TSTP Solution File: SEU346+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU346+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 13:31:08 EDT 2022
% Result : Theorem 43.67s 43.94s
% Output : Refutation 43.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU346+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 17:53:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.74/0.99 ============================== Prover9 ===============================
% 0.74/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.74/0.99 Process 19846 was started by sandbox2 on n024.cluster.edu,
% 0.74/0.99 Sun Jun 19 17:53:03 2022
% 0.74/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19693_n024.cluster.edu".
% 0.74/0.99 ============================== end of head ===========================
% 0.74/0.99
% 0.74/0.99 ============================== INPUT =================================
% 0.74/0.99
% 0.74/0.99 % Reading from file /tmp/Prover9_19693_n024.cluster.edu
% 0.74/0.99
% 0.74/0.99 set(prolog_style_variables).
% 0.74/0.99 set(auto2).
% 0.74/0.99 % set(auto2) -> set(auto).
% 0.74/0.99 % set(auto) -> set(auto_inference).
% 0.74/0.99 % set(auto) -> set(auto_setup).
% 0.74/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.74/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/0.99 % set(auto) -> set(auto_limits).
% 0.74/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/0.99 % set(auto) -> set(auto_denials).
% 0.74/0.99 % set(auto) -> set(auto_process).
% 0.74/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.74/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.74/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.74/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.74/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.74/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.74/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.74/0.99 % set(auto2) -> assign(stats, some).
% 0.74/0.99 % set(auto2) -> clear(echo_input).
% 0.74/0.99 % set(auto2) -> set(quiet).
% 0.74/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.74/0.99 % set(auto2) -> clear(print_given).
% 0.74/0.99 assign(lrs_ticks,-1).
% 0.74/0.99 assign(sos_limit,10000).
% 0.74/0.99 assign(order,kbo).
% 0.74/0.99 set(lex_order_vars).
% 0.74/0.99 clear(print_given).
% 0.74/0.99
% 0.74/0.99 % formulas(sos). % not echoed (93 formulas)
% 0.74/0.99
% 0.74/0.99 ============================== end of input ==========================
% 0.74/0.99
% 0.74/0.99 % From the command line: assign(max_seconds, 300).
% 0.74/0.99
% 0.74/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/0.99
% 0.74/0.99 % Formulas that are not ordinary clauses:
% 0.74/0.99 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].
% 0.74/0.99 2 (all A (latt_str(A) -> (strict_latt_str(A) -> A = latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A))))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 3 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 4 (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].
% 0.74/0.99 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].
% 0.74/0.99 6 (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].
% 0.74/0.99 7 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 8 (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].
% 0.74/0.99 9 (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].
% 0.74/0.99 10 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 11 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) <-> in(ordered_pair(B,C),the_InternalRel(A))))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 12 (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].
% 0.74/0.99 13 (all A all B all C (function(B) & quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) -> strict_latt_str(latt_str_of(A,B,C)) & latt_str(latt_str_of(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 14 (all A all B all C all D (-empty_carrier(A) & lattice(A) & latt_str(A) & -empty_carrier(B) & lattice(B) & latt_str(B) & element(C,the_carrier(A)) & element(D,the_carrier(B)) -> element(k10_filter_1(A,B,C,D),the_carrier(k8_filter_1(A,B))))) # label(dt_k10_filter_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 15 (all A all B all C all D (-empty(A) & -empty(B) & element(C,A) & element(D,B) -> element(ordered_pair_as_product_element(A,B,C,D),cartesian_product2(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 16 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 17 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 18 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 19 (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].
% 0.74/0.99 20 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 21 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 22 (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].
% 0.74/0.99 23 (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].
% 0.74/0.99 24 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 25 (all A all B (-empty_carrier(A) & latt_str(A) & -empty_carrier(B) & latt_str(B) -> strict_latt_str(k8_filter_1(A,B)) & latt_str(k8_filter_1(A,B)))) # label(dt_k8_filter_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 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].
% 0.74/0.99 27 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 28 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 29 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 30 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 31 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 32 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 33 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 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].
% 0.74/0.99 35 (all A (meet_semilatt_str(A) -> function(the_L_meet(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 36 (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].
% 0.74/0.99 37 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 38 (all A (join_semilatt_str(A) -> function(the_L_join(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 39 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 40 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 41 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 42 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 43 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 44 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 45 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 46 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 47 (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].
% 0.74/0.99 48 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 49 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 50 (all A (-empty_carrier(A) & join_commutative(A) & join_semilatt_str(A) -> relation(the_L_join(A)) & function(the_L_join(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v1_binop_1(the_L_join(A),the_carrier(A)) & v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc2_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 51 (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].
% 0.74/0.99 52 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 53 (all A (-empty_carrier(A) & join_associative(A) & join_semilatt_str(A) -> relation(the_L_join(A)) & function(the_L_join(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v2_binop_1(the_L_join(A),the_carrier(A)) & v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc3_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 54 (all A all B all C (-empty(A) & function(B) & quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) -> -empty_carrier(latt_str_of(A,B,C)) & strict_latt_str(latt_str_of(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 55 (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].
% 0.74/0.99 56 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 57 (all A (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) -> relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v1_binop_1(the_L_meet(A),the_carrier(A)) & v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc4_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 58 (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].
% 0.74/0.99 59 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 60 (all A (-empty_carrier(A) & meet_associative(A) & meet_semilatt_str(A) -> relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v2_binop_1(the_L_meet(A),the_carrier(A)) & v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc5_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 61 (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].
% 0.74/0.99 62 (all A all B all C (function(B) & quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) -> (all D all E all F (latt_str_of(A,B,C) = latt_str_of(D,E,F) -> A = D & B = E & C = F)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 63 (exists A (rel_str(A) & strict_rel_str(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 64 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 65 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 66 (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].
% 0.74/0.99 67 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 68 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 69 (exists A (latt_str(A) & strict_latt_str(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 70 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 71 (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].
% 0.74/0.99 72 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 73 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & lattice(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 74 (all A all B all C all D (-empty_carrier(A) & lattice(A) & latt_str(A) & -empty_carrier(B) & lattice(B) & latt_str(B) & element(C,the_carrier(A)) & element(D,the_carrier(B)) -> k10_filter_1(A,B,C,D) = ordered_pair(C,D))) # label(redefinition_k10_filter_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 75 (all A all B all C all D (-empty(A) & -empty(B) & element(C,A) & element(D,B) -> ordered_pair_as_product_element(A,B,C,D) = ordered_pair(C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 76 (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].
% 0.74/0.99 77 (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].
% 0.74/0.99 78 (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].
% 0.74/0.99 79 (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].
% 0.74/0.99 80 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 81 (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].
% 0.74/0.99 82 (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].
% 0.74/0.99 83 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 84 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 85 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A)) <-> below_refl(A,B,C)))))))) # label(t32_filter_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 86 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 87 (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].
% 0.74/0.99 88 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 89 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 90 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 91 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/0.99 92 -(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(negated_conjecture) # label(non_clause). [assumption].
% 0.74/0.99
% 0.74/0.99 ============================== end of process non-clausal formulas ===
% 0.74/0.99
% 0.74/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/0.99
% 0.74/0.99 ============================== PREDICATE ELIMINATION =================
% 0.74/0.99 93 -relation_of2(A,B,B) | rel_str(rel_str_of(B,A)) # label(dt_g1_orders_2) # label(axiom). [clausify(12)].
% 0.74/0.99 94 -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)].
% 0.74/0.99 95 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -related(A,B,C) | in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(11)].
% 0.74/0.99 96 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | related(A,B,C) | -in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(11)].
% 0.74/0.99 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(93,b,94,a)].
% 0.74/0.99 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -element(D,the_carrier(rel_str_of(B,A))) | -related(rel_str_of(B,A),C,D) | in(ordered_pair(C,D),the_InternalRel(rel_str_of(B,A))). [resolve(93,b,95,a)].
% 0.74/0.99 Derived: -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -element(D,the_carrier(rel_str_of(B,A))) | related(rel_str_of(B,A),C,D) | -in(ordered_pair(C,D),the_InternalRel(rel_str_of(B,A))). [resolve(93,b,96,a)].
% 0.74/0.99 97 empty_carrier(A) | -lattice(A) | -latt_str(A) | rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(22)].
% 0.74/0.99 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(97,d,94,a)].
% 0.74/0.99 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),B,C) | in(ordered_pair(B,C),the_InternalRel(poset_of_lattice(A))). [resolve(97,d,95,a)].
% 0.74/0.99 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | related(poset_of_lattice(A),B,C) | -in(ordered_pair(B,C),the_InternalRel(poset_of_lattice(A))). [resolve(97,d,96,a)].
% 0.74/0.99 98 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(28)].
% 0.74/0.99 Derived: one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(98,a,93,b)].
% 0.74/0.99 Derived: one_sorted_str(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(98,a,97,d)].
% 0.74/0.99 99 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(36)].
% 0.74/0.99 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(99,a,93,b)].
% 0.74/0.99 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(99,a,97,d)].
% 0.74/0.99 100 rel_str(c2) # label(existence_l1_orders_2) # label(axiom). [clausify(40)].
% 0.74/0.99 Derived: -strict_rel_str(c2) | rel_str_of(the_carrier(c2),the_InternalRel(c2)) = c2. [resolve(100,a,94,a)].
% 0.74/0.99 Derived: -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | -related(c2,A,B) | in(ordered_pair(A,B),the_InternalRel(c2)). [resolve(100,a,95,a)].
% 0.74/0.99 Derived: -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | related(c2,A,B) | -in(ordered_pair(A,B),the_InternalRel(c2)). [resolve(100,a,96,a)].
% 0.74/0.99 Derived: one_sorted_str(c2). [resolve(100,a,98,a)].
% 0.74/0.99 Derived: relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(100,a,99,a)].
% 0.74/0.99 101 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | relation(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(51)].
% 0.74/0.99 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(101,d,93,b)].
% 0.74/0.99 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(101,d,97,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | relation(the_InternalRel(c2)). [resolve(101,d,100,a)].
% 0.74/0.99 102 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | reflexive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(51)].
% 0.74/0.99 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(102,d,93,b)].
% 0.74/0.99 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(102,d,97,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(102,d,100,a)].
% 0.74/0.99 103 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | antisymmetric(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(51)].
% 0.74/0.99 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(103,d,93,b)].
% 0.74/0.99 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(103,d,97,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | antisymmetric(the_InternalRel(c2)). [resolve(103,d,100,a)].
% 0.74/0.99 104 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | transitive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(51)].
% 0.74/0.99 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(104,d,93,b)].
% 0.74/0.99 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(104,d,97,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | transitive(the_InternalRel(c2)). [resolve(104,d,100,a)].
% 0.74/0.99 105 -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(51)].
% 0.74/0.99 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(105,d,93,b)].
% 0.74/0.99 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(105,d,97,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | v1_partfun1(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(105,d,100,a)].
% 0.74/0.99 106 rel_str(c6) # label(rc1_orders_2) # label(axiom). [clausify(63)].
% 0.74/0.99 Derived: -strict_rel_str(c6) | rel_str_of(the_carrier(c6),the_InternalRel(c6)) = c6. [resolve(106,a,94,a)].
% 0.74/0.99 Derived: -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | -related(c6,A,B) | in(ordered_pair(A,B),the_InternalRel(c6)). [resolve(106,a,95,a)].
% 0.74/0.99 Derived: -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | related(c6,A,B) | -in(ordered_pair(A,B),the_InternalRel(c6)). [resolve(106,a,96,a)].
% 0.74/0.99 Derived: one_sorted_str(c6). [resolve(106,a,98,a)].
% 0.74/0.99 Derived: relation_of2_as_subset(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(106,a,99,a)].
% 0.74/0.99 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | relation(the_InternalRel(c6)). [resolve(106,a,101,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | reflexive(the_InternalRel(c6)). [resolve(106,a,102,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | antisymmetric(the_InternalRel(c6)). [resolve(106,a,103,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | transitive(the_InternalRel(c6)). [resolve(106,a,104,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | v1_partfun1(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(106,a,105,d)].
% 0.74/0.99 107 rel_str(c8) # label(rc2_orders_2) # label(axiom). [clausify(66)].
% 0.74/0.99 Derived: -strict_rel_str(c8) | rel_str_of(the_carrier(c8),the_InternalRel(c8)) = c8. [resolve(107,a,94,a)].
% 0.74/0.99 Derived: -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | -related(c8,A,B) | in(ordered_pair(A,B),the_InternalRel(c8)). [resolve(107,a,95,a)].
% 0.74/0.99 Derived: -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | related(c8,A,B) | -in(ordered_pair(A,B),the_InternalRel(c8)). [resolve(107,a,96,a)].
% 0.74/0.99 Derived: one_sorted_str(c8). [resolve(107,a,98,a)].
% 0.74/0.99 Derived: relation_of2_as_subset(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(107,a,99,a)].
% 0.74/0.99 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | relation(the_InternalRel(c8)). [resolve(107,a,101,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | reflexive(the_InternalRel(c8)). [resolve(107,a,102,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | antisymmetric(the_InternalRel(c8)). [resolve(107,a,103,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | transitive(the_InternalRel(c8)). [resolve(107,a,104,d)].
% 0.74/0.99 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | v1_partfun1(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(107,a,105,d)].
% 0.74/0.99 108 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(79)].
% 0.74/0.99 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(108,c,93,b)].
% 0.74/0.99 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(108,c,97,d)].
% 0.74/0.99 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(108,c,100,a)].
% 0.74/0.99 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(108,c,106,a)].
% 0.74/0.99 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(108,c,107,a)].
% 0.74/0.99 109 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(79)].
% 0.74/0.99 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(109,c,93,b)].
% 0.74/0.99 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(109,c,97,d)].
% 0.74/1.00 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(109,c,100,a)].
% 0.74/1.00 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(109,c,106,a)].
% 0.74/1.00 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(109,c,107,a)].
% 0.74/1.00 110 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(82)].
% 0.74/1.00 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(110,c,93,b)].
% 0.74/1.00 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(110,c,97,d)].
% 0.74/1.00 Derived: empty_carrier(c2) | -reflexive_relstr(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | related_reflexive(c2,A,A). [resolve(110,c,100,a)].
% 0.74/1.00 Derived: empty_carrier(c6) | -reflexive_relstr(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | related_reflexive(c6,A,A). [resolve(110,c,106,a)].
% 0.74/1.00 Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -element(A,the_carrier(c8)) | -element(B,the_carrier(c8)) | related_reflexive(c8,A,A). [resolve(110,c,107,a)].
% 0.74/1.00 111 -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | strict_latt_str(latt_str_of(B,A,C)) # label(dt_g3_lattices) # label(axiom). [clausify(13)].
% 0.74/1.00 112 -latt_str(A) | -strict_latt_str(A) | latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)) = A # label(abstractness_v3_lattices) # label(axiom). [clausify(2)].
% 0.74/1.00 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -latt_str(latt_str_of(B,A,C)) | latt_str_of(the_carrier(latt_str_of(B,A,C)),the_L_join(latt_str_of(B,A,C)),the_L_meet(latt_str_of(B,A,C))) = latt_str_of(B,A,C). [resolve(111,g,112,b)].
% 0.74/1.00 113 empty_carrier(A) | -latt_str(A) | empty_carrier(B) | -latt_str(B) | strict_latt_str(k8_filter_1(A,B)) # label(dt_k8_filter_1) # label(axiom). [clausify(25)].
% 0.74/1.00 Derived: empty_carrier(A) | -latt_str(A) | empty_carrier(B) | -latt_str(B) | -latt_str(k8_filter_1(A,B)) | latt_str_of(the_carrier(k8_filter_1(A,B)),the_L_join(k8_filter_1(A,B)),the_L_meet(k8_filter_1(A,B))) = k8_filter_1(A,B). [resolve(113,e,112,b)].
% 0.74/1.00 114 empty(A) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A) | strict_latt_str(latt_str_of(A,B,C)) # label(fc3_lattices) # label(axiom). [clausify(54)].
% 0.74/1.00 115 strict_latt_str(c10) # label(rc3_lattices) # label(axiom). [clausify(69)].
% 0.74/1.00 Derived: -latt_str(c10) | latt_str_of(the_carrier(c10),the_L_join(c10),the_L_meet(c10)) = c10. [resolve(115,a,112,b)].
% 0.74/1.00 116 strict_latt_str(c12) # label(rc6_lattices) # label(axiom). [clausify(72)].
% 0.74/1.00 Derived: -latt_str(c12) | latt_str_of(the_carrier(c12),the_L_join(c12),the_L_meet(c12)) = c12. [resolve(116,a,112,b)].
% 0.74/1.00 117 strict_latt_str(c13) # label(rc9_lattices) # label(axiom). [clausify(73)].
% 0.74/1.00 Derived: -latt_str(c13) | latt_str_of(the_carrier(c13),the_L_join(c13),the_L_meet(c13)) = c13. [resolve(117,a,112,b)].
% 0.74/1.00 118 -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(6)].
% 0.74/1.00 119 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(4)].
% 0.74/1.00 120 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | relation(the_L_join(A)) # label(fc2_lattice2) # label(axiom). [clausify(50)].
% 0.74/1.00 Derived: empty_carrier(A) | -join_semilatt_str(A) | relation(the_L_join(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(120,b,119,d)].
% 0.74/1.00 121 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | function(the_L_join(A)) # label(fc2_lattice2) # label(axiom). [clausify(50)].
% 0.74/1.00 Derived: empty_carrier(A) | -join_semilatt_str(A) | function(the_L_join(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(121,b,119,d)].
% 0.74/1.00 122 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(50)].
% 0.74/1.00 Derived: empty_carrier(A) | -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(122,b,119,d)].
% 0.74/1.00 123 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | v1_binop_1(the_L_join(A),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(50)].
% 0.74/1.00 Derived: empty_carrier(A) | -join_semilatt_str(A) | v1_binop_1(the_L_join(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(123,b,119,d)].
% 0.74/1.00 124 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(50)].
% 0.74/1.00 Derived: empty_carrier(A) | -join_semilatt_str(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(124,b,119,d)].
% 0.74/1.00 125 join_commutative(c13) # label(rc9_lattices) # label(axiom). [clausify(73)].
% 0.74/1.00 Derived: empty_carrier(c13) | -join_semilatt_str(c13) | relation(the_L_join(c13)). [resolve(125,a,120,b)].
% 0.74/1.00 Derived: empty_carrier(c13) | -join_semilatt_str(c13) | function(the_L_join(c13)). [resolve(125,a,121,b)].
% 0.74/1.00 Derived: empty_carrier(c13) | -join_semilatt_str(c13) | quasi_total(the_L_join(c13),cartesian_product2(the_carrier(c13),the_carrier(c13)),the_carrier(c13)). [resolve(125,a,122,b)].
% 0.74/1.00 Derived: empty_carrier(c13) | -join_semilatt_str(c13) | v1_binop_1(the_L_join(c13),the_carrier(c13)). [resolve(125,a,123,b)].
% 0.74/1.00 Derived: empty_carrier(c13) | -join_semilatt_str(c13) | v1_partfun1(the_L_join(c13),cartesian_product2(the_carrier(c13),the_carrier(c13)),the_carrier(c13)). [resolve(125,a,124,b)].
% 0.74/1.00 126 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | relation(the_L_join(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.74/1.00 127 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_associative(A) # label(cc1_lattices) # label(axiom). [clausify(4)].
% 0.74/1.00 128 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | function(the_L_join(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.74/1.00 129 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.74/1.00 130 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | v2_binop_1(the_L_join(A),the_carrier(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.74/1.00 Derived: empty_carrier(A) | -join_semilatt_str(A) | v2_binop_1(the_L_join(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(130,b,127,d)].
% 0.74/1.01 131 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.74/1.01 132 join_associative(c13) # label(rc9_lattices) # label(axiom). [clausify(73)].
% 0.74/1.01 Derived: empty_carrier(c13) | -join_semilatt_str(c13) | v2_binop_1(the_L_join(c13),the_carrier(c13)). [resolve(132,a,130,b)].
% 0.74/1.01 133 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | relation(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(57)].
% 0.74/1.01 134 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(4)].
% 0.74/1.01 Derived: empty_carrier(A) | -meet_semilatt_str(A) | relation(the_L_meet(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(133,b,134,d)].
% 0.74/1.01 135 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | function(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(57)].
% 0.74/1.01 Derived: empty_carrier(A) | -meet_semilatt_str(A) | function(the_L_meet(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(135,b,134,d)].
% 0.74/1.01 136 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(57)].
% 0.74/1.01 Derived: empty_carrier(A) | -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(136,b,134,d)].
% 0.74/1.01 137 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | v1_binop_1(the_L_meet(A),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(57)].
% 0.74/1.01 Derived: empty_carrier(A) | -meet_semilatt_str(A) | v1_binop_1(the_L_meet(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(137,b,134,d)].
% 0.74/1.01 138 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(57)].
% 0.74/1.01 Derived: empty_carrier(A) | -meet_semilatt_str(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(138,b,134,d)].
% 0.74/1.01 139 meet_commutative(c13) # label(rc9_lattices) # label(axiom). [clausify(73)].
% 0.74/1.01 Derived: empty_carrier(c13) | -meet_semilatt_str(c13) | relation(the_L_meet(c13)). [resolve(139,a,133,b)].
% 0.74/1.01 Derived: empty_carrier(c13) | -meet_semilatt_str(c13) | function(the_L_meet(c13)). [resolve(139,a,135,b)].
% 0.74/1.01 Derived: empty_carrier(c13) | -meet_semilatt_str(c13) | quasi_total(the_L_meet(c13),cartesian_product2(the_carrier(c13),the_carrier(c13)),the_carrier(c13)). [resolve(139,a,136,b)].
% 0.74/1.01 Derived: empty_carrier(c13) | -meet_semilatt_str(c13) | v1_binop_1(the_L_meet(c13),the_carrier(c13)). [resolve(139,a,137,b)].
% 0.74/1.01 Derived: empty_carrier(c13) | -meet_semilatt_str(c13) | v1_partfun1(the_L_meet(c13),cartesian_product2(the_carrier(c13),the_carrier(c13)),the_carrier(c13)). [resolve(139,a,138,b)].
% 0.74/1.01 140 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(78)].
% 0.74/1.01 Derived: empty_carrier(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) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(140,b,134,d)].
% 0.74/1.01 Derived: empty_carrier(c13) | -meet_absorbing(c13) | -join_absorbing(c13) | -latt_str(c13) | -element(A,the_carrier(c13)) | -element(B,the_carrier(c13)) | -below_refl(c13,A,B) | below(c13,A,B). [resolve(140,b,139,a)].
% 0.74/1.01 141 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(78)].
% 0.74/1.02 Derived: empty_carrier(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) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(141,b,134,d)].
% 0.74/1.02 Derived: empty_carrier(c13) | -meet_absorbing(c13) | -join_absorbing(c13) | -latt_str(c13) | -element(A,the_carrier(c13)) | -element(B,the_carrier(c13)) | below_refl(c13,A,B) | -below(c13,A,B). [resolve(141,b,139,a)].
% 0.74/1.02 142 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(81)].
% 0.74/1.02 Derived: empty_carrier(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) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(142,b,134,d)].
% 0.74/1.02 Derived: empty_carrier(c13) | -meet_absorbing(c13) | -join_absorbing(c13) | -latt_str(c13) | -element(A,the_carrier(c13)) | -element(B,the_carrier(c13)) | below_refl(c13,A,A). [resolve(142,b,139,a)].
% 0.74/1.02 143 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | relation(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(60)].
% 0.74/1.02 144 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_associative(A) # label(cc1_lattices) # label(axiom). [clausify(4)].
% 0.74/1.02 145 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | function(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(60)].
% 0.74/1.02 146 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(60)].
% 0.74/1.02 147 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(60)].
% 0.74/1.02 Derived: empty_carrier(A) | -meet_semilatt_str(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(147,b,144,d)].
% 0.74/1.02 148 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(60)].
% 0.74/1.02 149 meet_associative(c13) # label(rc9_lattices) # label(axiom). [clausify(73)].
% 0.74/1.02 Derived: empty_carrier(c13) | -meet_semilatt_str(c13) | v2_binop_1(the_L_meet(c13),the_carrier(c13)). [resolve(149,a,147,b)].
% 0.74/1.02 150 -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(55)].
% 0.74/1.02 151 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(19)].
% 0.74/1.02 Derived: -antisymmetric(k2_lattice3(A)) | -transitive(k2_lattice3(A)) | -v1_partfun1(k2_lattice3(A),B,B) | -relation_of2(k2_lattice3(A),B,B) | strict_rel_str(rel_str_of(B,k2_lattice3(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(150,a,151,d)].
% 0.74/1.02 152 -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(55)].
% 0.74/1.02 Derived: -antisymmetric(k2_lattice3(A)) | -transitive(k2_lattice3(A)) | -v1_partfun1(k2_lattice3(A),B,B) | -relation_of2(k2_lattice3(A),B,B) | reflexive_relstr(rel_str_of(B,k2_lattice3(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(152,a,151,d)].
% 0.74/1.02 153 -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(55)].
% 0.74/1.02 Derived: -antisymmetric(k2_lattice3(A)) | -transitive(k2_lattice3(A)) | -v1_partfun1(k2_lattice3(A),B,B) | -relation_of2(k2_lattice3(A),B,B) | transitive_relstr(rel_str_of(B,k2_lattice3(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(153,a,151,d)].
% 0.74/1.02 154 -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(55)].
% 0.74/1.02 Derived: -antisymmetric(k2_lattice3(A)) | -transitive(k2_lattice3(A)) | -v1_partfun1(k2_lattice3(A),B,B) | -relation_of2(k2_lattice3(A),B,B) | antisymmetric_relstr(rel_str_of(B,k2_lattice3(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(154,a,151,d)].
% 0.74/1.02 155 -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(102,d,93,b)].
% 0.74/1.02 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(155,d,150,a)].
% 0.74/1.02 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(155,d,152,a)].
% 0.74/1.02 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(155,d,153,a)].
% 0.74/1.02 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(155,d,154,a)].
% 0.74/1.02 156 -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(102,d,97,d)].
% 0.74/1.02 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A) | -antisymmetric(the_InternalRel(poset_of_lattice(A))) | -transitive(the_InternalRel(poset_of_lattice(A))) | -v1_partfun1(the_InternalRel(poset_of_lattice(A)),B,B) | -relation_of2(the_InternalRel(poset_of_lattice(A)),B,B) | strict_rel_str(rel_str_of(B,the_InternalRel(poset_of_lattice(A)))). [resolve(156,d,150,a)].
% 0.74/1.02 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A) | -antisymmetric(the_InternalRel(poset_of_lattice(A))) | -transitive(the_InternalRel(poset_of_lattice(A))) | -v1_partfun1(the_InternalRel(poset_of_lattice(A)),B,B) | -relation_of2(the_InternalRel(poset_of_lattice(A)),B,B) | reflexive_relstr(rel_str_of(B,the_InternalRel(poset_of_lattice(A)))). [resolve(156,d,152,a)].
% 0.74/1.02 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A) | -antisymmetric(the_InternalRel(poset_of_lattice(A))) | -transitive(the_InternalRel(poset_of_lattice(A))) | -v1_partfun1(the_InternalRel(poset_of_lattice(A)),B,B) | -relation_of2(the_InternalRel(poset_of_lattice(A)),B,B) | transitive_relstr(rel_str_of(B,the_InternalRel(poset_of_lattice(A)))). [resolve(156,d,153,a)].
% 0.74/1.02 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A) | -antisymmetric(the_InternalRel(poset_of_lattice(A))) | -transitive(the_InternalRel(poset_of_lattice(A))) | -v1_partfun1(the_InternalRel(poset_of_lattice(A)),B,B) | -relation_of2(the_InternalRel(poset_of_lattice(A)),B,B) | antisymmetric_relstr(rel_str_of(B,the_InternalRel(poset_of_lattice(A)))). [resolve(156,d,154,a)].
% 0.74/1.02 157 -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(102,d,100,a)].
% 0.74/1.02 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(157,d,150,a)].
% 0.74/1.02 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(157,d,152,a)].
% 0.74/1.02 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(157,d,153,a)].
% 0.74/1.02 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(157,d,154,a)].
% 0.74/1.02 158 -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | reflexive(the_InternalRel(c6)). [resolve(106,a,102,d)].
% 0.74/1.02 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(158,d,150,a)].
% 0.74/1.02 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(158,d,152,a)].
% 0.74/1.02 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(158,d,153,a)].
% 0.74/1.02 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(158,d,154,a)].
% 0.74/1.02 159 -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | reflexive(the_InternalRel(c8)). [resolve(107,a,102,d)].
% 0.74/1.02 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(159,d,150,a)].
% 0.74/1.02 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(159,d,152,a)].
% 0.74/1.02 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(159,d,153,a)].
% 0.74/1.02 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(159,d,154,a)].
% 0.74/1.02 160 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(34)].
% 0.74/1.02 161 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(19)].
% 0.74/1.02 Derived: element(k2_lattice3(A),powerset(cartesian_product2(the_carrier(A),the_carrier(A)))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(160,a,161,d)].
% 0.74/1.02 162 -meet_semilatt_str(A) | relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u1_lattices) # label(axiom). [clausify(35)].
% 0.74/1.02 Derived: -meet_semilatt_str(A) | element(the_L_meet(A),powerset(cartesian_product2(cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))). [resolve(162,b,160,a)].
% 0.74/1.02 163 -join_semilatt_str(A) | relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u2_lattices) # label(axiom). [clausify(38)].
% 0.74/1.02 Derived: -join_semilatt_str(A) | element(the_L_join(A),powerset(cartesian_product2(cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))). [resolve(163,b,160,a)].
% 0.74/1.02 164 relation_of2_as_subset(f3(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(46)].
% 0.74/1.02 Derived: element(f3(A,B),powerset(cartesian_product2(A,B))). [resolve(164,a,160,a)].
% 0.74/1.02 165 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(77)].
% 0.74/1.02 Derived: relation_of2(k2_lattice3(A),the_carrier(A),the_carrier(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(165,a,161,d)].
% 0.74/1.02 Derived: relation_of2(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -meet_semilatt_str(A). [resolve(165,a,162,b)].
% 0.74/1.02 Derived: relation_of2(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -join_semilatt_str(A). [resolve(165,a,163,b)].
% 0.74/1.02 Derived: relation_of2(f3(A,B),A,B). [resolve(165,a,164,a)].
% 0.74/1.02 166 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(77)].
% 0.74/1.02 Derived: -relation_of2(A,B,C) | element(A,powerset(cartesian_product2(B,C))). [resolve(166,a,160,a)].
% 0.74/1.02 167 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(99,a,93,b)].
% 0.74/1.02 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(167,a,160,a)].
% 0.74/1.02 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(167,a,165,a)].
% 0.74/1.02 168 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(99,a,97,d)].
% 0.74/1.02 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | element(the_InternalRel(poset_of_lattice(A)),powerset(cartesian_product2(the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))))). [resolve(168,a,160,a)].
% 0.74/1.02 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | relation_of2(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))). [resolve(168,a,165,a)].
% 0.74/1.03 169 relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(100,a,99,a)].
% 0.74/1.03 Derived: element(the_InternalRel(c2),powerset(cartesian_product2(the_carrier(c2),the_carrier(c2)))). [resolve(169,a,160,a)].
% 0.74/1.03 Derived: relation_of2(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(169,a,165,a)].
% 0.74/1.03 170 relation_of2_as_subset(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(106,a,99,a)].
% 0.74/1.03 Derived: element(the_InternalRel(c6),powerset(cartesian_product2(the_carrier(c6),the_carrier(c6)))). [resolve(170,a,160,a)].
% 0.74/1.03 Derived: relation_of2(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(170,a,165,a)].
% 0.74/1.03 171 relation_of2_as_subset(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(107,a,99,a)].
% 0.74/1.03 Derived: element(the_InternalRel(c8),powerset(cartesian_product2(the_carrier(c8),the_carrier(c8)))). [resolve(171,a,160,a)].
% 0.74/1.03 Derived: relation_of2(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(171,a,165,a)].
% 0.74/1.03 172 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(48)].
% 0.74/1.03 173 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(27)].
% 0.74/1.03 174 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(30)].
% 0.74/1.03 175 one_sorted_str(c3) # label(existence_l1_struct_0) # label(axiom). [clausify(41)].
% 0.74/1.03 Derived: empty_carrier(A) | -empty(the_carrier(A)) | -meet_semilatt_str(A). [resolve(172,b,173,b)].
% 0.74/1.03 Derived: empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(172,b,174,b)].
% 0.74/1.03 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(172,b,175,a)].
% 0.74/1.03 176 one_sorted_str(c11) # label(rc3_struct_0) # label(axiom). [clausify(70)].
% 0.74/1.03 Derived: empty_carrier(c11) | -empty(the_carrier(c11)). [resolve(176,a,172,b)].
% 0.74/1.03 177 empty_carrier(A) | -one_sorted_str(A) | element(f6(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(71)].
% 0.74/1.03 Derived: empty_carrier(A) | element(f6(A),powerset(the_carrier(A))) | -meet_semilatt_str(A). [resolve(177,b,173,b)].
% 0.74/1.03 Derived: empty_carrier(A) | element(f6(A),powerset(the_carrier(A))) | -join_semilatt_str(A). [resolve(177,b,174,b)].
% 0.74/1.03 Derived: empty_carrier(c3) | element(f6(c3),powerset(the_carrier(c3))). [resolve(177,b,175,a)].
% 0.74/1.03 Derived: empty_carrier(c11) | element(f6(c11),powerset(the_carrier(c11))). [resolve(177,b,176,a)].
% 0.74/1.03 178 empty_carrier(A) | -one_sorted_str(A) | -empty(f6(A)) # label(rc5_struct_0) # label(axiom). [clausify(71)].
% 0.74/1.03 Derived: empty_carrier(A) | -empty(f6(A)) | -meet_semilatt_str(A). [resolve(178,b,173,b)].
% 0.74/1.03 Derived: empty_carrier(A) | -empty(f6(A)) | -join_semilatt_str(A). [resolve(178,b,174,b)].
% 0.74/1.03 Derived: empty_carrier(c3) | -empty(f6(c3)). [resolve(178,b,175,a)].
% 0.74/1.03 Derived: empty_carrier(c11) | -empty(f6(c11)). [resolve(178,b,176,a)].
% 0.74/1.03 179 one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(98,a,93,b)].
% 0.74/1.03 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(the_carrier(rel_str_of(B,A))). [resolve(179,a,172,b)].
% 0.74/1.03 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | element(f6(rel_str_of(B,A)),powerset(the_carrier(rel_str_of(B,A)))). [resolve(179,a,177,b)].
% 0.74/1.03 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(f6(rel_str_of(B,A))). [resolve(179,a,178,b)].
% 0.74/1.03 180 one_sorted_str(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(98,a,97,d)].
% 0.74/1.03 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(poset_of_lattice(A)) | -empty(the_carrier(poset_of_lattice(A))). [resolve(180,a,172,b)].
% 0.74/1.03 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(poset_of_lattice(A)) | element(f6(poset_of_lattice(A)),powerset(the_carrier(poset_of_lattice(A)))). [resolve(180,a,177,b)].
% 0.74/1.03 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(poset_of_lattice(A)) | -empty(f6(poset_of_lattice(A))). [resolve(180,a,178,b)].
% 43.67/43.94 181 one_sorted_str(c2). [resolve(100,a,98,a)].
% 43.67/43.94 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(181,a,172,b)].
% 43.67/43.94 Derived: empty_carrier(c2) | element(f6(c2),powerset(the_carrier(c2))). [resolve(181,a,177,b)].
% 43.67/43.94 Derived: empty_carrier(c2) | -empty(f6(c2)). [resolve(181,a,178,b)].
% 43.67/43.94 182 one_sorted_str(c6). [resolve(106,a,98,a)].
% 43.67/43.94 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(182,a,172,b)].
% 43.67/43.94 Derived: empty_carrier(c6) | element(f6(c6),powerset(the_carrier(c6))). [resolve(182,a,177,b)].
% 43.67/43.94 Derived: empty_carrier(c6) | -empty(f6(c6)). [resolve(182,a,178,b)].
% 43.67/43.94 183 one_sorted_str(c8). [resolve(107,a,98,a)].
% 43.67/43.94 Derived: empty_carrier(c8) | -empty(the_carrier(c8)). [resolve(183,a,172,b)].
% 43.67/43.94 Derived: empty_carrier(c8) | element(f6(c8),powerset(the_carrier(c8))). [resolve(183,a,177,b)].
% 43.67/43.94 Derived: empty_carrier(c8) | -empty(f6(c8)). [resolve(183,a,178,b)].
% 43.67/43.94 184 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(86)].
% 43.67/43.94 185 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(80)].
% 43.67/43.94 186 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(86)].
% 43.67/43.94 Derived: element(A,powerset(A)). [resolve(184,b,185,a)].
% 43.67/43.94
% 43.67/43.94 ============================== end predicate elimination =============
% 43.67/43.94
% 43.67/43.94 Auto_denials: (non-Horn, no changes).
% 43.67/43.94
% 43.67/43.94 Term ordering decisions:
% 43.67/43.94 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. rel_str_of=1. cartesian_product2=1. ordered_pair=1. k8_filter_1=1. cast_to_el_of_LattPOSet=1. unordered_pair=1. f1=1. f3=1. the_carrier=1. the_InternalRel=1. poset_of_lattice=1. k2_lattice3=1. powerset=1. the_L_join=1. the_L_meet=1. relation_of_lattice=1. singleton=1. f2=1. f4=1. f5=1. f6=1. latt_str_of=1. ordered_pair_as_product_element=1. k10_filter_1=1.
% 43.67/43.94
% 43.67/43.94 ============================== end of process initial clauses ========
% 43.67/43.94
% 43.67/43.94 ============================== CLAUSES FOR SEARCH ====================
% 43.67/43.94
% 43.67/43.94 ============================== end of clauses for search =============
% 43.67/43.94
% 43.67/43.94 ============================== SEARCH ================================
% 43.67/43.94
% 43.67/43.94 % Starting search at 0.09 seconds.
% 43.67/43.94
% 43.67/43.94 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 129 (0.00 of 0.27 sec).
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=32.000, iters=3531
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=31.000, iters=3454
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=29.000, iters=3353
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=28.000, iters=3349
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=27.000, iters=3358
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=26.000, iters=4095
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=24.000, iters=3571
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=23.000, iters=3407
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=22.000, iters=4305
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=21.000, iters=3544
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=20.000, iters=4618
% 43.67/43.94
% 43.67/43.94 Low Water (keep): wt=19.000, iters=3360
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=3369, wt=61.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=3132, wt=58.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=3131, wt=57.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=4487, wt=56.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=3150, wt=53.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=4261, wt=52.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=4271, wt=50.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=3356, wt=49.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=4273, wt=48.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=3357, wt=47.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=4284, wt=46.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=3141, wt=45.000
% 43.67/43.94
% 43.67/43.94 Low Water (displace): id=8181, wt=44.000
% 43.67/43.94
% 43.67/43.94 ============================== PROOF =================================
% 43.67/43.94 % SZS status Theorem
% 43.67/43.94 % SZS output start Refutation
% 43.67/43.94
% 43.67/43.94 % Proof 1 at 42.39 (+ 0.57) seconds.
% 43.67/43.94 % Length of proof is 107.
% 43.67/43.94 % Level of proof is 13.
% 43.67/43.94 % Maximum clause weight is 36.000.
% 43.67/43.94 % Given clauses 16020.
% 43.67/43.94
% 43.67/43.94 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].
% 43.67/43.94 7 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 43.67/43.94 8 (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].
% 43.67/43.94 9 (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].
% 43.67/43.94 10 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 43.67/43.94 11 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) <-> in(ordered_pair(B,C),the_InternalRel(A))))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption].
% 43.67/43.94 12 (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].
% 43.67/43.94 19 (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].
% 43.67/43.94 22 (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].
% 43.67/43.94 30 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 43.67/43.94 31 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 43.67/43.94 48 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 43.67/43.94 58 (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].
% 43.67/43.94 61 (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].
% 43.67/43.94 74 (all A all B all C all D (-empty_carrier(A) & lattice(A) & latt_str(A) & -empty_carrier(B) & lattice(B) & latt_str(B) & element(C,the_carrier(A)) & element(D,the_carrier(B)) -> k10_filter_1(A,B,C,D) = ordered_pair(C,D))) # label(redefinition_k10_filter_1) # label(axiom) # label(non_clause). [assumption].
% 43.67/43.94 75 (all A all B all C all D (-empty(A) & -empty(B) & element(C,A) & element(D,B) -> ordered_pair_as_product_element(A,B,C,D) = ordered_pair(C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption].
% 43.67/43.94 76 (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].
% 43.67/43.94 77 (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].
% 43.67/43.94 79 (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].
% 43.67/43.94 85 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A)) <-> below_refl(A,B,C)))))))) # label(t32_filter_1) # label(axiom) # label(non_clause). [assumption].
% 43.67/43.94 92 -(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(negated_conjecture) # label(non_clause). [assumption].
% 43.67/43.94 93 -relation_of2(A,B,B) | rel_str(rel_str_of(B,A)) # label(dt_g1_orders_2) # label(axiom). [clausify(12)].
% 43.67/43.94 94 -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)].
% 43.67/43.94 95 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -related(A,B,C) | in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(11)].
% 43.67/43.94 96 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | related(A,B,C) | -in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(11)].
% 43.67/43.94 97 empty_carrier(A) | -lattice(A) | -latt_str(A) | rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(22)].
% 43.67/43.94 108 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(79)].
% 43.67/43.94 109 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(79)].
% 43.67/43.94 161 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(19)].
% 43.67/43.94 165 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(77)].
% 43.67/43.94 172 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(48)].
% 43.67/43.94 174 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(30)].
% 43.67/43.94 190 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(7)].
% 43.67/43.94 191 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(8)].
% 43.67/43.94 192 empty_carrier(A) | -lattice(A) | -latt_str(A) | rel_str_of(the_carrier(A),k2_lattice3(A)) = poset_of_lattice(A). [copy(191),flip(d)].
% 43.67/43.94 193 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(9)].
% 43.67/43.94 194 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(10)].
% 43.67/43.94 195 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(194),rewrite([190(4)])].
% 43.67/43.94 203 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(22)].
% 43.67/43.94 204 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(22)].
% 43.67/43.94 210 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(31)].
% 43.67/43.94 226 empty_carrier(A) | -lattice(A) | -latt_str(A) | -empty_carrier(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(58)].
% 43.67/43.94 228 -relation_of2(A,B,B) | rel_str_of(C,D) != rel_str_of(B,A) | C = B # label(free_g1_orders_2) # label(axiom). [clausify(61)].
% 43.67/43.94 229 -relation_of2(A,B,B) | rel_str_of(C,D) != rel_str_of(B,A) | D = A # label(free_g1_orders_2) # label(axiom). [clausify(61)].
% 43.67/43.94 254 empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(B) | -lattice(B) | -latt_str(B) | -element(C,the_carrier(A)) | -element(D,the_carrier(B)) | k10_filter_1(A,B,C,D) = ordered_pair(C,D) # label(redefinition_k10_filter_1) # label(axiom). [clausify(74)].
% 43.67/43.94 255 empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(B) | -lattice(B) | -latt_str(B) | -element(C,the_carrier(A)) | -element(D,the_carrier(B)) | k10_filter_1(A,B,C,D) = unordered_pair(singleton(C),unordered_pair(C,D)). [copy(254),rewrite([195(12)])].
% 43.67/43.94 256 empty(A) | empty(B) | -element(C,A) | -element(D,B) | ordered_pair_as_product_element(A,B,C,D) = ordered_pair(C,D) # label(redefinition_k1_domain_1) # label(axiom). [clausify(75)].
% 43.67/43.94 257 empty(A) | empty(B) | -element(C,A) | -element(D,B) | ordered_pair_as_product_element(A,B,C,D) = unordered_pair(singleton(C),unordered_pair(C,D)). [copy(256),rewrite([195(6)])].
% 43.67/43.94 258 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation_of_lattice(A) = k2_lattice3(A) # label(redefinition_k2_lattice3) # label(axiom). [clausify(76)].
% 43.67/43.94 261 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A)) | below_refl(A,B,C) # label(t32_filter_1) # label(axiom). [clausify(85)].
% 43.67/43.94 262 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A)) | -below_refl(A,B,C) # label(t32_filter_1) # label(axiom). [clausify(85)].
% 43.67/43.94 268 -empty_carrier(c14) # label(t7_lattice3) # label(negated_conjecture). [clausify(92)].
% 43.67/43.94 269 lattice(c14) # label(t7_lattice3) # label(negated_conjecture). [clausify(92)].
% 43.67/43.94 270 latt_str(c14) # label(t7_lattice3) # label(negated_conjecture). [clausify(92)].
% 43.67/43.94 271 element(c15,the_carrier(c14)) # label(t7_lattice3) # label(negated_conjecture). [clausify(92)].
% 43.67/43.94 272 element(c16,the_carrier(c14)) # label(t7_lattice3) # label(negated_conjecture). [clausify(92)].
% 43.67/43.94 273 below_refl(c14,c15,c16) | related_reflexive(poset_of_lattice(c14),cast_to_el_of_LattPOSet(c14,c15),cast_to_el_of_LattPOSet(c14,c16)) # label(t7_lattice3) # label(negated_conjecture). [clausify(92)].
% 43.67/43.94 274 -below_refl(c14,c15,c16) | -related_reflexive(poset_of_lattice(c14),cast_to_el_of_LattPOSet(c14,c15),cast_to_el_of_LattPOSet(c14,c16)) # label(t7_lattice3) # label(negated_conjecture). [clausify(92)].
% 43.67/43.94 278 -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -element(D,the_carrier(rel_str_of(B,A))) | related(rel_str_of(B,A),C,D) | -in(ordered_pair(C,D),the_InternalRel(rel_str_of(B,A))). [resolve(93,b,96,a)].
% 43.67/43.94 279 -relation_of2(A,B,B) | -element(C,the_carrier(rel_str_of(B,A))) | -element(D,the_carrier(rel_str_of(B,A))) | related(rel_str_of(B,A),C,D) | -in(unordered_pair(singleton(C),unordered_pair(C,D)),the_InternalRel(rel_str_of(B,A))). [copy(278),rewrite([195(10)])].
% 43.67/43.94 280 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(97,d,94,a)].
% 43.67/43.94 281 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),B,C) | in(ordered_pair(B,C),the_InternalRel(poset_of_lattice(A))). [resolve(97,d,95,a)].
% 43.67/43.94 282 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | -element(C,the_carrier(poset_of_lattice(A))) | -related(poset_of_lattice(A),B,C) | in(unordered_pair(singleton(B),unordered_pair(B,C)),the_InternalRel(poset_of_lattice(A))). [copy(281),rewrite([195(12)])].
% 43.67/43.94 321 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(108,c,97,d)].
% 43.67/43.94 326 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(109,c,93,b)].
% 43.67/43.94 400 relation_of2(k2_lattice3(A),the_carrier(A),the_carrier(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(165,a,161,d)].
% 43.67/43.94 416 empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(172,b,174,b)].
% 43.67/43.94 579 relation_of_lattice(c14) = k2_lattice3(c14). [resolve(269,a,258,b),unit_del(a,268),unit_del(b,270)].
% 43.67/43.94 580 -empty_carrier(poset_of_lattice(c14)). [resolve(269,a,226,b),unit_del(a,268),unit_del(b,270)].
% 43.67/43.94 583 reflexive_relstr(poset_of_lattice(c14)). [resolve(269,a,204,b),unit_del(a,268),unit_del(b,270)].
% 43.67/43.94 584 strict_rel_str(poset_of_lattice(c14)). [resolve(269,a,203,b),unit_del(a,268),unit_del(b,270)].
% 43.67/43.94 588 rel_str_of(the_carrier(c14),k2_lattice3(c14)) = poset_of_lattice(c14). [resolve(269,a,192,b),unit_del(a,268),unit_del(b,270)].
% 43.67/43.94 591 join_semilatt_str(c14). [resolve(270,a,210,a)].
% 43.67/43.94 599 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | k10_filter_1(c14,A,c15,B) = unordered_pair(singleton(c15),unordered_pair(B,c15)). [resolve(271,a,255,g),rewrite([190(18)]),unit_del(a,268),unit_del(b,269),unit_del(c,270)].
% 43.67/43.94 605 cast_to_el_of_LattPOSet(c14,c15) = c15. [resolve(271,a,193,d),unit_del(a,268),unit_del(b,269),unit_del(c,270)].
% 43.67/43.94 611 -below_refl(c14,c15,c16) | -related_reflexive(poset_of_lattice(c14),c15,cast_to_el_of_LattPOSet(c14,c16)). [back_rewrite(274),rewrite([605(9)])].
% 43.67/43.94 612 below_refl(c14,c15,c16) | related_reflexive(poset_of_lattice(c14),c15,cast_to_el_of_LattPOSet(c14,c16)). [back_rewrite(273),rewrite([605(9)])].
% 43.67/43.94 614 empty(A) | empty(the_carrier(c14)) | -element(B,A) | ordered_pair_as_product_element(A,the_carrier(c14),B,c16) = unordered_pair(singleton(B),unordered_pair(B,c16)). [resolve(272,a,257,d)].
% 43.67/43.94 623 cast_to_el_of_LattPOSet(c14,c16) = c16. [resolve(272,a,193,d),unit_del(a,268),unit_del(b,269),unit_del(c,270)].
% 43.67/43.94 624 empty(the_carrier(c14)) | -element(A,the_carrier(c14)) | ordered_pair_as_product_element(the_carrier(c14),the_carrier(c14),A,c16) = unordered_pair(singleton(A),unordered_pair(A,c16)). [factor(614,a,b)].
% 43.67/43.94 629 below_refl(c14,c15,c16) | related_reflexive(poset_of_lattice(c14),c15,c16). [back_rewrite(612),rewrite([623(10)])].
% 43.67/43.94 630 -below_refl(c14,c15,c16) | -related_reflexive(poset_of_lattice(c14),c15,c16). [back_rewrite(611),rewrite([623(10)])].
% 43.67/43.94 648 relation_of2(k2_lattice3(c14),the_carrier(c14),the_carrier(c14)). [resolve(400,c,269,a),unit_del(b,268),unit_del(c,270)].
% 43.67/43.94 949 -empty(the_carrier(c14)). [resolve(591,a,416,c),unit_del(a,268)].
% 43.67/43.94 962 -element(A,the_carrier(c14)) | ordered_pair_as_product_element(the_carrier(c14),the_carrier(c14),A,c16) = unordered_pair(singleton(A),unordered_pair(A,c16)). [back_unit_del(624),unit_del(a,949)].
% 43.67/43.94 997 rel_str_of(the_carrier(poset_of_lattice(c14)),the_InternalRel(poset_of_lattice(c14))) = poset_of_lattice(c14). [resolve(584,a,280,d),unit_del(a,268),unit_del(b,269),unit_del(c,270)].
% 43.67/43.94 2056 -element(A,the_carrier(poset_of_lattice(c14))) | -element(B,the_carrier(poset_of_lattice(c14))) | related(poset_of_lattice(c14),A,B) | -in(unordered_pair(singleton(A),unordered_pair(A,B)),the_InternalRel(poset_of_lattice(c14))). [resolve(648,a,279,a),rewrite([588(5),588(9),588(13),588(19)])].
% 43.67/43.94 2057 rel_str_of(A,B) != poset_of_lattice(c14) | k2_lattice3(c14) = B. [resolve(648,a,229,a),rewrite([588(6)]),flip(b)].
% 43.67/43.94 2058 rel_str_of(A,B) != poset_of_lattice(c14) | the_carrier(c14) = A. [resolve(648,a,228,a),rewrite([588(6)]),flip(b)].
% 43.67/43.94 2429 -element(A,the_carrier(poset_of_lattice(c14))) | -element(B,the_carrier(poset_of_lattice(c14))) | related_reflexive(poset_of_lattice(c14),A,B) | -related(poset_of_lattice(c14),A,B). [para(588(a,1),326(f,1)),rewrite([588(5),588(8),588(11),588(15),588(19)]),unit_del(a,580),unit_del(b,583),unit_del(g,648)].
% 43.67/43.94 2592 unordered_pair(singleton(c15),unordered_pair(c15,c16)) = k10_filter_1(c14,c14,c15,c16). [resolve(599,d,272,a),rewrite([190(16)]),flip(d),unit_del(a,268),unit_del(b,269),unit_del(c,270)].
% 43.67/43.94 2846 related_reflexive(poset_of_lattice(c14),c15,c16) | in(ordered_pair_as_product_element(the_carrier(c14),the_carrier(c14),c15,c16),k2_lattice3(c14)). [resolve(629,a,262,g),rewrite([579(28)]),unit_del(b,268),unit_del(c,269),unit_del(d,270),unit_del(e,271),unit_del(f,272)].
% 43.67/43.94 6638 the_InternalRel(poset_of_lattice(c14)) = k2_lattice3(c14). [resolve(2057,a,997,a),flip(a)].
% 43.67/43.94 6703 -element(A,the_carrier(poset_of_lattice(c14))) | -element(B,the_carrier(poset_of_lattice(c14))) | related(poset_of_lattice(c14),A,B) | -in(unordered_pair(singleton(A),unordered_pair(A,B)),k2_lattice3(c14)). [back_rewrite(2056),rewrite([6638(17)])].
% 43.67/43.95 6705 rel_str_of(the_carrier(poset_of_lattice(c14)),k2_lattice3(c14)) = poset_of_lattice(c14). [back_rewrite(997),rewrite([6638(6)])].
% 43.67/43.95 6746 the_carrier(poset_of_lattice(c14)) = the_carrier(c14). [resolve(2058,a,6705,a),flip(a)].
% 43.67/43.95 6753 -element(A,the_carrier(c14)) | -element(B,the_carrier(c14)) | related(poset_of_lattice(c14),A,B) | -in(unordered_pair(singleton(A),unordered_pair(A,B)),k2_lattice3(c14)). [back_rewrite(6703),rewrite([6746(3),6746(6)])].
% 43.67/43.95 6893 -element(A,the_carrier(c14)) | -element(B,the_carrier(c14)) | related_reflexive(poset_of_lattice(c14),A,B) | -related(poset_of_lattice(c14),A,B). [back_rewrite(2429),rewrite([6746(3),6746(6)])].
% 43.67/43.95 10409 ordered_pair_as_product_element(the_carrier(c14),the_carrier(c14),c15,c16) = k10_filter_1(c14,c14,c15,c16). [resolve(962,a,271,a),rewrite([2592(13)])].
% 43.67/43.95 10413 related_reflexive(poset_of_lattice(c14),c15,c16) | in(k10_filter_1(c14,c14,c15,c16),k2_lattice3(c14)). [back_rewrite(2846),rewrite([10409(12)])].
% 43.67/43.95 13646 -in(k10_filter_1(c14,c14,c15,c16),k2_lattice3(c14)) | below_refl(c14,c15,c16). [para(10409(a,1),261(f,1)),rewrite([579(21)]),unit_del(a,268),unit_del(b,269),unit_del(c,270),unit_del(d,271),unit_del(e,272)].
% 43.67/43.95 13648 in(k10_filter_1(c14,c14,c15,c16),k2_lattice3(c14)) | related(poset_of_lattice(c14),c15,c16). [resolve(10413,a,321,e),rewrite([6746(18),6746(22)]),unit_del(b,580),unit_del(c,583),unit_del(d,271),unit_del(e,272),unit_del(g,268),unit_del(h,269),unit_del(i,270)].
% 43.67/43.95 14087 in(k10_filter_1(c14,c14,c15,c16),k2_lattice3(c14)). [resolve(13648,b,282,f),rewrite([6746(18),6746(22),2592(28),6638(30)]),merge(g),unit_del(b,268),unit_del(c,269),unit_del(d,270),unit_del(e,271),unit_del(f,272)].
% 43.67/43.95 14088 below_refl(c14,c15,c16). [back_unit_del(13646),unit_del(a,14087)].
% 43.67/43.95 14089 -related_reflexive(poset_of_lattice(c14),c15,c16). [back_unit_del(630),unit_del(a,14088)].
% 43.67/43.95 24621 related(poset_of_lattice(c14),c15,c16). [para(2592(a,1),6753(d,1)),unit_del(a,271),unit_del(b,272),unit_del(d,14087)].
% 43.67/43.95 24636 $F. [resolve(24621,a,6893,d),unit_del(a,271),unit_del(b,272),unit_del(c,14089)].
% 43.67/43.95
% 43.67/43.95 % SZS output end Refutation
% 43.67/43.95 ============================== end of proof ==========================
% 43.67/43.95
% 43.67/43.95 ============================== STATISTICS ============================
% 43.67/43.95
% 43.67/43.95 Given=16020. Generated=1015508. Kept=24396. proofs=1.
% 43.67/43.95 Usable=15806. Sos=6546. Demods=1157. Limbo=0, Disabled=2385. Hints=0.
% 43.67/43.95 Megabytes=28.02.
% 43.67/43.95 User_CPU=42.39, System_CPU=0.58, Wall_clock=43.
% 43.67/43.95
% 43.67/43.95 ============================== end of statistics =====================
% 43.67/43.95
% 43.67/43.95 ============================== end of search =========================
% 43.67/43.95
% 43.67/43.95 THEOREM PROVED
% 43.67/43.95 % SZS status Theorem
% 43.67/43.95
% 43.67/43.95 Exiting with 1 proof.
% 43.67/43.95
% 43.67/43.95 Process 19846 exit (max_proofs) Sun Jun 19 17:53:46 2022
% 43.67/43.95 Prover9 interrupted
%------------------------------------------------------------------------------