TSTP Solution File: SEU358+1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SEU358+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:26:09 EDT 2023
% Result : Theorem 83.08s 10.95s
% Output : CNFRefutation 83.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 35
% Syntax : Number of formulae : 279 ( 39 unt; 0 def)
% Number of atoms : 1441 ( 108 equ)
% Maximal formula atoms : 50 ( 5 avg)
% Number of connectives : 1906 ( 744 ~; 838 |; 202 &)
% ( 23 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 2 con; 0-3 aty)
% Number of variables : 542 ( 16 sgn; 215 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( reflexive(k2_lattice3(X1))
& antisymmetric(k2_lattice3(X1))
& transitive(k2_lattice3(X1))
& v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',dt_k2_lattice3) ).
fof(t29_yellow_0,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( join_of_latt_set(X1,X2) = join_on_relstr(poset_of_lattice(X1),X2)
& meet_of_latt_set(X1,X2) = meet_on_relstr(poset_of_lattice(X1),X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t29_yellow_0) ).
fof(rc5_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',rc5_struct_0) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',dt_l1_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',dt_l3_lattices) ).
fof(d2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',d2_lattice3) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',redefinition_m2_relset_1) ).
fof(dt_k3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',dt_k3_lattice3) ).
fof(free_g1_orders_2,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ! [X3,X4] :
( rel_str_of(X1,X2) = rel_str_of(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',free_g1_orders_2) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t5_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',existence_m1_subset_1) ).
fof(abstractness_v1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( strict_rel_str(X1)
=> X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',abstractness_v1_orders_2) ).
fof(dt_k16_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(meet_of_latt_set(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',dt_k16_lattice3) ).
fof(dt_k15_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',dt_k15_lattice3) ).
fof(dt_k5_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',dt_k5_lattice3) ).
fof(d3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',d3_lattice3) ).
fof(d21_lattice3,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('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',d21_lattice3) ).
fof(fc1_orders_2,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& relation_of2(X2,X1,X1) )
=> ( ~ empty_carrier(rel_str_of(X1,X2))
& strict_rel_str(rel_str_of(X1,X2)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',fc1_orders_2) ).
fof(d4_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',d4_lattice3) ).
fof(t28_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t28_lattice3) ).
fof(t34_lattice3,axiom,
! [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('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t34_lattice3) ).
fof(t7_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t7_lattice3) ).
fof(t30_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t30_lattice3) ).
fof(t16_yellow_0,axiom,
! [X1] :
( ( antisymmetric_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( ex_inf_of_relstr_set(X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& relstr_element_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_element_smaller(X1,X2,X4)
=> related(X1,X4,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t16_yellow_0) ).
fof(t15_yellow_0,axiom,
! [X1] :
( ( antisymmetric_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( ex_sup_of_relstr_set(X1,X2)
<=> ? [X3] :
( element(X3,the_carrier(X1))
& relstr_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X4)
=> related(X1,X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t15_yellow_0) ).
fof(redefinition_r3_orders_2,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',redefinition_r3_orders_2) ).
fof(cc1_lattices,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('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',cc1_lattices) ).
fof(redefinition_r3_lattices,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('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',redefinition_r3_lattices) ).
fof(d10_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( ex_inf_of_relstr_set(X1,X2)
=> ( X3 = meet_on_relstr(X1,X2)
<=> ( relstr_element_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_element_smaller(X1,X2,X4)
=> related(X1,X4,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',d10_yellow_0) ).
fof(dt_k2_yellow_0,axiom,
! [X1,X2] :
( rel_str(X1)
=> element(meet_on_relstr(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',dt_k2_yellow_0) ).
fof(t31_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t31_lattice3) ).
fof(d9_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2,X3] :
( element(X3,the_carrier(X1))
=> ( ex_sup_of_relstr_set(X1,X2)
=> ( X3 = join_on_relstr(X1,X2)
<=> ( relstr_set_smaller(X1,X2,X3)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_set_smaller(X1,X2,X4)
=> related(X1,X3,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',d9_yellow_0) ).
fof(dt_k1_yellow_0,axiom,
! [X1,X2] :
( rel_str(X1)
=> element(join_on_relstr(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',dt_k1_yellow_0) ).
fof(t29_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_element_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_set_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p',t29_lattice3) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( reflexive(k2_lattice3(X1))
& antisymmetric(k2_lattice3(X1))
& transitive(k2_lattice3(X1))
& v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_lattice3]) ).
fof(c_0_36,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( join_of_latt_set(X1,X2) = join_on_relstr(poset_of_lattice(X1),X2)
& meet_of_latt_set(X1,X2) = meet_on_relstr(poset_of_lattice(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t29_yellow_0])]) ).
fof(c_0_37,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc5_struct_0]) ).
fof(c_0_38,plain,
! [X54] :
( ~ meet_semilatt_str(X54)
| one_sorted_str(X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(c_0_39,plain,
! [X57] :
( ( meet_semilatt_str(X57)
| ~ latt_str(X57) )
& ( join_semilatt_str(X57)
| ~ latt_str(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_40,plain,
! [X45] :
( ( reflexive(k2_lattice3(X45))
| empty_carrier(X45)
| ~ lattice(X45)
| ~ latt_str(X45) )
& ( antisymmetric(k2_lattice3(X45))
| empty_carrier(X45)
| ~ lattice(X45)
| ~ latt_str(X45) )
& ( transitive(k2_lattice3(X45))
| empty_carrier(X45)
| ~ lattice(X45)
| ~ latt_str(X45) )
& ( v1_partfun1(k2_lattice3(X45),the_carrier(X45),the_carrier(X45))
| empty_carrier(X45)
| ~ lattice(X45)
| ~ latt_str(X45) )
& ( relation_of2_as_subset(k2_lattice3(X45),the_carrier(X45),the_carrier(X45))
| empty_carrier(X45)
| ~ lattice(X45)
| ~ latt_str(X45) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_41,negated_conjecture,
( ~ empty_carrier(esk26_0)
& lattice(esk26_0)
& complete_latt_str(esk26_0)
& latt_str(esk26_0)
& ( join_of_latt_set(esk26_0,esk27_0) != join_on_relstr(poset_of_lattice(esk26_0),esk27_0)
| meet_of_latt_set(esk26_0,esk27_0) != meet_on_relstr(poset_of_lattice(esk26_0),esk27_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_42,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1)) ),
inference(fof_simplification,[status(thm)],[d2_lattice3]) ).
fof(c_0_43,plain,
! [X104] :
( ( element(esk21_1(X104),powerset(the_carrier(X104)))
| empty_carrier(X104)
| ~ one_sorted_str(X104) )
& ( ~ empty(esk21_1(X104))
| empty_carrier(X104)
| ~ one_sorted_str(X104) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
cnf(c_0_44,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_46,plain,
! [X107,X108,X109] :
( ( ~ relation_of2_as_subset(X109,X107,X108)
| relation_of2(X109,X107,X108) )
& ( ~ relation_of2(X109,X107,X108)
| relation_of2_as_subset(X109,X107,X108) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_47,plain,
( relation_of2_as_subset(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,negated_conjecture,
lattice(esk26_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,negated_conjecture,
latt_str(esk26_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,negated_conjecture,
~ empty_carrier(esk26_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_51,plain,
! [X27] :
( empty_carrier(X27)
| ~ lattice(X27)
| ~ latt_str(X27)
| poset_of_lattice(X27) = rel_str_of(the_carrier(X27),k2_lattice3(X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])]) ).
fof(c_0_52,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_lattice3]) ).
cnf(c_0_53,plain,
( element(esk21_1(X1),powerset(the_carrier(X1)))
| empty_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_54,plain,
( one_sorted_str(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_55,plain,
! [X90,X91,X92,X93] :
( ( X90 = X92
| rel_str_of(X90,X91) != rel_str_of(X92,X93)
| ~ relation_of2(X91,X90,X90) )
& ( X91 = X93
| rel_str_of(X90,X91) != rel_str_of(X92,X93)
| ~ relation_of2(X91,X90,X90) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])]) ).
cnf(c_0_56,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,negated_conjecture,
relation_of2_as_subset(k2_lattice3(esk26_0),the_carrier(esk26_0),the_carrier(esk26_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_58,plain,
( empty_carrier(X1)
| poset_of_lattice(X1) = rel_str_of(the_carrier(X1),k2_lattice3(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_59,plain,
! [X48] :
( ( strict_rel_str(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) )
& ( reflexive_relstr(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) )
& ( transitive_relstr(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) )
& ( antisymmetric_relstr(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) )
& ( rel_str(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
fof(c_0_60,plain,
! [X169,X170,X171] :
( ~ in(X169,X170)
| ~ element(X170,powerset(X171))
| ~ empty(X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_61,plain,
( element(esk21_1(X1),powerset(the_carrier(X1)))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_62,plain,
! [X147,X148] :
( ~ element(X147,X148)
| empty(X148)
| in(X147,X148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_63,plain,
! [X70] : element(esk10_1(X70),X70),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_64,plain,
( X1 = X2
| rel_str_of(X3,X1) != rel_str_of(X4,X2)
| ~ relation_of2(X1,X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,negated_conjecture,
relation_of2(k2_lattice3(esk26_0),the_carrier(esk26_0),the_carrier(esk26_0)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_66,negated_conjecture,
rel_str_of(the_carrier(esk26_0),k2_lattice3(esk26_0)) = poset_of_lattice(esk26_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_48]),c_0_49])]),c_0_50]) ).
fof(c_0_67,plain,
! [X6] :
( ~ rel_str(X6)
| ~ strict_rel_str(X6)
| X6 = rel_str_of(the_carrier(X6),the_InternalRel(X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])]) ).
cnf(c_0_68,plain,
( strict_rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
( rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_70,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,negated_conjecture,
element(esk21_1(esk26_0),powerset(the_carrier(esk26_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_49]),c_0_50]) ).
cnf(c_0_72,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
element(esk10_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_74,negated_conjecture,
( k2_lattice3(esk26_0) = X1
| rel_str_of(X2,X1) != poset_of_lattice(esk26_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_75,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ strict_rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_76,negated_conjecture,
strict_rel_str(poset_of_lattice(esk26_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_77,negated_conjecture,
rel_str(poset_of_lattice(esk26_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_48]),c_0_49])]),c_0_50]) ).
fof(c_0_78,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(meet_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k16_lattice3]) ).
fof(c_0_79,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> element(join_of_latt_set(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k15_lattice3]) ).
cnf(c_0_80,negated_conjecture,
( ~ empty(the_carrier(esk26_0))
| ~ in(X1,esk21_1(esk26_0)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_81,plain,
( empty(X1)
| in(esk10_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
fof(c_0_82,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattice3]) ).
cnf(c_0_83,plain,
( X1 = X2
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| ~ relation_of2(X3,X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_84,negated_conjecture,
the_InternalRel(poset_of_lattice(esk26_0)) = k2_lattice3(esk26_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75])]),c_0_76]),c_0_77])]) ).
fof(c_0_85,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d3_lattice3]) ).
fof(c_0_86,plain,
! [X41,X42] :
( empty_carrier(X41)
| ~ latt_str(X41)
| element(meet_of_latt_set(X41,X42),the_carrier(X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])]) ).
fof(c_0_87,plain,
! [X39,X40] :
( empty_carrier(X39)
| ~ latt_str(X39)
| element(join_of_latt_set(X39,X40),the_carrier(X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])]) ).
fof(c_0_88,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)],[d21_lattice3]) ).
fof(c_0_89,plain,
! [X1,X2] :
( ( ~ empty(X1)
& relation_of2(X2,X1,X1) )
=> ( ~ empty_carrier(rel_str_of(X1,X2))
& strict_rel_str(rel_str_of(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc1_orders_2]) ).
cnf(c_0_90,plain,
( empty_carrier(X1)
| ~ empty(esk21_1(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_91,negated_conjecture,
( empty(esk21_1(esk26_0))
| ~ empty(the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
fof(c_0_92,plain,
! [X51,X52] :
( empty_carrier(X51)
| ~ lattice(X51)
| ~ latt_str(X51)
| ~ element(X52,the_carrier(poset_of_lattice(X51)))
| element(cast_to_el_of_lattice(X51,X52),the_carrier(X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])]) ).
cnf(c_0_93,negated_conjecture,
( the_carrier(esk26_0) = X1
| rel_str_of(X1,X2) != poset_of_lattice(esk26_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_65]),c_0_66]) ).
cnf(c_0_94,negated_conjecture,
rel_str_of(the_carrier(poset_of_lattice(esk26_0)),k2_lattice3(esk26_0)) = poset_of_lattice(esk26_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_84]),c_0_76]),c_0_77])]) ).
fof(c_0_95,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d4_lattice3]) ).
fof(c_0_96,plain,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t28_lattice3]) ).
fof(c_0_97,plain,
! [X28,X29] :
( empty_carrier(X28)
| ~ lattice(X28)
| ~ latt_str(X28)
| ~ element(X29,the_carrier(X28))
| cast_to_el_of_LattPOSet(X28,X29) = X29 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])]) ).
cnf(c_0_98,plain,
( empty_carrier(X1)
| element(meet_of_latt_set(X1,X2),the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_99,plain,
! [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)],[t34_lattice3]) ).
fof(c_0_100,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below_refl(X1,X2,X3)
<=> related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[t7_lattice3]) ).
fof(c_0_101,plain,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t30_lattice3]) ).
cnf(c_0_102,plain,
( empty_carrier(X1)
| element(join_of_latt_set(X1,X2),the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_103,plain,
! [X20,X21,X22,X23] :
( ( latt_element_smaller(X20,X22,X21)
| X22 != join_of_latt_set(X20,X21)
| ~ element(X22,the_carrier(X20))
| empty_carrier(X20)
| ~ lattice(X20)
| ~ complete_latt_str(X20)
| ~ latt_str(X20)
| empty_carrier(X20)
| ~ latt_str(X20) )
& ( ~ element(X23,the_carrier(X20))
| ~ latt_element_smaller(X20,X23,X21)
| below(X20,X22,X23)
| X22 != join_of_latt_set(X20,X21)
| ~ element(X22,the_carrier(X20))
| empty_carrier(X20)
| ~ lattice(X20)
| ~ complete_latt_str(X20)
| ~ latt_str(X20)
| empty_carrier(X20)
| ~ latt_str(X20) )
& ( element(esk2_3(X20,X21,X22),the_carrier(X20))
| ~ latt_element_smaller(X20,X22,X21)
| X22 = join_of_latt_set(X20,X21)
| ~ element(X22,the_carrier(X20))
| empty_carrier(X20)
| ~ lattice(X20)
| ~ complete_latt_str(X20)
| ~ latt_str(X20)
| empty_carrier(X20)
| ~ latt_str(X20) )
& ( latt_element_smaller(X20,esk2_3(X20,X21,X22),X21)
| ~ latt_element_smaller(X20,X22,X21)
| X22 = join_of_latt_set(X20,X21)
| ~ element(X22,the_carrier(X20))
| empty_carrier(X20)
| ~ lattice(X20)
| ~ complete_latt_str(X20)
| ~ latt_str(X20)
| empty_carrier(X20)
| ~ latt_str(X20) )
& ( ~ below(X20,X22,esk2_3(X20,X21,X22))
| ~ latt_element_smaller(X20,X22,X21)
| X22 = join_of_latt_set(X20,X21)
| ~ element(X22,the_carrier(X20))
| empty_carrier(X20)
| ~ lattice(X20)
| ~ complete_latt_str(X20)
| ~ latt_str(X20)
| empty_carrier(X20)
| ~ latt_str(X20) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])])])]) ).
fof(c_0_104,plain,
! [X77,X78] :
( ( ~ empty_carrier(rel_str_of(X77,X78))
| empty(X77)
| ~ relation_of2(X78,X77,X77) )
& ( strict_rel_str(rel_str_of(X77,X78))
| empty(X77)
| ~ relation_of2(X78,X77,X77) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])])]) ).
cnf(c_0_105,negated_conjecture,
( ~ one_sorted_str(esk26_0)
| ~ empty(the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_50]) ).
cnf(c_0_106,plain,
( empty_carrier(X1)
| element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_107,negated_conjecture,
the_carrier(poset_of_lattice(esk26_0)) = the_carrier(esk26_0),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
fof(c_0_108,plain,
! [X30,X31] :
( empty_carrier(X30)
| ~ lattice(X30)
| ~ latt_str(X30)
| ~ element(X31,the_carrier(poset_of_lattice(X30)))
| cast_to_el_of_lattice(X30,X31) = X31 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])]) ).
fof(c_0_109,plain,
! [X130,X131,X133,X134,X135] :
( ( element(esk24_2(X130,X131),the_carrier(X130))
| ~ ex_inf_of_relstr_set(X130,X131)
| ~ antisymmetric_relstr(X130)
| ~ rel_str(X130) )
& ( relstr_element_smaller(X130,X131,esk24_2(X130,X131))
| ~ ex_inf_of_relstr_set(X130,X131)
| ~ antisymmetric_relstr(X130)
| ~ rel_str(X130) )
& ( ~ element(X133,the_carrier(X130))
| ~ relstr_element_smaller(X130,X131,X133)
| related(X130,X133,esk24_2(X130,X131))
| ~ ex_inf_of_relstr_set(X130,X131)
| ~ antisymmetric_relstr(X130)
| ~ rel_str(X130) )
& ( element(esk25_3(X130,X134,X135),the_carrier(X130))
| ~ element(X135,the_carrier(X130))
| ~ relstr_element_smaller(X130,X134,X135)
| ex_inf_of_relstr_set(X130,X134)
| ~ antisymmetric_relstr(X130)
| ~ rel_str(X130) )
& ( relstr_element_smaller(X130,X134,esk25_3(X130,X134,X135))
| ~ element(X135,the_carrier(X130))
| ~ relstr_element_smaller(X130,X134,X135)
| ex_inf_of_relstr_set(X130,X134)
| ~ antisymmetric_relstr(X130)
| ~ rel_str(X130) )
& ( ~ related(X130,esk25_3(X130,X134,X135),X135)
| ~ element(X135,the_carrier(X130))
| ~ relstr_element_smaller(X130,X134,X135)
| ex_inf_of_relstr_set(X130,X134)
| ~ antisymmetric_relstr(X130)
| ~ rel_str(X130) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_yellow_0])])])])])]) ).
cnf(c_0_110,plain,
( antisymmetric_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_111,plain,
! [X139,X140,X141] :
( ( ~ latt_set_smaller(X140,X141,X139)
| relstr_element_smaller(poset_of_lattice(X140),X139,cast_to_el_of_LattPOSet(X140,X141))
| ~ element(X141,the_carrier(X140))
| empty_carrier(X140)
| ~ lattice(X140)
| ~ latt_str(X140) )
& ( ~ relstr_element_smaller(poset_of_lattice(X140),X139,cast_to_el_of_LattPOSet(X140,X141))
| latt_set_smaller(X140,X141,X139)
| ~ element(X141,the_carrier(X140))
| empty_carrier(X140)
| ~ lattice(X140)
| ~ latt_str(X140) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])])]) ).
cnf(c_0_112,plain,
( empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_113,negated_conjecture,
element(meet_of_latt_set(esk26_0,X1),the_carrier(esk26_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_49]),c_0_50]) ).
fof(c_0_114,plain,
! [X158,X159,X160,X161,X162] :
( ( latt_set_smaller(X158,X159,X160)
| X159 != meet_of_latt_set(X158,X160)
| ~ element(X159,the_carrier(X158))
| empty_carrier(X158)
| ~ lattice(X158)
| ~ complete_latt_str(X158)
| ~ latt_str(X158) )
& ( ~ element(X161,the_carrier(X158))
| ~ latt_set_smaller(X158,X161,X160)
| below_refl(X158,X161,X159)
| X159 != meet_of_latt_set(X158,X160)
| ~ element(X159,the_carrier(X158))
| empty_carrier(X158)
| ~ lattice(X158)
| ~ complete_latt_str(X158)
| ~ latt_str(X158) )
& ( element(esk29_3(X158,X159,X162),the_carrier(X158))
| ~ latt_set_smaller(X158,X159,X162)
| X159 = meet_of_latt_set(X158,X162)
| ~ element(X159,the_carrier(X158))
| empty_carrier(X158)
| ~ lattice(X158)
| ~ complete_latt_str(X158)
| ~ latt_str(X158) )
& ( latt_set_smaller(X158,esk29_3(X158,X159,X162),X162)
| ~ latt_set_smaller(X158,X159,X162)
| X159 = meet_of_latt_set(X158,X162)
| ~ element(X159,the_carrier(X158))
| empty_carrier(X158)
| ~ lattice(X158)
| ~ complete_latt_str(X158)
| ~ latt_str(X158) )
& ( ~ below_refl(X158,esk29_3(X158,X159,X162),X159)
| ~ latt_set_smaller(X158,X159,X162)
| X159 = meet_of_latt_set(X158,X162)
| ~ element(X159,the_carrier(X158))
| empty_carrier(X158)
| ~ lattice(X158)
| ~ complete_latt_str(X158)
| ~ latt_str(X158) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_99])])])])])]) ).
fof(c_0_115,plain,
! [X175,X176,X177] :
( ( ~ below_refl(X175,X176,X177)
| related_reflexive(poset_of_lattice(X175),cast_to_el_of_LattPOSet(X175,X176),cast_to_el_of_LattPOSet(X175,X177))
| ~ element(X177,the_carrier(X175))
| ~ element(X176,the_carrier(X175))
| empty_carrier(X175)
| ~ lattice(X175)
| ~ latt_str(X175) )
& ( ~ related_reflexive(poset_of_lattice(X175),cast_to_el_of_LattPOSet(X175,X176),cast_to_el_of_LattPOSet(X175,X177))
| below_refl(X175,X176,X177)
| ~ element(X177,the_carrier(X175))
| ~ element(X176,the_carrier(X175))
| empty_carrier(X175)
| ~ lattice(X175)
| ~ latt_str(X175) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])])]) ).
fof(c_0_116,plain,
! [X123,X124,X126,X127,X128] :
( ( element(esk22_2(X123,X124),the_carrier(X123))
| ~ ex_sup_of_relstr_set(X123,X124)
| ~ antisymmetric_relstr(X123)
| ~ rel_str(X123) )
& ( relstr_set_smaller(X123,X124,esk22_2(X123,X124))
| ~ ex_sup_of_relstr_set(X123,X124)
| ~ antisymmetric_relstr(X123)
| ~ rel_str(X123) )
& ( ~ element(X126,the_carrier(X123))
| ~ relstr_set_smaller(X123,X124,X126)
| related(X123,esk22_2(X123,X124),X126)
| ~ ex_sup_of_relstr_set(X123,X124)
| ~ antisymmetric_relstr(X123)
| ~ rel_str(X123) )
& ( element(esk23_3(X123,X127,X128),the_carrier(X123))
| ~ element(X128,the_carrier(X123))
| ~ relstr_set_smaller(X123,X127,X128)
| ex_sup_of_relstr_set(X123,X127)
| ~ antisymmetric_relstr(X123)
| ~ rel_str(X123) )
& ( relstr_set_smaller(X123,X127,esk23_3(X123,X127,X128))
| ~ element(X128,the_carrier(X123))
| ~ relstr_set_smaller(X123,X127,X128)
| ex_sup_of_relstr_set(X123,X127)
| ~ antisymmetric_relstr(X123)
| ~ rel_str(X123) )
& ( ~ related(X123,X128,esk23_3(X123,X127,X128))
| ~ element(X128,the_carrier(X123))
| ~ relstr_set_smaller(X123,X127,X128)
| ex_sup_of_relstr_set(X123,X127)
| ~ antisymmetric_relstr(X123)
| ~ rel_str(X123) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[t15_yellow_0])])])])])]) ).
fof(c_0_117,plain,
! [X152,X153,X154] :
( ( ~ latt_element_smaller(X153,X154,X152)
| relstr_set_smaller(poset_of_lattice(X153),X152,cast_to_el_of_LattPOSet(X153,X154))
| ~ element(X154,the_carrier(X153))
| empty_carrier(X153)
| ~ lattice(X153)
| ~ latt_str(X153) )
& ( ~ relstr_set_smaller(poset_of_lattice(X153),X152,cast_to_el_of_LattPOSet(X153,X154))
| latt_element_smaller(X153,X154,X152)
| ~ element(X154,the_carrier(X153))
| empty_carrier(X153)
| ~ lattice(X153)
| ~ latt_str(X153) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_101])])])]) ).
cnf(c_0_118,negated_conjecture,
element(join_of_latt_set(esk26_0,X1),the_carrier(esk26_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_49]),c_0_50]) ).
cnf(c_0_119,plain,
( latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X1)
| X2 != join_of_latt_set(X1,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
fof(c_0_120,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& rel_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> ( related_reflexive(X1,X2,X3)
<=> related(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_orders_2]) ).
cnf(c_0_121,plain,
( empty(X1)
| ~ empty_carrier(rel_str_of(X1,X2))
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_122,negated_conjecture,
~ empty(the_carrier(esk26_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_54]),c_0_49])]) ).
cnf(c_0_123,negated_conjecture,
( element(cast_to_el_of_lattice(esk26_0,X1),the_carrier(esk26_0))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_124,plain,
( empty_carrier(X1)
| cast_to_el_of_lattice(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_125,plain,
( element(esk25_3(X1,X2,X3),the_carrier(X1))
| ex_inf_of_relstr_set(X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ relstr_element_smaller(X1,X2,X3)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_126,negated_conjecture,
antisymmetric_relstr(poset_of_lattice(esk26_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_127,plain,
( relstr_element_smaller(poset_of_lattice(X1),X3,cast_to_el_of_LattPOSet(X1,X2))
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_128,negated_conjecture,
cast_to_el_of_LattPOSet(esk26_0,meet_of_latt_set(esk26_0,X1)) = meet_of_latt_set(esk26_0,X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_129,plain,
( latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| X2 != meet_of_latt_set(X1,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_130,plain,
( relstr_element_smaller(X1,X2,esk25_3(X1,X2,X3))
| ex_inf_of_relstr_set(X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ relstr_element_smaller(X1,X2,X3)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_131,plain,
( related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
fof(c_0_132,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)],[cc1_lattices]) ).
cnf(c_0_133,plain,
( element(esk23_3(X1,X2,X3),the_carrier(X1))
| ex_sup_of_relstr_set(X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ relstr_set_smaller(X1,X2,X3)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_134,plain,
( relstr_set_smaller(poset_of_lattice(X1),X3,cast_to_el_of_LattPOSet(X1,X2))
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_135,negated_conjecture,
cast_to_el_of_LattPOSet(esk26_0,join_of_latt_set(esk26_0,X1)) = join_of_latt_set(esk26_0,X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_118]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_136,plain,
( empty_carrier(X1)
| latt_element_smaller(X1,X2,X3)
| X2 != join_of_latt_set(X1,X3)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(cn,[status(thm)],[c_0_119]) ).
cnf(c_0_137,plain,
( relstr_set_smaller(X1,X2,esk23_3(X1,X2,X3))
| ex_sup_of_relstr_set(X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ relstr_set_smaller(X1,X2,X3)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
fof(c_0_138,plain,
! [X113,X114,X115] :
( ( ~ related_reflexive(X113,X114,X115)
| related(X113,X114,X115)
| empty_carrier(X113)
| ~ reflexive_relstr(X113)
| ~ rel_str(X113)
| ~ element(X114,the_carrier(X113))
| ~ element(X115,the_carrier(X113)) )
& ( ~ related(X113,X114,X115)
| related_reflexive(X113,X114,X115)
| empty_carrier(X113)
| ~ reflexive_relstr(X113)
| ~ rel_str(X113)
| ~ element(X114,the_carrier(X113))
| ~ element(X115,the_carrier(X113)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])])]) ).
cnf(c_0_139,plain,
( reflexive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_140,negated_conjecture,
( ~ relation_of2(k2_lattice3(esk26_0),the_carrier(esk26_0),the_carrier(esk26_0))
| ~ empty_carrier(poset_of_lattice(esk26_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_66]),c_0_122]) ).
cnf(c_0_141,negated_conjecture,
( cast_to_el_of_LattPOSet(esk26_0,cast_to_el_of_lattice(esk26_0,X1)) = cast_to_el_of_lattice(esk26_0,X1)
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_123]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_142,negated_conjecture,
( cast_to_el_of_lattice(esk26_0,X1) = X1
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_107]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_143,negated_conjecture,
( ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1)
| element(esk25_3(poset_of_lattice(esk26_0),X1,X2),the_carrier(esk26_0))
| ~ relstr_element_smaller(poset_of_lattice(esk26_0),X1,X2)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_107]),c_0_126]),c_0_77])]) ).
cnf(c_0_144,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X2))
| ~ latt_set_smaller(esk26_0,meet_of_latt_set(esk26_0,X2),X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_113]),c_0_128]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_145,plain,
( latt_set_smaller(X1,meet_of_latt_set(X1,X2),X2)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_129]),c_0_98]) ).
cnf(c_0_146,negated_conjecture,
complete_latt_str(esk26_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_147,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(esk26_0),X1,esk25_3(poset_of_lattice(esk26_0),X1,X2))
| ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ relstr_element_smaller(poset_of_lattice(esk26_0),X1,X2)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_107]),c_0_126]),c_0_77])]) ).
cnf(c_0_148,negated_conjecture,
( related_reflexive(poset_of_lattice(esk26_0),cast_to_el_of_LattPOSet(esk26_0,X1),cast_to_el_of_LattPOSet(esk26_0,cast_to_el_of_lattice(esk26_0,X2)))
| ~ below_refl(esk26_0,X1,cast_to_el_of_lattice(esk26_0,X2))
| ~ element(X1,the_carrier(esk26_0))
| ~ element(X2,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_123]),c_0_48]),c_0_49])]),c_0_50]) ).
fof(c_0_149,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)],[redefinition_r3_lattices]) ).
fof(c_0_150,plain,
! [X5] :
( ( ~ empty_carrier(X5)
| empty_carrier(X5)
| ~ lattice(X5)
| ~ latt_str(X5) )
& ( join_commutative(X5)
| empty_carrier(X5)
| ~ lattice(X5)
| ~ latt_str(X5) )
& ( join_associative(X5)
| empty_carrier(X5)
| ~ lattice(X5)
| ~ latt_str(X5) )
& ( meet_commutative(X5)
| empty_carrier(X5)
| ~ lattice(X5)
| ~ latt_str(X5) )
& ( meet_associative(X5)
| empty_carrier(X5)
| ~ lattice(X5)
| ~ latt_str(X5) )
& ( meet_absorbing(X5)
| empty_carrier(X5)
| ~ lattice(X5)
| ~ latt_str(X5) )
& ( join_absorbing(X5)
| empty_carrier(X5)
| ~ lattice(X5)
| ~ latt_str(X5) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])])]) ).
cnf(c_0_151,plain,
( below(X2,X4,X1)
| empty_carrier(X2)
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| ~ latt_element_smaller(X2,X1,X3)
| X4 != join_of_latt_set(X2,X3)
| ~ element(X4,the_carrier(X2))
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_152,negated_conjecture,
( ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| element(esk23_3(poset_of_lattice(esk26_0),X1,X2),the_carrier(esk26_0))
| ~ relstr_set_smaller(poset_of_lattice(esk26_0),X1,X2)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_107]),c_0_126]),c_0_77])]) ).
cnf(c_0_153,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X2))
| ~ latt_element_smaller(esk26_0,join_of_latt_set(esk26_0,X2),X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_118]),c_0_135]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_154,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)],[inference(er,[status(thm)],[c_0_136]),c_0_102]) ).
cnf(c_0_155,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk26_0),X1,esk23_3(poset_of_lattice(esk26_0),X1,X2))
| ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ relstr_set_smaller(poset_of_lattice(esk26_0),X1,X2)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_107]),c_0_126]),c_0_77])]) ).
cnf(c_0_156,plain,
( related(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(X1,X2,X3)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_157,negated_conjecture,
reflexive_relstr(poset_of_lattice(esk26_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_158,negated_conjecture,
~ empty_carrier(poset_of_lattice(esk26_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_65])]) ).
cnf(c_0_159,negated_conjecture,
( related_reflexive(poset_of_lattice(esk26_0),cast_to_el_of_LattPOSet(esk26_0,X1),meet_of_latt_set(esk26_0,X2))
| ~ below_refl(esk26_0,X1,meet_of_latt_set(esk26_0,X2))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_113]),c_0_128]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_160,negated_conjecture,
( cast_to_el_of_LattPOSet(esk26_0,X1) = X1
| ~ element(X1,the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_161,plain,
( below_refl(X2,X1,X4)
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| ~ latt_set_smaller(X2,X1,X3)
| X4 != meet_of_latt_set(X2,X3)
| ~ element(X4,the_carrier(X2))
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_162,negated_conjecture,
( ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1)
| element(esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X2)),the_carrier(esk26_0))
| ~ latt_set_smaller(esk26_0,meet_of_latt_set(esk26_0,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_113])]) ).
cnf(c_0_163,negated_conjecture,
latt_set_smaller(esk26_0,meet_of_latt_set(esk26_0,X1),X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_164,plain,
( latt_set_smaller(X1,X3,X2)
| empty_carrier(X1)
| ~ relstr_element_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_165,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(esk26_0),X1,esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X2)))
| ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ latt_set_smaller(esk26_0,meet_of_latt_set(esk26_0,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_144]),c_0_113])]) ).
cnf(c_0_166,negated_conjecture,
( related_reflexive(poset_of_lattice(esk26_0),join_of_latt_set(esk26_0,X1),cast_to_el_of_LattPOSet(esk26_0,cast_to_el_of_lattice(esk26_0,X2)))
| ~ below_refl(esk26_0,join_of_latt_set(esk26_0,X1),cast_to_el_of_lattice(esk26_0,X2))
| ~ element(X2,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_135]),c_0_118])]) ).
fof(c_0_167,plain,
! [X110,X111,X112] :
( ( ~ below_refl(X110,X111,X112)
| below(X110,X111,X112)
| empty_carrier(X110)
| ~ meet_commutative(X110)
| ~ meet_absorbing(X110)
| ~ join_absorbing(X110)
| ~ latt_str(X110)
| ~ element(X111,the_carrier(X110))
| ~ element(X112,the_carrier(X110)) )
& ( ~ below(X110,X111,X112)
| below_refl(X110,X111,X112)
| empty_carrier(X110)
| ~ meet_commutative(X110)
| ~ meet_absorbing(X110)
| ~ join_absorbing(X110)
| ~ latt_str(X110)
| ~ element(X111,the_carrier(X110))
| ~ element(X112,the_carrier(X110)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])]) ).
cnf(c_0_168,plain,
( join_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_169,plain,
( meet_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_170,plain,
( meet_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_171,plain,
( empty_carrier(X2)
| below(X2,X4,X1)
| X4 != join_of_latt_set(X2,X3)
| ~ latt_str(X2)
| ~ lattice(X2)
| ~ complete_latt_str(X2)
| ~ latt_element_smaller(X2,X1,X3)
| ~ element(X4,the_carrier(X2))
| ~ element(X1,the_carrier(X2)) ),
inference(cn,[status(thm)],[c_0_151]) ).
cnf(c_0_172,negated_conjecture,
( ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| element(esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X2)),the_carrier(esk26_0))
| ~ latt_element_smaller(esk26_0,join_of_latt_set(esk26_0,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_118])]) ).
cnf(c_0_173,negated_conjecture,
latt_element_smaller(esk26_0,join_of_latt_set(esk26_0,X1),X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_146]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_174,plain,
( latt_element_smaller(X1,X3,X2)
| empty_carrier(X1)
| ~ relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_175,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk26_0),X1,esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X2)))
| ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ latt_element_smaller(esk26_0,join_of_latt_set(esk26_0,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_153]),c_0_118])]) ).
cnf(c_0_176,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ related_reflexive(poset_of_lattice(X1),cast_to_el_of_LattPOSet(X1,X2),cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_177,negated_conjecture,
( related(poset_of_lattice(esk26_0),X1,X2)
| ~ related_reflexive(poset_of_lattice(esk26_0),X1,X2)
| ~ element(X2,the_carrier(esk26_0))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_107]),c_0_157]),c_0_77])]),c_0_158]) ).
cnf(c_0_178,negated_conjecture,
( related_reflexive(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X2))
| ~ below_refl(esk26_0,X1,meet_of_latt_set(esk26_0,X2))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_179,plain,
( below_refl(X1,X2,meet_of_latt_set(X1,X3))
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ complete_latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_161]),c_0_98]) ).
cnf(c_0_180,negated_conjecture,
( ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1)
| element(esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X1)),the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_181,negated_conjecture,
( latt_set_smaller(esk26_0,X1,X2)
| ~ relstr_element_smaller(poset_of_lattice(esk26_0),X2,X1)
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_160]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_182,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(esk26_0),X1,esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X1)))
| ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1) ),
inference(spm,[status(thm)],[c_0_165,c_0_163]) ).
cnf(c_0_183,negated_conjecture,
( related_reflexive(poset_of_lattice(esk26_0),join_of_latt_set(esk26_0,X1),cast_to_el_of_LattPOSet(esk26_0,X2))
| ~ below_refl(esk26_0,join_of_latt_set(esk26_0,X1),X2)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_166,c_0_142]) ).
cnf(c_0_184,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_185,negated_conjecture,
join_absorbing(esk26_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_186,negated_conjecture,
meet_absorbing(esk26_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_187,negated_conjecture,
meet_commutative(esk26_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_188,plain,
( below(X1,join_of_latt_set(X1,X2),X3)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ complete_latt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_171]),c_0_102]) ).
cnf(c_0_189,negated_conjecture,
( ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| element(esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X1)),the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_190,negated_conjecture,
( latt_element_smaller(esk26_0,X1,X2)
| ~ relstr_set_smaller(poset_of_lattice(esk26_0),X2,X1)
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_160]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_191,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk26_0),X1,esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X1)))
| ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1) ),
inference(spm,[status(thm)],[c_0_175,c_0_173]) ).
cnf(c_0_192,negated_conjecture,
( below_refl(esk26_0,X1,X2)
| ~ related_reflexive(poset_of_lattice(esk26_0),cast_to_el_of_LattPOSet(esk26_0,X1),X2)
| ~ element(X2,the_carrier(esk26_0))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_160]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_193,plain,
( related_reflexive(X1,X2,X3)
| empty_carrier(X1)
| ~ related(X1,X2,X3)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
fof(c_0_194,plain,
! [X15,X16,X17,X18] :
( ( relstr_element_smaller(X15,X16,X17)
| X17 != meet_on_relstr(X15,X16)
| ~ ex_inf_of_relstr_set(X15,X16)
| ~ element(X17,the_carrier(X15))
| ~ rel_str(X15) )
& ( ~ element(X18,the_carrier(X15))
| ~ relstr_element_smaller(X15,X16,X18)
| related(X15,X18,X17)
| X17 != meet_on_relstr(X15,X16)
| ~ ex_inf_of_relstr_set(X15,X16)
| ~ element(X17,the_carrier(X15))
| ~ rel_str(X15) )
& ( element(esk1_3(X15,X16,X17),the_carrier(X15))
| ~ relstr_element_smaller(X15,X16,X17)
| X17 = meet_on_relstr(X15,X16)
| ~ ex_inf_of_relstr_set(X15,X16)
| ~ element(X17,the_carrier(X15))
| ~ rel_str(X15) )
& ( relstr_element_smaller(X15,X16,esk1_3(X15,X16,X17))
| ~ relstr_element_smaller(X15,X16,X17)
| X17 = meet_on_relstr(X15,X16)
| ~ ex_inf_of_relstr_set(X15,X16)
| ~ element(X17,the_carrier(X15))
| ~ rel_str(X15) )
& ( ~ related(X15,esk1_3(X15,X16,X17),X17)
| ~ relstr_element_smaller(X15,X16,X17)
| X17 = meet_on_relstr(X15,X16)
| ~ ex_inf_of_relstr_set(X15,X16)
| ~ element(X17,the_carrier(X15))
| ~ rel_str(X15) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_yellow_0])])])])]) ).
fof(c_0_195,plain,
! [X46,X47] :
( ~ rel_str(X46)
| element(meet_on_relstr(X46,X47),the_carrier(X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_yellow_0])]) ).
cnf(c_0_196,plain,
( ex_inf_of_relstr_set(X1,X2)
| ~ related(X1,esk25_3(X1,X2,X3),X3)
| ~ element(X3,the_carrier(X1))
| ~ relstr_element_smaller(X1,X2,X3)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_197,negated_conjecture,
( related(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X2))
| ~ below_refl(esk26_0,X1,meet_of_latt_set(esk26_0,X2))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_113])]) ).
cnf(c_0_198,negated_conjecture,
( below_refl(esk26_0,esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X1)),meet_of_latt_set(esk26_0,X2))
| ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ latt_set_smaller(esk26_0,esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X1)),X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_146]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_199,negated_conjecture,
( latt_set_smaller(esk26_0,esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X1)),X1)
| ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_180]) ).
cnf(c_0_200,negated_conjecture,
( related_reflexive(poset_of_lattice(esk26_0),join_of_latt_set(esk26_0,X1),X2)
| ~ below_refl(esk26_0,join_of_latt_set(esk26_0,X1),X2)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_183,c_0_160]) ).
cnf(c_0_201,negated_conjecture,
( below_refl(esk26_0,X1,cast_to_el_of_lattice(esk26_0,X2))
| ~ below(esk26_0,X1,cast_to_el_of_lattice(esk26_0,X2))
| ~ element(X1,the_carrier(esk26_0))
| ~ element(X2,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_123]),c_0_185]),c_0_186]),c_0_187]),c_0_49])]),c_0_50]) ).
cnf(c_0_202,negated_conjecture,
( ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| below(esk26_0,join_of_latt_set(esk26_0,X2),esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X1)))
| ~ latt_element_smaller(esk26_0,esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X1)),X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_146]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_203,negated_conjecture,
( ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| latt_element_smaller(esk26_0,esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X1)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_189]) ).
fof(c_0_204,plain,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[t31_lattice3]) ).
cnf(c_0_205,negated_conjecture,
( below_refl(esk26_0,X1,X2)
| ~ related_reflexive(poset_of_lattice(esk26_0),X1,X2)
| ~ element(X2,the_carrier(esk26_0))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_192,c_0_160]) ).
cnf(c_0_206,negated_conjecture,
( related_reflexive(poset_of_lattice(esk26_0),X1,X2)
| ~ related(poset_of_lattice(esk26_0),X1,X2)
| ~ element(X2,the_carrier(esk26_0))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_107]),c_0_157]),c_0_77])]),c_0_158]) ).
cnf(c_0_207,plain,
( related(X2,X1,X4)
| ~ element(X1,the_carrier(X2))
| ~ relstr_element_smaller(X2,X3,X1)
| X4 != meet_on_relstr(X2,X3)
| ~ ex_inf_of_relstr_set(X2,X3)
| ~ element(X4,the_carrier(X2))
| ~ rel_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_208,plain,
( element(meet_on_relstr(X1,X2),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_209,negated_conjecture,
( ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ below_refl(esk26_0,esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X2)),meet_of_latt_set(esk26_0,X2))
| ~ relstr_element_smaller(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X2))
| ~ element(esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X2)),the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_126]),c_0_107]),c_0_113]),c_0_77])]) ).
cnf(c_0_210,negated_conjecture,
( below_refl(esk26_0,esk25_3(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X1)),meet_of_latt_set(esk26_0,X1))
| ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1) ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
fof(c_0_211,plain,
! [X32,X33,X34,X35] :
( ( relstr_set_smaller(X32,X33,X34)
| X34 != join_on_relstr(X32,X33)
| ~ ex_sup_of_relstr_set(X32,X33)
| ~ element(X34,the_carrier(X32))
| ~ rel_str(X32) )
& ( ~ element(X35,the_carrier(X32))
| ~ relstr_set_smaller(X32,X33,X35)
| related(X32,X34,X35)
| X34 != join_on_relstr(X32,X33)
| ~ ex_sup_of_relstr_set(X32,X33)
| ~ element(X34,the_carrier(X32))
| ~ rel_str(X32) )
& ( element(esk3_3(X32,X33,X34),the_carrier(X32))
| ~ relstr_set_smaller(X32,X33,X34)
| X34 = join_on_relstr(X32,X33)
| ~ ex_sup_of_relstr_set(X32,X33)
| ~ element(X34,the_carrier(X32))
| ~ rel_str(X32) )
& ( relstr_set_smaller(X32,X33,esk3_3(X32,X33,X34))
| ~ relstr_set_smaller(X32,X33,X34)
| X34 = join_on_relstr(X32,X33)
| ~ ex_sup_of_relstr_set(X32,X33)
| ~ element(X34,the_carrier(X32))
| ~ rel_str(X32) )
& ( ~ related(X32,X34,esk3_3(X32,X33,X34))
| ~ relstr_set_smaller(X32,X33,X34)
| X34 = join_on_relstr(X32,X33)
| ~ ex_sup_of_relstr_set(X32,X33)
| ~ element(X34,the_carrier(X32))
| ~ rel_str(X32) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_yellow_0])])])])]) ).
fof(c_0_212,plain,
! [X43,X44] :
( ~ rel_str(X43)
| element(join_on_relstr(X43,X44),the_carrier(X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_yellow_0])]) ).
cnf(c_0_213,plain,
( ex_sup_of_relstr_set(X1,X3)
| ~ related(X1,X2,esk23_3(X1,X3,X2))
| ~ element(X2,the_carrier(X1))
| ~ relstr_set_smaller(X1,X3,X2)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_214,negated_conjecture,
( related(poset_of_lattice(esk26_0),join_of_latt_set(esk26_0,X1),X2)
| ~ below_refl(esk26_0,join_of_latt_set(esk26_0,X1),X2)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_200]),c_0_118])]) ).
cnf(c_0_215,negated_conjecture,
( below_refl(esk26_0,X1,X2)
| ~ below(esk26_0,X1,X2)
| ~ element(X1,the_carrier(esk26_0))
| ~ element(X2,the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_201,c_0_142]) ).
cnf(c_0_216,negated_conjecture,
( ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| below(esk26_0,join_of_latt_set(esk26_0,X1),esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X1))) ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
fof(c_0_217,plain,
! [X155,X156,X157] :
( ( ~ relstr_set_smaller(poset_of_lattice(X156),X155,X157)
| latt_element_smaller(X156,cast_to_el_of_lattice(X156,X157),X155)
| ~ element(X157,the_carrier(poset_of_lattice(X156)))
| empty_carrier(X156)
| ~ lattice(X156)
| ~ latt_str(X156) )
& ( ~ latt_element_smaller(X156,cast_to_el_of_lattice(X156,X157),X155)
| relstr_set_smaller(poset_of_lattice(X156),X155,X157)
| ~ element(X157,the_carrier(poset_of_lattice(X156)))
| empty_carrier(X156)
| ~ lattice(X156)
| ~ latt_str(X156) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_204])])])]) ).
cnf(c_0_218,negated_conjecture,
( below_refl(esk26_0,X1,X2)
| ~ related(poset_of_lattice(esk26_0),X1,X2)
| ~ element(X2,the_carrier(esk26_0))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_219,plain,
( related(X1,X2,meet_on_relstr(X1,X3))
| ~ relstr_element_smaller(X1,X3,X2)
| ~ ex_inf_of_relstr_set(X1,X3)
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_207]),c_0_208]) ).
cnf(c_0_220,negated_conjecture,
element(meet_on_relstr(poset_of_lattice(esk26_0),X1),the_carrier(esk26_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_107]),c_0_77])]) ).
cnf(c_0_221,negated_conjecture,
( ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ relstr_element_smaller(poset_of_lattice(esk26_0),X1,meet_of_latt_set(esk26_0,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_180]) ).
fof(c_0_222,plain,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_element_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_set_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[t29_lattice3]) ).
cnf(c_0_223,plain,
( relstr_element_smaller(X1,X2,X3)
| X3 != meet_on_relstr(X1,X2)
| ~ ex_inf_of_relstr_set(X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_224,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_225,plain,
( related(X2,X4,X1)
| ~ element(X1,the_carrier(X2))
| ~ relstr_set_smaller(X2,X3,X1)
| X4 != join_on_relstr(X2,X3)
| ~ ex_sup_of_relstr_set(X2,X3)
| ~ element(X4,the_carrier(X2))
| ~ rel_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_226,plain,
( element(join_on_relstr(X1,X2),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_227,negated_conjecture,
( ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ below_refl(esk26_0,join_of_latt_set(esk26_0,X2),esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X2)))
| ~ relstr_set_smaller(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X2))
| ~ element(esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X2)),the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_126]),c_0_107]),c_0_118]),c_0_77])]) ).
cnf(c_0_228,negated_conjecture,
( below_refl(esk26_0,join_of_latt_set(esk26_0,X1),esk23_3(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X1)))
| ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_118])]),c_0_189]) ).
cnf(c_0_229,plain,
( relstr_set_smaller(poset_of_lattice(X1),X3,X2)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X3)
| ~ element(X2,the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_230,negated_conjecture,
( below_refl(esk26_0,X1,meet_on_relstr(poset_of_lattice(esk26_0),X2))
| ~ relstr_element_smaller(poset_of_lattice(esk26_0),X2,X1)
| ~ ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X2)
| ~ element(X1,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_220]),c_0_107]),c_0_77])]) ).
cnf(c_0_231,negated_conjecture,
ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_144]),c_0_163])]) ).
cnf(c_0_232,plain,
( element(esk29_3(X1,X2,X3),the_carrier(X1))
| X2 = meet_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
fof(c_0_233,plain,
! [X142,X143,X144] :
( ( ~ relstr_element_smaller(poset_of_lattice(X143),X142,X144)
| latt_set_smaller(X143,cast_to_el_of_lattice(X143,X144),X142)
| ~ element(X144,the_carrier(poset_of_lattice(X143)))
| empty_carrier(X143)
| ~ lattice(X143)
| ~ latt_str(X143) )
& ( ~ latt_set_smaller(X143,cast_to_el_of_lattice(X143,X144),X142)
| relstr_element_smaller(poset_of_lattice(X143),X142,X144)
| ~ element(X144,the_carrier(poset_of_lattice(X143)))
| empty_carrier(X143)
| ~ lattice(X143)
| ~ latt_str(X143) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_222])])])]) ).
cnf(c_0_234,plain,
( latt_set_smaller(X1,esk29_3(X1,X2,X3),X3)
| X2 = meet_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_235,plain,
( relstr_element_smaller(X1,X2,meet_on_relstr(X1,X2))
| ~ ex_inf_of_relstr_set(X1,X2)
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_223]),c_0_208]) ).
cnf(c_0_236,plain,
( X2 = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| empty_carrier(X1)
| ~ below(X1,X2,esk2_3(X1,X3,X2))
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_237,negated_conjecture,
( below(esk26_0,X1,cast_to_el_of_lattice(esk26_0,X2))
| ~ below_refl(esk26_0,X1,cast_to_el_of_lattice(esk26_0,X2))
| ~ element(X1,the_carrier(esk26_0))
| ~ element(X2,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_123]),c_0_185]),c_0_186]),c_0_187]),c_0_49])]),c_0_50]) ).
cnf(c_0_238,plain,
( related(X1,join_on_relstr(X1,X2),X3)
| ~ relstr_set_smaller(X1,X2,X3)
| ~ ex_sup_of_relstr_set(X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_225]),c_0_226]) ).
cnf(c_0_239,negated_conjecture,
element(join_on_relstr(poset_of_lattice(esk26_0),X1),the_carrier(esk26_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_107]),c_0_77])]) ).
cnf(c_0_240,negated_conjecture,
( ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ relstr_set_smaller(poset_of_lattice(esk26_0),X1,join_of_latt_set(esk26_0,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_189]) ).
cnf(c_0_241,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk26_0),X1,X2)
| ~ latt_element_smaller(esk26_0,X2,X1)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_142]),c_0_107]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_242,plain,
( element(esk2_3(X1,X2,X3),the_carrier(X1))
| X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_243,plain,
( latt_element_smaller(X1,esk2_3(X1,X2,X3),X2)
| X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_244,plain,
( relstr_set_smaller(X1,X2,X3)
| X3 != join_on_relstr(X1,X2)
| ~ ex_sup_of_relstr_set(X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_245,plain,
( X2 = meet_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ below_refl(X1,esk29_3(X1,X2,X3),X2)
| ~ latt_set_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_246,negated_conjecture,
( below_refl(esk26_0,X1,meet_on_relstr(poset_of_lattice(esk26_0),X2))
| ~ relstr_element_smaller(poset_of_lattice(esk26_0),X2,X1)
| ~ element(X1,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_230,c_0_231])]) ).
cnf(c_0_247,negated_conjecture,
( meet_on_relstr(poset_of_lattice(esk26_0),X1) = meet_of_latt_set(esk26_0,X2)
| element(esk29_3(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X2),the_carrier(esk26_0))
| ~ latt_set_smaller(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_220]),c_0_146]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_248,plain,
( relstr_element_smaller(poset_of_lattice(X1),X3,X2)
| empty_carrier(X1)
| ~ latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X3)
| ~ element(X2,the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_249,negated_conjecture,
( meet_on_relstr(poset_of_lattice(esk26_0),X1) = meet_of_latt_set(esk26_0,X2)
| latt_set_smaller(esk26_0,esk29_3(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X2),X2)
| ~ latt_set_smaller(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_220]),c_0_146]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_250,negated_conjecture,
( latt_set_smaller(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X1)
| ~ ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_235]),c_0_220]),c_0_77])]) ).
cnf(c_0_251,plain,
( X2 = join_of_latt_set(X1,X3)
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ below(X1,X2,esk2_3(X1,X3,X2)) ),
inference(cn,[status(thm)],[c_0_236]) ).
cnf(c_0_252,negated_conjecture,
( below(esk26_0,X1,X2)
| ~ below_refl(esk26_0,X1,X2)
| ~ element(X1,the_carrier(esk26_0))
| ~ element(X2,the_carrier(esk26_0)) ),
inference(spm,[status(thm)],[c_0_237,c_0_142]) ).
cnf(c_0_253,negated_conjecture,
( below_refl(esk26_0,join_on_relstr(poset_of_lattice(esk26_0),X1),X2)
| ~ relstr_set_smaller(poset_of_lattice(esk26_0),X1,X2)
| ~ ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_238]),c_0_239]),c_0_107]),c_0_77])]) ).
cnf(c_0_254,negated_conjecture,
ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_241]),c_0_173]),c_0_118])]) ).
cnf(c_0_255,plain,
( X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| element(esk2_3(X1,X2,X3),the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1)) ),
inference(cn,[status(thm)],[c_0_242]) ).
cnf(c_0_256,plain,
( X3 = join_of_latt_set(X1,X2)
| empty_carrier(X1)
| latt_element_smaller(X1,esk2_3(X1,X2,X3),X2)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_element_smaller(X1,X3,X2)
| ~ element(X3,the_carrier(X1)) ),
inference(cn,[status(thm)],[c_0_243]) ).
cnf(c_0_257,plain,
( relstr_set_smaller(X1,X2,join_on_relstr(X1,X2))
| ~ ex_sup_of_relstr_set(X1,X2)
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_244]),c_0_226]) ).
cnf(c_0_258,negated_conjecture,
( meet_on_relstr(poset_of_lattice(esk26_0),X1) = meet_of_latt_set(esk26_0,X2)
| ~ latt_set_smaller(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X2)
| ~ relstr_element_smaller(poset_of_lattice(esk26_0),X1,esk29_3(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X2)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_246]),c_0_146]),c_0_220]),c_0_48]),c_0_49])]),c_0_50]),c_0_247]) ).
cnf(c_0_259,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(esk26_0),X1,X2)
| ~ latt_set_smaller(esk26_0,X2,X1)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_142]),c_0_107]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_260,negated_conjecture,
( meet_on_relstr(poset_of_lattice(esk26_0),X1) = meet_of_latt_set(esk26_0,X1)
| latt_set_smaller(esk26_0,esk29_3(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X1),X1)
| ~ ex_inf_of_relstr_set(poset_of_lattice(esk26_0),X1) ),
inference(spm,[status(thm)],[c_0_249,c_0_250]) ).
cnf(c_0_261,negated_conjecture,
( X1 = join_of_latt_set(esk26_0,X2)
| ~ below_refl(esk26_0,X1,esk2_3(esk26_0,X2,X1))
| ~ latt_element_smaller(esk26_0,X1,X2)
| ~ element(esk2_3(esk26_0,X2,X1),the_carrier(esk26_0))
| ~ element(X1,the_carrier(esk26_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_252]),c_0_146]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_262,negated_conjecture,
( below_refl(esk26_0,join_on_relstr(poset_of_lattice(esk26_0),X1),X2)
| ~ relstr_set_smaller(poset_of_lattice(esk26_0),X1,X2)
| ~ element(X2,the_carrier(esk26_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_253,c_0_254])]) ).
cnf(c_0_263,negated_conjecture,
( join_on_relstr(poset_of_lattice(esk26_0),X1) = join_of_latt_set(esk26_0,X2)
| element(esk2_3(esk26_0,X2,join_on_relstr(poset_of_lattice(esk26_0),X1)),the_carrier(esk26_0))
| ~ latt_element_smaller(esk26_0,join_on_relstr(poset_of_lattice(esk26_0),X1),X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_239]),c_0_146]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_264,negated_conjecture,
( join_on_relstr(poset_of_lattice(esk26_0),X1) = join_of_latt_set(esk26_0,X2)
| latt_element_smaller(esk26_0,esk2_3(esk26_0,X2,join_on_relstr(poset_of_lattice(esk26_0),X1)),X2)
| ~ latt_element_smaller(esk26_0,join_on_relstr(poset_of_lattice(esk26_0),X1),X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_239]),c_0_146]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_265,negated_conjecture,
( latt_element_smaller(esk26_0,join_on_relstr(poset_of_lattice(esk26_0),X1),X1)
| ~ ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_257]),c_0_239]),c_0_77])]) ).
cnf(c_0_266,negated_conjecture,
( meet_on_relstr(poset_of_lattice(esk26_0),X1) = meet_of_latt_set(esk26_0,X2)
| ~ latt_set_smaller(esk26_0,esk29_3(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X2),X1)
| ~ latt_set_smaller(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_247]) ).
cnf(c_0_267,negated_conjecture,
( meet_on_relstr(poset_of_lattice(esk26_0),X1) = meet_of_latt_set(esk26_0,X1)
| latt_set_smaller(esk26_0,esk29_3(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_260,c_0_231])]) ).
cnf(c_0_268,negated_conjecture,
latt_set_smaller(esk26_0,meet_on_relstr(poset_of_lattice(esk26_0),X1),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_231])]) ).
cnf(c_0_269,negated_conjecture,
( join_on_relstr(poset_of_lattice(esk26_0),X1) = join_of_latt_set(esk26_0,X2)
| ~ relstr_set_smaller(poset_of_lattice(esk26_0),X1,esk2_3(esk26_0,X2,join_on_relstr(poset_of_lattice(esk26_0),X1)))
| ~ latt_element_smaller(esk26_0,join_on_relstr(poset_of_lattice(esk26_0),X1),X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_262]),c_0_239])]),c_0_263]) ).
cnf(c_0_270,negated_conjecture,
( join_on_relstr(poset_of_lattice(esk26_0),X1) = join_of_latt_set(esk26_0,X1)
| latt_element_smaller(esk26_0,esk2_3(esk26_0,X1,join_on_relstr(poset_of_lattice(esk26_0),X1)),X1)
| ~ ex_sup_of_relstr_set(poset_of_lattice(esk26_0),X1) ),
inference(spm,[status(thm)],[c_0_264,c_0_265]) ).
cnf(c_0_271,negated_conjecture,
( join_of_latt_set(esk26_0,esk27_0) != join_on_relstr(poset_of_lattice(esk26_0),esk27_0)
| meet_of_latt_set(esk26_0,esk27_0) != meet_on_relstr(poset_of_lattice(esk26_0),esk27_0) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_272,negated_conjecture,
meet_on_relstr(poset_of_lattice(esk26_0),X1) = meet_of_latt_set(esk26_0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_267]),c_0_268])]) ).
cnf(c_0_273,negated_conjecture,
( join_on_relstr(poset_of_lattice(esk26_0),X1) = join_of_latt_set(esk26_0,X2)
| ~ latt_element_smaller(esk26_0,esk2_3(esk26_0,X2,join_on_relstr(poset_of_lattice(esk26_0),X1)),X1)
| ~ latt_element_smaller(esk26_0,join_on_relstr(poset_of_lattice(esk26_0),X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_241]),c_0_263]) ).
cnf(c_0_274,negated_conjecture,
( join_on_relstr(poset_of_lattice(esk26_0),X1) = join_of_latt_set(esk26_0,X1)
| latt_element_smaller(esk26_0,esk2_3(esk26_0,X1,join_on_relstr(poset_of_lattice(esk26_0),X1)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_270,c_0_254])]) ).
cnf(c_0_275,negated_conjecture,
latt_element_smaller(esk26_0,join_on_relstr(poset_of_lattice(esk26_0),X1),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_265,c_0_254])]) ).
cnf(c_0_276,negated_conjecture,
join_on_relstr(poset_of_lattice(esk26_0),esk27_0) != join_of_latt_set(esk26_0,esk27_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_271,c_0_272])]) ).
cnf(c_0_277,negated_conjecture,
join_on_relstr(poset_of_lattice(esk26_0),X1) = join_of_latt_set(esk26_0,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_274]),c_0_275])]) ).
cnf(c_0_278,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_276,c_0_277])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SEU358+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n029.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 2400
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Oct 2 08:39:06 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.73jJPlkLXG/E---3.1_28630.p
% 83.08/10.95 # Version: 3.1pre001
% 83.08/10.95 # Preprocessing class: FSLSSMSSSSSNFFN.
% 83.08/10.95 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.08/10.95 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 83.08/10.95 # Starting new_bool_3 with 300s (1) cores
% 83.08/10.95 # Starting new_bool_1 with 300s (1) cores
% 83.08/10.95 # Starting sh5l with 300s (1) cores
% 83.08/10.95 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 28709 completed with status 0
% 83.08/10.95 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 83.08/10.95 # Preprocessing class: FSLSSMSSSSSNFFN.
% 83.08/10.95 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.08/10.95 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 83.08/10.95 # No SInE strategy applied
% 83.08/10.95 # Search class: FGHSM-FSLM31-SFFFFFNN
% 83.08/10.95 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 83.08/10.95 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 811s (1) cores
% 83.08/10.95 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 83.08/10.95 # Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 83.08/10.95 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 83.08/10.95 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 83.08/10.95 # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 28720 completed with status 0
% 83.08/10.95 # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 83.08/10.95 # Preprocessing class: FSLSSMSSSSSNFFN.
% 83.08/10.95 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.08/10.95 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 83.08/10.95 # No SInE strategy applied
% 83.08/10.95 # Search class: FGHSM-FSLM31-SFFFFFNN
% 83.08/10.95 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 83.08/10.95 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 811s (1) cores
% 83.08/10.95 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 83.08/10.95 # Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 83.08/10.95 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 83.08/10.95 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 83.08/10.95 # Preprocessing time : 0.003 s
% 83.08/10.95 # Presaturation interreduction done
% 83.08/10.95
% 83.08/10.95 # Proof found!
% 83.08/10.95 # SZS status Theorem
% 83.08/10.95 # SZS output start CNFRefutation
% See solution above
% 83.08/10.95 # Parsed axioms : 87
% 83.08/10.95 # Removed by relevancy pruning/SinE : 0
% 83.08/10.95 # Initial clauses : 172
% 83.08/10.95 # Removed in clause preprocessing : 8
% 83.08/10.95 # Initial clauses in saturation : 164
% 83.08/10.95 # Processed clauses : 37888
% 83.08/10.95 # ...of these trivial : 105
% 83.08/10.95 # ...subsumed : 27945
% 83.08/10.95 # ...remaining for further processing : 9838
% 83.08/10.95 # Other redundant clauses eliminated : 19
% 83.08/10.95 # Clauses deleted for lack of memory : 0
% 83.08/10.95 # Backward-subsumed : 358
% 83.08/10.95 # Backward-rewritten : 1505
% 83.08/10.95 # Generated clauses : 275088
% 83.08/10.95 # ...of the previous two non-redundant : 265637
% 83.08/10.95 # ...aggressively subsumed : 0
% 83.08/10.95 # Contextual simplify-reflections : 448
% 83.08/10.95 # Paramodulations : 274886
% 83.08/10.95 # Factorizations : 175
% 83.08/10.95 # NegExts : 0
% 83.08/10.95 # Equation resolutions : 25
% 83.08/10.95 # Total rewrite steps : 58783
% 83.08/10.95 # Propositional unsat checks : 1
% 83.08/10.95 # Propositional check models : 0
% 83.08/10.95 # Propositional check unsatisfiable : 0
% 83.08/10.95 # Propositional clauses : 0
% 83.08/10.95 # Propositional clauses after purity: 0
% 83.08/10.95 # Propositional unsat core size : 0
% 83.08/10.95 # Propositional preprocessing time : 0.000
% 83.08/10.95 # Propositional encoding time : 0.113
% 83.08/10.95 # Propositional solver time : 0.165
% 83.08/10.95 # Success case prop preproc time : 0.000
% 83.08/10.95 # Success case prop encoding time : 0.000
% 83.08/10.95 # Success case prop solver time : 0.000
% 83.08/10.95 # Current number of processed clauses : 7806
% 83.08/10.95 # Positive orientable unit clauses : 149
% 83.08/10.95 # Positive unorientable unit clauses: 0
% 83.08/10.95 # Negative unit clauses : 25
% 83.08/10.95 # Non-unit-clauses : 7632
% 83.08/10.95 # Current number of unprocessed clauses: 226334
% 83.08/10.95 # ...number of literals in the above : 948023
% 83.08/10.95 # Current number of archived formulas : 0
% 83.08/10.95 # Current number of archived clauses : 2023
% 83.08/10.95 # Clause-clause subsumption calls (NU) : 6393340
% 83.08/10.95 # Rec. Clause-clause subsumption calls : 2285709
% 83.08/10.95 # Non-unit clause-clause subsumptions : 26388
% 83.08/10.95 # Unit Clause-clause subsumption calls : 47057
% 83.08/10.95 # Rewrite failures with RHS unbound : 0
% 83.08/10.95 # BW rewrite match attempts : 583
% 83.08/10.95 # BW rewrite match successes : 39
% 83.08/10.95 # Condensation attempts : 0
% 83.08/10.95 # Condensation successes : 0
% 83.08/10.95 # Termbank termtop insertions : 8388657
% 83.08/10.95
% 83.08/10.95 # -------------------------------------------------
% 83.08/10.95 # User time : 10.087 s
% 83.08/10.95 # System time : 0.204 s
% 83.08/10.95 # Total time : 10.291 s
% 83.08/10.95 # Maximum resident set size: 2452 pages
% 83.08/10.95
% 83.08/10.95 # -------------------------------------------------
% 83.08/10.95 # User time : 49.890 s
% 83.08/10.95 # System time : 1.504 s
% 83.08/10.95 # Total time : 51.394 s
% 83.08/10.95 # Maximum resident set size: 1860 pages
% 83.08/10.95 % E---3.1 exiting
% 83.08/10.95 % E---3.1 exiting
%------------------------------------------------------------------------------