TSTP Solution File: SEU358+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU358+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 13:31:14 EDT 2022
% Result : Timeout 300.05s 300.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU358+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 : n013.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 03:30:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.07 ============================== Prover9 ===============================
% 0.43/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.07 Process 7521 was started by sandbox2 on n013.cluster.edu,
% 0.43/1.07 Sun Jun 19 03:30:14 2022
% 0.43/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7367_n013.cluster.edu".
% 0.43/1.07 ============================== end of head ===========================
% 0.43/1.07
% 0.43/1.07 ============================== INPUT =================================
% 0.43/1.07
% 0.43/1.07 % Reading from file /tmp/Prover9_7367_n013.cluster.edu
% 0.43/1.07
% 0.43/1.07 set(prolog_style_variables).
% 0.43/1.07 set(auto2).
% 0.43/1.07 % set(auto2) -> set(auto).
% 0.43/1.07 % set(auto) -> set(auto_inference).
% 0.43/1.07 % set(auto) -> set(auto_setup).
% 0.43/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.07 % set(auto) -> set(auto_limits).
% 0.43/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.07 % set(auto) -> set(auto_denials).
% 0.43/1.07 % set(auto) -> set(auto_process).
% 0.43/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.07 % set(auto2) -> assign(stats, some).
% 0.43/1.07 % set(auto2) -> clear(echo_input).
% 0.43/1.07 % set(auto2) -> set(quiet).
% 0.43/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.07 % set(auto2) -> clear(print_given).
% 0.43/1.07 assign(lrs_ticks,-1).
% 0.43/1.07 assign(sos_limit,10000).
% 0.43/1.07 assign(order,kbo).
% 0.43/1.07 set(lex_order_vars).
% 0.43/1.07 clear(print_given).
% 0.43/1.07
% 0.43/1.07 % formulas(sos). % not echoed (87 formulas)
% 0.43/1.07
% 0.43/1.07 ============================== end of input ==========================
% 0.43/1.07
% 0.43/1.07 % From the command line: assign(max_seconds, 300).
% 0.43/1.07
% 0.43/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.07
% 0.43/1.07 % Formulas that are not ordinary clauses:
% 0.43/1.07 1 (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].
% 0.43/1.07 2 (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].
% 0.43/1.07 3 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 4 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 5 (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].
% 0.43/1.07 6 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 7 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (ex_inf_of_relstr_set(A,B) -> (C = meet_on_relstr(A,B) <-> relstr_element_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_element_smaller(A,B,D) -> related(A,D,C)))))))))) # label(d10_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 8 (all A (-empty_carrier(A) & latt_str(A) -> (-empty_carrier(A) & lattice(A) & complete_latt_str(A) & latt_str(A) -> (all B all C (element(C,the_carrier(A)) -> (C = join_of_latt_set(A,B) <-> latt_element_smaller(A,C,B) & (all D (element(D,the_carrier(A)) -> (latt_element_smaller(A,D,B) -> below(A,C,D)))))))))) # label(d21_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 9 (all A (-empty_carrier(A) & latt_str(A) -> (all B meet_of_latt_set(A,B) = join_of_latt_set(A,a_2_2_lattice3(A,B))))) # label(d22_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.07 10 (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].
% 0.43/1.08 11 (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].
% 0.43/1.08 12 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(poset_of_lattice(A))) -> cast_to_el_of_lattice(A,B) = B)))) # label(d4_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 13 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (ex_sup_of_relstr_set(A,B) -> (C = join_on_relstr(A,B) <-> relstr_set_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) -> related(A,C,D)))))))))) # label(d9_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 14 (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].
% 0.43/1.08 15 (all A all B (-empty_carrier(A) & latt_str(A) -> element(join_of_latt_set(A,B),the_carrier(A)))) # label(dt_k15_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 16 (all A all B (-empty_carrier(A) & latt_str(A) -> element(meet_of_latt_set(A,B),the_carrier(A)))) # label(dt_k16_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 17 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 18 (all A all B (rel_str(A) -> element(join_on_relstr(A,B),the_carrier(A)))) # label(dt_k1_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 19 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 20 (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].
% 0.43/1.08 21 (all A all B (rel_str(A) -> element(meet_on_relstr(A,B),the_carrier(A)))) # label(dt_k2_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 22 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 23 (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].
% 0.43/1.08 24 (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].
% 0.43/1.08 25 (all A all B (-empty_carrier(A) & lattice(A) & latt_str(A) & element(B,the_carrier(poset_of_lattice(A))) -> element(cast_to_el_of_lattice(A,B),the_carrier(A)))) # label(dt_k5_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 26 (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].
% 0.43/1.08 27 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 28 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 29 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 30 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 31 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 32 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 33 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 34 (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].
% 0.43/1.08 35 (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].
% 0.43/1.08 36 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 37 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 38 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 39 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 40 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 41 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 42 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 43 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 44 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 45 (all A all B (finite(A) & finite(B) -> finite(cartesian_product2(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 46 (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].
% 0.43/1.08 47 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 48 (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].
% 0.43/1.08 49 (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].
% 0.43/1.08 50 (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].
% 0.43/1.08 51 (all A all B all C (-empty_carrier(B) & latt_str(B) -> (in(A,a_2_2_lattice3(B,C)) <-> (exists D (element(D,the_carrier(B)) & A = D & latt_set_smaller(B,D,C)))))) # label(fraenkel_a_2_2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 52 (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].
% 0.43/1.08 53 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 54 (exists A (rel_str(A) & strict_rel_str(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 55 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 56 (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].
% 0.43/1.08 57 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 58 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 59 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 60 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 61 (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].
% 0.43/1.08 62 (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].
% 0.43/1.08 63 (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].
% 0.43/1.08 64 (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].
% 0.43/1.08 65 (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].
% 0.43/1.08 66 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 67 (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].
% 0.43/1.08 68 (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].
% 0.43/1.08 69 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (ex_sup_of_relstr_set(A,B) <-> (exists C (element(C,the_carrier(A)) & relstr_set_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) -> related(A,C,D)))))))))) # label(t15_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 70 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (ex_inf_of_relstr_set(A,B) <-> (exists C (element(C,the_carrier(A)) & relstr_element_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_element_smaller(A,B,D) -> related(A,D,C)))))))))) # label(t16_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 71 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 72 (all A all B (-empty_carrier(B) & lattice(B) & latt_str(B) -> (all C (element(C,the_carrier(B)) -> (latt_set_smaller(B,C,A) <-> relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))))))) # label(t28_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 73 (all A all B (-empty_carrier(B) & lattice(B) & latt_str(B) -> (all C (element(C,the_carrier(poset_of_lattice(B))) -> (relstr_element_smaller(poset_of_lattice(B),A,C) <-> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A)))))) # label(t29_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 74 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 75 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 76 (all A all B (-empty_carrier(B) & lattice(B) & latt_str(B) -> (all C (element(C,the_carrier(B)) -> (latt_element_smaller(B,C,A) <-> relstr_set_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))))))) # label(t30_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 77 (all A all B (-empty_carrier(B) & lattice(B) & latt_str(B) -> (all C (element(C,the_carrier(poset_of_lattice(B))) -> (relstr_set_smaller(poset_of_lattice(B),A,C) <-> latt_element_smaller(B,cast_to_el_of_lattice(B,C),A)))))) # label(t31_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 78 (all A (-empty_carrier(A) & lattice(A) & complete_latt_str(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (B = meet_of_latt_set(A,C) <-> latt_set_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (latt_set_smaller(A,D,C) -> below_refl(A,D,B)))))))))) # label(t34_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 79 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 80 (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].
% 0.43/1.08 81 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 82 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 83 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 84 (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].
% 0.43/1.08 85 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.08 86 -(all A (-empty_carrier(A) & lattice(A) & complete_latt_str(A) & latt_str(A) -> (all B (join_of_latt_set(A,B) = join_on_relstr(poset_of_lattice(A),B) & meet_of_latt_set(A,B) = meet_on_relstr(poset_of_lattice(A),B))))) # label(t29_yellow_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.08
% 0.43/1.08 ============================== end of process non-clausal formulas ===
% 0.43/1.08
% 0.43/1.08 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.08
% 0.43/1.08 ============================== PREDICATE ELIMINATION =================
% 0.43/1.08 87 latt_str(c5) # label(existence_l3_lattices) # label(axiom). [clausify(41)].
% 0.43/1.08 88 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(1)].
% 0.43/1.08 89 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_associative(A) # label(cc1_lattices) # label(axiom). [clausify(1)].
% 0.43/1.08 90 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(1)].
% 0.43/1.08 91 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_associative(A) # label(cc1_lattices) # label(axiom). [clausify(1)].
% 0.43/1.08 92 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(1)].
% 0.43/1.08 93 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(1)].
% 0.43/1.08 94 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) != B | latt_element_smaller(A,B,C) # label(d21_lattice3) # label(axiom). [clausify(8)].
% 0.43/1.08 95 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) != B | -element(D,the_carrier(A)) | -latt_element_smaller(A,D,C) | below(A,B,D) # label(d21_lattice3) # label(axiom). [clausify(8)].
% 0.43/1.08 96 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) = B | -latt_element_smaller(A,B,C) | element(f2(A,C,B),the_carrier(A)) # label(d21_lattice3) # label(axiom). [clausify(8)].
% 0.43/1.08 97 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) = B | -latt_element_smaller(A,B,C) | latt_element_smaller(A,f2(A,C,B),C) # label(d21_lattice3) # label(axiom). [clausify(8)].
% 0.43/1.08 98 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) = B | -latt_element_smaller(A,B,C) | -below(A,B,f2(A,C,B)) # label(d21_lattice3) # label(axiom). [clausify(8)].
% 0.43/1.08 99 empty_carrier(A) | -latt_str(A) | meet_of_latt_set(A,B) = join_of_latt_set(A,a_2_2_lattice3(A,B)) # label(d22_lattice3) # label(axiom). [clausify(9)].
% 0.43/1.08 100 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(10)].
% 0.43/1.08 101 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(11)].
% 0.43/1.08 102 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | cast_to_el_of_lattice(A,B) = B # label(d4_lattice3) # label(axiom). [clausify(12)].
% 0.43/1.08 103 empty_carrier(A) | -latt_str(A) | element(join_of_latt_set(A,B),the_carrier(A)) # label(dt_k15_lattice3) # label(axiom). [clausify(15)].
% 0.43/1.08 104 empty_carrier(A) | -latt_str(A) | element(meet_of_latt_set(A,B),the_carrier(A)) # label(dt_k16_lattice3) # label(axiom). [clausify(16)].
% 0.43/1.08 105 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(20)].
% 0.43/1.08 106 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(20)].
% 0.43/1.08 107 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(20)].
% 0.43/1.08 108 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(20)].
% 0.43/1.08 109 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(20)].
% 0.43/1.08 110 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(23)].
% 0.43/1.08 111 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(23)].
% 0.43/1.08 112 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(23)].
% 0.43/1.08 113 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(23)].
% 0.43/1.08 114 empty_carrier(A) | -lattice(A) | -latt_str(A) | rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(23)].
% 0.43/1.08 115 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(24)].
% 0.43/1.08 116 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | element(cast_to_el_of_lattice(A,B),the_carrier(A)) # label(dt_k5_lattice3) # label(axiom). [clausify(25)].
% 0.43/1.08 117 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation(relation_of_lattice(A)) # label(dt_k9_filter_1) # label(axiom). [clausify(26)].
% 0.43/1.08 118 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(31)].
% 0.43/1.08 119 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(31)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | join_commutative(c5). [resolve(87,a,88,a)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | join_associative(c5). [resolve(87,a,89,a)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | meet_commutative(c5). [resolve(87,a,90,a)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | meet_associative(c5). [resolve(87,a,91,a)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | meet_absorbing(c5). [resolve(87,a,92,a)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | join_absorbing(c5). [resolve(87,a,93,a)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | join_of_latt_set(c5,B) != A | latt_element_smaller(c5,A,B). [resolve(87,a,94,b)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | join_of_latt_set(c5,B) != A | -element(C,the_carrier(c5)) | -latt_element_smaller(c5,C,B) | below(c5,A,C). [resolve(87,a,95,b)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | join_of_latt_set(c5,B) = A | -latt_element_smaller(c5,A,B) | element(f2(c5,B,A),the_carrier(c5)). [resolve(87,a,96,b)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | join_of_latt_set(c5,B) = A | -latt_element_smaller(c5,A,B) | latt_element_smaller(c5,f2(c5,B,A),B). [resolve(87,a,97,b)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | join_of_latt_set(c5,B) = A | -latt_element_smaller(c5,A,B) | -below(c5,A,f2(c5,B,A)). [resolve(87,a,98,b)].
% 0.43/1.08 Derived: empty_carrier(c5) | meet_of_latt_set(c5,A) = join_of_latt_set(c5,a_2_2_lattice3(c5,A)). [resolve(87,a,99,b)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | poset_of_lattice(c5) = rel_str_of(the_carrier(c5),k2_lattice3(c5)). [resolve(87,a,100,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | cast_to_el_of_LattPOSet(c5,A) = A. [resolve(87,a,101,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | cast_to_el_of_lattice(c5,A) = A. [resolve(87,a,102,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | element(join_of_latt_set(c5,A),the_carrier(c5)). [resolve(87,a,103,b)].
% 0.43/1.08 Derived: empty_carrier(c5) | element(meet_of_latt_set(c5,A),the_carrier(c5)). [resolve(87,a,104,b)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | reflexive(k2_lattice3(c5)). [resolve(87,a,105,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | antisymmetric(k2_lattice3(c5)). [resolve(87,a,106,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | transitive(k2_lattice3(c5)). [resolve(87,a,107,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | v1_partfun1(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(87,a,108,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(87,a,109,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | strict_rel_str(poset_of_lattice(c5)). [resolve(87,a,110,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | reflexive_relstr(poset_of_lattice(c5)). [resolve(87,a,111,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | transitive_relstr(poset_of_lattice(c5)). [resolve(87,a,112,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | antisymmetric_relstr(poset_of_lattice(c5)). [resolve(87,a,113,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | rel_str(poset_of_lattice(c5)). [resolve(87,a,114,c)].
% 0.43/1.08 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(87,a,115,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | element(cast_to_el_of_lattice(c5,A),the_carrier(c5)). [resolve(87,a,116,c)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | relation(relation_of_lattice(c5)). [resolve(87,a,117,c)].
% 0.43/1.08 Derived: meet_semilatt_str(c5). [resolve(87,a,118,a)].
% 0.43/1.08 Derived: join_semilatt_str(c5). [resolve(87,a,119,a)].
% 0.43/1.08 120 empty_carrier(A) | -lattice(A) | -latt_str(A) | -empty_carrier(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(50)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -empty_carrier(poset_of_lattice(c5)). [resolve(120,c,87,a)].
% 0.43/1.08 121 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(50)].
% 0.43/1.08 122 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(50)].
% 0.43/1.08 123 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(50)].
% 0.43/1.08 124 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(50)].
% 0.43/1.08 125 empty_carrier(A) | -latt_str(A) | -in(B,a_2_2_lattice3(A,C)) | element(f7(B,A,C),the_carrier(A)) # label(fraenkel_a_2_2_lattice3) # label(axiom). [clausify(51)].
% 0.43/1.08 Derived: empty_carrier(c5) | -in(A,a_2_2_lattice3(c5,B)) | element(f7(A,c5,B),the_carrier(c5)). [resolve(125,b,87,a)].
% 0.43/1.08 126 empty_carrier(A) | -latt_str(A) | -in(B,a_2_2_lattice3(A,C)) | f7(B,A,C) = B # label(fraenkel_a_2_2_lattice3) # label(axiom). [clausify(51)].
% 0.43/1.08 Derived: empty_carrier(c5) | -in(A,a_2_2_lattice3(c5,B)) | f7(A,c5,B) = A. [resolve(126,b,87,a)].
% 0.43/1.08 127 empty_carrier(A) | -latt_str(A) | -in(B,a_2_2_lattice3(A,C)) | latt_set_smaller(A,f7(B,A,C),C) # label(fraenkel_a_2_2_lattice3) # label(axiom). [clausify(51)].
% 0.43/1.08 Derived: empty_carrier(c5) | -in(A,a_2_2_lattice3(c5,B)) | latt_set_smaller(c5,f7(A,c5,B),B). [resolve(127,b,87,a)].
% 0.43/1.08 128 empty_carrier(A) | -latt_str(A) | in(B,a_2_2_lattice3(A,C)) | -element(D,the_carrier(A)) | D != B | -latt_set_smaller(A,D,C) # label(fraenkel_a_2_2_lattice3) # label(axiom). [clausify(51)].
% 0.43/1.08 Derived: empty_carrier(c5) | in(A,a_2_2_lattice3(c5,B)) | -element(C,the_carrier(c5)) | C != A | -latt_set_smaller(c5,C,B). [resolve(128,b,87,a)].
% 0.43/1.08 129 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation_of_lattice(A) = k2_lattice3(A) # label(redefinition_k2_lattice3) # label(axiom). [clausify(62)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | relation_of_lattice(c5) = k2_lattice3(c5). [resolve(129,c,87,a)].
% 0.43/1.08 130 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(64)].
% 0.43/1.08 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(130,e,87,a)].
% 0.43/1.08 131 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(64)].
% 0.43/1.08 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(131,e,87,a)].
% 0.43/1.08 132 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(67)].
% 0.43/1.08 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(132,e,87,a)].
% 0.43/1.08 133 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -latt_set_smaller(A,B,C) | relstr_element_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B)) # label(t28_lattice3) # label(axiom). [clausify(72)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | -latt_set_smaller(c5,A,B) | relstr_element_smaller(poset_of_lattice(c5),B,cast_to_el_of_LattPOSet(c5,A)). [resolve(133,c,87,a)].
% 0.43/1.08 134 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | latt_set_smaller(A,B,C) | -relstr_element_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B)) # label(t28_lattice3) # label(axiom). [clausify(72)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | latt_set_smaller(c5,A,B) | -relstr_element_smaller(poset_of_lattice(c5),B,cast_to_el_of_LattPOSet(c5,A)). [resolve(134,c,87,a)].
% 0.43/1.08 135 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -relstr_element_smaller(poset_of_lattice(A),C,B) | latt_set_smaller(A,cast_to_el_of_lattice(A,B),C) # label(t29_lattice3) # label(axiom). [clausify(73)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -relstr_element_smaller(poset_of_lattice(c5),B,A) | latt_set_smaller(c5,cast_to_el_of_lattice(c5,A),B). [resolve(135,c,87,a)].
% 0.43/1.08 136 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | relstr_element_smaller(poset_of_lattice(A),C,B) | -latt_set_smaller(A,cast_to_el_of_lattice(A,B),C) # label(t29_lattice3) # label(axiom). [clausify(73)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | relstr_element_smaller(poset_of_lattice(c5),B,A) | -latt_set_smaller(c5,cast_to_el_of_lattice(c5,A),B). [resolve(136,c,87,a)].
% 0.43/1.08 137 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -latt_element_smaller(A,B,C) | relstr_set_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B)) # label(t30_lattice3) # label(axiom). [clausify(76)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | -latt_element_smaller(c5,A,B) | relstr_set_smaller(poset_of_lattice(c5),B,cast_to_el_of_LattPOSet(c5,A)). [resolve(137,c,87,a)].
% 0.43/1.08 138 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | latt_element_smaller(A,B,C) | -relstr_set_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B)) # label(t30_lattice3) # label(axiom). [clausify(76)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | latt_element_smaller(c5,A,B) | -relstr_set_smaller(poset_of_lattice(c5),B,cast_to_el_of_LattPOSet(c5,A)). [resolve(138,c,87,a)].
% 0.43/1.08 139 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -relstr_set_smaller(poset_of_lattice(A),C,B) | latt_element_smaller(A,cast_to_el_of_lattice(A,B),C) # label(t31_lattice3) # label(axiom). [clausify(77)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -relstr_set_smaller(poset_of_lattice(c5),B,A) | latt_element_smaller(c5,cast_to_el_of_lattice(c5,A),B). [resolve(139,c,87,a)].
% 0.43/1.08 140 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | relstr_set_smaller(poset_of_lattice(A),C,B) | -latt_element_smaller(A,cast_to_el_of_lattice(A,B),C) # label(t31_lattice3) # label(axiom). [clausify(77)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | relstr_set_smaller(poset_of_lattice(c5),B,A) | -latt_element_smaller(c5,cast_to_el_of_lattice(c5,A),B). [resolve(140,c,87,a)].
% 0.43/1.08 141 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | -element(B,the_carrier(A)) | meet_of_latt_set(A,C) != B | latt_set_smaller(A,B,C) # label(t34_lattice3) # label(axiom). [clausify(78)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | meet_of_latt_set(c5,B) != A | latt_set_smaller(c5,A,B). [resolve(141,d,87,a)].
% 0.43/1.08 142 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | -element(B,the_carrier(A)) | meet_of_latt_set(A,C) != B | -element(D,the_carrier(A)) | -latt_set_smaller(A,D,C) | below_refl(A,D,B) # label(t34_lattice3) # label(axiom). [clausify(78)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | meet_of_latt_set(c5,B) != A | -element(C,the_carrier(c5)) | -latt_set_smaller(c5,C,B) | below_refl(c5,C,A). [resolve(142,d,87,a)].
% 0.43/1.08 143 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | -element(B,the_carrier(A)) | meet_of_latt_set(A,C) = B | -latt_set_smaller(A,B,C) | element(f16(A,B,C),the_carrier(A)) # label(t34_lattice3) # label(axiom). [clausify(78)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | meet_of_latt_set(c5,B) = A | -latt_set_smaller(c5,A,B) | element(f16(c5,A,B),the_carrier(c5)). [resolve(143,d,87,a)].
% 0.43/1.08 144 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | -element(B,the_carrier(A)) | meet_of_latt_set(A,C) = B | -latt_set_smaller(A,B,C) | latt_set_smaller(A,f16(A,B,C),C) # label(t34_lattice3) # label(axiom). [clausify(78)].
% 0.43/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | meet_of_latt_set(c5,B) = A | -latt_set_smaller(c5,A,B) | latt_set_smaller(c5,f16(c5,A,B),B). [resolve(144,d,87,a)].
% 0.43/1.08 145 empty_carrier(A) | -lattice(A) | -complete_latt_str(A) | -latt_str(A) | -element(B,the_carrier(A)) | meet_of_latt_set(A,C) = B | -latt_set_smaller(A,B,C) | -below_refl(A,f16(A,B,C),B) # label(t34_lattice3) # label(axiom). [clausify(78)].
% 0.80/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -complete_latt_str(c5) | -element(A,the_carrier(c5)) | meet_of_latt_set(c5,B) = A | -latt_set_smaller(c5,A,B) | -below_refl(c5,f16(c5,A,B),A). [resolve(145,d,87,a)].
% 0.80/1.08 146 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(84)].
% 0.80/1.08 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(146,c,87,a)].
% 0.80/1.08 147 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(84)].
% 0.80/1.08 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(147,c,87,a)].
% 0.80/1.08 148 latt_str(c12) # label(t29_yellow_0) # label(negated_conjecture). [clausify(86)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | join_commutative(c12). [resolve(148,a,88,a)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | join_associative(c12). [resolve(148,a,89,a)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | meet_commutative(c12). [resolve(148,a,90,a)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | meet_associative(c12). [resolve(148,a,91,a)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | meet_absorbing(c12). [resolve(148,a,92,a)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | join_absorbing(c12). [resolve(148,a,93,a)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | join_of_latt_set(c12,B) != A | latt_element_smaller(c12,A,B). [resolve(148,a,94,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | join_of_latt_set(c12,B) != A | -element(C,the_carrier(c12)) | -latt_element_smaller(c12,C,B) | below(c12,A,C). [resolve(148,a,95,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | join_of_latt_set(c12,B) = A | -latt_element_smaller(c12,A,B) | element(f2(c12,B,A),the_carrier(c12)). [resolve(148,a,96,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | join_of_latt_set(c12,B) = A | -latt_element_smaller(c12,A,B) | latt_element_smaller(c12,f2(c12,B,A),B). [resolve(148,a,97,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | join_of_latt_set(c12,B) = A | -latt_element_smaller(c12,A,B) | -below(c12,A,f2(c12,B,A)). [resolve(148,a,98,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | meet_of_latt_set(c12,A) = join_of_latt_set(c12,a_2_2_lattice3(c12,A)). [resolve(148,a,99,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | poset_of_lattice(c12) = rel_str_of(the_carrier(c12),k2_lattice3(c12)). [resolve(148,a,100,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | cast_to_el_of_LattPOSet(c12,A) = A. [resolve(148,a,101,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | cast_to_el_of_lattice(c12,A) = A. [resolve(148,a,102,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | element(join_of_latt_set(c12,A),the_carrier(c12)). [resolve(148,a,103,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | element(meet_of_latt_set(c12,A),the_carrier(c12)). [resolve(148,a,104,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | reflexive(k2_lattice3(c12)). [resolve(148,a,105,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | antisymmetric(k2_lattice3(c12)). [resolve(148,a,106,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | transitive(k2_lattice3(c12)). [resolve(148,a,107,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | v1_partfun1(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(148,a,108,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | relation_of2_as_subset(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(148,a,109,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | strict_rel_str(poset_of_lattice(c12)). [resolve(148,a,110,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | reflexive_relstr(poset_of_lattice(c12)). [resolve(148,a,111,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | transitive_relstr(poset_of_lattice(c12)). [resolve(148,a,112,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | antisymmetric_relstr(poset_of_lattice(c12)). [resolve(148,a,113,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | rel_str(poset_of_lattice(c12)). [resolve(148,a,114,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | element(cast_to_el_of_LattPOSet(c12,A),the_carrier(poset_of_lattice(c12))). [resolve(148,a,115,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | element(cast_to_el_of_lattice(c12,A),the_carrier(c12)). [resolve(148,a,116,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | relation(relation_of_lattice(c12)). [resolve(148,a,117,c)].
% 0.80/1.08 Derived: meet_semilatt_str(c12). [resolve(148,a,118,a)].
% 0.80/1.08 Derived: join_semilatt_str(c12). [resolve(148,a,119,a)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -empty_carrier(poset_of_lattice(c12)). [resolve(148,a,120,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -in(A,a_2_2_lattice3(c12,B)) | element(f7(A,c12,B),the_carrier(c12)). [resolve(148,a,125,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | -in(A,a_2_2_lattice3(c12,B)) | f7(A,c12,B) = A. [resolve(148,a,126,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | -in(A,a_2_2_lattice3(c12,B)) | latt_set_smaller(c12,f7(A,c12,B),B). [resolve(148,a,127,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | in(A,a_2_2_lattice3(c12,B)) | -element(C,the_carrier(c12)) | C != A | -latt_set_smaller(c12,C,B). [resolve(148,a,128,b)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | relation_of_lattice(c12) = k2_lattice3(c12). [resolve(148,a,129,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -meet_commutative(c12) | -meet_absorbing(c12) | -join_absorbing(c12) | -element(A,the_carrier(c12)) | -element(B,the_carrier(c12)) | -below_refl(c12,A,B) | below(c12,A,B). [resolve(148,a,130,e)].
% 0.80/1.08 Derived: empty_carrier(c12) | -meet_commutative(c12) | -meet_absorbing(c12) | -join_absorbing(c12) | -element(A,the_carrier(c12)) | -element(B,the_carrier(c12)) | below_refl(c12,A,B) | -below(c12,A,B). [resolve(148,a,131,e)].
% 0.80/1.08 Derived: empty_carrier(c12) | -meet_commutative(c12) | -meet_absorbing(c12) | -join_absorbing(c12) | -element(A,the_carrier(c12)) | -element(B,the_carrier(c12)) | below_refl(c12,A,A). [resolve(148,a,132,e)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | -latt_set_smaller(c12,A,B) | relstr_element_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [resolve(148,a,133,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | latt_set_smaller(c12,A,B) | -relstr_element_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [resolve(148,a,134,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -relstr_element_smaller(poset_of_lattice(c12),B,A) | latt_set_smaller(c12,cast_to_el_of_lattice(c12,A),B). [resolve(148,a,135,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | relstr_element_smaller(poset_of_lattice(c12),B,A) | -latt_set_smaller(c12,cast_to_el_of_lattice(c12,A),B). [resolve(148,a,136,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | -latt_element_smaller(c12,A,B) | relstr_set_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [resolve(148,a,137,c)].
% 0.80/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | latt_element_smaller(c12,A,B) | -relstr_set_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [resolve(148,a,138,c)].
% 0.80/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -relstr_set_smaller(poset_of_lattice(c12),B,A) | latt_element_smaller(c12,cast_to_el_of_lattice(c12,A),B). [resolve(148,a,139,c)].
% 0.80/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | relstr_set_smaller(poset_of_lattice(c12),B,A) | -latt_element_smaller(c12,cast_to_el_of_lattice(c12,A),B). [resolve(148,a,140,c)].
% 0.80/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | meet_of_latt_set(c12,B) != A | latt_set_smaller(c12,A,B). [resolve(148,a,141,d)].
% 0.80/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | meet_of_latt_set(c12,B) != A | -element(C,the_carrier(c12)) | -latt_set_smaller(c12,C,B) | below_refl(c12,C,A). [resolve(148,a,142,d)].
% 0.80/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | meet_of_latt_set(c12,B) = A | -latt_set_smaller(c12,A,B) | element(f16(c12,A,B),the_carrier(c12)). [resolve(148,a,143,d)].
% 0.80/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | meet_of_latt_set(c12,B) = A | -latt_set_smaller(c12,A,B) | latt_set_smaller(c12,f16(c12,A,B),B). [resolve(148,a,144,d)].
% 0.80/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -complete_latt_str(c12) | -element(A,the_carrier(c12)) | meet_of_latt_set(c12,B) = A | -latt_set_smaller(c12,A,B) | -below_refl(c12,f16(c12,A,B),A). [resolve(148,a,145,d)].
% 0.80/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | -element(B,the_carrier(c12)) | -below_refl(c12,A,B) | related_reflexive(poset_of_lattice(c12),cast_to_el_of_LattPOSet(c12,A),cast_to_el_of_LattPOSet(c12,B)). [resolve(148,a,146,c)].
% 0.80/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | -element(B,the_carrier(c12)) | below_refl(c12,A,B) | -related_reflexive(poset_of_lattice(c12),cast_to_el_of_LattPOSet(c12,A),cast_to_el_of_LattPOSet(c12,B)). [resolve(148,a,147,c)].
% 0.80/1.09 149 -relation_of2(A,B,B) | rel_str(rel_str_of(B,A)) # label(dt_g1_orders_2) # label(axiom). [clausify(14)].
% 0.80/1.09 150 -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(2)].
% 0.80/1.09 151 -rel_str(A) | -element(B,the_carrier(A)) | -ex_inf_of_relstr_set(A,C) | meet_on_relstr(A,C) != B | relstr_element_smaller(A,C,B) # label(d10_yellow_0) # label(axiom). [clausify(7)].
% 0.80/1.09 152 -rel_str(A) | -element(B,the_carrier(A)) | -ex_inf_of_relstr_set(A,C) | meet_on_relstr(A,C) != B | -element(D,the_carrier(A)) | -relstr_element_smaller(A,C,D) | related(A,D,B) # label(d10_yellow_0) # label(axiom). [clausify(7)].
% 0.80/1.09 153 -rel_str(A) | -element(B,the_carrier(A)) | -ex_inf_of_relstr_set(A,C) | meet_on_relstr(A,C) = B | -relstr_element_smaller(A,C,B) | element(f1(A,C,B),the_carrier(A)) # label(d10_yellow_0) # label(axiom). [clausify(7)].
% 0.80/1.09 154 -rel_str(A) | -element(B,the_carrier(A)) | -ex_inf_of_relstr_set(A,C) | meet_on_relstr(A,C) = B | -relstr_element_smaller(A,C,B) | relstr_element_smaller(A,C,f1(A,C,B)) # label(d10_yellow_0) # label(axiom). [clausify(7)].
% 0.80/1.09 155 -rel_str(A) | -element(B,the_carrier(A)) | -ex_inf_of_relstr_set(A,C) | meet_on_relstr(A,C) = B | -relstr_element_smaller(A,C,B) | -related(A,f1(A,C,B),B) # label(d10_yellow_0) # label(axiom). [clausify(7)].
% 0.80/1.09 156 -rel_str(A) | -element(B,the_carrier(A)) | -ex_sup_of_relstr_set(A,C) | join_on_relstr(A,C) != B | relstr_set_smaller(A,C,B) # label(d9_yellow_0) # label(axiom). [clausify(13)].
% 0.80/1.09 157 -rel_str(A) | -element(B,the_carrier(A)) | -ex_sup_of_relstr_set(A,C) | join_on_relstr(A,C) != B | -element(D,the_carrier(A)) | -relstr_set_smaller(A,C,D) | related(A,B,D) # label(d9_yellow_0) # label(axiom). [clausify(13)].
% 0.80/1.09 158 -rel_str(A) | -element(B,the_carrier(A)) | -ex_sup_of_relstr_set(A,C) | join_on_relstr(A,C) = B | -relstr_set_smaller(A,C,B) | element(f3(A,C,B),the_carrier(A)) # label(d9_yellow_0) # label(axiom). [clausify(13)].
% 0.80/1.09 159 -rel_str(A) | -element(B,the_carrier(A)) | -ex_sup_of_relstr_set(A,C) | join_on_relstr(A,C) = B | -relstr_set_smaller(A,C,B) | relstr_set_smaller(A,C,f3(A,C,B)) # label(d9_yellow_0) # label(axiom). [clausify(13)].
% 0.80/1.09 160 -rel_str(A) | -element(B,the_carrier(A)) | -ex_sup_of_relstr_set(A,C) | join_on_relstr(A,C) = B | -relstr_set_smaller(A,C,B) | -related(A,B,f3(A,C,B)) # label(d9_yellow_0) # label(axiom). [clausify(13)].
% 0.80/1.09 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(149,b,150,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_inf_of_relstr_set(rel_str_of(B,A),D) | meet_on_relstr(rel_str_of(B,A),D) != C | relstr_element_smaller(rel_str_of(B,A),D,C). [resolve(149,b,151,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_inf_of_relstr_set(rel_str_of(B,A),D) | meet_on_relstr(rel_str_of(B,A),D) != C | -element(E,the_carrier(rel_str_of(B,A))) | -relstr_element_smaller(rel_str_of(B,A),D,E) | related(rel_str_of(B,A),E,C). [resolve(149,b,152,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_inf_of_relstr_set(rel_str_of(B,A),D) | meet_on_relstr(rel_str_of(B,A),D) = C | -relstr_element_smaller(rel_str_of(B,A),D,C) | element(f1(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))). [resolve(149,b,153,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_inf_of_relstr_set(rel_str_of(B,A),D) | meet_on_relstr(rel_str_of(B,A),D) = C | -relstr_element_smaller(rel_str_of(B,A),D,C) | relstr_element_smaller(rel_str_of(B,A),D,f1(rel_str_of(B,A),D,C)). [resolve(149,b,154,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_inf_of_relstr_set(rel_str_of(B,A),D) | meet_on_relstr(rel_str_of(B,A),D) = C | -relstr_element_smaller(rel_str_of(B,A),D,C) | -related(rel_str_of(B,A),f1(rel_str_of(B,A),D,C),C). [resolve(149,b,155,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_sup_of_relstr_set(rel_str_of(B,A),D) | join_on_relstr(rel_str_of(B,A),D) != C | relstr_set_smaller(rel_str_of(B,A),D,C). [resolve(149,b,156,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_sup_of_relstr_set(rel_str_of(B,A),D) | join_on_relstr(rel_str_of(B,A),D) != C | -element(E,the_carrier(rel_str_of(B,A))) | -relstr_set_smaller(rel_str_of(B,A),D,E) | related(rel_str_of(B,A),C,E). [resolve(149,b,157,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_sup_of_relstr_set(rel_str_of(B,A),D) | join_on_relstr(rel_str_of(B,A),D) = C | -relstr_set_smaller(rel_str_of(B,A),D,C) | element(f3(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))). [resolve(149,b,158,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_sup_of_relstr_set(rel_str_of(B,A),D) | join_on_relstr(rel_str_of(B,A),D) = C | -relstr_set_smaller(rel_str_of(B,A),D,C) | relstr_set_smaller(rel_str_of(B,A),D,f3(rel_str_of(B,A),D,C)). [resolve(149,b,159,a)].
% 0.80/1.09 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -ex_sup_of_relstr_set(rel_str_of(B,A),D) | join_on_relstr(rel_str_of(B,A),D) = C | -relstr_set_smaller(rel_str_of(B,A),D,C) | -related(rel_str_of(B,A),C,f3(rel_str_of(B,A),D,C)). [resolve(149,b,160,a)].
% 0.80/1.09 161 -rel_str(A) | element(join_on_relstr(A,B),the_carrier(A)) # label(dt_k1_yellow_0) # label(axiom). [clausify(18)].
% 0.80/1.09 Derived: element(join_on_relstr(rel_str_of(A,B),C),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(161,a,149,b)].
% 0.80/1.09 162 -rel_str(A) | element(meet_on_relstr(A,B),the_carrier(A)) # label(dt_k2_yellow_0) # label(axiom). [clausify(21)].
% 0.80/1.09 Derived: element(meet_on_relstr(rel_str_of(A,B),C),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(162,a,149,b)].
% 0.80/1.09 163 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(28)].
% 0.80/1.09 Derived: one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(163,a,149,b)].
% 0.80/1.09 164 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(35)].
% 0.80/1.09 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(164,a,149,b)].
% 0.80/1.09 165 rel_str(c2) # label(existence_l1_orders_2) # label(axiom). [clausify(38)].
% 0.80/1.09 Derived: -strict_rel_str(c2) | rel_str_of(the_carrier(c2),the_InternalRel(c2)) = c2. [resolve(165,a,150,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_inf_of_relstr_set(c2,B) | meet_on_relstr(c2,B) != A | relstr_element_smaller(c2,B,A). [resolve(165,a,151,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_inf_of_relstr_set(c2,B) | meet_on_relstr(c2,B) != A | -element(C,the_carrier(c2)) | -relstr_element_smaller(c2,B,C) | related(c2,C,A). [resolve(165,a,152,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_inf_of_relstr_set(c2,B) | meet_on_relstr(c2,B) = A | -relstr_element_smaller(c2,B,A) | element(f1(c2,B,A),the_carrier(c2)). [resolve(165,a,153,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_inf_of_relstr_set(c2,B) | meet_on_relstr(c2,B) = A | -relstr_element_smaller(c2,B,A) | relstr_element_smaller(c2,B,f1(c2,B,A)). [resolve(165,a,154,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_inf_of_relstr_set(c2,B) | meet_on_relstr(c2,B) = A | -relstr_element_smaller(c2,B,A) | -related(c2,f1(c2,B,A),A). [resolve(165,a,155,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_sup_of_relstr_set(c2,B) | join_on_relstr(c2,B) != A | relstr_set_smaller(c2,B,A). [resolve(165,a,156,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_sup_of_relstr_set(c2,B) | join_on_relstr(c2,B) != A | -element(C,the_carrier(c2)) | -relstr_set_smaller(c2,B,C) | related(c2,A,C). [resolve(165,a,157,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_sup_of_relstr_set(c2,B) | join_on_relstr(c2,B) = A | -relstr_set_smaller(c2,B,A) | element(f3(c2,B,A),the_carrier(c2)). [resolve(165,a,158,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_sup_of_relstr_set(c2,B) | join_on_relstr(c2,B) = A | -relstr_set_smaller(c2,B,A) | relstr_set_smaller(c2,B,f3(c2,B,A)). [resolve(165,a,159,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c2)) | -ex_sup_of_relstr_set(c2,B) | join_on_relstr(c2,B) = A | -relstr_set_smaller(c2,B,A) | -related(c2,A,f3(c2,B,A)). [resolve(165,a,160,a)].
% 0.80/1.09 Derived: element(join_on_relstr(c2,A),the_carrier(c2)). [resolve(165,a,161,a)].
% 0.80/1.09 Derived: element(meet_on_relstr(c2,A),the_carrier(c2)). [resolve(165,a,162,a)].
% 0.80/1.09 Derived: one_sorted_str(c2). [resolve(165,a,163,a)].
% 0.80/1.09 Derived: relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(165,a,164,a)].
% 0.80/1.09 166 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | relation(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(48)].
% 0.80/1.09 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(166,d,149,b)].
% 0.80/1.09 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | relation(the_InternalRel(c2)). [resolve(166,d,165,a)].
% 0.80/1.09 167 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | reflexive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(48)].
% 0.80/1.09 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(167,d,149,b)].
% 0.80/1.09 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(167,d,165,a)].
% 0.80/1.09 168 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | antisymmetric(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(48)].
% 0.80/1.09 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(168,d,149,b)].
% 0.80/1.09 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | antisymmetric(the_InternalRel(c2)). [resolve(168,d,165,a)].
% 0.80/1.09 169 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | transitive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(48)].
% 0.80/1.09 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(169,d,149,b)].
% 0.80/1.09 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | transitive(the_InternalRel(c2)). [resolve(169,d,165,a)].
% 0.80/1.09 170 -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(48)].
% 0.80/1.09 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(170,d,149,b)].
% 0.80/1.09 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | v1_partfun1(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(170,d,165,a)].
% 0.80/1.09 171 rel_str(c7) # label(rc1_orders_2) # label(axiom). [clausify(54)].
% 0.80/1.09 Derived: -strict_rel_str(c7) | rel_str_of(the_carrier(c7),the_InternalRel(c7)) = c7. [resolve(171,a,150,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_inf_of_relstr_set(c7,B) | meet_on_relstr(c7,B) != A | relstr_element_smaller(c7,B,A). [resolve(171,a,151,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_inf_of_relstr_set(c7,B) | meet_on_relstr(c7,B) != A | -element(C,the_carrier(c7)) | -relstr_element_smaller(c7,B,C) | related(c7,C,A). [resolve(171,a,152,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_inf_of_relstr_set(c7,B) | meet_on_relstr(c7,B) = A | -relstr_element_smaller(c7,B,A) | element(f1(c7,B,A),the_carrier(c7)). [resolve(171,a,153,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_inf_of_relstr_set(c7,B) | meet_on_relstr(c7,B) = A | -relstr_element_smaller(c7,B,A) | relstr_element_smaller(c7,B,f1(c7,B,A)). [resolve(171,a,154,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_inf_of_relstr_set(c7,B) | meet_on_relstr(c7,B) = A | -relstr_element_smaller(c7,B,A) | -related(c7,f1(c7,B,A),A). [resolve(171,a,155,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_sup_of_relstr_set(c7,B) | join_on_relstr(c7,B) != A | relstr_set_smaller(c7,B,A). [resolve(171,a,156,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_sup_of_relstr_set(c7,B) | join_on_relstr(c7,B) != A | -element(C,the_carrier(c7)) | -relstr_set_smaller(c7,B,C) | related(c7,A,C). [resolve(171,a,157,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_sup_of_relstr_set(c7,B) | join_on_relstr(c7,B) = A | -relstr_set_smaller(c7,B,A) | element(f3(c7,B,A),the_carrier(c7)). [resolve(171,a,158,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_sup_of_relstr_set(c7,B) | join_on_relstr(c7,B) = A | -relstr_set_smaller(c7,B,A) | relstr_set_smaller(c7,B,f3(c7,B,A)). [resolve(171,a,159,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c7)) | -ex_sup_of_relstr_set(c7,B) | join_on_relstr(c7,B) = A | -relstr_set_smaller(c7,B,A) | -related(c7,A,f3(c7,B,A)). [resolve(171,a,160,a)].
% 0.80/1.09 Derived: element(join_on_relstr(c7,A),the_carrier(c7)). [resolve(171,a,161,a)].
% 0.80/1.09 Derived: element(meet_on_relstr(c7,A),the_carrier(c7)). [resolve(171,a,162,a)].
% 0.80/1.09 Derived: one_sorted_str(c7). [resolve(171,a,163,a)].
% 0.80/1.09 Derived: relation_of2_as_subset(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)). [resolve(171,a,164,a)].
% 0.80/1.09 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | relation(the_InternalRel(c7)). [resolve(171,a,166,d)].
% 0.80/1.09 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | reflexive(the_InternalRel(c7)). [resolve(171,a,167,d)].
% 0.80/1.09 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | antisymmetric(the_InternalRel(c7)). [resolve(171,a,168,d)].
% 0.80/1.09 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | transitive(the_InternalRel(c7)). [resolve(171,a,169,d)].
% 0.80/1.09 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | v1_partfun1(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)). [resolve(171,a,170,d)].
% 0.80/1.09 172 rel_str(c9) # label(rc2_orders_2) # label(axiom). [clausify(56)].
% 0.80/1.09 Derived: -strict_rel_str(c9) | rel_str_of(the_carrier(c9),the_InternalRel(c9)) = c9. [resolve(172,a,150,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_inf_of_relstr_set(c9,B) | meet_on_relstr(c9,B) != A | relstr_element_smaller(c9,B,A). [resolve(172,a,151,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_inf_of_relstr_set(c9,B) | meet_on_relstr(c9,B) != A | -element(C,the_carrier(c9)) | -relstr_element_smaller(c9,B,C) | related(c9,C,A). [resolve(172,a,152,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_inf_of_relstr_set(c9,B) | meet_on_relstr(c9,B) = A | -relstr_element_smaller(c9,B,A) | element(f1(c9,B,A),the_carrier(c9)). [resolve(172,a,153,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_inf_of_relstr_set(c9,B) | meet_on_relstr(c9,B) = A | -relstr_element_smaller(c9,B,A) | relstr_element_smaller(c9,B,f1(c9,B,A)). [resolve(172,a,154,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_inf_of_relstr_set(c9,B) | meet_on_relstr(c9,B) = A | -relstr_element_smaller(c9,B,A) | -related(c9,f1(c9,B,A),A). [resolve(172,a,155,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_sup_of_relstr_set(c9,B) | join_on_relstr(c9,B) != A | relstr_set_smaller(c9,B,A). [resolve(172,a,156,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_sup_of_relstr_set(c9,B) | join_on_relstr(c9,B) != A | -element(C,the_carrier(c9)) | -relstr_set_smaller(c9,B,C) | related(c9,A,C). [resolve(172,a,157,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_sup_of_relstr_set(c9,B) | join_on_relstr(c9,B) = A | -relstr_set_smaller(c9,B,A) | element(f3(c9,B,A),the_carrier(c9)). [resolve(172,a,158,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_sup_of_relstr_set(c9,B) | join_on_relstr(c9,B) = A | -relstr_set_smaller(c9,B,A) | relstr_set_smaller(c9,B,f3(c9,B,A)). [resolve(172,a,159,a)].
% 0.80/1.09 Derived: -element(A,the_carrier(c9)) | -ex_sup_of_relstr_set(c9,B) | join_on_relstr(c9,B) = A | -relstr_set_smaller(c9,B,A) | -related(c9,A,f3(c9,B,A)). [resolve(172,a,160,a)].
% 0.80/1.09 Derived: element(join_on_relstr(c9,A),the_carrier(c9)). [resolve(172,a,161,a)].
% 0.80/1.09 Derived: element(meet_on_relstr(c9,A),the_carrier(c9)). [resolve(172,a,162,a)].
% 0.80/1.09 Derived: one_sorted_str(c9). [resolve(172,a,163,a)].
% 0.80/1.09 Derived: relation_of2_as_subset(the_InternalRel(c9),the_carrier(c9),the_carrier(c9)). [resolve(172,a,164,a)].
% 0.80/1.09 Derived: -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | relation(the_InternalRel(c9)). [resolve(172,a,166,d)].
% 0.80/1.09 Derived: -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | reflexive(the_InternalRel(c9)). [resolve(172,a,167,d)].
% 0.80/1.09 Derived: -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | antisymmetric(the_InternalRel(c9)). [resolve(172,a,168,d)].
% 0.80/1.09 Derived: -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | transitive(the_InternalRel(c9)). [resolve(172,a,169,d)].
% 0.80/1.09 Derived: -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | v1_partfun1(the_InternalRel(c9),the_carrier(c9),the_carrier(c9)). [resolve(172,a,170,d)].
% 0.80/1.09 173 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(65)].
% 0.80/1.09 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(173,c,149,b)].
% 0.80/1.09 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(173,c,165,a)].
% 0.80/1.09 Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | -related_reflexive(c7,A,B) | related(c7,A,B). [resolve(173,c,171,a)].
% 0.80/1.09 Derived: empty_carrier(c9) | -reflexive_relstr(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | -related_reflexive(c9,A,B) | related(c9,A,B). [resolve(173,c,172,a)].
% 0.80/1.09 174 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(65)].
% 0.80/1.09 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(174,c,149,b)].
% 0.80/1.09 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(174,c,165,a)].
% 0.80/1.09 Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | related_reflexive(c7,A,B) | -related(c7,A,B). [resolve(174,c,171,a)].
% 0.80/1.09 Derived: empty_carrier(c9) | -reflexive_relstr(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | related_reflexive(c9,A,B) | -related(c9,A,B). [resolve(174,c,172,a)].
% 0.80/1.09 175 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(68)].
% 0.80/1.09 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(175,c,149,b)].
% 0.80/1.09 Derived: empty_carrier(c2) | -reflexive_relstr(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | related_reflexive(c2,A,A). [resolve(175,c,165,a)].
% 0.80/1.09 Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | related_reflexive(c7,A,A). [resolve(175,c,171,a)].
% 0.80/1.09 Derived: empty_carrier(c9) | -reflexive_relstr(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | related_reflexive(c9,A,A). [resolve(175,c,172,a)].
% 0.80/1.09 176 -antisymmetric_relstr(A) | -rel_str(A) | -ex_sup_of_relstr_set(A,B) | element(f11(A,B),the_carrier(A)) # label(t15_yellow_0) # label(axiom). [clausify(69)].
% 0.80/1.09 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | -ex_sup_of_relstr_set(rel_str_of(A,B),C) | element(f11(rel_str_of(A,B),C),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(176,b,149,b)].
% 0.80/1.09 Derived: -antisymmetric_relstr(c2) | -ex_sup_of_relstr_set(c2,A) | element(f11(c2,A),the_carrier(c2)). [resolve(176,b,165,a)].
% 0.80/1.09 Derived: -antisymmetric_relstr(c7) | -ex_sup_of_relstr_set(c7,A) | element(f11(c7,A),the_carrier(c7)). [resolve(176,b,171,a)].
% 0.80/1.09 Derived: -antisymmetric_relstr(c9) | -ex_sup_of_relstr_set(c9,A) | element(f11(c9,A),the_carrier(c9)). [resolve(176,b,172,a)].
% 0.80/1.09 177 -antisymmetric_relstr(A) | -rel_str(A) | -ex_sup_of_relstr_set(A,B) | relstr_set_smaller(A,B,f11(A,B)) # label(t15_yellow_0) # label(axiom). [clausify(69)].
% 0.80/1.09 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | -ex_sup_of_relstr_set(rel_str_of(A,B),C) | relstr_set_smaller(rel_str_of(A,B),C,f11(rel_str_of(A,B),C)) | -relation_of2(B,A,A). [resolve(177,b,149,b)].
% 0.80/1.09 Derived: -antisymmetric_relstr(c2) | -ex_sup_of_relstr_set(c2,A) | relstr_set_smaller(c2,A,f11(c2,A)). [resolve(177,b,165,a)].
% 0.80/1.09 Derived: -antisymmetric_relstr(c7) | -ex_sup_of_relstr_set(c7,A) | relstr_set_smaller(c7,A,f11(c7,A)). [resolve(177,b,171,a)].
% 0.80/1.09 Derived: -antisymmetric_relstr(c9) | -ex_sup_of_relstr_set(c9,A) | relstr_set_smaller(c9,A,f11(c9,A)). [resolve(177,b,172,a)].
% 0.80/1.10 178 -antisymmetric_relstr(A) | -rel_str(A) | -ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | related(A,f11(A,B),C) # label(t15_yellow_0) # label(axiom). [clausify(69)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | -ex_sup_of_relstr_set(rel_str_of(A,B),C) | -element(D,the_carrier(rel_str_of(A,B))) | -relstr_set_smaller(rel_str_of(A,B),C,D) | related(rel_str_of(A,B),f11(rel_str_of(A,B),C),D) | -relation_of2(B,A,A). [resolve(178,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | -ex_sup_of_relstr_set(c2,A) | -element(B,the_carrier(c2)) | -relstr_set_smaller(c2,A,B) | related(c2,f11(c2,A),B). [resolve(178,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | -ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | related(c7,f11(c7,A),B). [resolve(178,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | -ex_sup_of_relstr_set(c9,A) | -element(B,the_carrier(c9)) | -relstr_set_smaller(c9,A,B) | related(c9,f11(c9,A),B). [resolve(178,b,172,a)].
% 0.80/1.10 179 -antisymmetric_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | element(f12(A,B,C),the_carrier(A)) # label(t15_yellow_0) # label(axiom). [clausify(69)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | ex_sup_of_relstr_set(rel_str_of(A,B),C) | -element(D,the_carrier(rel_str_of(A,B))) | -relstr_set_smaller(rel_str_of(A,B),C,D) | element(f12(rel_str_of(A,B),C,D),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(179,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | ex_sup_of_relstr_set(c2,A) | -element(B,the_carrier(c2)) | -relstr_set_smaller(c2,A,B) | element(f12(c2,A,B),the_carrier(c2)). [resolve(179,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | element(f12(c7,A,B),the_carrier(c7)). [resolve(179,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | ex_sup_of_relstr_set(c9,A) | -element(B,the_carrier(c9)) | -relstr_set_smaller(c9,A,B) | element(f12(c9,A,B),the_carrier(c9)). [resolve(179,b,172,a)].
% 0.80/1.10 180 -antisymmetric_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | relstr_set_smaller(A,B,f12(A,B,C)) # label(t15_yellow_0) # label(axiom). [clausify(69)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | ex_sup_of_relstr_set(rel_str_of(A,B),C) | -element(D,the_carrier(rel_str_of(A,B))) | -relstr_set_smaller(rel_str_of(A,B),C,D) | relstr_set_smaller(rel_str_of(A,B),C,f12(rel_str_of(A,B),C,D)) | -relation_of2(B,A,A). [resolve(180,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | ex_sup_of_relstr_set(c2,A) | -element(B,the_carrier(c2)) | -relstr_set_smaller(c2,A,B) | relstr_set_smaller(c2,A,f12(c2,A,B)). [resolve(180,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | relstr_set_smaller(c7,A,f12(c7,A,B)). [resolve(180,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | ex_sup_of_relstr_set(c9,A) | -element(B,the_carrier(c9)) | -relstr_set_smaller(c9,A,B) | relstr_set_smaller(c9,A,f12(c9,A,B)). [resolve(180,b,172,a)].
% 0.80/1.10 181 -antisymmetric_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | -related(A,C,f12(A,B,C)) # label(t15_yellow_0) # label(axiom). [clausify(69)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | ex_sup_of_relstr_set(rel_str_of(A,B),C) | -element(D,the_carrier(rel_str_of(A,B))) | -relstr_set_smaller(rel_str_of(A,B),C,D) | -related(rel_str_of(A,B),D,f12(rel_str_of(A,B),C,D)) | -relation_of2(B,A,A). [resolve(181,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | ex_sup_of_relstr_set(c2,A) | -element(B,the_carrier(c2)) | -relstr_set_smaller(c2,A,B) | -related(c2,B,f12(c2,A,B)). [resolve(181,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | -related(c7,B,f12(c7,A,B)). [resolve(181,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | ex_sup_of_relstr_set(c9,A) | -element(B,the_carrier(c9)) | -relstr_set_smaller(c9,A,B) | -related(c9,B,f12(c9,A,B)). [resolve(181,b,172,a)].
% 0.80/1.10 182 -antisymmetric_relstr(A) | -rel_str(A) | -ex_inf_of_relstr_set(A,B) | element(f13(A,B),the_carrier(A)) # label(t16_yellow_0) # label(axiom). [clausify(70)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | -ex_inf_of_relstr_set(rel_str_of(A,B),C) | element(f13(rel_str_of(A,B),C),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(182,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | -ex_inf_of_relstr_set(c2,A) | element(f13(c2,A),the_carrier(c2)). [resolve(182,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | -ex_inf_of_relstr_set(c7,A) | element(f13(c7,A),the_carrier(c7)). [resolve(182,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | -ex_inf_of_relstr_set(c9,A) | element(f13(c9,A),the_carrier(c9)). [resolve(182,b,172,a)].
% 0.80/1.10 183 -antisymmetric_relstr(A) | -rel_str(A) | -ex_inf_of_relstr_set(A,B) | relstr_element_smaller(A,B,f13(A,B)) # label(t16_yellow_0) # label(axiom). [clausify(70)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | -ex_inf_of_relstr_set(rel_str_of(A,B),C) | relstr_element_smaller(rel_str_of(A,B),C,f13(rel_str_of(A,B),C)) | -relation_of2(B,A,A). [resolve(183,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | -ex_inf_of_relstr_set(c2,A) | relstr_element_smaller(c2,A,f13(c2,A)). [resolve(183,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | -ex_inf_of_relstr_set(c7,A) | relstr_element_smaller(c7,A,f13(c7,A)). [resolve(183,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | -ex_inf_of_relstr_set(c9,A) | relstr_element_smaller(c9,A,f13(c9,A)). [resolve(183,b,172,a)].
% 0.80/1.10 184 -antisymmetric_relstr(A) | -rel_str(A) | -ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | related(A,C,f13(A,B)) # label(t16_yellow_0) # label(axiom). [clausify(70)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | -ex_inf_of_relstr_set(rel_str_of(A,B),C) | -element(D,the_carrier(rel_str_of(A,B))) | -relstr_element_smaller(rel_str_of(A,B),C,D) | related(rel_str_of(A,B),D,f13(rel_str_of(A,B),C)) | -relation_of2(B,A,A). [resolve(184,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | -ex_inf_of_relstr_set(c2,A) | -element(B,the_carrier(c2)) | -relstr_element_smaller(c2,A,B) | related(c2,B,f13(c2,A)). [resolve(184,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | -ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | related(c7,B,f13(c7,A)). [resolve(184,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | -ex_inf_of_relstr_set(c9,A) | -element(B,the_carrier(c9)) | -relstr_element_smaller(c9,A,B) | related(c9,B,f13(c9,A)). [resolve(184,b,172,a)].
% 0.80/1.10 185 -antisymmetric_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | element(f14(A,B,C),the_carrier(A)) # label(t16_yellow_0) # label(axiom). [clausify(70)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | ex_inf_of_relstr_set(rel_str_of(A,B),C) | -element(D,the_carrier(rel_str_of(A,B))) | -relstr_element_smaller(rel_str_of(A,B),C,D) | element(f14(rel_str_of(A,B),C,D),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(185,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | ex_inf_of_relstr_set(c2,A) | -element(B,the_carrier(c2)) | -relstr_element_smaller(c2,A,B) | element(f14(c2,A,B),the_carrier(c2)). [resolve(185,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | element(f14(c7,A,B),the_carrier(c7)). [resolve(185,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | ex_inf_of_relstr_set(c9,A) | -element(B,the_carrier(c9)) | -relstr_element_smaller(c9,A,B) | element(f14(c9,A,B),the_carrier(c9)). [resolve(185,b,172,a)].
% 0.80/1.10 186 -antisymmetric_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | relstr_element_smaller(A,B,f14(A,B,C)) # label(t16_yellow_0) # label(axiom). [clausify(70)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | ex_inf_of_relstr_set(rel_str_of(A,B),C) | -element(D,the_carrier(rel_str_of(A,B))) | -relstr_element_smaller(rel_str_of(A,B),C,D) | relstr_element_smaller(rel_str_of(A,B),C,f14(rel_str_of(A,B),C,D)) | -relation_of2(B,A,A). [resolve(186,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | ex_inf_of_relstr_set(c2,A) | -element(B,the_carrier(c2)) | -relstr_element_smaller(c2,A,B) | relstr_element_smaller(c2,A,f14(c2,A,B)). [resolve(186,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | relstr_element_smaller(c7,A,f14(c7,A,B)). [resolve(186,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | ex_inf_of_relstr_set(c9,A) | -element(B,the_carrier(c9)) | -relstr_element_smaller(c9,A,B) | relstr_element_smaller(c9,A,f14(c9,A,B)). [resolve(186,b,172,a)].
% 0.80/1.10 187 -antisymmetric_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | -related(A,f14(A,B,C),C) # label(t16_yellow_0) # label(axiom). [clausify(70)].
% 0.80/1.10 Derived: -antisymmetric_relstr(rel_str_of(A,B)) | ex_inf_of_relstr_set(rel_str_of(A,B),C) | -element(D,the_carrier(rel_str_of(A,B))) | -relstr_element_smaller(rel_str_of(A,B),C,D) | -related(rel_str_of(A,B),f14(rel_str_of(A,B),C,D),D) | -relation_of2(B,A,A). [resolve(187,b,149,b)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c2) | ex_inf_of_relstr_set(c2,A) | -element(B,the_carrier(c2)) | -relstr_element_smaller(c2,A,B) | -related(c2,f14(c2,A,B),B). [resolve(187,b,165,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c7) | ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | -related(c7,f14(c7,A,B),B). [resolve(187,b,171,a)].
% 0.80/1.10 Derived: -antisymmetric_relstr(c9) | ex_inf_of_relstr_set(c9,A) | -element(B,the_carrier(c9)) | -relstr_element_smaller(c9,A,B) | -related(c9,f14(c9,A,B),B). [resolve(187,b,172,a)].
% 0.80/1.10 188 empty_carrier(c5) | -lattice(c5) | rel_str(poset_of_lattice(c5)). [resolve(87,a,114,c)].
% 0.80/1.10 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(188,c,150,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_inf_of_relstr_set(poset_of_lattice(c5),B) | meet_on_relstr(poset_of_lattice(c5),B) != A | relstr_element_smaller(poset_of_lattice(c5),B,A). [resolve(188,c,151,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_inf_of_relstr_set(poset_of_lattice(c5),B) | meet_on_relstr(poset_of_lattice(c5),B) != A | -element(C,the_carrier(poset_of_lattice(c5))) | -relstr_element_smaller(poset_of_lattice(c5),B,C) | related(poset_of_lattice(c5),C,A). [resolve(188,c,152,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_inf_of_relstr_set(poset_of_lattice(c5),B) | meet_on_relstr(poset_of_lattice(c5),B) = A | -relstr_element_smaller(poset_of_lattice(c5),B,A) | element(f1(poset_of_lattice(c5),B,A),the_carrier(poset_of_lattice(c5))). [resolve(188,c,153,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_inf_of_relstr_set(poset_of_lattice(c5),B) | meet_on_relstr(poset_of_lattice(c5),B) = A | -relstr_element_smaller(poset_of_lattice(c5),B,A) | relstr_element_smaller(poset_of_lattice(c5),B,f1(poset_of_lattice(c5),B,A)). [resolve(188,c,154,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_inf_of_relstr_set(poset_of_lattice(c5),B) | meet_on_relstr(poset_of_lattice(c5),B) = A | -relstr_element_smaller(poset_of_lattice(c5),B,A) | -related(poset_of_lattice(c5),f1(poset_of_lattice(c5),B,A),A). [resolve(188,c,155,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_sup_of_relstr_set(poset_of_lattice(c5),B) | join_on_relstr(poset_of_lattice(c5),B) != A | relstr_set_smaller(poset_of_lattice(c5),B,A). [resolve(188,c,156,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_sup_of_relstr_set(poset_of_lattice(c5),B) | join_on_relstr(poset_of_lattice(c5),B) != A | -element(C,the_carrier(poset_of_lattice(c5))) | -relstr_set_smaller(poset_of_lattice(c5),B,C) | related(poset_of_lattice(c5),A,C). [resolve(188,c,157,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_sup_of_relstr_set(poset_of_lattice(c5),B) | join_on_relstr(poset_of_lattice(c5),B) = A | -relstr_set_smaller(poset_of_lattice(c5),B,A) | element(f3(poset_of_lattice(c5),B,A),the_carrier(poset_of_lattice(c5))). [resolve(188,c,158,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_sup_of_relstr_set(poset_of_lattice(c5),B) | join_on_relstr(poset_of_lattice(c5),B) = A | -relstr_set_smaller(poset_of_lattice(c5),B,A) | relstr_set_smaller(poset_of_lattice(c5),B,f3(poset_of_lattice(c5),B,A)). [resolve(188,c,159,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -ex_sup_of_relstr_set(poset_of_lattice(c5),B) | join_on_relstr(poset_of_lattice(c5),B) = A | -relstr_set_smaller(poset_of_lattice(c5),B,A) | -related(poset_of_lattice(c5),A,f3(poset_of_lattice(c5),B,A)). [resolve(188,c,160,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | element(join_on_relstr(poset_of_lattice(c5),A),the_carrier(poset_of_lattice(c5))). [resolve(188,c,161,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | element(meet_on_relstr(poset_of_lattice(c5),A),the_carrier(poset_of_lattice(c5))). [resolve(188,c,162,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | one_sorted_str(poset_of_lattice(c5)). [resolve(188,c,163,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))). [resolve(188,c,164,a)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -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))). [resolve(188,c,166,d)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -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))). [resolve(188,c,167,d)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -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))). [resolve(188,c,168,d)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -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))). [resolve(188,c,169,d)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -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))). [resolve(188,c,170,d)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | 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). [resolve(188,c,173,c)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | 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). [resolve(188,c,174,c)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | 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). [resolve(188,c,175,c)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | -ex_sup_of_relstr_set(poset_of_lattice(c5),A) | element(f11(poset_of_lattice(c5),A),the_carrier(poset_of_lattice(c5))). [resolve(188,c,176,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | -ex_sup_of_relstr_set(poset_of_lattice(c5),A) | relstr_set_smaller(poset_of_lattice(c5),A,f11(poset_of_lattice(c5),A)). [resolve(188,c,177,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | -ex_sup_of_relstr_set(poset_of_lattice(c5),A) | -element(B,the_carrier(poset_of_lattice(c5))) | -relstr_set_smaller(poset_of_lattice(c5),A,B) | related(poset_of_lattice(c5),f11(poset_of_lattice(c5),A),B). [resolve(188,c,178,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | ex_sup_of_relstr_set(poset_of_lattice(c5),A) | -element(B,the_carrier(poset_of_lattice(c5))) | -relstr_set_smaller(poset_of_lattice(c5),A,B) | element(f12(poset_of_lattice(c5),A,B),the_carrier(poset_of_lattice(c5))). [resolve(188,c,179,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | ex_sup_of_relstr_set(poset_of_lattice(c5),A) | -element(B,the_carrier(poset_of_lattice(c5))) | -relstr_set_smaller(poset_of_lattice(c5),A,B) | relstr_set_smaller(poset_of_lattice(c5),A,f12(poset_of_lattice(c5),A,B)). [resolve(188,c,180,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | ex_sup_of_relstr_set(poset_of_lattice(c5),A) | -element(B,the_carrier(poset_of_lattice(c5))) | -relstr_set_smaller(poset_of_lattice(c5),A,B) | -related(poset_of_lattice(c5),B,f12(poset_of_lattice(c5),A,B)). [resolve(188,c,181,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | -ex_inf_of_relstr_set(poset_of_lattice(c5),A) | element(f13(poset_of_lattice(c5),A),the_carrier(poset_of_lattice(c5))). [resolve(188,c,182,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | -ex_inf_of_relstr_set(poset_of_lattice(c5),A) | relstr_element_smaller(poset_of_lattice(c5),A,f13(poset_of_lattice(c5),A)). [resolve(188,c,183,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | -ex_inf_of_relstr_set(poset_of_lattice(c5),A) | -element(B,the_carrier(poset_of_lattice(c5))) | -relstr_element_smaller(poset_of_lattice(c5),A,B) | related(poset_of_lattice(c5),B,f13(poset_of_lattice(c5),A)). [resolve(188,c,184,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | ex_inf_of_relstr_set(poset_of_lattice(c5),A) | -element(B,the_carrier(poset_of_lattice(c5))) | -relstr_element_smaller(poset_of_lattice(c5),A,B) | element(f14(poset_of_lattice(c5),A,B),the_carrier(poset_of_lattice(c5))). [resolve(188,c,185,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | ex_inf_of_relstr_set(poset_of_lattice(c5),A) | -element(B,the_carrier(poset_of_lattice(c5))) | -relstr_element_smaller(poset_of_lattice(c5),A,B) | relstr_element_smaller(poset_of_lattice(c5),A,f14(poset_of_lattice(c5),A,B)). [resolve(188,c,186,b)].
% 0.80/1.10 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric_relstr(poset_of_lattice(c5)) | ex_inf_of_relstr_set(poset_of_lattice(c5),A) | -element(B,the_carrier(poset_of_lattice(c5))) | -relstr_element_smaller(poset_of_lattice(c5),A,B) | -related(poset_of_lattice(c5),f14(poset_of_lattice(c5),A,B),B). [resolve(188,c,187,b)].
% 0.80/1.10 189 empty_carrier(c12) | -lattice(c12) | rel_str(poset_of_lattice(c12)). [resolve(148,a,114,c)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -strict_rel_str(poset_of_lattice(c12)) | rel_str_of(the_carrier(poset_of_lattice(c12)),the_InternalRel(poset_of_lattice(c12))) = poset_of_lattice(c12). [resolve(189,c,150,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_inf_of_relstr_set(poset_of_lattice(c12),B) | meet_on_relstr(poset_of_lattice(c12),B) != A | relstr_element_smaller(poset_of_lattice(c12),B,A). [resolve(189,c,151,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_inf_of_relstr_set(poset_of_lattice(c12),B) | meet_on_relstr(poset_of_lattice(c12),B) != A | -element(C,the_carrier(poset_of_lattice(c12))) | -relstr_element_smaller(poset_of_lattice(c12),B,C) | related(poset_of_lattice(c12),C,A). [resolve(189,c,152,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_inf_of_relstr_set(poset_of_lattice(c12),B) | meet_on_relstr(poset_of_lattice(c12),B) = A | -relstr_element_smaller(poset_of_lattice(c12),B,A) | element(f1(poset_of_lattice(c12),B,A),the_carrier(poset_of_lattice(c12))). [resolve(189,c,153,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_inf_of_relstr_set(poset_of_lattice(c12),B) | meet_on_relstr(poset_of_lattice(c12),B) = A | -relstr_element_smaller(poset_of_lattice(c12),B,A) | relstr_element_smaller(poset_of_lattice(c12),B,f1(poset_of_lattice(c12),B,A)). [resolve(189,c,154,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_inf_of_relstr_set(poset_of_lattice(c12),B) | meet_on_relstr(poset_of_lattice(c12),B) = A | -relstr_element_smaller(poset_of_lattice(c12),B,A) | -related(poset_of_lattice(c12),f1(poset_of_lattice(c12),B,A),A). [resolve(189,c,155,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_sup_of_relstr_set(poset_of_lattice(c12),B) | join_on_relstr(poset_of_lattice(c12),B) != A | relstr_set_smaller(poset_of_lattice(c12),B,A). [resolve(189,c,156,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_sup_of_relstr_set(poset_of_lattice(c12),B) | join_on_relstr(poset_of_lattice(c12),B) != A | -element(C,the_carrier(poset_of_lattice(c12))) | -relstr_set_smaller(poset_of_lattice(c12),B,C) | related(poset_of_lattice(c12),A,C). [resolve(189,c,157,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_sup_of_relstr_set(poset_of_lattice(c12),B) | join_on_relstr(poset_of_lattice(c12),B) = A | -relstr_set_smaller(poset_of_lattice(c12),B,A) | element(f3(poset_of_lattice(c12),B,A),the_carrier(poset_of_lattice(c12))). [resolve(189,c,158,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_sup_of_relstr_set(poset_of_lattice(c12),B) | join_on_relstr(poset_of_lattice(c12),B) = A | -relstr_set_smaller(poset_of_lattice(c12),B,A) | relstr_set_smaller(poset_of_lattice(c12),B,f3(poset_of_lattice(c12),B,A)). [resolve(189,c,159,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -ex_sup_of_relstr_set(poset_of_lattice(c12),B) | join_on_relstr(poset_of_lattice(c12),B) = A | -relstr_set_smaller(poset_of_lattice(c12),B,A) | -related(poset_of_lattice(c12),A,f3(poset_of_lattice(c12),B,A)). [resolve(189,c,160,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | element(join_on_relstr(poset_of_lattice(c12),A),the_carrier(poset_of_lattice(c12))). [resolve(189,c,161,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | element(meet_on_relstr(poset_of_lattice(c12),A),the_carrier(poset_of_lattice(c12))). [resolve(189,c,162,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | one_sorted_str(poset_of_lattice(c12)). [resolve(189,c,163,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | relation_of2_as_subset(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))). [resolve(189,c,164,a)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | relation(the_InternalRel(poset_of_lattice(c12))). [resolve(189,c,166,d)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | reflexive(the_InternalRel(poset_of_lattice(c12))). [resolve(189,c,167,d)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | antisymmetric(the_InternalRel(poset_of_lattice(c12))). [resolve(189,c,168,d)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | transitive(the_InternalRel(poset_of_lattice(c12))). [resolve(189,c,169,d)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | v1_partfun1(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))). [resolve(189,c,170,d)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | -reflexive_relstr(poset_of_lattice(c12)) | -element(A,the_carrier(poset_of_lattice(c12))) | -element(B,the_carrier(poset_of_lattice(c12))) | -related_reflexive(poset_of_lattice(c12),A,B) | related(poset_of_lattice(c12),A,B). [resolve(189,c,173,c)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | -reflexive_relstr(poset_of_lattice(c12)) | -element(A,the_carrier(poset_of_lattice(c12))) | -element(B,the_carrier(poset_of_lattice(c12))) | related_reflexive(poset_of_lattice(c12),A,B) | -related(poset_of_lattice(c12),A,B). [resolve(189,c,174,c)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | -reflexive_relstr(poset_of_lattice(c12)) | -element(A,the_carrier(poset_of_lattice(c12))) | -element(B,the_carrier(poset_of_lattice(c12))) | related_reflexive(poset_of_lattice(c12),A,A). [resolve(189,c,175,c)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | -ex_sup_of_relstr_set(poset_of_lattice(c12),A) | element(f11(poset_of_lattice(c12),A),the_carrier(poset_of_lattice(c12))). [resolve(189,c,176,b)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | -ex_sup_of_relstr_set(poset_of_lattice(c12),A) | relstr_set_smaller(poset_of_lattice(c12),A,f11(poset_of_lattice(c12),A)). [resolve(189,c,177,b)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | -ex_sup_of_relstr_set(poset_of_lattice(c12),A) | -element(B,the_carrier(poset_of_lattice(c12))) | -relstr_set_smaller(poset_of_lattice(c12),A,B) | related(poset_of_lattice(c12),f11(poset_of_lattice(c12),A),B). [resolve(189,c,178,b)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | ex_sup_of_relstr_set(poset_of_lattice(c12),A) | -element(B,the_carrier(poset_of_lattice(c12))) | -relstr_set_smaller(poset_of_lattice(c12),A,B) | element(f12(poset_of_lattice(c12),A,B),the_carrier(poset_of_lattice(c12))). [resolve(189,c,179,b)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | ex_sup_of_relstr_set(poset_of_lattice(c12),A) | -element(B,the_carrier(poset_of_lattice(c12))) | -relstr_set_smaller(poset_of_lattice(c12),A,B) | relstr_set_smaller(poset_of_lattice(c12),A,f12(poset_of_lattice(c12),A,B)). [resolve(189,c,180,b)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | ex_sup_of_relstr_set(poset_of_lattice(c12),A) | -element(B,the_carrier(poset_of_lattice(c12))) | -relstr_set_smaller(poset_of_lattice(c12),A,B) | -related(poset_of_lattice(c12),B,f12(poset_of_lattice(c12),A,B)). [resolve(189,c,181,b)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | -ex_inf_of_relstr_set(poset_of_lattice(c12),A) | element(f13(poset_of_lattice(c12),A),the_carrier(poset_of_lattice(c12))). [resolve(189,c,182,b)].
% 0.80/1.10 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | -ex_inf_of_relstr_set(poset_of_lattice(c12),A) | relstr_element_smaller(poset_of_lattice(c12),A,f13(poset_of_lattice(c12),A)). [resolve(189,c,183,b)].
% 0.80/1.16 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | -ex_inf_of_relstr_set(poset_of_lattice(c12),A) | -element(B,the_carrier(poset_of_lattice(c12))) | -relstr_element_smaller(poset_of_lattice(c12),A,B) | related(poset_of_lattice(c12),B,f13(poset_of_lattice(c12),A)). [resolve(189,c,184,b)].
% 0.80/1.16 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | ex_inf_of_relstr_set(poset_of_lattice(c12),A) | -element(B,the_carrier(poset_of_lattice(c12))) | -relstr_element_smaller(poset_of_lattice(c12),A,B) | element(f14(poset_of_lattice(c12),A,B),the_carrier(poset_of_lattice(c12))). [resolve(189,c,185,b)].
% 0.80/1.16 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | ex_inf_of_relstr_set(poset_of_lattice(c12),A) | -element(B,the_carrier(poset_of_lattice(c12))) | -relstr_element_smaller(poset_of_lattice(c12),A,B) | relstr_element_smaller(poset_of_lattice(c12),A,f14(poset_of_lattice(c12),A,B)). [resolve(189,c,186,b)].
% 0.80/1.16 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric_relstr(poset_of_lattice(c12)) | ex_inf_of_relstr_set(poset_of_lattice(c12),A) | -element(B,the_carrier(poset_of_lattice(c12))) | -relstr_element_smaller(poset_of_lattice(c12),A,B) | -related(poset_of_lattice(c12),f14(poset_of_lattice(c12),A,B),B). [resolve(189,c,187,b)].
% 0.80/1.16 190 meet_semilatt_str(c1) # label(existence_l1_lattices) # label(axiom). [clausify(37)].
% 0.80/1.16 191 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(27)].
% 0.80/1.16 Derived: one_sorted_str(c1). [resolve(190,a,191,a)].
% 0.80/1.16 192 meet_semilatt_str(c5). [resolve(87,a,118,a)].
% 0.80/1.16 Derived: one_sorted_str(c5). [resolve(192,a,191,a)].
% 0.80/1.16 193 meet_semilatt_str(c12). [resolve(148,a,118,a)].
% 0.80/1.16 Derived: one_sorted_str(c12). [resolve(193,a,191,a)].
% 0.80/1.16 194 join_semilatt_str(c4) # label(existence_l2_lattices) # label(axiom). [clausify(40)].
% 0.80/1.16 195 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(30)].
% 0.80/1.16 Derived: one_sorted_str(c4). [resolve(194,a,195,a)].
% 0.80/1.16 196 join_semilatt_str(c5). [resolve(87,a,119,a)].
% 0.80/1.16 197 join_semilatt_str(c12). [resolve(148,a,119,a)].
% 0.80/1.16 198 relation_of2_as_subset(f6(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(44)].
% 0.80/1.16 199 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(34)].
% 0.80/1.16 Derived: element(f6(A,B),powerset(cartesian_product2(A,B))). [resolve(198,a,199,a)].
% 0.80/1.16 200 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(63)].
% 0.80/1.16 Derived: relation_of2(f6(A,B),A,B). [resolve(200,a,198,a)].
% 0.80/1.16 201 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(63)].
% 0.80/1.16 Derived: -relation_of2(A,B,C) | element(A,powerset(cartesian_product2(B,C))). [resolve(201,a,199,a)].
% 0.80/1.16 202 empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(87,a,109,c)].
% 0.80/1.16 Derived: empty_carrier(c5) | -lattice(c5) | element(k2_lattice3(c5),powerset(cartesian_product2(the_carrier(c5),the_carrier(c5)))). [resolve(202,c,199,a)].
% 0.80/1.16 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(202,c,200,a)].
% 0.80/1.16 203 empty_carrier(c12) | -lattice(c12) | relation_of2_as_subset(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(148,a,109,c)].
% 0.80/1.16 Derived: empty_carrier(c12) | -lattice(c12) | element(k2_lattice3(c12),powerset(cartesian_product2(the_carrier(c12),the_carrier(c12)))). [resolve(203,c,199,a)].
% 0.80/1.16 Derived: empty_carrier(c12) | -lattice(c12) | relation_of2(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(203,c,200,a)].
% 0.80/1.16 204 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(164,a,149,b)].
% 0.80/1.17 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(204,a,199,a)].
% 0.80/1.17 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(204,a,200,a)].
% 0.80/1.17 205 relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(165,a,164,a)].
% 0.80/1.17 Derived: element(the_InternalRel(c2),powerset(cartesian_product2(the_carrier(c2),the_carrier(c2)))). [resolve(205,a,199,a)].
% 0.80/1.17 Derived: relation_of2(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(205,a,200,a)].
% 0.80/1.17 206 relation_of2_as_subset(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)). [resolve(171,a,164,a)].
% 0.80/1.17 Derived: element(the_InternalRel(c7),powerset(cartesian_product2(the_carrier(c7),the_carrier(c7)))). [resolve(206,a,199,a)].
% 0.80/1.17 Derived: relation_of2(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)). [resolve(206,a,200,a)].
% 0.80/1.17 207 relation_of2_as_subset(the_InternalRel(c9),the_carrier(c9),the_carrier(c9)). [resolve(172,a,164,a)].
% 0.80/1.17 Derived: element(the_InternalRel(c9),powerset(cartesian_product2(the_carrier(c9),the_carrier(c9)))). [resolve(207,a,199,a)].
% 0.80/1.17 Derived: relation_of2(the_InternalRel(c9),the_carrier(c9),the_carrier(c9)). [resolve(207,a,200,a)].
% 0.80/1.17 208 empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))). [resolve(188,c,164,a)].
% 0.80/1.17 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(208,c,199,a)].
% 0.80/1.17 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(208,c,200,a)].
% 0.80/1.17 209 empty_carrier(c12) | -lattice(c12) | relation_of2_as_subset(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))). [resolve(189,c,164,a)].
% 0.80/1.17 Derived: empty_carrier(c12) | -lattice(c12) | element(the_InternalRel(poset_of_lattice(c12)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))))). [resolve(209,c,199,a)].
% 0.80/1.17 Derived: empty_carrier(c12) | -lattice(c12) | relation_of2(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))). [resolve(209,c,200,a)].
% 0.80/1.17 210 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(47)].
% 0.80/1.17 211 one_sorted_str(c3) # label(existence_l1_struct_0) # label(axiom). [clausify(39)].
% 0.80/1.17 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(210,b,211,a)].
% 0.80/1.17 212 one_sorted_str(c11) # label(rc3_struct_0) # label(axiom). [clausify(59)].
% 0.80/1.17 Derived: empty_carrier(c11) | -empty(the_carrier(c11)). [resolve(212,a,210,b)].
% 0.80/1.17 213 empty_carrier(A) | -one_sorted_str(A) | element(f10(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(61)].
% 0.80/1.17 Derived: empty_carrier(c3) | element(f10(c3),powerset(the_carrier(c3))). [resolve(213,b,211,a)].
% 0.80/1.17 Derived: empty_carrier(c11) | element(f10(c11),powerset(the_carrier(c11))). [resolve(213,b,212,a)].
% 0.80/1.17 214 empty_carrier(A) | -one_sorted_str(A) | -empty(f10(A)) # label(rc5_struct_0) # label(axiom). [clausify(61)].
% 0.80/1.17 Derived: empty_carrier(c3) | -empty(f10(c3)). [resolve(214,b,211,a)].
% 0.80/1.17 Derived: empty_carrier(c11) | -empty(f10(c11)). [resolve(214,b,212,a)].
% 0.80/1.17 215 one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(163,a,149,b)].
% 0.80/1.17 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(the_carrier(rel_str_of(B,A))). [resolve(215,a,210,b)].
% 0.80/1.17 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | element(f10(rel_str_of(B,A)),powerset(the_carrier(rel_str_of(B,A)))). [resolve(215,a,213,b)].
% 0.80/1.17 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(f10(rel_str_of(B,A))). [resolve(215,a,214,b)].
% 0.80/1.18 216 one_sorted_str(c2). [resolve(165,a,163,a)].
% 0.80/1.18 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(216,a,210,b)].
% 0.80/1.18 Derived: empty_carrier(c2) | element(f10(c2),powerset(the_carrier(c2))). [resolve(216,a,213,b)].
% 0.80/1.18 Derived: empty_carrier(c2) | -empty(f10(c2)). [resolve(216,a,214,b)].
% 0.80/1.18 217 one_sorted_str(c7). [resolve(171,a,163,a)].
% 0.80/1.18 Derived: empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(217,a,210,b)].
% 0.80/1.18 Derived: empty_carrier(c7) | element(f10(c7),powerset(the_carrier(c7))). [resolve(217,a,213,b)].
% 0.80/1.18 Derived: empty_carrier(c7) | -empty(f10(c7)). [resolve(217,a,214,b)].
% 0.80/1.18 218 one_sorted_str(c9). [resolve(172,a,163,a)].
% 0.80/1.18 Derived: empty_carrier(c9) | -empty(the_carrier(c9)). [resolve(218,a,210,b)].
% 0.80/1.18 Derived: empty_carrier(c9) | element(f10(c9),powerset(the_carrier(c9))). [resolve(218,a,213,b)].
% 0.80/1.18 Derived: empty_carrier(c9) | -empty(f10(c9)). [resolve(218,a,214,b)].
% 0.80/1.18 219 empty_carrier(c5) | -lattice(c5) | one_sorted_str(poset_of_lattice(c5)). [resolve(188,c,163,a)].
% 0.80/1.18 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -empty(the_carrier(poset_of_lattice(c5))). [resolve(219,c,210,b)].
% 0.80/1.18 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | element(f10(poset_of_lattice(c5)),powerset(the_carrier(poset_of_lattice(c5)))). [resolve(219,c,213,b)].
% 0.80/1.18 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -empty(f10(poset_of_lattice(c5))). [resolve(219,c,214,b)].
% 0.80/1.18 220 empty_carrier(c12) | -lattice(c12) | one_sorted_str(poset_of_lattice(c12)). [resolve(189,c,163,a)].
% 0.80/1.18 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | -empty(the_carrier(poset_of_lattice(c12))). [resolve(220,c,210,b)].
% 0.80/1.18 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | element(f10(poset_of_lattice(c12)),powerset(the_carrier(poset_of_lattice(c12)))). [resolve(220,c,213,b)].
% 0.80/1.18 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | -empty(f10(poset_of_lattice(c12))). [resolve(220,c,214,b)].
% 0.80/1.18 221 one_sorted_str(c1). [resolve(190,a,191,a)].
% 0.80/1.18 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(221,a,210,b)].
% 0.80/1.18 Derived: empty_carrier(c1) | element(f10(c1),powerset(the_carrier(c1))). [resolve(221,a,213,b)].
% 0.80/1.18 Derived: empty_carrier(c1) | -empty(f10(c1)). [resolve(221,a,214,b)].
% 0.80/1.18 222 one_sorted_str(c5). [resolve(192,a,191,a)].
% 0.80/1.18 Derived: empty_carrier(c5) | -empty(the_carrier(c5)). [resolve(222,a,210,b)].
% 0.80/1.18 Derived: empty_carrier(c5) | element(f10(c5),powerset(the_carrier(c5))). [resolve(222,a,213,b)].
% 0.80/1.18 Derived: empty_carrier(c5) | -empty(f10(c5)). [resolve(222,a,214,b)].
% 0.80/1.18 223 one_sorted_str(c12). [resolve(193,a,191,a)].
% 0.80/1.18 Derived: empty_carrier(c12) | -empty(the_carrier(c12)). [resolve(223,a,210,b)].
% 0.80/1.18 Derived: empty_carrier(c12) | element(f10(c12),powerset(the_carrier(c12))). [resolve(223,a,213,b)].
% 0.80/1.18 Derived: empty_carrier(c12) | -empty(f10(c12)). [resolve(223,a,214,b)].
% 0.80/1.18 224 one_sorted_str(c4). [resolve(194,a,195,a)].
% 0.80/1.18 Derived: empty_carrier(c4) | -empty(the_carrier(c4)). [resolve(224,a,210,b)].
% 0.80/1.18 Derived: empty_carrier(c4) | element(f10(c4),powerset(the_carrier(c4))). [resolve(224,a,213,b)].
% 0.80/1.18 Derived: empty_carrier(c4) | -empty(f10(c4)). [resolve(224,a,214,b)].
% 0.80/1.18 225 empty_carrier(c5) | -lattice(c5) | reflexive(k2_lattice3(c5)). [resolve(87,a,105,c)].
% 0.80/1.18 226 -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(49)].
% 0.80/1.18 227 -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(49)].
% 0.80/1.18 228 -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(49)].
% 0.80/1.18 229 -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(49)].
% 0.80/1.18 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(225,c,226,a)].
% 0.80/1.18 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(225,c,227,a)].
% 0.80/1.18 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(225,c,228,a)].
% 0.80/1.18 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(225,c,229,a)].
% 0.80/1.18 230 empty_carrier(c12) | -lattice(c12) | reflexive(k2_lattice3(c12)). [resolve(148,a,105,c)].
% 0.80/1.18 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric(k2_lattice3(c12)) | -transitive(k2_lattice3(c12)) | -v1_partfun1(k2_lattice3(c12),A,A) | -relation_of2(k2_lattice3(c12),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c12))). [resolve(230,c,226,a)].
% 0.80/1.18 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric(k2_lattice3(c12)) | -transitive(k2_lattice3(c12)) | -v1_partfun1(k2_lattice3(c12),A,A) | -relation_of2(k2_lattice3(c12),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c12))). [resolve(230,c,227,a)].
% 0.80/1.18 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric(k2_lattice3(c12)) | -transitive(k2_lattice3(c12)) | -v1_partfun1(k2_lattice3(c12),A,A) | -relation_of2(k2_lattice3(c12),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c12))). [resolve(230,c,228,a)].
% 0.80/1.18 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric(k2_lattice3(c12)) | -transitive(k2_lattice3(c12)) | -v1_partfun1(k2_lattice3(c12),A,A) | -relation_of2(k2_lattice3(c12),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c12))). [resolve(230,c,229,a)].
% 0.80/1.18 231 -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(167,d,149,b)].
% 0.80/1.18 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(231,d,226,a)].
% 0.80/1.18 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(231,d,227,a)].
% 0.80/1.18 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(231,d,228,a)].
% 0.80/1.18 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(231,d,229,a)].
% 0.91/1.18 232 -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(167,d,165,a)].
% 0.91/1.18 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(232,d,226,a)].
% 0.91/1.18 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(232,d,227,a)].
% 0.91/1.18 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(232,d,228,a)].
% 0.91/1.18 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(232,d,229,a)].
% 0.91/1.18 233 -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | reflexive(the_InternalRel(c7)). [resolve(171,a,167,d)].
% 0.91/1.18 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -antisymmetric(the_InternalRel(c7)) | -transitive(the_InternalRel(c7)) | -v1_partfun1(the_InternalRel(c7),A,A) | -relation_of2(the_InternalRel(c7),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c7))). [resolve(233,d,226,a)].
% 0.91/1.18 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -antisymmetric(the_InternalRel(c7)) | -transitive(the_InternalRel(c7)) | -v1_partfun1(the_InternalRel(c7),A,A) | -relation_of2(the_InternalRel(c7),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c7))). [resolve(233,d,227,a)].
% 0.91/1.18 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -antisymmetric(the_InternalRel(c7)) | -transitive(the_InternalRel(c7)) | -v1_partfun1(the_InternalRel(c7),A,A) | -relation_of2(the_InternalRel(c7),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c7))). [resolve(233,d,228,a)].
% 0.91/1.18 Derived: -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -antisymmetric(the_InternalRel(c7)) | -transitive(the_InternalRel(c7)) | -v1_partfun1(the_InternalRel(c7),A,A) | -relation_of2(the_InternalRel(c7),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c7))). [resolve(233,d,229,a)].
% 0.91/1.18 234 -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | reflexive(the_InternalRel(c9)). [resolve(172,a,167,d)].
% 0.91/1.18 Derived: -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | -antisymmetric(the_InternalRel(c9)) | -transitive(the_InternalRel(c9)) | -v1_partfun1(the_InternalRel(c9),A,A) | -relation_of2(the_InternalRel(c9),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c9))). [resolve(234,d,226,a)].
% 0.91/1.18 Derived: -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | -antisymmetric(the_InternalRel(c9)) | -transitive(the_InternalRel(c9)) | -v1_partfun1(the_InternalRel(c9),A,A) | -relation_of2(the_InternalRel(c9),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c9))). [resolve(234,d,227,a)].
% 0.91/1.18 Derived: -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | -antisymmetric(the_InternalRel(c9)) | -transitive(the_InternalRel(c9)) | -v1_partfun1(the_InternalRel(c9),A,A) | -relation_of2(the_InternalRel(c9),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c9))). [resolve(234,d,228,a)].
% 0.91/1.18 Derived: -reflexive_relstr(c9) | -transitive_relstr(c9) | -antisymmetric_relstr(c9) | -antisymmetric(the_InternalRel(c9)) | -transitive(the_InternalRel(c9)) | -v1_partfun1(the_InternalRel(c9),A,A) | -relation_of2(the_InternalRel(c9),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c9))). [resolve(234,d,229,a)].
% 0.91/1.18 235 empty_carrier(c5) | -lattice(c5) | -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))). [resolve(188,c,167,d)].
% 0.91/1.18 Derived: empty_carrier(c5) | -lattice(c5) | -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))) | -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(235,f,226,a)].
% 0.91/1.18 Derived: empty_carrier(c5) | -lattice(c5) | -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))) | -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(235,f,227,a)].
% 0.91/1.18 Derived: empty_carrier(c5) | -lattice(c5) | -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))) | -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(235,f,228,a)].
% 0.91/1.18 Derived: empty_carrier(c5) | -lattice(c5) | -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))) | -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(235,f,229,a)].
% 0.91/1.18 236 empty_carrier(c12) | -lattice(c12) | -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | reflexive(the_InternalRel(poset_of_lattice(c12))). [resolve(189,c,167,d)].
% 0.91/1.18 Derived: empty_carrier(c12) | -lattice(c12) | -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | -antisymmetric(the_InternalRel(poset_of_lattice(c12))) | -transitive(the_InternalRel(poset_of_lattice(c12))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c12)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c12)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c12)))). [resolve(236,f,226,a)].
% 0.91/1.18 Derived: empty_carrier(c12) | -lattice(c12) | -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | -antisymmetric(the_InternalRel(poset_of_lattice(c12))) | -transitive(the_InternalRel(poset_of_lattice(c12))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c12)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c12)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c12)))). [resolve(236,f,227,a)].
% 0.91/1.18 Derived: empty_carrier(c12) | -lattice(c12) | -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | -antisymmetric(the_InternalRel(poset_of_lattice(c12))) | -transitive(the_InternalRel(poset_of_lattice(c12))) | -v1_partfun1(the_InternalRel(poset_Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------