TSTP Solution File: SEU369+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU369+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 : 600s
% DateTime : Tue Jul 19 13:31:19 EDT 2022
% Result : Theorem 4.58s 4.85s
% Output : Refutation 4.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU369+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 20:04:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.86/1.13 ============================== Prover9 ===============================
% 0.86/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.86/1.13 Process 12439 was started by sandbox on n026.cluster.edu,
% 0.86/1.13 Sun Jun 19 20:04:11 2022
% 0.86/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12285_n026.cluster.edu".
% 0.86/1.13 ============================== end of head ===========================
% 0.86/1.13
% 0.86/1.13 ============================== INPUT =================================
% 0.86/1.13
% 0.86/1.13 % Reading from file /tmp/Prover9_12285_n026.cluster.edu
% 0.86/1.13
% 0.86/1.13 set(prolog_style_variables).
% 0.86/1.13 set(auto2).
% 0.86/1.13 % set(auto2) -> set(auto).
% 0.86/1.13 % set(auto) -> set(auto_inference).
% 0.86/1.13 % set(auto) -> set(auto_setup).
% 0.86/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.86/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.86/1.13 % set(auto) -> set(auto_limits).
% 0.86/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.86/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.86/1.13 % set(auto) -> set(auto_denials).
% 0.86/1.13 % set(auto) -> set(auto_process).
% 0.86/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.86/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.86/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.86/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.86/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.86/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.86/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.86/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.86/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.86/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.86/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.86/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.86/1.13 % set(auto2) -> assign(stats, some).
% 0.86/1.13 % set(auto2) -> clear(echo_input).
% 0.86/1.13 % set(auto2) -> set(quiet).
% 0.86/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.86/1.13 % set(auto2) -> clear(print_given).
% 0.86/1.13 assign(lrs_ticks,-1).
% 0.86/1.13 assign(sos_limit,10000).
% 0.86/1.13 assign(order,kbo).
% 0.86/1.13 set(lex_order_vars).
% 0.86/1.13 clear(print_given).
% 0.86/1.13
% 0.86/1.13 % formulas(sos). % not echoed (121 formulas)
% 0.86/1.13
% 0.86/1.13 ============================== end of input ==========================
% 0.86/1.13
% 0.86/1.13 % From the command line: assign(max_seconds, 300).
% 0.86/1.13
% 0.86/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.86/1.13
% 0.86/1.13 % Formulas that are not ordinary clauses:
% 0.86/1.13 1 (all A (rel_str(A) -> (strict_rel_str(A) -> A = rel_str_of(the_carrier(A),the_InternalRel(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 2 (all A (latt_str(A) -> (strict_latt_str(A) -> A = latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A))))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 3 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 4 (all A (latt_str(A) -> (-empty_carrier(A) & lattice(A) & complete_latt_str(A) -> -empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & lattice(A) & lower_bounded_semilattstr(A) & upper_bounded_semilattstr(A) & bounded_lattstr(A)))) # label(cc1_knaster) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 5 (all A (rel_str(A) -> (with_suprema_relstr(A) -> -empty_carrier(A)))) # label(cc1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 6 (all A (latt_str(A) -> (-empty_carrier(A) & lattice(A) -> -empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 7 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 8 (all A (rel_str(A) -> (-empty_carrier(A) & complete_relstr(A) -> -empty_carrier(A) & with_suprema_relstr(A) & with_infima_relstr(A)))) # label(cc1_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 9 (all A (rel_str(A) -> (with_infima_relstr(A) -> -empty_carrier(A)))) # label(cc2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 10 (all A (latt_str(A) -> (-empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) -> -empty_carrier(A) & lattice(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 11 (all A (rel_str(A) -> (-empty_carrier(A) & reflexive_relstr(A) & trivial_carrier(A) -> -empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & complete_relstr(A)))) # label(cc2_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 12 (all A (latt_str(A) -> (-empty_carrier(A) & lower_bounded_semilattstr(A) & upper_bounded_semilattstr(A) -> -empty_carrier(A) & bounded_lattstr(A)))) # label(cc3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 13 (all A (rel_str(A) -> (-empty_carrier(A) & complete_relstr(A) -> -empty_carrier(A) & bounded_relstr(A)))) # label(cc3_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 14 (all A (latt_str(A) -> (-empty_carrier(A) & bounded_lattstr(A) -> -empty_carrier(A) & lower_bounded_semilattstr(A) & upper_bounded_semilattstr(A)))) # label(cc4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 15 (all A (rel_str(A) -> (bounded_relstr(A) -> lower_bounded_relstr(A) & upper_bounded_relstr(A)))) # label(cc4_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 16 (all A (latt_str(A) -> (-empty_carrier(A) & boolean_lattstr(A) -> -empty_carrier(A) & distributive_lattstr(A) & lower_bounded_semilattstr(A) & upper_bounded_semilattstr(A) & bounded_lattstr(A) & complemented_lattstr(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 17 (all A (rel_str(A) -> (lower_bounded_relstr(A) & upper_bounded_relstr(A) -> bounded_relstr(A)))) # label(cc5_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 18 (all A (latt_str(A) -> (-empty_carrier(A) & distributive_lattstr(A) & bounded_lattstr(A) & complemented_lattstr(A) -> -empty_carrier(A) & boolean_lattstr(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 19 (all A (latt_str(A) -> (-empty_carrier(A) & lattice(A) & distributive_lattstr(A) -> -empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & lattice(A) & modular_lattstr(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 20 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 21 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)))) # label(d2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 22 (all A boole_POSet(A) = poset_of_lattice(boole_lattice(A))) # label(d2_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 23 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> cast_to_el_of_LattPOSet(A,B) = B)))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 24 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 25 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) <-> in(ordered_pair(B,C),the_InternalRel(A))))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 26 (all A all B (relation_of2(B,A,A) -> strict_rel_str(rel_str_of(A,B)) & rel_str(rel_str_of(A,B)))) # label(dt_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 27 (all A all B all C (function(B) & quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) -> strict_latt_str(latt_str_of(A,B,C)) & latt_str(latt_str_of(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 28 (all A (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 29 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 30 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 31 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 32 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A)))) # label(dt_k2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 33 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 34 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 35 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)))) # label(dt_k3_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 36 (all A (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))) # label(dt_k3_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 37 (all A all B (-empty_carrier(A) & lattice(A) & latt_str(A) & element(B,the_carrier(A)) -> element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A))))) # label(dt_k4_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 38 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 39 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> relation(relation_of_lattice(A)))) # label(dt_k9_filter_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 40 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 41 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 42 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 43 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 44 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 45 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 46 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 47 (all A all B all C (relation_of2_as_subset(C,A,B) -> element(C,powerset(cartesian_product2(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 48 (all A (meet_semilatt_str(A) -> function(the_L_meet(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 49 (all A (rel_str(A) -> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 50 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 51 (all A (join_semilatt_str(A) -> function(the_L_join(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 52 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 53 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 54 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 55 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 56 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 57 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 58 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 59 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 60 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)))) # label(fc1_knaster) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 61 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 62 (all A all B (-empty(A) & relation_of2(B,A,A) -> -empty_carrier(rel_str_of(A,B)) & strict_rel_str(rel_str_of(A,B)))) # label(fc1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 63 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 64 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 65 (all A all B (relation_of2(B,singleton(A),singleton(A)) -> -empty_carrier(rel_str_of(singleton(A),B)) & strict_rel_str(rel_str_of(singleton(A),B)) & trivial_carrier(rel_str_of(singleton(A),B)))) # label(fc1_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 66 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> -empty_carrier(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & with_suprema_relstr(poset_of_lattice(A)) & with_infima_relstr(poset_of_lattice(A)))) # label(fc1_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 67 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)))) # label(fc2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 68 (all A (reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & rel_str(A) -> relation(the_InternalRel(A)) & reflexive(the_InternalRel(A)) & antisymmetric(the_InternalRel(A)) & transitive(the_InternalRel(A)) & v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(fc2_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 69 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 70 (all A (-empty_carrier(A) & lattice(A) & upper_bounded_semilattstr(A) & latt_str(A) -> -empty_carrier(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & upper_bounded_relstr(poset_of_lattice(A)) & with_suprema_relstr(poset_of_lattice(A)) & with_infima_relstr(poset_of_lattice(A)))) # label(fc2_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 71 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)))) # label(fc3_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 72 (all A all B all C (-empty(A) & function(B) & quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) -> -empty_carrier(latt_str_of(A,B,C)) & strict_latt_str(latt_str_of(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 73 (all A all B (reflexive(B) & antisymmetric(B) & transitive(B) & v1_partfun1(B,A,A) & relation_of2(B,A,A) -> strict_rel_str(rel_str_of(A,B)) & reflexive_relstr(rel_str_of(A,B)) & transitive_relstr(rel_str_of(A,B)) & antisymmetric_relstr(rel_str_of(A,B)))) # label(fc3_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 74 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 75 (all A (-empty_carrier(A) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) -> -empty_carrier(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & lower_bounded_relstr(poset_of_lattice(A)) & with_suprema_relstr(poset_of_lattice(A)) & with_infima_relstr(poset_of_lattice(A)))) # label(fc3_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 76 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> -empty_carrier(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))) # label(fc4_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 77 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 78 (all A (-empty_carrier(A) & lattice(A) & complete_latt_str(A) & latt_str(A) -> -empty_carrier(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & lower_bounded_relstr(poset_of_lattice(A)) & upper_bounded_relstr(poset_of_lattice(A)) & bounded_relstr(poset_of_lattice(A)) & with_suprema_relstr(poset_of_lattice(A)) & with_infima_relstr(poset_of_lattice(A)) & complete_relstr(poset_of_lattice(A)))) # label(fc4_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 79 (all A (-empty_carrier(boole_POSet(A)) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)))) # label(fc7_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 80 (all A (-empty_carrier(boole_POSet(A)) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) # label(fc8_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 81 (all A all B (relation_of2(B,A,A) -> (all C all D (rel_str_of(A,B) = rel_str_of(C,D) -> A = C & B = D)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.13 82 (all A all B all C (function(B) & quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) -> (all D all E all F (latt_str_of(A,B,C) = latt_str_of(D,E,F) -> A = D & B = E & C = F)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 83 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & lattice(A) & distributive_lattstr(A) & modular_lattstr(A) & lower_bounded_semilattstr(A) & upper_bounded_semilattstr(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 84 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & lattice(A) & lower_bounded_semilattstr(A) & upper_bounded_semilattstr(A) & bounded_lattstr(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 85 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & lattice(A) & lower_bounded_semilattstr(A) & upper_bounded_semilattstr(A) & bounded_lattstr(A) & complemented_lattstr(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 86 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & lattice(A) & distributive_lattstr(A) & lower_bounded_semilattstr(A) & upper_bounded_semilattstr(A) & bounded_lattstr(A) & complemented_lattstr(A) & boolean_lattstr(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 87 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & complete_relstr(A))) # label(rc1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 88 (exists A (rel_str(A) & strict_rel_str(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 89 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 90 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 91 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & complete_relstr(A) & trivial_carrier(A))) # label(rc1_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 92 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & complete_relstr(A))) # label(rc2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 93 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A))) # label(rc2_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 94 (all A all B exists C (relation_of2(C,A,B) & relation(C) & function(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 95 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 96 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 97 (exists A (rel_str(A) & -empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & complete_relstr(A) & lower_bounded_relstr(A) & upper_bounded_relstr(A) & bounded_relstr(A))) # label(rc2_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 98 (exists A (latt_str(A) & strict_latt_str(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 99 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 100 (all A (-empty_carrier(A) & one_sorted_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & -empty(B))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 101 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 102 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & lattice(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 103 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> k2_lattice3(A) = relation_of_lattice(A))) # label(redefinition_k2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 104 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 105 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> (below_refl(A,B,C) <-> below(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 106 (all A all B all C (-empty_carrier(A) & reflexive_relstr(A) & rel_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> (related_reflexive(A,B,C) <-> related(A,B,C)))) # label(redefinition_r3_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 107 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 108 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> below_refl(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 109 (all A all B all C (-empty_carrier(A) & reflexive_relstr(A) & rel_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> related_reflexive(A,B,B))) # label(reflexivity_r3_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 110 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 111 (all A all B (element(B,the_carrier(boole_lattice(A))) -> (all C (element(C,the_carrier(boole_lattice(A))) -> (below(boole_lattice(A),B,C) <-> subset(B,C)))))) # label(t2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 112 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 113 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 114 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 115 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 116 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 117 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 118 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below_refl(A,B,C) <-> related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C))))))))) # label(t7_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 119 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.86/1.14 120 -(all A all B (element(B,the_carrier(boole_POSet(A))) -> (all C (element(C,the_carrier(boole_POSet(A))) -> (related_reflexive(boole_POSet(A),B,C) <-> subset(B,C)))))) # label(t2_yellow_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.86/1.14
% 0.86/1.14 ============================== end of process non-clausal formulas ===
% 0.86/1.14
% 0.86/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.86/1.14
% 0.86/1.14 ============================== PREDICATE ELIMINATION =================
% 0.86/1.14 121 -relation_of2(A,B,B) | rel_str(rel_str_of(B,A)) # label(dt_g1_orders_2) # label(axiom). [clausify(26)].
% 0.86/1.14 122 -rel_str(A) | -strict_rel_str(A) | rel_str_of(the_carrier(A),the_InternalRel(A)) = A # label(abstractness_v1_orders_2) # label(axiom). [clausify(1)].
% 0.86/1.14 123 -rel_str(A) | -with_suprema_relstr(A) | -empty_carrier(A) # label(cc1_lattice3) # label(axiom). [clausify(5)].
% 0.86/1.14 124 -rel_str(A) | empty_carrier(A) | -complete_relstr(A) | with_suprema_relstr(A) # label(cc1_yellow_0) # label(axiom). [clausify(8)].
% 0.86/1.14 125 -rel_str(A) | empty_carrier(A) | -complete_relstr(A) | with_infima_relstr(A) # label(cc1_yellow_0) # label(axiom). [clausify(8)].
% 0.86/1.14 126 -rel_str(A) | -with_infima_relstr(A) | -empty_carrier(A) # label(cc2_lattice3) # label(axiom). [clausify(9)].
% 0.86/1.14 127 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -trivial_carrier(A) | transitive_relstr(A) # label(cc2_yellow_0) # label(axiom). [clausify(11)].
% 0.86/1.14 128 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -trivial_carrier(A) | antisymmetric_relstr(A) # label(cc2_yellow_0) # label(axiom). [clausify(11)].
% 0.86/1.14 129 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -trivial_carrier(A) | complete_relstr(A) # label(cc2_yellow_0) # label(axiom). [clausify(11)].
% 0.86/1.14 130 -rel_str(A) | empty_carrier(A) | -complete_relstr(A) | bounded_relstr(A) # label(cc3_yellow_0) # label(axiom). [clausify(13)].
% 0.86/1.14 131 -rel_str(A) | -bounded_relstr(A) | lower_bounded_relstr(A) # label(cc4_yellow_0) # label(axiom). [clausify(15)].
% 0.86/1.14 132 -rel_str(A) | -bounded_relstr(A) | upper_bounded_relstr(A) # label(cc4_yellow_0) # label(axiom). [clausify(15)].
% 0.86/1.14 133 -rel_str(A) | -lower_bounded_relstr(A) | -upper_bounded_relstr(A) | bounded_relstr(A) # label(cc5_yellow_0) # label(axiom). [clausify(17)].
% 0.86/1.14 134 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -related(A,B,C) | in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(25)].
% 0.86/1.14 135 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | related(A,B,C) | -in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(25)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | -strict_rel_str(rel_str_of(B,A)) | rel_str_of(the_carrier(rel_str_of(B,A)),the_InternalRel(rel_str_of(B,A))) = rel_str_of(B,A). [resolve(121,b,122,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | -with_suprema_relstr(rel_str_of(B,A)) | -empty_carrier(rel_str_of(B,A)). [resolve(121,b,123,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -complete_relstr(rel_str_of(B,A)) | with_suprema_relstr(rel_str_of(B,A)). [resolve(121,b,124,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -complete_relstr(rel_str_of(B,A)) | with_infima_relstr(rel_str_of(B,A)). [resolve(121,b,125,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | -with_infima_relstr(rel_str_of(B,A)) | -empty_carrier(rel_str_of(B,A)). [resolve(121,b,126,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -trivial_carrier(rel_str_of(B,A)) | transitive_relstr(rel_str_of(B,A)). [resolve(121,b,127,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -trivial_carrier(rel_str_of(B,A)) | antisymmetric_relstr(rel_str_of(B,A)). [resolve(121,b,128,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -trivial_carrier(rel_str_of(B,A)) | complete_relstr(rel_str_of(B,A)). [resolve(121,b,129,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -complete_relstr(rel_str_of(B,A)) | bounded_relstr(rel_str_of(B,A)). [resolve(121,b,130,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | -bounded_relstr(rel_str_of(B,A)) | lower_bounded_relstr(rel_str_of(B,A)). [resolve(121,b,131,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | -bounded_relstr(rel_str_of(B,A)) | upper_bounded_relstr(rel_str_of(B,A)). [resolve(121,b,132,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | -lower_bounded_relstr(rel_str_of(B,A)) | -upper_bounded_relstr(rel_str_of(B,A)) | bounded_relstr(rel_str_of(B,A)). [resolve(121,b,133,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -element(D,the_carrier(rel_str_of(B,A))) | -related(rel_str_of(B,A),C,D) | in(ordered_pair(C,D),the_InternalRel(rel_str_of(B,A))). [resolve(121,b,134,a)].
% 0.86/1.14 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -element(D,the_carrier(rel_str_of(B,A))) | related(rel_str_of(B,A),C,D) | -in(ordered_pair(C,D),the_InternalRel(rel_str_of(B,A))). [resolve(121,b,135,a)].
% 0.86/1.14 136 empty_carrier(A) | -lattice(A) | -latt_str(A) | rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(35)].
% 0.86/1.14 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -strict_rel_str(poset_of_lattice(A)) | rel_str_of(the_carrier(poset_of_lattice(A)),the_InternalRel(poset_of_lattice(A))) = poset_of_lattice(A). [resolve(136,d,122,a)].
% 0.86/1.14 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -trivial_carrier(poset_of_lattice(A)) | complete_relstr(poset_of_lattice(A)). [resolve(136,d,129,a)].
% 0.86/1.14 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(poset_of_lattice(A)) | -complete_relstr(poset_of_lattice(A)) | bounded_relstr(poset_of_lattice(A)). [resolve(136,d,130,a)].
% 0.86/1.14 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -bounded_relstr(poset_of_lattice(A)) | lower_bounded_relstr(poset_of_lattice(A)). [resolve(136,d,131,a)].
% 0.86/1.14 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -bounded_relstr(poset_of_lattice(A)) | upper_bounded_relstr(poset_of_lattice(A)). [resolve(136,d,132,a)].
% 0.86/1.14 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -lower_bounded_relstr(poset_of_lattice(A)) | -upper_bounded_relstr(poset_of_lattice(A)) | bounded_relstr(poset_of_lattice(A)). [resolve(136,d,133,a)].
% 0.86/1.14 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),B,C) | in(ordered_pair(B,C),the_InternalRel(poset_of_lattice(A))). [resolve(136,d,134,a)].
% 0.86/1.14 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related(poset_of_lattice(A),B,C) | -in(ordered_pair(B,C),the_InternalRel(poset_of_lattice(A))). [resolve(136,d,135,a)].
% 0.86/1.14 137 rel_str(boole_POSet(A)) # label(dt_k3_yellow_1) # label(axiom). [clausify(36)].
% 0.86/1.14 Derived: -strict_rel_str(boole_POSet(A)) | rel_str_of(the_carrier(boole_POSet(A)),the_InternalRel(boole_POSet(A))) = boole_POSet(A). [resolve(137,a,122,a)].
% 0.86/1.14 Derived: -element(A,the_carrier(boole_POSet(B))) | -element(C,the_carrier(boole_POSet(B))) | -related(boole_POSet(B),A,C) | in(ordered_pair(A,C),the_InternalRel(boole_POSet(B))). [resolve(137,a,134,a)].
% 0.86/1.14 Derived: -element(A,the_carrier(boole_POSet(B))) | -element(C,the_carrier(boole_POSet(B))) | related(boole_POSet(B),A,C) | -in(ordered_pair(A,C),the_InternalRel(boole_POSet(B))). [resolve(137,a,135,a)].
% 0.86/1.14 138 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(41)].
% 0.86/1.14 Derived: one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(138,a,121,b)].
% 0.86/1.14 Derived: one_sorted_str(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(138,a,136,d)].
% 0.86/1.14 Derived: one_sorted_str(boole_POSet(A)). [resolve(138,a,137,a)].
% 0.86/1.14 139 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(49)].
% 0.86/1.14 Derived: relation_of2_as_subset(the_InternalRel(rel_str_of(A,B)),the_carrier(rel_str_of(A,B)),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(139,a,121,b)].
% 0.86/1.14 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(139,a,136,d)].
% 0.86/1.14 Derived: relation_of2_as_subset(the_InternalRel(boole_POSet(A)),the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))). [resolve(139,a,137,a)].
% 0.86/1.14 140 rel_str(c2) # label(existence_l1_orders_2) # label(axiom). [clausify(53)].
% 0.86/1.14 Derived: -strict_rel_str(c2) | rel_str_of(the_carrier(c2),the_InternalRel(c2)) = c2. [resolve(140,a,122,a)].
% 0.86/1.15 Derived: -with_suprema_relstr(c2) | -empty_carrier(c2). [resolve(140,a,123,a)].
% 0.86/1.15 Derived: empty_carrier(c2) | -complete_relstr(c2) | with_suprema_relstr(c2). [resolve(140,a,124,a)].
% 0.86/1.15 Derived: empty_carrier(c2) | -complete_relstr(c2) | with_infima_relstr(c2). [resolve(140,a,125,a)].
% 0.86/1.15 Derived: -with_infima_relstr(c2) | -empty_carrier(c2). [resolve(140,a,126,a)].
% 0.86/1.15 Derived: empty_carrier(c2) | -reflexive_relstr(c2) | -trivial_carrier(c2) | transitive_relstr(c2). [resolve(140,a,127,a)].
% 0.86/1.15 Derived: empty_carrier(c2) | -reflexive_relstr(c2) | -trivial_carrier(c2) | antisymmetric_relstr(c2). [resolve(140,a,128,a)].
% 0.86/1.15 Derived: empty_carrier(c2) | -reflexive_relstr(c2) | -trivial_carrier(c2) | complete_relstr(c2). [resolve(140,a,129,a)].
% 0.86/1.15 Derived: empty_carrier(c2) | -complete_relstr(c2) | bounded_relstr(c2). [resolve(140,a,130,a)].
% 0.86/1.15 Derived: -bounded_relstr(c2) | lower_bounded_relstr(c2). [resolve(140,a,131,a)].
% 0.86/1.15 Derived: -bounded_relstr(c2) | upper_bounded_relstr(c2). [resolve(140,a,132,a)].
% 0.86/1.15 Derived: -lower_bounded_relstr(c2) | -upper_bounded_relstr(c2) | bounded_relstr(c2). [resolve(140,a,133,a)].
% 0.86/1.15 Derived: -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | -related(c2,A,B) | in(ordered_pair(A,B),the_InternalRel(c2)). [resolve(140,a,134,a)].
% 0.86/1.15 Derived: -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | related(c2,A,B) | -in(ordered_pair(A,B),the_InternalRel(c2)). [resolve(140,a,135,a)].
% 0.86/1.15 Derived: one_sorted_str(c2). [resolve(140,a,138,a)].
% 0.86/1.15 Derived: relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(140,a,139,a)].
% 0.86/1.15 141 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | relation(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(68)].
% 0.86/1.15 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | relation(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(141,d,121,b)].
% 0.86/1.15 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | relation(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(141,d,136,d)].
% 0.86/1.15 Derived: -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | relation(the_InternalRel(boole_POSet(A))). [resolve(141,d,137,a)].
% 0.86/1.15 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | relation(the_InternalRel(c2)). [resolve(141,d,140,a)].
% 0.86/1.15 142 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | reflexive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(68)].
% 0.86/1.15 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | reflexive(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(142,d,121,b)].
% 0.86/1.15 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | reflexive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(142,d,136,d)].
% 0.86/1.15 Derived: -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | reflexive(the_InternalRel(boole_POSet(A))). [resolve(142,d,137,a)].
% 0.86/1.15 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(142,d,140,a)].
% 0.86/1.15 143 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | antisymmetric(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(68)].
% 0.86/1.15 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | antisymmetric(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(143,d,121,b)].
% 0.86/1.15 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | antisymmetric(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(143,d,136,d)].
% 0.86/1.15 Derived: -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | antisymmetric(the_InternalRel(boole_POSet(A))). [resolve(143,d,137,a)].
% 0.86/1.15 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | antisymmetric(the_InternalRel(c2)). [resolve(143,d,140,a)].
% 0.86/1.15 144 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | transitive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(68)].
% 0.86/1.15 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | transitive(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(144,d,121,b)].
% 0.86/1.15 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | transitive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(144,d,136,d)].
% 0.86/1.15 Derived: -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | transitive(the_InternalRel(boole_POSet(A))). [resolve(144,d,137,a)].
% 0.86/1.15 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | transitive(the_InternalRel(c2)). [resolve(144,d,140,a)].
% 0.86/1.15 145 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(fc2_orders_2) # label(axiom). [clausify(68)].
% 0.86/1.15 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | v1_partfun1(the_InternalRel(rel_str_of(A,B)),the_carrier(rel_str_of(A,B)),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(145,d,121,b)].
% 0.86/1.15 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | v1_partfun1(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(145,d,136,d)].
% 0.86/1.15 Derived: -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | v1_partfun1(the_InternalRel(boole_POSet(A)),the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))). [resolve(145,d,137,a)].
% 0.86/1.15 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | v1_partfun1(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(145,d,140,a)].
% 0.86/1.15 146 rel_str(c10) # label(rc1_lattice3) # label(axiom). [clausify(87)].
% 0.86/1.15 Derived: -strict_rel_str(c10) | rel_str_of(the_carrier(c10),the_InternalRel(c10)) = c10. [resolve(146,a,122,a)].
% 0.86/1.15 Derived: empty_carrier(c10) | -complete_relstr(c10) | with_suprema_relstr(c10). [resolve(146,a,124,a)].
% 0.86/1.15 Derived: empty_carrier(c10) | -complete_relstr(c10) | with_infima_relstr(c10). [resolve(146,a,125,a)].
% 0.86/1.15 Derived: empty_carrier(c10) | -complete_relstr(c10) | bounded_relstr(c10). [resolve(146,a,130,a)].
% 0.86/1.15 Derived: -bounded_relstr(c10) | lower_bounded_relstr(c10). [resolve(146,a,131,a)].
% 0.86/1.15 Derived: -bounded_relstr(c10) | upper_bounded_relstr(c10). [resolve(146,a,132,a)].
% 0.86/1.15 Derived: -lower_bounded_relstr(c10) | -upper_bounded_relstr(c10) | bounded_relstr(c10). [resolve(146,a,133,a)].
% 0.86/1.15 Derived: -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | -related(c10,A,B) | in(ordered_pair(A,B),the_InternalRel(c10)). [resolve(146,a,134,a)].
% 0.86/1.15 Derived: -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | related(c10,A,B) | -in(ordered_pair(A,B),the_InternalRel(c10)). [resolve(146,a,135,a)].
% 0.86/1.15 Derived: one_sorted_str(c10). [resolve(146,a,138,a)].
% 0.86/1.15 Derived: relation_of2_as_subset(the_InternalRel(c10),the_carrier(c10),the_carrier(c10)). [resolve(146,a,139,a)].
% 0.86/1.15 Derived: -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | relation(the_InternalRel(c10)). [resolve(146,a,141,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | reflexive(the_InternalRel(c10)). [resolve(146,a,142,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | antisymmetric(the_InternalRel(c10)). [resolve(146,a,143,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | transitive(the_InternalRel(c10)). [resolve(146,a,144,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | v1_partfun1(the_InternalRel(c10),the_carrier(c10),the_carrier(c10)). [resolve(146,a,145,d)].
% 0.86/1.16 147 rel_str(c11) # label(rc1_orders_2) # label(axiom). [clausify(88)].
% 0.86/1.16 Derived: -strict_rel_str(c11) | rel_str_of(the_carrier(c11),the_InternalRel(c11)) = c11. [resolve(147,a,122,a)].
% 0.86/1.16 Derived: -with_suprema_relstr(c11) | -empty_carrier(c11). [resolve(147,a,123,a)].
% 0.86/1.16 Derived: empty_carrier(c11) | -complete_relstr(c11) | with_suprema_relstr(c11). [resolve(147,a,124,a)].
% 0.86/1.16 Derived: empty_carrier(c11) | -complete_relstr(c11) | with_infima_relstr(c11). [resolve(147,a,125,a)].
% 0.86/1.16 Derived: -with_infima_relstr(c11) | -empty_carrier(c11). [resolve(147,a,126,a)].
% 0.86/1.16 Derived: empty_carrier(c11) | -reflexive_relstr(c11) | -trivial_carrier(c11) | transitive_relstr(c11). [resolve(147,a,127,a)].
% 0.86/1.16 Derived: empty_carrier(c11) | -reflexive_relstr(c11) | -trivial_carrier(c11) | antisymmetric_relstr(c11). [resolve(147,a,128,a)].
% 0.86/1.16 Derived: empty_carrier(c11) | -reflexive_relstr(c11) | -trivial_carrier(c11) | complete_relstr(c11). [resolve(147,a,129,a)].
% 0.86/1.16 Derived: empty_carrier(c11) | -complete_relstr(c11) | bounded_relstr(c11). [resolve(147,a,130,a)].
% 0.86/1.16 Derived: -bounded_relstr(c11) | lower_bounded_relstr(c11). [resolve(147,a,131,a)].
% 0.86/1.16 Derived: -bounded_relstr(c11) | upper_bounded_relstr(c11). [resolve(147,a,132,a)].
% 0.86/1.16 Derived: -lower_bounded_relstr(c11) | -upper_bounded_relstr(c11) | bounded_relstr(c11). [resolve(147,a,133,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | -related(c11,A,B) | in(ordered_pair(A,B),the_InternalRel(c11)). [resolve(147,a,134,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | related(c11,A,B) | -in(ordered_pair(A,B),the_InternalRel(c11)). [resolve(147,a,135,a)].
% 0.86/1.16 Derived: one_sorted_str(c11). [resolve(147,a,138,a)].
% 0.86/1.16 Derived: relation_of2_as_subset(the_InternalRel(c11),the_carrier(c11),the_carrier(c11)). [resolve(147,a,139,a)].
% 0.86/1.16 Derived: -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | relation(the_InternalRel(c11)). [resolve(147,a,141,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | reflexive(the_InternalRel(c11)). [resolve(147,a,142,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | antisymmetric(the_InternalRel(c11)). [resolve(147,a,143,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | transitive(the_InternalRel(c11)). [resolve(147,a,144,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | v1_partfun1(the_InternalRel(c11),the_carrier(c11),the_carrier(c11)). [resolve(147,a,145,d)].
% 0.86/1.16 148 rel_str(c13) # label(rc1_yellow_0) # label(axiom). [clausify(91)].
% 0.86/1.16 Derived: -strict_rel_str(c13) | rel_str_of(the_carrier(c13),the_InternalRel(c13)) = c13. [resolve(148,a,122,a)].
% 0.86/1.16 Derived: empty_carrier(c13) | -complete_relstr(c13) | bounded_relstr(c13). [resolve(148,a,130,a)].
% 0.86/1.16 Derived: -bounded_relstr(c13) | lower_bounded_relstr(c13). [resolve(148,a,131,a)].
% 0.86/1.16 Derived: -bounded_relstr(c13) | upper_bounded_relstr(c13). [resolve(148,a,132,a)].
% 0.86/1.16 Derived: -lower_bounded_relstr(c13) | -upper_bounded_relstr(c13) | bounded_relstr(c13). [resolve(148,a,133,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c13)) | -element(B,the_carrier(c13)) | -related(c13,A,B) | in(ordered_pair(A,B),the_InternalRel(c13)). [resolve(148,a,134,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c13)) | -element(B,the_carrier(c13)) | related(c13,A,B) | -in(ordered_pair(A,B),the_InternalRel(c13)). [resolve(148,a,135,a)].
% 0.86/1.16 Derived: one_sorted_str(c13). [resolve(148,a,138,a)].
% 0.86/1.16 Derived: relation_of2_as_subset(the_InternalRel(c13),the_carrier(c13),the_carrier(c13)). [resolve(148,a,139,a)].
% 0.86/1.16 Derived: -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | relation(the_InternalRel(c13)). [resolve(148,a,141,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | reflexive(the_InternalRel(c13)). [resolve(148,a,142,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | antisymmetric(the_InternalRel(c13)). [resolve(148,a,143,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | transitive(the_InternalRel(c13)). [resolve(148,a,144,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | v1_partfun1(the_InternalRel(c13),the_carrier(c13),the_carrier(c13)). [resolve(148,a,145,d)].
% 0.86/1.16 149 rel_str(c14) # label(rc2_lattice3) # label(axiom). [clausify(92)].
% 0.86/1.16 Derived: -strict_rel_str(c14) | rel_str_of(the_carrier(c14),the_InternalRel(c14)) = c14. [resolve(149,a,122,a)].
% 0.86/1.16 Derived: empty_carrier(c14) | -complete_relstr(c14) | bounded_relstr(c14). [resolve(149,a,130,a)].
% 0.86/1.16 Derived: -bounded_relstr(c14) | lower_bounded_relstr(c14). [resolve(149,a,131,a)].
% 0.86/1.16 Derived: -bounded_relstr(c14) | upper_bounded_relstr(c14). [resolve(149,a,132,a)].
% 0.86/1.16 Derived: -lower_bounded_relstr(c14) | -upper_bounded_relstr(c14) | bounded_relstr(c14). [resolve(149,a,133,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c14)) | -element(B,the_carrier(c14)) | -related(c14,A,B) | in(ordered_pair(A,B),the_InternalRel(c14)). [resolve(149,a,134,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c14)) | -element(B,the_carrier(c14)) | related(c14,A,B) | -in(ordered_pair(A,B),the_InternalRel(c14)). [resolve(149,a,135,a)].
% 0.86/1.16 Derived: one_sorted_str(c14). [resolve(149,a,138,a)].
% 0.86/1.16 Derived: relation_of2_as_subset(the_InternalRel(c14),the_carrier(c14),the_carrier(c14)). [resolve(149,a,139,a)].
% 0.86/1.16 Derived: -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | relation(the_InternalRel(c14)). [resolve(149,a,141,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | reflexive(the_InternalRel(c14)). [resolve(149,a,142,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | antisymmetric(the_InternalRel(c14)). [resolve(149,a,143,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | transitive(the_InternalRel(c14)). [resolve(149,a,144,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | v1_partfun1(the_InternalRel(c14),the_carrier(c14),the_carrier(c14)). [resolve(149,a,145,d)].
% 0.86/1.16 150 rel_str(c15) # label(rc2_orders_2) # label(axiom). [clausify(93)].
% 0.86/1.16 Derived: -strict_rel_str(c15) | rel_str_of(the_carrier(c15),the_InternalRel(c15)) = c15. [resolve(150,a,122,a)].
% 0.86/1.16 Derived: empty_carrier(c15) | -complete_relstr(c15) | with_suprema_relstr(c15). [resolve(150,a,124,a)].
% 0.86/1.16 Derived: empty_carrier(c15) | -complete_relstr(c15) | with_infima_relstr(c15). [resolve(150,a,125,a)].
% 0.86/1.16 Derived: empty_carrier(c15) | -reflexive_relstr(c15) | -trivial_carrier(c15) | complete_relstr(c15). [resolve(150,a,129,a)].
% 0.86/1.16 Derived: empty_carrier(c15) | -complete_relstr(c15) | bounded_relstr(c15). [resolve(150,a,130,a)].
% 0.86/1.16 Derived: -bounded_relstr(c15) | lower_bounded_relstr(c15). [resolve(150,a,131,a)].
% 0.86/1.16 Derived: -bounded_relstr(c15) | upper_bounded_relstr(c15). [resolve(150,a,132,a)].
% 0.86/1.16 Derived: -lower_bounded_relstr(c15) | -upper_bounded_relstr(c15) | bounded_relstr(c15). [resolve(150,a,133,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c15)) | -element(B,the_carrier(c15)) | -related(c15,A,B) | in(ordered_pair(A,B),the_InternalRel(c15)). [resolve(150,a,134,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c15)) | -element(B,the_carrier(c15)) | related(c15,A,B) | -in(ordered_pair(A,B),the_InternalRel(c15)). [resolve(150,a,135,a)].
% 0.86/1.16 Derived: one_sorted_str(c15). [resolve(150,a,138,a)].
% 0.86/1.16 Derived: relation_of2_as_subset(the_InternalRel(c15),the_carrier(c15),the_carrier(c15)). [resolve(150,a,139,a)].
% 0.86/1.16 Derived: -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | relation(the_InternalRel(c15)). [resolve(150,a,141,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | reflexive(the_InternalRel(c15)). [resolve(150,a,142,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | antisymmetric(the_InternalRel(c15)). [resolve(150,a,143,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | transitive(the_InternalRel(c15)). [resolve(150,a,144,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | v1_partfun1(the_InternalRel(c15),the_carrier(c15),the_carrier(c15)). [resolve(150,a,145,d)].
% 0.86/1.16 151 rel_str(c17) # label(rc2_yellow_0) # label(axiom). [clausify(97)].
% 0.86/1.16 Derived: -strict_rel_str(c17) | rel_str_of(the_carrier(c17),the_InternalRel(c17)) = c17. [resolve(151,a,122,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c17)) | -element(B,the_carrier(c17)) | -related(c17,A,B) | in(ordered_pair(A,B),the_InternalRel(c17)). [resolve(151,a,134,a)].
% 0.86/1.16 Derived: -element(A,the_carrier(c17)) | -element(B,the_carrier(c17)) | related(c17,A,B) | -in(ordered_pair(A,B),the_InternalRel(c17)). [resolve(151,a,135,a)].
% 0.86/1.16 Derived: one_sorted_str(c17). [resolve(151,a,138,a)].
% 0.86/1.16 Derived: relation_of2_as_subset(the_InternalRel(c17),the_carrier(c17),the_carrier(c17)). [resolve(151,a,139,a)].
% 0.86/1.16 Derived: -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | relation(the_InternalRel(c17)). [resolve(151,a,141,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | reflexive(the_InternalRel(c17)). [resolve(151,a,142,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | antisymmetric(the_InternalRel(c17)). [resolve(151,a,143,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | transitive(the_InternalRel(c17)). [resolve(151,a,144,d)].
% 0.86/1.16 Derived: -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | v1_partfun1(the_InternalRel(c17),the_carrier(c17),the_carrier(c17)). [resolve(151,a,145,d)].
% 0.86/1.16 152 empty_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -related_reflexive(A,B,C) | related(A,B,C) # label(redefinition_r3_orders_2) # label(axiom). [clausify(106)].
% 0.86/1.16 Derived: empty_carrier(rel_str_of(A,B)) | -reflexive_relstr(rel_str_of(A,B)) | -element(C,the_carrier(rel_str_of(A,B))) | -element(D,the_carrier(rel_str_of(A,B))) | -related_reflexive(rel_str_of(A,B),C,D) | related(rel_str_of(A,B),C,D) | -relation_of2(B,A,A). [resolve(152,c,121,b)].
% 0.86/1.16 Derived: empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related_reflexive(poset_of_lattice(A),B,C) | related(poset_of_lattice(A),B,C) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(152,c,136,d)].
% 0.86/1.16 Derived: empty_carrier(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | -element(B,the_carrier(boole_POSet(A))) | -element(C,the_carrier(boole_POSet(A))) | -related_reflexive(boole_POSet(A),B,C) | related(boole_POSet(A),B,C). [resolve(152,c,137,a)].
% 0.86/1.16 Derived: empty_carrier(c2) | -reflexive_relstr(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | -related_reflexive(c2,A,B) | related(c2,A,B). [resolve(152,c,140,a)].
% 0.86/1.16 Derived: empty_carrier(c10) | -reflexive_relstr(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | -related_reflexive(c10,A,B) | related(c10,A,B). [resolve(152,c,146,a)].
% 0.86/1.16 Derived: empty_carrier(c11) | -reflexive_relstr(c11) | -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | -related_reflexive(c11,A,B) | related(c11,A,B). [resolve(152,c,147,a)].
% 0.86/1.16 Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -element(A,the_carrier(c13)) | -element(B,the_carrier(c13)) | -related_reflexive(c13,A,B) | related(c13,A,B). [resolve(152,c,148,a)].
% 0.86/1.16 Derived: empty_carrier(c14) | -reflexive_relstr(c14) | -element(A,the_carrier(c14)) | -element(B,the_carrier(c14)) | -related_reflexive(c14,A,B) | related(c14,A,B). [resolve(152,c,149,a)].
% 0.86/1.16 Derived: empty_carrier(c15) | -reflexive_relstr(c15) | -element(A,the_carrier(c15)) | -element(B,the_carrier(c15)) | -related_reflexive(c15,A,B) | related(c15,A,B). [resolve(152,c,150,a)].
% 0.86/1.16 Derived: empty_carrier(c17) | -reflexive_relstr(c17) | -element(A,the_carrier(c17)) | -element(B,the_carrier(c17)) | -related_reflexive(c17,A,B) | related(c17,A,B). [resolve(152,c,151,a)].
% 0.86/1.16 153 empty_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | related_reflexive(A,B,C) | -related(A,B,C) # label(redefinition_r3_orders_2) # label(axiom). [clausify(106)].
% 0.86/1.16 Derived: empty_carrier(rel_str_of(A,B)) | -reflexive_relstr(rel_str_of(A,B)) | -element(C,the_carrier(rel_str_of(A,B))) | -element(D,the_carrier(rel_str_of(A,B))) | related_reflexive(rel_str_of(A,B),C,D) | -related(rel_str_of(A,B),C,D) | -relation_of2(B,A,A). [resolve(153,c,121,b)].
% 0.86/1.16 Derived: empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related_reflexive(poset_of_lattice(A),B,C) | -related(poset_of_lattice(A),B,C) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(153,c,136,d)].
% 0.86/1.16 Derived: empty_carrier(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | -element(B,the_carrier(boole_POSet(A))) | -element(C,the_carrier(boole_POSet(A))) | related_reflexive(boole_POSet(A),B,C) | -related(boole_POSet(A),B,C). [resolve(153,c,137,a)].
% 0.86/1.16 Derived: empty_carrier(c2) | -reflexive_relstr(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | related_reflexive(c2,A,B) | -related(c2,A,B). [resolve(153,c,140,a)].
% 0.86/1.16 Derived: empty_carrier(c10) | -reflexive_relstr(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | related_reflexive(c10,A,B) | -related(c10,A,B). [resolve(153,c,146,a)].
% 0.86/1.16 Derived: empty_carrier(c11) | -reflexive_relstr(c11) | -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | related_reflexive(c11,A,B) | -related(c11,A,B). [resolve(153,c,147,a)].
% 0.86/1.16 Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -element(A,the_carrier(c13)) | -element(B,the_carrier(c13)) | related_reflexive(c13,A,B) | -related(c13,A,B). [resolve(153,c,148,a)].
% 0.86/1.16 Derived: empty_carrier(c14) | -reflexive_relstr(c14) | -element(A,the_carrier(c14)) | -element(B,the_carrier(c14)) | related_reflexive(c14,A,B) | -related(c14,A,B). [resolve(153,c,149,a)].
% 0.86/1.16 Derived: empty_carrier(c15) | -reflexive_relstr(c15) | -element(A,the_carrier(c15)) | -element(B,the_carrier(c15)) | related_reflexive(c15,A,B) | -related(c15,A,B). [resolve(153,c,150,a)].
% 0.86/1.16 Derived: empty_carrier(c17) | -reflexive_relstr(c17) | -element(A,the_carrier(c17)) | -element(B,the_carrier(c17)) | related_reflexive(c17,A,B) | -related(c17,A,B). [resolve(153,c,151,a)].
% 0.86/1.16 154 empty_carrier(A) | -reflexive_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | related_reflexive(A,B,B) # label(reflexivity_r3_orders_2) # label(axiom). [clausify(109)].
% 0.86/1.16 Derived: empty_carrier(rel_str_of(A,B)) | -reflexive_relstr(rel_str_of(A,B)) | -element(C,the_carrier(rel_str_of(A,B))) | -element(D,the_carrier(rel_str_of(A,B))) | related_reflexive(rel_str_of(A,B),C,C) | -relation_of2(B,A,A). [resolve(154,c,121,b)].
% 0.86/1.16 Derived: empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related_reflexive(poset_of_lattice(A),B,B) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(154,c,136,d)].
% 0.86/1.16 Derived: empty_carrier(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | -element(B,the_carrier(boole_POSet(A))) | -element(C,the_carrier(boole_POSet(A))) | related_reflexive(boole_POSet(A),B,B). [resolve(154,c,137,a)].
% 0.86/1.18 Derived: empty_carrier(c2) | -reflexive_relstr(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | related_reflexive(c2,A,A). [resolve(154,c,140,a)].
% 0.86/1.18 Derived: empty_carrier(c10) | -reflexive_relstr(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | related_reflexive(c10,A,A). [resolve(154,c,146,a)].
% 0.86/1.18 Derived: empty_carrier(c11) | -reflexive_relstr(c11) | -element(A,the_carrier(c11)) | -element(B,the_carrier(c11)) | related_reflexive(c11,A,A). [resolve(154,c,147,a)].
% 0.86/1.18 Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -element(A,the_carrier(c13)) | -element(B,the_carrier(c13)) | related_reflexive(c13,A,A). [resolve(154,c,148,a)].
% 0.86/1.18 Derived: empty_carrier(c14) | -reflexive_relstr(c14) | -element(A,the_carrier(c14)) | -element(B,the_carrier(c14)) | related_reflexive(c14,A,A). [resolve(154,c,149,a)].
% 0.86/1.18 Derived: empty_carrier(c15) | -reflexive_relstr(c15) | -element(A,the_carrier(c15)) | -element(B,the_carrier(c15)) | related_reflexive(c15,A,A). [resolve(154,c,150,a)].
% 0.86/1.18 Derived: empty_carrier(c17) | -reflexive_relstr(c17) | -element(A,the_carrier(c17)) | -element(B,the_carrier(c17)) | related_reflexive(c17,A,A). [resolve(154,c,151,a)].
% 0.86/1.18 155 -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | latt_str(latt_str_of(B,A,C)) # label(dt_g3_lattices) # label(axiom). [clausify(27)].
% 0.86/1.18 156 -latt_str(A) | -strict_latt_str(A) | latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)) = A # label(abstractness_v3_lattices) # label(axiom). [clausify(2)].
% 0.86/1.18 157 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | join_commutative(A) # label(cc1_knaster) # label(axiom). [clausify(4)].
% 0.86/1.18 158 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | join_associative(A) # label(cc1_knaster) # label(axiom). [clausify(4)].
% 0.86/1.18 159 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | meet_commutative(A) # label(cc1_knaster) # label(axiom). [clausify(4)].
% 0.86/1.18 160 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | meet_associative(A) # label(cc1_knaster) # label(axiom). [clausify(4)].
% 0.86/1.18 161 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | meet_absorbing(A) # label(cc1_knaster) # label(axiom). [clausify(4)].
% 0.86/1.18 162 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | join_absorbing(A) # label(cc1_knaster) # label(axiom). [clausify(4)].
% 0.86/1.18 163 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | lower_bounded_semilattstr(A) # label(cc1_knaster) # label(axiom). [clausify(4)].
% 0.86/1.18 164 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | upper_bounded_semilattstr(A) # label(cc1_knaster) # label(axiom). [clausify(4)].
% 0.86/1.18 165 -latt_str(A) | empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | bounded_lattstr(A) # label(cc1_knaster) # label(axiom). [clausify(4)].
% 0.86/1.18 166 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(6)].
% 0.86/1.18 167 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_associative(A) # label(cc1_lattices) # label(axiom). [clausify(6)].
% 0.86/1.18 168 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(6)].
% 0.86/1.18 169 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_associative(A) # label(cc1_lattices) # label(axiom). [clausify(6)].
% 0.86/1.18 170 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(6)].
% 0.86/1.18 171 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(6)].
% 0.86/1.18 172 -latt_str(A) | empty_carrier(A) | -join_commutative(A) | -join_associative(A) | -meet_commutative(A) | -meet_associative(A) | -meet_absorbing(A) | -join_absorbing(A) | lattice(A) # label(cc2_lattices) # label(axiom). [clausify(10)].
% 0.86/1.18 173 -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -upper_bounded_semilattstr(A) | bounded_lattstr(A) # label(cc3_lattices) # label(axiom). [clausify(12)].
% 0.86/1.18 174 -latt_str(A) | empty_carrier(A) | -bounded_lattstr(A) | lower_bounded_semilattstr(A) # label(cc4_lattices) # label(axiom). [clausify(14)].
% 0.86/1.18 175 -latt_str(A) | empty_carrier(A) | -bounded_lattstr(A) | upper_bounded_semilattstr(A) # label(cc4_lattices) # label(axiom). [clausify(14)].
% 0.86/1.18 176 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | distributive_lattstr(A) # label(cc5_lattices) # label(axiom). [clausify(16)].
% 0.86/1.18 177 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | lower_bounded_semilattstr(A) # label(cc5_lattices) # label(axiom). [clausify(16)].
% 0.86/1.18 178 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | upper_bounded_semilattstr(A) # label(cc5_lattices) # label(axiom). [clausify(16)].
% 0.86/1.18 179 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | bounded_lattstr(A) # label(cc5_lattices) # label(axiom). [clausify(16)].
% 0.86/1.18 180 -latt_str(A) | empty_carrier(A) | -boolean_lattstr(A) | complemented_lattstr(A) # label(cc5_lattices) # label(axiom). [clausify(16)].
% 0.86/1.18 181 -latt_str(A) | empty_carrier(A) | -distributive_lattstr(A) | -bounded_lattstr(A) | -complemented_lattstr(A) | boolean_lattstr(A) # label(cc6_lattices) # label(axiom). [clausify(18)].
% 0.86/1.18 182 -latt_str(A) | empty_carrier(A) | -lattice(A) | -distributive_lattstr(A) | join_commutative(A) # label(cc7_lattices) # label(axiom). [clausify(19)].
% 0.86/1.18 183 -latt_str(A) | empty_carrier(A) | -lattice(A) | -distributive_lattstr(A) | join_associative(A) # label(cc7_lattices) # label(axiom). [clausify(19)].
% 0.86/1.18 184 -latt_str(A) | empty_carrier(A) | -lattice(A) | -distributive_lattstr(A) | meet_commutative(A) # label(cc7_lattices) # label(axiom). [clausify(19)].
% 0.86/1.18 185 -latt_str(A) | empty_carrier(A) | -lattice(A) | -distributive_lattstr(A) | meet_associative(A) # label(cc7_lattices) # label(axiom). [clausify(19)].
% 0.86/1.18 186 -latt_str(A) | empty_carrier(A) | -lattice(A) | -distributive_lattstr(A) | meet_absorbing(A) # label(cc7_lattices) # label(axiom). [clausify(19)].
% 0.86/1.18 187 -latt_str(A) | empty_carrier(A) | -lattice(A) | -distributive_lattstr(A) | join_absorbing(A) # label(cc7_lattices) # label(axiom). [clausify(19)].
% 0.86/1.18 188 -latt_str(A) | empty_carrier(A) | -lattice(A) | -distributive_lattstr(A) | modular_lattstr(A) # label(cc7_lattices) # label(axiom). [clausify(19)].
% 0.86/1.18 189 empty_carrier(A) | -lattice(A) | -latt_str(A) | poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)) # label(d2_lattice3) # label(axiom). [clausify(21)].
% 0.86/1.18 190 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | cast_to_el_of_LattPOSet(A,B) = B # label(d3_lattice3) # label(axiom). [clausify(23)].
% 0.86/1.18 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -strict_latt_str(latt_str_of(B,A,C)) | latt_str_of(the_carrier(latt_str_of(B,A,C)),the_L_join(latt_str_of(B,A,C)),the_L_meet(latt_str_of(B,A,C))) = latt_str_of(B,A,C). [resolve(155,g,156,a)].
% 0.86/1.18 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -complete_latt_str(latt_str_of(B,A,C)) | join_commutative(latt_str_of(B,A,C)). [resolve(155,g,157,a)].
% 0.86/1.18 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -complete_latt_str(latt_str_of(B,A,C)) | join_associative(latt_str_of(B,A,C)). [resolve(155,g,158,a)].
% 0.86/1.18 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -complete_latt_str(latt_str_of(B,A,C)) | meet_commutative(latt_str_of(B,A,C)). [resolve(155,g,159,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -complete_latt_str(latt_str_of(B,A,C)) | meet_associative(latt_str_of(B,A,C)). [resolve(155,g,160,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -complete_latt_str(latt_str_of(B,A,C)) | meet_absorbing(latt_str_of(B,A,C)). [resolve(155,g,161,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -complete_latt_str(latt_str_of(B,A,C)) | join_absorbing(latt_str_of(B,A,C)). [resolve(155,g,162,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -complete_latt_str(latt_str_of(B,A,C)) | lower_bounded_semilattstr(latt_str_of(B,A,C)). [resolve(155,g,163,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -complete_latt_str(latt_str_of(B,A,C)) | upper_bounded_semilattstr(latt_str_of(B,A,C)). [resolve(155,g,164,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -complete_latt_str(latt_str_of(B,A,C)) | bounded_lattstr(latt_str_of(B,A,C)). [resolve(155,g,165,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | join_commutative(latt_str_of(B,A,C)). [resolve(155,g,166,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | join_associative(latt_str_of(B,A,C)). [resolve(155,g,167,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | meet_commutative(latt_str_of(B,A,C)). [resolve(155,g,168,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | meet_associative(latt_str_of(B,A,C)). [resolve(155,g,169,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | meet_absorbing(latt_str_of(B,A,C)). [resolve(155,g,170,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | join_absorbing(latt_str_of(B,A,C)). [resolve(155,g,171,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -join_commutative(latt_str_of(B,A,C)) | -join_associative(latt_str_of(B,A,C)) | -meet_commutative(latt_str_of(B,A,C)) | -meet_associative(latt_str_of(B,A,C)) | -meet_absorbing(latt_str_of(B,A,C)) | -join_absorbing(latt_str_of(B,A,C)) | lattice(latt_str_of(B,A,C)). [resolve(155,g,172,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lower_bounded_semilattstr(latt_str_of(B,A,C)) | -upper_bounded_semilattstr(latt_str_of(B,A,C)) | bounded_lattstr(latt_str_of(B,A,C)). [resolve(155,g,173,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -bounded_lattstr(latt_str_of(B,A,C)) | lower_bounded_semilattstr(latt_str_of(B,A,C)). [resolve(155,g,174,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -bounded_lattstr(latt_str_of(B,A,C)) | upper_bounded_semilattstr(latt_str_of(B,A,C)). [resolve(155,g,175,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -boolean_lattstr(latt_str_of(B,A,C)) | distributive_lattstr(latt_str_of(B,A,C)). [resolve(155,g,176,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -boolean_lattstr(latt_str_of(B,A,C)) | lower_bounded_semilattstr(latt_str_of(B,A,C)). [resolve(155,g,177,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -boolean_lattstr(latt_str_of(B,A,C)) | upper_bounded_semilattstr(latt_str_of(B,A,C)). [resolve(155,g,178,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -boolean_lattstr(latt_str_of(B,A,C)) | bounded_lattstr(latt_str_of(B,A,C)). [resolve(155,g,179,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -boolean_lattstr(latt_str_of(B,A,C)) | complemented_lattstr(latt_str_of(B,A,C)). [resolve(155,g,180,a)].
% 0.86/1.19 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -distributive_lattstr(latt_str_of(B,A,C)) | -bounded_lattstr(latt_str_of(B,A,C)) | -complemented_lattstr(latt_str_of(B,A,C)) | boolean_lattstr(latt_str_of(B,A,C)). [resolve(155,g,181,a)].
% 0.86/1.20 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -distributive_lattstr(latt_str_of(B,A,C)) | modular_lattstr(latt_str_of(B,A,C)). [resolve(155,g,188,a)].
% 0.86/1.20 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | poset_of_lattice(latt_str_of(B,A,C)) = rel_str_of(the_carrier(latt_str_of(B,A,C)),k2_lattice3(latt_str_of(B,A,C))). [resolve(155,g,189,c)].
% 0.86/1.20 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | cast_to_el_of_LattPOSet(latt_str_of(B,A,C),D) = D. [resolve(155,g,190,c)].
% 0.86/1.20 191 latt_str(boole_lattice(A)) # label(dt_k1_lattice3) # label(axiom). [clausify(28)].
% 0.86/1.20 Derived: -strict_latt_str(boole_lattice(A)) | latt_str_of(the_carrier(boole_lattice(A)),the_L_join(boole_lattice(A)),the_L_meet(boole_lattice(A))) = boole_lattice(A). [resolve(191,a,156,a)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | poset_of_lattice(boole_lattice(A)) = rel_str_of(the_carrier(boole_lattice(A)),k2_lattice3(boole_lattice(A))). [resolve(191,a,189,c)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | cast_to_el_of_LattPOSet(boole_lattice(A),B) = B. [resolve(191,a,190,c)].
% 0.86/1.20 192 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(32)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | reflexive(k2_lattice3(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(192,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | reflexive(k2_lattice3(boole_lattice(A))). [resolve(192,c,191,a)].
% 0.86/1.20 193 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(32)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | antisymmetric(k2_lattice3(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(193,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | antisymmetric(k2_lattice3(boole_lattice(A))). [resolve(193,c,191,a)].
% 0.86/1.20 194 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(32)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | transitive(k2_lattice3(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(194,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | transitive(k2_lattice3(boole_lattice(A))). [resolve(194,c,191,a)].
% 0.86/1.20 195 empty_carrier(A) | -lattice(A) | -latt_str(A) | v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(32)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | v1_partfun1(k2_lattice3(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(195,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | v1_partfun1(k2_lattice3(boole_lattice(A)),the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(195,c,191,a)].
% 0.86/1.20 196 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(32)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | relation_of2_as_subset(k2_lattice3(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(196,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | relation_of2_as_subset(k2_lattice3(boole_lattice(A)),the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(196,c,191,a)].
% 0.86/1.20 197 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(35)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | strict_rel_str(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(197,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | strict_rel_str(poset_of_lattice(boole_lattice(A))). [resolve(197,c,191,a)].
% 0.86/1.20 198 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(35)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(198,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | reflexive_relstr(poset_of_lattice(boole_lattice(A))). [resolve(198,c,191,a)].
% 0.86/1.20 199 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(35)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(199,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | transitive_relstr(poset_of_lattice(boole_lattice(A))). [resolve(199,c,191,a)].
% 0.86/1.20 200 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(35)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(200,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | antisymmetric_relstr(poset_of_lattice(boole_lattice(A))). [resolve(200,c,191,a)].
% 0.86/1.20 201 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A))) # label(dt_k4_lattice3) # label(axiom). [clausify(37)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | element(cast_to_el_of_LattPOSet(latt_str_of(A,B,C),D),the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(201,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | element(cast_to_el_of_LattPOSet(boole_lattice(A),B),the_carrier(poset_of_lattice(boole_lattice(A)))). [resolve(201,c,191,a)].
% 0.86/1.20 202 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation(relation_of_lattice(A)) # label(dt_k9_filter_1) # label(axiom). [clausify(39)].
% 0.86/1.20 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | relation(relation_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(202,c,155,g)].
% 0.86/1.20 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | relation(relation_of_lattice(boole_lattice(A))). [resolve(202,c,191,a)].
% 0.86/1.20 203 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(44)].
% 0.86/1.20 Derived: meet_semilatt_str(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(203,a,155,g)].
% 0.86/1.20 Derived: meet_semilatt_str(boole_lattice(A)). [resolve(203,a,191,a)].
% 0.86/1.20 204 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(44)].
% 0.86/1.20 Derived: join_semilatt_str(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(204,a,155,g)].
% 0.86/1.20 Derived: join_semilatt_str(boole_lattice(A)). [resolve(204,a,191,a)].
% 0.86/1.20 205 latt_str(c5) # label(existence_l3_lattices) # label(axiom). [clausify(56)].
% 0.86/1.20 Derived: -strict_latt_str(c5) | latt_str_of(the_carrier(c5),the_L_join(c5),the_L_meet(c5)) = c5. [resolve(205,a,156,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | join_commutative(c5). [resolve(205,a,157,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | join_associative(c5). [resolve(205,a,158,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | meet_commutative(c5). [resolve(205,a,159,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | meet_associative(c5). [resolve(205,a,160,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | meet_absorbing(c5). [resolve(205,a,161,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | join_absorbing(c5). [resolve(205,a,162,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | lower_bounded_semilattstr(c5). [resolve(205,a,163,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | upper_bounded_semilattstr(c5). [resolve(205,a,164,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | bounded_lattstr(c5). [resolve(205,a,165,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | join_commutative(c5). [resolve(205,a,166,a)].
% 0.86/1.20 Derived: empty_carrier(c5) | -lattice(c5) | join_associative(c5). [resolve(205,a,167,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | meet_commutative(c5). [resolve(205,a,168,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | meet_associative(c5). [resolve(205,a,169,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | meet_absorbing(c5). [resolve(205,a,170,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | join_absorbing(c5). [resolve(205,a,171,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -join_commutative(c5) | -join_associative(c5) | -meet_commutative(c5) | -meet_associative(c5) | -meet_absorbing(c5) | -join_absorbing(c5) | lattice(c5). [resolve(205,a,172,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lower_bounded_semilattstr(c5) | -upper_bounded_semilattstr(c5) | bounded_lattstr(c5). [resolve(205,a,173,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -bounded_lattstr(c5) | lower_bounded_semilattstr(c5). [resolve(205,a,174,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -bounded_lattstr(c5) | upper_bounded_semilattstr(c5). [resolve(205,a,175,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -boolean_lattstr(c5) | distributive_lattstr(c5). [resolve(205,a,176,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -boolean_lattstr(c5) | lower_bounded_semilattstr(c5). [resolve(205,a,177,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -boolean_lattstr(c5) | upper_bounded_semilattstr(c5). [resolve(205,a,178,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -boolean_lattstr(c5) | bounded_lattstr(c5). [resolve(205,a,179,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -boolean_lattstr(c5) | complemented_lattstr(c5). [resolve(205,a,180,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -distributive_lattstr(c5) | -bounded_lattstr(c5) | -complemented_lattstr(c5) | boolean_lattstr(c5). [resolve(205,a,181,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | -distributive_lattstr(c5) | modular_lattstr(c5). [resolve(205,a,188,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | poset_of_lattice(c5) = rel_str_of(the_carrier(c5),k2_lattice3(c5)). [resolve(205,a,189,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | cast_to_el_of_LattPOSet(c5,A) = A. [resolve(205,a,190,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | reflexive(k2_lattice3(c5)). [resolve(205,a,192,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | antisymmetric(k2_lattice3(c5)). [resolve(205,a,193,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | transitive(k2_lattice3(c5)). [resolve(205,a,194,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | v1_partfun1(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(205,a,195,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(205,a,196,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | strict_rel_str(poset_of_lattice(c5)). [resolve(205,a,197,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | reflexive_relstr(poset_of_lattice(c5)). [resolve(205,a,198,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | transitive_relstr(poset_of_lattice(c5)). [resolve(205,a,199,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | antisymmetric_relstr(poset_of_lattice(c5)). [resolve(205,a,200,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | element(cast_to_el_of_LattPOSet(c5,A),the_carrier(poset_of_lattice(c5))). [resolve(205,a,201,c)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | relation(relation_of_lattice(c5)). [resolve(205,a,202,c)].
% 0.86/1.21 Derived: meet_semilatt_str(c5). [resolve(205,a,203,a)].
% 0.86/1.21 Derived: join_semilatt_str(c5). [resolve(205,a,204,a)].
% 0.86/1.21 206 empty_carrier(A) | -lattice(A) | -latt_str(A) | -empty_carrier(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(66)].
% 0.86/1.21 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -empty_carrier(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(206,c,155,g)].
% 0.86/1.21 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -empty_carrier(poset_of_lattice(boole_lattice(A))). [resolve(206,c,191,a)].
% 0.86/1.21 Derived: empty_carrier(c5) | -lattice(c5) | -empty_carrier(poset_of_lattice(c5)). [resolve(206,c,205,a)].
% 0.86/1.22 207 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(66)].
% 0.86/1.22 208 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(66)].
% 0.86/1.22 209 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(66)].
% 0.86/1.22 210 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(66)].
% 0.86/1.22 211 empty_carrier(A) | -lattice(A) | -latt_str(A) | with_suprema_relstr(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(66)].
% 0.86/1.22 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | with_suprema_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(211,c,155,g)].
% 0.86/1.22 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | with_suprema_relstr(poset_of_lattice(boole_lattice(A))). [resolve(211,c,191,a)].
% 0.86/1.22 Derived: empty_carrier(c5) | -lattice(c5) | with_suprema_relstr(poset_of_lattice(c5)). [resolve(211,c,205,a)].
% 0.86/1.22 212 empty_carrier(A) | -lattice(A) | -latt_str(A) | with_infima_relstr(poset_of_lattice(A)) # label(fc1_yellow_1) # label(axiom). [clausify(66)].
% 0.86/1.22 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | with_infima_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(212,c,155,g)].
% 0.86/1.22 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | with_infima_relstr(poset_of_lattice(boole_lattice(A))). [resolve(212,c,191,a)].
% 0.86/1.22 Derived: empty_carrier(c5) | -lattice(c5) | with_infima_relstr(poset_of_lattice(c5)). [resolve(212,c,205,a)].
% 0.86/1.22 213 empty_carrier(A) | -lattice(A) | -upper_bounded_semilattstr(A) | -latt_str(A) | -empty_carrier(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(70)].
% 0.86/1.22 214 empty_carrier(A) | -lattice(A) | -upper_bounded_semilattstr(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(70)].
% 0.86/1.22 215 empty_carrier(A) | -lattice(A) | -upper_bounded_semilattstr(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(70)].
% 0.86/1.22 216 empty_carrier(A) | -lattice(A) | -upper_bounded_semilattstr(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(70)].
% 0.86/1.22 217 empty_carrier(A) | -lattice(A) | -upper_bounded_semilattstr(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(70)].
% 0.86/1.22 218 empty_carrier(A) | -lattice(A) | -upper_bounded_semilattstr(A) | -latt_str(A) | upper_bounded_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(70)].
% 0.86/1.22 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -upper_bounded_semilattstr(latt_str_of(A,B,C)) | upper_bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(218,d,155,g)].
% 0.86/1.22 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -upper_bounded_semilattstr(boole_lattice(A)) | upper_bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(218,d,191,a)].
% 0.86/1.22 Derived: empty_carrier(c5) | -lattice(c5) | -upper_bounded_semilattstr(c5) | upper_bounded_relstr(poset_of_lattice(c5)). [resolve(218,d,205,a)].
% 0.86/1.22 219 empty_carrier(A) | -lattice(A) | -upper_bounded_semilattstr(A) | -latt_str(A) | with_suprema_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(70)].
% 0.86/1.24 220 empty_carrier(A) | -lattice(A) | -upper_bounded_semilattstr(A) | -latt_str(A) | with_infima_relstr(poset_of_lattice(A)) # label(fc2_yellow_1) # label(axiom). [clausify(70)].
% 0.86/1.24 221 empty_carrier(A) | -lattice(A) | -lower_bounded_semilattstr(A) | -latt_str(A) | -empty_carrier(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(75)].
% 0.86/1.24 222 empty_carrier(A) | -lattice(A) | -lower_bounded_semilattstr(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(75)].
% 0.86/1.24 223 empty_carrier(A) | -lattice(A) | -lower_bounded_semilattstr(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(75)].
% 0.86/1.24 224 empty_carrier(A) | -lattice(A) | -lower_bounded_semilattstr(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(75)].
% 0.86/1.24 225 empty_carrier(A) | -lattice(A) | -lower_bounded_semilattstr(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(75)].
% 0.86/1.24 226 empty_carrier(A) | -lattice(A) | -lower_bounded_semilattstr(A) | -latt_str(A) | lower_bounded_relstr(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(75)].
% 0.86/1.24 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -lower_bounded_semilattstr(latt_str_of(A,B,C)) | lower_bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(226,d,155,g)].
% 0.86/1.24 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -lower_bounded_semilattstr(boole_lattice(A)) | lower_bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(226,d,191,a)].
% 0.86/1.24 Derived: empty_carrier(c5) | -lattice(c5) | -lower_bounded_semilattstr(c5) | lower_bounded_relstr(poset_of_lattice(c5)). [resolve(226,d,205,a)].
% 0.86/1.24 227 empty_carrier(A) | -lattice(A) | -lower_bounded_semilattstr(A) | -latt_str(A) | with_suprema_relstr(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(75)].
% 0.86/1.24 228 empty_carrier(A) | -lattice(A) | -lower_bounded_semilattstr(A) | -latt_str(A) | with_infima_relstr(poset_of_lattice(A)) # label(fc3_yellow_1) # label(axiom). [clausify(75)].
% 0.86/1.24 229 empty_carrier(A) | -lattice(A) | -latt_str(A) | -empty_carrier(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(76)].
% 0.86/1.24 230 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(76)].
% 0.86/1.24 231 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(76)].
% 0.86/1.24 232 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(76)].
% 0.86/1.24 233 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(76)].
% 0.86/1.24 234 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | -empty_carrier(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 235 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 236 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 237 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 238 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 239 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | lower_bounded_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -complete_latt_str(latt_str_of(A,B,C)) | lower_bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(239,d,155,g)].
% 0.86/1.24 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -complete_latt_str(boole_lattice(A)) | lower_bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(239,d,191,a)].
% 0.86/1.24 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | lower_bounded_relstr(poset_of_lattice(c5)). [resolve(239,d,205,a)].
% 0.86/1.24 240 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | upper_bounded_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -complete_latt_str(latt_str_of(A,B,C)) | upper_bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(240,d,155,g)].
% 0.86/1.24 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -complete_latt_str(boole_lattice(A)) | upper_bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(240,d,191,a)].
% 0.86/1.24 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | upper_bounded_relstr(poset_of_lattice(c5)). [resolve(240,d,205,a)].
% 0.86/1.24 241 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | bounded_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -complete_latt_str(latt_str_of(A,B,C)) | bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(241,d,155,g)].
% 0.86/1.24 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -complete_latt_str(boole_lattice(A)) | bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(241,d,191,a)].
% 0.86/1.24 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | bounded_relstr(poset_of_lattice(c5)). [resolve(241,d,205,a)].
% 0.86/1.24 242 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | with_suprema_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 243 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | with_infima_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 244 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | complete_relstr(poset_of_lattice(A)) # label(fc4_yellow_1) # label(axiom). [clausify(78)].
% 0.86/1.24 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -complete_latt_str(latt_str_of(A,B,C)) | complete_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(244,d,155,g)].
% 0.86/1.24 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -complete_latt_str(boole_lattice(A)) | complete_relstr(poset_of_lattice(boole_lattice(A))). [resolve(244,d,191,a)].
% 0.86/1.24 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | complete_relstr(poset_of_lattice(c5)). [resolve(244,d,205,a)].
% 0.86/1.24 245 latt_str(c6) # label(rc10_lattices) # label(axiom). [clausify(83)].
% 0.86/1.24 Derived: -strict_latt_str(c6) | latt_str_of(the_carrier(c6),the_L_join(c6),the_L_meet(c6)) = c6. [resolve(245,a,156,a)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -complete_latt_str(c6) | bounded_lattstr(c6). [resolve(245,a,165,a)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lower_bounded_semilattstr(c6) | -upper_bounded_semilattstr(c6) | bounded_lattstr(c6). [resolve(245,a,173,a)].
% 0.86/1.25 Derived: empty_carrier(c6) | -boolean_lattstr(c6) | bounded_lattstr(c6). [resolve(245,a,179,a)].
% 0.86/1.25 Derived: empty_carrier(c6) | -boolean_lattstr(c6) | complemented_lattstr(c6). [resolve(245,a,180,a)].
% 0.86/1.25 Derived: empty_carrier(c6) | -distributive_lattstr(c6) | -bounded_lattstr(c6) | -complemented_lattstr(c6) | boolean_lattstr(c6). [resolve(245,a,181,a)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | poset_of_lattice(c6) = rel_str_of(the_carrier(c6),k2_lattice3(c6)). [resolve(245,a,189,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -element(A,the_carrier(c6)) | cast_to_el_of_LattPOSet(c6,A) = A. [resolve(245,a,190,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | reflexive(k2_lattice3(c6)). [resolve(245,a,192,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | antisymmetric(k2_lattice3(c6)). [resolve(245,a,193,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | transitive(k2_lattice3(c6)). [resolve(245,a,194,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | v1_partfun1(k2_lattice3(c6),the_carrier(c6),the_carrier(c6)). [resolve(245,a,195,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | relation_of2_as_subset(k2_lattice3(c6),the_carrier(c6),the_carrier(c6)). [resolve(245,a,196,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | strict_rel_str(poset_of_lattice(c6)). [resolve(245,a,197,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | reflexive_relstr(poset_of_lattice(c6)). [resolve(245,a,198,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | transitive_relstr(poset_of_lattice(c6)). [resolve(245,a,199,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | antisymmetric_relstr(poset_of_lattice(c6)). [resolve(245,a,200,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -element(A,the_carrier(c6)) | element(cast_to_el_of_LattPOSet(c6,A),the_carrier(poset_of_lattice(c6))). [resolve(245,a,201,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | relation(relation_of_lattice(c6)). [resolve(245,a,202,c)].
% 0.86/1.25 Derived: meet_semilatt_str(c6). [resolve(245,a,203,a)].
% 0.86/1.25 Derived: join_semilatt_str(c6). [resolve(245,a,204,a)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -empty_carrier(poset_of_lattice(c6)). [resolve(245,a,206,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | with_suprema_relstr(poset_of_lattice(c6)). [resolve(245,a,211,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | with_infima_relstr(poset_of_lattice(c6)). [resolve(245,a,212,c)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -upper_bounded_semilattstr(c6) | upper_bounded_relstr(poset_of_lattice(c6)). [resolve(245,a,218,d)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -lower_bounded_semilattstr(c6) | lower_bounded_relstr(poset_of_lattice(c6)). [resolve(245,a,226,d)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -complete_latt_str(c6) | lower_bounded_relstr(poset_of_lattice(c6)). [resolve(245,a,239,d)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -complete_latt_str(c6) | upper_bounded_relstr(poset_of_lattice(c6)). [resolve(245,a,240,d)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -complete_latt_str(c6) | bounded_relstr(poset_of_lattice(c6)). [resolve(245,a,241,d)].
% 0.86/1.25 Derived: empty_carrier(c6) | -lattice(c6) | -complete_latt_str(c6) | complete_relstr(poset_of_lattice(c6)). [resolve(245,a,244,d)].
% 0.86/1.25 246 latt_str(c7) # label(rc11_lattices) # label(axiom). [clausify(84)].
% 0.86/1.25 Derived: -strict_latt_str(c7) | latt_str_of(the_carrier(c7),the_L_join(c7),the_L_meet(c7)) = c7. [resolve(246,a,156,a)].
% 0.86/1.25 Derived: empty_carrier(c7) | -boolean_lattstr(c7) | distributive_lattstr(c7). [resolve(246,a,176,a)].
% 0.86/1.25 Derived: empty_carrier(c7) | -boolean_lattstr(c7) | complemented_lattstr(c7). [resolve(246,a,180,a)].
% 0.86/1.25 Derived: empty_carrier(c7) | -distributive_lattstr(c7) | -bounded_lattstr(c7) | -complemented_lattstr(c7) | boolean_lattstr(c7). [resolve(246,a,181,a)].
% 0.86/1.25 Derived: empty_carrier(c7) | -lattice(c7) | -distributive_lattstr(c7) | modular_lattstr(c7). [resolve(246,a,188,a)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | poset_of_lattice(c7) = rel_str_of(the_carrier(c7),k2_lattice3(c7)). [resolve(246,a,189,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | -element(A,the_carrier(c7)) | cast_to_el_of_LattPOSet(c7,A) = A. [resolve(246,a,190,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | reflexive(k2_lattice3(c7)). [resolve(246,a,192,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | antisymmetric(k2_lattice3(c7)). [resolve(246,a,193,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | transitive(k2_lattice3(c7)). [resolve(246,a,194,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | v1_partfun1(k2_lattice3(c7),the_carrier(c7),the_carrier(c7)). [resolve(246,a,195,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | relation_of2_as_subset(k2_lattice3(c7),the_carrier(c7),the_carrier(c7)). [resolve(246,a,196,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | strict_rel_str(poset_of_lattice(c7)). [resolve(246,a,197,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | reflexive_relstr(poset_of_lattice(c7)). [resolve(246,a,198,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | transitive_relstr(poset_of_lattice(c7)). [resolve(246,a,199,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | antisymmetric_relstr(poset_of_lattice(c7)). [resolve(246,a,200,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | -element(A,the_carrier(c7)) | element(cast_to_el_of_LattPOSet(c7,A),the_carrier(poset_of_lattice(c7))). [resolve(246,a,201,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | relation(relation_of_lattice(c7)). [resolve(246,a,202,c)].
% 0.86/1.26 Derived: meet_semilatt_str(c7). [resolve(246,a,203,a)].
% 0.86/1.26 Derived: join_semilatt_str(c7). [resolve(246,a,204,a)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | -empty_carrier(poset_of_lattice(c7)). [resolve(246,a,206,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | with_suprema_relstr(poset_of_lattice(c7)). [resolve(246,a,211,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | with_infima_relstr(poset_of_lattice(c7)). [resolve(246,a,212,c)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | -upper_bounded_semilattstr(c7) | upper_bounded_relstr(poset_of_lattice(c7)). [resolve(246,a,218,d)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | -lower_bounded_semilattstr(c7) | lower_bounded_relstr(poset_of_lattice(c7)). [resolve(246,a,226,d)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | -complete_latt_str(c7) | lower_bounded_relstr(poset_of_lattice(c7)). [resolve(246,a,239,d)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | -complete_latt_str(c7) | upper_bounded_relstr(poset_of_lattice(c7)). [resolve(246,a,240,d)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | -complete_latt_str(c7) | bounded_relstr(poset_of_lattice(c7)). [resolve(246,a,241,d)].
% 0.86/1.26 Derived: empty_carrier(c7) | -lattice(c7) | -complete_latt_str(c7) | complete_relstr(poset_of_lattice(c7)). [resolve(246,a,244,d)].
% 0.86/1.26 247 latt_str(c8) # label(rc12_lattices) # label(axiom). [clausify(85)].
% 0.86/1.26 Derived: -strict_latt_str(c8) | latt_str_of(the_carrier(c8),the_L_join(c8),the_L_meet(c8)) = c8. [resolve(247,a,156,a)].
% 0.86/1.26 Derived: empty_carrier(c8) | -boolean_lattstr(c8) | distributive_lattstr(c8). [resolve(247,a,176,a)].
% 0.86/1.26 Derived: empty_carrier(c8) | -distributive_lattstr(c8) | -bounded_lattstr(c8) | -complemented_lattstr(c8) | boolean_lattstr(c8). [resolve(247,a,181,a)].
% 0.86/1.26 Derived: empty_carrier(c8) | -lattice(c8) | -distributive_lattstr(c8) | modular_lattstr(c8). [resolve(247,a,188,a)].
% 0.86/1.26 Derived: empty_carrier(c8) | -lattice(c8) | poset_of_lattice(c8) = rel_str_of(the_carrier(c8),k2_lattice3(c8)). [resolve(247,a,189,c)].
% 0.86/1.26 Derived: empty_carrier(c8) | -lattice(c8) | -element(A,the_carrier(c8)) | cast_to_el_of_LattPOSet(c8,A) = A. [resolve(247,a,190,c)].
% 0.86/1.26 Derived: empty_carrier(c8) | -lattice(c8) | reflexive(k2_lattice3(c8)). [resolve(247,a,192,c)].
% 0.86/1.26 Derived: empty_carrier(c8) | -lattice(c8) | antisymmetric(k2_lattice3(c8)). [resolve(247,a,193,c)].
% 0.86/1.26 Derived: empty_carrier(c8) | -lattice(c8) | transitive(k2_lattice3(c8)). [resolve(247,a,194,c)].
% 0.86/1.26 Derived: empty_carrier(c8) | -lattice(c8) | v1_partfun1(k2_lattice3(c8),the_carrier(c8),the_carrier(c8)). [resolve(247,a,195,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | relation_of2_as_subset(k2_lattice3(c8),the_carrier(c8),the_carrier(c8)). [resolve(247,a,196,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | strict_rel_str(poset_of_lattice(c8)). [resolve(247,a,197,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | reflexive_relstr(poset_of_lattice(c8)). [resolve(247,a,198,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | transitive_relstr(poset_of_lattice(c8)). [resolve(247,a,199,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | antisymmetric_relstr(poset_of_lattice(c8)). [resolve(247,a,200,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | -element(A,the_carrier(c8)) | element(cast_to_el_of_LattPOSet(c8,A),the_carrier(poset_of_lattice(c8))). [resolve(247,a,201,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | relation(relation_of_lattice(c8)). [resolve(247,a,202,c)].
% 0.86/1.27 Derived: meet_semilatt_str(c8). [resolve(247,a,203,a)].
% 0.86/1.27 Derived: join_semilatt_str(c8). [resolve(247,a,204,a)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | -empty_carrier(poset_of_lattice(c8)). [resolve(247,a,206,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | with_suprema_relstr(poset_of_lattice(c8)). [resolve(247,a,211,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | with_infima_relstr(poset_of_lattice(c8)). [resolve(247,a,212,c)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | -upper_bounded_semilattstr(c8) | upper_bounded_relstr(poset_of_lattice(c8)). [resolve(247,a,218,d)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | -lower_bounded_semilattstr(c8) | lower_bounded_relstr(poset_of_lattice(c8)). [resolve(247,a,226,d)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | -complete_latt_str(c8) | lower_bounded_relstr(poset_of_lattice(c8)). [resolve(247,a,239,d)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | -complete_latt_str(c8) | upper_bounded_relstr(poset_of_lattice(c8)). [resolve(247,a,240,d)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | -complete_latt_str(c8) | bounded_relstr(poset_of_lattice(c8)). [resolve(247,a,241,d)].
% 0.86/1.27 Derived: empty_carrier(c8) | -lattice(c8) | -complete_latt_str(c8) | complete_relstr(poset_of_lattice(c8)). [resolve(247,a,244,d)].
% 0.86/1.27 248 latt_str(c9) # label(rc13_lattices) # label(axiom). [clausify(86)].
% 0.86/1.27 Derived: -strict_latt_str(c9) | latt_str_of(the_carrier(c9),the_L_join(c9),the_L_meet(c9)) = c9. [resolve(248,a,156,a)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -distributive_lattstr(c9) | modular_lattstr(c9). [resolve(248,a,188,a)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | poset_of_lattice(c9) = rel_str_of(the_carrier(c9),k2_lattice3(c9)). [resolve(248,a,189,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -element(A,the_carrier(c9)) | cast_to_el_of_LattPOSet(c9,A) = A. [resolve(248,a,190,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | reflexive(k2_lattice3(c9)). [resolve(248,a,192,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | antisymmetric(k2_lattice3(c9)). [resolve(248,a,193,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | transitive(k2_lattice3(c9)). [resolve(248,a,194,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | v1_partfun1(k2_lattice3(c9),the_carrier(c9),the_carrier(c9)). [resolve(248,a,195,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | relation_of2_as_subset(k2_lattice3(c9),the_carrier(c9),the_carrier(c9)). [resolve(248,a,196,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | strict_rel_str(poset_of_lattice(c9)). [resolve(248,a,197,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | reflexive_relstr(poset_of_lattice(c9)). [resolve(248,a,198,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | transitive_relstr(poset_of_lattice(c9)). [resolve(248,a,199,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | antisymmetric_relstr(poset_of_lattice(c9)). [resolve(248,a,200,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -element(A,the_carrier(c9)) | element(cast_to_el_of_LattPOSet(c9,A),the_carrier(poset_of_lattice(c9))). [resolve(248,a,201,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | relation(relation_of_lattice(c9)). [resolve(248,a,202,c)].
% 0.86/1.27 Derived: meet_semilatt_str(c9). [resolve(248,a,203,a)].
% 0.86/1.27 Derived: join_semilatt_str(c9). [resolve(248,a,204,a)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -empty_carrier(poset_of_lattice(c9)). [resolve(248,a,206,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | with_suprema_relstr(poset_of_lattice(c9)). [resolve(248,a,211,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | with_infima_relstr(poset_of_lattice(c9)). [resolve(248,a,212,c)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -upper_bounded_semilattstr(c9) | upper_bounded_relstr(poset_of_lattice(c9)). [resolve(248,a,218,d)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -lower_bounded_semilattstr(c9) | lower_bounded_relstr(poset_of_lattice(c9)). [resolve(248,a,226,d)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -complete_latt_str(c9) | lower_bounded_relstr(poset_of_lattice(c9)). [resolve(248,a,239,d)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -complete_latt_str(c9) | upper_bounded_relstr(poset_of_lattice(c9)). [resolve(248,a,240,d)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -complete_latt_str(c9) | bounded_relstr(poset_of_lattice(c9)). [resolve(248,a,241,d)].
% 0.86/1.27 Derived: empty_carrier(c9) | -lattice(c9) | -complete_latt_str(c9) | complete_relstr(poset_of_lattice(c9)). [resolve(248,a,244,d)].
% 0.86/1.27 249 latt_str(c18) # label(rc3_lattices) # label(axiom). [clausify(98)].
% 0.86/1.27 Derived: -strict_latt_str(c18) | latt_str_of(the_carrier(c18),the_L_join(c18),the_L_meet(c18)) = c18. [resolve(249,a,156,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | join_commutative(c18). [resolve(249,a,157,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | join_associative(c18). [resolve(249,a,158,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | meet_commutative(c18). [resolve(249,a,159,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | meet_associative(c18). [resolve(249,a,160,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | meet_absorbing(c18). [resolve(249,a,161,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | join_absorbing(c18). [resolve(249,a,162,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | lower_bounded_semilattstr(c18). [resolve(249,a,163,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | upper_bounded_semilattstr(c18). [resolve(249,a,164,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | bounded_lattstr(c18). [resolve(249,a,165,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | join_commutative(c18). [resolve(249,a,166,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | join_associative(c18). [resolve(249,a,167,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | meet_commutative(c18). [resolve(249,a,168,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | meet_associative(c18). [resolve(249,a,169,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | meet_absorbing(c18). [resolve(249,a,170,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lattice(c18) | join_absorbing(c18). [resolve(249,a,171,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -join_commutative(c18) | -join_associative(c18) | -meet_commutative(c18) | -meet_associative(c18) | -meet_absorbing(c18) | -join_absorbing(c18) | lattice(c18). [resolve(249,a,172,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -lower_bounded_semilattstr(c18) | -upper_bounded_semilattstr(c18) | bounded_lattstr(c18). [resolve(249,a,173,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -bounded_lattstr(c18) | lower_bounded_semilattstr(c18). [resolve(249,a,174,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -bounded_lattstr(c18) | upper_bounded_semilattstr(c18). [resolve(249,a,175,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -boolean_lattstr(c18) | distributive_lattstr(c18). [resolve(249,a,176,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -boolean_lattstr(c18) | lower_bounded_semilattstr(c18). [resolve(249,a,177,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -boolean_lattstr(c18) | upper_bounded_semilattstr(c18). [resolve(249,a,178,a)].
% 0.86/1.27 Derived: empty_carrier(c18) | -boolean_lattstr(c18) | bounded_lattstr(c18). [resolve(249,a,179,a)].
% 0.86/1.28 Derived: empty_carrier(c18) | -boolean_lattstr(c18) | complemented_lattstr(c18). [resolve(249,a,180,a)].
% 0.86/1.28 Derived: empty_carrier(c18) | -distributive_lattstr(c18) | -bounded_lattstr(c18) | -complemented_lattstr(c18) | boolean_lattstr(c18). [resolve(249,a,181,a)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -distributive_lattstr(c18) | modular_lattstr(c18). [resolve(249,a,188,a)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | poset_of_lattice(c18) = rel_str_of(the_carrier(c18),k2_lattice3(c18)). [resolve(249,a,189,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -element(A,the_carrier(c18)) | cast_to_el_of_LattPOSet(c18,A) = A. [resolve(249,a,190,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | reflexive(k2_lattice3(c18)). [resolve(249,a,192,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | antisymmetric(k2_lattice3(c18)). [resolve(249,a,193,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | transitive(k2_lattice3(c18)). [resolve(249,a,194,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | v1_partfun1(k2_lattice3(c18),the_carrier(c18),the_carrier(c18)). [resolve(249,a,195,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | relation_of2_as_subset(k2_lattice3(c18),the_carrier(c18),the_carrier(c18)). [resolve(249,a,196,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | strict_rel_str(poset_of_lattice(c18)). [resolve(249,a,197,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | reflexive_relstr(poset_of_lattice(c18)). [resolve(249,a,198,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | transitive_relstr(poset_of_lattice(c18)). [resolve(249,a,199,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | antisymmetric_relstr(poset_of_lattice(c18)). [resolve(249,a,200,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -element(A,the_carrier(c18)) | element(cast_to_el_of_LattPOSet(c18,A),the_carrier(poset_of_lattice(c18))). [resolve(249,a,201,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | relation(relation_of_lattice(c18)). [resolve(249,a,202,c)].
% 0.86/1.28 Derived: meet_semilatt_str(c18). [resolve(249,a,203,a)].
% 0.86/1.28 Derived: join_semilatt_str(c18). [resolve(249,a,204,a)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -empty_carrier(poset_of_lattice(c18)). [resolve(249,a,206,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | with_suprema_relstr(poset_of_lattice(c18)). [resolve(249,a,211,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | with_infima_relstr(poset_of_lattice(c18)). [resolve(249,a,212,c)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -upper_bounded_semilattstr(c18) | upper_bounded_relstr(poset_of_lattice(c18)). [resolve(249,a,218,d)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -lower_bounded_semilattstr(c18) | lower_bounded_relstr(poset_of_lattice(c18)). [resolve(249,a,226,d)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | lower_bounded_relstr(poset_of_lattice(c18)). [resolve(249,a,239,d)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | upper_bounded_relstr(poset_of_lattice(c18)). [resolve(249,a,240,d)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | bounded_relstr(poset_of_lattice(c18)). [resolve(249,a,241,d)].
% 0.86/1.28 Derived: empty_carrier(c18) | -lattice(c18) | -complete_latt_str(c18) | complete_relstr(poset_of_lattice(c18)). [resolve(249,a,244,d)].
% 0.86/1.28 250 latt_str(c20) # label(rc6_lattices) # label(axiom). [clausify(101)].
% 0.86/1.28 Derived: -strict_latt_str(c20) | latt_str_of(the_carrier(c20),the_L_join(c20),the_L_meet(c20)) = c20. [resolve(250,a,156,a)].
% 0.86/1.28 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | join_commutative(c20). [resolve(250,a,157,a)].
% 0.86/1.28 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | join_associative(c20). [resolve(250,a,158,a)].
% 0.86/1.28 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | meet_commutative(c20). [resolve(250,a,159,a)].
% 0.86/1.28 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | meet_associative(c20). [resolve(250,a,160,a)].
% 0.86/1.28 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | meet_absorbing(c20). [resolve(250,a,161,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | join_absorbing(c20). [resolve(250,a,162,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | lower_bounded_semilattstr(c20). [resolve(250,a,163,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | upper_bounded_semilattstr(c20). [resolve(250,a,164,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | bounded_lattstr(c20). [resolve(250,a,165,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | join_commutative(c20). [resolve(250,a,166,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | join_associative(c20). [resolve(250,a,167,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | meet_commutative(c20). [resolve(250,a,168,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | meet_associative(c20). [resolve(250,a,169,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | meet_absorbing(c20). [resolve(250,a,170,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | join_absorbing(c20). [resolve(250,a,171,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -join_commutative(c20) | -join_associative(c20) | -meet_commutative(c20) | -meet_associative(c20) | -meet_absorbing(c20) | -join_absorbing(c20) | lattice(c20). [resolve(250,a,172,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lower_bounded_semilattstr(c20) | -upper_bounded_semilattstr(c20) | bounded_lattstr(c20). [resolve(250,a,173,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -bounded_lattstr(c20) | lower_bounded_semilattstr(c20). [resolve(250,a,174,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -bounded_lattstr(c20) | upper_bounded_semilattstr(c20). [resolve(250,a,175,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -boolean_lattstr(c20) | distributive_lattstr(c20). [resolve(250,a,176,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -boolean_lattstr(c20) | lower_bounded_semilattstr(c20). [resolve(250,a,177,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -boolean_lattstr(c20) | upper_bounded_semilattstr(c20). [resolve(250,a,178,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -boolean_lattstr(c20) | bounded_lattstr(c20). [resolve(250,a,179,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -boolean_lattstr(c20) | complemented_lattstr(c20). [resolve(250,a,180,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -distributive_lattstr(c20) | -bounded_lattstr(c20) | -complemented_lattstr(c20) | boolean_lattstr(c20). [resolve(250,a,181,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -distributive_lattstr(c20) | modular_lattstr(c20). [resolve(250,a,188,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | poset_of_lattice(c20) = rel_str_of(the_carrier(c20),k2_lattice3(c20)). [resolve(250,a,189,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -element(A,the_carrier(c20)) | cast_to_el_of_LattPOSet(c20,A) = A. [resolve(250,a,190,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | reflexive(k2_lattice3(c20)). [resolve(250,a,192,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | antisymmetric(k2_lattice3(c20)). [resolve(250,a,193,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | transitive(k2_lattice3(c20)). [resolve(250,a,194,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | v1_partfun1(k2_lattice3(c20),the_carrier(c20),the_carrier(c20)). [resolve(250,a,195,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | relation_of2_as_subset(k2_lattice3(c20),the_carrier(c20),the_carrier(c20)). [resolve(250,a,196,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | strict_rel_str(poset_of_lattice(c20)). [resolve(250,a,197,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | reflexive_relstr(poset_of_lattice(c20)). [resolve(250,a,198,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | transitive_relstr(poset_of_lattice(c20)). [resolve(250,a,199,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | antisymmetric_relstr(poset_of_lattice(c20)). [resolve(250,a,200,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -element(A,the_carrier(c20)) | element(cast_to_el_of_LattPOSet(c20,A),the_carrier(poset_of_lattice(c20))). [resolve(250,a,201,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | relation(relation_of_lattice(c20)). [resolve(250,a,202,c)].
% 0.86/1.29 Derived: meet_semilatt_str(c20). [resolve(250,a,203,a)].
% 0.86/1.29 Derived: join_semilatt_str(c20). [resolve(250,a,204,a)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -empty_carrier(poset_of_lattice(c20)). [resolve(250,a,206,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | with_suprema_relstr(poset_of_lattice(c20)). [resolve(250,a,211,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | with_infima_relstr(poset_of_lattice(c20)). [resolve(250,a,212,c)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -upper_bounded_semilattstr(c20) | upper_bounded_relstr(poset_of_lattice(c20)). [resolve(250,a,218,d)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -lower_bounded_semilattstr(c20) | lower_bounded_relstr(poset_of_lattice(c20)). [resolve(250,a,226,d)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | lower_bounded_relstr(poset_of_lattice(c20)). [resolve(250,a,239,d)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | upper_bounded_relstr(poset_of_lattice(c20)). [resolve(250,a,240,d)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | bounded_relstr(poset_of_lattice(c20)). [resolve(250,a,241,d)].
% 0.86/1.29 Derived: empty_carrier(c20) | -lattice(c20) | -complete_latt_str(c20) | complete_relstr(poset_of_lattice(c20)). [resolve(250,a,244,d)].
% 0.86/1.29 251 latt_str(c21) # label(rc9_lattices) # label(axiom). [clausify(102)].
% 0.86/1.29 Derived: -strict_latt_str(c21) | latt_str_of(the_carrier(c21),the_L_join(c21),the_L_meet(c21)) = c21. [resolve(251,a,156,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | -complete_latt_str(c21) | lower_bounded_semilattstr(c21). [resolve(251,a,163,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | -complete_latt_str(c21) | upper_bounded_semilattstr(c21). [resolve(251,a,164,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | -complete_latt_str(c21) | bounded_lattstr(c21). [resolve(251,a,165,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lower_bounded_semilattstr(c21) | -upper_bounded_semilattstr(c21) | bounded_lattstr(c21). [resolve(251,a,173,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -bounded_lattstr(c21) | lower_bounded_semilattstr(c21). [resolve(251,a,174,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -bounded_lattstr(c21) | upper_bounded_semilattstr(c21). [resolve(251,a,175,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -boolean_lattstr(c21) | distributive_lattstr(c21). [resolve(251,a,176,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -boolean_lattstr(c21) | lower_bounded_semilattstr(c21). [resolve(251,a,177,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -boolean_lattstr(c21) | upper_bounded_semilattstr(c21). [resolve(251,a,178,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -boolean_lattstr(c21) | bounded_lattstr(c21). [resolve(251,a,179,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -boolean_lattstr(c21) | complemented_lattstr(c21). [resolve(251,a,180,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -distributive_lattstr(c21) | -bounded_lattstr(c21) | -complemented_lattstr(c21) | boolean_lattstr(c21). [resolve(251,a,181,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | -distributive_lattstr(c21) | modular_lattstr(c21). [resolve(251,a,188,a)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | poset_of_lattice(c21) = rel_str_of(the_carrier(c21),k2_lattice3(c21)). [resolve(251,a,189,c)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | -element(A,the_carrier(c21)) | cast_to_el_of_LattPOSet(c21,A) = A. [resolve(251,a,190,c)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | reflexive(k2_lattice3(c21)). [resolve(251,a,192,c)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | antisymmetric(k2_lattice3(c21)). [resolve(251,a,193,c)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | transitive(k2_lattice3(c21)). [resolve(251,a,194,c)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | v1_partfun1(k2_lattice3(c21),the_carrier(c21),the_carrier(c21)). [resolve(251,a,195,c)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | relation_of2_as_subset(k2_lattice3(c21),the_carrier(c21),the_carrier(c21)). [resolve(251,a,196,c)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | strict_rel_str(poset_of_lattice(c21)). [resolve(251,a,197,c)].
% 0.86/1.29 Derived: empty_carrier(c21) | -lattice(c21) | reflexive_relstr(poset_of_lattice(c21)). [resolve(251,a,198,c)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | transitive_relstr(poset_of_lattice(c21)). [resolve(251,a,199,c)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | antisymmetric_relstr(poset_of_lattice(c21)). [resolve(251,a,200,c)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | -element(A,the_carrier(c21)) | element(cast_to_el_of_LattPOSet(c21,A),the_carrier(poset_of_lattice(c21))). [resolve(251,a,201,c)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | relation(relation_of_lattice(c21)). [resolve(251,a,202,c)].
% 0.86/1.30 Derived: meet_semilatt_str(c21). [resolve(251,a,203,a)].
% 0.86/1.30 Derived: join_semilatt_str(c21). [resolve(251,a,204,a)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | -empty_carrier(poset_of_lattice(c21)). [resolve(251,a,206,c)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | with_suprema_relstr(poset_of_lattice(c21)). [resolve(251,a,211,c)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | with_infima_relstr(poset_of_lattice(c21)). [resolve(251,a,212,c)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | -upper_bounded_semilattstr(c21) | upper_bounded_relstr(poset_of_lattice(c21)). [resolve(251,a,218,d)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | -lower_bounded_semilattstr(c21) | lower_bounded_relstr(poset_of_lattice(c21)). [resolve(251,a,226,d)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | -complete_latt_str(c21) | lower_bounded_relstr(poset_of_lattice(c21)). [resolve(251,a,239,d)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | -complete_latt_str(c21) | upper_bounded_relstr(poset_of_lattice(c21)). [resolve(251,a,240,d)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | -complete_latt_str(c21) | bounded_relstr(poset_of_lattice(c21)). [resolve(251,a,241,d)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | -complete_latt_str(c21) | complete_relstr(poset_of_lattice(c21)). [resolve(251,a,244,d)].
% 0.86/1.30 252 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation_of_lattice(A) = k2_lattice3(A) # label(redefinition_k2_lattice3) # label(axiom). [clausify(103)].
% 0.86/1.30 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | relation_of_lattice(latt_str_of(A,B,C)) = k2_lattice3(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(252,c,155,g)].
% 0.86/1.30 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | relation_of_lattice(boole_lattice(A)) = k2_lattice3(boole_lattice(A)). [resolve(252,c,191,a)].
% 0.86/1.30 Derived: empty_carrier(c5) | -lattice(c5) | relation_of_lattice(c5) = k2_lattice3(c5). [resolve(252,c,205,a)].
% 0.86/1.30 Derived: empty_carrier(c6) | -lattice(c6) | relation_of_lattice(c6) = k2_lattice3(c6). [resolve(252,c,245,a)].
% 0.86/1.30 Derived: empty_carrier(c7) | -lattice(c7) | relation_of_lattice(c7) = k2_lattice3(c7). [resolve(252,c,246,a)].
% 0.86/1.30 Derived: empty_carrier(c8) | -lattice(c8) | relation_of_lattice(c8) = k2_lattice3(c8). [resolve(252,c,247,a)].
% 0.86/1.30 Derived: empty_carrier(c9) | -lattice(c9) | relation_of_lattice(c9) = k2_lattice3(c9). [resolve(252,c,248,a)].
% 0.86/1.30 Derived: empty_carrier(c18) | -lattice(c18) | relation_of_lattice(c18) = k2_lattice3(c18). [resolve(252,c,249,a)].
% 0.86/1.30 Derived: empty_carrier(c20) | -lattice(c20) | relation_of_lattice(c20) = k2_lattice3(c20). [resolve(252,c,250,a)].
% 0.86/1.30 Derived: empty_carrier(c21) | -lattice(c21) | relation_of_lattice(c21) = k2_lattice3(c21). [resolve(252,c,251,a)].
% 0.86/1.30 253 empty_carrier(A) | -meet_commutative(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | below(A,B,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(105)].
% 0.86/1.30 Derived: empty_carrier(latt_str_of(A,B,C)) | -meet_commutative(latt_str_of(A,B,C)) | -meet_absorbing(latt_str_of(A,B,C)) | -join_absorbing(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | -element(E,the_carrier(latt_str_of(A,B,C))) | -below_refl(latt_str_of(A,B,C),D,E) | below(latt_str_of(A,B,C),D,E) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(253,e,155,g)].
% 0.86/1.30 Derived: empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -meet_absorbing(boole_lattice(A)) | -join_absorbing(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | -below_refl(boole_lattice(A),B,C) | below(boole_lattice(A),B,C). [resolve(253,e,191,a)].
% 0.86/1.30 Derived: empty_carrier(c5) | -meet_commutative(c5) | -meet_absorbing(c5) | -join_absorbing(c5) | -element(A,the_carrier(c5)) | -element(B,the_carrier(c5)) | -below_refl(c5,A,B) | below(c5,A,B). [resolve(253,e,205,a)].
% 0.86/1.30 Derived: empty_carrier(c6) | -meet_commutative(c6) | -meet_absorbing(c6) | -join_absorbing(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | -below_refl(c6,A,B) | below(c6,A,B). [resolve(253,e,245,a)].
% 0.86/1.30 Derived: empty_carrier(c7) | -meet_commutative(c7) | -meet_absorbing(c7) | -join_absorbing(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | -below_refl(c7,A,B) | below(c7,A,B). [resolve(253,e,246,a)].
% 0.86/1.30 Derived: empty_carrier(c8) | -meet_commutative(c8) | -meet_absorbing(c8) | -join_absorbing(c8) | -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | -below_refl(c8,A,B) | below(c8,A,B). [resolve(253,e,247,a)].
% 0.86/1.30 Derived: empty_carrier(c9) | -meet_commutative(c9) | -meet_absorbing(c9) | -join_absorbing(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | -below_refl(c9,A,B) | below(c9,A,B). [resolve(253,e,248,a)].
% 0.86/1.30 Derived: empty_carrier(c18) | -meet_commutative(c18) | -meet_absorbing(c18) | -join_absorbing(c18) | -element(A,the_carrier(c18)) | -element(B,the_carrier(c18)) | -below_refl(c18,A,B) | below(c18,A,B). [resolve(253,e,249,a)].
% 0.86/1.30 Derived: empty_carrier(c20) | -meet_commutative(c20) | -meet_absorbing(c20) | -join_absorbing(c20) | -element(A,the_carrier(c20)) | -element(B,the_carrier(c20)) | -below_refl(c20,A,B) | below(c20,A,B). [resolve(253,e,250,a)].
% 0.86/1.30 Derived: empty_carrier(c21) | -meet_commutative(c21) | -meet_absorbing(c21) | -join_absorbing(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | -below_refl(c21,A,B) | below(c21,A,B). [resolve(253,e,251,a)].
% 0.86/1.30 254 empty_carrier(A) | -meet_commutative(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -below(A,B,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(105)].
% 0.86/1.30 Derived: empty_carrier(latt_str_of(A,B,C)) | -meet_commutative(latt_str_of(A,B,C)) | -meet_absorbing(latt_str_of(A,B,C)) | -join_absorbing(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | -element(E,the_carrier(latt_str_of(A,B,C))) | below_refl(latt_str_of(A,B,C),D,E) | -below(latt_str_of(A,B,C),D,E) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(254,e,155,g)].
% 0.86/1.30 Derived: empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -meet_absorbing(boole_lattice(A)) | -join_absorbing(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | below_refl(boole_lattice(A),B,C) | -below(boole_lattice(A),B,C). [resolve(254,e,191,a)].
% 0.86/1.30 Derived: empty_carrier(c5) | -meet_commutative(c5) | -meet_absorbing(c5) | -join_absorbing(c5) | -element(A,the_carrier(c5)) | -element(B,the_carrier(c5)) | below_refl(c5,A,B) | -below(c5,A,B). [resolve(254,e,205,a)].
% 0.86/1.30 Derived: empty_carrier(c6) | -meet_commutative(c6) | -meet_absorbing(c6) | -join_absorbing(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | below_refl(c6,A,B) | -below(c6,A,B). [resolve(254,e,245,a)].
% 0.86/1.30 Derived: empty_carrier(c7) | -meet_commutative(c7) | -meet_absorbing(c7) | -join_absorbing(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | below_refl(c7,A,B) | -below(c7,A,B). [resolve(254,e,246,a)].
% 0.86/1.30 Derived: empty_carrier(c8) | -meet_commutative(c8) | -meet_absorbing(c8) | -join_absorbing(c8) | -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | below_refl(c8,A,B) | -below(c8,A,B). [resolve(254,e,247,a)].
% 0.86/1.30 Derived: empty_carrier(c9) | -meet_commutative(c9) | -meet_absorbing(c9) | -join_absorbing(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | below_refl(c9,A,B) | -below(c9,A,B). [resolve(254,e,248,a)].
% 0.86/1.30 Derived: empty_carrier(c18) | -meet_commutative(c18) | -meet_absorbing(c18) | -join_absorbing(c18) | -element(A,the_carrier(c18)) | -element(B,the_carrier(c18)) | below_refl(c18,A,B) | -below(c18,A,B). [resolve(254,e,249,a)].
% 0.86/1.30 Derived: empty_carrier(c20) | -meet_commutative(c20) | -meet_absorbing(c20) | -join_absorbing(c20) | -element(A,the_carrier(c20)) | -element(B,the_carrier(c20)) | below_refl(c20,A,B) | -below(c20,A,B). [resolve(254,e,250,a)].
% 0.86/1.30 Derived: empty_carrier(c21) | -meet_commutative(c21) | -meet_absorbing(c21) | -join_absorbing(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | below_refl(c21,A,B) | -below(c21,A,B). [resolve(254,e,251,a)].
% 0.86/1.30 255 empty_carrier(A) | -meet_commutative(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,B) # label(reflexivity_r3_lattices) # label(axiom). [clausify(108)].
% 0.86/1.30 Derived: empty_carrier(latt_str_of(A,B,C)) | -meet_commutative(latt_str_of(A,B,C)) | -meet_absorbing(latt_str_of(A,B,C)) | -join_absorbing(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | -element(E,the_carrier(latt_str_of(A,B,C))) | below_refl(latt_str_of(A,B,C),D,D) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(255,e,155,g)].
% 0.86/1.30 Derived: empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -meet_absorbing(boole_lattice(A)) | -join_absorbing(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | below_refl(boole_lattice(A),B,B). [resolve(255,e,191,a)].
% 0.86/1.30 Derived: empty_carrier(c5) | -meet_commutative(c5) | -meet_absorbing(c5) | -join_absorbing(c5) | -element(A,the_carrier(c5)) | -element(B,the_carrier(c5)) | below_refl(c5,A,A). [resolve(255,e,205,a)].
% 0.86/1.30 Derived: empty_carrier(c6) | -meet_commutative(c6) | -meet_absorbing(c6) | -join_absorbing(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | below_refl(c6,A,A). [resolve(255,e,245,a)].
% 0.86/1.30 Derived: empty_carrier(c7) | -meet_commutative(c7) | -meet_absorbing(c7) | -join_absorbing(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | below_refl(c7,A,A). [resolve(255,e,246,a)].
% 0.86/1.30 Derived: empty_carrier(c8) | -meet_commutative(c8) | -meet_absorbing(c8) | -join_absorbing(c8) | -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | below_refl(c8,A,A). [resolve(255,e,247,a)].
% 0.86/1.30 Derived: empty_carrier(c9) | -meet_commutative(c9) | -meet_absorbing(c9) | -join_absorbing(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | below_refl(c9,A,A). [resolve(255,e,248,a)].
% 0.86/1.30 Derived: empty_carrier(c18) | -meet_commutative(c18) | -meet_absorbing(c18) | -join_absorbing(c18) | -element(A,the_carrier(c18)) | -element(B,the_carrier(c18)) | below_refl(c18,A,A). [resolve(255,e,249,a)].
% 0.86/1.30 Derived: empty_carrier(c20) | -meet_commutative(c20) | -meet_absorbing(c20) | -join_absorbing(c20) | -element(A,the_carrier(c20)) | -element(B,the_carrier(c20)) | below_refl(c20,A,A). [resolve(255,e,250,a)].
% 0.86/1.30 Derived: empty_carrier(c21) | -meet_commutative(c21) | -meet_absorbing(c21) | -join_absorbing(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | below_refl(c21,A,A). [resolve(255,e,251,a)].
% 0.86/1.30 256 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C)) # label(t7_lattice3) # label(axiom). [clausify(118)].
% 0.86/1.31 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | -element(E,the_carrier(latt_str_of(A,B,C))) | -below_refl(latt_str_of(A,B,C),D,E) | related_reflexive(poset_of_lattice(latt_str_of(A,B,C)),cast_to_el_of_LattPOSet(latt_str_of(A,B,C),D),cast_to_el_of_LattPOSet(latt_str_of(A,B,C),E)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(256,c,155,g)].
% 0.86/1.31 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | -below_refl(boole_lattice(A),B,C) | related_reflexive(poset_of_lattice(boole_lattice(A)),cast_to_el_of_LattPOSet(boole_lattice(A),B),cast_to_el_of_LattPOSet(boole_lattice(A),C)). [resolve(256,c,191,a)].
% 0.86/1.31 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | -element(B,the_carrier(c5)) | -below_refl(c5,A,B) | related_reflexive(poset_of_lattice(c5),cast_to_el_of_LattPOSet(c5,A),cast_to_el_of_LattPOSet(c5,B)). [resolve(256,c,205,a)].
% 0.86/1.31 Derived: empty_carrier(c6) | -lattice(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | -below_refl(c6,A,B) | related_reflexive(poset_of_lattice(c6),cast_to_el_of_LattPOSet(c6,A),cast_to_el_of_LattPOSet(c6,B)). [resolve(256,c,245,a)].
% 0.86/1.31 Derived: empty_carrier(c7) | -lattice(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | -below_refl(c7,A,B) | related_reflexive(poset_of_lattice(c7),cast_to_el_of_LattPOSet(c7,A),cast_to_el_of_LattPOSet(c7,B)). [resolve(256,c,246,a)].
% 0.86/1.31 Derived: empty_carrier(c8) | -lattice(c8) | -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | -below_refl(c8,A,B) | related_reflexive(poset_of_lattice(c8),cast_to_el_of_LattPOSet(c8,A),cast_to_el_of_LattPOSet(c8,B)). [resolve(256,c,247,a)].
% 0.86/1.31 Derived: empty_carrier(c9) | -lattice(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | -below_refl(c9,A,B) | related_reflexive(poset_of_lattice(c9),cast_to_el_of_LattPOSet(c9,A),cast_to_el_of_LattPOSet(c9,B)). [resolve(256,c,248,a)].
% 0.86/1.31 Derived: empty_carrier(c18) | -lattice(c18) | -element(A,the_carrier(c18)) | -element(B,the_carrier(c18)) | -below_refl(c18,A,B) | related_reflexive(poset_of_lattice(c18),cast_to_el_of_LattPOSet(c18,A),cast_to_el_of_LattPOSet(c18,B)). [resolve(256,c,249,a)].
% 0.86/1.31 Derived: empty_carrier(c20) | -lattice(c20) | -element(A,the_carrier(c20)) | -element(B,the_carrier(c20)) | -below_refl(c20,A,B) | related_reflexive(poset_of_lattice(c20),cast_to_el_of_LattPOSet(c20,A),cast_to_el_of_LattPOSet(c20,B)). [resolve(256,c,250,a)].
% 0.86/1.31 Derived: empty_carrier(c21) | -lattice(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | -below_refl(c21,A,B) | related_reflexive(poset_of_lattice(c21),cast_to_el_of_LattPOSet(c21,A),cast_to_el_of_LattPOSet(c21,B)). [resolve(256,c,251,a)].
% 0.86/1.31 257 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C)) # label(t7_lattice3) # label(axiom). [clausify(118)].
% 0.86/1.31 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | -element(E,the_carrier(latt_str_of(A,B,C))) | below_refl(latt_str_of(A,B,C),D,E) | -related_reflexive(poset_of_lattice(latt_str_of(A,B,C)),cast_to_el_of_LattPOSet(latt_str_of(A,B,C),D),cast_to_el_of_LattPOSet(latt_str_of(A,B,C),E)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(257,c,155,g)].
% 0.86/1.31 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | below_refl(boole_lattice(A),B,C) | -related_reflexive(poset_of_lattice(boole_lattice(A)),cast_to_el_of_LattPOSet(boole_lattice(A),B),cast_to_el_of_LattPOSet(boole_lattice(A),C)). [resolve(257,c,191,a)].
% 0.86/1.31 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | -element(B,the_carrier(c5)) | below_refl(c5,A,B) | -related_reflexive(poset_of_lattice(c5),cast_to_el_of_LattPOSet(c5,A),cast_to_el_of_LattPOSet(c5,B)). [resolve(257,c,205,a)].
% 0.86/1.31 Derived: empty_carrier(c6) | -lattice(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | below_refl(c6,A,B) | -related_reflexive(poset_of_lattice(c6),cast_to_el_of_LattPOSet(c6,A),cast_to_el_of_LattPOSet(c6,B)). [resolve(257,c,245,a)].
% 0.86/1.31 Derived: empty_carrier(c7) | -lattice(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | below_refl(c7,A,B) | -related_reflexive(poset_of_lattice(c7),cast_to_el_of_LattPOSet(c7,A),cast_to_el_of_LattPOSet(c7,B)). [resolve(257,c,246,a)].
% 0.86/1.31 Derived: empty_carrier(c8) | -lattice(c8) | -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | below_refl(c8,A,B) | -related_reflexive(poset_of_lattice(c8),cast_to_el_of_LattPOSet(c8,A),cast_to_el_of_LattPOSet(c8,B)). [resolve(257,c,247,a)].
% 0.86/1.31 Derived: empty_carrier(c9) | -lattice(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | below_refl(c9,A,B) | -related_reflexive(poset_of_lattice(c9),cast_to_el_of_LattPOSet(c9,A),cast_to_el_of_LattPOSet(c9,B)). [resolve(257,c,248,a)].
% 0.86/1.31 Derived: empty_carrier(c18) | -lattice(c18) | -element(A,the_carrier(c18)) | -element(B,the_carrier(c18)) | below_refl(c18,A,B) | -related_reflexive(poset_of_lattice(c18),cast_to_el_of_LattPOSet(c18,A),cast_to_el_of_LattPOSet(c18,B)). [resolve(257,c,249,a)].
% 0.86/1.31 Derived: empty_carrier(c20) | -lattice(c20) | -element(A,the_carrier(c20)) | -element(B,the_carrier(c20)) | below_refl(c20,A,B) | -related_reflexive(poset_of_lattice(c20),cast_to_el_of_LattPOSet(c20,A),cast_to_el_of_LattPOSet(c20,B)). [resolve(257,c,250,a)].
% 0.86/1.31 Derived: empty_carrier(c21) | -lattice(c21) | -element(A,the_carrier(c21)) | -element(B,the_carrier(c21)) | below_refl(c21,A,B) | -related_reflexive(poset_of_lattice(c21),cast_to_el_of_LattPOSet(c21,A),cast_to_el_of_LattPOSet(c21,B)). [resolve(257,c,251,a)].
% 0.86/1.31 258 empty_carrier(A) | -lattice(A) | -latt_str(A) | -strict_rel_str(poset_of_lattice(A)) | rel_str_of(the_carrier(poset_of_lattice(A)),the_InternalRel(poset_of_lattice(A))) = poset_of_lattice(A). [resolve(136,d,122,a)].
% 0.86/1.31 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -strict_rel_str(poset_of_lattice(latt_str_of(A,B,C))) | rel_str_of(the_carrier(poset_of_lattice(latt_str_of(A,B,C))),the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) = poset_of_lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(258,c,155,g)].
% 0.86/1.31 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -strict_rel_str(poset_of_lattice(boole_lattice(A))) | rel_str_of(the_carrier(poset_of_lattice(boole_lattice(A))),the_InternalRel(poset_of_lattice(boole_lattice(A)))) = poset_of_lattice(boole_lattice(A)). [resolve(258,c,191,a)].
% 0.86/1.31 Derived: empty_carrier(c5) | -lattice(c5) | -strict_rel_str(poset_of_lattice(c5)) | rel_str_of(the_carrier(poset_of_lattice(c5)),the_InternalRel(poset_of_lattice(c5))) = poset_of_lattice(c5). [resolve(258,c,205,a)].
% 0.86/1.31 Derived: empty_carrier(c6) | -lattice(c6) | -strict_rel_str(poset_of_lattice(c6)) | rel_str_of(the_carrier(poset_of_lattice(c6)),the_InternalRel(poset_of_lattice(c6))) = poset_of_lattice(c6). [resolve(258,c,245,a)].
% 0.86/1.31 Derived: empty_carrier(c7) | -lattice(c7) | -strict_rel_str(poset_of_lattice(c7)) | rel_str_of(the_carrier(poset_of_lattice(c7)),the_InternalRel(poset_of_lattice(c7))) = poset_of_lattice(c7). [resolve(258,c,246,a)].
% 0.86/1.31 Derived: empty_carrier(c8) | -lattice(c8) | -strict_rel_str(poset_of_lattice(c8)) | rel_str_of(the_carrier(poset_of_lattice(c8)),the_InternalRel(poset_of_lattice(c8))) = poset_of_lattice(c8). [resolve(258,c,247,a)].
% 0.86/1.31 Derived: empty_carrier(c9) | -lattice(c9) | -strict_rel_str(poset_of_lattice(c9)) | rel_str_of(the_carrier(poset_of_lattice(c9)),the_InternalRel(poset_of_lattice(c9))) = poset_of_lattice(c9). [resolve(258,c,248,a)].
% 0.86/1.31 Derived: empty_carrier(c18) | -lattice(c18) | -strict_rel_str(poset_of_lattice(c18)) | rel_str_of(the_carrier(poset_of_lattice(c18)),the_InternalRel(poset_of_lattice(c18))) = poset_of_lattice(c18). [resolve(258,c,249,a)].
% 0.86/1.31 Derived: empty_carrier(c20) | -lattice(c20) | -strict_rel_str(poset_of_lattice(c20)) | rel_str_of(the_carrier(poset_of_lattice(c20)),the_InternalRel(poset_of_lattice(c20))) = poset_of_lattice(c20). [resolve(258,c,250,a)].
% 0.86/1.31 Derived: empty_carrier(c21) | -lattice(c21) | -strict_rel_str(poset_of_lattice(c21)) | rel_str_of(the_carrier(poset_of_lattice(c21)),the_InternalRel(poset_of_lattice(c21))) = poset_of_lattice(c21). [resolve(258,c,251,a)].
% 0.86/1.31 259 empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -trivial_carrier(poset_of_lattice(A)) | complete_relstr(poset_of_lattice(A)). [resolve(136,d,129,a)].
% 0.86/1.31 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | empty_carrier(poset_of_lattice(latt_str_of(A,B,C))) | -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -trivial_carrier(poset_of_lattice(latt_str_of(A,B,C))) | complete_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(259,c,155,g)].
% 0.86/1.31 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | empty_carrier(poset_of_lattice(boole_lattice(A))) | -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -trivial_carrier(poset_of_lattice(boole_lattice(A))) | complete_relstr(poset_of_lattice(boole_lattice(A))). [resolve(259,c,191,a)].
% 0.86/1.31 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -reflexive_relstr(poset_of_lattice(c5)) | -trivial_carrier(poset_of_lattice(c5)) | complete_relstr(poset_of_lattice(c5)). [resolve(259,c,205,a)].
% 0.86/1.31 Derived: empty_carrier(c6) | -lattice(c6) | empty_carrier(poset_of_lattice(c6)) | -reflexive_relstr(poset_of_lattice(c6)) | -trivial_carrier(poset_of_lattice(c6)) | complete_relstr(poset_of_lattice(c6)). [resolve(259,c,245,a)].
% 0.86/1.31 Derived: empty_carrier(c7) | -lattice(c7) | empty_carrier(poset_of_lattice(c7)) | -reflexive_relstr(poset_of_lattice(c7)) | -trivial_carrier(poset_of_lattice(c7)) | complete_relstr(poset_of_lattice(c7)). [resolve(259,c,246,a)].
% 0.86/1.31 Derived: empty_carrier(c8) | -lattice(c8) | empty_carrier(poset_of_lattice(c8)) | -reflexive_relstr(poset_of_lattice(c8)) | -trivial_carrier(poset_of_lattice(c8)) | complete_relstr(poset_of_lattice(c8)). [resolve(259,c,247,a)].
% 0.86/1.31 Derived: empty_carrier(c9) | -lattice(c9) | empty_carrier(poset_of_lattice(c9)) | -reflexive_relstr(poset_of_lattice(c9)) | -trivial_carrier(poset_of_lattice(c9)) | complete_relstr(poset_of_lattice(c9)). [resolve(259,c,248,a)].
% 0.86/1.31 Derived: empty_carrier(c18) | -lattice(c18) | empty_carrier(poset_of_lattice(c18)) | -reflexive_relstr(poset_of_lattice(c18)) | -trivial_carrier(poset_of_lattice(c18)) | complete_relstr(poset_of_lattice(c18)). [resolve(259,c,249,a)].
% 0.86/1.31 Derived: empty_carrier(c20) | -lattice(c20) | empty_carrier(poset_of_lattice(c20)) | -reflexive_relstr(poset_of_lattice(c20)) | -trivial_carrier(poset_of_lattice(c20)) | complete_relstr(poset_of_lattice(c20)). [resolve(259,c,250,a)].
% 0.86/1.31 Derived: empty_carrier(c21) | -lattice(c21) | empty_carrier(poset_of_lattice(c21)) | -reflexive_relstr(poset_of_lattice(c21)) | -trivial_carrier(poset_of_lattice(c21)) | complete_relstr(poset_of_lattice(c21)). [resolve(259,c,251,a)].
% 0.86/1.31 260 empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(poset_of_lattice(A)) | -complete_relstr(poset_of_lattice(A)) | bounded_relstr(poset_of_lattice(A)). [resolve(136,d,130,a)].
% 0.86/1.31 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | empty_carrier(poset_of_lattice(latt_str_of(A,B,C))) | -complete_relstr(poset_of_lattice(latt_str_of(A,B,C))) | bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(260,c,155,g)].
% 0.86/1.31 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | empty_carrier(poset_of_lattice(boole_lattice(A))) | -complete_relstr(poset_of_lattice(boole_lattice(A))) | bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(260,c,191,a)].
% 0.86/1.31 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -complete_relstr(poset_of_lattice(c5)) | bounded_relstr(poset_of_lattice(c5)). [resolve(260,c,205,a)].
% 0.86/1.31 Derived: empty_carrier(c6) | -lattice(c6) | empty_carrier(poset_of_lattice(c6)) | -complete_relstr(poset_of_lattice(c6)) | bounded_relstr(poset_of_lattice(c6)). [resolve(260,c,245,a)].
% 0.86/1.31 Derived: empty_carrier(c7) | -lattice(c7) | empty_carrier(poset_of_lattice(c7)) | -complete_relstr(poset_of_lattice(c7)) | bounded_relstr(poset_of_lattice(c7)). [resolve(260,c,246,a)].
% 0.86/1.31 Derived: empty_carrier(c8) | -lattice(c8) | empty_carrier(poset_of_lattice(c8)) | -complete_relstr(poset_of_lattice(c8)) | bounded_relstr(poset_of_lattice(c8)). [resolve(260,c,247,a)].
% 0.86/1.31 Derived: empty_carrier(c9) | -lattice(c9) | empty_carrier(poset_of_lattice(c9)) | -complete_relstr(poset_of_lattice(c9)) | bounded_relstr(poset_of_lattice(c9)). [resolve(260,c,248,a)].
% 0.86/1.31 Derived: empty_carrier(c18) | -lattice(c18) | empty_carrier(poset_of_lattice(c18)) | -complete_relstr(poset_of_lattice(c18)) | bounded_relstr(poset_of_lattice(c18)). [resolve(260,c,249,a)].
% 0.86/1.31 Derived: empty_carrier(c20) | -lattice(c20) | empty_carrier(poset_of_lattice(c20)) | -complete_relstr(poset_of_lattice(c20)) | bounded_relstr(poset_of_lattice(c20)). [resolve(260,c,250,a)].
% 0.86/1.31 Derived: empty_carrier(c21) | -lattice(c21) | empty_carrier(poset_of_lattice(c21)) | -complete_relstr(poset_of_lattice(c21)) | bounded_relstr(poset_of_lattice(c21)). [resolve(260,c,251,a)].
% 0.86/1.31 261 empty_carrier(A) | -lattice(A) | -latt_str(A) | -bounded_relstr(poset_of_lattice(A)) | lower_bounded_relstr(poset_of_lattice(A)). [resolve(136,d,131,a)].
% 0.86/1.31 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | lower_bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(261,c,155,g)].
% 0.86/1.31 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -bounded_relstr(poset_of_lattice(boole_lattice(A))) | lower_bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(261,c,191,a)].
% 0.86/1.31 Derived: empty_carrier(c5) | -lattice(c5) | -bounded_relstr(poset_of_lattice(c5)) | lower_bounded_relstr(poset_of_lattice(c5)). [resolve(261,c,205,a)].
% 0.86/1.31 Derived: empty_carrier(c6) | -lattice(c6) | -bounded_relstr(poset_of_lattice(c6)) | lower_bounded_relstr(poset_of_lattice(c6)). [resolve(261,c,245,a)].
% 0.86/1.31 Derived: empty_carrier(c7) | -lattice(c7) | -bounded_relstr(poset_of_lattice(c7)) | lower_bounded_relstr(poset_of_lattice(c7)). [resolve(261,c,246,a)].
% 0.86/1.31 Derived: empty_carrier(c8) | -lattice(c8) | -bounded_relstr(poset_of_lattice(c8)) | lower_bounded_relstr(poset_of_lattice(c8)). [resolve(261,c,247,a)].
% 0.86/1.31 Derived: empty_carrier(c9) | -lattice(c9) | -bounded_relstr(poset_of_lattice(c9)) | lower_bounded_relstr(poset_of_lattice(c9)). [resolve(261,c,248,a)].
% 0.86/1.31 Derived: empty_carrier(c18) | -lattice(c18) | -bounded_relstr(poset_of_lattice(c18)) | lower_bounded_relstr(poset_of_lattice(c18)). [resolve(261,c,249,a)].
% 0.86/1.31 Derived: empty_carrier(c20) | -lattice(c20) | -bounded_relstr(poset_of_lattice(c20)) | lower_bounded_relstr(poset_of_lattice(c20)). [resolve(261,c,250,a)].
% 0.86/1.31 Derived: empty_carrier(c21) | -lattice(c21) | -bounded_relstr(poset_of_lattice(c21)) | lower_bounded_relstr(poset_of_lattice(c21)). [resolve(261,c,251,a)].
% 0.86/1.32 262 empty_carrier(A) | -lattice(A) | -latt_str(A) | -bounded_relstr(poset_of_lattice(A)) | upper_bounded_relstr(poset_of_lattice(A)). [resolve(136,d,132,a)].
% 0.86/1.32 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | upper_bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(262,c,155,g)].
% 0.86/1.32 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -bounded_relstr(poset_of_lattice(boole_lattice(A))) | upper_bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(262,c,191,a)].
% 0.86/1.32 Derived: empty_carrier(c5) | -lattice(c5) | -bounded_relstr(poset_of_lattice(c5)) | upper_bounded_relstr(poset_of_lattice(c5)). [resolve(262,c,205,a)].
% 0.86/1.32 Derived: empty_carrier(c6) | -lattice(c6) | -bounded_relstr(poset_of_lattice(c6)) | upper_bounded_relstr(poset_of_lattice(c6)). [resolve(262,c,245,a)].
% 0.86/1.32 Derived: empty_carrier(c7) | -lattice(c7) | -bounded_relstr(poset_of_lattice(c7)) | upper_bounded_relstr(poset_of_lattice(c7)). [resolve(262,c,246,a)].
% 0.86/1.32 Derived: empty_carrier(c8) | -lattice(c8) | -bounded_relstr(poset_of_lattice(c8)) | upper_bounded_relstr(poset_of_lattice(c8)). [resolve(262,c,247,a)].
% 0.86/1.32 Derived: empty_carrier(c9) | -lattice(c9) | -bounded_relstr(poset_of_lattice(c9)) | upper_bounded_relstr(poset_of_lattice(c9)). [resolve(262,c,248,a)].
% 0.86/1.32 Derived: empty_carrier(c18) | -lattice(c18) | -bounded_relstr(poset_of_lattice(c18)) | upper_bounded_relstr(poset_of_lattice(c18)). [resolve(262,c,249,a)].
% 0.86/1.32 Derived: empty_carrier(c20) | -lattice(c20) | -bounded_relstr(poset_of_lattice(c20)) | upper_bounded_relstr(poset_of_lattice(c20)). [resolve(262,c,250,a)].
% 0.86/1.32 Derived: empty_carrier(c21) | -lattice(c21) | -bounded_relstr(poset_of_lattice(c21)) | upper_bounded_relstr(poset_of_lattice(c21)). [resolve(262,c,251,a)].
% 0.86/1.32 263 empty_carrier(A) | -lattice(A) | -latt_str(A) | -lower_bounded_relstr(poset_of_lattice(A)) | -upper_bounded_relstr(poset_of_lattice(A)) | bounded_relstr(poset_of_lattice(A)). [resolve(136,d,133,a)].
% 0.86/1.32 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -lower_bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -upper_bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | bounded_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(263,c,155,g)].
% 0.86/1.32 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -lower_bounded_relstr(poset_of_lattice(boole_lattice(A))) | -upper_bounded_relstr(poset_of_lattice(boole_lattice(A))) | bounded_relstr(poset_of_lattice(boole_lattice(A))). [resolve(263,c,191,a)].
% 0.86/1.32 Derived: empty_carrier(c5) | -lattice(c5) | -lower_bounded_relstr(poset_of_lattice(c5)) | -upper_bounded_relstr(poset_of_lattice(c5)) | bounded_relstr(poset_of_lattice(c5)). [resolve(263,c,205,a)].
% 0.86/1.32 Derived: empty_carrier(c6) | -lattice(c6) | -lower_bounded_relstr(poset_of_lattice(c6)) | -upper_bounded_relstr(poset_of_lattice(c6)) | bounded_relstr(poset_of_lattice(c6)). [resolve(263,c,245,a)].
% 0.86/1.32 Derived: empty_carrier(c7) | -lattice(c7) | -lower_bounded_relstr(poset_of_lattice(c7)) | -upper_bounded_relstr(poset_of_lattice(c7)) | bounded_relstr(poset_of_lattice(c7)). [resolve(263,c,246,a)].
% 0.86/1.32 Derived: empty_carrier(c8) | -lattice(c8) | -lower_bounded_relstr(poset_of_lattice(c8)) | -upper_bounded_relstr(poset_of_lattice(c8)) | bounded_relstr(poset_of_lattice(c8)). [resolve(263,c,247,a)].
% 0.86/1.32 Derived: empty_carrier(c9) | -lattice(c9) | -lower_bounded_relstr(poset_of_lattice(c9)) | -upper_bounded_relstr(poset_of_lattice(c9)) | bounded_relstr(poset_of_lattice(c9)). [resolve(263,c,248,a)].
% 0.86/1.32 Derived: empty_carrier(c18) | -lattice(c18) | -lower_bounded_relstr(poset_of_lattice(c18)) | -upper_bounded_relstr(poset_of_lattice(c18)) | bounded_relstr(poset_of_lattice(c18)). [resolve(263,c,249,a)].
% 0.86/1.32 Derived: empty_carrier(c20) | -lattice(c20) | -lower_bounded_relstr(poset_of_lattice(c20)) | -upper_bounded_relstr(poset_of_lattice(c20)) | bounded_relstr(poset_of_lattice(c20)). [resolve(263,c,250,a)].
% 0.86/1.32 Derived: empty_carrier(c21) | -lattice(c21) | -lower_bounded_relstr(poset_of_lattice(c21)) | -upper_bounded_relstr(poset_of_lattice(c21)) | bounded_relstr(poset_of_lattice(c21)). [resolve(263,c,251,a)].
% 0.86/1.32 264 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),B,C) | in(ordered_pair(B,C),the_InternalRel(poset_of_lattice(A))). [resolve(136,d,134,a)].
% 0.86/1.32 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -element(D,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | -element(E,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | -related(poset_of_lattice(latt_str_of(A,B,C)),D,E) | in(ordered_pair(D,E),the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(264,c,155,g)].
% 0.86/1.32 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -element(B,the_carrier(poset_of_lattice(boole_lattice(A)))) | -element(C,the_carrier(poset_of_lattice(boole_lattice(A)))) | -related(poset_of_lattice(boole_lattice(A)),B,C) | in(ordered_pair(B,C),the_InternalRel(poset_of_lattice(boole_lattice(A)))). [resolve(264,c,191,a)].
% 0.86/1.32 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -element(B,the_carrier(poset_of_lattice(c5))) | -related(poset_of_lattice(c5),A,B) | in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c5))). [resolve(264,c,205,a)].
% 0.86/1.32 Derived: empty_carrier(c6) | -lattice(c6) | -element(A,the_carrier(poset_of_lattice(c6))) | -element(B,the_carrier(poset_of_lattice(c6))) | -related(poset_of_lattice(c6),A,B) | in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c6))). [resolve(264,c,245,a)].
% 0.86/1.32 Derived: empty_carrier(c7) | -lattice(c7) | -element(A,the_carrier(poset_of_lattice(c7))) | -element(B,the_carrier(poset_of_lattice(c7))) | -related(poset_of_lattice(c7),A,B) | in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c7))). [resolve(264,c,246,a)].
% 0.86/1.32 Derived: empty_carrier(c8) | -lattice(c8) | -element(A,the_carrier(poset_of_lattice(c8))) | -element(B,the_carrier(poset_of_lattice(c8))) | -related(poset_of_lattice(c8),A,B) | in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c8))). [resolve(264,c,247,a)].
% 0.86/1.32 Derived: empty_carrier(c9) | -lattice(c9) | -element(A,the_carrier(poset_of_lattice(c9))) | -element(B,the_carrier(poset_of_lattice(c9))) | -related(poset_of_lattice(c9),A,B) | in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c9))). [resolve(264,c,248,a)].
% 0.86/1.32 Derived: empty_carrier(c18) | -lattice(c18) | -element(A,the_carrier(poset_of_lattice(c18))) | -element(B,the_carrier(poset_of_lattice(c18))) | -related(poset_of_lattice(c18),A,B) | in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c18))). [resolve(264,c,249,a)].
% 0.86/1.32 Derived: empty_carrier(c20) | -lattice(c20) | -element(A,the_carrier(poset_of_lattice(c20))) | -element(B,the_carrier(poset_of_lattice(c20))) | -related(poset_of_lattice(c20),A,B) | in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c20))). [resolve(264,c,250,a)].
% 0.86/1.32 Derived: empty_carrier(c21) | -lattice(c21) | -element(A,the_carrier(poset_of_lattice(c21))) | -element(B,the_carrier(poset_of_lattice(c21))) | -related(poset_of_lattice(c21),A,B) | in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c21))). [resolve(264,c,251,a)].
% 0.86/1.32 265 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related(poset_of_lattice(A),B,C) | -in(ordered_pair(B,C),the_InternalRel(poset_of_lattice(A))). [resolve(136,d,135,a)].
% 0.86/1.32 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -element(D,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | -element(E,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | related(poset_of_lattice(latt_str_of(A,B,C)),D,E) | -in(ordered_pair(D,E),the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(265,c,155,g)].
% 0.86/1.32 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -element(B,the_carrier(poset_of_lattice(boole_lattice(A)))) | -element(C,the_carrier(poset_of_lattice(boole_lattice(A)))) | related(poset_of_lattice(boole_lattice(A)),B,C) | -in(ordered_pair(B,C),the_InternalRel(poset_of_lattice(boole_lattice(A)))). [resolve(265,c,191,a)].
% 0.86/1.32 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -element(B,the_carrier(poset_of_lattice(c5))) | related(poset_of_lattice(c5),A,B) | -in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c5))). [resolve(265,c,205,a)].
% 0.86/1.32 Derived: empty_carrier(c6) | -lattice(c6) | -element(A,the_carrier(poset_of_lattice(c6))) | -element(B,the_carrier(poset_of_lattice(c6))) | related(poset_of_lattice(c6),A,B) | -in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c6))). [resolve(265,c,245,a)].
% 0.86/1.32 Derived: empty_carrier(c7) | -lattice(c7) | -element(A,the_carrier(poset_of_lattice(c7))) | -element(B,the_carrier(poset_of_lattice(c7))) | related(poset_of_lattice(c7),A,B) | -in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c7))). [resolve(265,c,246,a)].
% 0.86/1.32 Derived: empty_carrier(c8) | -lattice(c8) | -element(A,the_carrier(poset_of_lattice(c8))) | -element(B,the_carrier(poset_of_lattice(c8))) | related(poset_of_lattice(c8),A,B) | -in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c8))). [resolve(265,c,247,a)].
% 0.86/1.32 Derived: empty_carrier(c9) | -lattice(c9) | -element(A,the_carrier(poset_of_lattice(c9))) | -element(B,the_carrier(poset_of_lattice(c9))) | related(poset_of_lattice(c9),A,B) | -in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c9))). [resolve(265,c,248,a)].
% 0.86/1.32 Derived: empty_carrier(c18) | -lattice(c18) | -element(A,the_carrier(poset_of_lattice(c18))) | -element(B,the_carrier(poset_of_lattice(c18))) | related(poset_of_lattice(c18),A,B) | -in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c18))). [resolve(265,c,249,a)].
% 0.86/1.32 Derived: empty_carrier(c20) | -lattice(c20) | -element(A,the_carrier(poset_of_lattice(c20))) | -element(B,the_carrier(poset_of_lattice(c20))) | related(poset_of_lattice(c20),A,B) | -in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c20))). [resolve(265,c,250,a)].
% 0.86/1.32 Derived: empty_carrier(c21) | -lattice(c21) | -element(A,the_carrier(poset_of_lattice(c21))) | -element(B,the_carrier(poset_of_lattice(c21))) | related(poset_of_lattice(c21),A,B) | -in(ordered_pair(A,B),the_InternalRel(poset_of_lattice(c21))). [resolve(265,c,251,a)].
% 0.86/1.32 266 one_sorted_str(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(138,a,136,d)].
% 0.86/1.32 Derived: one_sorted_str(poset_of_lattice(latt_str_of(A,B,C))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(266,d,155,g)].
% 0.86/1.32 Derived: one_sorted_str(poset_of_lattice(boole_lattice(A))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(266,d,191,a)].
% 0.86/1.32 Derived: one_sorted_str(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5). [resolve(266,d,205,a)].
% 0.86/1.32 Derived: one_sorted_str(poset_of_lattice(c6)) | empty_carrier(c6) | -lattice(c6). [resolve(266,d,245,a)].
% 0.86/1.32 Derived: one_sorted_str(poset_of_lattice(c7)) | empty_carrier(c7) | -lattice(c7). [resolve(266,d,246,a)].
% 0.86/1.32 Derived: one_sorted_str(poset_of_lattice(c8)) | empty_carrier(c8) | -lattice(c8). [resolve(266,d,247,a)].
% 0.86/1.33 Derived: one_sorted_str(poset_of_lattice(c9)) | empty_carrier(c9) | -lattice(c9). [resolve(266,d,248,a)].
% 0.86/1.33 Derived: one_sorted_str(poset_of_lattice(c18)) | empty_carrier(c18) | -lattice(c18). [resolve(266,d,249,a)].
% 0.86/1.33 Derived: one_sorted_str(poset_of_lattice(c20)) | empty_carrier(c20) | -lattice(c20). [resolve(266,d,250,a)].
% 0.86/1.33 Derived: one_sorted_str(poset_of_lattice(c21)) | empty_carrier(c21) | -lattice(c21). [resolve(266,d,251,a)].
% 0.86/1.33 267 relation_of2_as_subset(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(139,a,136,d)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),the_carrier(poset_of_lattice(latt_str_of(A,B,C))),the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(267,d,155,g)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(boole_lattice(A))),the_carrier(poset_of_lattice(boole_lattice(A))),the_carrier(poset_of_lattice(boole_lattice(A)))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(267,d,191,a)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(267,d,205,a)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c6)),the_carrier(poset_of_lattice(c6)),the_carrier(poset_of_lattice(c6))) | empty_carrier(c6) | -lattice(c6). [resolve(267,d,245,a)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c7)),the_carrier(poset_of_lattice(c7)),the_carrier(poset_of_lattice(c7))) | empty_carrier(c7) | -lattice(c7). [resolve(267,d,246,a)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c8)),the_carrier(poset_of_lattice(c8)),the_carrier(poset_of_lattice(c8))) | empty_carrier(c8) | -lattice(c8). [resolve(267,d,247,a)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c9)),the_carrier(poset_of_lattice(c9)),the_carrier(poset_of_lattice(c9))) | empty_carrier(c9) | -lattice(c9). [resolve(267,d,248,a)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c18)),the_carrier(poset_of_lattice(c18)),the_carrier(poset_of_lattice(c18))) | empty_carrier(c18) | -lattice(c18). [resolve(267,d,249,a)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c20)),the_carrier(poset_of_lattice(c20)),the_carrier(poset_of_lattice(c20))) | empty_carrier(c20) | -lattice(c20). [resolve(267,d,250,a)].
% 0.86/1.33 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c21)),the_carrier(poset_of_lattice(c21)),the_carrier(poset_of_lattice(c21))) | empty_carrier(c21) | -lattice(c21). [resolve(267,d,251,a)].
% 0.86/1.33 268 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | relation(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(141,d,136,d)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | relation(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(268,g,155,g)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | relation(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(268,g,191,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | relation(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(268,g,205,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | relation(the_InternalRel(poset_of_lattice(c6))) | empty_carrier(c6) | -lattice(c6). [resolve(268,g,245,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | relation(the_InternalRel(poset_of_lattice(c7))) | empty_carrier(c7) | -lattice(c7). [resolve(268,g,246,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | relation(the_InternalRel(poset_of_lattice(c8))) | empty_carrier(c8) | -lattice(c8). [resolve(268,g,247,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | relation(the_InternalRel(poset_of_lattice(c9))) | empty_carrier(c9) | -lattice(c9). [resolve(268,g,248,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | relation(the_InternalRel(poset_of_lattice(c18))) | empty_carrier(c18) | -lattice(c18). [resolve(268,g,249,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | relation(the_InternalRel(poset_of_lattice(c20))) | empty_carrier(c20) | -lattice(c20). [resolve(268,g,250,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | relation(the_InternalRel(poset_of_lattice(c21))) | empty_carrier(c21) | -lattice(c21). [resolve(268,g,251,a)].
% 0.86/1.33 269 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | reflexive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(142,d,136,d)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | reflexive(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(269,g,155,g)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | reflexive(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(269,g,191,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | reflexive(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(269,g,205,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | reflexive(the_InternalRel(poset_of_lattice(c6))) | empty_carrier(c6) | -lattice(c6). [resolve(269,g,245,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | reflexive(the_InternalRel(poset_of_lattice(c7))) | empty_carrier(c7) | -lattice(c7). [resolve(269,g,246,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | reflexive(the_InternalRel(poset_of_lattice(c8))) | empty_carrier(c8) | -lattice(c8). [resolve(269,g,247,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | reflexive(the_InternalRel(poset_of_lattice(c9))) | empty_carrier(c9) | -lattice(c9). [resolve(269,g,248,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | reflexive(the_InternalRel(poset_of_lattice(c18))) | empty_carrier(c18) | -lattice(c18). [resolve(269,g,249,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | reflexive(the_InternalRel(poset_of_lattice(c20))) | empty_carrier(c20) | -lattice(c20). [resolve(269,g,250,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | reflexive(the_InternalRel(poset_of_lattice(c21))) | empty_carrier(c21) | -lattice(c21). [resolve(269,g,251,a)].
% 0.86/1.33 270 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | antisymmetric(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(143,d,136,d)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | antisymmetric(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(270,g,155,g)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | antisymmetric(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(270,g,191,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | antisymmetric(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(270,g,205,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | antisymmetric(the_InternalRel(poset_of_lattice(c6))) | empty_carrier(c6) | -lattice(c6). [resolve(270,g,245,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | antisymmetric(the_InternalRel(poset_of_lattice(c7))) | empty_carrier(c7) | -lattice(c7). [resolve(270,g,246,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | antisymmetric(the_InternalRel(poset_of_lattice(c8))) | empty_carrier(c8) | -lattice(c8). [resolve(270,g,247,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | antisymmetric(the_InternalRel(poset_of_lattice(c9))) | empty_carrier(c9) | -lattice(c9). [resolve(270,g,248,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | antisymmetric(the_InternalRel(poset_of_lattice(c18))) | empty_carrier(c18) | -lattice(c18). [resolve(270,g,249,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | antisymmetric(the_InternalRel(poset_of_lattice(c20))) | empty_carrier(c20) | -lattice(c20). [resolve(270,g,250,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | antisymmetric(the_InternalRel(poset_of_lattice(c21))) | empty_carrier(c21) | -lattice(c21). [resolve(270,g,251,a)].
% 0.86/1.33 271 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | transitive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(144,d,136,d)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | transitive(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(271,g,155,g)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | transitive(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(271,g,191,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | transitive(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(271,g,205,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | transitive(the_InternalRel(poset_of_lattice(c6))) | empty_carrier(c6) | -lattice(c6). [resolve(271,g,245,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | transitive(the_InternalRel(poset_of_lattice(c7))) | empty_carrier(c7) | -lattice(c7). [resolve(271,g,246,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | transitive(the_InternalRel(poset_of_lattice(c8))) | empty_carrier(c8) | -lattice(c8). [resolve(271,g,247,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | transitive(the_InternalRel(poset_of_lattice(c9))) | empty_carrier(c9) | -lattice(c9). [resolve(271,g,248,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | transitive(the_InternalRel(poset_of_lattice(c18))) | empty_carrier(c18) | -lattice(c18). [resolve(271,g,249,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | transitive(the_InternalRel(poset_of_lattice(c20))) | empty_carrier(c20) | -lattice(c20). [resolve(271,g,250,a)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | transitive(the_InternalRel(poset_of_lattice(c21))) | empty_carrier(c21) | -lattice(c21). [resolve(271,g,251,a)].
% 0.86/1.33 272 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | v1_partfun1(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(145,d,136,d)].
% 0.86/1.33 Derived: -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | v1_partfun1(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),the_carrier(poset_of_lattice(latt_str_of(A,B,C))),the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(272,g,155,g)].
% 0.86/1.34 Derived: -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | v1_partfun1(the_InternalRel(poset_of_lattice(boole_lattice(A))),the_carrier(poset_of_lattice(boole_lattice(A))),the_carrier(poset_of_lattice(boole_lattice(A)))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(272,g,191,a)].
% 0.86/1.34 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | v1_partfun1(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(272,g,205,a)].
% 0.86/1.34 Derived: -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | v1_partfun1(the_InternalRel(poset_of_lattice(c6)),the_carrier(poset_of_lattice(c6)),the_carrier(poset_of_lattice(c6))) | empty_carrier(c6) | -lattice(c6). [resolve(272,g,245,a)].
% 0.86/1.34 Derived: -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | v1_partfun1(the_InternalRel(poset_of_lattice(c7)),the_carrier(poset_of_lattice(c7)),the_carrier(poset_of_lattice(c7))) | empty_carrier(c7) | -lattice(c7). [resolve(272,g,246,a)].
% 0.86/1.34 Derived: -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | v1_partfun1(the_InternalRel(poset_of_lattice(c8)),the_carrier(poset_of_lattice(c8)),the_carrier(poset_of_lattice(c8))) | empty_carrier(c8) | -lattice(c8). [resolve(272,g,247,a)].
% 0.86/1.34 Derived: -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | v1_partfun1(the_InternalRel(poset_of_lattice(c9)),the_carrier(poset_of_lattice(c9)),the_carrier(poset_of_lattice(c9))) | empty_carrier(c9) | -lattice(c9). [resolve(272,g,248,a)].
% 0.86/1.34 Derived: -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | v1_partfun1(the_InternalRel(poset_of_lattice(c18)),the_carrier(poset_of_lattice(c18)),the_carrier(poset_of_lattice(c18))) | empty_carrier(c18) | -lattice(c18). [resolve(272,g,249,a)].
% 0.86/1.34 Derived: -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | v1_partfun1(the_InternalRel(poset_of_lattice(c20)),the_carrier(poset_of_lattice(c20)),the_carrier(poset_of_lattice(c20))) | empty_carrier(c20) | -lattice(c20). [resolve(272,g,250,a)].
% 0.86/1.34 Derived: -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | v1_partfun1(the_InternalRel(poset_of_lattice(c21)),the_carrier(poset_of_lattice(c21)),the_carrier(poset_of_lattice(c21))) | empty_carrier(c21) | -lattice(c21). [resolve(272,g,251,a)].
% 0.86/1.34 273 empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related_reflexive(poset_of_lattice(A),B,C) | related(poset_of_lattice(A),B,C) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(152,c,136,d)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(latt_str_of(A,B,C))) | -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -element(D,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | -element(E,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | -related_reflexive(poset_of_lattice(latt_str_of(A,B,C)),D,E) | related(poset_of_lattice(latt_str_of(A,B,C)),D,E) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(273,i,155,g)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(boole_lattice(A))) | -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -element(B,the_carrier(poset_of_lattice(boole_lattice(A)))) | -element(C,the_carrier(poset_of_lattice(boole_lattice(A)))) | -related_reflexive(poset_of_lattice(boole_lattice(A)),B,C) | related(poset_of_lattice(boole_lattice(A)),B,C) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(273,i,191,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c5)) | -reflexive_relstr(poset_of_lattice(c5)) | -element(A,the_carrier(poset_of_lattice(c5))) | -element(B,the_carrier(poset_of_lattice(c5))) | -related_reflexive(poset_of_lattice(c5),A,B) | related(poset_of_lattice(c5),A,B) | empty_carrier(c5) | -lattice(c5). [resolve(273,i,205,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c6)) | -reflexive_relstr(poset_of_lattice(c6)) | -element(A,the_carrier(poset_of_lattice(c6))) | -element(B,the_carrier(poset_of_lattice(c6))) | -related_reflexive(poset_of_lattice(c6),A,B) | related(poset_of_lattice(c6),A,B) | empty_carrier(c6) | -lattice(c6). [resolve(273,i,245,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c7)) | -reflexive_relstr(poset_of_lattice(c7)) | -element(A,the_carrier(poset_of_lattice(c7))) | -element(B,the_carrier(poset_of_lattice(c7))) | -related_reflexive(poset_of_lattice(c7),A,B) | related(poset_of_lattice(c7),A,B) | empty_carrier(c7) | -lattice(c7). [resolve(273,i,246,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c8)) | -reflexive_relstr(poset_of_lattice(c8)) | -element(A,the_carrier(poset_of_lattice(c8))) | -element(B,the_carrier(poset_of_lattice(c8))) | -related_reflexive(poset_of_lattice(c8),A,B) | related(poset_of_lattice(c8),A,B) | empty_carrier(c8) | -lattice(c8). [resolve(273,i,247,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c9)) | -reflexive_relstr(poset_of_lattice(c9)) | -element(A,the_carrier(poset_of_lattice(c9))) | -element(B,the_carrier(poset_of_lattice(c9))) | -related_reflexive(poset_of_lattice(c9),A,B) | related(poset_of_lattice(c9),A,B) | empty_carrier(c9) | -lattice(c9). [resolve(273,i,248,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c18)) | -reflexive_relstr(poset_of_lattice(c18)) | -element(A,the_carrier(poset_of_lattice(c18))) | -element(B,the_carrier(poset_of_lattice(c18))) | -related_reflexive(poset_of_lattice(c18),A,B) | related(poset_of_lattice(c18),A,B) | empty_carrier(c18) | -lattice(c18). [resolve(273,i,249,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c20)) | -reflexive_relstr(poset_of_lattice(c20)) | -element(A,the_carrier(poset_of_lattice(c20))) | -element(B,the_carrier(poset_of_lattice(c20))) | -related_reflexive(poset_of_lattice(c20),A,B) | related(poset_of_lattice(c20),A,B) | empty_carrier(c20) | -lattice(c20). [resolve(273,i,250,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c21)) | -reflexive_relstr(poset_of_lattice(c21)) | -element(A,the_carrier(poset_of_lattice(c21))) | -element(B,the_carrier(poset_of_lattice(c21))) | -related_reflexive(poset_of_lattice(c21),A,B) | related(poset_of_lattice(c21),A,B) | empty_carrier(c21) | -lattice(c21). [resolve(273,i,251,a)].
% 0.86/1.34 274 empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related_reflexive(poset_of_lattice(A),B,C) | -related(poset_of_lattice(A),B,C) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(153,c,136,d)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(latt_str_of(A,B,C))) | -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -element(D,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | -element(E,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | related_reflexive(poset_of_lattice(latt_str_of(A,B,C)),D,E) | -related(poset_of_lattice(latt_str_of(A,B,C)),D,E) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(274,i,155,g)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(boole_lattice(A))) | -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -element(B,the_carrier(poset_of_lattice(boole_lattice(A)))) | -element(C,the_carrier(poset_of_lattice(boole_lattice(A)))) | related_reflexive(poset_of_lattice(boole_lattice(A)),B,C) | -related(poset_of_lattice(boole_lattice(A)),B,C) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(274,i,191,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c5)) | -reflexive_relstr(poset_of_lattice(c5)) | -element(A,the_carrier(poset_of_lattice(c5))) | -element(B,the_carrier(poset_of_lattice(c5))) | related_reflexive(poset_of_lattice(c5),A,B) | -related(poset_of_lattice(c5),A,B) | empty_carrier(c5) | -lattice(c5). [resolve(274,i,205,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c6)) | -reflexive_relstr(poset_of_lattice(c6)) | -element(A,the_carrier(poset_of_lattice(c6))) | -element(B,the_carrier(poset_of_lattice(c6))) | related_reflexive(poset_of_lattice(c6),A,B) | -related(poset_of_lattice(c6),A,B) | empty_carrier(c6) | -lattice(c6). [resolve(274,i,245,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c7)) | -reflexive_relstr(poset_of_lattice(c7)) | -element(A,the_carrier(poset_of_lattice(c7))) | -element(B,the_carrier(poset_of_lattice(c7))) | related_reflexive(poset_of_lattice(c7),A,B) | -related(poset_of_lattice(c7),A,B) | empty_carrier(c7) | -lattice(c7). [resolve(274,i,246,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c8)) | -reflexive_relstr(poset_of_lattice(c8)) | -element(A,the_carrier(poset_of_lattice(c8))) | -element(B,the_carrier(poset_of_lattice(c8))) | related_reflexive(poset_of_lattice(c8),A,B) | -related(poset_of_lattice(c8),A,B) | empty_carrier(c8) | -lattice(c8). [resolve(274,i,247,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c9)) | -reflexive_relstr(poset_of_lattice(c9)) | -element(A,the_carrier(poset_of_lattice(c9))) | -element(B,the_carrier(poset_of_lattice(c9))) | related_reflexive(poset_of_lattice(c9),A,B) | -related(poset_of_lattice(c9),A,B) | empty_carrier(c9) | -lattice(c9). [resolve(274,i,248,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c18)) | -reflexive_relstr(poset_of_lattice(c18)) | -element(A,the_carrier(poset_of_lattice(c18))) | -element(B,the_carrier(poset_of_lattice(c18))) | related_reflexive(poset_of_lattice(c18),A,B) | -related(poset_of_lattice(c18),A,B) | empty_carrier(c18) | -lattice(c18). [resolve(274,i,249,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c20)) | -reflexive_relstr(poset_of_lattice(c20)) | -element(A,the_carrier(poset_of_lattice(c20))) | -element(B,the_carrier(poset_of_lattice(c20))) | related_reflexive(poset_of_lattice(c20),A,B) | -related(poset_of_lattice(c20),A,B) | empty_carrier(c20) | -lattice(c20). [resolve(274,i,250,a)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(c21)) | -reflexive_relstr(poset_of_lattice(c21)) | -element(A,the_carrier(poset_of_lattice(c21))) | -element(B,the_carrier(poset_of_lattice(c21))) | related_reflexive(poset_of_lattice(c21),A,B) | -related(poset_of_lattice(c21),A,B) | empty_carrier(c21) | -lattice(c21). [resolve(274,i,251,a)].
% 0.86/1.34 275 empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related_reflexive(poset_of_lattice(A),B,B) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(154,c,136,d)].
% 0.86/1.34 Derived: empty_carrier(poset_of_lattice(latt_str_of(A,B,C))) | -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -element(D,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | -element(E,the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | related_reflexive(poset_of_lattice(latt_str_of(A,B,C)),D,D) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(275,h,155,g)].
% 0.86/1.45 Derived: empty_carrier(poset_of_lattice(boole_lattice(A))) | -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -element(B,the_carrier(poset_of_lattice(boole_lattice(A)))) | -element(C,the_carrier(poset_of_lattice(boole_lattice(A)))) | related_reflexive(poset_of_lattice(boole_lattice(A)),B,B) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(275,h,191,a)].
% 0.86/1.45 Derived: empty_carrier(poset_of_lattice(c5)) | -reflexive_relstr(poset_of_lattice(c5)) | -element(A,the_carrier(poset_of_lattice(c5))) | -element(B,the_carrier(poset_of_lattice(c5))) | related_reflexive(poset_of_lattice(c5),A,A) | empty_carrier(c5) | -lattice(c5). [resolve(275,h,205,a)].
% 0.86/1.45 Derived: empty_carrier(poset_of_lattice(c6)) | -reflexive_relstr(poset_of_lattice(c6)) | -element(A,the_carrier(poset_of_lattice(c6))) | -element(B,the_carrier(poset_of_lattice(c6))) | related_reflexive(poset_of_lattice(c6),A,A) | empty_carrier(c6) | -lattice(c6). [resolve(275,h,245,a)].
% 0.86/1.45 Derived: empty_carrier(poset_of_lattice(c7)) | -reflexive_relstr(poset_of_lattice(c7)) | -element(A,the_carrier(poset_of_lattice(c7))) | -element(B,the_carrier(poset_of_lattice(c7))) | related_reflexive(poset_of_lattice(c7),A,A) | empty_carrier(c7) | -lattice(c7). [resolve(275,h,246,a)].
% 0.86/1.45 Derived: empty_carrier(poset_of_lattice(c8)) | -reflexive_relstr(poset_of_lattice(c8)) | -element(A,the_carrier(poset_of_lattice(c8))) | -element(B,the_carrier(poset_of_lattice(c8))) | related_reflexive(poset_of_lattice(c8),A,A) | empty_carrier(c8) | -lattice(c8). [resolve(275,h,247,a)].
% 0.86/1.45 Derived: empty_carrier(poset_of_lattice(c9)) | -reflexive_relstr(poset_of_lattice(c9)) | -element(A,the_carrier(poset_of_lattice(c9))) | -element(B,the_carrier(poset_of_lattice(c9))) | related_reflexive(poset_of_lattice(c9),A,A) | empty_carrier(c9) | -lattice(c9). [resolve(275,h,248,a)].
% 0.86/1.45 Derived: empty_carrier(poset_of_lattice(c18)) | -reflexive_relstr(poset_of_lattice(c18)) | -element(A,the_carrier(poset_of_lattice(c18))) | -element(B,the_carrier(poset_of_lattice(c18))) | related_reflexive(poset_of_lattice(c18),A,A) | empty_carrier(c18) | -lattice(c18). [resolve(275,h,249,a)].
% 0.86/1.45 Derived: empty_carrier(poset_of_lattice(c20)) | -reflexive_relstr(poset_of_lattice(c20)) | -element(A,the_carrier(poset_of_lattice(c20))) | -element(B,the_carrier(poset_of_lattice(c20))) | related_reflexive(poset_of_lattice(c20),A,A) | empty_carrier(c20) | -lattice(c20). [resolve(275,h,250,a)].
% 0.86/1.45 Derived: empty_carrier(poset_of_lattice(c21)) | -reflexive_relstr(poset_of_lattice(c21)) | -element(A,the_carrier(poset_of_lattice(c21))) | -element(B,the_carrier(poset_of_lattice(c21))) | related_reflexive(poset_of_lattice(c21),A,A) | empty_carrier(c21) | -lattice(c21). [resolve(275,h,251,a)].
% 0.86/1.45 276 meet_semilatt_str(c1) # label(existence_l1_lattices) # label(axiom). [clausify(52)].
% 0.86/1.45 277 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(40)].
% 0.86/1.45 278 -meet_semilatt_str(A) | function(the_L_meet(A)) # label(dt_u1_lattices) # label(axiom). [clausify(48)].
% 0.86/1.45 279 -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u1_lattices) # label(axiom). [clausify(48)].
% 0.86/1.45 280 -meet_semilatt_str(A) | relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u1_lattices) # label(axiom). [clausify(48)].
% 0.86/1.45 Derived: one_sorted_str(c1). [resolve(276,a,277,a)].
% 0.86/1.45 Derived: function(the_L_meet(c1)). [resolve(276,a,278,a)].
% 0.86/1.45 Derived: quasi_total(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(276,a,279,a)].
% 0.86/1.45 Derived: relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(276,a,280,a)].
% 0.86/1.45 281 meet_semilatt_str(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(203,a,155,g)].
% 0.86/1.46 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | one_sorted_str(latt_str_of(B,A,C)). [resolve(281,a,277,a)].
% 0.86/1.46 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | function(the_L_meet(latt_str_of(B,A,C))). [resolve(281,a,278,a)].
% 0.86/1.46 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | quasi_total(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(281,a,279,a)].
% 0.86/1.46 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2_as_subset(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(281,a,280,a)].
% 0.86/1.46 282 meet_semilatt_str(boole_lattice(A)). [resolve(203,a,191,a)].
% 0.86/1.46 Derived: one_sorted_str(boole_lattice(A)). [resolve(282,a,277,a)].
% 0.86/1.46 Derived: function(the_L_meet(boole_lattice(A))). [resolve(282,a,278,a)].
% 0.86/1.46 Derived: quasi_total(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(282,a,279,a)].
% 0.86/1.46 Derived: relation_of2_as_subset(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(282,a,280,a)].
% 0.86/1.46 283 meet_semilatt_str(c5). [resolve(205,a,203,a)].
% 0.86/1.46 Derived: one_sorted_str(c5). [resolve(283,a,277,a)].
% 0.86/1.46 Derived: function(the_L_meet(c5)). [resolve(283,a,278,a)].
% 0.86/1.46 Derived: quasi_total(the_L_meet(c5),cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)). [resolve(283,a,279,a)].
% 0.86/1.46 Derived: relation_of2_as_subset(the_L_meet(c5),cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)). [resolve(283,a,280,a)].
% 0.86/1.46 284 meet_semilatt_str(c6). [resolve(245,a,203,a)].
% 0.86/1.46 Derived: one_sorted_str(c6). [resolve(284,a,277,a)].
% 0.86/1.46 Derived: function(the_L_meet(c6)). [resolve(284,a,278,a)].
% 0.86/1.46 Derived: quasi_total(the_L_meet(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(284,a,279,a)].
% 0.86/1.46 Derived: relation_of2_as_subset(the_L_meet(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(284,a,280,a)].
% 0.86/1.46 285 meet_semilatt_str(c7). [resolve(246,a,203,a)].
% 0.86/1.46 Derived: one_sorted_str(c7). [resolve(285,a,277,a)].
% 0.86/1.46 Derived: function(the_L_meet(c7)). [resolve(285,a,278,a)].
% 0.86/1.46 Derived: quasi_total(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(285,a,279,a)].
% 0.86/1.46 Derived: relation_of2_as_subset(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(285,a,280,a)].
% 0.86/1.46 286 meet_semilatt_str(c8). [resolve(247,a,203,a)].
% 0.86/1.46 Derived: one_sorted_str(c8). [resolve(286,a,277,a)].
% 0.86/1.46 Derived: function(the_L_meet(c8)). [resolve(286,a,278,a)].
% 0.86/1.46 Derived: quasi_total(the_L_meet(c8),cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)). [resolve(286,a,279,a)].
% 0.86/1.46 Derived: relation_of2_as_subset(the_L_meet(c8),cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)). [resolve(286,a,280,a)].
% 0.86/1.46 287 meet_semilatt_str(c9). [resolve(248,a,203,a)].
% 0.86/1.46 Derived: one_sorted_str(c9). [resolve(287,a,277,a)].
% 0.86/1.46 Derived: function(the_L_meet(c9)). [resolve(287,a,278,a)].
% 0.86/1.46 Derived: quasi_total(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(287,a,279,a)].
% 0.86/1.50 Derived: relation_of2_as_subset(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(287,a,280,a)].
% 0.86/1.50 288 meet_semilatt_str(c18). [resolve(249,a,203,a)].
% 0.86/1.50 Derived: one_sorted_str(c18). [resolve(288,a,277,a)].
% 0.86/1.50 Derived: function(the_L_meet(c18)). [resolve(288,a,278,a)].
% 0.86/1.50 Derived: quasi_total(the_L_meet(c18),cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)). [resolve(288,a,279,a)].
% 0.86/1.50 Derived: relation_of2_as_subset(the_L_meet(c18),cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)). [resolve(288,a,280,a)].
% 0.86/1.50 289 meet_semilatt_str(c20). [resolve(250,a,203,a)].
% 0.86/1.50 Derived: one_sorted_str(c20). [resolve(289,a,277,a)].
% 0.86/1.50 Derived: function(the_L_meet(c20)). [resolve(289,a,278,a)].
% 0.86/1.50 Derived: quasi_total(the_L_meet(c20),cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)). [resolve(289,a,279,a)].
% 0.86/1.50 Derived: relation_of2_as_subset(the_L_meet(c20),cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)). [resolve(289,a,280,a)].
% 0.86/1.50 290 meet_semilatt_str(c21). [resolve(251,a,203,a)].
% 0.86/1.50 Derived: one_sorted_str(c21). [resolve(290,a,277,a)].
% 0.86/1.50 Derived: function(the_L_meet(c21)). [resolve(290,a,278,a)].
% 0.86/1.50 Derived: quasi_total(the_L_meet(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(290,a,279,a)].
% 0.86/1.50 Derived: relation_of2_as_subset(the_L_meet(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(290,a,280,a)].
% 0.86/1.50 291 join_semilatt_str(c4) # label(existence_l2_lattices) # label(axiom). [clausify(55)].
% 0.86/1.50 292 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(43)].
% 0.86/1.50 293 -join_semilatt_str(A) | function(the_L_join(A)) # label(dt_u2_lattices) # label(axiom). [clausify(51)].
% 0.86/1.50 294 -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u2_lattices) # label(axiom). [clausify(51)].
% 0.86/1.50 295 -join_semilatt_str(A) | relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u2_lattices) # label(axiom). [clausify(51)].
% 0.86/1.50 Derived: one_sorted_str(c4). [resolve(291,a,292,a)].
% 0.86/1.50 Derived: function(the_L_join(c4)). [resolve(291,a,293,a)].
% 0.86/1.50 Derived: quasi_total(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(291,a,294,a)].
% 0.86/1.50 Derived: relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(291,a,295,a)].
% 0.86/1.50 296 join_semilatt_str(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(204,a,155,g)].
% 0.86/1.50 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | function(the_L_join(latt_str_of(B,A,C))). [resolve(296,a,293,a)].
% 0.86/1.50 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | quasi_total(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(296,a,294,a)].
% 0.86/1.50 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2_as_subset(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(296,a,295,a)].
% 0.86/1.50 297 join_semilatt_str(boole_lattice(A)). [resolve(204,a,191,a)].
% 0.86/1.50 Derived: function(the_L_join(boole_lattice(A))). [resolve(297,a,293,a)].
% 0.86/1.55 Derived: quasi_total(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(297,a,294,a)].
% 0.86/1.55 Derived: relation_of2_as_subset(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(297,a,295,a)].
% 0.86/1.55 298 join_semilatt_str(c5). [resolve(205,a,204,a)].
% 0.86/1.55 Derived: function(the_L_join(c5)). [resolve(298,a,293,a)].
% 0.86/1.55 Derived: quasi_total(the_L_join(c5),cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)). [resolve(298,a,294,a)].
% 0.86/1.55 Derived: relation_of2_as_subset(the_L_join(c5),cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)). [resolve(298,a,295,a)].
% 0.86/1.55 299 join_semilatt_str(c6). [resolve(245,a,204,a)].
% 0.86/1.55 Derived: function(the_L_join(c6)). [resolve(299,a,293,a)].
% 0.86/1.55 Derived: quasi_total(the_L_join(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(299,a,294,a)].
% 0.86/1.55 Derived: relation_of2_as_subset(the_L_join(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(299,a,295,a)].
% 0.86/1.55 300 join_semilatt_str(c7). [resolve(246,a,204,a)].
% 0.86/1.55 Derived: function(the_L_join(c7)). [resolve(300,a,293,a)].
% 0.86/1.55 Derived: quasi_total(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(300,a,294,a)].
% 0.86/1.55 Derived: relation_of2_as_subset(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(300,a,295,a)].
% 0.86/1.55 301 join_semilatt_str(c8). [resolve(247,a,204,a)].
% 0.86/1.55 Derived: function(the_L_join(c8)). [resolve(301,a,293,a)].
% 0.86/1.55 Derived: quasi_total(the_L_join(c8),cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)). [resolve(301,a,294,a)].
% 0.86/1.55 Derived: relation_of2_as_subset(the_L_join(c8),cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)). [resolve(301,a,295,a)].
% 0.86/1.55 302 join_semilatt_str(c9). [resolve(248,a,204,a)].
% 0.86/1.55 Derived: function(the_L_join(c9)). [resolve(302,a,293,a)].
% 0.86/1.55 Derived: quasi_total(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(302,a,294,a)].
% 0.86/1.55 Derived: relation_of2_as_subset(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(302,a,295,a)].
% 0.86/1.55 303 join_semilatt_str(c18). [resolve(249,a,204,a)].
% 0.86/1.55 Derived: function(the_L_join(c18)). [resolve(303,a,293,a)].
% 0.86/1.55 Derived: quasi_total(the_L_join(c18),cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)). [resolve(303,a,294,a)].
% 0.86/1.55 Derived: relation_of2_as_subset(the_L_join(c18),cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)). [resolve(303,a,295,a)].
% 0.86/1.55 304 join_semilatt_str(c20). [resolve(250,a,204,a)].
% 0.86/1.55 Derived: function(the_L_join(c20)). [resolve(304,a,293,a)].
% 0.86/1.55 Derived: quasi_total(the_L_join(c20),cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)). [resolve(304,a,294,a)].
% 0.86/1.55 Derived: relation_of2_as_subset(the_L_join(c20),cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)). [resolve(304,a,295,a)].
% 0.86/1.55 305 join_semilatt_str(c21). [resolve(251,a,204,a)].
% 0.86/1.55 Derived: function(the_L_join(c21)). [resolve(305,a,293,a)].
% 0.86/1.55 Derived: quasi_total(the_L_join(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(305,a,294,a)].
% 0.86/1.55 Derived: relation_of2_as_subset(the_L_join(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(305,a,295,a)].
% 0.86/1.55 306 relation_of2_as_subset(f3(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(59)].
% 0.86/1.55 307 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(47)].
% 0.86/1.55 Derived: element(f3(A,B),powerset(cartesian_product2(A,B))). [resolve(306,a,307,a)].
% 0.86/1.55 308 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(104)].
% 0.86/1.55 Derived: relation_of2(f3(A,B),A,B). [resolve(308,a,306,a)].
% 0.86/1.55 309 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(104)].
% 0.86/1.56 Derived: -relation_of2(A,B,C) | element(A,powerset(cartesian_product2(B,C))). [resolve(309,a,307,a)].
% 0.86/1.56 310 relation_of2_as_subset(the_InternalRel(rel_str_of(A,B)),the_carrier(rel_str_of(A,B)),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(139,a,121,b)].
% 0.86/1.56 Derived: -relation_of2(A,B,B) | element(the_InternalRel(rel_str_of(B,A)),powerset(cartesian_product2(the_carrier(rel_str_of(B,A)),the_carrier(rel_str_of(B,A))))). [resolve(310,a,307,a)].
% 0.86/1.56 Derived: -relation_of2(A,B,B) | relation_of2(the_InternalRel(rel_str_of(B,A)),the_carrier(rel_str_of(B,A)),the_carrier(rel_str_of(B,A))). [resolve(310,a,308,a)].
% 0.86/1.56 311 relation_of2_as_subset(the_InternalRel(boole_POSet(A)),the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))). [resolve(139,a,137,a)].
% 0.86/1.56 Derived: element(the_InternalRel(boole_POSet(A)),powerset(cartesian_product2(the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))))). [resolve(311,a,307,a)].
% 0.86/1.56 Derived: relation_of2(the_InternalRel(boole_POSet(A)),the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))). [resolve(311,a,308,a)].
% 0.86/1.56 312 relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(140,a,139,a)].
% 0.86/1.56 Derived: element(the_InternalRel(c2),powerset(cartesian_product2(the_carrier(c2),the_carrier(c2)))). [resolve(312,a,307,a)].
% 0.86/1.56 Derived: relation_of2(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(312,a,308,a)].
% 0.86/1.56 313 relation_of2_as_subset(the_InternalRel(c10),the_carrier(c10),the_carrier(c10)). [resolve(146,a,139,a)].
% 0.86/1.56 Derived: element(the_InternalRel(c10),powerset(cartesian_product2(the_carrier(c10),the_carrier(c10)))). [resolve(313,a,307,a)].
% 0.86/1.56 Derived: relation_of2(the_InternalRel(c10),the_carrier(c10),the_carrier(c10)). [resolve(313,a,308,a)].
% 0.86/1.56 314 relation_of2_as_subset(the_InternalRel(c11),the_carrier(c11),the_carrier(c11)). [resolve(147,a,139,a)].
% 0.86/1.56 Derived: element(the_InternalRel(c11),powerset(cartesian_product2(the_carrier(c11),the_carrier(c11)))). [resolve(314,a,307,a)].
% 0.86/1.56 Derived: relation_of2(the_InternalRel(c11),the_carrier(c11),the_carrier(c11)). [resolve(314,a,308,a)].
% 0.86/1.56 315 relation_of2_as_subset(the_InternalRel(c13),the_carrier(c13),the_carrier(c13)). [resolve(148,a,139,a)].
% 0.86/1.56 Derived: element(the_InternalRel(c13),powerset(cartesian_product2(the_carrier(c13),the_carrier(c13)))). [resolve(315,a,307,a)].
% 0.86/1.56 Derived: relation_of2(the_InternalRel(c13),the_carrier(c13),the_carrier(c13)). [resolve(315,a,308,a)].
% 0.86/1.56 316 relation_of2_as_subset(the_InternalRel(c14),the_carrier(c14),the_carrier(c14)). [resolve(149,a,139,a)].
% 0.86/1.56 Derived: element(the_InternalRel(c14),powerset(cartesian_product2(the_carrier(c14),the_carrier(c14)))). [resolve(316,a,307,a)].
% 0.86/1.56 Derived: relation_of2(the_InternalRel(c14),the_carrier(c14),the_carrier(c14)). [resolve(316,a,308,a)].
% 0.86/1.56 317 relation_of2_as_subset(the_InternalRel(c15),the_carrier(c15),the_carrier(c15)). [resolve(150,a,139,a)].
% 0.86/1.56 Derived: element(the_InternalRel(c15),powerset(cartesian_product2(the_carrier(c15),the_carrier(c15)))). [resolve(317,a,307,a)].
% 0.86/1.56 Derived: relation_of2(the_InternalRel(c15),the_carrier(c15),the_carrier(c15)). [resolve(317,a,308,a)].
% 0.86/1.56 318 relation_of2_as_subset(the_InternalRel(c17),the_carrier(c17),the_carrier(c17)). [resolve(151,a,139,a)].
% 0.86/1.56 Derived: element(the_InternalRel(c17),powerset(cartesian_product2(the_carrier(c17),the_carrier(c17)))). [resolve(318,a,307,a)].
% 0.86/1.56 Derived: relation_of2(the_InternalRel(c17),the_carrier(c17),the_carrier(c17)). [resolve(318,a,308,a)].
% 0.86/1.56 319 empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | relation_of2_as_subset(k2_lattice3(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(196,c,155,g)].
% 0.86/1.56 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | element(k2_lattice3(latt_str_of(A,B,C)),powerset(cartesian_product2(the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))))). [resolve(319,c,307,a)].
% 0.86/1.57 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | relation_of2(k2_lattice3(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))). [resolve(319,c,308,a)].
% 0.86/1.57 320 empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | relation_of2_as_subset(k2_lattice3(boole_lattice(A)),the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(196,c,191,a)].
% 0.86/1.57 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | element(k2_lattice3(boole_lattice(A)),powerset(cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))))). [resolve(320,c,307,a)].
% 0.86/1.57 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | relation_of2(k2_lattice3(boole_lattice(A)),the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(320,c,308,a)].
% 0.86/1.57 321 empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(205,a,196,c)].
% 0.86/1.57 Derived: empty_carrier(c5) | -lattice(c5) | element(k2_lattice3(c5),powerset(cartesian_product2(the_carrier(c5),the_carrier(c5)))). [resolve(321,c,307,a)].
% 0.86/1.57 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(321,c,308,a)].
% 0.86/1.57 322 empty_carrier(c6) | -lattice(c6) | relation_of2_as_subset(k2_lattice3(c6),the_carrier(c6),the_carrier(c6)). [resolve(245,a,196,c)].
% 0.86/1.57 Derived: empty_carrier(c6) | -lattice(c6) | element(k2_lattice3(c6),powerset(cartesian_product2(the_carrier(c6),the_carrier(c6)))). [resolve(322,c,307,a)].
% 0.86/1.57 Derived: empty_carrier(c6) | -lattice(c6) | relation_of2(k2_lattice3(c6),the_carrier(c6),the_carrier(c6)). [resolve(322,c,308,a)].
% 0.86/1.57 323 empty_carrier(c7) | -lattice(c7) | relation_of2_as_subset(k2_lattice3(c7),the_carrier(c7),the_carrier(c7)). [resolve(246,a,196,c)].
% 0.86/1.57 Derived: empty_carrier(c7) | -lattice(c7) | element(k2_lattice3(c7),powerset(cartesian_product2(the_carrier(c7),the_carrier(c7)))). [resolve(323,c,307,a)].
% 0.86/1.57 Derived: empty_carrier(c7) | -lattice(c7) | relation_of2(k2_lattice3(c7),the_carrier(c7),the_carrier(c7)). [resolve(323,c,308,a)].
% 0.86/1.57 324 empty_carrier(c8) | -lattice(c8) | relation_of2_as_subset(k2_lattice3(c8),the_carrier(c8),the_carrier(c8)). [resolve(247,a,196,c)].
% 0.86/1.57 Derived: empty_carrier(c8) | -lattice(c8) | element(k2_lattice3(c8),powerset(cartesian_product2(the_carrier(c8),the_carrier(c8)))). [resolve(324,c,307,a)].
% 0.86/1.57 Derived: empty_carrier(c8) | -lattice(c8) | relation_of2(k2_lattice3(c8),the_carrier(c8),the_carrier(c8)). [resolve(324,c,308,a)].
% 0.86/1.57 325 empty_carrier(c9) | -lattice(c9) | relation_of2_as_subset(k2_lattice3(c9),the_carrier(c9),the_carrier(c9)). [resolve(248,a,196,c)].
% 0.86/1.57 Derived: empty_carrier(c9) | -lattice(c9) | element(k2_lattice3(c9),powerset(cartesian_product2(the_carrier(c9),the_carrier(c9)))). [resolve(325,c,307,a)].
% 0.86/1.57 Derived: empty_carrier(c9) | -lattice(c9) | relation_of2(k2_lattice3(c9),the_carrier(c9),the_carrier(c9)). [resolve(325,c,308,a)].
% 0.86/1.57 326 empty_carrier(c18) | -lattice(c18) | relation_of2_as_subset(k2_lattice3(c18),the_carrier(c18),the_carrier(c18)). [resolve(249,a,196,c)].
% 0.86/1.57 Derived: empty_carrier(c18) | -lattice(c18) | element(k2_lattice3(c18),powerset(cartesian_product2(the_carrier(c18),the_carrier(c18)))). [resolve(326,c,307,a)].
% 0.86/1.57 Derived: empty_carrier(c18) | -lattice(c18) | relation_of2(k2_lattice3(c18),the_carrier(c18),the_carrier(c18)). [resolve(326,c,308,a)].
% 0.86/1.57 327 empty_carrier(c20) | -lattice(c20) | relation_of2_as_subset(k2_lattice3(c20),the_carrier(c20),the_carrier(c20)). [resolve(250,a,196,c)].
% 0.86/1.57 Derived: empty_carrier(c20) | -lattice(c20) | element(k2_lattice3(c20),powerset(cartesian_product2(the_carrier(c20),the_carrier(c20)))). [resolve(327,c,307,a)].
% 0.86/1.59 Derived: empty_carrier(c20) | -lattice(c20) | relation_of2(k2_lattice3(c20),the_carrier(c20),the_carrier(c20)). [resolve(327,c,308,a)].
% 0.86/1.59 328 empty_carrier(c21) | -lattice(c21) | relation_of2_as_subset(k2_lattice3(c21),the_carrier(c21),the_carrier(c21)). [resolve(251,a,196,c)].
% 0.86/1.59 Derived: empty_carrier(c21) | -lattice(c21) | element(k2_lattice3(c21),powerset(cartesian_product2(the_carrier(c21),the_carrier(c21)))). [resolve(328,c,307,a)].
% 0.86/1.59 Derived: empty_carrier(c21) | -lattice(c21) | relation_of2(k2_lattice3(c21),the_carrier(c21),the_carrier(c21)). [resolve(328,c,308,a)].
% 0.86/1.59 329 relation_of2_as_subset(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),the_carrier(poset_of_lattice(latt_str_of(A,B,C))),the_carrier(poset_of_lattice(latt_str_of(A,B,C)))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(267,d,155,g)].
% 0.86/1.59 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | element(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),powerset(cartesian_product2(the_carrier(poset_of_lattice(latt_str_of(A,B,C))),the_carrier(poset_of_lattice(latt_str_of(A,B,C)))))). [resolve(329,a,307,a)].
% 0.86/1.59 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | relation_of2(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),the_carrier(poset_of_lattice(latt_str_of(A,B,C))),the_carrier(poset_of_lattice(latt_str_of(A,B,C)))). [resolve(329,a,308,a)].
% 0.86/1.59 330 relation_of2_as_subset(the_InternalRel(poset_of_lattice(boole_lattice(A))),the_carrier(poset_of_lattice(boole_lattice(A))),the_carrier(poset_of_lattice(boole_lattice(A)))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(267,d,191,a)].
% 0.86/1.59 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | element(the_InternalRel(poset_of_lattice(boole_lattice(A))),powerset(cartesian_product2(the_carrier(poset_of_lattice(boole_lattice(A))),the_carrier(poset_of_lattice(boole_lattice(A)))))). [resolve(330,a,307,a)].
% 0.86/1.59 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | relation_of2(the_InternalRel(poset_of_lattice(boole_lattice(A))),the_carrier(poset_of_lattice(boole_lattice(A))),the_carrier(poset_of_lattice(boole_lattice(A)))). [resolve(330,a,308,a)].
% 0.86/1.59 331 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(267,d,205,a)].
% 0.86/1.59 Derived: empty_carrier(c5) | -lattice(c5) | element(the_InternalRel(poset_of_lattice(c5)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))))). [resolve(331,a,307,a)].
% 0.86/1.59 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))). [resolve(331,a,308,a)].
% 0.86/1.59 332 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c6)),the_carrier(poset_of_lattice(c6)),the_carrier(poset_of_lattice(c6))) | empty_carrier(c6) | -lattice(c6). [resolve(267,d,245,a)].
% 0.86/1.59 Derived: empty_carrier(c6) | -lattice(c6) | element(the_InternalRel(poset_of_lattice(c6)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c6)),the_carrier(poset_of_lattice(c6))))). [resolve(332,a,307,a)].
% 0.86/1.59 Derived: empty_carrier(c6) | -lattice(c6) | relation_of2(the_InternalRel(poset_of_lattice(c6)),the_carrier(poset_of_lattice(c6)),the_carrier(poset_of_lattice(c6))). [resolve(332,a,308,a)].
% 0.86/1.60 333 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c7)),the_carrier(poset_of_lattice(c7)),the_carrier(poset_of_lattice(c7))) | empty_carrier(c7) | -lattice(c7). [resolve(267,d,246,a)].
% 0.86/1.60 Derived: empty_carrier(c7) | -lattice(c7) | element(the_InternalRel(poset_of_lattice(c7)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c7)),the_carrier(poset_of_lattice(c7))))). [resolve(333,a,307,a)].
% 0.86/1.60 Derived: empty_carrier(c7) | -lattice(c7) | relation_of2(the_InternalRel(poset_of_lattice(c7)),the_carrier(poset_of_lattice(c7)),the_carrier(poset_of_lattice(c7))). [resolve(333,a,308,a)].
% 0.86/1.60 334 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c8)),the_carrier(poset_of_lattice(c8)),the_carrier(poset_of_lattice(c8))) | empty_carrier(c8) | -lattice(c8). [resolve(267,d,247,a)].
% 0.86/1.60 Derived: empty_carrier(c8) | -lattice(c8) | element(the_InternalRel(poset_of_lattice(c8)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c8)),the_carrier(poset_of_lattice(c8))))). [resolve(334,a,307,a)].
% 0.86/1.60 Derived: empty_carrier(c8) | -lattice(c8) | relation_of2(the_InternalRel(poset_of_lattice(c8)),the_carrier(poset_of_lattice(c8)),the_carrier(poset_of_lattice(c8))). [resolve(334,a,308,a)].
% 0.86/1.60 335 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c9)),the_carrier(poset_of_lattice(c9)),the_carrier(poset_of_lattice(c9))) | empty_carrier(c9) | -lattice(c9). [resolve(267,d,248,a)].
% 0.86/1.60 Derived: empty_carrier(c9) | -lattice(c9) | element(the_InternalRel(poset_of_lattice(c9)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c9)),the_carrier(poset_of_lattice(c9))))). [resolve(335,a,307,a)].
% 0.86/1.60 Derived: empty_carrier(c9) | -lattice(c9) | relation_of2(the_InternalRel(poset_of_lattice(c9)),the_carrier(poset_of_lattice(c9)),the_carrier(poset_of_lattice(c9))). [resolve(335,a,308,a)].
% 0.86/1.60 336 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c18)),the_carrier(poset_of_lattice(c18)),the_carrier(poset_of_lattice(c18))) | empty_carrier(c18) | -lattice(c18). [resolve(267,d,249,a)].
% 0.86/1.60 Derived: empty_carrier(c18) | -lattice(c18) | element(the_InternalRel(poset_of_lattice(c18)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c18)),the_carrier(poset_of_lattice(c18))))). [resolve(336,a,307,a)].
% 0.86/1.60 Derived: empty_carrier(c18) | -lattice(c18) | relation_of2(the_InternalRel(poset_of_lattice(c18)),the_carrier(poset_of_lattice(c18)),the_carrier(poset_of_lattice(c18))). [resolve(336,a,308,a)].
% 0.86/1.60 337 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c20)),the_carrier(poset_of_lattice(c20)),the_carrier(poset_of_lattice(c20))) | empty_carrier(c20) | -lattice(c20). [resolve(267,d,250,a)].
% 0.86/1.60 Derived: empty_carrier(c20) | -lattice(c20) | element(the_InternalRel(poset_of_lattice(c20)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c20)),the_carrier(poset_of_lattice(c20))))). [resolve(337,a,307,a)].
% 0.86/1.60 Derived: empty_carrier(c20) | -lattice(c20) | relation_of2(the_InternalRel(poset_of_lattice(c20)),the_carrier(poset_of_lattice(c20)),the_carrier(poset_of_lattice(c20))). [resolve(337,a,308,a)].
% 0.86/1.60 338 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c21)),the_carrier(poset_of_lattice(c21)),the_carrier(poset_of_lattice(c21))) | empty_carrier(c21) | -lattice(c21). [resolve(267,d,251,a)].
% 0.86/1.60 Derived: empty_carrier(c21) | -lattice(c21) | element(the_InternalRel(poset_of_lattice(c21)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c21)),the_carrier(poset_of_lattice(c21))))). [resolve(338,a,307,a)].
% 0.86/1.60 Derived: empty_carrier(c21) | -lattice(c21) | relation_of2(the_InternalRel(poset_of_lattice(c21)),the_carrier(poset_of_lattice(c21)),the_carrier(poset_of_lattice(c21))). [resolve(338,a,308,a)].
% 0.86/1.60 339 relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(276,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(c1),powerset(cartesian_product2(cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)))). [resolve(339,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(339,a,308,a)].
% 0.86/1.60 340 -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2_as_subset(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(281,a,280,a)].
% 0.86/1.60 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | element(the_L_meet(latt_str_of(B,A,C)),powerset(cartesian_product2(cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))))). [resolve(340,g,307,a)].
% 0.86/1.60 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(340,g,308,a)].
% 0.86/1.60 341 relation_of2_as_subset(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(282,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(boole_lattice(A)),powerset(cartesian_product2(cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))))). [resolve(341,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(341,a,308,a)].
% 0.86/1.60 342 relation_of2_as_subset(the_L_meet(c5),cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)). [resolve(283,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(c5),powerset(cartesian_product2(cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)))). [resolve(342,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(c5),cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)). [resolve(342,a,308,a)].
% 0.86/1.60 343 relation_of2_as_subset(the_L_meet(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(284,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(c6),powerset(cartesian_product2(cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)))). [resolve(343,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(343,a,308,a)].
% 0.86/1.60 344 relation_of2_as_subset(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(285,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(c7),powerset(cartesian_product2(cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)))). [resolve(344,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(344,a,308,a)].
% 0.86/1.60 345 relation_of2_as_subset(the_L_meet(c8),cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)). [resolve(286,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(c8),powerset(cartesian_product2(cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)))). [resolve(345,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(c8),cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)). [resolve(345,a,308,a)].
% 0.86/1.60 346 relation_of2_as_subset(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(287,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(c9),powerset(cartesian_product2(cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)))). [resolve(346,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(346,a,308,a)].
% 0.86/1.60 347 relation_of2_as_subset(the_L_meet(c18),cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)). [resolve(288,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(c18),powerset(cartesian_product2(cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)))). [resolve(347,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(c18),cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)). [resolve(347,a,308,a)].
% 0.86/1.60 348 relation_of2_as_subset(the_L_meet(c20),cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)). [resolve(289,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(c20),powerset(cartesian_product2(cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)))). [resolve(348,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(c20),cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)). [resolve(348,a,308,a)].
% 0.86/1.60 349 relation_of2_as_subset(the_L_meet(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(290,a,280,a)].
% 0.86/1.60 Derived: element(the_L_meet(c21),powerset(cartesian_product2(cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)))). [resolve(349,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_meet(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(349,a,308,a)].
% 0.86/1.60 350 relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(291,a,295,a)].
% 0.86/1.60 Derived: element(the_L_join(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(350,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(350,a,308,a)].
% 0.86/1.60 351 -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2_as_subset(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(296,a,295,a)].
% 0.86/1.60 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | element(the_L_join(latt_str_of(B,A,C)),powerset(cartesian_product2(cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))))). [resolve(351,g,307,a)].
% 0.86/1.60 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(351,g,308,a)].
% 0.86/1.60 352 relation_of2_as_subset(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(297,a,295,a)].
% 0.86/1.60 Derived: element(the_L_join(boole_lattice(A)),powerset(cartesian_product2(cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))))). [resolve(352,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(352,a,308,a)].
% 0.86/1.60 353 relation_of2_as_subset(the_L_join(c5),cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)). [resolve(298,a,295,a)].
% 0.86/1.60 Derived: element(the_L_join(c5),powerset(cartesian_product2(cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)))). [resolve(353,a,307,a)].
% 0.86/1.60 Derived: relation_of2(the_L_join(c5),cartesian_product2(the_carrier(c5),the_carrier(c5)),the_carrier(c5)). [resolve(353,a,308,a)].
% 0.86/1.60 354 relation_of2_as_subset(the_L_join(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(299,a,295,a)].
% 0.86/1.60 Derived: element(the_L_join(c6),powerset(cartesian_product2(cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)))). [resolve(354,a,307,a)].
% 0.86/1.62 Derived: relation_of2(the_L_join(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(354,a,308,a)].
% 0.86/1.62 355 relation_of2_as_subset(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(300,a,295,a)].
% 0.86/1.62 Derived: element(the_L_join(c7),powerset(cartesian_product2(cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)))). [resolve(355,a,307,a)].
% 0.86/1.62 Derived: relation_of2(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(355,a,308,a)].
% 0.86/1.62 356 relation_of2_as_subset(the_L_join(c8),cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)). [resolve(301,a,295,a)].
% 0.86/1.62 Derived: element(the_L_join(c8),powerset(cartesian_product2(cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)))). [resolve(356,a,307,a)].
% 0.86/1.62 Derived: relation_of2(the_L_join(c8),cartesian_product2(the_carrier(c8),the_carrier(c8)),the_carrier(c8)). [resolve(356,a,308,a)].
% 0.86/1.62 357 relation_of2_as_subset(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(302,a,295,a)].
% 0.86/1.62 Derived: element(the_L_join(c9),powerset(cartesian_product2(cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)))). [resolve(357,a,307,a)].
% 0.86/1.62 Derived: relation_of2(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(357,a,308,a)].
% 0.86/1.62 358 relation_of2_as_subset(the_L_join(c18),cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)). [resolve(303,a,295,a)].
% 0.86/1.62 Derived: element(the_L_join(c18),powerset(cartesian_product2(cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)))). [resolve(358,a,307,a)].
% 0.86/1.62 Derived: relation_of2(the_L_join(c18),cartesian_product2(the_carrier(c18),the_carrier(c18)),the_carrier(c18)). [resolve(358,a,308,a)].
% 0.86/1.62 359 relation_of2_as_subset(the_L_join(c20),cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)). [resolve(304,a,295,a)].
% 0.86/1.62 Derived: element(the_L_join(c20),powerset(cartesian_product2(cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)))). [resolve(359,a,307,a)].
% 0.86/1.62 Derived: relation_of2(the_L_join(c20),cartesian_product2(the_carrier(c20),the_carrier(c20)),the_carrier(c20)). [resolve(359,a,308,a)].
% 0.86/1.62 360 relation_of2_as_subset(the_L_join(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(305,a,295,a)].
% 0.86/1.62 Derived: element(the_L_join(c21),powerset(cartesian_product2(cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)))). [resolve(360,a,307,a)].
% 0.86/1.62 Derived: relation_of2(the_L_join(c21),cartesian_product2(the_carrier(c21),the_carrier(c21)),the_carrier(c21)). [resolve(360,a,308,a)].
% 0.86/1.62 361 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(63)].
% 0.86/1.62 362 one_sorted_str(c3) # label(existence_l1_struct_0) # label(axiom). [clausify(54)].
% 0.86/1.62 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(361,b,362,a)].
% 0.86/1.62 363 one_sorted_str(c19) # label(rc3_struct_0) # label(axiom). [clausify(99)].
% 0.86/1.62 Derived: empty_carrier(c19) | -empty(the_carrier(c19)). [resolve(363,a,361,b)].
% 0.86/1.62 364 empty_carrier(A) | -one_sorted_str(A) | element(f7(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(100)].
% 0.86/1.62 Derived: empty_carrier(c3) | element(f7(c3),powerset(the_carrier(c3))). [resolve(364,b,362,a)].
% 0.86/1.62 Derived: empty_carrier(c19) | element(f7(c19),powerset(the_carrier(c19))). [resolve(364,b,363,a)].
% 0.86/1.62 365 empty_carrier(A) | -one_sorted_str(A) | -empty(f7(A)) # label(rc5_struct_0) # label(axiom). [clausify(100)].
% 0.86/1.62 Derived: empty_carrier(c3) | -empty(f7(c3)). [resolve(365,b,362,a)].
% 0.86/1.62 Derived: empty_carrier(c19) | -empty(f7(c19)). [resolve(365,b,363,a)].
% 0.86/1.62 366 one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(138,a,121,b)].
% 0.86/1.62 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(the_carrier(rel_str_of(B,A))). [resolve(366,a,361,b)].
% 0.86/1.62 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | element(f7(rel_str_of(B,A)),powerset(the_carrier(rel_str_of(B,A)))). [resolve(366,a,364,b)].
% 0.86/1.64 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(f7(rel_str_of(B,A))). [resolve(366,a,365,b)].
% 0.86/1.64 367 one_sorted_str(boole_POSet(A)). [resolve(138,a,137,a)].
% 0.86/1.64 Derived: empty_carrier(boole_POSet(A)) | -empty(the_carrier(boole_POSet(A))). [resolve(367,a,361,b)].
% 0.86/1.64 Derived: empty_carrier(boole_POSet(A)) | element(f7(boole_POSet(A)),powerset(the_carrier(boole_POSet(A)))). [resolve(367,a,364,b)].
% 0.86/1.64 Derived: empty_carrier(boole_POSet(A)) | -empty(f7(boole_POSet(A))). [resolve(367,a,365,b)].
% 0.86/1.64 368 one_sorted_str(c2). [resolve(140,a,138,a)].
% 0.86/1.64 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(368,a,361,b)].
% 0.86/1.64 Derived: empty_carrier(c2) | element(f7(c2),powerset(the_carrier(c2))). [resolve(368,a,364,b)].
% 0.86/1.64 Derived: empty_carrier(c2) | -empty(f7(c2)). [resolve(368,a,365,b)].
% 0.86/1.64 369 one_sorted_str(c10). [resolve(146,a,138,a)].
% 0.86/1.64 Derived: empty_carrier(c10) | -empty(the_carrier(c10)). [resolve(369,a,361,b)].
% 0.86/1.65 Derived: empty_carrier(c10) | element(f7(c10),powerset(the_carrier(c10))). [resolve(369,a,364,b)].
% 0.86/1.65 Derived: empty_carrier(c10) | -empty(f7(c10)). [resolve(369,a,365,b)].
% 0.86/1.65 370 one_sorted_str(c11). [resolve(147,a,138,a)].
% 0.86/1.65 Derived: empty_carrier(c11) | -empty(the_carrier(c11)). [resolve(370,a,361,b)].
% 0.86/1.65 Derived: empty_carrier(c11) | element(f7(c11),powerset(the_carrier(c11))). [resolve(370,a,364,b)].
% 0.86/1.65 Derived: empty_carrier(c11) | -empty(f7(c11)). [resolve(370,a,365,b)].
% 0.86/1.65 371 one_sorted_str(c13). [resolve(148,a,138,a)].
% 0.86/1.65 Derived: empty_carrier(c13) | -empty(the_carrier(c13)). [resolve(371,a,361,b)].
% 0.86/1.65 Derived: empty_carrier(c13) | element(f7(c13),powerset(the_carrier(c13))). [resolve(371,a,364,b)].
% 0.86/1.65 Derived: empty_carrier(c13) | -empty(f7(c13)). [resolve(371,a,365,b)].
% 0.86/1.65 372 one_sorted_str(c14). [resolve(149,a,138,a)].
% 0.86/1.65 Derived: empty_carrier(c14) | -empty(the_carrier(c14)). [resolve(372,a,361,b)].
% 0.86/1.65 Derived: empty_carrier(c14) | element(f7(c14),powerset(the_carrier(c14))). [resolve(372,a,364,b)].
% 0.86/1.65 Derived: empty_carrier(c14) | -empty(f7(c14)). [resolve(372,a,365,b)].
% 0.86/1.65 373 one_sorted_str(c15). [resolve(150,a,138,a)].
% 0.86/1.65 Derived: empty_carrier(c15) | -empty(the_carrier(c15)). [resolve(373,a,361,b)].
% 0.86/1.65 Derived: empty_carrier(c15) | element(f7(c15),powerset(the_carrier(c15))). [resolve(373,a,364,b)].
% 0.86/1.65 Derived: empty_carrier(c15) | -empty(f7(c15)). [resolve(373,a,365,b)].
% 0.86/1.65 374 one_sorted_str(c17). [resolve(151,a,138,a)].
% 0.86/1.65 Derived: empty_carrier(c17) | -empty(the_carrier(c17)). [resolve(374,a,361,b)].
% 0.86/1.65 Derived: empty_carrier(c17) | element(f7(c17),powerset(the_carrier(c17))). [resolve(374,a,364,b)].
% 0.86/1.65 Derived: empty_carrier(c17) | -empty(f7(c17)). [resolve(374,a,365,b)].
% 0.86/1.65 375 one_sorted_str(poset_of_lattice(latt_str_of(A,B,C))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(266,d,155,g)].
% 0.86/1.65 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | empty_carrier(poset_of_lattice(latt_str_of(A,B,C))) | -empty(the_carrier(poset_of_lattice(latt_str_of(A,B,C)))). [resolve(375,a,361,b)].
% 0.86/1.65 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | empty_carrier(poset_of_lattice(latt_str_of(A,B,C))) | element(f7(poset_of_lattice(latt_str_of(A,B,C))),powerset(the_carrier(poset_of_lattice(latt_str_of(A,B,C))))). [resolve(375,a,364,b)].
% 0.86/1.65 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | empty_carrier(poset_of_lattice(latt_str_of(A,B,C))) | -empty(f7(poset_of_lattice(latt_str_of(A,B,C)))). [resolve(375,a,365,b)].
% 1.40/1.65 376 one_sorted_str(poset_of_lattice(boole_lattice(A))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(266,d,191,a)].
% 1.40/1.65 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | empty_carrier(poset_of_lattice(boole_lattice(A))) | -empty(the_carrier(poset_of_lattice(boole_lattice(A)))). [resolve(376,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | empty_carrier(poset_of_lattice(boole_lattice(A))) | element(f7(poset_of_lattice(boole_lattice(A))),powerset(the_carrier(poset_of_lattice(boole_lattice(A))))). [resolve(376,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | empty_carrier(poset_of_lattice(boole_lattice(A))) | -empty(f7(poset_of_lattice(boole_lattice(A)))). [resolve(376,a,365,b)].
% 1.40/1.65 377 one_sorted_str(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5). [resolve(266,d,205,a)].
% 1.40/1.65 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -empty(the_carrier(poset_of_lattice(c5))). [resolve(377,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | element(f7(poset_of_lattice(c5)),powerset(the_carrier(poset_of_lattice(c5)))). [resolve(377,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -empty(f7(poset_of_lattice(c5))). [resolve(377,a,365,b)].
% 1.40/1.65 378 one_sorted_str(poset_of_lattice(c6)) | empty_carrier(c6) | -lattice(c6). [resolve(266,d,245,a)].
% 1.40/1.65 Derived: empty_carrier(c6) | -lattice(c6) | empty_carrier(poset_of_lattice(c6)) | -empty(the_carrier(poset_of_lattice(c6))). [resolve(378,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c6) | -lattice(c6) | empty_carrier(poset_of_lattice(c6)) | element(f7(poset_of_lattice(c6)),powerset(the_carrier(poset_of_lattice(c6)))). [resolve(378,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c6) | -lattice(c6) | empty_carrier(poset_of_lattice(c6)) | -empty(f7(poset_of_lattice(c6))). [resolve(378,a,365,b)].
% 1.40/1.65 379 one_sorted_str(poset_of_lattice(c7)) | empty_carrier(c7) | -lattice(c7). [resolve(266,d,246,a)].
% 1.40/1.65 Derived: empty_carrier(c7) | -lattice(c7) | empty_carrier(poset_of_lattice(c7)) | -empty(the_carrier(poset_of_lattice(c7))). [resolve(379,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c7) | -lattice(c7) | empty_carrier(poset_of_lattice(c7)) | element(f7(poset_of_lattice(c7)),powerset(the_carrier(poset_of_lattice(c7)))). [resolve(379,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c7) | -lattice(c7) | empty_carrier(poset_of_lattice(c7)) | -empty(f7(poset_of_lattice(c7))). [resolve(379,a,365,b)].
% 1.40/1.65 380 one_sorted_str(poset_of_lattice(c8)) | empty_carrier(c8) | -lattice(c8). [resolve(266,d,247,a)].
% 1.40/1.65 Derived: empty_carrier(c8) | -lattice(c8) | empty_carrier(poset_of_lattice(c8)) | -empty(the_carrier(poset_of_lattice(c8))). [resolve(380,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c8) | -lattice(c8) | empty_carrier(poset_of_lattice(c8)) | element(f7(poset_of_lattice(c8)),powerset(the_carrier(poset_of_lattice(c8)))). [resolve(380,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c8) | -lattice(c8) | empty_carrier(poset_of_lattice(c8)) | -empty(f7(poset_of_lattice(c8))). [resolve(380,a,365,b)].
% 1.40/1.65 381 one_sorted_str(poset_of_lattice(c9)) | empty_carrier(c9) | -lattice(c9). [resolve(266,d,248,a)].
% 1.40/1.65 Derived: empty_carrier(c9) | -lattice(c9) | empty_carrier(poset_of_lattice(c9)) | -empty(the_carrier(poset_of_lattice(c9))). [resolve(381,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c9) | -lattice(c9) | empty_carrier(poset_of_lattice(c9)) | element(f7(poset_of_lattice(c9)),powerset(the_carrier(poset_of_lattice(c9)))). [resolve(381,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c9) | -lattice(c9) | empty_carrier(poset_of_lattice(c9)) | -empty(f7(poset_of_lattice(c9))). [resolve(381,a,365,b)].
% 1.40/1.65 382 one_sorted_str(poset_of_lattice(c18)) | empty_carrier(c18) | -lattice(c18). [resolve(266,d,249,a)].
% 1.40/1.65 Derived: empty_carrier(c18) | -lattice(c18) | empty_carrier(poset_of_lattice(c18)) | -empty(the_carrier(poset_of_lattice(c18))). [resolve(382,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c18) | -lattice(c18) | empty_carrier(poset_of_lattice(c18)) | element(f7(poset_of_lattice(c18)),powerset(the_carrier(poset_of_lattice(c18)))). [resolve(382,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c18) | -lattice(c18) | empty_carrier(poset_of_lattice(c18)) | -empty(f7(poset_of_lattice(c18))). [resolve(382,a,365,b)].
% 1.40/1.65 383 one_sorted_str(poset_of_lattice(c20)) | empty_carrier(c20) | -lattice(c20). [resolve(266,d,250,a)].
% 1.40/1.65 Derived: empty_carrier(c20) | -lattice(c20) | empty_carrier(poset_of_lattice(c20)) | -empty(the_carrier(poset_of_lattice(c20))). [resolve(383,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c20) | -lattice(c20) | empty_carrier(poset_of_lattice(c20)) | element(f7(poset_of_lattice(c20)),powerset(the_carrier(poset_of_lattice(c20)))). [resolve(383,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c20) | -lattice(c20) | empty_carrier(poset_of_lattice(c20)) | -empty(f7(poset_of_lattice(c20))). [resolve(383,a,365,b)].
% 1.40/1.65 384 one_sorted_str(poset_of_lattice(c21)) | empty_carrier(c21) | -lattice(c21). [resolve(266,d,251,a)].
% 1.40/1.65 Derived: empty_carrier(c21) | -lattice(c21) | empty_carrier(poset_of_lattice(c21)) | -empty(the_carrier(poset_of_lattice(c21))). [resolve(384,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c21) | -lattice(c21) | empty_carrier(poset_of_lattice(c21)) | element(f7(poset_of_lattice(c21)),powerset(the_carrier(poset_of_lattice(c21)))). [resolve(384,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c21) | -lattice(c21) | empty_carrier(poset_of_lattice(c21)) | -empty(f7(poset_of_lattice(c21))). [resolve(384,a,365,b)].
% 1.40/1.65 385 one_sorted_str(c1). [resolve(276,a,277,a)].
% 1.40/1.65 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(385,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c1) | element(f7(c1),powerset(the_carrier(c1))). [resolve(385,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c1) | -empty(f7(c1)). [resolve(385,a,365,b)].
% 1.40/1.65 386 -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | one_sorted_str(latt_str_of(B,A,C)). [resolve(281,a,277,a)].
% 1.40/1.65 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -empty(the_carrier(latt_str_of(B,A,C))). [resolve(386,g,361,b)].
% 1.40/1.65 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | element(f7(latt_str_of(B,A,C)),powerset(the_carrier(latt_str_of(B,A,C)))). [resolve(386,g,364,b)].
% 1.40/1.65 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -empty(f7(latt_str_of(B,A,C))). [resolve(386,g,365,b)].
% 1.40/1.65 387 one_sorted_str(boole_lattice(A)). [resolve(282,a,277,a)].
% 1.40/1.65 Derived: empty_carrier(boole_lattice(A)) | -empty(the_carrier(boole_lattice(A))). [resolve(387,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(boole_lattice(A)) | element(f7(boole_lattice(A)),powerset(the_carrier(boole_lattice(A)))). [resolve(387,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(boole_lattice(A)) | -empty(f7(boole_lattice(A))). [resolve(387,a,365,b)].
% 1.40/1.65 388 one_sorted_str(c5). [resolve(283,a,277,a)].
% 1.40/1.65 Derived: empty_carrier(c5) | -empty(the_carrier(c5)). [resolve(388,a,361,b)].
% 1.40/1.65 Derived: empty_carrier(c5) | element(f7(c5),powerset(the_carrier(c5))). [resolve(388,a,364,b)].
% 1.40/1.65 Derived: empty_carrier(c5) | -empty(f7(c5)). [resolve(388,a,365,b)].
% 1.40/1.65 389 one_sorted_str(c6). [resolve(284,a,277,a)].
% 1.40/1.65 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(389,a,361,b)].
% 1.43/1.72 Derived: empty_carrier(c6) | element(f7(c6),powerset(the_carrier(c6))). [resolve(389,a,364,b)].
% 1.43/1.72 Derived: empty_carrier(c6) | -empty(f7(c6)). [resolve(389,a,365,b)].
% 1.43/1.72 390 one_sorted_str(c7). [resolve(285,a,277,a)].
% 1.43/1.72 Derived: empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(390,a,361,b)].
% 1.43/1.72 Derived: empty_carrier(c7) | element(f7(c7),powerset(the_carrier(c7))). [resolve(390,a,364,b)].
% 1.43/1.72 Derived: empty_carrier(c7) | -empty(f7(c7)). [resolve(390,a,365,b)].
% 1.43/1.72 391 one_sorted_str(c8). [resolve(286,a,277,a)].
% 1.43/1.72 Derived: empty_carrier(c8) | -empty(the_carrier(c8)). [resolve(391,a,361,b)].
% 1.43/1.72 Derived: empty_carrier(c8) | element(f7(c8),powerset(the_carrier(c8))). [resolve(391,a,364,b)].
% 1.43/1.72 Derived: empty_carrier(c8) | -empty(f7(c8)). [resolve(391,a,365,b)].
% 1.43/1.72 392 one_sorted_str(c9). [resolve(287,a,277,a)].
% 1.43/1.72 Derived: empty_carrier(c9) | -empty(the_carrier(c9)). [resolve(392,a,361,b)].
% 1.43/1.72 Derived: empty_carrier(c9) | element(f7(c9),powerset(the_carrier(c9))). [resolve(392,a,364,b)].
% 1.43/1.72 Derived: empty_carrier(c9) | -empty(f7(c9)). [resolve(392,a,365,b)].
% 1.43/1.72 393 one_sorted_str(c18). [resolve(288,a,277,a)].
% 1.43/1.72 Derived: empty_carrier(c18) | -empty(the_carrier(c18)). [resolve(393,a,361,b)].
% 1.43/1.72 Derived: empty_carrier(c18) | element(f7(c18),powerset(the_carrier(c18))). [resolve(393,a,364,b)].
% 1.43/1.72 Derived: empty_carrier(c18) | -empty(f7(c18)). [resolve(393,a,365,b)].
% 1.43/1.72 394 one_sorted_str(c20). [resolve(289,a,277,a)].
% 1.43/1.72 Derived: empty_carrier(c20) | -empty(the_carrier(c20)). [resolve(394,a,361,b)].
% 1.43/1.72 Derived: empty_carrier(c20) | element(f7(c20),powerset(the_carrier(c20))). [resolve(394,a,364,b)].
% 1.43/1.72 Derived: empty_carrier(c20) | -empty(f7(c20)). [resolve(394,a,365,b)].
% 1.43/1.72 395 one_sorted_str(c21). [resolve(290,a,277,a)].
% 1.43/1.72 Derived: empty_carrier(c21) | -empty(the_carrier(c21)). [resolve(395,a,361,b)].
% 1.43/1.72 Derived: empty_carrier(c21) | element(f7(c21),powerset(the_carrier(c21))). [resolve(395,a,364,b)].
% 1.43/1.72 Derived: empty_carrier(c21) | -empty(f7(c21)). [resolve(395,a,365,b)].
% 1.43/1.72 396 one_sorted_str(c4). [resolve(291,a,292,a)].
% 1.43/1.72 Derived: empty_carrier(c4) | -empty(the_carrier(c4)). [resolve(396,a,361,b)].
% 1.43/1.72 Derived: empty_carrier(c4) | element(f7(c4),powerset(the_carrier(c4))). [resolve(396,a,364,b)].
% 1.43/1.72 Derived: empty_carrier(c4) | -empty(f7(c4)). [resolve(396,a,365,b)].
% 1.43/1.72 397 -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | reflexive(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(142,d,121,b)].
% 1.43/1.72 398 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | strict_rel_str(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(73)].
% 1.43/1.72 399 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | reflexive_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(73)].
% 1.43/1.72 400 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | transitive_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(73)].
% 1.43/1.72 401 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | antisymmetric_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(73)].
% 1.43/1.72 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | strict_rel_str(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(397,d,398,a)].
% 1.43/1.72 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | reflexive_relstr(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(397,d,399,a)].
% 1.43/1.72 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | transitive_relstr(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(397,d,400,a)].
% 1.43/1.72 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | antisymmetric_relstr(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(397,d,401,a)].
% 1.43/1.72 402 -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | reflexive(the_InternalRel(boole_POSet(A))). [resolve(142,d,137,a)].
% 1.43/1.72 Derived: -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | -antisymmetric(the_InternalRel(boole_POSet(A))) | -transitive(the_InternalRel(boole_POSet(A))) | -v1_partfun1(the_InternalRel(boole_POSet(A)),B,B) | -relation_of2(the_InternalRel(boole_POSet(A)),B,B) | strict_rel_str(rel_str_of(B,the_InternalRel(boole_POSet(A)))). [resolve(402,d,398,a)].
% 1.43/1.72 Derived: -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | -antisymmetric(the_InternalRel(boole_POSet(A))) | -transitive(the_InternalRel(boole_POSet(A))) | -v1_partfun1(the_InternalRel(boole_POSet(A)),B,B) | -relation_of2(the_InternalRel(boole_POSet(A)),B,B) | reflexive_relstr(rel_str_of(B,the_InternalRel(boole_POSet(A)))). [resolve(402,d,399,a)].
% 1.43/1.72 Derived: -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | -antisymmetric(the_InternalRel(boole_POSet(A))) | -transitive(the_InternalRel(boole_POSet(A))) | -v1_partfun1(the_InternalRel(boole_POSet(A)),B,B) | -relation_of2(the_InternalRel(boole_POSet(A)),B,B) | transitive_relstr(rel_str_of(B,the_InternalRel(boole_POSet(A)))). [resolve(402,d,400,a)].
% 1.43/1.72 Derived: -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | -antisymmetric(the_InternalRel(boole_POSet(A))) | -transitive(the_InternalRel(boole_POSet(A))) | -v1_partfun1(the_InternalRel(boole_POSet(A)),B,B) | -relation_of2(the_InternalRel(boole_POSet(A)),B,B) | antisymmetric_relstr(rel_str_of(B,the_InternalRel(boole_POSet(A)))). [resolve(402,d,401,a)].
% 1.43/1.72 403 -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(142,d,140,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c2))). [resolve(403,d,398,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c2))). [resolve(403,d,399,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c2))). [resolve(403,d,400,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c2))). [resolve(403,d,401,a)].
% 1.43/1.72 404 -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | reflexive(the_InternalRel(c10)). [resolve(146,a,142,d)].
% 1.43/1.72 Derived: -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | -antisymmetric(the_InternalRel(c10)) | -transitive(the_InternalRel(c10)) | -v1_partfun1(the_InternalRel(c10),A,A) | -relation_of2(the_InternalRel(c10),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c10))). [resolve(404,d,398,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | -antisymmetric(the_InternalRel(c10)) | -transitive(the_InternalRel(c10)) | -v1_partfun1(the_InternalRel(c10),A,A) | -relation_of2(the_InternalRel(c10),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c10))). [resolve(404,d,399,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | -antisymmetric(the_InternalRel(c10)) | -transitive(the_InternalRel(c10)) | -v1_partfun1(the_InternalRel(c10),A,A) | -relation_of2(the_InternalRel(c10),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c10))). [resolve(404,d,400,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | -antisymmetric(the_InternalRel(c10)) | -transitive(the_InternalRel(c10)) | -v1_partfun1(the_InternalRel(c10),A,A) | -relation_of2(the_InternalRel(c10),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c10))). [resolve(404,d,401,a)].
% 1.43/1.72 405 -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | reflexive(the_InternalRel(c11)). [resolve(147,a,142,d)].
% 1.43/1.72 Derived: -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | -antisymmetric(the_InternalRel(c11)) | -transitive(the_InternalRel(c11)) | -v1_partfun1(the_InternalRel(c11),A,A) | -relation_of2(the_InternalRel(c11),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c11))). [resolve(405,d,398,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | -antisymmetric(the_InternalRel(c11)) | -transitive(the_InternalRel(c11)) | -v1_partfun1(the_InternalRel(c11),A,A) | -relation_of2(the_InternalRel(c11),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c11))). [resolve(405,d,399,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | -antisymmetric(the_InternalRel(c11)) | -transitive(the_InternalRel(c11)) | -v1_partfun1(the_InternalRel(c11),A,A) | -relation_of2(the_InternalRel(c11),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c11))). [resolve(405,d,400,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c11) | -transitive_relstr(c11) | -antisymmetric_relstr(c11) | -antisymmetric(the_InternalRel(c11)) | -transitive(the_InternalRel(c11)) | -v1_partfun1(the_InternalRel(c11),A,A) | -relation_of2(the_InternalRel(c11),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c11))). [resolve(405,d,401,a)].
% 1.43/1.72 406 -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | reflexive(the_InternalRel(c13)). [resolve(148,a,142,d)].
% 1.43/1.72 Derived: -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | -antisymmetric(the_InternalRel(c13)) | -transitive(the_InternalRel(c13)) | -v1_partfun1(the_InternalRel(c13),A,A) | -relation_of2(the_InternalRel(c13),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c13))). [resolve(406,d,398,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | -antisymmetric(the_InternalRel(c13)) | -transitive(the_InternalRel(c13)) | -v1_partfun1(the_InternalRel(c13),A,A) | -relation_of2(the_InternalRel(c13),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c13))). [resolve(406,d,399,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | -antisymmetric(the_InternalRel(c13)) | -transitive(the_InternalRel(c13)) | -v1_partfun1(the_InternalRel(c13),A,A) | -relation_of2(the_InternalRel(c13),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c13))). [resolve(406,d,400,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | -antisymmetric(the_InternalRel(c13)) | -transitive(the_InternalRel(c13)) | -v1_partfun1(the_InternalRel(c13),A,A) | -relation_of2(the_InternalRel(c13),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c13))). [resolve(406,d,401,a)].
% 1.43/1.72 407 -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | reflexive(the_InternalRel(c14)). [resolve(149,a,142,d)].
% 1.43/1.72 Derived: -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | -antisymmetric(the_InternalRel(c14)) | -transitive(the_InternalRel(c14)) | -v1_partfun1(the_InternalRel(c14),A,A) | -relation_of2(the_InternalRel(c14),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c14))). [resolve(407,d,398,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | -antisymmetric(the_InternalRel(c14)) | -transitive(the_InternalRel(c14)) | -v1_partfun1(the_InternalRel(c14),A,A) | -relation_of2(the_InternalRel(c14),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c14))). [resolve(407,d,399,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | -antisymmetric(the_InternalRel(c14)) | -transitive(the_InternalRel(c14)) | -v1_partfun1(the_InternalRel(c14),A,A) | -relation_of2(the_InternalRel(c14),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c14))). [resolve(407,d,400,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c14) | -transitive_relstr(c14) | -antisymmetric_relstr(c14) | -antisymmetric(the_InternalRel(c14)) | -transitive(the_InternalRel(c14)) | -v1_partfun1(the_InternalRel(c14),A,A) | -relation_of2(the_InternalRel(c14),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c14))). [resolve(407,d,401,a)].
% 1.43/1.72 408 -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | reflexive(the_InternalRel(c15)). [resolve(150,a,142,d)].
% 1.43/1.72 Derived: -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | -antisymmetric(the_InternalRel(c15)) | -transitive(the_InternalRel(c15)) | -v1_partfun1(the_InternalRel(c15),A,A) | -relation_of2(the_InternalRel(c15),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c15))). [resolve(408,d,398,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | -antisymmetric(the_InternalRel(c15)) | -transitive(the_InternalRel(c15)) | -v1_partfun1(the_InternalRel(c15),A,A) | -relation_of2(the_InternalRel(c15),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c15))). [resolve(408,d,399,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | -antisymmetric(the_InternalRel(c15)) | -transitive(the_InternalRel(c15)) | -v1_partfun1(the_InternalRel(c15),A,A) | -relation_of2(the_InternalRel(c15),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c15))). [resolve(408,d,400,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c15) | -transitive_relstr(c15) | -antisymmetric_relstr(c15) | -antisymmetric(the_InternalRel(c15)) | -transitive(the_InternalRel(c15)) | -v1_partfun1(the_InternalRel(c15),A,A) | -relation_of2(the_InternalRel(c15),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c15))). [resolve(408,d,401,a)].
% 1.43/1.72 409 -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | reflexive(the_InternalRel(c17)). [resolve(151,a,142,d)].
% 1.43/1.72 Derived: -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | -antisymmetric(the_InternalRel(c17)) | -transitive(the_InternalRel(c17)) | -v1_partfun1(the_InternalRel(c17),A,A) | -relation_of2(the_InternalRel(c17),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c17))). [resolve(409,d,398,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | -antisymmetric(the_InternalRel(c17)) | -transitive(the_InternalRel(c17)) | -v1_partfun1(the_InternalRel(c17),A,A) | -relation_of2(the_InternalRel(c17),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c17))). [resolve(409,d,399,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | -antisymmetric(the_InternalRel(c17)) | -transitive(the_InternalRel(c17)) | -v1_partfun1(the_InternalRel(c17),A,A) | -relation_of2(the_InternalRel(c17),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c17))). [resolve(409,d,400,a)].
% 1.43/1.72 Derived: -reflexive_relstr(c17) | -transitive_relstr(c17) | -antisymmetric_relstr(c17) | -antisymmetric(the_InternalRel(c17)) | -transitive(the_InternalRel(c17)) | -v1_partfun1(the_InternalRel(c17),A,A) | -relation_of2(the_InternalRel(c17),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c17))). [resolve(409,d,401,a)].
% 1.43/1.72 410 empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | reflexive(k2_lattice3(latt_str_of(A,B,C))) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(192,c,155,g)].
% 1.43/1.72 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -antisymmetric(k2_lattice3(latt_str_of(A,B,C))) | -transitive(k2_lattice3(latt_str_of(A,B,C))) | -v1_partfun1(k2_lattice3(latt_str_of(A,B,C)),D,D) | -relation_of2(k2_lattice3(latt_str_of(A,B,C)),D,D) | strict_rel_str(rel_str_of(D,k2_lattice3(latt_str_of(A,B,C)))). [resolve(410,c,398,a)].
% 1.43/1.72 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -antisymmetric(k2_lattice3(latt_str_of(A,B,C))) | -transitive(k2_lattice3(latt_str_of(A,B,C))) | -v1_partfun1(k2_lattice3(latt_str_of(A,B,C)),D,D) | -relation_of2(k2_lattice3(latt_str_of(A,B,C)),D,D) | reflexive_relstr(rel_str_of(D,k2_lattice3(latt_str_of(A,B,C)))). [resolve(410,c,399,a)].
% 1.43/1.72 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -antisymmetric(k2_lattice3(latt_str_of(A,B,C))) | -transitive(k2_lattice3(latt_str_of(A,B,C))) | -v1_partfun1(k2_lattice3(latt_str_of(A,B,C)),D,D) | -relation_of2(k2_lattice3(latt_str_of(A,B,C)),D,D) | transitive_relstr(rel_str_of(D,k2_lattice3(latt_str_of(A,B,C)))). [resolve(410,c,400,a)].
% 1.43/1.72 Derived: empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -antisymmetric(k2_lattice3(latt_str_of(A,B,C))) | -transitive(k2_lattice3(latt_str_of(A,B,C))) | -v1_partfun1(k2_lattice3(latt_str_of(A,B,C)),D,D) | -relation_of2(k2_lattice3(latt_str_of(A,B,C)),D,D) | antisymmetric_relstr(rel_str_of(D,k2_lattice3(latt_str_of(A,B,C)))). [resolve(410,c,401,a)].
% 1.43/1.72 411 empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | reflexive(k2_lattice3(boole_lattice(A))). [resolve(192,c,191,a)].
% 1.43/1.72 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -antisymmetric(k2_lattice3(boole_lattice(A))) | -transitive(k2_lattice3(boole_lattice(A))) | -v1_partfun1(k2_lattice3(boole_lattice(A)),B,B) | -relation_of2(k2_lattice3(boole_lattice(A)),B,B) | strict_rel_str(rel_str_of(B,k2_lattice3(boole_lattice(A)))). [resolve(411,c,398,a)].
% 1.43/1.72 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -antisymmetric(k2_lattice3(boole_lattice(A))) | -transitive(k2_lattice3(boole_lattice(A))) | -v1_partfun1(k2_lattice3(boole_lattice(A)),B,B) | -relation_of2(k2_lattice3(boole_lattice(A)),B,B) | reflexive_relstr(rel_str_of(B,k2_lattice3(boole_lattice(A)))). [resolve(411,c,399,a)].
% 1.43/1.73 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -antisymmetric(k2_lattice3(boole_lattice(A))) | -transitive(k2_lattice3(boole_lattice(A))) | -v1_partfun1(k2_lattice3(boole_lattice(A)),B,B) | -relation_of2(k2_lattice3(boole_lattice(A)),B,B) | transitive_relstr(rel_str_of(B,k2_lattice3(boole_lattice(A)))). [resolve(411,c,400,a)].
% 1.43/1.73 Derived: empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -antisymmetric(k2_lattice3(boole_lattice(A))) | -transitive(k2_lattice3(boole_lattice(A))) | -v1_partfun1(k2_lattice3(boole_lattice(A)),B,B) | -relation_of2(k2_lattice3(boole_lattice(A)),B,B) | antisymmetric_relstr(rel_str_of(B,k2_lattice3(boole_lattice(A)))). [resolve(411,c,401,a)].
% 1.43/1.73 412 empty_carrier(c5) | -lattice(c5) | reflexive(k2_lattice3(c5)). [resolve(205,a,192,c)].
% 1.43/1.73 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric(k2_lattice3(c5)) | -transitive(k2_lattice3(c5)) | -v1_partfun1(k2_lattice3(c5),A,A) | -relation_of2(k2_lattice3(c5),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c5))). [resolve(412,c,398,a)].
% 1.43/1.73 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric(k2_lattice3(c5)) | -transitive(k2_lattice3(c5)) | -v1_partfun1(k2_lattice3(c5),A,A) | -relation_of2(k2_lattice3(c5),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c5))). [resolve(412,c,399,a)].
% 1.43/1.73 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric(k2_lattice3(c5)) | -transitive(k2_lattice3(c5)) | -v1_partfun1(k2_lattice3(c5),A,A) | -relation_of2(k2_lattice3(c5),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c5))). [resolve(412,c,400,a)].
% 1.43/1.73 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric(k2_lattice3(c5)) | -transitive(k2_lattice3(c5)) | -v1_partfun1(k2_lattice3(c5),A,A) | -relation_of2(k2_lattice3(c5),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c5))). [resolve(412,c,401,a)].
% 1.43/1.73 413 empty_carrier(c6) | -lattice(c6) | reflexive(k2_lattice3(c6)). [resolve(245,a,192,c)].
% 1.43/1.73 Derived: empty_carrier(c6) | -lattice(c6) | -antisymmetric(k2_lattice3(c6)) | -transitive(k2_lattice3(c6)) | -v1_partfun1(k2_lattice3(c6),A,A) | -relation_of2(k2_lattice3(c6),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c6))). [resolve(413,c,398,a)].
% 1.43/1.73 Derived: empty_carrier(c6) | -lattice(c6) | -antisymmetric(k2_lattice3(c6)) | -transitive(k2_lattice3(c6)) | -v1_partfun1(k2_lattice3(c6),A,A) | -relation_of2(k2_lattice3(c6),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c6))). [resolve(413,c,399,a)].
% 1.43/1.73 Derived: empty_carrier(c6) | -lattice(c6) | -antisymmetric(k2_lattice3(c6)) | -transitive(k2_lattice3(c6)) | -v1_partfun1(k2_lattice3(c6),A,A) | -relation_of2(k2_lattice3(c6),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c6))). [resolve(413,c,400,a)].
% 1.43/1.73 Derived: empty_carrier(c6) | -lattice(c6) | -antisymmetric(k2_lattice3(c6)) | -transitive(k2_lattice3(c6)) | -v1_partfun1(k2_lattice3(c6),A,A) | -relation_of2(k2_lattice3(c6),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c6))). [resolve(413,c,401,a)].
% 1.43/1.73 414 empty_carrier(c7) | -lattice(c7) | reflexive(k2_lattice3(c7)). [resolve(246,a,192,c)].
% 1.43/1.73 Derived: empty_carrier(c7) | -lattice(c7) | -antisymmetric(k2_lattice3(c7)) | -transitive(k2_lattice3(c7)) | -v1_partfun1(k2_lattice3(c7),A,A) | -relation_of2(k2_lattice3(c7),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c7))). [resolve(414,c,398,a)].
% 1.43/1.73 Derived: empty_carrier(c7) | -lattice(c7) | -antisymmetric(k2_lattice3(c7)) | -transitive(k2_lattice3(c7)) | -v1_partfun1(k2_lattice3(c7),A,A) | -relation_of2(k2_lattice3(c7),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c7))). [resolve(414,c,399,a)].
% 1.43/1.73 Derived: empty_carrier(c7) | -lattice(c7) | -antisymmetric(k2_lattice3(c7)) | -transitive(k2_lattice3(c7)) | -v1_partfun1(k2_lattice3(c7),A,A) | -relation_of2(k2_lattice3(c7),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c7))). [resolve(414,c,400,a)].
% 1.43/1.73 Derived: empty_carrier(c7) | -lattice(c7) | -antisymmetric(k2_lattice3(c7)) | -transitive(k2_lattice3(c7)) | -v1_partfun1(k2_lattice3(c7),A,A) | -relation_of2(k2_lattice3(c7),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c7))). [resolve(414,c,401,a)].
% 1.43/1.73 415 empty_carrier(c8) | -lattice(c8) | reflexive(k2_lattice3(c8)). [resolve(247,a,192,c)].
% 1.43/1.74 Derived: empty_carrier(c8) | -lattice(c8) | -antisymmetric(k2_lattice3(c8)) | -transitive(k2_lattice3(c8)) | -v1_partfun1(k2_lattice3(c8),A,A) | -relation_of2(k2_lattice3(c8),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c8))). [resolve(415,c,398,a)].
% 1.43/1.74 Derived: empty_carrier(c8) | -lattice(c8) | -antisymmetric(k2_lattice3(c8)) | -transitive(k2_lattice3(c8)) | -v1_partfun1(k2_lattice3(c8),A,A) | -relation_of2(k2_lattice3(c8),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c8))). [resolve(415,c,399,a)].
% 1.43/1.74 Derived: empty_carrier(c8) | -lattice(c8) | -antisymmetric(k2_lattice3(c8)) | -transitive(k2_lattice3(c8)) | -v1_partfun1(k2_lattice3(c8),A,A) | -relation_of2(k2_lattice3(c8),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c8))). [resolve(415,c,400,a)].
% 1.43/1.74 Derived: empty_carrier(c8) | -lattice(c8) | -antisymmetric(k2_lattice3(c8)) | -transitive(k2_lattice3(c8)) | -v1_partfun1(k2_lattice3(c8),A,A) | -relation_of2(k2_lattice3(c8),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c8))). [resolve(415,c,401,a)].
% 1.43/1.74 416 empty_carrier(c9) | -lattice(c9) | reflexive(k2_lattice3(c9)). [resolve(248,a,192,c)].
% 1.43/1.74 Derived: empty_carrier(c9) | -lattice(c9) | -antisymmetric(k2_lattice3(c9)) | -transitive(k2_lattice3(c9)) | -v1_partfun1(k2_lattice3(c9),A,A) | -relation_of2(k2_lattice3(c9),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c9))). [resolve(416,c,398,a)].
% 1.43/1.74 Derived: empty_carrier(c9) | -lattice(c9) | -antisymmetric(k2_lattice3(c9)) | -transitive(k2_lattice3(c9)) | -v1_partfun1(k2_lattice3(c9),A,A) | -relation_of2(k2_lattice3(c9),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c9))). [resolve(416,c,399,a)].
% 1.43/1.74 Derived: empty_carrier(c9) | -lattice(c9) | -antisymmetric(k2_lattice3(c9)) | -transitive(k2_lattice3(c9)) | -v1_partfun1(k2_lattice3(c9),A,A) | -relation_of2(k2_lattice3(c9),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c9))). [resolve(416,c,400,a)].
% 1.43/1.74 Derived: empty_carrier(c9) | -lattice(c9) | -antisymmetric(k2_lattice3(c9)) | -transitive(k2_lattice3(c9)) | -v1_partfun1(k2_lattice3(c9),A,A) | -relation_of2(k2_lattice3(c9),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c9))). [resolve(416,c,401,a)].
% 1.43/1.74 417 empty_carrier(c18) | -lattice(c18) | reflexive(k2_lattice3(c18)). [resolve(249,a,192,c)].
% 1.43/1.74 Derived: empty_carrier(c18) | -lattice(c18) | -antisymmetric(k2_lattice3(c18)) | -transitive(k2_lattice3(c18)) | -v1_partfun1(k2_lattice3(c18),A,A) | -relation_of2(k2_lattice3(c18),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c18))). [resolve(417,c,398,a)].
% 1.43/1.74 Derived: empty_carrier(c18) | -lattice(c18) | -antisymmetric(k2_lattice3(c18)) | -transitive(k2_lattice3(c18)) | -v1_partfun1(k2_lattice3(c18),A,A) | -relation_of2(k2_lattice3(c18),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c18))). [resolve(417,c,399,a)].
% 1.43/1.74 Derived: empty_carrier(c18) | -lattice(c18) | -antisymmetric(k2_lattice3(c18)) | -transitive(k2_lattice3(c18)) | -v1_partfun1(k2_lattice3(c18),A,A) | -relation_of2(k2_lattice3(c18),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c18))). [resolve(417,c,400,a)].
% 1.43/1.74 Derived: empty_carrier(c18) | -lattice(c18) | -antisymmetric(k2_lattice3(c18)) | -transitive(k2_lattice3(c18)) | -v1_partfun1(k2_lattice3(c18),A,A) | -relation_of2(k2_lattice3(c18),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c18))). [resolve(417,c,401,a)].
% 1.43/1.74 418 empty_carrier(c20) | -lattice(c20) | reflexive(k2_lattice3(c20)). [resolve(250,a,192,c)].
% 1.43/1.74 Derived: empty_carrier(c20) | -lattice(c20) | -antisymmetric(k2_lattice3(c20)) | -transitive(k2_lattice3(c20)) | -v1_partfun1(k2_lattice3(c20),A,A) | -relation_of2(k2_lattice3(c20),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c20))). [resolve(418,c,398,a)].
% 1.43/1.74 Derived: empty_carrier(c20) | -lattice(c20) | -antisymmetric(k2_lattice3(c20)) | -transitive(k2_lattice3(c20)) | -v1_partfun1(k2_lattice3(c20),A,A) | -relation_of2(k2_lattice3(c20),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c20))). [resolve(418,c,399,a)].
% 1.43/1.74 Derived: empty_carrier(c20) | -lattice(c20) | -antisymmetric(k2_lattice3(c20)) | -transitive(k2_lattice3(c20)) | -v1_partfun1(k2_lattice3(c20),A,A) | -relation_of2(k2_lattice3(c20),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c20))). [resolve(418,c,400,a)].
% 1.50/1.75 Derived: empty_carrier(c20) | -lattice(c20) | -antisymmetric(k2_lattice3(c20)) | -transitive(k2_lattice3(c20)) | -v1_partfun1(k2_lattice3(c20),A,A) | -relation_of2(k2_lattice3(c20),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c20))). [resolve(418,c,401,a)].
% 1.50/1.75 419 empty_carrier(c21) | -lattice(c21) | reflexive(k2_lattice3(c21)). [resolve(251,a,192,c)].
% 1.50/1.75 Derived: empty_carrier(c21) | -lattice(c21) | -antisymmetric(k2_lattice3(c21)) | -transitive(k2_lattice3(c21)) | -v1_partfun1(k2_lattice3(c21),A,A) | -relation_of2(k2_lattice3(c21),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c21))). [resolve(419,c,398,a)].
% 1.50/1.75 Derived: empty_carrier(c21) | -lattice(c21) | -antisymmetric(k2_lattice3(c21)) | -transitive(k2_lattice3(c21)) | -v1_partfun1(k2_lattice3(c21),A,A) | -relation_of2(k2_lattice3(c21),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c21))). [resolve(419,c,399,a)].
% 1.50/1.75 Derived: empty_carrier(c21) | -lattice(c21) | -antisymmetric(k2_lattice3(c21)) | -transitive(k2_lattice3(c21)) | -v1_partfun1(k2_lattice3(c21),A,A) | -relation_of2(k2_lattice3(c21),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c21))). [resolve(419,c,400,a)].
% 1.50/1.75 Derived: empty_carrier(c21) | -lattice(c21) | -antisymmetric(k2_lattice3(c21)) | -transitive(k2_lattice3(c21)) | -v1_partfun1(k2_lattice3(c21),A,A) | -relation_of2(k2_lattice3(c21),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c21))). [resolve(419,c,401,a)].
% 1.50/1.75 420 -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | reflexive(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(269,g,155,g)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -antisymmetric(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -transitive(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -v1_partfun1(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),D,D) | -relation_of2(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),D,D) | strict_rel_str(rel_str_of(D,the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))))). [resolve(420,d,398,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -antisymmetric(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -transitive(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -v1_partfun1(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),D,D) | -relation_of2(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),D,D) | reflexive_relstr(rel_str_of(D,the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))))). [resolve(420,d,399,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -antisymmetric(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -transitive(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -v1_partfun1(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),D,D) | -relation_of2(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),D,D) | transitive_relstr(rel_str_of(D,the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))))). [resolve(420,d,400,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -transitive_relstr(poset_of_lattice(latt_str_of(A,B,C))) | -antisymmetric_relstr(poset_of_lattice(latt_str_of(A,B,C))) | empty_carrier(latt_str_of(A,B,C)) | -lattice(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | -antisymmetric(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -transitive(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C)))) | -v1_partfun1(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),D,D) | -relation_of2(the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))),D,D) | antisymmetric_relstr(rel_str_of(D,the_InternalRel(poset_of_lattice(latt_str_of(A,B,C))))). [resolve(420,d,401,a)].
% 1.50/1.75 421 -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | reflexive(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)). [resolve(269,g,191,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -antisymmetric(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | -transitive(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | -v1_partfun1(the_InternalRel(poset_of_lattice(boole_lattice(A))),B,B) | -relation_of2(the_InternalRel(poset_of_lattice(boole_lattice(A))),B,B) | strict_rel_str(rel_str_of(B,the_InternalRel(poset_of_lattice(boole_lattice(A))))). [resolve(421,d,398,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -antisymmetric(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | -transitive(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | -v1_partfun1(the_InternalRel(poset_of_lattice(boole_lattice(A))),B,B) | -relation_of2(the_InternalRel(poset_of_lattice(boole_lattice(A))),B,B) | reflexive_relstr(rel_str_of(B,the_InternalRel(poset_of_lattice(boole_lattice(A))))). [resolve(421,d,399,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -antisymmetric(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | -transitive(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | -v1_partfun1(the_InternalRel(poset_of_lattice(boole_lattice(A))),B,B) | -relation_of2(the_InternalRel(poset_of_lattice(boole_lattice(A))),B,B) | transitive_relstr(rel_str_of(B,the_InternalRel(poset_of_lattice(boole_lattice(A))))). [resolve(421,d,400,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(boole_lattice(A))) | -transitive_relstr(poset_of_lattice(boole_lattice(A))) | -antisymmetric_relstr(poset_of_lattice(boole_lattice(A))) | empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -antisymmetric(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | -transitive(the_InternalRel(poset_of_lattice(boole_lattice(A)))) | -v1_partfun1(the_InternalRel(poset_of_lattice(boole_lattice(A))),B,B) | -relation_of2(the_InternalRel(poset_of_lattice(boole_lattice(A))),B,B) | antisymmetric_relstr(rel_str_of(B,the_InternalRel(poset_of_lattice(boole_lattice(A))))). [resolve(421,d,401,a)].
% 1.50/1.75 422 -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | reflexive(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(269,g,205,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(422,d,398,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(422,d,399,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(422,d,400,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(422,d,401,a)].
% 1.50/1.75 423 -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | reflexive(the_InternalRel(poset_of_lattice(c6))) | empty_carrier(c6) | -lattice(c6). [resolve(269,g,245,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | empty_carrier(c6) | -lattice(c6) | -antisymmetric(the_InternalRel(poset_of_lattice(c6))) | -transitive(the_InternalRel(poset_of_lattice(c6))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c6)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c6)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c6)))). [resolve(423,d,398,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | empty_carrier(c6) | -lattice(c6) | -antisymmetric(the_InternalRel(poset_of_lattice(c6))) | -transitive(the_InternalRel(poset_of_lattice(c6))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c6)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c6)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c6)))). [resolve(423,d,399,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | empty_carrier(c6) | -lattice(c6) | -antisymmetric(the_InternalRel(poset_of_lattice(c6))) | -transitive(the_InternalRel(poset_of_lattice(c6))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c6)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c6)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c6)))). [resolve(423,d,400,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c6)) | -transitive_relstr(poset_of_lattice(c6)) | -antisymmetric_relstr(poset_of_lattice(c6)) | empty_carrier(c6) | -lattice(c6) | -antisymmetric(the_InternalRel(poset_of_lattice(c6))) | -transitive(the_InternalRel(poset_of_lattice(c6))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c6)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c6)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c6)))). [resolve(423,d,401,a)].
% 1.50/1.75 424 -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | reflexive(the_InternalRel(poset_of_lattice(c7))) | empty_carrier(c7) | -lattice(c7). [resolve(269,g,246,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | empty_carrier(c7) | -lattice(c7) | -antisymmetric(the_InternalRel(poset_of_lattice(c7))) | -transitive(the_InternalRel(poset_of_lattice(c7))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c7)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c7)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c7)))). [resolve(424,d,398,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | empty_carrier(c7) | -lattice(c7) | -antisymmetric(the_InternalRel(poset_of_lattice(c7))) | -transitive(the_InternalRel(poset_of_lattice(c7))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c7)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c7)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c7)))). [resolve(424,d,399,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | empty_carrier(c7) | -lattice(c7) | -antisymmetric(the_InternalRel(poset_of_lattice(c7))) | -transitive(the_InternalRel(poset_of_lattice(c7))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c7)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c7)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c7)))). [resolve(424,d,400,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c7)) | -transitive_relstr(poset_of_lattice(c7)) | -antisymmetric_relstr(poset_of_lattice(c7)) | empty_carrier(c7) | -lattice(c7) | -antisymmetric(the_InternalRel(poset_of_lattice(c7))) | -transitive(the_InternalRel(poset_of_lattice(c7))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c7)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c7)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c7)))). [resolve(424,d,401,a)].
% 1.50/1.75 425 -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | reflexive(the_InternalRel(poset_of_lattice(c8))) | empty_carrier(c8) | -lattice(c8). [resolve(269,g,247,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | empty_carrier(c8) | -lattice(c8) | -antisymmetric(the_InternalRel(poset_of_lattice(c8))) | -transitive(the_InternalRel(poset_of_lattice(c8))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c8)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c8)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c8)))). [resolve(425,d,398,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | empty_carrier(c8) | -lattice(c8) | -antisymmetric(the_InternalRel(poset_of_lattice(c8))) | -transitive(the_InternalRel(poset_of_lattice(c8))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c8)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c8)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c8)))). [resolve(425,d,399,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | empty_carrier(c8) | -lattice(c8) | -antisymmetric(the_InternalRel(poset_of_lattice(c8))) | -transitive(the_InternalRel(poset_of_lattice(c8))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c8)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c8)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c8)))). [resolve(425,d,400,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c8)) | -transitive_relstr(poset_of_lattice(c8)) | -antisymmetric_relstr(poset_of_lattice(c8)) | empty_carrier(c8) | -lattice(c8) | -antisymmetric(the_InternalRel(poset_of_lattice(c8))) | -transitive(the_InternalRel(poset_of_lattice(c8))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c8)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c8)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c8)))). [resolve(425,d,401,a)].
% 1.50/1.75 426 -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | reflexive(the_InternalRel(poset_of_lattice(c9))) | empty_carrier(c9) | -lattice(c9). [resolve(269,g,248,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | empty_carrier(c9) | -lattice(c9) | -antisymmetric(the_InternalRel(poset_of_lattice(c9))) | -transitive(the_InternalRel(poset_of_lattice(c9))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c9)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c9)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c9)))). [resolve(426,d,398,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | empty_carrier(c9) | -lattice(c9) | -antisymmetric(the_InternalRel(poset_of_lattice(c9))) | -transitive(the_InternalRel(poset_of_lattice(c9))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c9)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c9)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c9)))). [resolve(426,d,399,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | empty_carrier(c9) | -lattice(c9) | -antisymmetric(the_InternalRel(poset_of_lattice(c9))) | -transitive(the_InternalRel(poset_of_lattice(c9))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c9)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c9)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c9)))). [resolve(426,d,400,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c9)) | -transitive_relstr(poset_of_lattice(c9)) | -antisymmetric_relstr(poset_of_lattice(c9)) | empty_carrier(c9) | -lattice(c9) | -antisymmetric(the_InternalRel(poset_of_lattice(c9))) | -transitive(the_InternalRel(poset_of_lattice(c9))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c9)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c9)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c9)))). [resolve(426,d,401,a)].
% 1.50/1.75 427 -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | reflexive(the_InternalRel(poset_of_lattice(c18))) | empty_carrier(c18) | -lattice(c18). [resolve(269,g,249,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | empty_carrier(c18) | -lattice(c18) | -antisymmetric(the_InternalRel(poset_of_lattice(c18))) | -transitive(the_InternalRel(poset_of_lattice(c18))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c18)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c18)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c18)))). [resolve(427,d,398,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | empty_carrier(c18) | -lattice(c18) | -antisymmetric(the_InternalRel(poset_of_lattice(c18))) | -transitive(the_InternalRel(poset_of_lattice(c18))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c18)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c18)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c18)))). [resolve(427,d,399,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | empty_carrier(c18) | -lattice(c18) | -antisymmetric(the_InternalRel(poset_of_lattice(c18))) | -transitive(the_InternalRel(poset_of_lattice(c18))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c18)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c18)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c18)))). [resolve(427,d,400,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c18)) | -transitive_relstr(poset_of_lattice(c18)) | -antisymmetric_relstr(poset_of_lattice(c18)) | empty_carrier(c18) | -lattice(c18) | -antisymmetric(the_InternalRel(poset_of_lattice(c18))) | -transitive(the_InternalRel(poset_of_lattice(c18))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c18)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c18)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c18)))). [resolve(427,d,401,a)].
% 1.50/1.75 428 -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | reflexive(the_InternalRel(poset_of_lattice(c20))) | empty_carrier(c20) | -lattice(c20). [resolve(269,g,250,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | empty_carrier(c20) | -lattice(c20) | -antisymmetric(the_InternalRel(poset_of_lattice(c20))) | -transitive(the_InternalRel(poset_of_lattice(c20))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c20)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c20)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c20)))). [resolve(428,d,398,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | empty_carrier(c20) | -lattice(c20) | -antisymmetric(the_InternalRel(poset_of_lattice(c20))) | -transitive(the_InternalRel(poset_of_lattice(c20))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c20)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c20)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c20)))). [resolve(428,d,399,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | empty_carrier(c20) | -lattice(c20) | -antisymmetric(the_InternalRel(poset_of_lattice(c20))) | -transitive(the_InternalRel(poset_of_lattice(c20))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c20)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c20)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c20)))). [resolve(428,d,400,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c20)) | -transitive_relstr(poset_of_lattice(c20)) | -antisymmetric_relstr(poset_of_lattice(c20)) | empty_carrier(c20) | -lattice(c20) | -antisymmetric(the_InternalRel(poset_of_lattice(c20))) | -transitive(the_InternalRel(poset_of_lattice(c20))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c20)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c20)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c20)))). [resolve(428,d,401,a)].
% 1.50/1.75 429 -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | reflexive(the_InternalRel(poset_of_lattice(c21))) | empty_carrier(c21) | -lattice(c21). [resolve(269,g,251,a)].
% 1.50/1.75 Derived: -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | empty_carrier(c21) | -lattice(c21) | -antisymmetric(the_InternalRel(poset_of_lattice(c21))) | -transitive(the_InternalRel(poset_of_lattice(c21))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c21)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c21)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c21)))). [resolve(429,d,398,a)].
% 4.58/4.85 Derived: -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | empty_carrier(c21) | -lattice(c21) | -antisymmetric(the_InternalRel(poset_of_lattice(c21))) | -transitive(the_InternalRel(poset_of_lattice(c21))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c21)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c21)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c21)))). [resolve(429,d,399,a)].
% 4.58/4.85 Derived: -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | empty_carrier(c21) | -lattice(c21) | -antisymmetric(the_InternalRel(poset_of_lattice(c21))) | -transitive(the_InternalRel(poset_of_lattice(c21))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c21)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c21)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c21)))). [resolve(429,d,400,a)].
% 4.58/4.85 Derived: -reflexive_relstr(poset_of_lattice(c21)) | -transitive_relstr(poset_of_lattice(c21)) | -antisymmetric_relstr(poset_of_lattice(c21)) | empty_carrier(c21) | -lattice(c21) | -antisymmetric(the_InternalRel(poset_of_lattice(c21))) | -transitive(the_InternalRel(poset_of_lattice(c21))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c21)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c21)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c21)))). [resolve(429,d,401,a)].
% 4.58/4.85
% 4.58/4.85 ============================== end predicate elimination =============
% 4.58/4.85
% 4.58/4.85 Auto_denials: (non-Horn, no changes).
% 4.58/4.85
% 4.58/4.85 Term ordering decisions:
% 4.58/4.85 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. cartesian_product2=1. rel_str_of=1. cast_to_el_of_LattPOSet=1. ordered_pair=1. unordered_pair=1. f1=1. f3=1. f5=1. poset_of_lattice=1. the_carrier=1. the_InternalRel=1. boole_lattice=1. k2_lattice3=1. boole_POSet=1. powerset=1. the_L_join=1. the_L_meet=1. relation_of_lattice=1. singleton=1. f2=1. f4=1. f6=1. f7=1. latt_str_of=1.
% 4.58/4.85
% 4.58/4.85 ============================== end of process initial clauses ========
% 4.58/4.85
% 4.58/4.85 ============================== CLAUSES FOR SEARCH ====================
% 4.58/4.85
% 4.58/4.85 ============================== end of clauses for search =============
% 4.58/4.85
% 4.58/4.85 ============================== SEARCH ================================
% 4.58/4.85
% 4.58/4.85 % Starting search at 0.80 seconds.
% 4.58/4.85
% 4.58/4.85 Low Water (keep): wt=76.000, iters=3648
% 4.58/4.85
% 4.58/4.85 Low Water (keep): wt=65.000, iters=3352
% 4.58/4.85
% 4.58/4.85 Low Water (keep): wt=64.000, iters=3709
% 4.58/4.85
% 4.58/4.85 Low Water (keep): wt=53.000, iters=3671
% 4.58/4.85
% 4.58/4.85 Low Water (keep): wt=52.000, iters=3583
% 4.58/4.85
% 4.58/4.85 Low Water (keep): wt=50.000, iters=3650
% 4.58/4.85
% 4.58/4.85 Low Water (keep): wt=49.000, iters=3556
% 4.58/4.85
% 4.58/4.85 Low Water (keep): wt=48.000, iters=3362
% 4.58/4.85
% 4.58/4.85 Low Water (keep): wt=44.000, iters=3580
% 4.58/4.85
% 4.58/4.85 ============================== PROOF =================================
% 4.58/4.85 % SZS status Theorem
% 4.58/4.85 % SZS output start Refutation
% 4.58/4.85
% 4.58/4.85 % Proof 1 at 3.72 (+ 0.02) seconds.
% 4.58/4.85 % Length of proof is 81.
% 4.58/4.85 % Level of proof is 19.
% 4.58/4.85 % Maximum clause weight is 27.000.
% 4.58/4.85 % Given clauses 5037.
% 4.58/4.85
% 4.58/4.85 1 (all A (rel_str(A) -> (strict_rel_str(A) -> A = rel_str_of(the_carrier(A),the_InternalRel(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 21 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)))) # label(d2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 22 (all A boole_POSet(A) = poset_of_lattice(boole_lattice(A))) # label(d2_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 23 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> cast_to_el_of_LattPOSet(A,B) = B)))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 28 (all A (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 32 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A)))) # label(dt_k2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 36 (all A (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))) # label(dt_k3_yellow_1) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 60 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)))) # label(fc1_knaster) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 81 (all A all B (relation_of2(B,A,A) -> (all C all D (rel_str_of(A,B) = rel_str_of(C,D) -> A = C & B = D)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 104 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 105 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> (below_refl(A,B,C) <-> below(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 111 (all A all B (element(B,the_carrier(boole_lattice(A))) -> (all C (element(C,the_carrier(boole_lattice(A))) -> (below(boole_lattice(A),B,C) <-> subset(B,C)))))) # label(t2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 118 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below_refl(A,B,C) <-> related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C))))))))) # label(t7_lattice3) # label(axiom) # label(non_clause). [assumption].
% 4.58/4.85 120 -(all A all B (element(B,the_carrier(boole_POSet(A))) -> (all C (element(C,the_carrier(boole_POSet(A))) -> (related_reflexive(boole_POSet(A),B,C) <-> subset(B,C)))))) # label(t2_yellow_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.58/4.85 122 -rel_str(A) | -strict_rel_str(A) | rel_str_of(the_carrier(A),the_InternalRel(A)) = A # label(abstractness_v1_orders_2) # label(axiom). [clausify(1)].
% 4.58/4.85 137 rel_str(boole_POSet(A)) # label(dt_k3_yellow_1) # label(axiom). [clausify(36)].
% 4.58/4.85 189 empty_carrier(A) | -lattice(A) | -latt_str(A) | poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)) # label(d2_lattice3) # label(axiom). [clausify(21)].
% 4.58/4.85 190 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | cast_to_el_of_LattPOSet(A,B) = B # label(d3_lattice3) # label(axiom). [clausify(23)].
% 4.58/4.85 191 latt_str(boole_lattice(A)) # label(dt_k1_lattice3) # label(axiom). [clausify(28)].
% 4.58/4.85 196 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(32)].
% 4.58/4.85 253 empty_carrier(A) | -meet_commutative(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | below(A,B,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(105)].
% 4.58/4.86 254 empty_carrier(A) | -meet_commutative(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -below(A,B,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(105)].
% 4.58/4.86 256 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C)) # label(t7_lattice3) # label(axiom). [clausify(118)].
% 4.58/4.86 257 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C)) # label(t7_lattice3) # label(axiom). [clausify(118)].
% 4.58/4.86 308 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(104)].
% 4.58/4.86 320 empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | relation_of2_as_subset(k2_lattice3(boole_lattice(A)),the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(196,c,191,a)].
% 4.58/4.86 432 boole_POSet(A) = poset_of_lattice(boole_lattice(A)) # label(d2_yellow_1) # label(axiom). [clausify(22)].
% 4.58/4.86 438 strict_rel_str(boole_POSet(A)) # label(dt_k3_yellow_1) # label(axiom). [clausify(36)].
% 4.58/4.86 439 strict_rel_str(poset_of_lattice(boole_lattice(A))). [copy(438),rewrite([432(1)])].
% 4.58/4.86 442 -empty_carrier(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(60)].
% 4.58/4.86 445 meet_commutative(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(60)].
% 4.58/4.86 447 meet_absorbing(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(60)].
% 4.58/4.86 448 join_absorbing(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(60)].
% 4.58/4.86 449 lattice(boole_lattice(A)) # label(fc1_knaster) # label(axiom). [clausify(60)].
% 4.58/4.86 492 -relation_of2(A,B,B) | rel_str_of(C,D) != rel_str_of(B,A) | C = B # label(free_g1_orders_2) # label(axiom). [clausify(81)].
% 4.58/4.86 493 -relation_of2(A,B,B) | rel_str_of(C,D) != rel_str_of(B,A) | D = A # label(free_g1_orders_2) # label(axiom). [clausify(81)].
% 4.58/4.86 611 -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | -below(boole_lattice(B),A,C) | subset(A,C) # label(t2_lattice3) # label(axiom). [clausify(111)].
% 4.58/4.86 612 -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | below(boole_lattice(B),A,C) | -subset(A,C) # label(t2_lattice3) # label(axiom). [clausify(111)].
% 4.58/4.86 621 element(c23,the_carrier(boole_POSet(c22))) # label(t2_yellow_1) # label(negated_conjecture). [clausify(120)].
% 4.58/4.86 622 element(c23,the_carrier(poset_of_lattice(boole_lattice(c22)))). [copy(621),rewrite([432(3)])].
% 4.58/4.86 623 element(c24,the_carrier(boole_POSet(c22))) # label(t2_yellow_1) # label(negated_conjecture). [clausify(120)].
% 4.58/4.86 624 element(c24,the_carrier(poset_of_lattice(boole_lattice(c22)))). [copy(623),rewrite([432(3)])].
% 4.58/4.86 625 related_reflexive(boole_POSet(c22),c23,c24) | subset(c23,c24) # label(t2_yellow_1) # label(negated_conjecture). [clausify(120)].
% 4.58/4.86 626 related_reflexive(poset_of_lattice(boole_lattice(c22)),c23,c24) | subset(c23,c24). [copy(625),rewrite([432(2)])].
% 4.58/4.86 627 -related_reflexive(boole_POSet(c22),c23,c24) | -subset(c23,c24) # label(t2_yellow_1) # label(negated_conjecture). [clausify(120)].
% 4.58/4.86 628 -related_reflexive(poset_of_lattice(boole_lattice(c22)),c23,c24) | -subset(c23,c24). [copy(627),rewrite([432(2)])].
% 4.58/4.86 645 -strict_rel_str(boole_POSet(A)) | rel_str_of(the_carrier(boole_POSet(A)),the_InternalRel(boole_POSet(A))) = boole_POSet(A). [resolve(137,a,122,a)].
% 4.58/4.86 646 rel_str_of(the_carrier(poset_of_lattice(boole_lattice(A))),the_InternalRel(poset_of_lattice(boole_lattice(A)))) = poset_of_lattice(boole_lattice(A)). [copy(645),rewrite([432(1),432(4),432(7),432(11)]),unit_del(a,439)].
% 4.58/4.86 870 empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | poset_of_lattice(boole_lattice(A)) = rel_str_of(the_carrier(boole_lattice(A)),k2_lattice3(boole_lattice(A))). [resolve(191,a,189,c)].
% 4.58/4.86 871 rel_str_of(the_carrier(boole_lattice(A)),k2_lattice3(boole_lattice(A))) = poset_of_lattice(boole_lattice(A)). [copy(870),flip(c),unit_del(a,442),unit_del(b,449)].
% 4.58/4.86 872 empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | cast_to_el_of_LattPOSet(boole_lattice(A),B) = B. [resolve(191,a,190,c)].
% 4.58/4.86 873 -element(A,the_carrier(boole_lattice(B))) | cast_to_el_of_LattPOSet(boole_lattice(B),A) = A. [copy(872),unit_del(a,442),unit_del(b,449)].
% 4.58/4.86 1348 empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -meet_absorbing(boole_lattice(A)) | -join_absorbing(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | -below_refl(boole_lattice(A),B,C) | below(boole_lattice(A),B,C). [resolve(253,e,191,a)].
% 4.58/4.86 1349 -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | -below_refl(boole_lattice(B),A,C) | below(boole_lattice(B),A,C). [copy(1348),unit_del(a,442),unit_del(b,445),unit_del(c,447),unit_del(d,448)].
% 4.58/4.86 1365 empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -meet_absorbing(boole_lattice(A)) | -join_absorbing(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | below_refl(boole_lattice(A),B,C) | -below(boole_lattice(A),B,C). [resolve(254,e,191,a)].
% 4.58/4.86 1366 -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | below_refl(boole_lattice(B),A,C) | -below(boole_lattice(B),A,C). [copy(1365),unit_del(a,442),unit_del(b,445),unit_del(c,447),unit_del(d,448)].
% 4.58/4.86 1399 empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | -below_refl(boole_lattice(A),B,C) | related_reflexive(poset_of_lattice(boole_lattice(A)),cast_to_el_of_LattPOSet(boole_lattice(A),B),cast_to_el_of_LattPOSet(boole_lattice(A),C)). [resolve(256,c,191,a)].
% 4.58/4.86 1400 -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | -below_refl(boole_lattice(B),A,C) | related_reflexive(poset_of_lattice(boole_lattice(B)),cast_to_el_of_LattPOSet(boole_lattice(B),A),cast_to_el_of_LattPOSet(boole_lattice(B),C)). [copy(1399),unit_del(a,442),unit_del(b,449)].
% 4.58/4.86 1416 empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | below_refl(boole_lattice(A),B,C) | -related_reflexive(poset_of_lattice(boole_lattice(A)),cast_to_el_of_LattPOSet(boole_lattice(A),B),cast_to_el_of_LattPOSet(boole_lattice(A),C)). [resolve(257,c,191,a)].
% 4.58/4.86 1417 -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | below_refl(boole_lattice(B),A,C) | -related_reflexive(poset_of_lattice(boole_lattice(B)),cast_to_el_of_LattPOSet(boole_lattice(B),A),cast_to_el_of_LattPOSet(boole_lattice(B),C)). [copy(1416),unit_del(a,442),unit_del(b,449)].
% 4.58/4.86 1725 empty_carrier(boole_lattice(A)) | -lattice(boole_lattice(A)) | relation_of2(k2_lattice3(boole_lattice(A)),the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(320,c,308,a)].
% 4.58/4.86 1726 relation_of2(k2_lattice3(boole_lattice(A)),the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))). [copy(1725),unit_del(a,442),unit_del(b,449)].
% 4.58/4.86 5072 poset_of_lattice(boole_lattice(A)) != rel_str_of(B,C) | k2_lattice3(boole_lattice(A)) = C. [resolve(1726,a,493,a),rewrite([871(6)]),flip(a),flip(b)].
% 4.58/4.86 5073 poset_of_lattice(boole_lattice(A)) != rel_str_of(B,C) | the_carrier(boole_lattice(A)) = B. [resolve(1726,a,492,a),rewrite([871(6)]),flip(a),flip(b)].
% 4.58/4.86 8248 the_InternalRel(poset_of_lattice(boole_lattice(A))) = k2_lattice3(boole_lattice(A)). [resolve(5072,a,646,a(flip)),flip(a)].
% 4.58/4.86 8272 rel_str_of(the_carrier(poset_of_lattice(boole_lattice(A))),k2_lattice3(boole_lattice(A))) = poset_of_lattice(boole_lattice(A)). [back_rewrite(646),rewrite([8248(6)])].
% 4.58/4.86 8349 the_carrier(poset_of_lattice(boole_lattice(A))) = the_carrier(boole_lattice(A)). [resolve(8272,a,5073,a(flip)),flip(a)].
% 4.58/4.86 8382 element(c24,the_carrier(boole_lattice(c22))). [back_rewrite(624),rewrite([8349(5)])].
% 4.58/4.86 8383 element(c23,the_carrier(boole_lattice(c22))). [back_rewrite(622),rewrite([8349(5)])].
% 4.58/4.86 8386 cast_to_el_of_LattPOSet(boole_lattice(c22),c24) = c24. [resolve(8382,a,873,a)].
% 4.58/4.86 8389 cast_to_el_of_LattPOSet(boole_lattice(c22),c23) = c23. [resolve(8383,a,873,a)].
% 4.58/4.86 8391 -element(A,the_carrier(boole_lattice(c22))) | below_refl(boole_lattice(c22),A,c24) | -related_reflexive(poset_of_lattice(boole_lattice(c22)),cast_to_el_of_LattPOSet(boole_lattice(c22),A),c24). [para(8386(a,1),1417(d,3)),unit_del(b,8382)].
% 4.58/4.86 11707 below_refl(boole_lattice(c22),c23,c24) | -related_reflexive(poset_of_lattice(boole_lattice(c22)),c23,c24). [para(8389(a,1),8391(c,2)),unit_del(a,8383)].
% 4.58/4.86 11710 below_refl(boole_lattice(c22),c23,c24) | subset(c23,c24). [resolve(11707,b,626,a)].
% 4.58/4.86 11711 subset(c23,c24) | below(boole_lattice(c22),c23,c24). [resolve(11710,a,1349,c),unit_del(b,8383),unit_del(c,8382)].
% 4.58/4.86 11712 subset(c23,c24). [resolve(11711,b,611,c),merge(d),unit_del(b,8383),unit_del(c,8382)].
% 4.58/4.86 11713 -related_reflexive(poset_of_lattice(boole_lattice(c22)),c23,c24). [back_unit_del(628),unit_del(b,11712)].
% 4.58/4.86 11715 -element(c23,the_carrier(boole_lattice(A))) | -element(c24,the_carrier(boole_lattice(A))) | below(boole_lattice(A),c23,c24). [resolve(11712,a,612,d)].
% 4.58/4.86 11734 below(boole_lattice(c22),c23,c24). [resolve(11715,b,8382,a),unit_del(a,8383)].
% 4.58/4.86 11735 below_refl(boole_lattice(c22),c23,c24). [resolve(11734,a,1366,d),unit_del(a,8383),unit_del(b,8382)].
% 4.58/4.86 11736 $F. [resolve(11735,a,1400,c),rewrite([8389(17),8386(18)]),unit_del(a,8383),unit_del(b,8382),unit_del(c,11713)].
% 4.58/4.86
% 4.58/4.86 % SZS output end Refutation
% 4.58/4.86 ============================== end of proof ==========================
% 4.58/4.86
% 4.58/4.86 ============================== STATISTICS ============================
% 4.58/4.86
% 4.58/4.86 Given=5037. Generated=17336. Kept=10696. proofs=1.
% 4.58/4.86 Usable=4629. Sos=4896. Demods=115. Limbo=0, Disabled=2756. Hints=0.
% 4.58/4.86 Megabytes=22.43.
% 4.58/4.86 User_CPU=3.73, System_CPU=0.02, Wall_clock=4.
% 4.58/4.86
% 4.58/4.86 ============================== end of statistics =====================
% 4.58/4.86
% 4.58/4.86 ============================== end of search =========================
% 4.58/4.86
% 4.58/4.86 THEOREM PROVED
% 4.58/4.86 % SZS status Theorem
% 4.58/4.86
% 4.58/4.86 Exiting with 1 proof.
% 4.58/4.86
% 4.58/4.86 Process 12439 exit (max_proofs) Sun Jun 19 20:04:15 2022
% 4.58/4.86 Prover9 interrupted
%------------------------------------------------------------------------------