)],[5606,theory(equality)]) ).
cnf(5618,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| $false
| ~ lattice(esk5_0)
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[5575,105,theory(equality)]) ).
cnf(5619,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| $false
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[5618,106,theory(equality)]) ).
cnf(5620,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[5619,104,theory(equality)]) ).
cnf(5621,negated_conjecture,
( latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0))
| empty_carrier(esk5_0) ),
inference(cn,[status(thm)],[5620,theory(equality)]) ).
cnf(5622,negated_conjecture,
latt_element_smaller(esk5_0,esk6_0,a_2_2_lattice3(esk5_0,esk7_0)),
inference(sr,[status(thm)],[5621,107,theory(equality)]) ).
cnf(5644,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ in(X1,a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(X1,the_carrier(esk5_0))
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[65,5622,theory(equality)]) ).
cnf(5648,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ in(X1,a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(X1,the_carrier(esk5_0))
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[5644,108,theory(equality)]) ).
cnf(5649,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ in(X1,a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(X1,the_carrier(esk5_0))
| $false
| $false ),
inference(rw,[status(thm)],[5648,104,theory(equality)]) ).
cnf(5650,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ in(X1,a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(X1,the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[5649,theory(equality)]) ).
cnf(5651,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| ~ in(X1,a_2_2_lattice3(esk5_0,esk7_0))
| ~ element(X1,the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[5650,107,theory(equality)]) ).
cnf(5741,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[5651,267,theory(equality)]) ).
cnf(5763,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,X1,esk7_0)
| $false ),
inference(rw,[status(thm)],[5741,104,theory(equality)]) ).
cnf(5764,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| empty_carrier(esk5_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,X1,esk7_0) ),
inference(cn,[status(thm)],[5763,theory(equality)]) ).
cnf(5765,negated_conjecture,
( below(esk5_0,X1,esk6_0)
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_set_smaller(esk5_0,X1,esk7_0) ),
inference(sr,[status(thm)],[5764,107,theory(equality)]) ).
cnf(5767,negated_conjecture,
( ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ latt_set_smaller(esk5_0,esk8_0,esk7_0)
| ~ element(esk8_0,the_carrier(esk5_0)) ),
inference(spm,[status(thm)],[5590,5765,theory(equality)]) ).
cnf(5837,negated_conjecture,
( ~ latt_set_smaller(esk5_0,esk6_0,esk7_0)
| ~ latt_set_smaller(esk5_0,esk8_0,esk7_0) ),
inference(csr,[status(thm)],[5767,5607]) ).
cnf(5838,negated_conjecture,
~ latt_set_smaller(esk5_0,esk6_0,esk7_0),
inference(csr,[status(thm)],[5837,5605]) ).
cnf(6088,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X2)
| latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X2)),X1)
| latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X2)),X2) ),
inference(spm,[status(thm)],[4284,3694,theory(equality)]) ).
cnf(6596,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X2)
| element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X2)),the_carrier(esk5_0)) ),
inference(spm,[status(thm)],[4315,3785,theory(equality)]) ).
cnf(8619,negated_conjecture,
( a_2_3_lattice3(esk5_0,X3) = a_2_2_lattice3(esk5_0,X3)
| latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X3),a_2_2_lattice3(esk5_0,X3)),X3) ),
inference(ef,[status(thm)],[6088,theory(equality)]) ).
cnf(8642,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| empty_carrier(esk5_0)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),a_2_3_lattice3(esk5_0,X1))
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[424,8619,theory(equality)]) ).
cnf(8652,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| empty_carrier(esk5_0)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),a_2_3_lattice3(esk5_0,X1))
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0))
| $false ),
inference(rw,[status(thm)],[8642,104,theory(equality)]) ).
cnf(8653,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| empty_carrier(esk5_0)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),a_2_3_lattice3(esk5_0,X1))
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[8652,theory(equality)]) ).
cnf(8654,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),a_2_3_lattice3(esk5_0,X1))
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[8653,107,theory(equality)]) ).
cnf(11160,plain,
( below(X1,esk1_3(X2,X3,a_2_3_lattice3(X1,X4)),X5)
| latt_element_smaller(X2,X3,a_2_3_lattice3(X1,X4))
| empty_carrier(X1)
| empty_carrier(X2)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X5,X4)
| ~ element(X5,the_carrier(X1))
| ~ element(X3,the_carrier(X2))
| ~ latt_str(X1)
| ~ latt_str(X2) ),
inference(csr,[status(thm)],[1088,63]) ).
cnf(11163,plain,
( latt_element_smaller(X1,X2,a_2_3_lattice3(X1,X3))
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ in(X2,X3) ),
inference(spm,[status(thm)],[62,11160,theory(equality)]) ).
cnf(76883,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| ~ in(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),a_2_3_lattice3(esk5_0,X1)) ),
inference(csr,[status(thm)],[8654,4315]) ).
cnf(76890,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| empty_carrier(esk5_0)
| ~ complete_latt_str(esk5_0)
| ~ lattice(esk5_0)
| ~ latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),X1)
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[76883,271,theory(equality)]) ).
cnf(76903,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| empty_carrier(esk5_0)
| $false
| ~ lattice(esk5_0)
| ~ latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),X1)
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[76890,105,theory(equality)]) ).
cnf(76904,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| empty_carrier(esk5_0)
| $false
| $false
| ~ latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),X1)
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[76903,106,theory(equality)]) ).
cnf(76905,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| empty_carrier(esk5_0)
| $false
| $false
| ~ latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),X1)
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0))
| $false ),
inference(rw,[status(thm)],[76904,104,theory(equality)]) ).
cnf(76906,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| empty_carrier(esk5_0)
| ~ latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),X1)
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[76905,theory(equality)]) ).
cnf(76907,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| ~ latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),X1)
| ~ element(esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[76906,107,theory(equality)]) ).
cnf(77034,negated_conjecture,
( a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1)
| ~ latt_set_smaller(esk5_0,esk9_2(a_2_3_lattice3(esk5_0,X1),a_2_2_lattice3(esk5_0,X1)),X1) ),
inference(csr,[status(thm)],[76907,6596]) ).
cnf(77035,negated_conjecture,
a_2_3_lattice3(esk5_0,X1) = a_2_2_lattice3(esk5_0,X1),
inference(csr,[status(thm)],[77034,8619]) ).
cnf(77065,negated_conjecture,
( latt_element_smaller(esk5_0,X1,a_2_2_lattice3(esk5_0,X2))
| empty_carrier(esk5_0)
| ~ complete_latt_str(esk5_0)
| ~ lattice(esk5_0)
| ~ in(X1,X2)
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[11163,77035,theory(equality)]) ).
cnf(78631,negated_conjecture,
( latt_element_smaller(esk5_0,X1,a_2_2_lattice3(esk5_0,X2))
| empty_carrier(esk5_0)
| $false
| ~ lattice(esk5_0)
| ~ in(X1,X2)
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[77065,105,theory(equality)]) ).
cnf(78632,negated_conjecture,
( latt_element_smaller(esk5_0,X1,a_2_2_lattice3(esk5_0,X2))
| empty_carrier(esk5_0)
| $false
| $false
| ~ in(X1,X2)
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[78631,106,theory(equality)]) ).
cnf(78633,negated_conjecture,
( latt_element_smaller(esk5_0,X1,a_2_2_lattice3(esk5_0,X2))
| empty_carrier(esk5_0)
| $false
| $false
| ~ in(X1,X2)
| ~ element(X1,the_carrier(esk5_0))
| $false ),
inference(rw,[status(thm)],[78632,104,theory(equality)]) ).
cnf(78634,negated_conjecture,
( latt_element_smaller(esk5_0,X1,a_2_2_lattice3(esk5_0,X2))
| empty_carrier(esk5_0)
| ~ in(X1,X2)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[78633,theory(equality)]) ).
cnf(78635,negated_conjecture,
( latt_element_smaller(esk5_0,X1,a_2_2_lattice3(esk5_0,X2))
| ~ in(X1,X2)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[78634,107,theory(equality)]) ).
cnf(80840,negated_conjecture,
( below(esk5_0,X1,X2)
| empty_carrier(esk5_0)
| join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,X3)) != X1
| ~ complete_latt_str(esk5_0)
| ~ lattice(esk5_0)
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_str(esk5_0)
| ~ in(X2,X3) ),
inference(spm,[status(thm)],[135,78635,theory(equality)]) ).
cnf(80848,negated_conjecture,
( below(esk5_0,X1,X2)
| empty_carrier(esk5_0)
| join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,X3)) != X1
| $false
| ~ lattice(esk5_0)
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_str(esk5_0)
| ~ in(X2,X3) ),
inference(rw,[status(thm)],[80840,105,theory(equality)]) ).
cnf(80849,negated_conjecture,
( below(esk5_0,X1,X2)
| empty_carrier(esk5_0)
| join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,X3)) != X1
| $false
| $false
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_str(esk5_0)
| ~ in(X2,X3) ),
inference(rw,[status(thm)],[80848,106,theory(equality)]) ).
cnf(80850,negated_conjecture,
( below(esk5_0,X1,X2)
| empty_carrier(esk5_0)
| join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,X3)) != X1
| $false
| $false
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0))
| $false
| ~ in(X2,X3) ),
inference(rw,[status(thm)],[80849,104,theory(equality)]) ).
cnf(80851,negated_conjecture,
( below(esk5_0,X1,X2)
| empty_carrier(esk5_0)
| join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,X3)) != X1
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0))
| ~ in(X2,X3) ),
inference(cn,[status(thm)],[80850,theory(equality)]) ).
cnf(80852,negated_conjecture,
( below(esk5_0,X1,X2)
| join_of_latt_set(esk5_0,a_2_2_lattice3(esk5_0,X3)) != X1
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0))
| ~ in(X2,X3) ),
inference(sr,[status(thm)],[80851,107,theory(equality)]) ).
cnf(84599,negated_conjecture,
( below(esk5_0,X1,X2)
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,X3) != X1
| ~ in(X2,X3)
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[80852,214,theory(equality)]) ).
cnf(84635,negated_conjecture,
( below(esk5_0,X1,X2)
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,X3) != X1
| ~ in(X2,X3)
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0))
| $false ),
inference(rw,[status(thm)],[84599,104,theory(equality)]) ).
cnf(84636,negated_conjecture,
( below(esk5_0,X1,X2)
| empty_carrier(esk5_0)
| meet_of_latt_set(esk5_0,X3) != X1
| ~ in(X2,X3)
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[84635,theory(equality)]) ).
cnf(84637,negated_conjecture,
( below(esk5_0,X1,X2)
| meet_of_latt_set(esk5_0,X3) != X1
| ~ in(X2,X3)
| ~ element(X2,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[84636,107,theory(equality)]) ).
cnf(84646,negated_conjecture,
( below(esk5_0,meet_of_latt_set(esk5_0,X1),X2)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(esk5_0))
| ~ element(meet_of_latt_set(esk5_0,X1),the_carrier(esk5_0)) ),
inference(er,[status(thm)],[84637,theory(equality)]) ).
cnf(84671,negated_conjecture,
( below(esk5_0,esk6_0,X1)
| ~ in(X1,esk7_0)
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ element(X1,the_carrier(esk5_0)) ),
inference(spm,[status(thm)],[84646,5571,theory(equality)]) ).
cnf(84680,negated_conjecture,
( below(esk5_0,esk6_0,X1)
| ~ in(X1,esk7_0)
| $false
| ~ element(X1,the_carrier(esk5_0)) ),
inference(rw,[status(thm)],[84671,108,theory(equality)]) ).
cnf(84681,negated_conjecture,
( below(esk5_0,esk6_0,X1)
| ~ in(X1,esk7_0)
| ~ element(X1,the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[84680,theory(equality)]) ).
cnf(84700,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| empty_carrier(esk5_0)
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0)
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0)
| ~ element(esk11_3(esk5_0,esk6_0,X1),the_carrier(esk5_0)) ),
inference(spm,[status(thm)],[142,84681,theory(equality)]) ).
cnf(84702,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| empty_carrier(esk5_0)
| $false
| ~ latt_str(esk5_0)
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0)
| ~ element(esk11_3(esk5_0,esk6_0,X1),the_carrier(esk5_0)) ),
inference(rw,[status(thm)],[84700,108,theory(equality)]) ).
cnf(84703,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| empty_carrier(esk5_0)
| $false
| $false
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0)
| ~ element(esk11_3(esk5_0,esk6_0,X1),the_carrier(esk5_0)) ),
inference(rw,[status(thm)],[84702,104,theory(equality)]) ).
cnf(84704,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| empty_carrier(esk5_0)
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0)
| ~ element(esk11_3(esk5_0,esk6_0,X1),the_carrier(esk5_0)) ),
inference(cn,[status(thm)],[84703,theory(equality)]) ).
cnf(84705,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0)
| ~ element(esk11_3(esk5_0,esk6_0,X1),the_carrier(esk5_0)) ),
inference(sr,[status(thm)],[84704,107,theory(equality)]) ).
cnf(84819,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| empty_carrier(esk5_0)
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0)
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[84705,144,theory(equality)]) ).
cnf(84824,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| empty_carrier(esk5_0)
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0)
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[84819,108,theory(equality)]) ).
cnf(84825,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| empty_carrier(esk5_0)
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0)
| $false
| $false ),
inference(rw,[status(thm)],[84824,104,theory(equality)]) ).
cnf(84826,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| empty_carrier(esk5_0)
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0) ),
inference(cn,[status(thm)],[84825,theory(equality)]) ).
cnf(84827,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,X1)
| ~ in(esk11_3(esk5_0,esk6_0,X1),esk7_0) ),
inference(sr,[status(thm)],[84826,107,theory(equality)]) ).
cnf(84848,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,esk7_0)
| empty_carrier(esk5_0)
| ~ element(esk6_0,the_carrier(esk5_0))
| ~ latt_str(esk5_0) ),
inference(spm,[status(thm)],[84827,143,theory(equality)]) ).
cnf(84849,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,esk7_0)
| empty_carrier(esk5_0)
| $false
| ~ latt_str(esk5_0) ),
inference(rw,[status(thm)],[84848,108,theory(equality)]) ).
cnf(84850,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,esk7_0)
| empty_carrier(esk5_0)
| $false
| $false ),
inference(rw,[status(thm)],[84849,104,theory(equality)]) ).
cnf(84851,negated_conjecture,
( latt_set_smaller(esk5_0,esk6_0,esk7_0)
| empty_carrier(esk5_0) ),
inference(cn,[status(thm)],[84850,theory(equality)]) ).
cnf(84852,negated_conjecture,
empty_carrier(esk5_0),
inference(sr,[status(thm)],[84851,5838,theory(equality)]) ).
cnf(84853,negated_conjecture,
$false,
inference(sr,[status(thm)],[84852,107,theory(equality)]) ).
cnf(84854,negated_conjecture,
$false,
84853,
[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/SEU351+1.p
% --creating new selector for []
% -running prover on /tmp/tmpE44kEP/sel_SEU351+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU351+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU351+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU351+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
%
%------------------------------------------------------------------------------