%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU346+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:11:33 PM UTC 2026
% Result : Theorem 176.94s 126.60s
% Output : CNFRefutation 186.84s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_1547)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_k10_filter_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2)
& element(X3,the_carrier(X1))
& element(X4,the_carrier(X2)) )
=> k10_filter_1(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_filter_1) ).
fof(redefinition_k1_domain_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
fof(t32_filter_1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
fof(fc3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& function(X2)
& quasi_total(X2,cartesian_product2(X1,X1),X1)
& relation_of2(X2,cartesian_product2(X1,X1),X1)
& function(X3)
& quasi_total(X3,cartesian_product2(X1,X1),X1)
& relation_of2(X3,cartesian_product2(X1,X1),X1) )
=> ( ~ empty_carrier(latt_str_of(X1,X2,X3))
& strict_latt_str(latt_str_of(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).
fof(dt_k10_filter_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2)
& element(X3,the_carrier(X1))
& element(X4,the_carrier(X2)) )
=> element(k10_filter_1(X1,X2,X3,X4),the_carrier(k8_filter_1(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_1) ).
fof(dt_k1_domain_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> element(ordered_pair_as_product_element(X1,X2,X3,X4),cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(d9_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( related(X1,X2,X3)
<=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
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/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(t7_lattice3,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',t7_lattice3) ).
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/sandbox/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
fof(reflexivity_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,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
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/sandbox/benchmark/theBenchmark.p',fc1_orders_2) ).
fof(reflexivity_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,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
fof(fc5_lattice2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_associative(X1)
& meet_semilatt_str(X1) )
=> ( relation(the_L_meet(X1))
& function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v2_binop_1(the_L_meet(X1),the_carrier(X1))
& v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_lattice2) ).
fof(fc4_lattice2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1) )
=> ( relation(the_L_meet(X1))
& function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v1_binop_1(the_L_meet(X1),the_carrier(X1))
& v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice2) ).
fof(fc3_lattice2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_associative(X1)
& join_semilatt_str(X1) )
=> ( relation(the_L_join(X1))
& function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v2_binop_1(the_L_join(X1),the_carrier(X1))
& v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice2) ).
fof(fc2_lattice2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ( relation(the_L_join(X1))
& function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v1_binop_1(the_L_join(X1),the_carrier(X1))
& v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_lattice2) ).
fof(dt_k4_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X1)) )
=> element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice3) ).
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/sandbox/benchmark/theBenchmark.p',dt_k2_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/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(cc2_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattices) ).
fof(fc4_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(dt_k8_filter_1,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& latt_str(X2) )
=> ( strict_latt_str(k8_filter_1(X1,X2))
& latt_str(k8_filter_1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_1) ).
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/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
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/sandbox/benchmark/theBenchmark.p',d2_lattice3) ).
fof(fc3_subset_1,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(fc4_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(poset_of_lattice(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)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice3) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_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/sandbox/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(dt_k9_filter_1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation(relation_of_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_1) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(redefinition_k2_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
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/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc9_lattices,axiom,
? [X1] :
( latt_str(X1)
& ~ empty_carrier(X1)
& strict_latt_str(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).
fof(rc6_lattices,axiom,
? [X1] :
( latt_str(X1)
& ~ empty_carrier(X1)
& strict_latt_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).
fof(rc3_struct_0,axiom,
? [X1] :
( one_sorted_str(X1)
& ~ empty_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(rc2_orders_2,axiom,
? [X1] :
( rel_str(X1)
& ~ empty_carrier(X1)
& strict_rel_str(X1)
& reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_orders_2) ).
fof(free_g3_lattices,axiom,
! [X1,X2,X3] :
( ( function(X2)
& quasi_total(X2,cartesian_product2(X1,X1),X1)
& relation_of2(X2,cartesian_product2(X1,X1),X1)
& function(X3)
& quasi_total(X3,cartesian_product2(X1,X1),X1)
& relation_of2(X3,cartesian_product2(X1,X1),X1) )
=> ! [X4,X5,X6] :
( latt_str_of(X1,X2,X3) = latt_str_of(X4,X5,X6)
=> ( X1 = X4
& X2 = X5
& X3 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(dt_g3_lattices,axiom,
! [X1,X2,X3] :
( ( function(X2)
& quasi_total(X2,cartesian_product2(X1,X1),X1)
& relation_of2(X2,cartesian_product2(X1,X1),X1)
& function(X3)
& quasi_total(X3,cartesian_product2(X1,X1),X1)
& relation_of2(X3,cartesian_product2(X1,X1),X1) )
=> ( strict_latt_str(latt_str_of(X1,X2,X3))
& latt_str(latt_str_of(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).
fof(fc3_orders_2,axiom,
! [X1,X2] :
( ( reflexive(X2)
& antisymmetric(X2)
& transitive(X2)
& v1_partfun1(X2,X1,X1)
& relation_of2(X2,X1,X1) )
=> ( strict_rel_str(rel_str_of(X1,X2))
& reflexive_relstr(rel_str_of(X1,X2))
& transitive_relstr(rel_str_of(X1,X2))
& antisymmetric_relstr(rel_str_of(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_orders_2) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
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/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(dt_u1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> ( function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(dt_u2_lattices,axiom,
! [X1] :
( join_semilatt_str(X1)
=> ( function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_g1_orders_2,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ( strict_rel_str(rel_str_of(X1,X2))
& rel_str(rel_str_of(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
fof(fc2_orders_2,axiom,
! [X1] :
( ( reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1)
& rel_str(X1) )
=> ( relation(the_InternalRel(X1))
& reflexive(the_InternalRel(X1))
& antisymmetric(the_InternalRel(X1))
& transitive(the_InternalRel(X1))
& v1_partfun1(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_orders_2) ).
fof(abstractness_v3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( strict_latt_str(X1)
=> X1 = latt_str_of(the_carrier(X1),the_L_join(X1),the_L_meet(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
fof(existence_m2_relset_1,axiom,
! [X1,X2] :
? [X3] : relation_of2_as_subset(X3,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(existence_m1_relset_1,axiom,
! [X1,X2] :
? [X3] : relation_of2(X3,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(dt_u1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
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/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(dt_l2_lattices,axiom,
! [X1] :
( join_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(dt_l1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(existence_l2_lattices,axiom,
? [X1] : join_semilatt_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
fof(existence_l1_struct_0,axiom,
? [X1] : one_sorted_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l1_lattices,axiom,
? [X1] : meet_semilatt_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(rc3_lattices,axiom,
? [X1] :
( latt_str(X1)
& strict_latt_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).
fof(existence_l3_lattices,axiom,
? [X1] : latt_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).
fof(rc1_orders_2,axiom,
? [X1] :
( rel_str(X1)
& strict_rel_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_orders_2) ).
fof(existence_l1_orders_2,axiom,
? [X1] : rel_str(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_83,plain,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2)
& element(X3,the_carrier(X1))
& element(X4,the_carrier(X2)) )
=> k10_filter_1(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k10_filter_1]) ).
fof(i_0_84,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_domain_1]) ).
fof(i_0_85,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t32_filter_1]) ).
fof(i_0_86,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& function(X2)
& quasi_total(X2,cartesian_product2(X1,X1),X1)
& relation_of2(X2,cartesian_product2(X1,X1),X1)
& function(X3)
& quasi_total(X3,cartesian_product2(X1,X1),X1)
& relation_of2(X3,cartesian_product2(X1,X1),X1) )
=> ( ~ empty_carrier(latt_str_of(X1,X2,X3))
& strict_latt_str(latt_str_of(X1,X2,X3)) ) ),
inference(fof_simplification,[status(thm)],[fc3_lattices]) ).
fof(i_0_87,plain,
! [X1,X2,X3,X4] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2)
& element(X3,the_carrier(X1))
& element(X4,the_carrier(X2)) )
=> element(k10_filter_1(X1,X2,X3,X4),the_carrier(k8_filter_1(X1,X2))) ),
inference(fof_simplification,[status(thm)],[dt_k10_filter_1]) ).
fof(i_0_88,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> element(ordered_pair_as_product_element(X1,X2,X3,X4),cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[dt_k1_domain_1]) ).
fof(i_0_89,plain,
! [X268,X269,X270,X271] :
( empty_carrier(X268)
| ~ lattice(X268)
| ~ latt_str(X268)
| empty_carrier(X269)
| ~ lattice(X269)
| ~ latt_str(X269)
| ~ element(X270,the_carrier(X268))
| ~ element(X271,the_carrier(X269))
| k10_filter_1(X268,X269,X270,X271) = ordered_pair(X270,X271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_83])]) ).
fof(i_0_90,plain,
! [X176,X177] : ordered_pair(X176,X177) = unordered_pair(unordered_pair(X176,X177),singleton(X176)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_91,plain,
! [X272,X273,X274,X275] :
( empty(X272)
| empty(X273)
| ~ element(X274,X272)
| ~ element(X275,X273)
| ordered_pair_as_product_element(X272,X273,X274,X275) = ordered_pair(X274,X275) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_84])]) ).
fof(i_0_92,plain,
! [X178,X179,X180] :
( ( ~ related(X178,X179,X180)
| in(ordered_pair(X179,X180),the_InternalRel(X178))
| ~ element(X180,the_carrier(X178))
| ~ element(X179,the_carrier(X178))
| ~ rel_str(X178) )
& ( ~ in(ordered_pair(X179,X180),the_InternalRel(X178))
| related(X178,X179,X180)
| ~ element(X180,the_carrier(X178))
| ~ element(X179,the_carrier(X178))
| ~ rel_str(X178) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])]) ).
fof(i_0_93,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(i_0_94,negated_conjecture,
~ ! [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)],[inference(assume_negation,[status(cth)],[t7_lattice3])]) ).
fof(i_0_95,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]) ).
fof(i_0_96,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,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).
fof(i_0_97,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]) ).
fof(i_0_98,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,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_orders_2]) ).
fof(i_0_99,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_associative(X1)
& meet_semilatt_str(X1) )
=> ( relation(the_L_meet(X1))
& function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v2_binop_1(the_L_meet(X1),the_carrier(X1))
& v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc5_lattice2]) ).
fof(i_0_100,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1) )
=> ( relation(the_L_meet(X1))
& function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v1_binop_1(the_L_meet(X1),the_carrier(X1))
& v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc4_lattice2]) ).
fof(i_0_101,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_associative(X1)
& join_semilatt_str(X1) )
=> ( relation(the_L_join(X1))
& function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v2_binop_1(the_L_join(X1),the_carrier(X1))
& v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc3_lattice2]) ).
fof(i_0_102,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ( relation(the_L_join(X1))
& function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& v1_binop_1(the_L_join(X1),the_carrier(X1))
& v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc2_lattice2]) ).
fof(i_0_103,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X1)) )
=> element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k4_lattice3]) ).
fof(i_0_104,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(i_0_105,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(i_0_106,plain,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc2_lattices]) ).
fof(i_0_107,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc4_subset_1]) ).
fof(i_0_108,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1)
& ~ empty_carrier(X2)
& latt_str(X2) )
=> ( strict_latt_str(k8_filter_1(X1,X2))
& latt_str(k8_filter_1(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[dt_k8_filter_1]) ).
fof(i_0_109,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(i_0_110,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(i_0_111,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc3_subset_1]) ).
fof(i_0_112,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_113,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(poset_of_lattice(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)) ) ),
inference(fof_simplification,[status(thm)],[fc4_lattice3]) ).
fof(i_0_114,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_115,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]) ).
fof(i_0_116,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation(relation_of_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k9_filter_1]) ).
fof(i_0_117,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(i_0_118,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> k2_lattice3(X1) = relation_of_lattice(X1) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_lattice3]) ).
fof(i_0_119,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]) ).
fof(i_0_120,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(i_0_121,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_122,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_123,plain,
? [X1] :
( latt_str(X1)
& ~ empty_carrier(X1)
& strict_latt_str(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& lattice(X1) ),
inference(fof_simplification,[status(thm)],[rc9_lattices]) ).
fof(i_0_124,plain,
? [X1] :
( latt_str(X1)
& ~ empty_carrier(X1)
& strict_latt_str(X1) ),
inference(fof_simplification,[status(thm)],[rc6_lattices]) ).
fof(i_0_125,plain,
? [X1] :
( one_sorted_str(X1)
& ~ empty_carrier(X1) ),
inference(fof_simplification,[status(thm)],[rc3_struct_0]) ).
fof(i_0_126,plain,
? [X1] :
( rel_str(X1)
& ~ empty_carrier(X1)
& strict_rel_str(X1)
& reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1) ),
inference(fof_simplification,[status(thm)],[rc2_orders_2]) ).
fof(i_0_127,plain,
! [X297,X298,X299] :
( ( ~ in(ordered_pair_as_product_element(the_carrier(X297),the_carrier(X297),X298,X299),relation_of_lattice(X297))
| below_refl(X297,X298,X299)
| ~ element(X299,the_carrier(X297))
| ~ element(X298,the_carrier(X297))
| empty_carrier(X297)
| ~ lattice(X297)
| ~ latt_str(X297) )
& ( ~ below_refl(X297,X298,X299)
| in(ordered_pair_as_product_element(the_carrier(X297),the_carrier(X297),X298,X299),relation_of_lattice(X297))
| ~ element(X299,the_carrier(X297))
| ~ element(X298,the_carrier(X297))
| empty_carrier(X297)
| ~ lattice(X297)
| ~ latt_str(X297) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_85])])])]) ).
fof(i_0_128,plain,
! [X232,X233,X234] :
( ( ~ empty_carrier(latt_str_of(X232,X233,X234))
| empty(X232)
| ~ function(X233)
| ~ quasi_total(X233,cartesian_product2(X232,X232),X232)
| ~ relation_of2(X233,cartesian_product2(X232,X232),X232)
| ~ function(X234)
| ~ quasi_total(X234,cartesian_product2(X232,X232),X232)
| ~ relation_of2(X234,cartesian_product2(X232,X232),X232) )
& ( strict_latt_str(latt_str_of(X232,X233,X234))
| empty(X232)
| ~ function(X233)
| ~ quasi_total(X233,cartesian_product2(X232,X232),X232)
| ~ relation_of2(X233,cartesian_product2(X232,X232),X232)
| ~ function(X234)
| ~ quasi_total(X234,cartesian_product2(X232,X232),X232)
| ~ relation_of2(X234,cartesian_product2(X232,X232),X232) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_86])])]) ).
fof(i_0_129,plain,
! [X248,X249,X250,X251,X252,X253] :
( ( X248 = X251
| latt_str_of(X248,X249,X250) != latt_str_of(X251,X252,X253)
| ~ function(X249)
| ~ quasi_total(X249,cartesian_product2(X248,X248),X248)
| ~ relation_of2(X249,cartesian_product2(X248,X248),X248)
| ~ function(X250)
| ~ quasi_total(X250,cartesian_product2(X248,X248),X248)
| ~ relation_of2(X250,cartesian_product2(X248,X248),X248) )
& ( X249 = X252
| latt_str_of(X248,X249,X250) != latt_str_of(X251,X252,X253)
| ~ function(X249)
| ~ quasi_total(X249,cartesian_product2(X248,X248),X248)
| ~ relation_of2(X249,cartesian_product2(X248,X248),X248)
| ~ function(X250)
| ~ quasi_total(X250,cartesian_product2(X248,X248),X248)
| ~ relation_of2(X250,cartesian_product2(X248,X248),X248) )
& ( X250 = X253
| latt_str_of(X248,X249,X250) != latt_str_of(X251,X252,X253)
| ~ function(X249)
| ~ quasi_total(X249,cartesian_product2(X248,X248),X248)
| ~ relation_of2(X249,cartesian_product2(X248,X248),X248)
| ~ function(X250)
| ~ quasi_total(X250,cartesian_product2(X248,X248),X248)
| ~ relation_of2(X250,cartesian_product2(X248,X248),X248) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g3_lattices])])])]) ).
fof(i_0_130,plain,
! [X186,X187,X188,X189] :
( empty_carrier(X186)
| ~ lattice(X186)
| ~ latt_str(X186)
| empty_carrier(X187)
| ~ lattice(X187)
| ~ latt_str(X187)
| ~ element(X188,the_carrier(X186))
| ~ element(X189,the_carrier(X187))
| element(k10_filter_1(X186,X187,X188,X189),the_carrier(k8_filter_1(X186,X187))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_87])]) ).
fof(i_0_131,plain,
! [X183,X184,X185] :
( ( strict_latt_str(latt_str_of(X183,X184,X185))
| ~ function(X184)
| ~ quasi_total(X184,cartesian_product2(X183,X183),X183)
| ~ relation_of2(X184,cartesian_product2(X183,X183),X183)
| ~ function(X185)
| ~ quasi_total(X185,cartesian_product2(X183,X183),X183)
| ~ relation_of2(X185,cartesian_product2(X183,X183),X183) )
& ( latt_str(latt_str_of(X183,X184,X185))
| ~ function(X184)
| ~ quasi_total(X184,cartesian_product2(X183,X183),X183)
| ~ relation_of2(X184,cartesian_product2(X183,X183),X183)
| ~ function(X185)
| ~ quasi_total(X185,cartesian_product2(X183,X183),X183)
| ~ relation_of2(X185,cartesian_product2(X183,X183),X183) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_g3_lattices])])]) ).
fof(i_0_132,plain,
! [X190,X191,X192,X193] :
( empty(X190)
| empty(X191)
| ~ element(X192,X190)
| ~ element(X193,X191)
| element(ordered_pair_as_product_element(X190,X191,X192,X193),cartesian_product2(X190,X191)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_88])]) ).
cnf(i_0_133,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| k10_filter_1(X1,X2,X3,X4) = ordered_pair(X3,X4)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ element(X3,the_carrier(X1))
| ~ element(X4,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_89]) ).
cnf(i_0_134,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_90]) ).
cnf(i_0_135,plain,
( empty(X1)
| empty(X2)
| ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4)
| ~ element(X3,X1)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_91]) ).
cnf(i_0_136,plain,
( related(X3,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X3))
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ rel_str(X3) ),
inference(split_conjunct,[status(thm)],[i_0_92]) ).
cnf(i_0_137,plain,
( in(ordered_pair(X2,X3),the_InternalRel(X1))
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_92]) ).
fof(i_0_138,plain,
! [X280,X281,X282] :
( ( ~ below_refl(X280,X281,X282)
| below(X280,X281,X282)
| empty_carrier(X280)
| ~ meet_commutative(X280)
| ~ meet_absorbing(X280)
| ~ join_absorbing(X280)
| ~ latt_str(X280)
| ~ element(X281,the_carrier(X280))
| ~ element(X282,the_carrier(X280)) )
& ( ~ below(X280,X281,X282)
| below_refl(X280,X281,X282)
| empty_carrier(X280)
| ~ meet_commutative(X280)
| ~ meet_absorbing(X280)
| ~ join_absorbing(X280)
| ~ latt_str(X280)
| ~ element(X281,the_carrier(X280))
| ~ element(X282,the_carrier(X280)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_93])])]) ).
fof(i_0_139,negated_conjecture,
( ~ empty_carrier(esk20_0)
& lattice(esk20_0)
& latt_str(esk20_0)
& element(esk21_0,the_carrier(esk20_0))
& element(esk22_0,the_carrier(esk20_0))
& ( ~ below_refl(esk20_0,esk21_0,esk22_0)
| ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) )
& ( below_refl(esk20_0,esk21_0,esk22_0)
| related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_94])])]) ).
fof(i_0_140,plain,
! [X283,X284,X285] :
( ( ~ related_reflexive(X283,X284,X285)
| related(X283,X284,X285)
| empty_carrier(X283)
| ~ reflexive_relstr(X283)
| ~ rel_str(X283)
| ~ element(X284,the_carrier(X283))
| ~ element(X285,the_carrier(X283)) )
& ( ~ related(X283,X284,X285)
| related_reflexive(X283,X284,X285)
| empty_carrier(X283)
| ~ reflexive_relstr(X283)
| ~ rel_str(X283)
| ~ element(X284,the_carrier(X283))
| ~ element(X285,the_carrier(X283)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_95])])]) ).
fof(i_0_141,plain,
! [X235,X236] :
( ( strict_rel_str(rel_str_of(X235,X236))
| ~ reflexive(X236)
| ~ antisymmetric(X236)
| ~ transitive(X236)
| ~ v1_partfun1(X236,X235,X235)
| ~ relation_of2(X236,X235,X235) )
& ( reflexive_relstr(rel_str_of(X235,X236))
| ~ reflexive(X236)
| ~ antisymmetric(X236)
| ~ transitive(X236)
| ~ v1_partfun1(X236,X235,X235)
| ~ relation_of2(X236,X235,X235) )
& ( transitive_relstr(rel_str_of(X235,X236))
| ~ reflexive(X236)
| ~ antisymmetric(X236)
| ~ transitive(X236)
| ~ v1_partfun1(X236,X235,X235)
| ~ relation_of2(X236,X235,X235) )
& ( antisymmetric_relstr(rel_str_of(X235,X236))
| ~ reflexive(X236)
| ~ antisymmetric(X236)
| ~ transitive(X236)
| ~ v1_partfun1(X236,X235,X235)
| ~ relation_of2(X236,X235,X235) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_orders_2])])]) ).
fof(i_0_142,plain,
! [X205,X206,X207] :
( ~ relation_of2_as_subset(X207,X205,X206)
| element(X207,powerset(cartesian_product2(X205,X206))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(i_0_143,plain,
! [X287,X288,X289] :
( empty_carrier(X287)
| ~ meet_commutative(X287)
| ~ meet_absorbing(X287)
| ~ join_absorbing(X287)
| ~ latt_str(X287)
| ~ element(X288,the_carrier(X287))
| ~ element(X289,the_carrier(X287))
| below_refl(X287,X288,X288) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_96])]) ).
fof(i_0_144,plain,
! [X277,X278,X279] :
( ( ~ relation_of2_as_subset(X279,X277,X278)
| relation_of2(X279,X277,X278) )
& ( ~ relation_of2(X279,X277,X278)
| relation_of2_as_subset(X279,X277,X278) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(i_0_145,plain,
! [X224,X225] :
( ( ~ empty_carrier(rel_str_of(X224,X225))
| empty(X224)
| ~ relation_of2(X225,X224,X224) )
& ( strict_rel_str(rel_str_of(X224,X225))
| empty(X224)
| ~ relation_of2(X225,X224,X224) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_97])])]) ).
fof(i_0_146,plain,
! [X290,X291,X292] :
( empty_carrier(X290)
| ~ reflexive_relstr(X290)
| ~ rel_str(X290)
| ~ element(X291,the_carrier(X290))
| ~ element(X292,the_carrier(X290))
| related_reflexive(X290,X291,X291) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_98])]) ).
fof(i_0_147,plain,
! [X243] :
( ( relation(the_L_meet(X243))
| empty_carrier(X243)
| ~ meet_associative(X243)
| ~ meet_semilatt_str(X243) )
& ( function(the_L_meet(X243))
| empty_carrier(X243)
| ~ meet_associative(X243)
| ~ meet_semilatt_str(X243) )
& ( quasi_total(the_L_meet(X243),cartesian_product2(the_carrier(X243),the_carrier(X243)),the_carrier(X243))
| empty_carrier(X243)
| ~ meet_associative(X243)
| ~ meet_semilatt_str(X243) )
& ( v2_binop_1(the_L_meet(X243),the_carrier(X243))
| empty_carrier(X243)
| ~ meet_associative(X243)
| ~ meet_semilatt_str(X243) )
& ( v1_partfun1(the_L_meet(X243),cartesian_product2(the_carrier(X243),the_carrier(X243)),the_carrier(X243))
| empty_carrier(X243)
| ~ meet_associative(X243)
| ~ meet_semilatt_str(X243) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_99])])]) ).
fof(i_0_148,plain,
! [X239] :
( ( relation(the_L_meet(X239))
| empty_carrier(X239)
| ~ meet_commutative(X239)
| ~ meet_semilatt_str(X239) )
& ( function(the_L_meet(X239))
| empty_carrier(X239)
| ~ meet_commutative(X239)
| ~ meet_semilatt_str(X239) )
& ( quasi_total(the_L_meet(X239),cartesian_product2(the_carrier(X239),the_carrier(X239)),the_carrier(X239))
| empty_carrier(X239)
| ~ meet_commutative(X239)
| ~ meet_semilatt_str(X239) )
& ( v1_binop_1(the_L_meet(X239),the_carrier(X239))
| empty_carrier(X239)
| ~ meet_commutative(X239)
| ~ meet_semilatt_str(X239) )
& ( v1_partfun1(the_L_meet(X239),cartesian_product2(the_carrier(X239),the_carrier(X239)),the_carrier(X239))
| empty_carrier(X239)
| ~ meet_commutative(X239)
| ~ meet_semilatt_str(X239) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_100])])]) ).
fof(i_0_149,plain,
! [X231] :
( ( relation(the_L_join(X231))
| empty_carrier(X231)
| ~ join_associative(X231)
| ~ join_semilatt_str(X231) )
& ( function(the_L_join(X231))
| empty_carrier(X231)
| ~ join_associative(X231)
| ~ join_semilatt_str(X231) )
& ( quasi_total(the_L_join(X231),cartesian_product2(the_carrier(X231),the_carrier(X231)),the_carrier(X231))
| empty_carrier(X231)
| ~ join_associative(X231)
| ~ join_semilatt_str(X231) )
& ( v2_binop_1(the_L_join(X231),the_carrier(X231))
| empty_carrier(X231)
| ~ join_associative(X231)
| ~ join_semilatt_str(X231) )
& ( v1_partfun1(the_L_join(X231),cartesian_product2(the_carrier(X231),the_carrier(X231)),the_carrier(X231))
| empty_carrier(X231)
| ~ join_associative(X231)
| ~ join_semilatt_str(X231) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_101])])]) ).
fof(i_0_150,plain,
! [X228] :
( ( relation(the_L_join(X228))
| empty_carrier(X228)
| ~ join_commutative(X228)
| ~ join_semilatt_str(X228) )
& ( function(the_L_join(X228))
| empty_carrier(X228)
| ~ join_commutative(X228)
| ~ join_semilatt_str(X228) )
& ( quasi_total(the_L_join(X228),cartesian_product2(the_carrier(X228),the_carrier(X228)),the_carrier(X228))
| empty_carrier(X228)
| ~ join_commutative(X228)
| ~ join_semilatt_str(X228) )
& ( v1_binop_1(the_L_join(X228),the_carrier(X228))
| empty_carrier(X228)
| ~ join_commutative(X228)
| ~ join_semilatt_str(X228) )
& ( v1_partfun1(the_L_join(X228),cartesian_product2(the_carrier(X228),the_carrier(X228)),the_carrier(X228))
| empty_carrier(X228)
| ~ join_commutative(X228)
| ~ join_semilatt_str(X228) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_102])])]) ).
fof(i_0_151,plain,
! [X244,X245,X246,X247] :
( ( X244 = X246
| rel_str_of(X244,X245) != rel_str_of(X246,X247)
| ~ relation_of2(X245,X244,X244) )
& ( X245 = X247
| rel_str_of(X244,X245) != rel_str_of(X246,X247)
| ~ relation_of2(X245,X244,X244) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])]) ).
fof(i_0_152,plain,
! [X208] :
( ( function(the_L_meet(X208))
| ~ meet_semilatt_str(X208) )
& ( quasi_total(the_L_meet(X208),cartesian_product2(the_carrier(X208),the_carrier(X208)),the_carrier(X208))
| ~ meet_semilatt_str(X208) )
& ( relation_of2_as_subset(the_L_meet(X208),cartesian_product2(the_carrier(X208),the_carrier(X208)),the_carrier(X208))
| ~ meet_semilatt_str(X208) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
fof(i_0_153,plain,
! [X210] :
( ( function(the_L_join(X210))
| ~ join_semilatt_str(X210) )
& ( quasi_total(the_L_join(X210),cartesian_product2(the_carrier(X210),the_carrier(X210)),the_carrier(X210))
| ~ join_semilatt_str(X210) )
& ( relation_of2_as_subset(the_L_join(X210),cartesian_product2(the_carrier(X210),the_carrier(X210)),the_carrier(X210))
| ~ join_semilatt_str(X210) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
fof(i_0_154,plain,
! [X167,X168,X169] :
( ~ element(X169,powerset(cartesian_product2(X167,X168)))
| relation(X169) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(i_0_155,plain,
! [X181,X182] :
( ( strict_rel_str(rel_str_of(X181,X182))
| ~ relation_of2(X182,X181,X181) )
& ( rel_str(rel_str_of(X181,X182))
| ~ relation_of2(X182,X181,X181) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_g1_orders_2])])]) ).
fof(i_0_156,plain,
! [X196,X197] :
( empty_carrier(X196)
| ~ lattice(X196)
| ~ latt_str(X196)
| ~ element(X197,the_carrier(X196))
| element(cast_to_el_of_LattPOSet(X196,X197),the_carrier(poset_of_lattice(X196))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_103])]) ).
fof(i_0_157,plain,
! [X229] :
( ( relation(the_InternalRel(X229))
| ~ reflexive_relstr(X229)
| ~ transitive_relstr(X229)
| ~ antisymmetric_relstr(X229)
| ~ rel_str(X229) )
& ( reflexive(the_InternalRel(X229))
| ~ reflexive_relstr(X229)
| ~ transitive_relstr(X229)
| ~ antisymmetric_relstr(X229)
| ~ rel_str(X229) )
& ( antisymmetric(the_InternalRel(X229))
| ~ reflexive_relstr(X229)
| ~ transitive_relstr(X229)
| ~ antisymmetric_relstr(X229)
| ~ rel_str(X229) )
& ( transitive(the_InternalRel(X229))
| ~ reflexive_relstr(X229)
| ~ transitive_relstr(X229)
| ~ antisymmetric_relstr(X229)
| ~ rel_str(X229) )
& ( v1_partfun1(the_InternalRel(X229),the_carrier(X229),the_carrier(X229))
| ~ reflexive_relstr(X229)
| ~ transitive_relstr(X229)
| ~ antisymmetric_relstr(X229)
| ~ rel_str(X229) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_orders_2])])]) ).
fof(i_0_158,plain,
! [X194] :
( ( reflexive(k2_lattice3(X194))
| empty_carrier(X194)
| ~ lattice(X194)
| ~ latt_str(X194) )
& ( antisymmetric(k2_lattice3(X194))
| empty_carrier(X194)
| ~ lattice(X194)
| ~ latt_str(X194) )
& ( transitive(k2_lattice3(X194))
| empty_carrier(X194)
| ~ lattice(X194)
| ~ latt_str(X194) )
& ( v1_partfun1(k2_lattice3(X194),the_carrier(X194),the_carrier(X194))
| empty_carrier(X194)
| ~ lattice(X194)
| ~ latt_str(X194) )
& ( relation_of2_as_subset(k2_lattice3(X194),the_carrier(X194),the_carrier(X194))
| empty_carrier(X194)
| ~ lattice(X194)
| ~ latt_str(X194) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_104])])]) ).
fof(i_0_159,plain,
! [X163] :
( ~ latt_str(X163)
| ~ strict_latt_str(X163)
| X163 = latt_str_of(the_carrier(X163),the_L_join(X163),the_L_meet(X163)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_lattices])]) ).
fof(i_0_160,plain,
! [X221,X222] : relation_of2_as_subset(esk8_2(X221,X222),X221,X222),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m2_relset_1])]) ).
fof(i_0_161,plain,
! [X216,X217] : relation_of2(esk6_2(X216,X217),X216,X217),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_relset_1])]) ).
fof(i_0_162,plain,
! [X209] :
( ~ rel_str(X209)
| relation_of2_as_subset(the_InternalRel(X209),the_carrier(X209),the_carrier(X209)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])]) ).
fof(i_0_163,plain,
! [X302,X303,X304] :
( ~ in(X302,X303)
| ~ element(X303,powerset(X304))
| element(X302,X304) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_164,plain,
! [X174,X175] :
( empty_carrier(X174)
| ~ lattice(X174)
| ~ latt_str(X174)
| ~ element(X175,the_carrier(X174))
| cast_to_el_of_LattPOSet(X174,X175) = X175 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_105])])]) ).
fof(i_0_165,plain,
! [X305,X306,X307] :
( ~ in(X305,X306)
| ~ element(X306,powerset(X307))
| ~ empty(X307) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_166,plain,
! [X170] :
( ( ~ empty_carrier(X170)
| empty_carrier(X170)
| ~ join_commutative(X170)
| ~ join_associative(X170)
| ~ meet_commutative(X170)
| ~ meet_associative(X170)
| ~ meet_absorbing(X170)
| ~ join_absorbing(X170)
| ~ latt_str(X170) )
& ( lattice(X170)
| empty_carrier(X170)
| ~ join_commutative(X170)
| ~ join_associative(X170)
| ~ meet_commutative(X170)
| ~ meet_associative(X170)
| ~ meet_absorbing(X170)
| ~ join_absorbing(X170)
| ~ latt_str(X170) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_106])])]) ).
fof(i_0_167,plain,
! [X241,X242] :
( empty(X241)
| empty(X242)
| ~ empty(cartesian_product2(X241,X242)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_107])]) ).
fof(i_0_168,plain,
! [X198,X199] :
( ( strict_latt_str(k8_filter_1(X198,X199))
| empty_carrier(X198)
| ~ latt_str(X198)
| empty_carrier(X199)
| ~ latt_str(X199) )
& ( latt_str(k8_filter_1(X198,X199))
| empty_carrier(X198)
| ~ latt_str(X198)
| empty_carrier(X199)
| ~ latt_str(X199) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_108])])]) ).
fof(i_0_169,plain,
! [X264] :
( ( element(esk17_1(X264),powerset(the_carrier(X264)))
| empty_carrier(X264)
| ~ one_sorted_str(X264) )
& ( ~ empty(esk17_1(X264))
| empty_carrier(X264)
| ~ one_sorted_str(X264) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_109])])])]) ).
fof(i_0_170,plain,
! [X173] :
( empty_carrier(X173)
| ~ lattice(X173)
| ~ latt_str(X173)
| poset_of_lattice(X173) = rel_str_of(the_carrier(X173),k2_lattice3(X173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_110])]) ).
fof(i_0_171,plain,
! [X237,X238] : ~ empty(unordered_pair(X237,X238)),
inference(variable_rename,[status(thm)],[i_0_111]) ).
fof(i_0_172,plain,
! [X300,X301] :
( ( ~ element(X300,powerset(X301))
| subset(X300,X301) )
& ( ~ subset(X300,X301)
| element(X300,powerset(X301)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_173,plain,
! [X164,X165] :
( ~ in(X164,X165)
| ~ in(X165,X164) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_112])]) ).
fof(i_0_174,plain,
! [X162] :
( ~ rel_str(X162)
| ~ strict_rel_str(X162)
| X162 = rel_str_of(the_carrier(X162),the_InternalRel(X162)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])]) ).
fof(i_0_175,plain,
! [X295,X296] :
( ~ element(X295,X296)
| empty(X296)
| in(X295,X296) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_176,plain,
! [X293,X294] :
( ~ in(X293,X294)
| element(X293,X294) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_177,plain,
! [X240] :
( ( ~ empty_carrier(poset_of_lattice(X240))
| empty_carrier(X240)
| ~ lattice(X240)
| ~ latt_str(X240) )
& ( strict_rel_str(poset_of_lattice(X240))
| empty_carrier(X240)
| ~ lattice(X240)
| ~ latt_str(X240) )
& ( reflexive_relstr(poset_of_lattice(X240))
| empty_carrier(X240)
| ~ lattice(X240)
| ~ latt_str(X240) )
& ( transitive_relstr(poset_of_lattice(X240))
| empty_carrier(X240)
| ~ lattice(X240)
| ~ latt_str(X240) )
& ( antisymmetric_relstr(poset_of_lattice(X240))
| empty_carrier(X240)
| ~ lattice(X240)
| ~ latt_str(X240) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_113])])]) ).
fof(i_0_178,plain,
! [X255] :
( ( element(esk10_1(X255),powerset(X255))
| empty(X255) )
& ( ~ empty(esk10_1(X255))
| empty(X255) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_114])])])]) ).
fof(i_0_179,plain,
! [X309,X310] :
( ~ in(X309,X310)
| ~ empty(X310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_180,plain,
! [X195] :
( ( strict_rel_str(poset_of_lattice(X195))
| empty_carrier(X195)
| ~ lattice(X195)
| ~ latt_str(X195) )
& ( reflexive_relstr(poset_of_lattice(X195))
| empty_carrier(X195)
| ~ lattice(X195)
| ~ latt_str(X195) )
& ( transitive_relstr(poset_of_lattice(X195))
| empty_carrier(X195)
| ~ lattice(X195)
| ~ latt_str(X195) )
& ( antisymmetric_relstr(poset_of_lattice(X195))
| empty_carrier(X195)
| ~ lattice(X195)
| ~ latt_str(X195) )
& ( rel_str(poset_of_lattice(X195))
| empty_carrier(X195)
| ~ lattice(X195)
| ~ latt_str(X195) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_115])])]) ).
fof(i_0_181,plain,
! [X200] :
( empty_carrier(X200)
| ~ lattice(X200)
| ~ latt_str(X200)
| relation(relation_of_lattice(X200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_116])]) ).
fof(i_0_182,plain,
! [X226] :
( empty_carrier(X226)
| ~ one_sorted_str(X226)
| ~ empty(the_carrier(X226)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_117])]) ).
fof(i_0_183,plain,
! [X171,X172] : unordered_pair(X171,X172) = unordered_pair(X172,X171),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_184,plain,
! [X276] :
( empty_carrier(X276)
| ~ lattice(X276)
| ~ latt_str(X276)
| k2_lattice3(X276) = relation_of_lattice(X276) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_118])]) ).
fof(i_0_185,plain,
! [X259] :
( element(esk13_1(X259),powerset(X259))
& empty(esk13_1(X259)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_186,plain,
! [X166] :
( ( ~ empty_carrier(X166)
| empty_carrier(X166)
| ~ lattice(X166)
| ~ latt_str(X166) )
& ( join_commutative(X166)
| empty_carrier(X166)
| ~ lattice(X166)
| ~ latt_str(X166) )
& ( join_associative(X166)
| empty_carrier(X166)
| ~ lattice(X166)
| ~ latt_str(X166) )
& ( meet_commutative(X166)
| empty_carrier(X166)
| ~ lattice(X166)
| ~ latt_str(X166) )
& ( meet_associative(X166)
| empty_carrier(X166)
| ~ lattice(X166)
| ~ latt_str(X166) )
& ( meet_absorbing(X166)
| empty_carrier(X166)
| ~ lattice(X166)
| ~ latt_str(X166) )
& ( join_absorbing(X166)
| empty_carrier(X166)
| ~ lattice(X166)
| ~ latt_str(X166) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_119])])]) ).
fof(i_0_187,plain,
! [X219] : element(esk7_1(X219),X219),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_188,plain,
! [X230] : ~ empty(singleton(X230)),
inference(variable_rename,[status(thm)],[i_0_120]) ).
fof(i_0_189,plain,
! [X227] : ~ empty(powerset(X227)),
inference(variable_rename,[status(thm)],[i_0_121]) ).
fof(i_0_190,plain,
! [X314,X315] :
( ~ empty(X314)
| X314 = X315
| ~ empty(X315) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_191,plain,
! [X286] : subset(X286,X286),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_192,plain,
! [X204] :
( ( meet_semilatt_str(X204)
| ~ latt_str(X204) )
& ( join_semilatt_str(X204)
| ~ latt_str(X204) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(i_0_193,plain,
! [X203] :
( ~ join_semilatt_str(X203)
| one_sorted_str(X203) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_lattices])]) ).
fof(i_0_194,plain,
! [X201] :
( ~ meet_semilatt_str(X201)
| one_sorted_str(X201) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(i_0_195,plain,
! [X202] :
( ~ rel_str(X202)
| one_sorted_str(X202) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])]) ).
fof(i_0_196,plain,
! [X308] :
( ~ empty(X308)
| X308 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_197,plain,
~ empty(esk14_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_122])]) ).
fof(i_0_198,plain,
( latt_str(esk19_0)
& ~ empty_carrier(esk19_0)
& strict_latt_str(esk19_0)
& join_commutative(esk19_0)
& join_associative(esk19_0)
& meet_commutative(esk19_0)
& meet_associative(esk19_0)
& meet_absorbing(esk19_0)
& join_absorbing(esk19_0)
& lattice(esk19_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_123])]) ).
fof(i_0_199,plain,
( latt_str(esk18_0)
& ~ empty_carrier(esk18_0)
& strict_latt_str(esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_124])]) ).
fof(i_0_200,plain,
( one_sorted_str(esk16_0)
& ~ empty_carrier(esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_125])]) ).
fof(i_0_201,plain,
( rel_str(esk12_0)
& ~ empty_carrier(esk12_0)
& strict_rel_str(esk12_0)
& reflexive_relstr(esk12_0)
& transitive_relstr(esk12_0)
& antisymmetric_relstr(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_126])]) ).
fof(i_0_202,plain,
join_semilatt_str(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l2_lattices])]) ).
fof(i_0_203,plain,
one_sorted_str(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_struct_0])]) ).
fof(i_0_204,plain,
meet_semilatt_str(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_lattices])]) ).
fof(i_0_205,plain,
empty(esk11_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(i_0_206,plain,
( latt_str(esk15_0)
& strict_latt_str(esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_lattices])]) ).
fof(i_0_207,plain,
latt_str(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l3_lattices])]) ).
fof(i_0_208,plain,
( rel_str(esk9_0)
& strict_rel_str(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_orders_2])]) ).
fof(i_0_209,plain,
rel_str(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_l1_orders_2])]) ).
cnf(i_0_210,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_211,plain,
( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| 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)],[i_0_127]),
[final] ).
cnf(i_0_212,plain,
( empty(X1)
| ~ empty_carrier(latt_str_of(X1,X2,X3))
| ~ function(X2)
| ~ quasi_total(X2,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X2,cartesian_product2(X1,X1),X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_213,plain,
( X1 = X2
| latt_str_of(X1,X3,X4) != latt_str_of(X2,X5,X6)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1)
| ~ function(X4)
| ~ quasi_total(X4,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X4,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_214,plain,
( X1 = X2
| latt_str_of(X3,X1,X4) != latt_str_of(X5,X2,X6)
| ~ function(X1)
| ~ quasi_total(X1,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X1,cartesian_product2(X3,X3),X3)
| ~ function(X4)
| ~ quasi_total(X4,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X4,cartesian_product2(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_215,plain,
( X1 = X2
| latt_str_of(X3,X4,X1) != latt_str_of(X5,X6,X2)
| ~ function(X4)
| ~ quasi_total(X4,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X4,cartesian_product2(X3,X3),X3)
| ~ function(X1)
| ~ quasi_total(X1,cartesian_product2(X3,X3),X3)
| ~ relation_of2(X1,cartesian_product2(X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_216,plain,
( empty_carrier(X1)
| empty_carrier(X2)
| element(k10_filter_1(X1,X2,X3,X4),the_carrier(k8_filter_1(X1,X2)))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ lattice(X2)
| ~ latt_str(X2)
| ~ element(X3,the_carrier(X1))
| ~ element(X4,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_217,plain,
( strict_latt_str(latt_str_of(X1,X2,X3))
| empty(X1)
| ~ function(X2)
| ~ quasi_total(X2,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X2,cartesian_product2(X1,X1),X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_218,plain,
( strict_latt_str(latt_str_of(X1,X2,X3))
| ~ function(X2)
| ~ quasi_total(X2,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X2,cartesian_product2(X1,X1),X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_219,plain,
( latt_str(latt_str_of(X1,X2,X3))
| ~ function(X2)
| ~ quasi_total(X2,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X2,cartesian_product2(X1,X1),X1)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X1),X1)
| ~ relation_of2(X3,cartesian_product2(X1,X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_220,plain,
( empty(X1)
| empty(X2)
| element(ordered_pair_as_product_element(X1,X2,X3,X4),cartesian_product2(X1,X2))
| ~ element(X3,X1)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_221,plain,
( k10_filter_1(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3))
| empty_carrier(X2)
| empty_carrier(X1)
| ~ latt_str(X2)
| ~ latt_str(X1)
| ~ lattice(X2)
| ~ lattice(X1)
| ~ element(X4,the_carrier(X2))
| ~ element(X3,the_carrier(X1)) ),
inference(rw,[status(thm)],[i_0_133,c_0_134]),
[final] ).
cnf(i_0_222,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3))
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(rw,[status(thm)],[i_0_135,c_0_134]),
[final] ).
cnf(i_0_223,plain,
( related(X3,X1,X2)
| ~ rel_str(X3)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3)) ),
inference(rw,[status(thm)],[i_0_136,c_0_134]),
[final] ).
cnf(i_0_224,plain,
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(rw,[status(thm)],[i_0_137,c_0_134]),
[final] ).
cnf(i_0_225,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)],[i_0_138]),
[final] ).
cnf(i_0_226,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)],[i_0_138]),
[final] ).
cnf(i_0_227,negated_conjecture,
( ~ below_refl(esk20_0,esk21_0,esk22_0)
| ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_228,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)],[i_0_140]),
[final] ).
cnf(i_0_229,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)],[i_0_140]),
[final] ).
cnf(i_0_230,plain,
( antisymmetric_relstr(rel_str_of(X1,X2))
| ~ reflexive(X2)
| ~ antisymmetric(X2)
| ~ transitive(X2)
| ~ v1_partfun1(X2,X1,X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_141]),
[final] ).
cnf(i_0_231,plain,
( transitive_relstr(rel_str_of(X1,X2))
| ~ reflexive(X2)
| ~ antisymmetric(X2)
| ~ transitive(X2)
| ~ v1_partfun1(X2,X1,X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_141]),
[final] ).
cnf(i_0_232,plain,
( reflexive_relstr(rel_str_of(X1,X2))
| ~ reflexive(X2)
| ~ antisymmetric(X2)
| ~ transitive(X2)
| ~ v1_partfun1(X2,X1,X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_141]),
[final] ).
cnf(i_0_233,plain,
( strict_rel_str(rel_str_of(X1,X2))
| ~ reflexive(X2)
| ~ antisymmetric(X2)
| ~ transitive(X2)
| ~ v1_partfun1(X2,X1,X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_141]),
[final] ).
cnf(i_0_234,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_142]),
[final] ).
cnf(i_0_235,plain,
( empty_carrier(X1)
| below_refl(X1,X2,X2)
| ~ 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)],[i_0_143]),
[final] ).
cnf(i_0_236,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk22_0)
| related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_237,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_238,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_239,plain,
( empty(X1)
| ~ empty_carrier(rel_str_of(X1,X2))
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_145]),
[final] ).
cnf(i_0_240,plain,
( empty_carrier(X1)
| related_reflexive(X1,X2,X2)
| ~ reflexive_relstr(X1)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_146]),
[final] ).
cnf(i_0_241,plain,
( v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_242,plain,
( v1_partfun1(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_243,plain,
( v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_244,plain,
( v1_partfun1(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_245,plain,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_246,plain,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_247,plain,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_248,plain,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_249,plain,
( X1 = X2
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| ~ relation_of2(X3,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_250,plain,
( X1 = X2
| rel_str_of(X3,X1) != rel_str_of(X4,X2)
| ~ relation_of2(X1,X3,X3) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_251,plain,
( relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_252,plain,
( relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_153]),
[final] ).
cnf(i_0_253,plain,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_254,plain,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_153]),
[final] ).
cnf(i_0_255,plain,
( strict_rel_str(rel_str_of(X1,X2))
| empty(X1)
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_145]),
[final] ).
cnf(i_0_256,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_257,plain,
( strict_rel_str(rel_str_of(X1,X2))
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_258,plain,
( rel_str(rel_str_of(X1,X2))
| ~ relation_of2(X2,X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_259,plain,
( empty_carrier(X1)
| element(cast_to_el_of_LattPOSet(X1,X2),the_carrier(poset_of_lattice(X1)))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_156]),
[final] ).
cnf(i_0_260,plain,
( v1_partfun1(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_261,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)],[i_0_158]),
[final] ).
cnf(i_0_262,plain,
( v1_partfun1(k2_lattice3(X1),the_carrier(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_263,plain,
( X1 = latt_str_of(the_carrier(X1),the_L_join(X1),the_L_meet(X1))
| ~ latt_str(X1)
| ~ strict_latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_159]),
[final] ).
cnf(i_0_264,plain,
relation_of2_as_subset(esk8_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[i_0_160]),
[final] ).
cnf(i_0_265,plain,
relation_of2(esk6_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_266,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_267,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_268,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)],[i_0_164]),
[final] ).
cnf(i_0_269,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_165]),
[final] ).
cnf(i_0_270,plain,
( lattice(X1)
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_associative(X1)
| ~ meet_commutative(X1)
| ~ meet_associative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_271,plain,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_272,plain,
( strict_latt_str(k8_filter_1(X1,X2))
| empty_carrier(X1)
| empty_carrier(X2)
| ~ latt_str(X1)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_273,plain,
( latt_str(k8_filter_1(X1,X2))
| empty_carrier(X1)
| empty_carrier(X2)
| ~ latt_str(X1)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_274,plain,
( element(esk17_1(X1),powerset(the_carrier(X1)))
| empty_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_169]),
[final] ).
cnf(i_0_275,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)],[i_0_170]),
[final] ).
cnf(i_0_276,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_277,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_172]),
[final] ).
cnf(i_0_278,plain,
( v2_binop_1(the_L_meet(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_279,plain,
( v2_binop_1(the_L_join(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_280,plain,
( v1_binop_1(the_L_meet(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_281,plain,
( v1_binop_1(the_L_join(X1),the_carrier(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_282,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_173]),
[final] ).
cnf(i_0_283,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_172]),
[final] ).
cnf(i_0_284,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ strict_rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_174]),
[final] ).
cnf(i_0_285,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_175]),
[final] ).
cnf(i_0_286,plain,
( transitive(the_InternalRel(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_287,plain,
( antisymmetric(the_InternalRel(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_288,plain,
( reflexive(the_InternalRel(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_289,plain,
( relation(the_InternalRel(X1))
| ~ reflexive_relstr(X1)
| ~ transitive_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_290,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_176]),
[final] ).
cnf(i_0_291,plain,
( empty_carrier(X1)
| ~ empty_carrier(poset_of_lattice(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_177]),
[final] ).
cnf(i_0_292,plain,
( element(esk10_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_178]),
[final] ).
cnf(i_0_293,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_294,plain,
( antisymmetric_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_177]),
[final] ).
cnf(i_0_295,plain,
( antisymmetric_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_296,plain,
( transitive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_177]),
[final] ).
cnf(i_0_297,plain,
( transitive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_298,plain,
( reflexive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_177]),
[final] ).
cnf(i_0_299,plain,
( reflexive_relstr(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_300,plain,
( transitive(k2_lattice3(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_301,plain,
( antisymmetric(k2_lattice3(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_302,plain,
( reflexive(k2_lattice3(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_303,plain,
( function(the_L_meet(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_304,plain,
( function(the_L_meet(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_305,plain,
( function(the_L_join(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_306,plain,
( function(the_L_join(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_307,plain,
( empty_carrier(X1)
| relation(relation_of_lattice(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_181]),
[final] ).
cnf(i_0_308,plain,
( relation(the_L_meet(X1))
| empty_carrier(X1)
| ~ meet_associative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_309,plain,
( relation(the_L_meet(X1))
| empty_carrier(X1)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_310,plain,
( relation(the_L_join(X1))
| empty_carrier(X1)
| ~ join_associative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_311,plain,
( relation(the_L_join(X1))
| empty_carrier(X1)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_312,plain,
( strict_rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_177]),
[final] ).
cnf(i_0_313,plain,
( strict_rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_314,plain,
( rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_315,plain,
( empty_carrier(X1)
| ~ empty(esk17_1(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_169]),
[final] ).
cnf(i_0_316,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_182]),
[final] ).
cnf(i_0_317,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_183]),
[final] ).
cnf(i_0_318,plain,
( empty_carrier(X1)
| k2_lattice3(X1) = relation_of_lattice(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_184]),
[final] ).
cnf(i_0_319,plain,
element(esk13_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_185]),
[final] ).
cnf(i_0_320,plain,
( join_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_321,plain,
( meet_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_322,plain,
( meet_associative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_323,plain,
( meet_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_324,plain,
( join_associative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_325,plain,
( join_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_326,plain,
( empty(X1)
| ~ empty(esk10_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_178]),
[final] ).
cnf(i_0_327,plain,
element(esk7_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_187]),
[final] ).
cnf(i_0_328,plain,
( function(the_L_meet(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_329,plain,
( function(the_L_join(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_153]),
[final] ).
cnf(i_0_330,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_188]),
[final] ).
cnf(i_0_331,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_189]),
[final] ).
cnf(i_0_332,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_190]),
[final] ).
cnf(i_0_333,negated_conjecture,
element(esk22_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_334,negated_conjecture,
element(esk21_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_335,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_191]),
[final] ).
cnf(i_0_336,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_192]),
[final] ).
cnf(i_0_337,plain,
( one_sorted_str(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_193]),
[final] ).
cnf(i_0_338,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_194]),
[final] ).
cnf(i_0_339,plain,
( one_sorted_str(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_195]),
[final] ).
cnf(i_0_340,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[i_0_192]),
[final] ).
cnf(i_0_341,plain,
empty(esk13_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_185]),
[final] ).
cnf(i_0_342,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_196]),
[final] ).
cnf(i_0_343,plain,
~ empty(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_197]),
[final] ).
cnf(i_0_344,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_345,plain,
~ empty_carrier(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_346,plain,
~ empty_carrier(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_199]),
[final] ).
cnf(i_0_347,plain,
~ empty_carrier(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_348,plain,
~ empty_carrier(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_349,plain,
join_semilatt_str(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_202]),
[final] ).
cnf(i_0_350,plain,
one_sorted_str(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_200]),
[final] ).
cnf(i_0_351,plain,
one_sorted_str(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_203]),
[final] ).
cnf(i_0_352,plain,
meet_semilatt_str(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_204]),
[final] ).
cnf(i_0_353,plain,
antisymmetric_relstr(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_354,plain,
transitive_relstr(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_355,plain,
reflexive_relstr(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_356,plain,
empty(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_205]),
[final] ).
cnf(i_0_357,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_358,plain,
join_absorbing(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_359,plain,
meet_absorbing(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_360,plain,
meet_associative(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_361,plain,
meet_commutative(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_362,plain,
join_associative(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_363,plain,
join_commutative(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_364,negated_conjecture,
lattice(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_365,plain,
lattice(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_366,plain,
strict_latt_str(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_367,plain,
strict_latt_str(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_199]),
[final] ).
cnf(i_0_368,plain,
strict_latt_str(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_206]),
[final] ).
cnf(i_0_369,negated_conjecture,
latt_str(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_370,plain,
latt_str(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_198]),
[final] ).
cnf(i_0_371,plain,
latt_str(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_199]),
[final] ).
cnf(i_0_372,plain,
latt_str(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_206]),
[final] ).
cnf(i_0_373,plain,
latt_str(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_207]),
[final] ).
cnf(i_0_374,plain,
strict_rel_str(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_375,plain,
strict_rel_str(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_376,plain,
rel_str(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_201]),
[final] ).
cnf(i_0_377,plain,
rel_str(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_208]),
[final] ).
cnf(i_0_378,plain,
rel_str(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_209]),
[final] ).
cnf(i_0_379,axiom,
X1 = X1 ).
cnf(i_0_380,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_381,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_382,axiom,
( X1 != X2
| ordered_pair_as_product_element(X1,X3,X4,X5) = ordered_pair_as_product_element(X2,X3,X4,X5) ) ).
cnf(i_0_383,axiom,
( X1 != X2
| ordered_pair_as_product_element(X3,X1,X4,X5) = ordered_pair_as_product_element(X3,X2,X4,X5) ) ).
cnf(i_0_384,axiom,
( X1 != X2
| ordered_pair_as_product_element(X3,X4,X1,X5) = ordered_pair_as_product_element(X3,X4,X2,X5) ) ).
cnf(i_0_385,axiom,
( X1 != X2
| ordered_pair_as_product_element(X3,X4,X5,X1) = ordered_pair_as_product_element(X3,X4,X5,X2) ) ).
cnf(i_0_386,axiom,
( X1 != X2
| poset_of_lattice(X1) = poset_of_lattice(X2) ) ).
cnf(i_0_387,axiom,
( X1 != X2
| cast_to_el_of_LattPOSet(X1,X3) = cast_to_el_of_LattPOSet(X2,X3) ) ).
cnf(i_0_388,axiom,
( X1 != X2
| cast_to_el_of_LattPOSet(X3,X1) = cast_to_el_of_LattPOSet(X3,X2) ) ).
cnf(i_0_389,axiom,
( X1 != X2
| rel_str_of(X1,X3) = rel_str_of(X2,X3) ) ).
cnf(i_0_390,axiom,
( X1 != X2
| rel_str_of(X3,X1) = rel_str_of(X3,X2) ) ).
cnf(i_0_391,axiom,
( X1 != X2
| k2_lattice3(X1) = k2_lattice3(X2) ) ).
cnf(i_0_392,axiom,
( X1 != X2
| relation_of_lattice(X1) = relation_of_lattice(X2) ) ).
cnf(i_0_393,axiom,
( X1 != X2
| latt_str_of(X1,X3,X4) = latt_str_of(X2,X3,X4) ) ).
cnf(i_0_394,axiom,
( X1 != X2
| latt_str_of(X3,X1,X4) = latt_str_of(X3,X2,X4) ) ).
cnf(i_0_395,axiom,
( X1 != X2
| latt_str_of(X3,X4,X1) = latt_str_of(X3,X4,X2) ) ).
cnf(i_0_396,axiom,
( X1 != X2
| k10_filter_1(X1,X3,X4,X5) = k10_filter_1(X2,X3,X4,X5) ) ).
cnf(i_0_397,axiom,
( X1 != X2
| k10_filter_1(X3,X1,X4,X5) = k10_filter_1(X3,X2,X4,X5) ) ).
cnf(i_0_398,axiom,
( X1 != X2
| k10_filter_1(X3,X4,X1,X5) = k10_filter_1(X3,X4,X2,X5) ) ).
cnf(i_0_399,axiom,
( X1 != X2
| k10_filter_1(X3,X4,X5,X1) = k10_filter_1(X3,X4,X5,X2) ) ).
cnf(i_0_400,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_401,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_402,axiom,
( X1 != X2
| ~ below_refl(X1,X3,X4)
| below_refl(X2,X3,X4) ) ).
cnf(i_0_403,axiom,
( X1 != X2
| ~ below_refl(X3,X1,X4)
| below_refl(X3,X2,X4) ) ).
cnf(i_0_404,axiom,
( X1 != X2
| ~ below_refl(X3,X4,X1)
| below_refl(X3,X4,X2) ) ).
cnf(i_0_405,axiom,
( X1 != X2
| ~ relation_of2(X1,X3,X4)
| relation_of2(X2,X3,X4) ) ).
cnf(i_0_406,axiom,
( X1 != X2
| ~ relation_of2(X3,X1,X4)
| relation_of2(X3,X2,X4) ) ).
cnf(i_0_407,axiom,
( X1 != X2
| ~ relation_of2(X3,X4,X1)
| relation_of2(X3,X4,X2) ) ).
cnf(i_0_408,axiom,
( X1 != X2
| ~ strict_latt_str(X1)
| strict_latt_str(X2) ) ).
cnf(i_0_409,axiom,
( X1 != X2
| ~ related(X1,X3,X4)
| related(X2,X3,X4) ) ).
cnf(i_0_410,axiom,
( X1 != X2
| ~ related(X3,X1,X4)
| related(X3,X2,X4) ) ).
cnf(i_0_411,axiom,
( X1 != X2
| ~ related(X3,X4,X1)
| related(X3,X4,X2) ) ).
cnf(i_0_412,axiom,
( X1 != X2
| ~ rel_str(X1)
| rel_str(X2) ) ).
cnf(i_0_413,axiom,
( X1 != X2
| ~ below(X1,X3,X4)
| below(X2,X3,X4) ) ).
cnf(i_0_414,axiom,
( X1 != X2
| ~ below(X3,X1,X4)
| below(X3,X2,X4) ) ).
cnf(i_0_415,axiom,
( X1 != X2
| ~ below(X3,X4,X1)
| below(X3,X4,X2) ) ).
cnf(i_0_416,axiom,
( X1 != X2
| ~ meet_commutative(X1)
| meet_commutative(X2) ) ).
cnf(i_0_417,axiom,
( X1 != X2
| ~ meet_absorbing(X1)
| meet_absorbing(X2) ) ).
cnf(i_0_418,axiom,
( X1 != X2
| ~ join_absorbing(X1)
| join_absorbing(X2) ) ).
cnf(i_0_419,axiom,
( X1 != X2
| ~ related_reflexive(X1,X3,X4)
| related_reflexive(X2,X3,X4) ) ).
cnf(i_0_420,axiom,
( X1 != X2
| ~ related_reflexive(X3,X1,X4)
| related_reflexive(X3,X2,X4) ) ).
cnf(i_0_421,axiom,
( X1 != X2
| ~ related_reflexive(X3,X4,X1)
| related_reflexive(X3,X4,X2) ) ).
cnf(i_0_422,axiom,
( X1 != X2
| ~ reflexive_relstr(X1)
| reflexive_relstr(X2) ) ).
cnf(i_0_423,axiom,
( X1 != X2
| ~ empty_carrier(X1)
| empty_carrier(X2) ) ).
cnf(i_0_424,axiom,
( X1 != X2
| ~ antisymmetric_relstr(X1)
| antisymmetric_relstr(X2) ) ).
cnf(i_0_425,axiom,
( X1 != X2
| ~ reflexive(X1)
| reflexive(X2) ) ).
cnf(i_0_426,axiom,
( X1 != X2
| ~ antisymmetric(X1)
| antisymmetric(X2) ) ).
cnf(i_0_427,axiom,
( X1 != X2
| ~ transitive(X1)
| transitive(X2) ) ).
cnf(i_0_428,axiom,
( X1 != X2
| ~ v1_partfun1(X1,X3,X4)
| v1_partfun1(X2,X3,X4) ) ).
cnf(i_0_429,axiom,
( X1 != X2
| ~ v1_partfun1(X3,X1,X4)
| v1_partfun1(X3,X2,X4) ) ).
cnf(i_0_430,axiom,
( X1 != X2
| ~ v1_partfun1(X3,X4,X1)
| v1_partfun1(X3,X4,X2) ) ).
cnf(i_0_431,axiom,
( X1 != X2
| ~ transitive_relstr(X1)
| transitive_relstr(X2) ) ).
cnf(i_0_432,axiom,
( X1 != X2
| ~ strict_rel_str(X1)
| strict_rel_str(X2) ) ).
cnf(i_0_433,axiom,
( X1 != X2
| ~ relation_of2_as_subset(X1,X3,X4)
| relation_of2_as_subset(X2,X3,X4) ) ).
cnf(i_0_434,axiom,
( X1 != X2
| ~ relation_of2_as_subset(X3,X1,X4)
| relation_of2_as_subset(X3,X2,X4) ) ).
cnf(i_0_435,axiom,
( X1 != X2
| ~ relation_of2_as_subset(X3,X4,X1)
| relation_of2_as_subset(X3,X4,X2) ) ).
cnf(i_0_436,axiom,
( X1 != X2
| ~ meet_associative(X1)
| meet_associative(X2) ) ).
cnf(i_0_437,axiom,
( X1 != X2
| ~ meet_semilatt_str(X1)
| meet_semilatt_str(X2) ) ).
cnf(i_0_438,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_439,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_440,axiom,
( X1 != X2
| ~ join_associative(X1)
| join_associative(X2) ) ).
cnf(i_0_441,axiom,
( X1 != X2
| ~ join_semilatt_str(X1)
| join_semilatt_str(X2) ) ).
cnf(i_0_442,axiom,
( X1 != X2
| ~ join_commutative(X1)
| join_commutative(X2) ) ).
cnf(i_0_443,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_444,axiom,
( X1 != X2
| ~ one_sorted_str(X1)
| one_sorted_str(X2) ) ).
cnf(i_0_445,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_446,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_447,axiom,
( X1 != X2
| ~ v2_binop_1(X1,X3)
| v2_binop_1(X2,X3) ) ).
cnf(i_0_448,axiom,
( X1 != X2
| ~ v2_binop_1(X3,X1)
| v2_binop_1(X3,X2) ) ).
cnf(i_0_449,axiom,
( X1 != X2
| ~ v1_binop_1(X1,X3)
| v1_binop_1(X2,X3) ) ).
cnf(i_0_450,axiom,
( X1 != X2
| ~ v1_binop_1(X3,X1)
| v1_binop_1(X3,X2) ) ).
cnf(i_0_451,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_452,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_453,axiom,
( X1 != X2
| ~ lattice(X1)
| lattice(X2) ) ).
cnf(i_0_454,axiom,
( X1 != X2
| ~ latt_str(X1)
| latt_str(X2) ) ).
cnf(i_0_455,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_456,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_457,axiom,
( X1 != X2
| ~ quasi_total(X1,X3,X4)
| quasi_total(X2,X3,X4) ) ).
cnf(i_0_458,axiom,
( X1 != X2
| ~ quasi_total(X3,X1,X4)
| quasi_total(X3,X2,X4) ) ).
cnf(i_0_459,axiom,
( X1 != X2
| ~ quasi_total(X3,X4,X1)
| quasi_total(X3,X4,X2) ) ).
cnf(i_0_1802,plain,
element(empty_set,powerset(esk13_1(X1))),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1548,i_0_1552,i_0_1515,i_0_1543,i_0_1556,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_346,i_0_356,i_0_344,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451]) ).
cnf(i_0_1804,plain,
powerset(unordered_pair(X1,X2)) != powerset(esk13_1(X3)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1515,i_0_1543,i_0_1556,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_346,i_0_356,i_0_344,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452]) ).
cnf(i_0_1806,plain,
below(esk20_0,cast_to_el_of_LattPOSet(esk20_0,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),esk22_0),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_346,i_0_356,i_0_344,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414]) ).
cnf(i_0_1808,plain,
below(esk20_0,cast_to_el_of_LattPOSet(esk20_0,esk22_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_346,i_0_356,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415]) ).
cnf(i_0_1809,plain,
~ element(the_carrier(esk20_0),powerset(esk11_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_346,i_0_356,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269]) ).
cnf(i_0_1811,plain,
empty(esk7_1(powerset(empty_set))),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_346,i_0_356,i_0_327,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285]) ).
cnf(i_0_1818,plain,
in(cast_to_el_of_LattPOSet(esk20_0,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),the_carrier(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_346,i_0_356,i_0_327,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438]) ).
cnf(i_0_1820,plain,
~ empty(k10_filter_1(esk20_0,esk20_0,esk22_0,esk22_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455]) ).
cnf(i_0_1822,plain,
the_carrier(esk20_0) != esk11_0,
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439]) ).
cnf(i_0_1824,plain,
~ empty_carrier(poset_of_lattice(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291]) ).
cnf(i_0_1826,plain,
antisymmetric_relstr(poset_of_lattice(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295]) ).
cnf(i_0_1828,plain,
transitive_relstr(poset_of_lattice(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297]) ).
cnf(i_0_1830,plain,
reflexive_relstr(poset_of_lattice(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299]) ).
cnf(i_0_1832,plain,
transitive(k2_lattice3(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300]) ).
cnf(i_0_1834,plain,
antisymmetric(k2_lattice3(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301]) ).
cnf(i_0_1836,plain,
reflexive(k2_lattice3(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302]) ).
cnf(i_0_1838,plain,
relation(relation_of_lattice(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307]) ).
cnf(i_0_1840,plain,
strict_rel_str(poset_of_lattice(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313]) ).
cnf(i_0_1842,plain,
rel_str(poset_of_lattice(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_377,i_0_372,i_0_276,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314]) ).
cnf(i_0_1844,plain,
v2_binop_1(the_L_meet(esk20_0),the_carrier(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_377,i_0_372,i_0_276,i_0_467,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278]) ).
cnf(i_0_1846,plain,
v2_binop_1(the_L_join(esk20_0),the_carrier(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279]) ).
cnf(i_0_1848,plain,
v1_binop_1(the_L_meet(esk20_0),the_carrier(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280]) ).
cnf(i_0_1850,plain,
v1_binop_1(the_L_join(esk20_0),the_carrier(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281]) ).
cnf(i_0_1852,plain,
k2_lattice3(esk20_0) = relation_of_lattice(esk20_0),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318]) ).
cnf(i_0_1854,plain,
relation_of2_as_subset(k2_lattice3(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261]) ).
cnf(i_0_1856,plain,
v1_partfun1(k2_lattice3(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262]) ).
cnf(i_0_1858,plain,
poset_of_lattice(esk20_0) = rel_str_of(the_carrier(esk20_0),k2_lattice3(esk20_0)),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275]) ).
cnf(i_0_1860,plain,
transitive(the_InternalRel(poset_of_lattice(esk19_0))),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1596,i_0_1598,i_0_1600,i_0_1620,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_286]) ).
cnf(i_0_1862,plain,
antisymmetric(the_InternalRel(poset_of_lattice(esk19_0))),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1596,i_0_1598,i_0_1600,i_0_1620,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_286,i_0_287]) ).
cnf(i_0_1864,plain,
reflexive(the_InternalRel(poset_of_lattice(esk19_0))),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1596,i_0_1598,i_0_1600,i_0_1620,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_286,i_0_287,i_0_288]) ).
cnf(i_0_1866,plain,
relation(the_InternalRel(poset_of_lattice(esk19_0))),
inference(scs_inference,[],[i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1556,i_0_1596,i_0_1598,i_0_1600,i_0_1620,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1676,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_467,i_0_346,i_0_356,i_0_327,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_286,i_0_287,i_0_288,i_0_289]) ).
cnf(i_0_1873,plain,
related(esk12_0,esk7_1(the_carrier(esk12_0)),esk7_1(the_carrier(esk12_0))),
inference(scs_inference,[],[i_0_333,i_0_1547,i_0_478,i_0_1799,i_0_1521,i_0_1803,i_0_1805,i_0_1548,i_0_1552,i_0_1584,i_0_1590,i_0_1515,i_0_1543,i_0_1545,i_0_1556,i_0_1596,i_0_1598,i_0_1600,i_0_1620,i_0_1581,i_0_1669,i_0_1574,i_0_1585,i_0_1501,i_0_1791,i_0_1795,i_0_1807,i_0_1817,i_0_1662,i_0_1676,i_0_1666,i_0_469,i_0_541,i_0_473,i_0_264,i_0_265,i_0_1729,i_0_532,i_0_580,i_0_368,i_0_375,i_0_576,i_0_605,i_0_498,i_0_502,i_0_504,i_0_377,i_0_372,i_0_276,i_0_465,i_0_331,i_0_467,i_0_346,i_0_356,i_0_327,i_0_1813,i_0_355,i_0_376,i_0_500,i_0_364,i_0_369,i_0_344,i_0_514,i_0_348,i_0_290,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_293,i_0_282,i_0_380,i_0_315,i_0_271,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_414,i_0_415,i_0_269,i_0_285,i_0_403,i_0_404,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_286,i_0_287,i_0_288,i_0_289,i_0_222,i_0_240,i_0_229]) ).
cnf(i_0_1971,plain,
relation_of2(esk8_2(X1,esk22_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(rename_variables,[],[i_0_1550]) ).
cnf(i_0_1975,plain,
relation_of2_as_subset(esk6_2(X1,esk22_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2002,plain,
in(esk7_1(unordered_pair(X1,X2)),unordered_pair(X2,X1)),
inference(rename_variables,[],[i_0_1592]) ).
cnf(i_0_2039,plain,
~ empty(esk10_1(esk17_1(esk12_0))),
inference(scs_inference,[],[i_0_1563,i_0_326]) ).
cnf(i_0_2041,plain,
function(the_L_meet(esk5_0)),
inference(scs_inference,[],[i_0_1563,i_0_624,i_0_326,i_0_328]) ).
cnf(i_0_2043,plain,
function(the_L_join(esk4_0)),
inference(scs_inference,[],[i_0_1563,i_0_624,i_0_349,i_0_326,i_0_328,i_0_329]) ).
cnf(i_0_2045,plain,
element(esk10_1(esk17_1(esk12_0)),powerset(esk17_1(esk12_0))),
inference(scs_inference,[],[i_0_1563,i_0_624,i_0_349,i_0_326,i_0_328,i_0_329,i_0_292]) ).
cnf(i_0_2150,plain,
~ empty(esk10_1(cartesian_product2(esk14_0,esk14_0))),
inference(scs_inference,[],[i_0_1565,i_0_326]) ).
cnf(i_0_2152,plain,
function(the_L_meet(esk1_0)),
inference(scs_inference,[],[i_0_1565,i_0_352,i_0_326,i_0_328]) ).
cnf(i_0_2154,plain,
function(the_L_join(esk20_0)),
inference(scs_inference,[],[i_0_1565,i_0_352,i_0_465,i_0_326,i_0_328,i_0_329]) ).
cnf(i_0_2156,plain,
element(esk10_1(cartesian_product2(esk14_0,esk14_0)),powerset(cartesian_product2(esk14_0,esk14_0))),
inference(scs_inference,[],[i_0_1565,i_0_352,i_0_465,i_0_326,i_0_328,i_0_329,i_0_292]) ).
cnf(i_0_2166,plain,
element(esk22_0,powerset(cast_to_el_of_LattPOSet(esk20_0,esk22_0))),
inference(scs_inference,[],[i_0_1565,i_0_1558,i_0_352,i_0_465,i_0_326,i_0_328,i_0_329,i_0_292,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283]) ).
cnf(i_0_2211,plain,
relation_of2(esk8_2(X1,esk22_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(rename_variables,[],[i_0_1550]) ).
cnf(i_0_2215,plain,
relation_of2_as_subset(esk6_2(X1,esk22_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2240,plain,
in(esk7_1(unordered_pair(X1,X2)),unordered_pair(X2,X1)),
inference(rename_variables,[],[i_0_1592]) ).
cnf(i_0_2252,plain,
~ empty(esk10_1(the_carrier(esk12_0))),
inference(scs_inference,[],[i_0_1579,i_0_326]) ).
cnf(i_0_2254,plain,
function(the_L_meet(esk19_0)),
inference(scs_inference,[],[i_0_1579,i_0_525,i_0_326,i_0_328]) ).
cnf(i_0_2256,plain,
element(esk10_1(the_carrier(esk12_0)),powerset(the_carrier(esk12_0))),
inference(scs_inference,[],[i_0_1579,i_0_525,i_0_326,i_0_328,i_0_292]) ).
cnf(i_0_2262,plain,
function(the_L_join(esk19_0)),
inference(scs_inference,[],[i_0_1579,i_0_525,i_0_523,i_0_326,i_0_328,i_0_292,i_0_251,i_0_253,i_0_329]) ).
cnf(i_0_2396,plain,
relation_of2(esk8_2(X1,esk22_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(rename_variables,[],[i_0_1550]) ).
cnf(i_0_2398,plain,
relation_of2(esk8_2(esk22_0,X1),cast_to_el_of_LattPOSet(esk20_0,esk22_0),X1),
inference(rename_variables,[],[i_0_1548]) ).
cnf(i_0_2404,plain,
relation_of2_as_subset(esk6_2(X1,esk22_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2406,plain,
relation_of2_as_subset(esk6_2(esk22_0,X1),cast_to_el_of_LattPOSet(esk20_0,esk22_0),X1),
inference(rename_variables,[],[i_0_1552]) ).
cnf(i_0_2582,plain,
relation_of2(esk8_2(esk22_0,X1),cast_to_el_of_LattPOSet(esk20_0,esk22_0),X1),
inference(rename_variables,[],[i_0_1548]) ).
cnf(i_0_2694,plain,
relation_of2(esk8_2(X1,esk22_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(rename_variables,[],[i_0_1550]) ).
cnf(i_0_2784,plain,
relation_of2(esk8_2(esk22_0,X1),cast_to_el_of_LattPOSet(esk20_0,esk22_0),X1),
inference(rename_variables,[],[i_0_1548]) ).
cnf(i_0_2834,plain,
relation_of2(esk8_2(X1,esk22_0),X1,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(rename_variables,[],[i_0_1550]) ).
cnf(i_0_622,plain,
relation(esk13_1(cartesian_product2(X1,X2))),
inference(equality_inference,[],[617]) ).
cnf(i_0_628,plain,
~ in(esk14_0,esk7_1(esk14_0)),
inference(scs_inference,[],[i_0_611,i_0_373,i_0_340,i_0_336,i_0_282]) ).
cnf(i_0_630,plain,
one_sorted_str(esk5_0),
inference(scs_inference,[],[i_0_611,i_0_373,i_0_340,i_0_336,i_0_282,i_0_338]) ).
cnf(i_0_632,plain,
~ in(X1,esk7_1(powerset(esk11_0))),
inference(scs_inference,[],[i_0_611,i_0_373,i_0_327,i_0_356,i_0_340,i_0_336,i_0_282,i_0_338,i_0_269]) ).
cnf(i_0_635,plain,
in(esk7_1(powerset(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_611,i_0_373,i_0_331,i_0_327,i_0_633,i_0_356,i_0_340,i_0_336,i_0_282,i_0_338,i_0_269,i_0_285]) ).
cnf(i_0_638,plain,
~ in(the_carrier(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)),
inference(scs_inference,[],[i_0_506,i_0_611,i_0_578,i_0_373,i_0_331,i_0_327,i_0_633,i_0_356,i_0_340,i_0_336,i_0_282,i_0_338,i_0_269,i_0_285,i_0_439]) ).
cnf(i_0_639,plain,
esk11_0 != powerset(X1),
inference(scs_inference,[],[i_0_506,i_0_611,i_0_578,i_0_373,i_0_331,i_0_327,i_0_633,i_0_356,i_0_340,i_0_336,i_0_282,i_0_338,i_0_269,i_0_285,i_0_439,i_0_455]) ).
cnf(i_0_732,plain,
~ in(the_carrier(esk20_0),esk22_0),
inference(equality_inference,[],[726]) ).
cnf(i_0_733,plain,
latt_str(esk15_0),
inference(equality_inference,[],[727]) ).
cnf(i_0_734,plain,
meet_semilatt_str(esk1_0),
inference(equality_inference,[],[728]) ).
cnf(i_0_735,plain,
~ in(unordered_pair(X1,X2),esk7_1(unordered_pair(X1,X2))),
inference(equality_inference,[],[729]) ).
cnf(i_0_780,plain,
one_sorted_str(esk18_0),
inference(equality_inference,[],[775]) ).
cnf(i_0_1681,plain,
relation(empty_set),
inference(scs_inference,[],[i_0_333,i_0_335,i_0_1557,i_0_493,i_0_508,i_0_510,i_0_514,i_0_471,i_0_1553,i_0_473,i_0_1524,i_0_1527,i_0_1549,i_0_1551,i_0_1568,i_0_538,i_0_345,i_0_553,i_0_484,i_0_534,i_0_365,i_0_363,i_0_358,i_0_359,i_0_360,i_0_361,i_0_362,i_0_504,i_0_626,i_0_467,i_0_525,i_0_523,i_0_317,i_0_366,i_0_374,i_0_378,i_0_465,i_0_353,i_0_354,i_0_355,i_0_376,i_0_370,i_0_343,i_0_331,i_0_341,i_0_327,i_0_1562,i_0_1588,i_0_1667,i_0_1672,i_0_500,i_0_364,i_0_344,i_0_369,i_0_348,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_293,i_0_380,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_315,i_0_271,i_0_239,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_414,i_0_415,i_0_403,i_0_404,i_0_269,i_0_285,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_308,i_0_309,i_0_310,i_0_311,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_241,i_0_242,i_0_243,i_0_244,i_0_286,i_0_287,i_0_288,i_0_289,i_0_272,i_0_273,i_0_260,i_0_220,i_0_259,i_0_222,i_0_240,i_0_211,i_0_235,i_0_216,i_0_221,i_0_225,i_0_617]) ).
cnf(i_0_1682,plain,
~ in(esk10_1(esk14_0),esk7_1(esk10_1(esk14_0))),
inference(scs_inference,[],[i_0_333,i_0_335,i_0_1557,i_0_493,i_0_508,i_0_510,i_0_514,i_0_471,i_0_1553,i_0_473,i_0_1524,i_0_1527,i_0_1549,i_0_1551,i_0_1568,i_0_538,i_0_345,i_0_553,i_0_484,i_0_534,i_0_365,i_0_363,i_0_358,i_0_359,i_0_360,i_0_361,i_0_362,i_0_504,i_0_626,i_0_467,i_0_525,i_0_523,i_0_317,i_0_366,i_0_374,i_0_378,i_0_465,i_0_353,i_0_354,i_0_355,i_0_376,i_0_370,i_0_343,i_0_331,i_0_341,i_0_327,i_0_1562,i_0_1588,i_0_1667,i_0_1672,i_0_500,i_0_364,i_0_344,i_0_369,i_0_348,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_293,i_0_380,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_315,i_0_271,i_0_239,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_414,i_0_415,i_0_403,i_0_404,i_0_269,i_0_285,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_308,i_0_309,i_0_310,i_0_311,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_241,i_0_242,i_0_243,i_0_244,i_0_286,i_0_287,i_0_288,i_0_289,i_0_272,i_0_273,i_0_260,i_0_220,i_0_259,i_0_222,i_0_240,i_0_211,i_0_235,i_0_216,i_0_221,i_0_225,i_0_617,i_0_282]) ).
cnf(i_0_1685,plain,
reflexive(relation_of_lattice(esk19_0)),
inference(scs_inference,[],[i_0_333,i_0_335,i_0_1557,i_0_493,i_0_508,i_0_510,i_0_514,i_0_471,i_0_1553,i_0_473,i_0_1524,i_0_1527,i_0_1549,i_0_1551,i_0_1568,i_0_1575,i_0_538,i_0_345,i_0_553,i_0_484,i_0_534,i_0_365,i_0_363,i_0_358,i_0_359,i_0_360,i_0_361,i_0_362,i_0_504,i_0_626,i_0_467,i_0_525,i_0_523,i_0_317,i_0_366,i_0_374,i_0_378,i_0_465,i_0_353,i_0_354,i_0_355,i_0_376,i_0_370,i_0_343,i_0_331,i_0_341,i_0_327,i_0_1562,i_0_1588,i_0_1667,i_0_1672,i_0_500,i_0_364,i_0_344,i_0_369,i_0_348,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_293,i_0_380,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_315,i_0_271,i_0_239,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_414,i_0_415,i_0_403,i_0_404,i_0_269,i_0_285,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_308,i_0_309,i_0_310,i_0_311,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_241,i_0_242,i_0_243,i_0_244,i_0_286,i_0_287,i_0_288,i_0_289,i_0_272,i_0_273,i_0_260,i_0_220,i_0_259,i_0_222,i_0_240,i_0_211,i_0_235,i_0_216,i_0_221,i_0_225,i_0_617,i_0_282,i_0_405,i_0_425]) ).
cnf(i_0_1686,plain,
antisymmetric(relation_of_lattice(esk19_0)),
inference(scs_inference,[],[i_0_333,i_0_335,i_0_1557,i_0_493,i_0_508,i_0_510,i_0_514,i_0_471,i_0_1553,i_0_473,i_0_1524,i_0_1527,i_0_1549,i_0_1551,i_0_1568,i_0_1575,i_0_538,i_0_345,i_0_553,i_0_484,i_0_534,i_0_365,i_0_363,i_0_358,i_0_359,i_0_360,i_0_361,i_0_362,i_0_504,i_0_626,i_0_467,i_0_525,i_0_523,i_0_317,i_0_366,i_0_374,i_0_378,i_0_465,i_0_353,i_0_354,i_0_355,i_0_376,i_0_370,i_0_343,i_0_331,i_0_341,i_0_327,i_0_1562,i_0_1588,i_0_1667,i_0_1672,i_0_500,i_0_364,i_0_344,i_0_369,i_0_348,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_293,i_0_380,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_315,i_0_271,i_0_239,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_414,i_0_415,i_0_403,i_0_404,i_0_269,i_0_285,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_308,i_0_309,i_0_310,i_0_311,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_241,i_0_242,i_0_243,i_0_244,i_0_286,i_0_287,i_0_288,i_0_289,i_0_272,i_0_273,i_0_260,i_0_220,i_0_259,i_0_222,i_0_240,i_0_211,i_0_235,i_0_216,i_0_221,i_0_225,i_0_617,i_0_282,i_0_405,i_0_425,i_0_426]) ).
cnf(i_0_1687,plain,
transitive(relation_of_lattice(esk19_0)),
inference(scs_inference,[],[i_0_333,i_0_335,i_0_1557,i_0_493,i_0_508,i_0_510,i_0_514,i_0_471,i_0_1553,i_0_473,i_0_1524,i_0_1527,i_0_1549,i_0_1551,i_0_1568,i_0_1575,i_0_538,i_0_345,i_0_553,i_0_484,i_0_534,i_0_365,i_0_363,i_0_358,i_0_359,i_0_360,i_0_361,i_0_362,i_0_504,i_0_626,i_0_467,i_0_525,i_0_523,i_0_317,i_0_366,i_0_374,i_0_378,i_0_465,i_0_353,i_0_354,i_0_355,i_0_376,i_0_370,i_0_343,i_0_331,i_0_341,i_0_327,i_0_1562,i_0_1588,i_0_1667,i_0_1672,i_0_500,i_0_364,i_0_344,i_0_369,i_0_348,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_293,i_0_380,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_315,i_0_271,i_0_239,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_414,i_0_415,i_0_403,i_0_404,i_0_269,i_0_285,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_308,i_0_309,i_0_310,i_0_311,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_241,i_0_242,i_0_243,i_0_244,i_0_286,i_0_287,i_0_288,i_0_289,i_0_272,i_0_273,i_0_260,i_0_220,i_0_259,i_0_222,i_0_240,i_0_211,i_0_235,i_0_216,i_0_221,i_0_225,i_0_617,i_0_282,i_0_405,i_0_425,i_0_426,i_0_427]) ).
cnf(i_0_1688,plain,
v1_partfun1(relation_of_lattice(esk19_0),the_carrier(esk19_0),the_carrier(esk19_0)),
inference(scs_inference,[],[i_0_333,i_0_335,i_0_1557,i_0_493,i_0_508,i_0_510,i_0_514,i_0_471,i_0_1553,i_0_473,i_0_1524,i_0_1527,i_0_1549,i_0_1551,i_0_1568,i_0_1575,i_0_538,i_0_345,i_0_553,i_0_484,i_0_534,i_0_365,i_0_363,i_0_358,i_0_359,i_0_360,i_0_361,i_0_362,i_0_504,i_0_626,i_0_467,i_0_525,i_0_523,i_0_317,i_0_366,i_0_374,i_0_378,i_0_465,i_0_353,i_0_354,i_0_355,i_0_376,i_0_370,i_0_343,i_0_331,i_0_341,i_0_327,i_0_1562,i_0_1588,i_0_1667,i_0_1672,i_0_500,i_0_364,i_0_344,i_0_369,i_0_348,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_293,i_0_380,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_315,i_0_271,i_0_239,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_414,i_0_415,i_0_403,i_0_404,i_0_269,i_0_285,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_308,i_0_309,i_0_310,i_0_311,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_241,i_0_242,i_0_243,i_0_244,i_0_286,i_0_287,i_0_288,i_0_289,i_0_272,i_0_273,i_0_260,i_0_220,i_0_259,i_0_222,i_0_240,i_0_211,i_0_235,i_0_216,i_0_221,i_0_225,i_0_617,i_0_282,i_0_405,i_0_425,i_0_426,i_0_427,i_0_428]) ).
cnf(i_0_1689,plain,
relation_of2_as_subset(relation_of_lattice(esk19_0),the_carrier(esk19_0),the_carrier(esk19_0)),
inference(scs_inference,[],[i_0_333,i_0_335,i_0_1557,i_0_493,i_0_508,i_0_510,i_0_514,i_0_471,i_0_1553,i_0_473,i_0_1524,i_0_1527,i_0_1549,i_0_1551,i_0_1568,i_0_1575,i_0_538,i_0_345,i_0_553,i_0_484,i_0_534,i_0_365,i_0_363,i_0_358,i_0_359,i_0_360,i_0_361,i_0_362,i_0_504,i_0_626,i_0_467,i_0_525,i_0_523,i_0_317,i_0_366,i_0_374,i_0_378,i_0_465,i_0_353,i_0_354,i_0_355,i_0_376,i_0_370,i_0_343,i_0_331,i_0_341,i_0_327,i_0_1562,i_0_1588,i_0_1667,i_0_1672,i_0_500,i_0_364,i_0_344,i_0_369,i_0_348,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401,i_0_326,i_0_328,i_0_329,i_0_283,i_0_257,i_0_258,i_0_292,i_0_234,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_342,i_0_293,i_0_380,i_0_406,i_0_407,i_0_434,i_0_435,i_0_445,i_0_446,i_0_451,i_0_452,i_0_315,i_0_271,i_0_239,i_0_274,i_0_284,i_0_249,i_0_263,i_0_316,i_0_414,i_0_415,i_0_403,i_0_404,i_0_269,i_0_285,i_0_438,i_0_455,i_0_439,i_0_291,i_0_295,i_0_297,i_0_299,i_0_300,i_0_301,i_0_302,i_0_307,i_0_308,i_0_309,i_0_310,i_0_311,i_0_313,i_0_314,i_0_278,i_0_279,i_0_280,i_0_281,i_0_318,i_0_261,i_0_262,i_0_275,i_0_241,i_0_242,i_0_243,i_0_244,i_0_286,i_0_287,i_0_288,i_0_289,i_0_272,i_0_273,i_0_260,i_0_220,i_0_259,i_0_222,i_0_240,i_0_211,i_0_235,i_0_216,i_0_221,i_0_225,i_0_617,i_0_282,i_0_405,i_0_425,i_0_426,i_0_427,i_0_428,i_0_433]) ).
cnf(i_0_1903,plain,
related(esk12_0,esk7_1(the_carrier(esk12_0)),esk7_1(the_carrier(esk12_0))),
inference(equality_inference,[],[1880]) ).
cnf(i_0_1905,plain,
v1_partfun1(relation_of_lattice(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(equality_inference,[],[1887]) ).
cnf(i_0_1906,plain,
relation_of2_as_subset(relation_of_lattice(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(equality_inference,[],[1888]) ).
cnf(i_0_1907,plain,
~ in(the_carrier(esk20_0),powerset(esk11_0)),
inference(equality_inference,[],[1889]) ).
cnf(i_0_1908,plain,
strict_latt_str(k8_filter_1(esk18_0,esk18_0)),
inference(equality_inference,[],[1892]) ).
cnf(i_0_1909,plain,
latt_str(k8_filter_1(esk18_0,esk18_0)),
inference(equality_inference,[],[1894]) ).
cnf(i_0_1911,plain,
below(esk20_0,esk7_1(the_carrier(esk20_0)),esk7_1(the_carrier(esk20_0))),
inference(equality_inference,[],[1899]) ).
cnf(i_0_1913,plain,
~ empty(esk10_1(k10_filter_1(esk20_0,esk20_0,esk22_0,esk22_0))),
inference(scs_inference,[],[i_0_1820,i_0_326]) ).
cnf(i_0_1915,plain,
function(the_L_meet(esk15_0)),
inference(scs_inference,[],[i_0_1820,i_0_603,i_0_326,i_0_328]) ).
cnf(i_0_1917,plain,
function(the_L_join(esk18_0)),
inference(scs_inference,[],[i_0_1820,i_0_603,i_0_574,i_0_326,i_0_328,i_0_329]) ).
cnf(i_0_1921,plain,
relation_of2_as_subset(the_InternalRel(esk12_0),the_carrier(esk12_0),the_carrier(esk12_0)),
inference(scs_inference,[],[i_0_1820,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266]) ).
cnf(i_0_1931,plain,
element(empty_set,powerset(X1)),
inference(scs_inference,[],[i_0_1798,i_0_1820,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283]) ).
cnf(i_0_1933,plain,
esk7_1(powerset(empty_set)) = empty_set,
inference(scs_inference,[],[i_0_1798,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342]) ).
cnf(i_0_1939,plain,
poset_of_lattice(esk11_0) = poset_of_lattice(empty_set),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386]) ).
cnf(i_0_1940,plain,
cast_to_el_of_LattPOSet(esk11_0,X1) = cast_to_el_of_LattPOSet(empty_set,X1),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387]) ).
cnf(i_0_1941,plain,
cast_to_el_of_LattPOSet(X1,esk11_0) = cast_to_el_of_LattPOSet(X1,empty_set),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388]) ).
cnf(i_0_1942,plain,
rel_str_of(esk11_0,X1) = rel_str_of(empty_set,X1),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389]) ).
cnf(i_0_1943,plain,
rel_str_of(X1,esk11_0) = rel_str_of(X1,empty_set),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390]) ).
cnf(i_0_1944,plain,
k2_lattice3(esk11_0) = k2_lattice3(empty_set),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391]) ).
cnf(i_0_1945,plain,
relation_of_lattice(esk11_0) = relation_of_lattice(empty_set),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392]) ).
cnf(i_0_1946,plain,
latt_str_of(esk11_0,X1,X2) = latt_str_of(empty_set,X1,X2),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393]) ).
cnf(i_0_1947,plain,
latt_str_of(X1,esk11_0,X2) = latt_str_of(X1,empty_set,X2),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394]) ).
cnf(i_0_1948,plain,
latt_str_of(X1,X2,esk11_0) = latt_str_of(X1,X2,empty_set),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395]) ).
cnf(i_0_1949,plain,
k10_filter_1(esk11_0,X1,X2,X3) = k10_filter_1(empty_set,X1,X2,X3),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396]) ).
cnf(i_0_1950,plain,
k10_filter_1(X1,esk11_0,X2,X3) = k10_filter_1(X1,empty_set,X2,X3),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397]) ).
cnf(i_0_1951,plain,
k10_filter_1(X1,X2,esk11_0,X3) = k10_filter_1(X1,X2,empty_set,X3),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398]) ).
cnf(i_0_1952,plain,
k10_filter_1(X1,X2,X3,esk11_0) = k10_filter_1(X1,X2,X3,empty_set),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399]) ).
cnf(i_0_1953,plain,
unordered_pair(esk11_0,X1) = unordered_pair(empty_set,X1),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400]) ).
cnf(i_0_1954,plain,
unordered_pair(X1,esk11_0) = unordered_pair(X1,empty_set),
inference(scs_inference,[],[i_0_1798,i_0_1748,i_0_1820,i_0_1811,i_0_603,i_0_574,i_0_376,i_0_326,i_0_328,i_0_329,i_0_292,i_0_266,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283,i_0_342,i_0_382,i_0_383,i_0_384,i_0_385,i_0_386,i_0_387,i_0_388,i_0_389,i_0_390,i_0_391,i_0_392,i_0_393,i_0_394,i_0_395,i_0_396,i_0_397,i_0_398,i_0_399,i_0_400,i_0_401]) ).
cnf(i_0_2055,plain,
element(esk13_1(esk13_1(X1)),powerset(empty_set)),
inference(scs_inference,[],[i_0_1563,i_0_1800,i_0_624,i_0_349,i_0_326,i_0_328,i_0_329,i_0_292,i_0_251,i_0_252,i_0_253,i_0_254,i_0_283]) ).
cnf(i_0_2343,plain,
~ empty(esk10_1(relation_of_lattice(esk20_0))),
inference(scs_inference,[],[i_0_1770,i_0_326]) ).
cnf(i_0_2345,plain,
element(esk10_1(relation_of_lattice(esk20_0)),powerset(relation_of_lattice(esk20_0))),
inference(scs_inference,[],[i_0_1770,i_0_326,i_0_292]) ).
cnf(i_0_2422,plain,
~ in(unordered_pair(X1,X2),powerset(esk13_1(X3))),
inference(rename_variables,[],[i_0_1718]) ).
cnf(i_0_2432,plain,
~ empty(esk10_1(esk17_1(esk18_0))),
inference(scs_inference,[],[i_0_1775,i_0_326]) ).
cnf(i_0_2434,plain,
element(esk10_1(esk17_1(esk18_0)),powerset(esk17_1(esk18_0))),
inference(scs_inference,[],[i_0_1775,i_0_326,i_0_292]) ).
cnf(i_0_2507,plain,
~ empty(esk10_1(the_carrier(esk18_0))),
inference(scs_inference,[],[i_0_1788,i_0_326]) ).
cnf(i_0_2509,plain,
element(esk10_1(the_carrier(esk18_0)),powerset(the_carrier(esk18_0))),
inference(scs_inference,[],[i_0_1788,i_0_326,i_0_292]) ).
cnf(i_0_2625,plain,
strict_rel_str(rel_str_of(X1,esk6_2(X1,X1))),
inference(rename_variables,[],[i_0_1728]) ).
cnf(c_0_1938,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
i_0_238 ).
cnf(c_0_1939,plain,
relation_of2_as_subset(relation_of_lattice(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)),
i_0_1906 ).
cnf(c_0_1940,plain,
poset_of_lattice(esk20_0) = rel_str_of(the_carrier(esk20_0),k2_lattice3(esk20_0)),
i_0_1858 ).
cnf(c_0_1941,plain,
k2_lattice3(esk20_0) = relation_of_lattice(esk20_0),
i_0_1852 ).
cnf(c_0_1942,plain,
( X1 = X2
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| ~ relation_of2(X3,X1,X1) ),
i_0_249 ).
cnf(c_0_1943,plain,
relation_of2(relation_of_lattice(esk20_0),the_carrier(esk20_0),the_carrier(esk20_0)),
inference(spm,[status(thm)],[c_0_1938,c_0_1939]) ).
cnf(c_0_1944,plain,
rel_str_of(the_carrier(esk20_0),relation_of_lattice(esk20_0)) = poset_of_lattice(esk20_0),
inference(rw,[status(thm)],[c_0_1940,c_0_1941]) ).
cnf(c_0_1945,plain,
( the_carrier(esk20_0) = X1
| rel_str_of(X1,X2) != poset_of_lattice(esk20_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1942,c_0_1943]),c_0_1944]) ).
cnf(c_0_1946,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ strict_rel_str(X1) ),
i_0_284 ).
cnf(c_0_1947,plain,
( the_carrier(esk20_0) = the_carrier(X1)
| X1 != poset_of_lattice(esk20_0)
| ~ strict_rel_str(X1)
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_1945,c_0_1946]) ).
cnf(c_0_1948,plain,
strict_rel_str(poset_of_lattice(esk20_0)),
i_0_1840 ).
cnf(c_0_1949,plain,
rel_str(poset_of_lattice(esk20_0)),
i_0_1842 ).
cnf(c_0_1950,plain,
in(cast_to_el_of_LattPOSet(esk20_0,cast_to_el_of_LattPOSet(esk20_0,esk22_0)),the_carrier(esk20_0)),
i_0_1818 ).
cnf(c_0_1951,plain,
( empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
i_0_268 ).
cnf(c_0_1952,negated_conjecture,
latt_str(esk20_0),
i_0_369 ).
cnf(c_0_1953,negated_conjecture,
lattice(esk20_0),
i_0_364 ).
cnf(c_0_1954,negated_conjecture,
element(esk22_0,the_carrier(esk20_0)),
i_0_333 ).
cnf(c_0_1955,negated_conjecture,
~ empty_carrier(esk20_0),
i_0_344 ).
cnf(c_0_1956,negated_conjecture,
( ~ below_refl(esk20_0,esk21_0,esk22_0)
| ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ),
i_0_227 ).
cnf(c_0_1957,plain,
( X1 = X2
| rel_str_of(X3,X1) != rel_str_of(X4,X2)
| ~ relation_of2(X1,X3,X3) ),
i_0_250 ).
cnf(c_0_1958,plain,
the_carrier(poset_of_lattice(esk20_0)) = the_carrier(esk20_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1947,c_0_1948]),c_0_1949])]) ).
cnf(c_0_1959,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
i_0_316 ).
cnf(c_0_1960,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
i_0_338 ).
cnf(c_0_1961,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)) ),
i_0_229 ).
cnf(c_0_1962,negated_conjecture,
( below_refl(esk20_0,esk21_0,esk22_0)
| related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0)) ),
i_0_236 ).
cnf(c_0_1963,plain,
reflexive_relstr(poset_of_lattice(esk20_0)),
i_0_1830 ).
cnf(c_0_1964,plain,
~ empty_carrier(poset_of_lattice(esk20_0)),
i_0_1824 ).
cnf(c_0_1965,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
i_0_290 ).
cnf(c_0_1966,plain,
in(cast_to_el_of_LattPOSet(esk20_0,esk22_0),the_carrier(esk20_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_1950,c_0_1951]),c_0_1952]),c_0_1953]),c_0_1954])]),c_0_1955]) ).
cnf(c_0_1967,negated_conjecture,
( ~ related_reflexive(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),esk22_0)
| ~ below_refl(esk20_0,esk21_0,esk22_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_1956,c_0_1951]),c_0_1952]),c_0_1953]),c_0_1954])]),c_0_1955]) ).
cnf(c_0_1968,negated_conjecture,
element(esk21_0,the_carrier(esk20_0)),
i_0_334 ).
cnf(c_0_1969,plain,
( relation_of_lattice(esk20_0) = X1
| rel_str_of(X2,X1) != poset_of_lattice(esk20_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1957,c_0_1943]),c_0_1944]) ).
cnf(c_0_1970,plain,
rel_str_of(the_carrier(esk20_0),the_InternalRel(poset_of_lattice(esk20_0))) = poset_of_lattice(esk20_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1946,c_0_1958]),c_0_1948]),c_0_1949])]) ).
cnf(c_0_1971,plain,
( empty_carrier(X1)
| ~ meet_semilatt_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_1959,c_0_1960]) ).
cnf(c_0_1972,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
i_0_340 ).
cnf(c_0_1973,negated_conjecture,
( related(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))
| below_refl(esk20_0,esk21_0,esk22_0)
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk22_0),the_carrier(poset_of_lattice(esk20_0)))
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(poset_of_lattice(esk20_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1961,c_0_1962]),c_0_1963]),c_0_1949])]),c_0_1964]) ).
cnf(c_0_1974,plain,
element(cast_to_el_of_LattPOSet(esk20_0,esk22_0),the_carrier(esk20_0)),
inference(spm,[status(thm)],[c_0_1965,c_0_1966]) ).
cnf(c_0_1975,plain,
( ~ related_reflexive(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| ~ below_refl(esk20_0,esk21_0,esk22_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_1967,c_0_1951]),c_0_1952]),c_0_1953]),c_0_1968])]),c_0_1955]) ).
cnf(c_0_1976,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)) ),
i_0_228 ).
cnf(c_0_1977,plain,
( related(X1,X2,X3)
| ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1)) ),
i_0_223 ).
cnf(c_0_1978,plain,
the_InternalRel(poset_of_lattice(esk20_0)) = relation_of_lattice(esk20_0),
inference(spm,[status(thm)],[c_0_1969,c_0_1970]) ).
cnf(c_0_1979,plain,
( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| empty_carrier(X1)
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
i_0_211 ).
cnf(c_0_1980,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3))
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
i_0_222 ).
cnf(c_0_1981,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_1971,c_0_1972]) ).
cnf(c_0_1982,negated_conjecture,
( related(poset_of_lattice(esk20_0),cast_to_el_of_LattPOSet(esk20_0,esk21_0),cast_to_el_of_LattPOSet(esk20_0,esk22_0))
| below_refl(esk20_0,esk21_0,esk22_0)
| ~ element(cast_to_el_of_LattPOSet(esk20_0,esk21_0),the_carrier(esk20_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1973,c_0_1958]),c_0_1974]),c_0_1958])]) ).
cnf(c_0_1983,plain,
( ~ related(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| ~ element(esk22_0,the_carrier(poset_of_lattice(esk20_0)))
| ~ element(esk21_0,the_carrier(poset_of_lattice(esk20_0)))
| ~ below_refl(esk20_0,esk21_0,esk22_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1975,c_0_1976]),c_0_1963]),c_0_1949])]),c_0_1964]) ).
cnf(c_0_1984,plain,
( related(poset_of_lattice(esk20_0),X1,X2)
| ~ element(X2,the_carrier(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_of_lattice(esk20_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1977,c_0_1978]),c_0_1949]),c_0_1958]),c_0_1958])]) ).
cnf(c_0_1985,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_of_lattice(X3))
| empty_carrier(X3)
| ~ latt_str(X3)
| ~ lattice(X3)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ below_refl(X3,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_1979,c_0_1980]),c_0_1981]) ).
cnf(c_0_1986,plain,
( below_refl(X1,X2,X3)
| empty_carrier(X1)
| ~ in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
i_0_210 ).
cnf(c_0_1987,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3))
| ~ rel_str(X3)
| ~ related(X3,X1,X2)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3)) ),
i_0_224 ).
cnf(c_0_1988,plain,
( related(poset_of_lattice(esk20_0),esk21_0,cast_to_el_of_LattPOSet(esk20_0,esk22_0))
| below_refl(esk20_0,esk21_0,esk22_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_1982,c_0_1951]),c_0_1968]),c_0_1952]),c_0_1953])]),c_0_1955]) ).
cnf(c_0_1989,plain,
( ~ related(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| ~ below_refl(esk20_0,esk21_0,esk22_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1983,c_0_1958]),c_0_1954]),c_0_1958]),c_0_1968])]) ).
cnf(c_0_1990,plain,
( related(poset_of_lattice(esk20_0),X1,X2)
| ~ element(X2,the_carrier(esk20_0))
| ~ element(X1,the_carrier(esk20_0))
| ~ below_refl(esk20_0,X1,X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1984,c_0_1985]),c_0_1952]),c_0_1953])]),c_0_1955]) ).
cnf(c_0_1991,plain,
( empty_carrier(X1)
| below_refl(X1,X2,X3)
| ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),relation_of_lattice(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_1986,c_0_1980]),c_0_1981]) ).
cnf(c_0_1992,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_of_lattice(esk20_0))
| ~ related(poset_of_lattice(esk20_0),X1,X2)
| ~ element(X2,the_carrier(esk20_0))
| ~ element(X1,the_carrier(esk20_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1987,c_0_1978]),c_0_1949]),c_0_1958]),c_0_1958])]) ).
cnf(c_0_1993,plain,
( related(poset_of_lattice(esk20_0),esk21_0,esk22_0)
| below_refl(esk20_0,esk21_0,esk22_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_1988,c_0_1951]),c_0_1952]),c_0_1953]),c_0_1954])]),c_0_1955]) ).
cnf(c_0_1994,plain,
~ below_refl(esk20_0,esk21_0,esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1989,c_0_1990]),c_0_1954]),c_0_1968])]) ).
cnf(c_0_1995,plain,
( below_refl(esk20_0,X1,X2)
| ~ related(poset_of_lattice(esk20_0),X1,X2)
| ~ element(X2,the_carrier(esk20_0))
| ~ element(X1,the_carrier(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1991,c_0_1992]),c_0_1952]),c_0_1953])]),c_0_1955]) ).
cnf(c_0_1996,plain,
related(poset_of_lattice(esk20_0),esk21_0,esk22_0),
inference(sr,[status(thm)],[c_0_1993,c_0_1994]) ).
cnf(c_0_1997,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1995,c_0_1996]),c_0_1954]),c_0_1968])]),c_0_1994]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU346+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 03:10:02 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 176.94/126.60 % Version : CSE_E---1.7
% 176.94/126.60 % Problem : theBenchmark.p
% 176.94/126.60 % SZS status Theorem for theBenchmark.p
% 176.94/126.60 % SZS output start CNFRefutation
% See solution above
% 186.84/136.59 % Total time : 126.094s
%------------------------------------------------------------------------------