TSTP Solution File: SEU349+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU349+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 13:31:10 EDT 2022
% Result : Timeout 300.01s 300.29s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU349+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 08:20:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.75/1.02 ============================== Prover9 ===============================
% 0.75/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.02 Process 25780 was started by sandbox2 on n005.cluster.edu,
% 0.75/1.02 Mon Jun 20 08:20:39 2022
% 0.75/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25626_n005.cluster.edu".
% 0.75/1.02 ============================== end of head ===========================
% 0.75/1.02
% 0.75/1.02 ============================== INPUT =================================
% 0.75/1.02
% 0.75/1.02 % Reading from file /tmp/Prover9_25626_n005.cluster.edu
% 0.75/1.02
% 0.75/1.02 set(prolog_style_variables).
% 0.75/1.02 set(auto2).
% 0.75/1.02 % set(auto2) -> set(auto).
% 0.75/1.02 % set(auto) -> set(auto_inference).
% 0.75/1.02 % set(auto) -> set(auto_setup).
% 0.75/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.02 % set(auto) -> set(auto_limits).
% 0.75/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.02 % set(auto) -> set(auto_denials).
% 0.75/1.02 % set(auto) -> set(auto_process).
% 0.75/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.02 % set(auto2) -> assign(stats, some).
% 0.75/1.02 % set(auto2) -> clear(echo_input).
% 0.75/1.02 % set(auto2) -> set(quiet).
% 0.75/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.02 % set(auto2) -> clear(print_given).
% 0.75/1.02 assign(lrs_ticks,-1).
% 0.75/1.02 assign(sos_limit,10000).
% 0.75/1.02 assign(order,kbo).
% 0.75/1.02 set(lex_order_vars).
% 0.75/1.02 clear(print_given).
% 0.75/1.02
% 0.75/1.02 % formulas(sos). % not echoed (71 formulas)
% 0.75/1.02
% 0.75/1.02 ============================== end of input ==========================
% 0.75/1.02
% 0.75/1.02 % From the command line: assign(max_seconds, 300).
% 0.75/1.02
% 0.75/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.02
% 0.75/1.02 % Formulas that are not ordinary clauses:
% 0.75/1.02 1 (all A (rel_str(A) -> (strict_rel_str(A) -> A = rel_str_of(the_carrier(A),the_InternalRel(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 2 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 3 (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].
% 0.75/1.02 4 (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].
% 0.75/1.02 5 (all A (latt_str(A) -> (-empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) -> -empty_carrier(A) & lattice(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 6 (all A (-empty_carrier(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (latt_element_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,C) -> below(A,D,B)))))))))) # label(d17_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 7 (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].
% 0.75/1.02 8 (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].
% 0.75/1.02 9 (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].
% 0.75/1.02 10 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (relstr_set_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,B) -> related(A,D,C))))))))) # label(d9_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 11 (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].
% 0.75/1.02 12 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 13 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 14 (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].
% 0.75/1.02 15 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 16 (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].
% 0.75/1.02 17 (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].
% 0.75/1.02 18 (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].
% 0.75/1.02 19 (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].
% 0.75/1.02 20 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 21 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 22 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 23 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 24 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 25 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 26 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 27 (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].
% 0.75/1.02 28 (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].
% 0.75/1.02 29 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 30 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 31 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 32 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 33 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 34 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 35 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 36 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 37 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 38 (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].
% 0.75/1.02 39 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 40 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 41 (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].
% 0.75/1.02 42 (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].
% 0.75/1.02 43 (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].
% 0.75/1.02 44 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 45 (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].
% 0.75/1.02 46 (exists A (rel_str(A) & strict_rel_str(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 47 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 48 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 49 (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].
% 0.75/1.02 50 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 51 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 52 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 53 (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].
% 0.75/1.02 54 (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].
% 0.75/1.02 55 (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].
% 0.75/1.02 56 (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].
% 0.75/1.02 57 (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].
% 0.75/1.02 58 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 59 (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].
% 0.75/1.03 60 (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].
% 0.75/1.03 61 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 62 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 63 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 64 (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].
% 0.75/1.03 65 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 66 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 67 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 68 (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].
% 0.75/1.03 69 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 70 -(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(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.03
% 0.75/1.03 ============================== end of process non-clausal formulas ===
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.03
% 0.75/1.03 ============================== PREDICATE ELIMINATION =================
% 0.75/1.03 71 -relation_of2(A,B,B) | rel_str(rel_str_of(B,A)) # label(dt_g1_orders_2) # label(axiom). [clausify(11)].
% 0.75/1.03 72 -rel_str(A) | -strict_rel_str(A) | rel_str_of(the_carrier(A),the_InternalRel(A)) = A # label(abstractness_v1_orders_2) # label(axiom). [clausify(1)].
% 0.75/1.03 73 -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | -element(D,the_carrier(A)) | -in(D,C) | related(A,D,B) # label(d9_lattice3) # label(axiom). [clausify(10)].
% 0.75/1.03 74 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,B) | element(f2(A,C,B),the_carrier(A)) # label(d9_lattice3) # label(axiom). [clausify(10)].
% 0.75/1.03 75 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,B) | in(f2(A,C,B),C) # label(d9_lattice3) # label(axiom). [clausify(10)].
% 0.75/1.03 76 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,C,B) | -related(A,f2(A,C,B),B) # label(d9_lattice3) # label(axiom). [clausify(10)].
% 0.75/1.03 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(71,b,72,a)].
% 0.75/1.03 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -relstr_set_smaller(rel_str_of(B,A),D,C) | -element(E,the_carrier(rel_str_of(B,A))) | -in(E,D) | related(rel_str_of(B,A),E,C). [resolve(71,b,73,a)].
% 0.75/1.03 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),D,C) | element(f2(rel_str_of(B,A),D,C),the_carrier(rel_str_of(B,A))). [resolve(71,b,74,a)].
% 0.75/1.03 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),D,C) | in(f2(rel_str_of(B,A),D,C),D). [resolve(71,b,75,a)].
% 0.75/1.03 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | relstr_set_smaller(rel_str_of(B,A),D,C) | -related(rel_str_of(B,A),f2(rel_str_of(B,A),D,C),C). [resolve(71,b,76,a)].
% 0.75/1.03 77 empty_carrier(A) | -lattice(A) | -latt_str(A) | rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(16)].
% 0.75/1.03 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -strict_rel_str(poset_of_lattice(A)) | rel_str_of(the_carrier(poset_of_lattice(A)),the_InternalRel(poset_of_lattice(A))) = poset_of_lattice(A). [resolve(77,d,72,a)].
% 0.75/1.03 Derived: 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) | -element(D,the_carrier(poset_of_lattice(A))) | -in(D,C) | related(poset_of_lattice(A),D,B). [resolve(77,d,73,a)].
% 0.75/1.03 Derived: 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) | element(f2(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))). [resolve(77,d,74,a)].
% 0.75/1.03 Derived: 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) | in(f2(poset_of_lattice(A),C,B),C). [resolve(77,d,75,a)].
% 0.75/1.03 Derived: 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) | -related(poset_of_lattice(A),f2(poset_of_lattice(A),C,B),B). [resolve(77,d,76,a)].
% 0.75/1.03 78 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(21)].
% 0.75/1.03 Derived: one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(78,a,71,b)].
% 0.75/1.03 Derived: one_sorted_str(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(78,a,77,d)].
% 0.75/1.03 79 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(28)].
% 0.75/1.03 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(79,a,71,b)].
% 0.75/1.03 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(79,a,77,d)].
% 0.75/1.03 80 rel_str(c2) # label(existence_l1_orders_2) # label(axiom). [clausify(31)].
% 0.75/1.03 Derived: -strict_rel_str(c2) | rel_str_of(the_carrier(c2),the_InternalRel(c2)) = c2. [resolve(80,a,72,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c2)) | -relstr_set_smaller(c2,B,A) | -element(C,the_carrier(c2)) | -in(C,B) | related(c2,C,A). [resolve(80,a,73,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c2)) | relstr_set_smaller(c2,B,A) | element(f2(c2,B,A),the_carrier(c2)). [resolve(80,a,74,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c2)) | relstr_set_smaller(c2,B,A) | in(f2(c2,B,A),B). [resolve(80,a,75,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c2)) | relstr_set_smaller(c2,B,A) | -related(c2,f2(c2,B,A),A). [resolve(80,a,76,a)].
% 0.75/1.03 Derived: one_sorted_str(c2). [resolve(80,a,78,a)].
% 0.75/1.03 Derived: relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(80,a,79,a)].
% 0.75/1.03 81 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | relation(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(41)].
% 0.75/1.03 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(81,d,71,b)].
% 0.75/1.03 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | relation(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(81,d,77,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | relation(the_InternalRel(c2)). [resolve(81,d,80,a)].
% 0.75/1.03 82 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | reflexive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(41)].
% 0.75/1.03 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(82,d,71,b)].
% 0.75/1.03 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | reflexive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(82,d,77,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(82,d,80,a)].
% 0.75/1.03 83 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | antisymmetric(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(41)].
% 0.75/1.03 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(83,d,71,b)].
% 0.75/1.03 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | antisymmetric(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(83,d,77,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | antisymmetric(the_InternalRel(c2)). [resolve(83,d,80,a)].
% 0.75/1.03 84 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | transitive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(41)].
% 0.75/1.03 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(84,d,71,b)].
% 0.75/1.03 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | transitive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(84,d,77,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | transitive(the_InternalRel(c2)). [resolve(84,d,80,a)].
% 0.75/1.03 85 -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(41)].
% 0.75/1.03 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(85,d,71,b)].
% 0.75/1.03 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | v1_partfun1(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(85,d,77,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | v1_partfun1(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(85,d,80,a)].
% 0.75/1.03 86 rel_str(c6) # label(rc1_orders_2) # label(axiom). [clausify(46)].
% 0.75/1.03 Derived: -strict_rel_str(c6) | rel_str_of(the_carrier(c6),the_InternalRel(c6)) = c6. [resolve(86,a,72,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c6)) | -relstr_set_smaller(c6,B,A) | -element(C,the_carrier(c6)) | -in(C,B) | related(c6,C,A). [resolve(86,a,73,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c6)) | relstr_set_smaller(c6,B,A) | element(f2(c6,B,A),the_carrier(c6)). [resolve(86,a,74,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c6)) | relstr_set_smaller(c6,B,A) | in(f2(c6,B,A),B). [resolve(86,a,75,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c6)) | relstr_set_smaller(c6,B,A) | -related(c6,f2(c6,B,A),A). [resolve(86,a,76,a)].
% 0.75/1.03 Derived: one_sorted_str(c6). [resolve(86,a,78,a)].
% 0.75/1.03 Derived: relation_of2_as_subset(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(86,a,79,a)].
% 0.75/1.03 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | relation(the_InternalRel(c6)). [resolve(86,a,81,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | reflexive(the_InternalRel(c6)). [resolve(86,a,82,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | antisymmetric(the_InternalRel(c6)). [resolve(86,a,83,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | transitive(the_InternalRel(c6)). [resolve(86,a,84,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | v1_partfun1(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(86,a,85,d)].
% 0.75/1.03 87 rel_str(c8) # label(rc2_orders_2) # label(axiom). [clausify(49)].
% 0.75/1.03 Derived: -strict_rel_str(c8) | rel_str_of(the_carrier(c8),the_InternalRel(c8)) = c8. [resolve(87,a,72,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c8)) | -relstr_set_smaller(c8,B,A) | -element(C,the_carrier(c8)) | -in(C,B) | related(c8,C,A). [resolve(87,a,73,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c8)) | relstr_set_smaller(c8,B,A) | element(f2(c8,B,A),the_carrier(c8)). [resolve(87,a,74,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c8)) | relstr_set_smaller(c8,B,A) | in(f2(c8,B,A),B). [resolve(87,a,75,a)].
% 0.75/1.03 Derived: -element(A,the_carrier(c8)) | relstr_set_smaller(c8,B,A) | -related(c8,f2(c8,B,A),A). [resolve(87,a,76,a)].
% 0.75/1.03 Derived: one_sorted_str(c8). [resolve(87,a,78,a)].
% 0.75/1.03 Derived: relation_of2_as_subset(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(87,a,79,a)].
% 0.75/1.03 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | relation(the_InternalRel(c8)). [resolve(87,a,81,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | reflexive(the_InternalRel(c8)). [resolve(87,a,82,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | antisymmetric(the_InternalRel(c8)). [resolve(87,a,83,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | transitive(the_InternalRel(c8)). [resolve(87,a,84,d)].
% 0.75/1.03 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | v1_partfun1(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(87,a,85,d)].
% 0.75/1.03 88 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(57)].
% 0.75/1.03 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(88,c,71,b)].
% 0.75/1.03 Derived: empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related_reflexive(poset_of_lattice(A),B,C) | related(poset_of_lattice(A),B,C) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(88,c,77,d)].
% 0.75/1.03 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(88,c,80,a)].
% 0.75/1.03 Derived: empty_carrier(c6) | -reflexive_relstr(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | -related_reflexive(c6,A,B) | related(c6,A,B). [resolve(88,c,86,a)].
% 0.75/1.03 Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | -related_reflexive(c8,A,B) | related(c8,A,B). [resolve(88,c,87,a)].
% 0.75/1.03 89 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(57)].
% 0.75/1.03 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(89,c,71,b)].
% 0.75/1.03 Derived: empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related_reflexive(poset_of_lattice(A),B,C) | -related(poset_of_lattice(A),B,C) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(89,c,77,d)].
% 0.75/1.03 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(89,c,80,a)].
% 0.75/1.03 Derived: empty_carrier(c6) | -reflexive_relstr(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | related_reflexive(c6,A,B) | -related(c6,A,B). [resolve(89,c,86,a)].
% 0.75/1.03 Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | related_reflexive(c8,A,B) | -related(c8,A,B). [resolve(89,c,87,a)].
% 0.75/1.03 90 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(60)].
% 0.75/1.03 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(90,c,71,b)].
% 0.75/1.03 Derived: empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related_reflexive(poset_of_lattice(A),B,B) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(90,c,77,d)].
% 0.75/1.03 Derived: empty_carrier(c2) | -reflexive_relstr(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | related_reflexive(c2,A,A). [resolve(90,c,80,a)].
% 0.75/1.03 Derived: empty_carrier(c6) | -reflexive_relstr(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | related_reflexive(c6,A,A). [resolve(90,c,86,a)].
% 0.75/1.03 Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | related_reflexive(c8,A,A). [resolve(90,c,87,a)].
% 0.75/1.03 91 latt_str(c5) # label(existence_l3_lattices) # label(axiom). [clausify(34)].
% 0.75/1.03 92 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.75/1.03 93 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_associative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.75/1.03 94 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.75/1.03 95 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_associative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.75/1.03 96 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.75/1.03 97 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.75/1.03 98 -latt_str(A) | empty_carrier(A) | -join_commutative(A) | -join_associative(A) | -meet_commutative(A) | -meet_associative(A) | -meet_absorbing(A) | -join_absorbing(A) | lattice(A) # label(cc2_lattices) # label(axiom). [clausify(5)].
% 0.75/1.03 99 empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -latt_element_smaller(A,B,C) | -element(D,the_carrier(A)) | -in(D,C) | below(A,D,B) # label(d17_lattice3) # label(axiom). [clausify(6)].
% 0.75/1.03 100 empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | latt_element_smaller(A,B,C) | element(f1(A,B,C),the_carrier(A)) # label(d17_lattice3) # label(axiom). [clausify(6)].
% 0.75/1.03 101 empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | latt_element_smaller(A,B,C) | in(f1(A,B,C),C) # label(d17_lattice3) # label(axiom). [clausify(6)].
% 0.75/1.03 102 empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | latt_element_smaller(A,B,C) | -below(A,f1(A,B,C),B) # label(d17_lattice3) # label(axiom). [clausify(6)].
% 0.75/1.03 103 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(7)].
% 0.75/1.03 104 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(8)].
% 0.75/1.04 105 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(9)].
% 0.75/1.04 106 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(14)].
% 0.75/1.04 107 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(14)].
% 0.75/1.04 108 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(14)].
% 0.75/1.04 109 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(14)].
% 0.75/1.04 110 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(14)].
% 0.75/1.04 111 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(16)].
% 0.75/1.04 112 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(16)].
% 0.75/1.04 113 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(16)].
% 0.75/1.04 114 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(16)].
% 0.75/1.04 115 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(17)].
% 0.75/1.04 116 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(18)].
% 0.75/1.04 117 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation(relation_of_lattice(A)) # label(dt_k9_filter_1) # label(axiom). [clausify(19)].
% 0.75/1.04 118 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(24)].
% 0.75/1.04 119 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(24)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | join_commutative(c5). [resolve(91,a,92,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | join_associative(c5). [resolve(91,a,93,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | meet_commutative(c5). [resolve(91,a,94,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | meet_associative(c5). [resolve(91,a,95,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | meet_absorbing(c5). [resolve(91,a,96,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | join_absorbing(c5). [resolve(91,a,97,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -join_commutative(c5) | -join_associative(c5) | -meet_commutative(c5) | -meet_associative(c5) | -meet_absorbing(c5) | -join_absorbing(c5) | lattice(c5). [resolve(91,a,98,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -element(A,the_carrier(c5)) | -latt_element_smaller(c5,A,B) | -element(C,the_carrier(c5)) | -in(C,B) | below(c5,C,A). [resolve(91,a,99,b)].
% 0.75/1.04 Derived: empty_carrier(c5) | -element(A,the_carrier(c5)) | latt_element_smaller(c5,A,B) | element(f1(c5,A,B),the_carrier(c5)). [resolve(91,a,100,b)].
% 0.75/1.04 Derived: empty_carrier(c5) | -element(A,the_carrier(c5)) | latt_element_smaller(c5,A,B) | in(f1(c5,A,B),B). [resolve(91,a,101,b)].
% 0.75/1.04 Derived: empty_carrier(c5) | -element(A,the_carrier(c5)) | latt_element_smaller(c5,A,B) | -below(c5,f1(c5,A,B),A). [resolve(91,a,102,b)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | poset_of_lattice(c5) = rel_str_of(the_carrier(c5),k2_lattice3(c5)). [resolve(91,a,103,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | cast_to_el_of_LattPOSet(c5,A) = A. [resolve(91,a,104,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | cast_to_el_of_lattice(c5,A) = A. [resolve(91,a,105,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | reflexive(k2_lattice3(c5)). [resolve(91,a,106,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | antisymmetric(k2_lattice3(c5)). [resolve(91,a,107,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | transitive(k2_lattice3(c5)). [resolve(91,a,108,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | v1_partfun1(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(91,a,109,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(91,a,110,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | strict_rel_str(poset_of_lattice(c5)). [resolve(91,a,111,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | reflexive_relstr(poset_of_lattice(c5)). [resolve(91,a,112,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | transitive_relstr(poset_of_lattice(c5)). [resolve(91,a,113,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | antisymmetric_relstr(poset_of_lattice(c5)). [resolve(91,a,114,c)].
% 0.75/1.04 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(91,a,115,c)].
% 0.75/1.04 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(91,a,116,c)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | relation(relation_of_lattice(c5)). [resolve(91,a,117,c)].
% 0.75/1.04 Derived: meet_semilatt_str(c5). [resolve(91,a,118,a)].
% 0.75/1.04 Derived: join_semilatt_str(c5). [resolve(91,a,119,a)].
% 0.75/1.04 120 empty_carrier(A) | -lattice(A) | -latt_str(A) | -empty_carrier(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(43)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | -empty_carrier(poset_of_lattice(c5)). [resolve(120,c,91,a)].
% 0.75/1.04 121 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(43)].
% 0.75/1.04 122 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(43)].
% 0.75/1.04 123 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(43)].
% 0.75/1.04 124 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(43)].
% 0.75/1.04 125 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation_of_lattice(A) = k2_lattice3(A) # label(redefinition_k2_lattice3) # label(axiom). [clausify(54)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | relation_of_lattice(c5) = k2_lattice3(c5). [resolve(125,c,91,a)].
% 0.75/1.04 126 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(56)].
% 0.75/1.04 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(126,e,91,a)].
% 0.75/1.04 127 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(56)].
% 0.75/1.04 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(127,e,91,a)].
% 0.75/1.04 128 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(59)].
% 0.75/1.04 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(128,e,91,a)].
% 0.75/1.04 129 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(68)].
% 0.75/1.04 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(129,c,91,a)].
% 0.75/1.04 130 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(68)].
% 0.75/1.04 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(130,c,91,a)].
% 0.75/1.04 131 latt_str(c12) # label(t30_lattice3) # label(negated_conjecture). [clausify(70)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | join_commutative(c12). [resolve(131,a,92,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | join_associative(c12). [resolve(131,a,93,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | meet_commutative(c12). [resolve(131,a,94,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | meet_associative(c12). [resolve(131,a,95,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | meet_absorbing(c12). [resolve(131,a,96,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | join_absorbing(c12). [resolve(131,a,97,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -join_commutative(c12) | -join_associative(c12) | -meet_commutative(c12) | -meet_associative(c12) | -meet_absorbing(c12) | -join_absorbing(c12) | lattice(c12). [resolve(131,a,98,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -element(A,the_carrier(c12)) | -latt_element_smaller(c12,A,B) | -element(C,the_carrier(c12)) | -in(C,B) | below(c12,C,A). [resolve(131,a,99,b)].
% 0.75/1.04 Derived: empty_carrier(c12) | -element(A,the_carrier(c12)) | latt_element_smaller(c12,A,B) | element(f1(c12,A,B),the_carrier(c12)). [resolve(131,a,100,b)].
% 0.75/1.04 Derived: empty_carrier(c12) | -element(A,the_carrier(c12)) | latt_element_smaller(c12,A,B) | in(f1(c12,A,B),B). [resolve(131,a,101,b)].
% 0.75/1.04 Derived: empty_carrier(c12) | -element(A,the_carrier(c12)) | latt_element_smaller(c12,A,B) | -below(c12,f1(c12,A,B),A). [resolve(131,a,102,b)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | poset_of_lattice(c12) = rel_str_of(the_carrier(c12),k2_lattice3(c12)). [resolve(131,a,103,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | cast_to_el_of_LattPOSet(c12,A) = A. [resolve(131,a,104,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | cast_to_el_of_lattice(c12,A) = A. [resolve(131,a,105,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | reflexive(k2_lattice3(c12)). [resolve(131,a,106,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | antisymmetric(k2_lattice3(c12)). [resolve(131,a,107,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | transitive(k2_lattice3(c12)). [resolve(131,a,108,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | v1_partfun1(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(131,a,109,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | relation_of2_as_subset(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(131,a,110,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | strict_rel_str(poset_of_lattice(c12)). [resolve(131,a,111,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | reflexive_relstr(poset_of_lattice(c12)). [resolve(131,a,112,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | transitive_relstr(poset_of_lattice(c12)). [resolve(131,a,113,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | antisymmetric_relstr(poset_of_lattice(c12)). [resolve(131,a,114,c)].
% 0.75/1.04 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(131,a,115,c)].
% 0.75/1.04 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(131,a,116,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | relation(relation_of_lattice(c12)). [resolve(131,a,117,c)].
% 0.75/1.04 Derived: meet_semilatt_str(c12). [resolve(131,a,118,a)].
% 0.75/1.04 Derived: join_semilatt_str(c12). [resolve(131,a,119,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | -empty_carrier(poset_of_lattice(c12)). [resolve(131,a,120,c)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | relation_of_lattice(c12) = k2_lattice3(c12). [resolve(131,a,125,c)].
% 0.75/1.04 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(131,a,126,e)].
% 0.75/1.04 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(131,a,127,e)].
% 0.75/1.04 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(131,a,128,e)].
% 0.75/1.04 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(131,a,129,c)].
% 0.75/1.04 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(131,a,130,c)].
% 0.75/1.04 132 empty_carrier(A) | -lattice(A) | -latt_str(A) | -strict_rel_str(poset_of_lattice(A)) | rel_str_of(the_carrier(poset_of_lattice(A)),the_InternalRel(poset_of_lattice(A))) = poset_of_lattice(A). [resolve(77,d,72,a)].
% 0.75/1.04 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(132,c,91,a)].
% 0.75/1.04 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(132,c,131,a)].
% 0.75/1.04 133 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) | -element(D,the_carrier(poset_of_lattice(A))) | -in(D,C) | related(poset_of_lattice(A),D,B). [resolve(77,d,73,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | -relstr_set_smaller(poset_of_lattice(c5),B,A) | -element(C,the_carrier(poset_of_lattice(c5))) | -in(C,B) | related(poset_of_lattice(c5),C,A). [resolve(133,c,91,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | -relstr_set_smaller(poset_of_lattice(c12),B,A) | -element(C,the_carrier(poset_of_lattice(c12))) | -in(C,B) | related(poset_of_lattice(c12),C,A). [resolve(133,c,131,a)].
% 0.75/1.04 134 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) | element(f2(poset_of_lattice(A),C,B),the_carrier(poset_of_lattice(A))). [resolve(77,d,74,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | relstr_set_smaller(poset_of_lattice(c5),B,A) | element(f2(poset_of_lattice(c5),B,A),the_carrier(poset_of_lattice(c5))). [resolve(134,c,91,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | relstr_set_smaller(poset_of_lattice(c12),B,A) | element(f2(poset_of_lattice(c12),B,A),the_carrier(poset_of_lattice(c12))). [resolve(134,c,131,a)].
% 0.75/1.04 135 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) | in(f2(poset_of_lattice(A),C,B),C). [resolve(77,d,75,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | relstr_set_smaller(poset_of_lattice(c5),B,A) | in(f2(poset_of_lattice(c5),B,A),B). [resolve(135,c,91,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | relstr_set_smaller(poset_of_lattice(c12),B,A) | in(f2(poset_of_lattice(c12),B,A),B). [resolve(135,c,131,a)].
% 0.75/1.04 136 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) | -related(poset_of_lattice(A),f2(poset_of_lattice(A),C,B),B). [resolve(77,d,76,a)].
% 0.75/1.04 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | relstr_set_smaller(poset_of_lattice(c5),B,A) | -related(poset_of_lattice(c5),f2(poset_of_lattice(c5),B,A),A). [resolve(136,c,91,a)].
% 0.75/1.04 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | relstr_set_smaller(poset_of_lattice(c12),B,A) | -related(poset_of_lattice(c12),f2(poset_of_lattice(c12),B,A),A). [resolve(136,c,131,a)].
% 0.75/1.04 137 one_sorted_str(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(78,a,77,d)].
% 0.75/1.04 Derived: one_sorted_str(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5). [resolve(137,d,91,a)].
% 0.75/1.04 Derived: one_sorted_str(poset_of_lattice(c12)) | empty_carrier(c12) | -lattice(c12). [resolve(137,d,131,a)].
% 0.75/1.04 138 relation_of2_as_subset(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(79,a,77,d)].
% 0.75/1.04 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(138,d,91,a)].
% 0.75/1.04 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(138,d,131,a)].
% 0.75/1.04 139 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | relation(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(81,d,77,d)].
% 0.75/1.04 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | relation(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(139,g,91,a)].
% 0.75/1.04 Derived: -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))) | empty_carrier(c12) | -lattice(c12). [resolve(139,g,131,a)].
% 0.75/1.04 140 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | reflexive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(82,d,77,d)].
% 0.75/1.04 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | reflexive(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(140,g,91,a)].
% 0.75/1.04 Derived: -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))) | empty_carrier(c12) | -lattice(c12). [resolve(140,g,131,a)].
% 0.75/1.04 141 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | antisymmetric(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(83,d,77,d)].
% 0.75/1.04 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | antisymmetric(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(141,g,91,a)].
% 0.75/1.05 Derived: -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))) | empty_carrier(c12) | -lattice(c12). [resolve(141,g,131,a)].
% 0.75/1.05 142 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | transitive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(84,d,77,d)].
% 0.75/1.05 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | transitive(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(142,g,91,a)].
% 0.75/1.05 Derived: -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))) | empty_carrier(c12) | -lattice(c12). [resolve(142,g,131,a)].
% 0.75/1.05 143 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | v1_partfun1(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(85,d,77,d)].
% 0.75/1.05 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | v1_partfun1(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(143,g,91,a)].
% 0.75/1.05 Derived: -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))) | empty_carrier(c12) | -lattice(c12). [resolve(143,g,131,a)].
% 0.75/1.05 144 empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related_reflexive(poset_of_lattice(A),B,C) | related(poset_of_lattice(A),B,C) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(88,c,77,d)].
% 0.75/1.05 Derived: empty_carrier(poset_of_lattice(c5)) | -reflexive_relstr(poset_of_lattice(c5)) | -element(A,the_carrier(poset_of_lattice(c5))) | -element(B,the_carrier(poset_of_lattice(c5))) | -related_reflexive(poset_of_lattice(c5),A,B) | related(poset_of_lattice(c5),A,B) | empty_carrier(c5) | -lattice(c5). [resolve(144,i,91,a)].
% 0.75/1.05 Derived: 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) | empty_carrier(c12) | -lattice(c12). [resolve(144,i,131,a)].
% 0.75/1.05 145 empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related_reflexive(poset_of_lattice(A),B,C) | -related(poset_of_lattice(A),B,C) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(89,c,77,d)].
% 0.75/1.05 Derived: empty_carrier(poset_of_lattice(c5)) | -reflexive_relstr(poset_of_lattice(c5)) | -element(A,the_carrier(poset_of_lattice(c5))) | -element(B,the_carrier(poset_of_lattice(c5))) | related_reflexive(poset_of_lattice(c5),A,B) | -related(poset_of_lattice(c5),A,B) | empty_carrier(c5) | -lattice(c5). [resolve(145,i,91,a)].
% 0.75/1.05 Derived: 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) | empty_carrier(c12) | -lattice(c12). [resolve(145,i,131,a)].
% 0.75/1.05 146 empty_carrier(poset_of_lattice(A)) | -reflexive_relstr(poset_of_lattice(A)) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related_reflexive(poset_of_lattice(A),B,B) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(90,c,77,d)].
% 0.75/1.07 Derived: empty_carrier(poset_of_lattice(c5)) | -reflexive_relstr(poset_of_lattice(c5)) | -element(A,the_carrier(poset_of_lattice(c5))) | -element(B,the_carrier(poset_of_lattice(c5))) | related_reflexive(poset_of_lattice(c5),A,A) | empty_carrier(c5) | -lattice(c5). [resolve(146,h,91,a)].
% 0.75/1.07 Derived: 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) | empty_carrier(c12) | -lattice(c12). [resolve(146,h,131,a)].
% 0.75/1.07 147 meet_semilatt_str(c1) # label(existence_l1_lattices) # label(axiom). [clausify(30)].
% 0.75/1.07 148 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(20)].
% 0.75/1.07 Derived: one_sorted_str(c1). [resolve(147,a,148,a)].
% 0.75/1.07 149 meet_semilatt_str(c5). [resolve(91,a,118,a)].
% 0.75/1.07 Derived: one_sorted_str(c5). [resolve(149,a,148,a)].
% 0.75/1.07 150 meet_semilatt_str(c12). [resolve(131,a,118,a)].
% 0.75/1.07 Derived: one_sorted_str(c12). [resolve(150,a,148,a)].
% 0.75/1.07 151 join_semilatt_str(c4) # label(existence_l2_lattices) # label(axiom). [clausify(33)].
% 0.75/1.07 152 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(23)].
% 0.75/1.07 Derived: one_sorted_str(c4). [resolve(151,a,152,a)].
% 0.75/1.07 153 join_semilatt_str(c5). [resolve(91,a,119,a)].
% 0.75/1.07 154 join_semilatt_str(c12). [resolve(131,a,119,a)].
% 0.75/1.07 155 relation_of2_as_subset(f5(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(37)].
% 0.75/1.07 156 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(27)].
% 0.75/1.07 Derived: element(f5(A,B),powerset(cartesian_product2(A,B))). [resolve(155,a,156,a)].
% 0.75/1.07 157 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(55)].
% 0.75/1.07 Derived: relation_of2(f5(A,B),A,B). [resolve(157,a,155,a)].
% 0.75/1.07 158 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(55)].
% 0.75/1.07 Derived: -relation_of2(A,B,C) | element(A,powerset(cartesian_product2(B,C))). [resolve(158,a,156,a)].
% 0.75/1.07 159 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(79,a,71,b)].
% 0.75/1.07 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(159,a,156,a)].
% 0.75/1.07 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(159,a,157,a)].
% 0.75/1.07 160 relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(80,a,79,a)].
% 0.75/1.07 Derived: element(the_InternalRel(c2),powerset(cartesian_product2(the_carrier(c2),the_carrier(c2)))). [resolve(160,a,156,a)].
% 0.75/1.07 Derived: relation_of2(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(160,a,157,a)].
% 0.75/1.07 161 relation_of2_as_subset(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(86,a,79,a)].
% 0.75/1.07 Derived: element(the_InternalRel(c6),powerset(cartesian_product2(the_carrier(c6),the_carrier(c6)))). [resolve(161,a,156,a)].
% 0.75/1.07 Derived: relation_of2(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(161,a,157,a)].
% 0.75/1.07 162 relation_of2_as_subset(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(87,a,79,a)].
% 0.75/1.07 Derived: element(the_InternalRel(c8),powerset(cartesian_product2(the_carrier(c8),the_carrier(c8)))). [resolve(162,a,156,a)].
% 0.75/1.07 Derived: relation_of2(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(162,a,157,a)].
% 0.75/1.07 163 empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(91,a,110,c)].
% 0.75/1.07 Derived: empty_carrier(c5) | -lattice(c5) | element(k2_lattice3(c5),powerset(cartesian_product2(the_carrier(c5),the_carrier(c5)))). [resolve(163,c,156,a)].
% 0.75/1.07 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(163,c,157,a)].
% 0.75/1.07 164 empty_carrier(c12) | -lattice(c12) | relation_of2_as_subset(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(131,a,110,c)].
% 0.75/1.07 Derived: empty_carrier(c12) | -lattice(c12) | element(k2_lattice3(c12),powerset(cartesian_product2(the_carrier(c12),the_carrier(c12)))). [resolve(164,c,156,a)].
% 0.75/1.07 Derived: empty_carrier(c12) | -lattice(c12) | relation_of2(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(164,c,157,a)].
% 0.75/1.07 165 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(138,d,91,a)].
% 0.75/1.07 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(165,a,156,a)].
% 0.75/1.07 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(165,a,157,a)].
% 0.75/1.07 166 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(138,d,131,a)].
% 0.75/1.07 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(166,a,156,a)].
% 0.75/1.07 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(166,a,157,a)].
% 0.75/1.07 167 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(39)].
% 0.75/1.07 168 one_sorted_str(c3) # label(existence_l1_struct_0) # label(axiom). [clausify(32)].
% 0.75/1.07 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(167,b,168,a)].
% 0.75/1.07 169 one_sorted_str(c10) # label(rc3_struct_0) # label(axiom). [clausify(52)].
% 0.75/1.07 Derived: empty_carrier(c10) | -empty(the_carrier(c10)). [resolve(169,a,167,b)].
% 0.75/1.07 170 empty_carrier(A) | -one_sorted_str(A) | element(f8(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(53)].
% 0.75/1.07 Derived: empty_carrier(c3) | element(f8(c3),powerset(the_carrier(c3))). [resolve(170,b,168,a)].
% 0.75/1.07 Derived: empty_carrier(c10) | element(f8(c10),powerset(the_carrier(c10))). [resolve(170,b,169,a)].
% 0.75/1.07 171 empty_carrier(A) | -one_sorted_str(A) | -empty(f8(A)) # label(rc5_struct_0) # label(axiom). [clausify(53)].
% 0.75/1.07 Derived: empty_carrier(c3) | -empty(f8(c3)). [resolve(171,b,168,a)].
% 0.75/1.07 Derived: empty_carrier(c10) | -empty(f8(c10)). [resolve(171,b,169,a)].
% 0.75/1.07 172 one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(78,a,71,b)].
% 0.75/1.07 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(the_carrier(rel_str_of(B,A))). [resolve(172,a,167,b)].
% 0.75/1.07 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | element(f8(rel_str_of(B,A)),powerset(the_carrier(rel_str_of(B,A)))). [resolve(172,a,170,b)].
% 0.75/1.07 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(f8(rel_str_of(B,A))). [resolve(172,a,171,b)].
% 0.75/1.07 173 one_sorted_str(c2). [resolve(80,a,78,a)].
% 0.75/1.07 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(173,a,167,b)].
% 0.75/1.07 Derived: empty_carrier(c2) | element(f8(c2),powerset(the_carrier(c2))). [resolve(173,a,170,b)].
% 0.75/1.07 Derived: empty_carrier(c2) | -empty(f8(c2)). [resolve(173,a,171,b)].
% 0.75/1.07 174 one_sorted_str(c6). [resolve(86,a,78,a)].
% 0.75/1.07 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(174,a,167,b)].
% 0.75/1.07 Derived: empty_carrier(c6) | element(f8(c6),powerset(the_carrier(c6))). [resolve(174,a,170,b)].
% 0.75/1.07 Derived: empty_carrier(c6) | -empty(f8(c6)). [resolve(174,a,171,b)].
% 0.75/1.07 175 one_sorted_str(c8). [resolve(87,a,78,a)].
% 0.75/1.07 Derived: empty_carrier(c8) | -empty(the_carrier(c8)). [resolve(175,a,167,b)].
% 0.75/1.08 Derived: empty_carrier(c8) | element(f8(c8),powerset(the_carrier(c8))). [resolve(175,a,170,b)].
% 0.75/1.08 Derived: empty_carrier(c8) | -empty(f8(c8)). [resolve(175,a,171,b)].
% 0.75/1.08 176 one_sorted_str(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5). [resolve(137,d,91,a)].
% 0.75/1.08 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -empty(the_carrier(poset_of_lattice(c5))). [resolve(176,a,167,b)].
% 0.75/1.08 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | element(f8(poset_of_lattice(c5)),powerset(the_carrier(poset_of_lattice(c5)))). [resolve(176,a,170,b)].
% 0.75/1.08 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -empty(f8(poset_of_lattice(c5))). [resolve(176,a,171,b)].
% 0.75/1.08 177 one_sorted_str(poset_of_lattice(c12)) | empty_carrier(c12) | -lattice(c12). [resolve(137,d,131,a)].
% 0.75/1.08 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | -empty(the_carrier(poset_of_lattice(c12))). [resolve(177,a,167,b)].
% 0.75/1.08 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | element(f8(poset_of_lattice(c12)),powerset(the_carrier(poset_of_lattice(c12)))). [resolve(177,a,170,b)].
% 0.75/1.08 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | -empty(f8(poset_of_lattice(c12))). [resolve(177,a,171,b)].
% 0.75/1.08 178 one_sorted_str(c1). [resolve(147,a,148,a)].
% 0.75/1.08 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(178,a,167,b)].
% 0.75/1.08 Derived: empty_carrier(c1) | element(f8(c1),powerset(the_carrier(c1))). [resolve(178,a,170,b)].
% 0.75/1.08 Derived: empty_carrier(c1) | -empty(f8(c1)). [resolve(178,a,171,b)].
% 0.75/1.08 179 one_sorted_str(c5). [resolve(149,a,148,a)].
% 0.75/1.08 Derived: empty_carrier(c5) | -empty(the_carrier(c5)). [resolve(179,a,167,b)].
% 0.75/1.08 Derived: empty_carrier(c5) | element(f8(c5),powerset(the_carrier(c5))). [resolve(179,a,170,b)].
% 0.75/1.08 Derived: empty_carrier(c5) | -empty(f8(c5)). [resolve(179,a,171,b)].
% 0.75/1.08 180 one_sorted_str(c12). [resolve(150,a,148,a)].
% 0.75/1.08 Derived: empty_carrier(c12) | -empty(the_carrier(c12)). [resolve(180,a,167,b)].
% 0.75/1.08 Derived: empty_carrier(c12) | element(f8(c12),powerset(the_carrier(c12))). [resolve(180,a,170,b)].
% 0.75/1.08 Derived: empty_carrier(c12) | -empty(f8(c12)). [resolve(180,a,171,b)].
% 0.75/1.08 181 one_sorted_str(c4). [resolve(151,a,152,a)].
% 0.75/1.08 Derived: empty_carrier(c4) | -empty(the_carrier(c4)). [resolve(181,a,167,b)].
% 0.75/1.08 Derived: empty_carrier(c4) | element(f8(c4),powerset(the_carrier(c4))). [resolve(181,a,170,b)].
% 0.75/1.08 Derived: empty_carrier(c4) | -empty(f8(c4)). [resolve(181,a,171,b)].
% 0.75/1.08 182 -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(82,d,71,b)].
% 0.75/1.08 183 -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(42)].
% 0.75/1.08 184 -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(42)].
% 0.75/1.08 185 -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(42)].
% 0.75/1.08 186 -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(42)].
% 0.75/1.08 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(182,d,183,a)].
% 0.75/1.08 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(182,d,184,a)].
% 0.75/1.08 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(182,d,185,a)].
% 0.75/1.08 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(182,d,186,a)].
% 0.75/1.08 187 -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(82,d,80,a)].
% 0.75/1.08 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(187,d,183,a)].
% 0.75/1.08 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(187,d,184,a)].
% 0.75/1.08 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(187,d,185,a)].
% 0.75/1.08 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(187,d,186,a)].
% 0.75/1.08 188 -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | reflexive(the_InternalRel(c6)). [resolve(86,a,82,d)].
% 0.75/1.08 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | -antisymmetric(the_InternalRel(c6)) | -transitive(the_InternalRel(c6)) | -v1_partfun1(the_InternalRel(c6),A,A) | -relation_of2(the_InternalRel(c6),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c6))). [resolve(188,d,183,a)].
% 0.75/1.08 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | -antisymmetric(the_InternalRel(c6)) | -transitive(the_InternalRel(c6)) | -v1_partfun1(the_InternalRel(c6),A,A) | -relation_of2(the_InternalRel(c6),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c6))). [resolve(188,d,184,a)].
% 0.75/1.08 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | -antisymmetric(the_InternalRel(c6)) | -transitive(the_InternalRel(c6)) | -v1_partfun1(the_InternalRel(c6),A,A) | -relation_of2(the_InternalRel(c6),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c6))). [resolve(188,d,185,a)].
% 0.75/1.08 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | -antisymmetric(the_InternalRel(c6)) | -transitive(the_InternalRel(c6)) | -v1_partfun1(the_InternalRel(c6),A,A) | -relation_of2(the_InternalRel(c6),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c6))). [resolve(188,d,186,a)].
% 0.75/1.08 189 -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | reflexive(the_InternalRel(c8)). [resolve(87,a,82,d)].
% 0.75/1.08 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -antisymmetric(the_InternalRel(c8)) | -transitive(the_InternalRel(c8)) | -v1_partfun1(the_InternalRel(c8),A,A) | -relation_of2(the_InternalRel(c8),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c8))). [resolve(189,d,183,a)].
% 0.75/1.08 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -antisymmetric(the_InternalRel(c8)) | -transitive(the_InternalRel(c8)) | -v1_partfun1(the_InternalRel(c8),A,A) | -relation_of2(the_InternalRel(c8),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c8))). [resolve(189,d,184,a)].
% 0.75/1.08 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -antisymmetric(the_InternalRel(c8)) | -transitive(the_InternalRel(c8)) | -v1_partfun1(the_InternalRel(c8),A,A) | -relation_of2(the_InternalRel(c8),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c8))). [resolve(189,d,185,a)].
% 0.75/1.08 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -antisymmetric(the_InternalRel(c8)) | -transitive(the_InternalRel(c8)) | -v1_partfun1(the_InternalRel(c8),A,A) | -relation_of2(the_InternalRel(c8),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c8))). [resolve(189,d,186,a)].
% 0.75/1.08 190 empty_carrier(c5) | -lattice(c5) | reflexive(k2_lattice3(c5)). [resolve(91,a,106,c)].
% 0.75/1.08 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(190,c,183,a)].
% 0.75/1.08 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(190,c,184,a)].
% 0.75/1.08 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(190,c,185,a)].
% 0.75/1.08 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(190,c,186,a)].
% 0.75/1.08 191 empty_carrier(c12) | -lattice(c12) | reflexive(k2_lattice3(c12)). [resolve(131,a,106,c)].
% 0.75/1.08 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(191,c,183,a)].
% 0.75/1.08 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(191,c,184,a)].
% 0.75/1.08 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(191,c,185,a)].
% 0.75/1.08 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(191,c,186,a)].
% 0.75/1.08 192 -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | reflexive(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(140,g,91,a)].
% 0.75/1.08 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(192,d,183,a)].
% 0.75/1.09 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(192,d,184,a)].
% 0.75/1.09 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(192,d,185,a)].
% 0.75/1.09 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(192,d,186,a)].
% 0.75/1.09 193 -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))) | empty_carrier(c12) | -lattice(c12). [resolve(140,g,131,a)].
% 0.75/1.09 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | empty_carrier(c12) | -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(193,d,183,a)].
% 0.75/1.09 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | empty_carrier(c12) | -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(193,d,184,a)].
% 0.75/1.09 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | empty_carrier(c12) | -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) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c12)))). [resolve(193,d,185,a)].
% 0.75/1.09 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | empty_carrier(c12) | -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) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c12)))). [resolve(193,d,186,a)].
% 0.75/1.09 194 element(A,powerset(B)) | -subset(A,B) # labelCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------