%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SEU382+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 13:31:25 EDT 2022

% Result   : Theorem 1.21s 1.50s
% Output   : Refutation 1.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU382+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n005.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun 18 21:29:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.41/1.05  ============================== Prover9 ===============================
% 0.41/1.05  Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.05  Process 24559 was started by sandbox on n005.cluster.edu,
% 0.41/1.05  Sat Jun 18 21:29:39 2022
% 0.41/1.05  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24405_n005.cluster.edu".
% 0.41/1.05  ============================== end of head ===========================
% 0.41/1.05  
% 0.41/1.05  ============================== INPUT =================================
% 0.41/1.05  
% 0.41/1.05  % Reading from file /tmp/Prover9_24405_n005.cluster.edu
% 0.41/1.05  
% 0.41/1.05  set(prolog_style_variables).
% 0.41/1.05  set(auto2).
% 0.41/1.05      % set(auto2) -> set(auto).
% 0.41/1.05      % set(auto) -> set(auto_inference).
% 0.41/1.05      % set(auto) -> set(auto_setup).
% 0.41/1.05      % set(auto_setup) -> set(predicate_elim).
% 0.41/1.05      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.05      % set(auto) -> set(auto_limits).
% 0.41/1.05      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.05      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.05      % set(auto) -> set(auto_denials).
% 0.41/1.05      % set(auto) -> set(auto_process).
% 0.41/1.05      % set(auto2) -> assign(new_constants, 1).
% 0.41/1.05      % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.05      % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.05      % set(auto2) -> assign(max_hours, 1).
% 0.41/1.05      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.05      % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.05      % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.05      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.05      % set(auto2) -> set(sort_initial_sos).
% 0.41/1.05      % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.05      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.05      % set(auto2) -> assign(max_megs, 400).
% 0.41/1.05      % set(auto2) -> assign(stats, some).
% 0.41/1.05      % set(auto2) -> clear(echo_input).
% 0.41/1.05      % set(auto2) -> set(quiet).
% 0.41/1.05      % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.05      % set(auto2) -> clear(print_given).
% 0.41/1.05  assign(lrs_ticks,-1).
% 0.41/1.05  assign(sos_limit,10000).
% 0.41/1.05  assign(order,kbo).
% 0.41/1.05  set(lex_order_vars).
% 0.41/1.05  clear(print_given).
% 0.41/1.05  
% 0.41/1.05  % formulas(sos).  % not echoed (89 formulas)
% 0.41/1.05  
% 0.41/1.05  ============================== end of input ==========================
% 0.41/1.05  
% 0.41/1.05  % From the command line: assign(max_seconds, 300).
% 0.41/1.05  
% 0.41/1.05  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.05  
% 0.41/1.05  % Formulas that are not ordinary clauses:
% 0.41/1.05  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].
% 0.41/1.05  2 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  3 (all A (rel_str(A) -> (-empty_carrier(A) & reflexive_relstr(A) & complete_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & up_complete_relstr(A) & join_complete_relstr(A)))) # label(cc10_waybel_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  4 (all A (rel_str(A) -> (-empty_carrier(A) & boolean_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & upper_bounded_relstr(A) & distributive_relstr(A) & heyting_relstr(A)))) # label(cc10_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  5 (all A (rel_str(A) -> (-empty_carrier(A) & reflexive_relstr(A) & join_complete_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & lower_bounded_relstr(A)))) # label(cc11_waybel_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  6 (all A (rel_str(A) -> (-empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & lower_bounded_relstr(A) & up_complete_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & complete_relstr(A) & lower_bounded_relstr(A) & upper_bounded_relstr(A) & bounded_relstr(A)))) # label(cc12_waybel_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  7 (all A (rel_str(A) -> (-empty_carrier(A) & reflexive_relstr(A) & antisymmetric_relstr(A) & join_complete_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & antisymmetric_relstr(A) & with_infima_relstr(A)))) # label(cc13_waybel_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  8 (all A (rel_str(A) -> (-empty_carrier(A) & reflexive_relstr(A) & antisymmetric_relstr(A) & upper_bounded_relstr(A) & join_complete_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & upper_bounded_relstr(A)))) # label(cc14_waybel_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  9 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  10 (all A (rel_str(A) -> (with_suprema_relstr(A) -> -empty_carrier(A)))) # label(cc1_lattice3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  11 (all A (rel_str(A) -> (-empty_carrier(A) & complete_relstr(A) -> -empty_carrier(A) & with_suprema_relstr(A) & with_infima_relstr(A)))) # label(cc1_yellow_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  12 (all A (rel_str(A) -> (-empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & upper_bounded_relstr(A) & up_complete_relstr(A) & join_complete_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & upper_bounded_relstr(A) & bounded_relstr(A) & up_complete_relstr(A) & join_complete_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & complete_relstr(A)))) # label(cc1_yellow_2) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  13 (all A (rel_str(A) -> (empty_carrier(A) -> v1_yellow_3(A)))) # label(cc1_yellow_3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  14 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  15 (all A (rel_str(A) -> (with_infima_relstr(A) -> -empty_carrier(A)))) # label(cc2_lattice3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  16 (all A (rel_str(A) -> (-v1_yellow_3(A) -> -empty_carrier(A)))) # label(cc2_yellow_3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  17 (all A (rel_str(A) -> (-empty_carrier(A) & complete_relstr(A) -> -empty_carrier(A) & bounded_relstr(A)))) # label(cc3_yellow_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  18 (all A (rel_str(A) -> (-empty_carrier(A) & reflexive_relstr(A) -> -empty_carrier(A) & -v1_yellow_3(A)))) # label(cc3_yellow_3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  19 (all A (rel_str(A) -> (bounded_relstr(A) -> lower_bounded_relstr(A) & upper_bounded_relstr(A)))) # label(cc4_yellow_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  20 (all A (rel_str(A) -> (-empty_carrier(A) & heyting_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A)))) # label(cc5_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  21 (all A (rel_str(A) -> (lower_bounded_relstr(A) & upper_bounded_relstr(A) -> bounded_relstr(A)))) # label(cc5_yellow_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  22 (all A (rel_str(A) -> (-empty_carrier(A) & heyting_relstr(A) -> -empty_carrier(A) & distributive_relstr(A)))) # label(cc6_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  23 (all A (rel_str(A) -> (-empty_carrier(A) & heyting_relstr(A) -> -empty_carrier(A) & upper_bounded_relstr(A)))) # label(cc7_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  24 (all A (rel_str(A) -> (-empty_carrier(A) & boolean_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & lower_bounded_relstr(A) & upper_bounded_relstr(A) & bounded_relstr(A) & distributive_relstr(A) & complemented_relstr(A)))) # label(cc8_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  25 (all A (rel_str(A) -> (reflexive_relstr(A) & with_suprema_relstr(A) & up_complete_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & with_suprema_relstr(A) & upper_bounded_relstr(A)))) # label(cc9_waybel_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  26 (all A (rel_str(A) -> (-empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & bounded_relstr(A) & distributive_relstr(A) & complemented_relstr(A) -> -empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & lower_bounded_relstr(A) & upper_bounded_relstr(A) & bounded_relstr(A) & distributive_relstr(A) & complemented_relstr(A) & boolean_relstr(A)))) # label(cc9_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  27 (all A incl_POSet(A) = rel_str_of(A,inclusion_order(A))) # label(d1_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  28 (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].
% 0.41/1.05  29 (all A relation(inclusion_relation(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  30 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  31 (all A (reflexive(inclusion_order(A)) & antisymmetric(inclusion_order(A)) & transitive(inclusion_order(A)) & v1_partfun1(inclusion_order(A),A,A) & relation_of2_as_subset(inclusion_order(A),A,A))) # label(dt_k1_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  32 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  33 (all A (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A)))) # label(dt_k2_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  34 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  35 (all A (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))) # label(dt_k3_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  36 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  37 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  38 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  39 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  40 (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].
% 0.41/1.05  41 (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].
% 0.41/1.05  42 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  43 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  44 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  45 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  46 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  47 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  48 (all A (-v1_yellow_3(A) & rel_str(A) -> -empty(the_InternalRel(A)) & relation(the_InternalRel(A)))) # label(fc13_yellow_3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  49 (all A all B (finite(A) & finite(B) -> finite(cartesian_product2(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  50 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  51 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  52 (all A (-empty_carrier(boole_POSet(A)) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)))) # label(fc1_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  53 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  54 (all A (strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))) # label(fc5_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  55 (all A (-empty(A) -> -empty_carrier(incl_POSet(A)) & strict_rel_str(incl_POSet(A)) & reflexive_relstr(incl_POSet(A)) & transitive_relstr(incl_POSet(A)) & antisymmetric_relstr(incl_POSet(A)))) # label(fc6_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  56 (all A (-empty_carrier(boole_POSet(A)) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)))) # label(fc7_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  57 (all A (-empty_carrier(boole_POSet(A)) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) # label(fc8_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  58 (all A (-empty_carrier(boole_POSet(A)) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & distributive_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))) # label(fc9_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  59 (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].
% 0.41/1.05  60 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & complete_relstr(A) & lower_bounded_relstr(A) & upper_bounded_relstr(A) & bounded_relstr(A) & up_complete_relstr(A) & join_complete_relstr(A))) # label(rc13_waybel_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  61 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  62 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & complete_relstr(A))) # label(rc1_lattice3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  63 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  64 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  65 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & -v1_yellow_3(A))) # label(rc1_yellow_3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  66 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & complete_relstr(A))) # label(rc2_lattice3) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  67 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  68 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  69 (exists A (rel_str(A) & -empty_carrier(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & complete_relstr(A) & lower_bounded_relstr(A) & upper_bounded_relstr(A) & bounded_relstr(A))) # label(rc2_yellow_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  70 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  71 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  72 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  73 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & lower_bounded_relstr(A) & upper_bounded_relstr(A) & bounded_relstr(A) & distributive_relstr(A) & heyting_relstr(A) & complemented_relstr(A) & boolean_relstr(A))) # label(rc4_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  74 (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].
% 0.41/1.05  75 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & with_suprema_relstr(A) & with_infima_relstr(A) & upper_bounded_relstr(A) & distributive_relstr(A) & heyting_relstr(A))) # label(rc5_waybel_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  76 (all A inclusion_order(A) = inclusion_relation(A)) # label(redefinition_k1_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  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].
% 0.41/1.05  78 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  79 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  80 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  81 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  82 (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].
% 0.41/1.05  83 (all A boole_POSet(A) = incl_POSet(powerset(A))) # label(t4_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  84 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  85 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  86 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  87 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
% 0.41/1.05  88 -(all A the_carrier(boole_POSet(A)) = powerset(A)) # label(t4_waybel_7) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.41/1.05  
% 0.41/1.05  ============================== end of process non-clausal formulas ===
% 0.41/1.05  
% 0.41/1.05  ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/1.05  
% 0.41/1.05  ============================== PREDICATE ELIMINATION =================
% 0.41/1.05  89 -relation_of2(A,B,B) | rel_str(rel_str_of(B,A)) # label(dt_g1_orders_2) # label(axiom).  [clausify(28)].
% 0.41/1.05  90 -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)].
% 0.41/1.05  91 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -complete_relstr(A) | up_complete_relstr(A) # label(cc10_waybel_0) # label(axiom).  [clausify(3)].
% 0.41/1.05  92 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -complete_relstr(A) | join_complete_relstr(A) # label(cc10_waybel_0) # label(axiom).  [clausify(3)].
% 0.41/1.05  93 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | reflexive_relstr(A) # label(cc10_waybel_1) # label(axiom).  [clausify(4)].
% 0.41/1.05  94 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | transitive_relstr(A) # label(cc10_waybel_1) # label(axiom).  [clausify(4)].
% 0.41/1.05  95 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | antisymmetric_relstr(A) # label(cc10_waybel_1) # label(axiom).  [clausify(4)].
% 0.41/1.05  96 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | with_suprema_relstr(A) # label(cc10_waybel_1) # label(axiom).  [clausify(4)].
% 0.41/1.05  97 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | with_infima_relstr(A) # label(cc10_waybel_1) # label(axiom).  [clausify(4)].
% 0.41/1.05  98 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | upper_bounded_relstr(A) # label(cc10_waybel_1) # label(axiom).  [clausify(4)].
% 0.41/1.05  99 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | distributive_relstr(A) # label(cc10_waybel_1) # label(axiom).  [clausify(4)].
% 0.41/1.05  100 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | heyting_relstr(A) # label(cc10_waybel_1) # label(axiom).  [clausify(4)].
% 0.41/1.05  101 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -join_complete_relstr(A) | lower_bounded_relstr(A) # label(cc11_waybel_0) # label(axiom).  [clausify(5)].
% 0.41/1.05  102 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -with_suprema_relstr(A) | -lower_bounded_relstr(A) | -up_complete_relstr(A) | with_infima_relstr(A) # label(cc12_waybel_0) # label(axiom).  [clausify(6)].
% 0.41/1.05  103 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -with_suprema_relstr(A) | -lower_bounded_relstr(A) | -up_complete_relstr(A) | complete_relstr(A) # label(cc12_waybel_0) # label(axiom).  [clausify(6)].
% 0.41/1.05  104 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -with_suprema_relstr(A) | -lower_bounded_relstr(A) | -up_complete_relstr(A) | upper_bounded_relstr(A) # label(cc12_waybel_0) # label(axiom).  [clausify(6)].
% 0.41/1.05  105 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -with_suprema_relstr(A) | -lower_bounded_relstr(A) | -up_complete_relstr(A) | bounded_relstr(A) # label(cc12_waybel_0) # label(axiom).  [clausify(6)].
% 0.41/1.05  106 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -antisymmetric_relstr(A) | -join_complete_relstr(A) | with_infima_relstr(A) # label(cc13_waybel_0) # label(axiom).  [clausify(7)].
% 0.41/1.05  107 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -antisymmetric_relstr(A) | -upper_bounded_relstr(A) | -join_complete_relstr(A) | with_suprema_relstr(A) # label(cc14_waybel_0) # label(axiom).  [clausify(8)].
% 0.41/1.05  108 -rel_str(A) | -with_suprema_relstr(A) | -empty_carrier(A) # label(cc1_lattice3) # label(axiom).  [clausify(10)].
% 0.41/1.05  109 -rel_str(A) | empty_carrier(A) | -complete_relstr(A) | with_suprema_relstr(A) # label(cc1_yellow_0) # label(axiom).  [clausify(11)].
% 0.41/1.05  110 -rel_str(A) | empty_carrier(A) | -complete_relstr(A) | with_infima_relstr(A) # label(cc1_yellow_0) # label(axiom).  [clausify(11)].
% 0.41/1.05  111 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -upper_bounded_relstr(A) | -up_complete_relstr(A) | -join_complete_relstr(A) | lower_bounded_relstr(A) # label(cc1_yellow_2) # label(axiom).  [clausify(12)].
% 0.41/1.05  112 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -upper_bounded_relstr(A) | -up_complete_relstr(A) | -join_complete_relstr(A) | bounded_relstr(A) # label(cc1_yellow_2) # label(axiom).  [clausify(12)].
% 0.41/1.05  113 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -upper_bounded_relstr(A) | -up_complete_relstr(A) | -join_complete_relstr(A) | with_suprema_relstr(A) # label(cc1_yellow_2) # label(axiom).  [clausify(12)].
% 0.41/1.05  114 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -upper_bounded_relstr(A) | -up_complete_relstr(A) | -join_complete_relstr(A) | with_infima_relstr(A) # label(cc1_yellow_2) # label(axiom).  [clausify(12)].
% 0.41/1.05  115 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -upper_bounded_relstr(A) | -up_complete_relstr(A) | -join_complete_relstr(A) | complete_relstr(A) # label(cc1_yellow_2) # label(axiom).  [clausify(12)].
% 0.41/1.05  116 -rel_str(A) | -empty_carrier(A) | v1_yellow_3(A) # label(cc1_yellow_3) # label(axiom).  [clausify(13)].
% 0.41/1.05  117 -rel_str(A) | -with_infima_relstr(A) | -empty_carrier(A) # label(cc2_lattice3) # label(axiom).  [clausify(15)].
% 0.41/1.05  118 -rel_str(A) | v1_yellow_3(A) | -empty_carrier(A) # label(cc2_yellow_3) # label(axiom).  [clausify(16)].
% 0.41/1.05  119 -rel_str(A) | empty_carrier(A) | -complete_relstr(A) | bounded_relstr(A) # label(cc3_yellow_0) # label(axiom).  [clausify(17)].
% 0.41/1.05  120 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -v1_yellow_3(A) # label(cc3_yellow_3) # label(axiom).  [clausify(18)].
% 0.41/1.05  121 -rel_str(A) | -bounded_relstr(A) | lower_bounded_relstr(A) # label(cc4_yellow_0) # label(axiom).  [clausify(19)].
% 0.41/1.05  122 -rel_str(A) | -bounded_relstr(A) | upper_bounded_relstr(A) # label(cc4_yellow_0) # label(axiom).  [clausify(19)].
% 0.41/1.05  123 -rel_str(A) | empty_carrier(A) | -heyting_relstr(A) | reflexive_relstr(A) # label(cc5_waybel_1) # label(axiom).  [clausify(20)].
% 0.41/1.05  124 -rel_str(A) | empty_carrier(A) | -heyting_relstr(A) | transitive_relstr(A) # label(cc5_waybel_1) # label(axiom).  [clausify(20)].
% 0.41/1.05  125 -rel_str(A) | empty_carrier(A) | -heyting_relstr(A) | antisymmetric_relstr(A) # label(cc5_waybel_1) # label(axiom).  [clausify(20)].
% 0.41/1.05  126 -rel_str(A) | empty_carrier(A) | -heyting_relstr(A) | with_suprema_relstr(A) # label(cc5_waybel_1) # label(axiom).  [clausify(20)].
% 0.41/1.05  127 -rel_str(A) | empty_carrier(A) | -heyting_relstr(A) | with_infima_relstr(A) # label(cc5_waybel_1) # label(axiom).  [clausify(20)].
% 0.41/1.05  128 -rel_str(A) | -lower_bounded_relstr(A) | -upper_bounded_relstr(A) | bounded_relstr(A) # label(cc5_yellow_0) # label(axiom).  [clausify(21)].
% 0.41/1.05  129 -rel_str(A) | empty_carrier(A) | -heyting_relstr(A) | distributive_relstr(A) # label(cc6_waybel_1) # label(axiom).  [clausify(22)].
% 0.41/1.05  130 -rel_str(A) | empty_carrier(A) | -heyting_relstr(A) | upper_bounded_relstr(A) # label(cc7_waybel_1) # label(axiom).  [clausify(23)].
% 0.41/1.05  131 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | reflexive_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  132 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | transitive_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  133 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | antisymmetric_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  134 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | with_suprema_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  135 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | with_infima_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  136 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | lower_bounded_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  137 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | upper_bounded_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  138 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | bounded_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  139 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | distributive_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  140 -rel_str(A) | empty_carrier(A) | -boolean_relstr(A) | complemented_relstr(A) # label(cc8_waybel_1) # label(axiom).  [clausify(24)].
% 0.41/1.05  141 -rel_str(A) | -reflexive_relstr(A) | -with_suprema_relstr(A) | -up_complete_relstr(A) | -empty_carrier(A) # label(cc9_waybel_0) # label(axiom).  [clausify(25)].
% 0.41/1.05  142 -rel_str(A) | -reflexive_relstr(A) | -with_suprema_relstr(A) | -up_complete_relstr(A) | upper_bounded_relstr(A) # label(cc9_waybel_0) # label(axiom).  [clausify(25)].
% 0.41/1.05  143 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -with_suprema_relstr(A) | -with_infima_relstr(A) | -bounded_relstr(A) | -distributive_relstr(A) | -complemented_relstr(A) | lower_bounded_relstr(A) # label(cc9_waybel_1) # label(axiom).  [clausify(26)].
% 0.41/1.06  144 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -with_suprema_relstr(A) | -with_infima_relstr(A) | -bounded_relstr(A) | -distributive_relstr(A) | -complemented_relstr(A) | upper_bounded_relstr(A) # label(cc9_waybel_1) # label(axiom).  [clausify(26)].
% 0.41/1.06  145 -rel_str(A) | empty_carrier(A) | -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -with_suprema_relstr(A) | -with_infima_relstr(A) | -bounded_relstr(A) | -distributive_relstr(A) | -complemented_relstr(A) | boolean_relstr(A) # label(cc9_waybel_1) # label(axiom).  [clausify(26)].
% 0.41/1.06  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(89,b,90,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -complete_relstr(rel_str_of(B,A)) | up_complete_relstr(rel_str_of(B,A)).  [resolve(89,b,91,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -complete_relstr(rel_str_of(B,A)) | join_complete_relstr(rel_str_of(B,A)).  [resolve(89,b,92,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | reflexive_relstr(rel_str_of(B,A)).  [resolve(89,b,93,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | transitive_relstr(rel_str_of(B,A)).  [resolve(89,b,94,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | antisymmetric_relstr(rel_str_of(B,A)).  [resolve(89,b,95,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | with_suprema_relstr(rel_str_of(B,A)).  [resolve(89,b,96,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | with_infima_relstr(rel_str_of(B,A)).  [resolve(89,b,97,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | upper_bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,98,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | distributive_relstr(rel_str_of(B,A)).  [resolve(89,b,99,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | heyting_relstr(rel_str_of(B,A)).  [resolve(89,b,100,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -join_complete_relstr(rel_str_of(B,A)) | lower_bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,101,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -antisymmetric_relstr(rel_str_of(B,A)) | -with_suprema_relstr(rel_str_of(B,A)) | -lower_bounded_relstr(rel_str_of(B,A)) | -up_complete_relstr(rel_str_of(B,A)) | with_infima_relstr(rel_str_of(B,A)).  [resolve(89,b,102,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -antisymmetric_relstr(rel_str_of(B,A)) | -with_suprema_relstr(rel_str_of(B,A)) | -lower_bounded_relstr(rel_str_of(B,A)) | -up_complete_relstr(rel_str_of(B,A)) | complete_relstr(rel_str_of(B,A)).  [resolve(89,b,103,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -antisymmetric_relstr(rel_str_of(B,A)) | -with_suprema_relstr(rel_str_of(B,A)) | -lower_bounded_relstr(rel_str_of(B,A)) | -up_complete_relstr(rel_str_of(B,A)) | upper_bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,104,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -antisymmetric_relstr(rel_str_of(B,A)) | -with_suprema_relstr(rel_str_of(B,A)) | -lower_bounded_relstr(rel_str_of(B,A)) | -up_complete_relstr(rel_str_of(B,A)) | bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,105,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -antisymmetric_relstr(rel_str_of(B,A)) | -join_complete_relstr(rel_str_of(B,A)) | with_infima_relstr(rel_str_of(B,A)).  [resolve(89,b,106,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -antisymmetric_relstr(rel_str_of(B,A)) | -upper_bounded_relstr(rel_str_of(B,A)) | -join_complete_relstr(rel_str_of(B,A)) | with_suprema_relstr(rel_str_of(B,A)).  [resolve(89,b,107,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | -with_suprema_relstr(rel_str_of(B,A)) | -empty_carrier(rel_str_of(B,A)).  [resolve(89,b,108,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -complete_relstr(rel_str_of(B,A)) | with_suprema_relstr(rel_str_of(B,A)).  [resolve(89,b,109,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -complete_relstr(rel_str_of(B,A)) | with_infima_relstr(rel_str_of(B,A)).  [resolve(89,b,110,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -antisymmetric_relstr(rel_str_of(B,A)) | -upper_bounded_relstr(rel_str_of(B,A)) | -up_complete_relstr(rel_str_of(B,A)) | -join_complete_relstr(rel_str_of(B,A)) | bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,112,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -antisymmetric_relstr(rel_str_of(B,A)) | -upper_bounded_relstr(rel_str_of(B,A)) | -up_complete_relstr(rel_str_of(B,A)) | -join_complete_relstr(rel_str_of(B,A)) | complete_relstr(rel_str_of(B,A)).  [resolve(89,b,115,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | -empty_carrier(rel_str_of(B,A)) | v1_yellow_3(rel_str_of(B,A)).  [resolve(89,b,116,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | -with_infima_relstr(rel_str_of(B,A)) | -empty_carrier(rel_str_of(B,A)).  [resolve(89,b,117,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -complete_relstr(rel_str_of(B,A)) | bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,119,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -v1_yellow_3(rel_str_of(B,A)).  [resolve(89,b,120,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | -bounded_relstr(rel_str_of(B,A)) | lower_bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,121,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | -bounded_relstr(rel_str_of(B,A)) | upper_bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,122,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -heyting_relstr(rel_str_of(B,A)) | reflexive_relstr(rel_str_of(B,A)).  [resolve(89,b,123,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -heyting_relstr(rel_str_of(B,A)) | transitive_relstr(rel_str_of(B,A)).  [resolve(89,b,124,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -heyting_relstr(rel_str_of(B,A)) | antisymmetric_relstr(rel_str_of(B,A)).  [resolve(89,b,125,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -heyting_relstr(rel_str_of(B,A)) | with_suprema_relstr(rel_str_of(B,A)).  [resolve(89,b,126,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -heyting_relstr(rel_str_of(B,A)) | with_infima_relstr(rel_str_of(B,A)).  [resolve(89,b,127,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | -lower_bounded_relstr(rel_str_of(B,A)) | -upper_bounded_relstr(rel_str_of(B,A)) | bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,128,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -heyting_relstr(rel_str_of(B,A)) | distributive_relstr(rel_str_of(B,A)).  [resolve(89,b,129,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -heyting_relstr(rel_str_of(B,A)) | upper_bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,130,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | lower_bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,136,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,138,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -boolean_relstr(rel_str_of(B,A)) | complemented_relstr(rel_str_of(B,A)).  [resolve(89,b,140,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | -reflexive_relstr(rel_str_of(B,A)) | -with_suprema_relstr(rel_str_of(B,A)) | -up_complete_relstr(rel_str_of(B,A)) | upper_bounded_relstr(rel_str_of(B,A)).  [resolve(89,b,142,a)].
% 0.41/1.06  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -reflexive_relstr(rel_str_of(B,A)) | -transitive_relstr(rel_str_of(B,A)) | -antisymmetric_relstr(rel_str_of(B,A)) | -with_suprema_relstr(rel_str_of(B,A)) | -with_infima_relstr(rel_str_of(B,A)) | -bounded_relstr(rel_str_of(B,A)) | -distributive_relstr(rel_str_of(B,A)) | -complemented_relstr(rel_str_of(B,A)) | boolean_relstr(rel_str_of(B,A)).  [resolve(89,b,145,a)].
% 0.41/1.06  146 rel_str(incl_POSet(A)) # label(dt_k2_yellow_1) # label(axiom).  [clausify(33)].
% 0.41/1.06  Derived: -strict_rel_str(incl_POSet(A)) | rel_str_of(the_carrier(incl_POSet(A)),the_InternalRel(incl_POSet(A))) = incl_POSet(A).  [resolve(146,a,90,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -complete_relstr(incl_POSet(A)) | up_complete_relstr(incl_POSet(A)).  [resolve(146,a,91,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -complete_relstr(incl_POSet(A)) | join_complete_relstr(incl_POSet(A)).  [resolve(146,a,92,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -boolean_relstr(incl_POSet(A)) | with_suprema_relstr(incl_POSet(A)).  [resolve(146,a,96,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -boolean_relstr(incl_POSet(A)) | with_infima_relstr(incl_POSet(A)).  [resolve(146,a,97,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -boolean_relstr(incl_POSet(A)) | upper_bounded_relstr(incl_POSet(A)).  [resolve(146,a,98,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -boolean_relstr(incl_POSet(A)) | distributive_relstr(incl_POSet(A)).  [resolve(146,a,99,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -boolean_relstr(incl_POSet(A)) | heyting_relstr(incl_POSet(A)).  [resolve(146,a,100,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -join_complete_relstr(incl_POSet(A)) | lower_bounded_relstr(incl_POSet(A)).  [resolve(146,a,101,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -with_suprema_relstr(incl_POSet(A)) | -lower_bounded_relstr(incl_POSet(A)) | -up_complete_relstr(incl_POSet(A)) | with_infima_relstr(incl_POSet(A)).  [resolve(146,a,102,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -with_suprema_relstr(incl_POSet(A)) | -lower_bounded_relstr(incl_POSet(A)) | -up_complete_relstr(incl_POSet(A)) | complete_relstr(incl_POSet(A)).  [resolve(146,a,103,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -with_suprema_relstr(incl_POSet(A)) | -lower_bounded_relstr(incl_POSet(A)) | -up_complete_relstr(incl_POSet(A)) | upper_bounded_relstr(incl_POSet(A)).  [resolve(146,a,104,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -with_suprema_relstr(incl_POSet(A)) | -lower_bounded_relstr(incl_POSet(A)) | -up_complete_relstr(incl_POSet(A)) | bounded_relstr(incl_POSet(A)).  [resolve(146,a,105,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -join_complete_relstr(incl_POSet(A)) | with_infima_relstr(incl_POSet(A)).  [resolve(146,a,106,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -upper_bounded_relstr(incl_POSet(A)) | -join_complete_relstr(incl_POSet(A)) | with_suprema_relstr(incl_POSet(A)).  [resolve(146,a,107,a)].
% 0.41/1.06  Derived: -with_suprema_relstr(incl_POSet(A)) | -empty_carrier(incl_POSet(A)).  [resolve(146,a,108,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -complete_relstr(incl_POSet(A)) | with_suprema_relstr(incl_POSet(A)).  [resolve(146,a,109,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -complete_relstr(incl_POSet(A)) | with_infima_relstr(incl_POSet(A)).  [resolve(146,a,110,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -upper_bounded_relstr(incl_POSet(A)) | -up_complete_relstr(incl_POSet(A)) | -join_complete_relstr(incl_POSet(A)) | bounded_relstr(incl_POSet(A)).  [resolve(146,a,112,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -upper_bounded_relstr(incl_POSet(A)) | -up_complete_relstr(incl_POSet(A)) | -join_complete_relstr(incl_POSet(A)) | complete_relstr(incl_POSet(A)).  [resolve(146,a,115,a)].
% 0.41/1.06  Derived: -empty_carrier(incl_POSet(A)) | v1_yellow_3(incl_POSet(A)).  [resolve(146,a,116,a)].
% 0.41/1.06  Derived: -with_infima_relstr(incl_POSet(A)) | -empty_carrier(incl_POSet(A)).  [resolve(146,a,117,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -complete_relstr(incl_POSet(A)) | bounded_relstr(incl_POSet(A)).  [resolve(146,a,119,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -v1_yellow_3(incl_POSet(A)).  [resolve(146,a,120,a)].
% 0.41/1.06  Derived: -bounded_relstr(incl_POSet(A)) | lower_bounded_relstr(incl_POSet(A)).  [resolve(146,a,121,a)].
% 0.41/1.06  Derived: -bounded_relstr(incl_POSet(A)) | upper_bounded_relstr(incl_POSet(A)).  [resolve(146,a,122,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -heyting_relstr(incl_POSet(A)) | with_suprema_relstr(incl_POSet(A)).  [resolve(146,a,126,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -heyting_relstr(incl_POSet(A)) | with_infima_relstr(incl_POSet(A)).  [resolve(146,a,127,a)].
% 0.41/1.06  Derived: -lower_bounded_relstr(incl_POSet(A)) | -upper_bounded_relstr(incl_POSet(A)) | bounded_relstr(incl_POSet(A)).  [resolve(146,a,128,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -heyting_relstr(incl_POSet(A)) | distributive_relstr(incl_POSet(A)).  [resolve(146,a,129,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -heyting_relstr(incl_POSet(A)) | upper_bounded_relstr(incl_POSet(A)).  [resolve(146,a,130,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -boolean_relstr(incl_POSet(A)) | lower_bounded_relstr(incl_POSet(A)).  [resolve(146,a,136,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -boolean_relstr(incl_POSet(A)) | bounded_relstr(incl_POSet(A)).  [resolve(146,a,138,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -boolean_relstr(incl_POSet(A)) | complemented_relstr(incl_POSet(A)).  [resolve(146,a,140,a)].
% 0.41/1.06  Derived: -reflexive_relstr(incl_POSet(A)) | -with_suprema_relstr(incl_POSet(A)) | -up_complete_relstr(incl_POSet(A)) | upper_bounded_relstr(incl_POSet(A)).  [resolve(146,a,142,a)].
% 0.41/1.06  Derived: empty_carrier(incl_POSet(A)) | -reflexive_relstr(incl_POSet(A)) | -transitive_relstr(incl_POSet(A)) | -antisymmetric_relstr(incl_POSet(A)) | -with_suprema_relstr(incl_POSet(A)) | -with_infima_relstr(incl_POSet(A)) | -bounded_relstr(incl_POSet(A)) | -distributive_relstr(incl_POSet(A)) | -complemented_relstr(incl_POSet(A)) | boolean_relstr(incl_POSet(A)).  [resolve(146,a,145,a)].
% 0.41/1.06  147 rel_str(boole_POSet(A)) # label(dt_k3_yellow_1) # label(axiom).  [clausify(35)].
% 0.41/1.06  Derived: -strict_rel_str(boole_POSet(A)) | rel_str_of(the_carrier(boole_POSet(A)),the_InternalRel(boole_POSet(A))) = boole_POSet(A).  [resolve(147,a,90,a)].
% 0.41/1.06  Derived: empty_carrier(boole_POSet(A)) | -boolean_relstr(boole_POSet(A)) | heyting_relstr(boole_POSet(A)).  [resolve(147,a,100,a)].
% 0.41/1.06  Derived: empty_carrier(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | -v1_yellow_3(boole_POSet(A)).  [resolve(147,a,120,a)].
% 0.41/1.06  Derived: empty_carrier(boole_POSet(A)) | -reflexive_relstr(boole_POSet(A)) | -transitive_relstr(boole_POSet(A)) | -antisymmetric_relstr(boole_POSet(A)) | -with_suprema_relstr(boole_POSet(A)) | -with_infima_relstr(boole_POSet(A)) | -bounded_relstr(boole_POSet(A)) | -distributive_relstr(boole_POSet(A)) | -complemented_relstr(boole_POSet(A)) | boolean_relstr(boole_POSet(A)).  [resolve(147,a,145,a)].
% 0.41/1.07  148 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom).  [clausify(36)].
% 0.41/1.07  Derived: one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A).  [resolve(148,a,89,b)].
% 0.41/1.07  Derived: one_sorted_str(incl_POSet(A)).  [resolve(148,a,146,a)].
% 0.41/1.07  Derived: one_sorted_str(boole_POSet(A)).  [resolve(148,a,147,a)].
% 0.41/1.07  149 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom).  [clausify(41)].
% 0.41/1.07  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(149,a,89,b)].
% 0.41/1.07  Derived: relation_of2_as_subset(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))).  [resolve(149,a,146,a)].
% 0.41/1.07  Derived: relation_of2_as_subset(the_InternalRel(boole_POSet(A)),the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))).  [resolve(149,a,147,a)].
% 0.41/1.07  150 rel_str(c1) # label(existence_l1_orders_2) # label(axiom).  [clausify(43)].
% 0.41/1.07  Derived: -strict_rel_str(c1) | rel_str_of(the_carrier(c1),the_InternalRel(c1)) = c1.  [resolve(150,a,90,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -complete_relstr(c1) | up_complete_relstr(c1).  [resolve(150,a,91,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -complete_relstr(c1) | join_complete_relstr(c1).  [resolve(150,a,92,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | reflexive_relstr(c1).  [resolve(150,a,93,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | transitive_relstr(c1).  [resolve(150,a,94,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | antisymmetric_relstr(c1).  [resolve(150,a,95,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | with_suprema_relstr(c1).  [resolve(150,a,96,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | with_infima_relstr(c1).  [resolve(150,a,97,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | upper_bounded_relstr(c1).  [resolve(150,a,98,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | distributive_relstr(c1).  [resolve(150,a,99,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | heyting_relstr(c1).  [resolve(150,a,100,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -join_complete_relstr(c1) | lower_bounded_relstr(c1).  [resolve(150,a,101,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -transitive_relstr(c1) | -antisymmetric_relstr(c1) | -with_suprema_relstr(c1) | -lower_bounded_relstr(c1) | -up_complete_relstr(c1) | with_infima_relstr(c1).  [resolve(150,a,102,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -transitive_relstr(c1) | -antisymmetric_relstr(c1) | -with_suprema_relstr(c1) | -lower_bounded_relstr(c1) | -up_complete_relstr(c1) | complete_relstr(c1).  [resolve(150,a,103,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -transitive_relstr(c1) | -antisymmetric_relstr(c1) | -with_suprema_relstr(c1) | -lower_bounded_relstr(c1) | -up_complete_relstr(c1) | upper_bounded_relstr(c1).  [resolve(150,a,104,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -transitive_relstr(c1) | -antisymmetric_relstr(c1) | -with_suprema_relstr(c1) | -lower_bounded_relstr(c1) | -up_complete_relstr(c1) | bounded_relstr(c1).  [resolve(150,a,105,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -antisymmetric_relstr(c1) | -join_complete_relstr(c1) | with_infima_relstr(c1).  [resolve(150,a,106,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -antisymmetric_relstr(c1) | -upper_bounded_relstr(c1) | -join_complete_relstr(c1) | with_suprema_relstr(c1).  [resolve(150,a,107,a)].
% 0.41/1.07  Derived: -with_suprema_relstr(c1) | -empty_carrier(c1).  [resolve(150,a,108,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -complete_relstr(c1) | with_suprema_relstr(c1).  [resolve(150,a,109,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -complete_relstr(c1) | with_infima_relstr(c1).  [resolve(150,a,110,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -transitive_relstr(c1) | -antisymmetric_relstr(c1) | -upper_bounded_relstr(c1) | -up_complete_relstr(c1) | -join_complete_relstr(c1) | bounded_relstr(c1).  [resolve(150,a,112,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -transitive_relstr(c1) | -antisymmetric_relstr(c1) | -upper_bounded_relstr(c1) | -up_complete_relstr(c1) | -join_complete_relstr(c1) | complete_relstr(c1).  [resolve(150,a,115,a)].
% 0.41/1.07  Derived: -empty_carrier(c1) | v1_yellow_3(c1).  [resolve(150,a,116,a)].
% 0.41/1.07  Derived: -with_infima_relstr(c1) | -empty_carrier(c1).  [resolve(150,a,117,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -complete_relstr(c1) | bounded_relstr(c1).  [resolve(150,a,119,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -v1_yellow_3(c1).  [resolve(150,a,120,a)].
% 0.41/1.07  Derived: -bounded_relstr(c1) | lower_bounded_relstr(c1).  [resolve(150,a,121,a)].
% 0.41/1.07  Derived: -bounded_relstr(c1) | upper_bounded_relstr(c1).  [resolve(150,a,122,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -heyting_relstr(c1) | reflexive_relstr(c1).  [resolve(150,a,123,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -heyting_relstr(c1) | transitive_relstr(c1).  [resolve(150,a,124,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -heyting_relstr(c1) | antisymmetric_relstr(c1).  [resolve(150,a,125,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -heyting_relstr(c1) | with_suprema_relstr(c1).  [resolve(150,a,126,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -heyting_relstr(c1) | with_infima_relstr(c1).  [resolve(150,a,127,a)].
% 0.41/1.07  Derived: -lower_bounded_relstr(c1) | -upper_bounded_relstr(c1) | bounded_relstr(c1).  [resolve(150,a,128,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -heyting_relstr(c1) | distributive_relstr(c1).  [resolve(150,a,129,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -heyting_relstr(c1) | upper_bounded_relstr(c1).  [resolve(150,a,130,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | lower_bounded_relstr(c1).  [resolve(150,a,136,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | bounded_relstr(c1).  [resolve(150,a,138,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -boolean_relstr(c1) | complemented_relstr(c1).  [resolve(150,a,140,a)].
% 0.41/1.07  Derived: -reflexive_relstr(c1) | -with_suprema_relstr(c1) | -up_complete_relstr(c1) | upper_bounded_relstr(c1).  [resolve(150,a,142,a)].
% 0.41/1.07  Derived: empty_carrier(c1) | -reflexive_relstr(c1) | -transitive_relstr(c1) | -antisymmetric_relstr(c1) | -with_suprema_relstr(c1) | -with_infima_relstr(c1) | -bounded_relstr(c1) | -distributive_relstr(c1) | -complemented_relstr(c1) | boolean_relstr(c1).  [resolve(150,a,145,a)].
% 0.41/1.07  Derived: one_sorted_str(c1).  [resolve(150,a,148,a)].
% 0.41/1.07  Derived: relation_of2_as_subset(the_InternalRel(c1),the_carrier(c1),the_carrier(c1)).  [resolve(150,a,149,a)].
% 0.41/1.07  151 v1_yellow_3(A) | -rel_str(A) | -empty(the_InternalRel(A)) # label(fc13_yellow_3) # label(axiom).  [clausify(48)].
% 0.41/1.07  Derived: v1_yellow_3(rel_str_of(A,B)) | -empty(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A).  [resolve(151,b,89,b)].
% 0.41/1.07  Derived: v1_yellow_3(incl_POSet(A)) | -empty(the_InternalRel(incl_POSet(A))).  [resolve(151,b,146,a)].
% 0.41/1.07  Derived: v1_yellow_3(boole_POSet(A)) | -empty(the_InternalRel(boole_POSet(A))).  [resolve(151,b,147,a)].
% 0.41/1.07  Derived: v1_yellow_3(c1) | -empty(the_InternalRel(c1)).  [resolve(151,b,150,a)].
% 0.41/1.07  152 v1_yellow_3(A) | -rel_str(A) | relation(the_InternalRel(A)) # label(fc13_yellow_3) # label(axiom).  [clausify(48)].
% 0.41/1.07  Derived: v1_yellow_3(rel_str_of(A,B)) | relation(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A).  [resolve(152,b,89,b)].
% 0.41/1.07  Derived: v1_yellow_3(incl_POSet(A)) | relation(the_InternalRel(incl_POSet(A))).  [resolve(152,b,146,a)].
% 0.41/1.07  Derived: v1_yellow_3(boole_POSet(A)) | relation(the_InternalRel(boole_POSet(A))).  [resolve(152,b,147,a)].
% 0.41/1.07  Derived: v1_yellow_3(c1) | relation(the_InternalRel(c1)).  [resolve(152,b,150,a)].
% 0.41/1.07  153 rel_str(c3) # label(rc13_waybel_0) # label(axiom).  [clausify(60)].
% 0.41/1.07  Derived: -strict_rel_str(c3) | rel_str_of(the_carrier(c3),the_InternalRel(c3)) = c3.  [resolve(153,a,90,a)].
% 0.41/1.07  Derived: empty_carrier(c3) | -boolean_relstr(c3) | distributive_relstr(c3).  [resolve(153,a,99,a)].
% 0.41/1.08  Derived: empty_carrier(c3) | -boolean_relstr(c3) | heyting_relstr(c3).  [resolve(153,a,100,a)].
% 0.41/1.08  Derived: empty_carrier(c3) | -reflexive_relstr(c3) | -v1_yellow_3(c3).  [resolve(153,a,120,a)].
% 0.41/1.08  Derived: empty_carrier(c3) | -heyting_relstr(c3) | distributive_relstr(c3).  [resolve(153,a,129,a)].
% 0.41/1.08  Derived: empty_carrier(c3) | -boolean_relstr(c3) | complemented_relstr(c3).  [resolve(153,a,140,a)].
% 0.41/1.08  Derived: empty_carrier(c3) | -reflexive_relstr(c3) | -transitive_relstr(c3) | -antisymmetric_relstr(c3) | -with_suprema_relstr(c3) | -with_infima_relstr(c3) | -bounded_relstr(c3) | -distributive_relstr(c3) | -complemented_relstr(c3) | boolean_relstr(c3).  [resolve(153,a,145,a)].
% 0.41/1.08  Derived: one_sorted_str(c3).  [resolve(153,a,148,a)].
% 0.41/1.08  Derived: relation_of2_as_subset(the_InternalRel(c3),the_carrier(c3),the_carrier(c3)).  [resolve(153,a,149,a)].
% 0.41/1.08  Derived: v1_yellow_3(c3) | -empty(the_InternalRel(c3)).  [resolve(153,a,151,b)].
% 0.41/1.08  Derived: v1_yellow_3(c3) | relation(the_InternalRel(c3)).  [resolve(153,a,152,b)].
% 0.41/1.08  154 rel_str(c5) # label(rc1_lattice3) # label(axiom).  [clausify(62)].
% 0.41/1.08  Derived: -strict_rel_str(c5) | rel_str_of(the_carrier(c5),the_InternalRel(c5)) = c5.  [resolve(154,a,90,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -complete_relstr(c5) | up_complete_relstr(c5).  [resolve(154,a,91,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -complete_relstr(c5) | join_complete_relstr(c5).  [resolve(154,a,92,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -boolean_relstr(c5) | with_suprema_relstr(c5).  [resolve(154,a,96,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -boolean_relstr(c5) | with_infima_relstr(c5).  [resolve(154,a,97,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -boolean_relstr(c5) | upper_bounded_relstr(c5).  [resolve(154,a,98,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -boolean_relstr(c5) | distributive_relstr(c5).  [resolve(154,a,99,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -boolean_relstr(c5) | heyting_relstr(c5).  [resolve(154,a,100,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -join_complete_relstr(c5) | lower_bounded_relstr(c5).  [resolve(154,a,101,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | -with_suprema_relstr(c5) | -lower_bounded_relstr(c5) | -up_complete_relstr(c5) | with_infima_relstr(c5).  [resolve(154,a,102,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | -with_suprema_relstr(c5) | -lower_bounded_relstr(c5) | -up_complete_relstr(c5) | upper_bounded_relstr(c5).  [resolve(154,a,104,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | -with_suprema_relstr(c5) | -lower_bounded_relstr(c5) | -up_complete_relstr(c5) | bounded_relstr(c5).  [resolve(154,a,105,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -antisymmetric_relstr(c5) | -join_complete_relstr(c5) | with_infima_relstr(c5).  [resolve(154,a,106,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -antisymmetric_relstr(c5) | -upper_bounded_relstr(c5) | -join_complete_relstr(c5) | with_suprema_relstr(c5).  [resolve(154,a,107,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -complete_relstr(c5) | with_suprema_relstr(c5).  [resolve(154,a,109,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -complete_relstr(c5) | with_infima_relstr(c5).  [resolve(154,a,110,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | -upper_bounded_relstr(c5) | -up_complete_relstr(c5) | -join_complete_relstr(c5) | bounded_relstr(c5).  [resolve(154,a,112,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -complete_relstr(c5) | bounded_relstr(c5).  [resolve(154,a,119,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -v1_yellow_3(c5).  [resolve(154,a,120,a)].
% 0.41/1.08  Derived: -bounded_relstr(c5) | lower_bounded_relstr(c5).  [resolve(154,a,121,a)].
% 0.41/1.08  Derived: -bounded_relstr(c5) | upper_bounded_relstr(c5).  [resolve(154,a,122,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -heyting_relstr(c5) | with_suprema_relstr(c5).  [resolve(154,a,126,a)].
% 0.41/1.08  Derived: empty_carrier(c5) | -heyting_relstr(c5) | with_infima_relstr(c5).  [resolve(154,a,127,a)].
% 0.83/1.08  Derived: -lower_bounded_relstr(c5) | -upper_bounded_relstr(c5) | bounded_relstr(c5).  [resolve(154,a,128,a)].
% 0.83/1.08  Derived: empty_carrier(c5) | -heyting_relstr(c5) | distributive_relstr(c5).  [resolve(154,a,129,a)].
% 0.83/1.08  Derived: empty_carrier(c5) | -heyting_relstr(c5) | upper_bounded_relstr(c5).  [resolve(154,a,130,a)].
% 0.83/1.08  Derived: empty_carrier(c5) | -boolean_relstr(c5) | lower_bounded_relstr(c5).  [resolve(154,a,136,a)].
% 0.83/1.08  Derived: empty_carrier(c5) | -boolean_relstr(c5) | bounded_relstr(c5).  [resolve(154,a,138,a)].
% 0.83/1.08  Derived: empty_carrier(c5) | -boolean_relstr(c5) | complemented_relstr(c5).  [resolve(154,a,140,a)].
% 0.83/1.08  Derived: -reflexive_relstr(c5) | -with_suprema_relstr(c5) | -up_complete_relstr(c5) | upper_bounded_relstr(c5).  [resolve(154,a,142,a)].
% 0.83/1.08  Derived: empty_carrier(c5) | -reflexive_relstr(c5) | -transitive_relstr(c5) | -antisymmetric_relstr(c5) | -with_suprema_relstr(c5) | -with_infima_relstr(c5) | -bounded_relstr(c5) | -distributive_relstr(c5) | -complemented_relstr(c5) | boolean_relstr(c5).  [resolve(154,a,145,a)].
% 0.83/1.08  Derived: one_sorted_str(c5).  [resolve(154,a,148,a)].
% 0.83/1.08  Derived: relation_of2_as_subset(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)).  [resolve(154,a,149,a)].
% 0.83/1.08  Derived: v1_yellow_3(c5) | -empty(the_InternalRel(c5)).  [resolve(154,a,151,b)].
% 0.83/1.08  Derived: v1_yellow_3(c5) | relation(the_InternalRel(c5)).  [resolve(154,a,152,b)].
% 0.83/1.08  155 rel_str(c7) # label(rc1_yellow_3) # label(axiom).  [clausify(65)].
% 0.83/1.08  Derived: -strict_rel_str(c7) | rel_str_of(the_carrier(c7),the_InternalRel(c7)) = c7.  [resolve(155,a,90,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -complete_relstr(c7) | up_complete_relstr(c7).  [resolve(155,a,91,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -complete_relstr(c7) | join_complete_relstr(c7).  [resolve(155,a,92,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -boolean_relstr(c7) | with_suprema_relstr(c7).  [resolve(155,a,96,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -boolean_relstr(c7) | with_infima_relstr(c7).  [resolve(155,a,97,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -boolean_relstr(c7) | upper_bounded_relstr(c7).  [resolve(155,a,98,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -boolean_relstr(c7) | distributive_relstr(c7).  [resolve(155,a,99,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -boolean_relstr(c7) | heyting_relstr(c7).  [resolve(155,a,100,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -join_complete_relstr(c7) | lower_bounded_relstr(c7).  [resolve(155,a,101,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -with_suprema_relstr(c7) | -lower_bounded_relstr(c7) | -up_complete_relstr(c7) | with_infima_relstr(c7).  [resolve(155,a,102,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -with_suprema_relstr(c7) | -lower_bounded_relstr(c7) | -up_complete_relstr(c7) | complete_relstr(c7).  [resolve(155,a,103,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -with_suprema_relstr(c7) | -lower_bounded_relstr(c7) | -up_complete_relstr(c7) | upper_bounded_relstr(c7).  [resolve(155,a,104,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -with_suprema_relstr(c7) | -lower_bounded_relstr(c7) | -up_complete_relstr(c7) | bounded_relstr(c7).  [resolve(155,a,105,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -antisymmetric_relstr(c7) | -join_complete_relstr(c7) | with_infima_relstr(c7).  [resolve(155,a,106,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -antisymmetric_relstr(c7) | -upper_bounded_relstr(c7) | -join_complete_relstr(c7) | with_suprema_relstr(c7).  [resolve(155,a,107,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -complete_relstr(c7) | with_suprema_relstr(c7).  [resolve(155,a,109,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -complete_relstr(c7) | with_infima_relstr(c7).  [resolve(155,a,110,a)].
% 0.83/1.08  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -upper_bounded_relstr(c7) | -up_complete_relstr(c7) | -join_complete_relstr(c7) | bounded_relstr(c7).  [resolve(155,a,112,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -upper_bounded_relstr(c7) | -up_complete_relstr(c7) | -join_complete_relstr(c7) | complete_relstr(c7).  [resolve(155,a,115,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -complete_relstr(c7) | bounded_relstr(c7).  [resolve(155,a,119,a)].
% 0.83/1.09  Derived: -bounded_relstr(c7) | lower_bounded_relstr(c7).  [resolve(155,a,121,a)].
% 0.83/1.09  Derived: -bounded_relstr(c7) | upper_bounded_relstr(c7).  [resolve(155,a,122,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -heyting_relstr(c7) | with_suprema_relstr(c7).  [resolve(155,a,126,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -heyting_relstr(c7) | with_infima_relstr(c7).  [resolve(155,a,127,a)].
% 0.83/1.09  Derived: -lower_bounded_relstr(c7) | -upper_bounded_relstr(c7) | bounded_relstr(c7).  [resolve(155,a,128,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -heyting_relstr(c7) | distributive_relstr(c7).  [resolve(155,a,129,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -heyting_relstr(c7) | upper_bounded_relstr(c7).  [resolve(155,a,130,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -boolean_relstr(c7) | lower_bounded_relstr(c7).  [resolve(155,a,136,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -boolean_relstr(c7) | bounded_relstr(c7).  [resolve(155,a,138,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -boolean_relstr(c7) | complemented_relstr(c7).  [resolve(155,a,140,a)].
% 0.83/1.09  Derived: -reflexive_relstr(c7) | -with_suprema_relstr(c7) | -up_complete_relstr(c7) | upper_bounded_relstr(c7).  [resolve(155,a,142,a)].
% 0.83/1.09  Derived: empty_carrier(c7) | -reflexive_relstr(c7) | -transitive_relstr(c7) | -antisymmetric_relstr(c7) | -with_suprema_relstr(c7) | -with_infima_relstr(c7) | -bounded_relstr(c7) | -distributive_relstr(c7) | -complemented_relstr(c7) | boolean_relstr(c7).  [resolve(155,a,145,a)].
% 0.83/1.09  Derived: one_sorted_str(c7).  [resolve(155,a,148,a)].
% 0.83/1.09  Derived: relation_of2_as_subset(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)).  [resolve(155,a,149,a)].
% 0.83/1.09  Derived: v1_yellow_3(c7) | -empty(the_InternalRel(c7)).  [resolve(155,a,151,b)].
% 0.83/1.09  Derived: v1_yellow_3(c7) | relation(the_InternalRel(c7)).  [resolve(155,a,152,b)].
% 0.83/1.09  156 rel_str(c8) # label(rc2_lattice3) # label(axiom).  [clausify(66)].
% 0.83/1.09  Derived: -strict_rel_str(c8) | rel_str_of(the_carrier(c8),the_InternalRel(c8)) = c8.  [resolve(156,a,90,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -complete_relstr(c8) | up_complete_relstr(c8).  [resolve(156,a,91,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -complete_relstr(c8) | join_complete_relstr(c8).  [resolve(156,a,92,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -boolean_relstr(c8) | upper_bounded_relstr(c8).  [resolve(156,a,98,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -boolean_relstr(c8) | distributive_relstr(c8).  [resolve(156,a,99,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -boolean_relstr(c8) | heyting_relstr(c8).  [resolve(156,a,100,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -join_complete_relstr(c8) | lower_bounded_relstr(c8).  [resolve(156,a,101,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -with_suprema_relstr(c8) | -lower_bounded_relstr(c8) | -up_complete_relstr(c8) | upper_bounded_relstr(c8).  [resolve(156,a,104,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -with_suprema_relstr(c8) | -lower_bounded_relstr(c8) | -up_complete_relstr(c8) | bounded_relstr(c8).  [resolve(156,a,105,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -upper_bounded_relstr(c8) | -up_complete_relstr(c8) | -join_complete_relstr(c8) | bounded_relstr(c8).  [resolve(156,a,112,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -complete_relstr(c8) | bounded_relstr(c8).  [resolve(156,a,119,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -v1_yellow_3(c8).  [resolve(156,a,120,a)].
% 0.83/1.09  Derived: -bounded_relstr(c8) | lower_bounded_relstr(c8).  [resolve(156,a,121,a)].
% 0.83/1.09  Derived: -bounded_relstr(c8) | upper_bounded_relstr(c8).  [resolve(156,a,122,a)].
% 0.83/1.09  Derived: -lower_bounded_relstr(c8) | -upper_bounded_relstr(c8) | bounded_relstr(c8).  [resolve(156,a,128,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -heyting_relstr(c8) | distributive_relstr(c8).  [resolve(156,a,129,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -heyting_relstr(c8) | upper_bounded_relstr(c8).  [resolve(156,a,130,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -boolean_relstr(c8) | lower_bounded_relstr(c8).  [resolve(156,a,136,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -boolean_relstr(c8) | bounded_relstr(c8).  [resolve(156,a,138,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -boolean_relstr(c8) | complemented_relstr(c8).  [resolve(156,a,140,a)].
% 0.83/1.09  Derived: -reflexive_relstr(c8) | -with_suprema_relstr(c8) | -up_complete_relstr(c8) | upper_bounded_relstr(c8).  [resolve(156,a,142,a)].
% 0.83/1.09  Derived: empty_carrier(c8) | -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -with_suprema_relstr(c8) | -with_infima_relstr(c8) | -bounded_relstr(c8) | -distributive_relstr(c8) | -complemented_relstr(c8) | boolean_relstr(c8).  [resolve(156,a,145,a)].
% 0.83/1.09  Derived: one_sorted_str(c8).  [resolve(156,a,148,a)].
% 0.83/1.09  Derived: relation_of2_as_subset(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)).  [resolve(156,a,149,a)].
% 0.83/1.09  Derived: v1_yellow_3(c8) | -empty(the_InternalRel(c8)).  [resolve(156,a,151,b)].
% 0.83/1.09  Derived: v1_yellow_3(c8) | relation(the_InternalRel(c8)).  [resolve(156,a,152,b)].
% 0.83/1.09  157 rel_str(c10) # label(rc2_yellow_0) # label(axiom).  [clausify(69)].
% 0.83/1.09  Derived: -strict_rel_str(c10) | rel_str_of(the_carrier(c10),the_InternalRel(c10)) = c10.  [resolve(157,a,90,a)].
% 0.83/1.09  Derived: empty_carrier(c10) | -reflexive_relstr(c10) | -complete_relstr(c10) | up_complete_relstr(c10).  [resolve(157,a,91,a)].
% 0.83/1.09  Derived: empty_carrier(c10) | -reflexive_relstr(c10) | -complete_relstr(c10) | join_complete_relstr(c10).  [resolve(157,a,92,a)].
% 0.83/1.09  Derived: empty_carrier(c10) | -boolean_relstr(c10) | distributive_relstr(c10).  [resolve(157,a,99,a)].
% 0.83/1.09  Derived: empty_carrier(c10) | -boolean_relstr(c10) | heyting_relstr(c10).  [resolve(157,a,100,a)].
% 0.83/1.09  Derived: empty_carrier(c10) | -reflexive_relstr(c10) | -v1_yellow_3(c10).  [resolve(157,a,120,a)].
% 0.83/1.09  Derived: empty_carrier(c10) | -heyting_relstr(c10) | distributive_relstr(c10).  [resolve(157,a,129,a)].
% 0.83/1.09  Derived: empty_carrier(c10) | -boolean_relstr(c10) | complemented_relstr(c10).  [resolve(157,a,140,a)].
% 0.83/1.09  Derived: empty_carrier(c10) | -reflexive_relstr(c10) | -transitive_relstr(c10) | -antisymmetric_relstr(c10) | -with_suprema_relstr(c10) | -with_infima_relstr(c10) | -bounded_relstr(c10) | -distributive_relstr(c10) | -complemented_relstr(c10) | boolean_relstr(c10).  [resolve(157,a,145,a)].
% 0.83/1.09  Derived: one_sorted_str(c10).  [resolve(157,a,148,a)].
% 0.83/1.09  Derived: relation_of2_as_subset(the_InternalRel(c10),the_carrier(c10),the_carrier(c10)).  [resolve(157,a,149,a)].
% 0.83/1.09  Derived: v1_yellow_3(c10) | -empty(the_InternalRel(c10)).  [resolve(157,a,151,b)].
% 0.83/1.09  Derived: v1_yellow_3(c10) | relation(the_InternalRel(c10)).  [resolve(157,a,152,b)].
% 0.83/1.09  158 rel_str(c12) # label(rc4_waybel_1) # label(axiom).  [clausify(73)].
% 0.83/1.09  Derived: -strict_rel_str(c12) | rel_str_of(the_carrier(c12),the_InternalRel(c12)) = c12.  [resolve(158,a,90,a)].
% 0.83/1.09  Derived: empty_carrier(c12) | -reflexive_relstr(c12) | -complete_relstr(c12) | up_complete_relstr(c12).  [resolve(158,a,91,a)].
% 0.83/1.09  Derived: empty_carrier(c12) | -reflexive_relstr(c12) | -complete_relstr(c12) | join_complete_relstr(c12).  [resolve(158,a,92,a)].
% 0.83/1.09  Derived: empty_carrier(c12) | -reflexive_relstr(c12) | -transitive_relstr(c12) | -antisymmetric_relstr(c12) | -with_suprema_relstr(c12) | -lower_bounded_relstr(c12) | -up_complete_relstr(c12) | complete_relstr(c12).  [resolve(158,a,103,a)].
% 0.83/1.09  Derived: empty_carrier(c12) | -reflexive_relstr(c12) | -transitive_relstr(c12) | -antisymmetric_relstr(c12) | -upper_bounded_relstr(c12) | -up_complete_relstr(c12) | -join_complete_relstr(c12) | complete_relstr(c12).  [resolve(158,a,115,a)].
% 0.83/1.09  Derived: empty_carrier(c12) | -reflexive_relstr(c12) | -v1_yellow_3(c12).  [resolve(158,a,120,a)].
% 0.83/1.09  Derived: one_sorted_str(c12).  [resolve(158,a,148,a)].
% 0.83/1.09  Derived: relation_of2_as_subset(the_InternalRel(c12),the_carrier(c12),the_carrier(c12)).  [resolve(158,a,149,a)].
% 0.83/1.09  Derived: v1_yellow_3(c12) | -empty(the_InternalRel(c12)).  [resolve(158,a,151,b)].
% 0.91/1.18  Derived: v1_yellow_3(c12) | relation(the_InternalRel(c12)).  [resolve(158,a,152,b)].
% 0.91/1.18  159 rel_str(c13) # label(rc5_waybel_1) # label(axiom).  [clausify(75)].
% 0.91/1.18  Derived: -strict_rel_str(c13) | rel_str_of(the_carrier(c13),the_InternalRel(c13)) = c13.  [resolve(159,a,90,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -complete_relstr(c13) | up_complete_relstr(c13).  [resolve(159,a,91,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -complete_relstr(c13) | join_complete_relstr(c13).  [resolve(159,a,92,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -join_complete_relstr(c13) | lower_bounded_relstr(c13).  [resolve(159,a,101,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | -with_suprema_relstr(c13) | -lower_bounded_relstr(c13) | -up_complete_relstr(c13) | complete_relstr(c13).  [resolve(159,a,103,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | -with_suprema_relstr(c13) | -lower_bounded_relstr(c13) | -up_complete_relstr(c13) | bounded_relstr(c13).  [resolve(159,a,105,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | -upper_bounded_relstr(c13) | -up_complete_relstr(c13) | -join_complete_relstr(c13) | bounded_relstr(c13).  [resolve(159,a,112,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | -upper_bounded_relstr(c13) | -up_complete_relstr(c13) | -join_complete_relstr(c13) | complete_relstr(c13).  [resolve(159,a,115,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -complete_relstr(c13) | bounded_relstr(c13).  [resolve(159,a,119,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -v1_yellow_3(c13).  [resolve(159,a,120,a)].
% 0.91/1.18  Derived: -bounded_relstr(c13) | lower_bounded_relstr(c13).  [resolve(159,a,121,a)].
% 0.91/1.18  Derived: -lower_bounded_relstr(c13) | -upper_bounded_relstr(c13) | bounded_relstr(c13).  [resolve(159,a,128,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -boolean_relstr(c13) | lower_bounded_relstr(c13).  [resolve(159,a,136,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -boolean_relstr(c13) | bounded_relstr(c13).  [resolve(159,a,138,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -boolean_relstr(c13) | complemented_relstr(c13).  [resolve(159,a,140,a)].
% 0.91/1.18  Derived: empty_carrier(c13) | -reflexive_relstr(c13) | -transitive_relstr(c13) | -antisymmetric_relstr(c13) | -with_suprema_relstr(c13) | -with_infima_relstr(c13) | -bounded_relstr(c13) | -distributive_relstr(c13) | -complemented_relstr(c13) | boolean_relstr(c13).  [resolve(159,a,145,a)].
% 0.91/1.18  Derived: one_sorted_str(c13).  [resolve(159,a,148,a)].
% 0.91/1.18  Derived: relation_of2_as_subset(the_InternalRel(c13),the_carrier(c13),the_carrier(c13)).  [resolve(159,a,149,a)].
% 0.91/1.18  Derived: v1_yellow_3(c13) | -empty(the_InternalRel(c13)).  [resolve(159,a,151,b)].
% 0.91/1.18  Derived: v1_yellow_3(c13) | relation(the_InternalRel(c13)).  [resolve(159,a,152,b)].
% 0.91/1.18  160 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom).  [clausify(40)].
% 0.91/1.18  161 relation_of2_as_subset(inclusion_order(A),A,A) # label(dt_k1_yellow_1) # label(axiom).  [clausify(31)].
% 0.91/1.18  Derived: element(inclusion_order(A),powerset(cartesian_product2(A,A))).  [resolve(160,a,161,a)].
% 0.91/1.18  162 relation_of2_as_subset(f3(A,B),A,B) # label(existence_m2_relset_1) # label(axiom).  [clausify(47)].
% 0.91/1.18  Derived: element(f3(A,B),powerset(cartesian_product2(A,B))).  [resolve(162,a,160,a)].
% 0.91/1.18  163 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom).  [clausify(77)].
% 0.91/1.18  Derived: relation_of2(inclusion_order(A),A,A).  [resolve(163,a,161,a)].
% 0.91/1.18  Derived: relation_of2(f3(A,B),A,B).  [resolve(163,a,162,a)].
% 0.91/1.18  164 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom).  [clausify(77)].
% 0.91/1.18  Derived: -relation_of2(A,B,C) | element(A,powerset(cartesian_product2(B,C))).  [resolve(164,a,160,a)].
% 0.91/1.18  165 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(149,a,89,b)].
% 0.91/1.19  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(165,a,160,a)].
% 0.91/1.19  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(165,a,163,a)].
% 0.91/1.19  166 relation_of2_as_subset(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))).  [resolve(149,a,146,a)].
% 0.91/1.19  Derived: element(the_InternalRel(incl_POSet(A)),powerset(cartesian_product2(the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))))).  [resolve(166,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))).  [resolve(166,a,163,a)].
% 0.91/1.19  167 relation_of2_as_subset(the_InternalRel(boole_POSet(A)),the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))).  [resolve(149,a,147,a)].
% 0.91/1.19  Derived: element(the_InternalRel(boole_POSet(A)),powerset(cartesian_product2(the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))))).  [resolve(167,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(boole_POSet(A)),the_carrier(boole_POSet(A)),the_carrier(boole_POSet(A))).  [resolve(167,a,163,a)].
% 0.91/1.19  168 relation_of2_as_subset(the_InternalRel(c1),the_carrier(c1),the_carrier(c1)).  [resolve(150,a,149,a)].
% 0.91/1.19  Derived: element(the_InternalRel(c1),powerset(cartesian_product2(the_carrier(c1),the_carrier(c1)))).  [resolve(168,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(c1),the_carrier(c1),the_carrier(c1)).  [resolve(168,a,163,a)].
% 0.91/1.19  169 relation_of2_as_subset(the_InternalRel(c3),the_carrier(c3),the_carrier(c3)).  [resolve(153,a,149,a)].
% 0.91/1.19  Derived: element(the_InternalRel(c3),powerset(cartesian_product2(the_carrier(c3),the_carrier(c3)))).  [resolve(169,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(c3),the_carrier(c3),the_carrier(c3)).  [resolve(169,a,163,a)].
% 0.91/1.19  170 relation_of2_as_subset(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)).  [resolve(154,a,149,a)].
% 0.91/1.19  Derived: element(the_InternalRel(c5),powerset(cartesian_product2(the_carrier(c5),the_carrier(c5)))).  [resolve(170,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)).  [resolve(170,a,163,a)].
% 0.91/1.19  171 relation_of2_as_subset(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)).  [resolve(155,a,149,a)].
% 0.91/1.19  Derived: element(the_InternalRel(c7),powerset(cartesian_product2(the_carrier(c7),the_carrier(c7)))).  [resolve(171,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(c7),the_carrier(c7),the_carrier(c7)).  [resolve(171,a,163,a)].
% 0.91/1.19  172 relation_of2_as_subset(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)).  [resolve(156,a,149,a)].
% 0.91/1.19  Derived: element(the_InternalRel(c8),powerset(cartesian_product2(the_carrier(c8),the_carrier(c8)))).  [resolve(172,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)).  [resolve(172,a,163,a)].
% 0.91/1.19  173 relation_of2_as_subset(the_InternalRel(c10),the_carrier(c10),the_carrier(c10)).  [resolve(157,a,149,a)].
% 0.91/1.19  Derived: element(the_InternalRel(c10),powerset(cartesian_product2(the_carrier(c10),the_carrier(c10)))).  [resolve(173,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(c10),the_carrier(c10),the_carrier(c10)).  [resolve(173,a,163,a)].
% 0.91/1.19  174 relation_of2_as_subset(the_InternalRel(c12),the_carrier(c12),the_carrier(c12)).  [resolve(158,a,149,a)].
% 0.91/1.19  Derived: element(the_InternalRel(c12),powerset(cartesian_product2(the_carrier(c12),the_carrier(c12)))).  [resolve(174,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(c12),the_carrier(c12),the_carrier(c12)).  [resolve(174,a,163,a)].
% 0.91/1.19  175 relation_of2_as_subset(the_InternalRel(c13),the_carrier(c13),the_carrier(c13)).  [resolve(159,a,149,a)].
% 0.91/1.19  Derived: element(the_InternalRel(c13),powerset(cartesian_product2(the_carrier(c13),the_carrier(c13)))).  [resolve(175,a,160,a)].
% 0.91/1.19  Derived: relation_of2(the_InternalRel(c13),the_carrier(c13),the_carrier(c13)).  [resolve(175,a,163,a)].
% 0.91/1.19  176 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom).  [clausify(50)].
% 0.91/1.19  177 one_sorted_str(c2) # label(existence_l1_struct_0) # label(axiom).  [clausify(44)].
% 0.91/1.19  Derived: empty_carrier(c2) | -empty(the_carrier(c2)).  [resolve(176,b,177,a)].
% 0.91/1.19  178 one_sorted_str(c11) # label(rc3_struct_0) # label(axiom).  [clausify(71)].
% 0.91/1.19  Derived: empty_carrier(c11) | -empty(the_carrier(c11)).  [resolve(178,a,176,b)].
% 0.91/1.19  179 empty_carrier(A) | -one_sorted_str(A) | element(f8(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom).  [clausify(74)].
% 0.91/1.19  Derived: empty_carrier(c2) | element(f8(c2),powerset(the_carrier(c2))).  [resolve(179,b,177,a)].
% 0.91/1.19  Derived: empty_carrier(c11) | element(f8(c11),powerset(the_carrier(c11))).  [resolve(179,b,178,a)].
% 0.91/1.19  180 empty_carrier(A) | -one_sorted_str(A) | -empty(f8(A)) # label(rc5_struct_0) # label(axiom).  [clausify(74)].
% 0.91/1.19  Derived: empty_carrier(c2) | -empty(f8(c2)).  [resolve(180,b,177,a)].
% 0.91/1.19  Derived: empty_carrier(c11) | -empty(f8(c11)).  [resolve(180,b,178,a)].
% 0.91/1.19  181 one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A).  [resolve(148,a,89,b)].
% 0.91/1.19  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(the_carrier(rel_str_of(B,A))).  [resolve(181,a,176,b)].
% 0.91/1.19  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | element(f8(rel_str_of(B,A)),powerset(the_carrier(rel_str_of(B,A)))).  [resolve(181,a,179,b)].
% 0.91/1.19  Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(f8(rel_str_of(B,A))).  [resolve(181,a,180,b)].
% 0.91/1.19  182 one_sorted_str(incl_POSet(A)).  [resolve(148,a,146,a)].
% 0.91/1.19  Derived: empty_carrier(incl_POSet(A)) | -empty(the_carrier(incl_POSet(A))).  [resolve(182,a,176,b)].
% 0.91/1.19  Derived: empty_carrier(incl_POSet(A)) | element(f8(incl_POSet(A)),powerset(the_carrier(incl_POSet(A)))).  [resolve(182,a,179,b)].
% 0.91/1.19  Derived: empty_carrier(incl_POSet(A)) | -empty(f8(incl_POSet(A))).  [resolve(182,a,180,b)].
% 0.91/1.19  183 one_sorted_str(boole_POSet(A)).  [resolve(148,a,147,a)].
% 0.91/1.19  Derived: empty_carrier(boole_POSet(A)) | -empty(the_carrier(boole_POSet(A))).  [resolve(183,a,176,b)].
% 0.91/1.19  Derived: empty_carrier(boole_POSet(A)) | element(f8(boole_POSet(A)),powerset(the_carrier(boole_POSet(A)))).  [resolve(183,a,179,b)].
% 0.91/1.19  Derived: empty_carrier(boole_POSet(A)) | -empty(f8(boole_POSet(A))).  [resolve(183,a,180,b)].
% 0.91/1.19  184 one_sorted_str(c1).  [resolve(150,a,148,a)].
% 0.91/1.19  Derived: empty_carrier(c1) | -empty(the_carrier(c1)).  [resolve(184,a,176,b)].
% 0.91/1.19  Derived: empty_carrier(c1) | element(f8(c1),powerset(the_carrier(c1))).  [resolve(184,a,179,b)].
% 0.91/1.19  Derived: empty_carrier(c1) | -empty(f8(c1)).  [resolve(184,a,180,b)].
% 0.91/1.19  185 one_sorted_str(c3).  [resolve(153,a,148,a)].
% 0.91/1.19  Derived: empty_carrier(c3) | -empty(the_carrier(c3)).  [resolve(185,a,176,b)].
% 0.91/1.19  Derived: empty_carrier(c3) | element(f8(c3),powerset(the_carrier(c3))).  [resolve(185,a,179,b)].
% 0.91/1.19  Derived: empty_carrier(c3) | -empty(f8(c3)).  [resolve(185,a,180,b)].
% 0.91/1.19  186 one_sorted_str(c5).  [resolve(154,a,148,a)].
% 0.91/1.19  Derived: empty_carrier(c5) | -empty(the_carrier(c5)).  [resolve(186,a,176,b)].
% 0.91/1.19  Derived: empty_carrier(c5) | element(f8(c5),powerset(the_carrier(c5))).  [resolve(186,a,179,b)].
% 0.91/1.19  Derived: empty_carrier(c5) | -empty(f8(c5)).  [resolve(186,a,180,b)].
% 0.91/1.19  187 one_sorted_str(c7).  [resolve(155,a,148,a)].
% 0.91/1.19  Derived: empty_carrier(c7) | -empty(the_carrier(c7)).  [resolve(187,a,176,b)].
% 0.91/1.19  Derived: empty_carrier(c7) | element(f8(c7),powerset(the_carrier(c7))).  [resolve(187,a,179,b)].
% 0.91/1.19  Derived: empty_carrier(c7) | -empty(f8(c7)).  [resolve(187,a,180,b)].
% 0.91/1.19  188 one_sorted_str(c8).  [resolve(156,a,148,a)].
% 0.91/1.19  Derived: empty_carrier(c8) | -empty(the_carrier(c8)).  [resolve(188,a,176,b)].
% 0.91/1.19  Derived: empty_carrier(c8) | element(f8(c8),powerset(the_carrier(c8))).  [resolve(188,a,179,b)].
% 0.91/1.19  Derived: empty_carrier(c8) | -empty(f8(c8)).  [resolve(188,a,180,b)].
% 0.91/1.19  189 one_sorted_str(c10).  [resolve(157,a,148,a)].
% 0.91/1.19  Derived: empty_carrier(c10) | -empty(the_carrier(c10)).  [resolve(189,a,176,b)].
% 0.91/1.19  Derived: empty_carrier(c10) | element(f8(c10),powerset(the_carrier(c10))).  [resolve(189,a,179,b)].
% 0.91/1.19  Derived: empty_carrier(c10) | -empty(f8(c10)).  [resolve(189,a,180,b)].
% 0.91/1.19  190 one_sorted_str(c12).  [resolve(158,a,148,a)].
% 0.91/1.19  Derived: empty_carrier(c12) | -empty(the_carrier(c12)).  [resolve(190,a,176,b)].
% 1.21/1.50  Derived: empty_carrier(c12) | element(f8(c12),powerset(the_carrier(c12))).  [resolve(190,a,179,b)].
% 1.21/1.50  Derived: empty_carrier(c12) | -empty(f8(c12)).  [resolve(190,a,180,b)].
% 1.21/1.50  191 one_sorted_str(c13).  [resolve(159,a,148,a)].
% 1.21/1.50  Derived: empty_carrier(c13) | -empty(the_carrier(c13)).  [resolve(191,a,176,b)].
% 1.21/1.50  Derived: empty_carrier(c13) | element(f8(c13),powerset(the_carrier(c13))).  [resolve(191,a,179,b)].
% 1.21/1.50  Derived: empty_carrier(c13) | -empty(f8(c13)).  [resolve(191,a,180,b)].
% 1.21/1.50  192 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom).  [clausify(81)].
% 1.21/1.50  193 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom).  [clausify(78)].
% 1.21/1.50  194 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom).  [clausify(81)].
% 1.21/1.50  Derived: element(A,powerset(A)).  [resolve(192,b,193,a)].
% 1.21/1.50  
% 1.21/1.50  ============================== end predicate elimination =============
% 1.21/1.50  
% 1.21/1.50  Auto_denials:  (non-Horn, no changes).
% 1.21/1.50  
% 1.21/1.50  Term ordering decisions:
% 1.21/1.50  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. rel_str_of=1. cartesian_product2=1. f1=1. f3=1. incl_POSet=1. the_carrier=1. boole_POSet=1. the_InternalRel=1. powerset=1. inclusion_order=1. inclusion_relation=1. f2=1. f4=1. f5=1. f6=1. f7=1. f8=1.
% 1.21/1.50  
% 1.21/1.50  ============================== end of process initial clauses ========
% 1.21/1.50  
% 1.21/1.50  ============================== CLAUSES FOR SEARCH ====================
% 1.21/1.50  
% 1.21/1.50  ============================== end of clauses for search =============
% 1.21/1.50  
% 1.21/1.50  ============================== SEARCH ================================
% 1.21/1.50  
% 1.21/1.50  % Starting search at 0.20 seconds.
% 1.21/1.50  
% 1.21/1.50  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 90 (0.00 of 0.25 sec).
% 1.21/1.50  
% 1.21/1.50  Low Water (keep): wt=15.000, iters=3338
% 1.21/1.50  
% 1.21/1.50  Low Water (keep): wt=14.000, iters=3336
% 1.21/1.50  
% 1.21/1.50  Low Water (keep): wt=12.000, iters=3333
% 1.21/1.50  
% 1.21/1.50  ============================== PROOF =================================
% 1.21/1.50  % SZS status Theorem
% 1.21/1.50  % SZS output start Refutation
% 1.21/1.50  
% 1.21/1.50  % Proof 1 at 0.46 (+ 0.01) seconds.
% 1.21/1.50  % Length of proof is 28.
% 1.21/1.50  % Level of proof is 7.
% 1.21/1.50  % Maximum clause weight is 16.000.
% 1.21/1.50  % Given clauses 918.
% 1.21/1.50  
% 1.21/1.50  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].
% 1.21/1.50  27 (all A incl_POSet(A) = rel_str_of(A,inclusion_order(A))) # label(d1_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 1.21/1.50  33 (all A (strict_rel_str(incl_POSet(A)) & rel_str(incl_POSet(A)))) # label(dt_k2_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 1.21/1.50  41 (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].
% 1.21/1.50  59 (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].
% 1.21/1.50  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].
% 1.21/1.50  83 (all A boole_POSet(A) = incl_POSet(powerset(A))) # label(t4_yellow_1) # label(axiom) # label(non_clause).  [assumption].
% 1.21/1.50  88 -(all A the_carrier(boole_POSet(A)) = powerset(A)) # label(t4_waybel_7) # label(negated_conjecture) # label(non_clause).  [assumption].
% 1.21/1.50  90 -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)].
% 1.21/1.50  146 rel_str(incl_POSet(A)) # label(dt_k2_yellow_1) # label(axiom).  [clausify(33)].
% 1.21/1.50  149 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom).  [clausify(41)].
% 1.21/1.50  163 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom).  [clausify(77)].
% 1.21/1.50  166 relation_of2_as_subset(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))).  [resolve(149,a,146,a)].
% 1.21/1.50  198 incl_POSet(A) = rel_str_of(A,inclusion_order(A)) # label(d1_yellow_1) # label(axiom).  [clausify(27)].
% 1.21/1.50  200 strict_rel_str(incl_POSet(A)) # label(dt_k2_yellow_1) # label(axiom).  [clausify(33)].
% 1.21/1.50  201 strict_rel_str(rel_str_of(A,inclusion_order(A))).  [copy(200),rewrite([198(1)])].
% 1.21/1.50  236 -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(59)].
% 1.21/1.50  324 boole_POSet(A) = incl_POSet(powerset(A)) # label(t4_yellow_1) # label(axiom).  [clausify(83)].
% 1.21/1.50  325 boole_POSet(A) = rel_str_of(powerset(A),inclusion_order(powerset(A))).  [copy(324),rewrite([198(3)])].
% 1.21/1.50  330 powerset(c14) != the_carrier(boole_POSet(c14)) # label(t4_waybel_7) # label(negated_conjecture).  [clausify(88)].
% 1.21/1.50  331 the_carrier(rel_str_of(powerset(c14),inclusion_order(powerset(c14)))) != powerset(c14).  [copy(330),rewrite([325(4)]),flip(a)].
% 1.21/1.50  374 -strict_rel_str(incl_POSet(A)) | rel_str_of(the_carrier(incl_POSet(A)),the_InternalRel(incl_POSet(A))) = incl_POSet(A).  [resolve(146,a,90,a)].
% 1.21/1.50  375 rel_str_of(the_carrier(rel_str_of(A,inclusion_order(A))),the_InternalRel(rel_str_of(A,inclusion_order(A)))) = rel_str_of(A,inclusion_order(A)).  [copy(374),rewrite([198(1),198(4),198(7),198(11)]),unit_del(a,201)].
% 1.21/1.50  742 relation_of2(the_InternalRel(incl_POSet(A)),the_carrier(incl_POSet(A)),the_carrier(incl_POSet(A))).  [resolve(166,a,163,a)].
% 1.21/1.50  743 relation_of2(the_InternalRel(rel_str_of(A,inclusion_order(A))),the_carrier(rel_str_of(A,inclusion_order(A))),the_carrier(rel_str_of(A,inclusion_order(A)))).  [copy(742),rewrite([198(1),198(4),198(7)])].
% 1.21/1.50  969 rel_str_of(A,inclusion_order(A)) != rel_str_of(B,C) | the_carrier(rel_str_of(A,inclusion_order(A))) = B.  [resolve(743,a,236,a),rewrite([375(8)]),flip(a),flip(b)].
% 1.21/1.50  7753 the_carrier(rel_str_of(A,inclusion_order(A))) = A.  [xx_res(969,a)].
% 1.21/1.50  7754 $F.  [resolve(7753,a,331,a)].
% 1.21/1.50  
% 1.21/1.50  % SZS output end Refutation
% 1.21/1.50  ============================== end of proof ==========================
% 1.21/1.50  
% 1.21/1.50  ============================== STATISTICS ============================
% 1.21/1.50  
% 1.21/1.50  Given=918. Generated=8366. Kept=7346. proofs=1.
% 1.21/1.50  Usable=908. Sos=6378. Demods=19. Limbo=0, Disabled=667. Hints=0.
% 1.21/1.50  Megabytes=5.74.
% 1.21/1.50  User_CPU=0.46, System_CPU=0.01, Wall_clock=0.
% 1.21/1.50  
% 1.21/1.50  ============================== end of statistics =====================
% 1.21/1.50  
% 1.21/1.50  ============================== end of search =========================
% 1.21/1.50  
% 1.21/1.50  THEOREM PROVED
% 1.21/1.50  % SZS status Theorem
% 1.21/1.50  
% 1.21/1.50  Exiting with 1 proof.
% 1.21/1.50  
% 1.21/1.50  Process 24559 exit (max_proofs) Sat Jun 18 21:29:39 2022
% 1.21/1.50  Prover9 interrupted
%------------------------------------------------------------------------------