TSTP Solution File: SEU345+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU345+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 13:31:08 EDT 2022
% Result : Timeout 300.04s 300.34s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU345+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n021.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 06:47:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/1.05 ============================== Prover9 ===============================
% 0.42/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.05 Process 23894 was started by sandbox on n021.cluster.edu,
% 0.42/1.05 Mon Jun 20 06:47:34 2022
% 0.42/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23740_n021.cluster.edu".
% 0.42/1.05 ============================== end of head ===========================
% 0.42/1.05
% 0.42/1.05 ============================== INPUT =================================
% 0.42/1.05
% 0.42/1.05 % Reading from file /tmp/Prover9_23740_n021.cluster.edu
% 0.42/1.05
% 0.42/1.05 set(prolog_style_variables).
% 0.42/1.05 set(auto2).
% 0.42/1.05 % set(auto2) -> set(auto).
% 0.42/1.05 % set(auto) -> set(auto_inference).
% 0.42/1.05 % set(auto) -> set(auto_setup).
% 0.42/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.05 % set(auto) -> set(auto_limits).
% 0.42/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.05 % set(auto) -> set(auto_denials).
% 0.42/1.05 % set(auto) -> set(auto_process).
% 0.42/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.05 % set(auto2) -> assign(stats, some).
% 0.42/1.05 % set(auto2) -> clear(echo_input).
% 0.42/1.05 % set(auto2) -> set(quiet).
% 0.42/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.05 % set(auto2) -> clear(print_given).
% 0.42/1.05 assign(lrs_ticks,-1).
% 0.42/1.05 assign(sos_limit,10000).
% 0.42/1.05 assign(order,kbo).
% 0.42/1.05 set(lex_order_vars).
% 0.42/1.05 clear(print_given).
% 0.42/1.05
% 0.42/1.05 % formulas(sos). % not echoed (102 formulas)
% 0.42/1.05
% 0.42/1.05 ============================== end of input ==========================
% 0.42/1.05
% 0.42/1.05 % From the command line: assign(max_seconds, 300).
% 0.42/1.05
% 0.42/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.05
% 0.42/1.05 % Formulas that are not ordinary clauses:
% 0.42/1.05 1 (all A (latt_str(A) -> (strict_latt_str(A) -> A = latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A))))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 2 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 3 (all A (latt_str(A) -> (-empty_carrier(A) & lattice(A) -> -empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 4 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 5 (all A (latt_str(A) -> (-empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) -> -empty_carrier(A) & lattice(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 6 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 7 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 8 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 9 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> meet_commut(A,B,C) = meet_commut(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 10 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_union2(A,B,C) = subset_union2(A,C,B))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 11 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_intersection2(A,B,C) = subset_intersection2(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 12 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (lower_bounded_semilattstr(A) <-> (exists B (element(B,the_carrier(A)) & (all C (element(C,the_carrier(A)) -> meet(A,B,C) = B & meet(A,C,B) = B))))))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 13 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (lower_bounded_semilattstr(A) -> (all B (element(B,the_carrier(A)) -> (B = bottom_of_semilattstr(A) <-> (all C (element(C,the_carrier(A)) -> meet(A,B,C) = B & meet(A,C,B) = B)))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 14 (all A (relation(A) & function(A) -> (all B all C apply_binary(A,B,C) = apply(A,ordered_pair(B,C))))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 15 (all A all B (strict_latt_str(B) & latt_str(B) -> (B = boole_lattice(A) <-> the_carrier(B) = powerset(A) & (all C (element(C,powerset(A)) -> (all D (element(D,powerset(A)) -> apply_binary(the_L_join(B),C,D) = subset_union2(A,C,D) & apply_binary(the_L_meet(B),C,D) = subset_intersection2(A,C,D)))))))) # label(d1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 16 (all A (-empty_carrier(A) & join_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> join(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 17 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> meet(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C))))))) # label(d2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 18 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 19 (all A all B all C (function(B) & quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) -> strict_latt_str(latt_str_of(A,B,C)) & latt_str(latt_str_of(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 20 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 21 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 22 (all A (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 23 (all A all B all C (-empty_carrier(A) & join_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> element(join(A,B,C),the_carrier(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 24 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 25 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 26 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 27 (all A all B all C all D all E all F (-empty(A) & -empty(B) & function(D) & quasi_total(D,cartesian_product2(A,B),C) & relation_of2(D,cartesian_product2(A,B),C) & element(E,A) & element(F,B) -> element(apply_binary_as_element(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 28 (all A all B all C (-empty_carrier(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> element(meet(A,B,C),the_carrier(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 29 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 30 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 31 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 32 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 33 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> element(meet_commut(A,B,C),the_carrier(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 34 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> element(subset_union2(A,B,C),powerset(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 35 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 36 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> element(bottom_of_semilattstr(A),the_carrier(A)))) # label(dt_k5_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 37 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> element(subset_intersection2(A,B,C),powerset(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 38 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 39 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 40 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 41 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 42 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 43 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 44 (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].
% 0.42/1.05 45 (all A (meet_semilatt_str(A) -> function(the_L_meet(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 46 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 47 (all A (join_semilatt_str(A) -> function(the_L_join(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 48 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 49 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 50 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 51 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 52 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 53 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 54 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 55 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 56 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 57 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 58 (all A (-empty_carrier(A) & join_commutative(A) & join_semilatt_str(A) -> relation(the_L_join(A)) & function(the_L_join(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v1_binop_1(the_L_join(A),the_carrier(A)) & v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc2_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 59 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)))) # label(fc2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 60 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 61 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 62 (all A (-empty_carrier(A) & join_associative(A) & join_semilatt_str(A) -> relation(the_L_join(A)) & function(the_L_join(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v2_binop_1(the_L_join(A),the_carrier(A)) & v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc3_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 63 (all A all B all C (-empty(A) & function(B) & quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) -> -empty_carrier(latt_str_of(A,B,C)) & strict_latt_str(latt_str_of(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 64 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 65 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 66 (all A (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) -> relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v1_binop_1(the_L_meet(A),the_carrier(A)) & v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc4_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 67 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 68 (all A (-empty_carrier(A) & meet_associative(A) & meet_semilatt_str(A) -> relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v2_binop_1(the_L_meet(A),the_carrier(A)) & v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc5_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 69 (all A all B all C (function(B) & quasi_total(B,cartesian_product2(A,A),A) & relation_of2(B,cartesian_product2(A,A),A) & function(C) & quasi_total(C,cartesian_product2(A,A),A) & relation_of2(C,cartesian_product2(A,A),A) -> (all D all E all F (latt_str_of(A,B,C) = latt_str_of(D,E,F) -> A = D & B = E & C = F)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 70 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 71 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 72 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_union2(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 73 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_intersection2(A,B,B) = B)) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 74 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 75 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 76 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 77 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 78 (exists A (latt_str(A) & strict_latt_str(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 79 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 80 (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].
% 0.42/1.05 81 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 82 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) & lattice(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 83 (all A all B all C all D all E all F (-empty(A) & -empty(B) & function(D) & quasi_total(D,cartesian_product2(A,B),C) & relation_of2(D,cartesian_product2(A,B),C) & element(E,A) & element(F,B) -> apply_binary_as_element(A,B,C,D,E,F) = apply_binary(D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 84 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> meet_commut(A,B,C) = meet(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 85 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_union2(A,B,C) = set_union2(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 86 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_intersection2(A,B,C) = set_intersection2(B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 87 (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].
% 0.42/1.05 88 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 89 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 90 (all A all B (element(B,the_carrier(boole_lattice(A))) -> (all C (element(C,the_carrier(boole_lattice(A))) -> join(boole_lattice(A),B,C) = set_union2(B,C) & meet(boole_lattice(A),B,C) = set_intersection2(B,C))))) # label(t1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 91 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 92 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 93 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 94 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 95 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 96 (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].
% 0.42/1.05 97 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 98 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 99 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 100 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.05 101 -(all A (lower_bounded_semilattstr(boole_lattice(A)) & bottom_of_semilattstr(boole_lattice(A)) = empty_set)) # label(t3_lattice3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/1.05
% 0.42/1.05 ============================== end of process non-clausal formulas ===
% 0.42/1.05
% 0.42/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/1.05
% 0.42/1.05 ============================== PREDICATE ELIMINATION =================
% 0.42/1.05 102 -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | latt_str(latt_str_of(B,A,C)) # label(dt_g3_lattices) # label(axiom). [clausify(19)].
% 0.42/1.05 103 -latt_str(A) | -strict_latt_str(A) | latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)) = A # label(abstractness_v3_lattices) # label(axiom). [clausify(1)].
% 0.42/1.05 104 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.42/1.05 105 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_associative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.42/1.05 106 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.42/1.05 107 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_associative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.42/1.05 108 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.42/1.05 109 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.42/1.05 110 -latt_str(A) | empty_carrier(A) | -join_commutative(A) | -join_associative(A) | -meet_commutative(A) | -meet_associative(A) | -meet_absorbing(A) | -join_absorbing(A) | lattice(A) # label(cc2_lattices) # label(axiom). [clausify(5)].
% 0.42/1.05 111 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) != A | powerset(B) = the_carrier(A) # label(d1_lattice3) # label(axiom). [clausify(15)].
% 0.42/1.05 112 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) != A | -element(C,powerset(B)) | -element(D,powerset(B)) | apply_binary(the_L_join(A),C,D) = subset_union2(B,C,D) # label(d1_lattice3) # label(axiom). [clausify(15)].
% 0.42/1.05 113 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) != A | -element(C,powerset(B)) | -element(D,powerset(B)) | apply_binary(the_L_meet(A),C,D) = subset_intersection2(B,C,D) # label(d1_lattice3) # label(axiom). [clausify(15)].
% 0.42/1.05 114 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) = A | powerset(B) != the_carrier(A) | element(f4(B,A),powerset(B)) # label(d1_lattice3) # label(axiom). [clausify(15)].
% 0.42/1.05 115 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) = A | powerset(B) != the_carrier(A) | element(f5(B,A),powerset(B)) # label(d1_lattice3) # label(axiom). [clausify(15)].
% 0.42/1.05 116 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) = A | powerset(B) != the_carrier(A) | apply_binary(the_L_join(A),f4(B,A),f5(B,A)) != subset_union2(B,f4(B,A),f5(B,A)) | apply_binary(the_L_meet(A),f4(B,A),f5(B,A)) != subset_intersection2(B,f4(B,A),f5(B,A)) # label(d1_lattice3) # label(axiom). [clausify(15)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -strict_latt_str(latt_str_of(B,A,C)) | latt_str_of(the_carrier(latt_str_of(B,A,C)),the_L_join(latt_str_of(B,A,C)),the_L_meet(latt_str_of(B,A,C))) = latt_str_of(B,A,C). [resolve(102,g,103,a)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | join_commutative(latt_str_of(B,A,C)). [resolve(102,g,104,a)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | join_associative(latt_str_of(B,A,C)). [resolve(102,g,105,a)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | meet_commutative(latt_str_of(B,A,C)). [resolve(102,g,106,a)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | meet_associative(latt_str_of(B,A,C)). [resolve(102,g,107,a)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | meet_absorbing(latt_str_of(B,A,C)). [resolve(102,g,108,a)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lattice(latt_str_of(B,A,C)) | join_absorbing(latt_str_of(B,A,C)). [resolve(102,g,109,a)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -join_commutative(latt_str_of(B,A,C)) | -join_associative(latt_str_of(B,A,C)) | -meet_commutative(latt_str_of(B,A,C)) | -meet_associative(latt_str_of(B,A,C)) | -meet_absorbing(latt_str_of(B,A,C)) | -join_absorbing(latt_str_of(B,A,C)) | lattice(latt_str_of(B,A,C)). [resolve(102,g,110,a)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -strict_latt_str(latt_str_of(B,A,C)) | boole_lattice(D) != latt_str_of(B,A,C) | powerset(D) = the_carrier(latt_str_of(B,A,C)). [resolve(102,g,111,b)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -strict_latt_str(latt_str_of(B,A,C)) | boole_lattice(D) != latt_str_of(B,A,C) | -element(E,powerset(D)) | -element(F,powerset(D)) | apply_binary(the_L_join(latt_str_of(B,A,C)),E,F) = subset_union2(D,E,F). [resolve(102,g,112,b)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -strict_latt_str(latt_str_of(B,A,C)) | boole_lattice(D) != latt_str_of(B,A,C) | -element(E,powerset(D)) | -element(F,powerset(D)) | apply_binary(the_L_meet(latt_str_of(B,A,C)),E,F) = subset_intersection2(D,E,F). [resolve(102,g,113,b)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -strict_latt_str(latt_str_of(B,A,C)) | boole_lattice(D) = latt_str_of(B,A,C) | powerset(D) != the_carrier(latt_str_of(B,A,C)) | element(f4(D,latt_str_of(B,A,C)),powerset(D)). [resolve(102,g,114,b)].
% 0.42/1.05 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -strict_latt_str(latt_str_of(B,A,C)) | boole_lattice(D) = latt_str_of(B,A,C) | powerset(D) != the_carrier(latt_str_of(B,A,C)) | element(f5(D,latt_str_of(B,A,C)),powerset(D)). [resolve(102,g,115,b)].
% 0.42/1.06 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | -strict_latt_str(latt_str_of(B,A,C)) | boole_lattice(D) = latt_str_of(B,A,C) | powerset(D) != the_carrier(latt_str_of(B,A,C)) | apply_binary(the_L_join(latt_str_of(B,A,C)),f4(D,latt_str_of(B,A,C)),f5(D,latt_str_of(B,A,C))) != subset_union2(D,f4(D,latt_str_of(B,A,C)),f5(D,latt_str_of(B,A,C))) | apply_binary(the_L_meet(latt_str_of(B,A,C)),f4(D,latt_str_of(B,A,C)),f5(D,latt_str_of(B,A,C))) != subset_intersection2(D,f4(D,latt_str_of(B,A,C)),f5(D,latt_str_of(B,A,C))). [resolve(102,g,116,b)].
% 0.42/1.06 117 latt_str(boole_lattice(A)) # label(dt_k1_lattice3) # label(axiom). [clausify(22)].
% 0.42/1.06 Derived: -strict_latt_str(boole_lattice(A)) | latt_str_of(the_carrier(boole_lattice(A)),the_L_join(boole_lattice(A)),the_L_meet(boole_lattice(A))) = boole_lattice(A). [resolve(117,a,103,a)].
% 0.42/1.06 Derived: -strict_latt_str(boole_lattice(A)) | boole_lattice(B) != boole_lattice(A) | powerset(B) = the_carrier(boole_lattice(A)). [resolve(117,a,111,b)].
% 0.42/1.06 Derived: -strict_latt_str(boole_lattice(A)) | boole_lattice(B) != boole_lattice(A) | -element(C,powerset(B)) | -element(D,powerset(B)) | apply_binary(the_L_join(boole_lattice(A)),C,D) = subset_union2(B,C,D). [resolve(117,a,112,b)].
% 0.42/1.06 Derived: -strict_latt_str(boole_lattice(A)) | boole_lattice(B) != boole_lattice(A) | -element(C,powerset(B)) | -element(D,powerset(B)) | apply_binary(the_L_meet(boole_lattice(A)),C,D) = subset_intersection2(B,C,D). [resolve(117,a,113,b)].
% 0.42/1.06 Derived: -strict_latt_str(boole_lattice(A)) | boole_lattice(B) = boole_lattice(A) | powerset(B) != the_carrier(boole_lattice(A)) | element(f4(B,boole_lattice(A)),powerset(B)). [resolve(117,a,114,b)].
% 0.42/1.06 Derived: -strict_latt_str(boole_lattice(A)) | boole_lattice(B) = boole_lattice(A) | powerset(B) != the_carrier(boole_lattice(A)) | element(f5(B,boole_lattice(A)),powerset(B)). [resolve(117,a,115,b)].
% 0.42/1.06 Derived: -strict_latt_str(boole_lattice(A)) | boole_lattice(B) = boole_lattice(A) | powerset(B) != the_carrier(boole_lattice(A)) | apply_binary(the_L_join(boole_lattice(A)),f4(B,boole_lattice(A)),f5(B,boole_lattice(A))) != subset_union2(B,f4(B,boole_lattice(A)),f5(B,boole_lattice(A))) | apply_binary(the_L_meet(boole_lattice(A)),f4(B,boole_lattice(A)),f5(B,boole_lattice(A))) != subset_intersection2(B,f4(B,boole_lattice(A)),f5(B,boole_lattice(A))). [resolve(117,a,116,b)].
% 0.42/1.06 118 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(41)].
% 0.42/1.06 Derived: meet_semilatt_str(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(118,a,102,g)].
% 0.42/1.06 Derived: meet_semilatt_str(boole_lattice(A)). [resolve(118,a,117,a)].
% 0.42/1.06 119 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(41)].
% 0.42/1.06 Derived: join_semilatt_str(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(119,a,102,g)].
% 0.42/1.06 Derived: join_semilatt_str(boole_lattice(A)). [resolve(119,a,117,a)].
% 0.42/1.06 120 latt_str(c4) # label(existence_l3_lattices) # label(axiom). [clausify(51)].
% 0.42/1.06 Derived: -strict_latt_str(c4) | latt_str_of(the_carrier(c4),the_L_join(c4),the_L_meet(c4)) = c4. [resolve(120,a,103,a)].
% 0.42/1.06 Derived: empty_carrier(c4) | -lattice(c4) | join_commutative(c4). [resolve(120,a,104,a)].
% 0.42/1.06 Derived: empty_carrier(c4) | -lattice(c4) | join_associative(c4). [resolve(120,a,105,a)].
% 0.42/1.06 Derived: empty_carrier(c4) | -lattice(c4) | meet_commutative(c4). [resolve(120,a,106,a)].
% 0.42/1.06 Derived: empty_carrier(c4) | -lattice(c4) | meet_associative(c4). [resolve(120,a,107,a)].
% 0.42/1.06 Derived: empty_carrier(c4) | -lattice(c4) | meet_absorbing(c4). [resolve(120,a,108,a)].
% 0.42/1.06 Derived: empty_carrier(c4) | -lattice(c4) | join_absorbing(c4). [resolve(120,a,109,a)].
% 0.42/1.06 Derived: empty_carrier(c4) | -join_commutative(c4) | -join_associative(c4) | -meet_commutative(c4) | -meet_associative(c4) | -meet_absorbing(c4) | -join_absorbing(c4) | lattice(c4). [resolve(120,a,110,a)].
% 0.42/1.06 Derived: -strict_latt_str(c4) | boole_lattice(A) != c4 | powerset(A) = the_carrier(c4). [resolve(120,a,111,b)].
% 0.42/1.06 Derived: -strict_latt_str(c4) | boole_lattice(A) != c4 | -element(B,powerset(A)) | -element(C,powerset(A)) | apply_binary(the_L_join(c4),B,C) = subset_union2(A,B,C). [resolve(120,a,112,b)].
% 0.42/1.06 Derived: -strict_latt_str(c4) | boole_lattice(A) != c4 | -element(B,powerset(A)) | -element(C,powerset(A)) | apply_binary(the_L_meet(c4),B,C) = subset_intersection2(A,B,C). [resolve(120,a,113,b)].
% 0.42/1.06 Derived: -strict_latt_str(c4) | boole_lattice(A) = c4 | powerset(A) != the_carrier(c4) | element(f4(A,c4),powerset(A)). [resolve(120,a,114,b)].
% 0.42/1.06 Derived: -strict_latt_str(c4) | boole_lattice(A) = c4 | powerset(A) != the_carrier(c4) | element(f5(A,c4),powerset(A)). [resolve(120,a,115,b)].
% 0.42/1.06 Derived: -strict_latt_str(c4) | boole_lattice(A) = c4 | powerset(A) != the_carrier(c4) | apply_binary(the_L_join(c4),f4(A,c4),f5(A,c4)) != subset_union2(A,f4(A,c4),f5(A,c4)) | apply_binary(the_L_meet(c4),f4(A,c4),f5(A,c4)) != subset_intersection2(A,f4(A,c4),f5(A,c4)). [resolve(120,a,116,b)].
% 0.42/1.06 Derived: meet_semilatt_str(c4). [resolve(120,a,118,a)].
% 0.42/1.06 Derived: join_semilatt_str(c4). [resolve(120,a,119,a)].
% 0.42/1.06 121 latt_str(c7) # label(rc3_lattices) # label(axiom). [clausify(78)].
% 0.42/1.06 Derived: -strict_latt_str(c7) | latt_str_of(the_carrier(c7),the_L_join(c7),the_L_meet(c7)) = c7. [resolve(121,a,103,a)].
% 0.42/1.06 Derived: empty_carrier(c7) | -lattice(c7) | join_commutative(c7). [resolve(121,a,104,a)].
% 0.42/1.06 Derived: empty_carrier(c7) | -lattice(c7) | join_associative(c7). [resolve(121,a,105,a)].
% 0.42/1.06 Derived: empty_carrier(c7) | -lattice(c7) | meet_commutative(c7). [resolve(121,a,106,a)].
% 0.42/1.06 Derived: empty_carrier(c7) | -lattice(c7) | meet_associative(c7). [resolve(121,a,107,a)].
% 0.42/1.06 Derived: empty_carrier(c7) | -lattice(c7) | meet_absorbing(c7). [resolve(121,a,108,a)].
% 0.42/1.06 Derived: empty_carrier(c7) | -lattice(c7) | join_absorbing(c7). [resolve(121,a,109,a)].
% 0.42/1.06 Derived: empty_carrier(c7) | -join_commutative(c7) | -join_associative(c7) | -meet_commutative(c7) | -meet_associative(c7) | -meet_absorbing(c7) | -join_absorbing(c7) | lattice(c7). [resolve(121,a,110,a)].
% 0.42/1.06 Derived: -strict_latt_str(c7) | boole_lattice(A) != c7 | powerset(A) = the_carrier(c7). [resolve(121,a,111,b)].
% 0.42/1.06 Derived: -strict_latt_str(c7) | boole_lattice(A) != c7 | -element(B,powerset(A)) | -element(C,powerset(A)) | apply_binary(the_L_join(c7),B,C) = subset_union2(A,B,C). [resolve(121,a,112,b)].
% 0.42/1.06 Derived: -strict_latt_str(c7) | boole_lattice(A) != c7 | -element(B,powerset(A)) | -element(C,powerset(A)) | apply_binary(the_L_meet(c7),B,C) = subset_intersection2(A,B,C). [resolve(121,a,113,b)].
% 0.42/1.06 Derived: -strict_latt_str(c7) | boole_lattice(A) = c7 | powerset(A) != the_carrier(c7) | element(f4(A,c7),powerset(A)). [resolve(121,a,114,b)].
% 0.42/1.06 Derived: -strict_latt_str(c7) | boole_lattice(A) = c7 | powerset(A) != the_carrier(c7) | element(f5(A,c7),powerset(A)). [resolve(121,a,115,b)].
% 0.42/1.06 Derived: -strict_latt_str(c7) | boole_lattice(A) = c7 | powerset(A) != the_carrier(c7) | apply_binary(the_L_join(c7),f4(A,c7),f5(A,c7)) != subset_union2(A,f4(A,c7),f5(A,c7)) | apply_binary(the_L_meet(c7),f4(A,c7),f5(A,c7)) != subset_intersection2(A,f4(A,c7),f5(A,c7)). [resolve(121,a,116,b)].
% 0.42/1.06 Derived: meet_semilatt_str(c7). [resolve(121,a,118,a)].
% 0.42/1.06 Derived: join_semilatt_str(c7). [resolve(121,a,119,a)].
% 0.42/1.06 122 latt_str(c9) # label(rc6_lattices) # label(axiom). [clausify(81)].
% 0.42/1.06 Derived: -strict_latt_str(c9) | latt_str_of(the_carrier(c9),the_L_join(c9),the_L_meet(c9)) = c9. [resolve(122,a,103,a)].
% 0.42/1.06 Derived: empty_carrier(c9) | -lattice(c9) | join_commutative(c9). [resolve(122,a,104,a)].
% 0.42/1.06 Derived: empty_carrier(c9) | -lattice(c9) | join_associative(c9). [resolve(122,a,105,a)].
% 0.42/1.06 Derived: empty_carrier(c9) | -lattice(c9) | meet_commutative(c9). [resolve(122,a,106,a)].
% 0.42/1.06 Derived: empty_carrier(c9) | -lattice(c9) | meet_associative(c9). [resolve(122,a,107,a)].
% 0.42/1.07 Derived: empty_carrier(c9) | -lattice(c9) | meet_absorbing(c9). [resolve(122,a,108,a)].
% 0.42/1.07 Derived: empty_carrier(c9) | -lattice(c9) | join_absorbing(c9). [resolve(122,a,109,a)].
% 0.42/1.07 Derived: empty_carrier(c9) | -join_commutative(c9) | -join_associative(c9) | -meet_commutative(c9) | -meet_associative(c9) | -meet_absorbing(c9) | -join_absorbing(c9) | lattice(c9). [resolve(122,a,110,a)].
% 0.42/1.07 Derived: -strict_latt_str(c9) | boole_lattice(A) != c9 | powerset(A) = the_carrier(c9). [resolve(122,a,111,b)].
% 0.42/1.07 Derived: -strict_latt_str(c9) | boole_lattice(A) != c9 | -element(B,powerset(A)) | -element(C,powerset(A)) | apply_binary(the_L_join(c9),B,C) = subset_union2(A,B,C). [resolve(122,a,112,b)].
% 0.42/1.07 Derived: -strict_latt_str(c9) | boole_lattice(A) != c9 | -element(B,powerset(A)) | -element(C,powerset(A)) | apply_binary(the_L_meet(c9),B,C) = subset_intersection2(A,B,C). [resolve(122,a,113,b)].
% 0.42/1.07 Derived: -strict_latt_str(c9) | boole_lattice(A) = c9 | powerset(A) != the_carrier(c9) | element(f4(A,c9),powerset(A)). [resolve(122,a,114,b)].
% 0.42/1.07 Derived: -strict_latt_str(c9) | boole_lattice(A) = c9 | powerset(A) != the_carrier(c9) | element(f5(A,c9),powerset(A)). [resolve(122,a,115,b)].
% 0.42/1.07 Derived: -strict_latt_str(c9) | boole_lattice(A) = c9 | powerset(A) != the_carrier(c9) | apply_binary(the_L_join(c9),f4(A,c9),f5(A,c9)) != subset_union2(A,f4(A,c9),f5(A,c9)) | apply_binary(the_L_meet(c9),f4(A,c9),f5(A,c9)) != subset_intersection2(A,f4(A,c9),f5(A,c9)). [resolve(122,a,116,b)].
% 0.42/1.07 Derived: meet_semilatt_str(c9). [resolve(122,a,118,a)].
% 0.42/1.07 Derived: join_semilatt_str(c9). [resolve(122,a,119,a)].
% 0.42/1.07 123 latt_str(c10) # label(rc9_lattices) # label(axiom). [clausify(82)].
% 0.42/1.07 Derived: -strict_latt_str(c10) | latt_str_of(the_carrier(c10),the_L_join(c10),the_L_meet(c10)) = c10. [resolve(123,a,103,a)].
% 0.42/1.07 Derived: -strict_latt_str(c10) | boole_lattice(A) != c10 | powerset(A) = the_carrier(c10). [resolve(123,a,111,b)].
% 0.42/1.07 Derived: -strict_latt_str(c10) | boole_lattice(A) != c10 | -element(B,powerset(A)) | -element(C,powerset(A)) | apply_binary(the_L_join(c10),B,C) = subset_union2(A,B,C). [resolve(123,a,112,b)].
% 0.42/1.07 Derived: -strict_latt_str(c10) | boole_lattice(A) != c10 | -element(B,powerset(A)) | -element(C,powerset(A)) | apply_binary(the_L_meet(c10),B,C) = subset_intersection2(A,B,C). [resolve(123,a,113,b)].
% 0.42/1.07 Derived: -strict_latt_str(c10) | boole_lattice(A) = c10 | powerset(A) != the_carrier(c10) | element(f4(A,c10),powerset(A)). [resolve(123,a,114,b)].
% 0.42/1.07 Derived: -strict_latt_str(c10) | boole_lattice(A) = c10 | powerset(A) != the_carrier(c10) | element(f5(A,c10),powerset(A)). [resolve(123,a,115,b)].
% 0.42/1.07 Derived: -strict_latt_str(c10) | boole_lattice(A) = c10 | powerset(A) != the_carrier(c10) | apply_binary(the_L_join(c10),f4(A,c10),f5(A,c10)) != subset_union2(A,f4(A,c10),f5(A,c10)) | apply_binary(the_L_meet(c10),f4(A,c10),f5(A,c10)) != subset_intersection2(A,f4(A,c10),f5(A,c10)). [resolve(123,a,116,b)].
% 0.42/1.07 Derived: meet_semilatt_str(c10). [resolve(123,a,118,a)].
% 0.42/1.07 Derived: join_semilatt_str(c10). [resolve(123,a,119,a)].
% 0.42/1.07 124 -relation(A) | -function(A) | apply(A,ordered_pair(B,C)) = apply_binary(A,B,C) # label(d1_binop_1) # label(axiom). [clausify(14)].
% 0.42/1.07 125 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(4)].
% 0.42/1.07 Derived: -function(A) | apply(A,ordered_pair(B,C)) = apply_binary(A,B,C) | -element(A,powerset(cartesian_product2(D,E))). [resolve(124,a,125,b)].
% 0.42/1.07 126 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | relation(the_L_join(A)) # label(fc2_lattice2) # label(axiom). [clausify(58)].
% 0.42/1.07 Derived: empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | -function(the_L_join(A)) | apply(the_L_join(A),ordered_pair(B,C)) = apply_binary(the_L_join(A),B,C). [resolve(126,d,124,a)].
% 0.42/1.07 127 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | relation(the_L_join(A)) # label(fc3_lattice2) # label(axiom). [clausify(62)].
% 0.42/1.07 Derived: empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | -function(the_L_join(A)) | apply(the_L_join(A),ordered_pair(B,C)) = apply_binary(the_L_join(A),B,C). [resolve(127,d,124,a)].
% 0.42/1.07 128 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | relation(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(66)].
% 0.42/1.07 Derived: empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -function(the_L_meet(A)) | apply(the_L_meet(A),ordered_pair(B,C)) = apply_binary(the_L_meet(A),B,C). [resolve(128,d,124,a)].
% 0.42/1.07 129 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | relation(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(68)].
% 0.42/1.07 Derived: empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | -function(the_L_meet(A)) | apply(the_L_meet(A),ordered_pair(B,C)) = apply_binary(the_L_meet(A),B,C). [resolve(129,d,124,a)].
% 0.42/1.07 130 meet_semilatt_str(c1) # label(existence_l1_lattices) # label(axiom). [clausify(48)].
% 0.42/1.07 131 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet_commut(A,C,B) = meet_commut(A,B,C) # label(commutativity_k4_lattices) # label(axiom). [clausify(9)].
% 0.42/1.07 132 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | element(f1(A),the_carrier(A)) # label(d13_lattices) # label(axiom). [clausify(12)].
% 0.42/1.07 133 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,f1(A),B) = f1(A) # label(d13_lattices) # label(axiom). [clausify(12)].
% 0.42/1.07 134 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f1(A)) = f1(A) # label(d13_lattices) # label(axiom). [clausify(12)].
% 0.42/1.07 135 empty_carrier(A) | -meet_semilatt_str(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | element(f2(A,B),the_carrier(A)) # label(d13_lattices) # label(axiom). [clausify(12)].
% 0.42/1.07 136 empty_carrier(A) | -meet_semilatt_str(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f2(A,B)) != B | meet(A,f2(A,B),B) != B # label(d13_lattices) # label(axiom). [clausify(12)].
% 0.42/1.07 137 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,B,C) = B # label(d16_lattices) # label(axiom). [clausify(13)].
% 0.42/1.07 138 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,C,B) = B # label(d16_lattices) # label(axiom). [clausify(13)].
% 0.42/1.07 139 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | element(f3(A,B),the_carrier(A)) # label(d16_lattices) # label(axiom). [clausify(13)].
% 0.42/1.07 140 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | meet(A,B,f3(A,B)) != B | meet(A,f3(A,B),B) != B # label(d16_lattices) # label(axiom). [clausify(13)].
% 0.42/1.07 141 empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C) = meet(A,B,C) # label(d2_lattices) # label(axiom). [clausify(17)].
% 0.42/1.07 142 empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet(A,B,C),the_carrier(A)) # label(dt_k2_lattices) # label(axiom). [clausify(28)].
% 0.42/1.07 143 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet_commut(A,B,C),the_carrier(A)) # label(dt_k4_lattices) # label(axiom). [clausify(33)].
% 0.42/1.07 144 empty_carrier(A) | -meet_semilatt_str(A) | element(bottom_of_semilattstr(A),the_carrier(A)) # label(dt_k5_lattices) # label(axiom). [clausify(36)].
% 0.42/1.07 145 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(38)].
% 0.42/1.07 146 -meet_semilatt_str(A) | function(the_L_meet(A)) # label(dt_u1_lattices) # label(axiom). [clausify(45)].
% 0.42/1.07 147 -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u1_lattices) # label(axiom). [clausify(45)].
% 0.42/1.07 148 -meet_semilatt_str(A) | relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u1_lattices) # label(axiom). [clausify(45)].
% 0.42/1.07 Derived: empty_carrier(c1) | -meet_commutative(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | meet_commut(c1,B,A) = meet_commut(c1,A,B). [resolve(130,a,131,c)].
% 0.42/1.07 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | element(f1(c1),the_carrier(c1)). [resolve(130,a,132,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | meet(c1,f1(c1),A) = f1(c1). [resolve(130,a,133,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | meet(c1,A,f1(c1)) = f1(c1). [resolve(130,a,134,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | element(f2(c1,A),the_carrier(c1)). [resolve(130,a,135,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | meet(c1,A,f2(c1,A)) != A | meet(c1,f2(c1,A),A) != A. [resolve(130,a,136,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | bottom_of_semilattstr(c1) != A | -element(B,the_carrier(c1)) | meet(c1,A,B) = A. [resolve(130,a,137,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | bottom_of_semilattstr(c1) != A | -element(B,the_carrier(c1)) | meet(c1,B,A) = A. [resolve(130,a,138,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | bottom_of_semilattstr(c1) = A | element(f3(c1,A),the_carrier(c1)). [resolve(130,a,139,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | bottom_of_semilattstr(c1) = A | meet(c1,A,f3(c1,A)) != A | meet(c1,f3(c1,A),A) != A. [resolve(130,a,140,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | apply_binary_as_element(the_carrier(c1),the_carrier(c1),the_carrier(c1),the_L_meet(c1),A,B) = meet(c1,A,B). [resolve(130,a,141,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | element(meet(c1,A,B),the_carrier(c1)). [resolve(130,a,142,b)].
% 0.42/1.07 Derived: empty_carrier(c1) | -meet_commutative(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | element(meet_commut(c1,A,B),the_carrier(c1)). [resolve(130,a,143,c)].
% 0.42/1.07 Derived: empty_carrier(c1) | element(bottom_of_semilattstr(c1),the_carrier(c1)). [resolve(130,a,144,b)].
% 0.42/1.07 Derived: one_sorted_str(c1). [resolve(130,a,145,a)].
% 0.42/1.07 Derived: function(the_L_meet(c1)). [resolve(130,a,146,a)].
% 0.42/1.07 Derived: quasi_total(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(130,a,147,a)].
% 0.42/1.07 Derived: relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(130,a,148,a)].
% 0.42/1.07 149 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | function(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(66)].
% 0.42/1.07 150 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(66)].
% 0.42/1.07 151 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | v1_binop_1(the_L_meet(A),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(66)].
% 0.42/1.07 Derived: empty_carrier(c1) | -meet_commutative(c1) | v1_binop_1(the_L_meet(c1),the_carrier(c1)). [resolve(151,c,130,a)].
% 0.42/1.07 152 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(66)].
% 0.42/1.07 Derived: empty_carrier(c1) | -meet_commutative(c1) | v1_partfun1(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(152,c,130,a)].
% 0.42/1.08 153 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | function(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(68)].
% 0.42/1.08 154 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(68)].
% 0.42/1.08 155 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(68)].
% 0.42/1.08 Derived: empty_carrier(c1) | -meet_associative(c1) | v2_binop_1(the_L_meet(c1),the_carrier(c1)). [resolve(155,c,130,a)].
% 0.42/1.08 156 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(68)].
% 0.42/1.08 Derived: empty_carrier(c1) | -meet_associative(c1) | v1_partfun1(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(156,c,130,a)].
% 0.42/1.08 157 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet(A,B,C) = meet_commut(A,B,C) # label(redefinition_k4_lattices) # label(axiom). [clausify(84)].
% 0.42/1.08 Derived: empty_carrier(c1) | -meet_commutative(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | meet(c1,A,B) = meet_commut(c1,A,B). [resolve(157,c,130,a)].
% 0.42/1.08 158 meet_semilatt_str(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(118,a,102,g)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -meet_commutative(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | -element(E,the_carrier(latt_str_of(B,A,C))) | meet_commut(latt_str_of(B,A,C),E,D) = meet_commut(latt_str_of(B,A,C),D,E). [resolve(158,a,131,c)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lower_bounded_semilattstr(latt_str_of(B,A,C)) | element(f1(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,132,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lower_bounded_semilattstr(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | meet(latt_str_of(B,A,C),f1(latt_str_of(B,A,C)),D) = f1(latt_str_of(B,A,C)). [resolve(158,a,133,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lower_bounded_semilattstr(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | meet(latt_str_of(B,A,C),D,f1(latt_str_of(B,A,C))) = f1(latt_str_of(B,A,C)). [resolve(158,a,134,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | lower_bounded_semilattstr(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | element(f2(latt_str_of(B,A,C),D),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,135,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | lower_bounded_semilattstr(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | meet(latt_str_of(B,A,C),D,f2(latt_str_of(B,A,C),D)) != D | meet(latt_str_of(B,A,C),f2(latt_str_of(B,A,C),D),D) != D. [resolve(158,a,136,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lower_bounded_semilattstr(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | bottom_of_semilattstr(latt_str_of(B,A,C)) != D | -element(E,the_carrier(latt_str_of(B,A,C))) | meet(latt_str_of(B,A,C),D,E) = D. [resolve(158,a,137,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lower_bounded_semilattstr(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | bottom_of_semilattstr(latt_str_of(B,A,C)) != D | -element(E,the_carrier(latt_str_of(B,A,C))) | meet(latt_str_of(B,A,C),E,D) = D. [resolve(158,a,138,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lower_bounded_semilattstr(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | bottom_of_semilattstr(latt_str_of(B,A,C)) = D | element(f3(latt_str_of(B,A,C),D),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,139,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -lower_bounded_semilattstr(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | bottom_of_semilattstr(latt_str_of(B,A,C)) = D | meet(latt_str_of(B,A,C),D,f3(latt_str_of(B,A,C),D)) != D | meet(latt_str_of(B,A,C),f3(latt_str_of(B,A,C),D),D) != D. [resolve(158,a,140,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | -element(E,the_carrier(latt_str_of(B,A,C))) | apply_binary_as_element(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C)),the_L_meet(latt_str_of(B,A,C)),D,E) = meet(latt_str_of(B,A,C),D,E). [resolve(158,a,141,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | -element(E,the_carrier(latt_str_of(B,A,C))) | element(meet(latt_str_of(B,A,C),D,E),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,142,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -meet_commutative(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | -element(E,the_carrier(latt_str_of(B,A,C))) | element(meet_commut(latt_str_of(B,A,C),D,E),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,143,c)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | element(bottom_of_semilattstr(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,144,b)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | one_sorted_str(latt_str_of(B,A,C)). [resolve(158,a,145,a)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | function(the_L_meet(latt_str_of(B,A,C))). [resolve(158,a,146,a)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | quasi_total(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,147,a)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2_as_subset(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,148,a)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -meet_commutative(latt_str_of(B,A,C)) | v1_binop_1(the_L_meet(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,151,c)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -meet_commutative(latt_str_of(B,A,C)) | v1_partfun1(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,152,c)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -meet_associative(latt_str_of(B,A,C)) | v2_binop_1(the_L_meet(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,155,c)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -meet_associative(latt_str_of(B,A,C)) | v1_partfun1(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,156,c)].
% 0.42/1.08 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -meet_commutative(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | -element(E,the_carrier(latt_str_of(B,A,C))) | meet(latt_str_of(B,A,C),D,E) = meet_commut(latt_str_of(B,A,C),D,E). [resolve(158,a,157,c)].
% 0.42/1.08 159 meet_semilatt_str(boole_lattice(A)). [resolve(118,a,117,a)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | meet_commut(boole_lattice(A),C,B) = meet_commut(boole_lattice(A),B,C). [resolve(159,a,131,c)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -lower_bounded_semilattstr(boole_lattice(A)) | element(f1(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(159,a,132,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -lower_bounded_semilattstr(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | meet(boole_lattice(A),f1(boole_lattice(A)),B) = f1(boole_lattice(A)). [resolve(159,a,133,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -lower_bounded_semilattstr(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | meet(boole_lattice(A),B,f1(boole_lattice(A))) = f1(boole_lattice(A)). [resolve(159,a,134,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | lower_bounded_semilattstr(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | element(f2(boole_lattice(A),B),the_carrier(boole_lattice(A))). [resolve(159,a,135,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | lower_bounded_semilattstr(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | meet(boole_lattice(A),B,f2(boole_lattice(A),B)) != B | meet(boole_lattice(A),f2(boole_lattice(A),B),B) != B. [resolve(159,a,136,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -lower_bounded_semilattstr(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | bottom_of_semilattstr(boole_lattice(A)) != B | -element(C,the_carrier(boole_lattice(A))) | meet(boole_lattice(A),B,C) = B. [resolve(159,a,137,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -lower_bounded_semilattstr(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | bottom_of_semilattstr(boole_lattice(A)) != B | -element(C,the_carrier(boole_lattice(A))) | meet(boole_lattice(A),C,B) = B. [resolve(159,a,138,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -lower_bounded_semilattstr(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | bottom_of_semilattstr(boole_lattice(A)) = B | element(f3(boole_lattice(A),B),the_carrier(boole_lattice(A))). [resolve(159,a,139,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -lower_bounded_semilattstr(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | bottom_of_semilattstr(boole_lattice(A)) = B | meet(boole_lattice(A),B,f3(boole_lattice(A),B)) != B | meet(boole_lattice(A),f3(boole_lattice(A),B),B) != B. [resolve(159,a,140,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | apply_binary_as_element(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A)),the_L_meet(boole_lattice(A)),B,C) = meet(boole_lattice(A),B,C). [resolve(159,a,141,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | element(meet(boole_lattice(A),B,C),the_carrier(boole_lattice(A))). [resolve(159,a,142,b)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | element(meet_commut(boole_lattice(A),B,C),the_carrier(boole_lattice(A))). [resolve(159,a,143,c)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | element(bottom_of_semilattstr(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(159,a,144,b)].
% 0.42/1.08 Derived: one_sorted_str(boole_lattice(A)). [resolve(159,a,145,a)].
% 0.42/1.08 Derived: function(the_L_meet(boole_lattice(A))). [resolve(159,a,146,a)].
% 0.42/1.08 Derived: quasi_total(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(159,a,147,a)].
% 0.42/1.08 Derived: relation_of2_as_subset(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(159,a,148,a)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | v1_binop_1(the_L_meet(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(159,a,151,c)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | v1_partfun1(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(159,a,152,c)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -meet_associative(boole_lattice(A)) | v2_binop_1(the_L_meet(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(159,a,155,c)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -meet_associative(boole_lattice(A)) | v1_partfun1(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(159,a,156,c)].
% 0.42/1.08 Derived: empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | meet(boole_lattice(A),B,C) = meet_commut(boole_lattice(A),B,C). [resolve(159,a,157,c)].
% 0.42/1.08 160 meet_semilatt_str(c4). [resolve(120,a,118,a)].
% 0.42/1.08 Derived: empty_carrier(c4) | -meet_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | meet_commut(c4,B,A) = meet_commut(c4,A,B). [resolve(160,a,131,c)].
% 0.42/1.08 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | element(f1(c4),the_carrier(c4)). [resolve(160,a,132,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | meet(c4,f1(c4),A) = f1(c4). [resolve(160,a,133,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | meet(c4,A,f1(c4)) = f1(c4). [resolve(160,a,134,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | element(f2(c4,A),the_carrier(c4)). [resolve(160,a,135,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | meet(c4,A,f2(c4,A)) != A | meet(c4,f2(c4,A),A) != A. [resolve(160,a,136,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | bottom_of_semilattstr(c4) != A | -element(B,the_carrier(c4)) | meet(c4,A,B) = A. [resolve(160,a,137,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | bottom_of_semilattstr(c4) != A | -element(B,the_carrier(c4)) | meet(c4,B,A) = A. [resolve(160,a,138,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | bottom_of_semilattstr(c4) = A | element(f3(c4,A),the_carrier(c4)). [resolve(160,a,139,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | -lower_bounded_semilattstr(c4) | -element(A,the_carrier(c4)) | bottom_of_semilattstr(c4) = A | meet(c4,A,f3(c4,A)) != A | meet(c4,f3(c4,A),A) != A. [resolve(160,a,140,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | apply_binary_as_element(the_carrier(c4),the_carrier(c4),the_carrier(c4),the_L_meet(c4),A,B) = meet(c4,A,B). [resolve(160,a,141,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(meet(c4,A,B),the_carrier(c4)). [resolve(160,a,142,b)].
% 0.42/1.08 Derived: empty_carrier(c4) | -meet_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(meet_commut(c4,A,B),the_carrier(c4)). [resolve(160,a,143,c)].
% 0.42/1.08 Derived: empty_carrier(c4) | element(bottom_of_semilattstr(c4),the_carrier(c4)). [resolve(160,a,144,b)].
% 0.42/1.08 Derived: one_sorted_str(c4). [resolve(160,a,145,a)].
% 0.42/1.08 Derived: function(the_L_meet(c4)). [resolve(160,a,146,a)].
% 0.42/1.08 Derived: quasi_total(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(160,a,147,a)].
% 0.42/1.08 Derived: relation_of2_as_subset(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(160,a,148,a)].
% 0.42/1.08 Derived: empty_carrier(c4) | -meet_commutative(c4) | v1_binop_1(the_L_meet(c4),the_carrier(c4)). [resolve(160,a,151,c)].
% 0.42/1.08 Derived: empty_carrier(c4) | -meet_commutative(c4) | v1_partfun1(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(160,a,152,c)].
% 0.42/1.08 Derived: empty_carrier(c4) | -meet_associative(c4) | v2_binop_1(the_L_meet(c4),the_carrier(c4)). [resolve(160,a,155,c)].
% 0.42/1.08 Derived: empty_carrier(c4) | -meet_associative(c4) | v1_partfun1(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(160,a,156,c)].
% 0.42/1.09 Derived: empty_carrier(c4) | -meet_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | meet(c4,A,B) = meet_commut(c4,A,B). [resolve(160,a,157,c)].
% 0.42/1.09 161 meet_semilatt_str(c7). [resolve(121,a,118,a)].
% 0.42/1.09 Derived: empty_carrier(c7) | -meet_commutative(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | meet_commut(c7,B,A) = meet_commut(c7,A,B). [resolve(161,a,131,c)].
% 0.42/1.09 Derived: empty_carrier(c7) | -lower_bounded_semilattstr(c7) | element(f1(c7),the_carrier(c7)). [resolve(161,a,132,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | -lower_bounded_semilattstr(c7) | -element(A,the_carrier(c7)) | meet(c7,f1(c7),A) = f1(c7). [resolve(161,a,133,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | -lower_bounded_semilattstr(c7) | -element(A,the_carrier(c7)) | meet(c7,A,f1(c7)) = f1(c7). [resolve(161,a,134,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | lower_bounded_semilattstr(c7) | -element(A,the_carrier(c7)) | element(f2(c7,A),the_carrier(c7)). [resolve(161,a,135,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | lower_bounded_semilattstr(c7) | -element(A,the_carrier(c7)) | meet(c7,A,f2(c7,A)) != A | meet(c7,f2(c7,A),A) != A. [resolve(161,a,136,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | -lower_bounded_semilattstr(c7) | -element(A,the_carrier(c7)) | bottom_of_semilattstr(c7) != A | -element(B,the_carrier(c7)) | meet(c7,A,B) = A. [resolve(161,a,137,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | -lower_bounded_semilattstr(c7) | -element(A,the_carrier(c7)) | bottom_of_semilattstr(c7) != A | -element(B,the_carrier(c7)) | meet(c7,B,A) = A. [resolve(161,a,138,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | -lower_bounded_semilattstr(c7) | -element(A,the_carrier(c7)) | bottom_of_semilattstr(c7) = A | element(f3(c7,A),the_carrier(c7)). [resolve(161,a,139,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | -lower_bounded_semilattstr(c7) | -element(A,the_carrier(c7)) | bottom_of_semilattstr(c7) = A | meet(c7,A,f3(c7,A)) != A | meet(c7,f3(c7,A),A) != A. [resolve(161,a,140,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | apply_binary_as_element(the_carrier(c7),the_carrier(c7),the_carrier(c7),the_L_meet(c7),A,B) = meet(c7,A,B). [resolve(161,a,141,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | element(meet(c7,A,B),the_carrier(c7)). [resolve(161,a,142,b)].
% 0.42/1.09 Derived: empty_carrier(c7) | -meet_commutative(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | element(meet_commut(c7,A,B),the_carrier(c7)). [resolve(161,a,143,c)].
% 0.42/1.09 Derived: empty_carrier(c7) | element(bottom_of_semilattstr(c7),the_carrier(c7)). [resolve(161,a,144,b)].
% 0.42/1.09 Derived: one_sorted_str(c7). [resolve(161,a,145,a)].
% 0.42/1.09 Derived: function(the_L_meet(c7)). [resolve(161,a,146,a)].
% 0.42/1.09 Derived: quasi_total(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(161,a,147,a)].
% 0.42/1.09 Derived: relation_of2_as_subset(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(161,a,148,a)].
% 0.42/1.09 Derived: empty_carrier(c7) | -meet_commutative(c7) | v1_binop_1(the_L_meet(c7),the_carrier(c7)). [resolve(161,a,151,c)].
% 0.42/1.09 Derived: empty_carrier(c7) | -meet_commutative(c7) | v1_partfun1(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(161,a,152,c)].
% 0.42/1.09 Derived: empty_carrier(c7) | -meet_associative(c7) | v2_binop_1(the_L_meet(c7),the_carrier(c7)). [resolve(161,a,155,c)].
% 0.42/1.09 Derived: empty_carrier(c7) | -meet_associative(c7) | v1_partfun1(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(161,a,156,c)].
% 0.42/1.09 Derived: empty_carrier(c7) | -meet_commutative(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | meet(c7,A,B) = meet_commut(c7,A,B). [resolve(161,a,157,c)].
% 0.42/1.09 162 meet_semilatt_str(c9). [resolve(122,a,118,a)].
% 0.42/1.09 Derived: empty_carrier(c9) | -meet_commutative(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | meet_commut(c9,B,A) = meet_commut(c9,A,B). [resolve(162,a,131,c)].
% 0.42/1.09 Derived: empty_carrier(c9) | -lower_bounded_semilattstr(c9) | element(f1(c9),the_carrier(c9)). [resolve(162,a,132,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | -lower_bounded_semilattstr(c9) | -element(A,the_carrier(c9)) | meet(c9,f1(c9),A) = f1(c9). [resolve(162,a,133,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | -lower_bounded_semilattstr(c9) | -element(A,the_carrier(c9)) | meet(c9,A,f1(c9)) = f1(c9). [resolve(162,a,134,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | lower_bounded_semilattstr(c9) | -element(A,the_carrier(c9)) | element(f2(c9,A),the_carrier(c9)). [resolve(162,a,135,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | lower_bounded_semilattstr(c9) | -element(A,the_carrier(c9)) | meet(c9,A,f2(c9,A)) != A | meet(c9,f2(c9,A),A) != A. [resolve(162,a,136,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | -lower_bounded_semilattstr(c9) | -element(A,the_carrier(c9)) | bottom_of_semilattstr(c9) != A | -element(B,the_carrier(c9)) | meet(c9,A,B) = A. [resolve(162,a,137,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | -lower_bounded_semilattstr(c9) | -element(A,the_carrier(c9)) | bottom_of_semilattstr(c9) != A | -element(B,the_carrier(c9)) | meet(c9,B,A) = A. [resolve(162,a,138,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | -lower_bounded_semilattstr(c9) | -element(A,the_carrier(c9)) | bottom_of_semilattstr(c9) = A | element(f3(c9,A),the_carrier(c9)). [resolve(162,a,139,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | -lower_bounded_semilattstr(c9) | -element(A,the_carrier(c9)) | bottom_of_semilattstr(c9) = A | meet(c9,A,f3(c9,A)) != A | meet(c9,f3(c9,A),A) != A. [resolve(162,a,140,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | apply_binary_as_element(the_carrier(c9),the_carrier(c9),the_carrier(c9),the_L_meet(c9),A,B) = meet(c9,A,B). [resolve(162,a,141,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | element(meet(c9,A,B),the_carrier(c9)). [resolve(162,a,142,b)].
% 0.78/1.09 Derived: empty_carrier(c9) | -meet_commutative(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | element(meet_commut(c9,A,B),the_carrier(c9)). [resolve(162,a,143,c)].
% 0.78/1.09 Derived: empty_carrier(c9) | element(bottom_of_semilattstr(c9),the_carrier(c9)). [resolve(162,a,144,b)].
% 0.78/1.09 Derived: one_sorted_str(c9). [resolve(162,a,145,a)].
% 0.78/1.09 Derived: function(the_L_meet(c9)). [resolve(162,a,146,a)].
% 0.78/1.09 Derived: quasi_total(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(162,a,147,a)].
% 0.78/1.09 Derived: relation_of2_as_subset(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(162,a,148,a)].
% 0.78/1.09 Derived: empty_carrier(c9) | -meet_commutative(c9) | v1_binop_1(the_L_meet(c9),the_carrier(c9)). [resolve(162,a,151,c)].
% 0.78/1.09 Derived: empty_carrier(c9) | -meet_commutative(c9) | v1_partfun1(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(162,a,152,c)].
% 0.78/1.09 Derived: empty_carrier(c9) | -meet_associative(c9) | v2_binop_1(the_L_meet(c9),the_carrier(c9)). [resolve(162,a,155,c)].
% 0.78/1.09 Derived: empty_carrier(c9) | -meet_associative(c9) | v1_partfun1(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(162,a,156,c)].
% 0.78/1.09 Derived: empty_carrier(c9) | -meet_commutative(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | meet(c9,A,B) = meet_commut(c9,A,B). [resolve(162,a,157,c)].
% 0.78/1.09 163 meet_semilatt_str(c10). [resolve(123,a,118,a)].
% 0.78/1.09 Derived: empty_carrier(c10) | -meet_commutative(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | meet_commut(c10,B,A) = meet_commut(c10,A,B). [resolve(163,a,131,c)].
% 0.78/1.09 Derived: empty_carrier(c10) | -lower_bounded_semilattstr(c10) | element(f1(c10),the_carrier(c10)). [resolve(163,a,132,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | -lower_bounded_semilattstr(c10) | -element(A,the_carrier(c10)) | meet(c10,f1(c10),A) = f1(c10). [resolve(163,a,133,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | -lower_bounded_semilattstr(c10) | -element(A,the_carrier(c10)) | meet(c10,A,f1(c10)) = f1(c10). [resolve(163,a,134,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | lower_bounded_semilattstr(c10) | -element(A,the_carrier(c10)) | element(f2(c10,A),the_carrier(c10)). [resolve(163,a,135,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | lower_bounded_semilattstr(c10) | -element(A,the_carrier(c10)) | meet(c10,A,f2(c10,A)) != A | meet(c10,f2(c10,A),A) != A. [resolve(163,a,136,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | -lower_bounded_semilattstr(c10) | -element(A,the_carrier(c10)) | bottom_of_semilattstr(c10) != A | -element(B,the_carrier(c10)) | meet(c10,A,B) = A. [resolve(163,a,137,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | -lower_bounded_semilattstr(c10) | -element(A,the_carrier(c10)) | bottom_of_semilattstr(c10) != A | -element(B,the_carrier(c10)) | meet(c10,B,A) = A. [resolve(163,a,138,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | -lower_bounded_semilattstr(c10) | -element(A,the_carrier(c10)) | bottom_of_semilattstr(c10) = A | element(f3(c10,A),the_carrier(c10)). [resolve(163,a,139,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | -lower_bounded_semilattstr(c10) | -element(A,the_carrier(c10)) | bottom_of_semilattstr(c10) = A | meet(c10,A,f3(c10,A)) != A | meet(c10,f3(c10,A),A) != A. [resolve(163,a,140,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | apply_binary_as_element(the_carrier(c10),the_carrier(c10),the_carrier(c10),the_L_meet(c10),A,B) = meet(c10,A,B). [resolve(163,a,141,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | element(meet(c10,A,B),the_carrier(c10)). [resolve(163,a,142,b)].
% 0.78/1.09 Derived: empty_carrier(c10) | -meet_commutative(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | element(meet_commut(c10,A,B),the_carrier(c10)). [resolve(163,a,143,c)].
% 0.78/1.09 Derived: empty_carrier(c10) | element(bottom_of_semilattstr(c10),the_carrier(c10)). [resolve(163,a,144,b)].
% 0.78/1.09 Derived: one_sorted_str(c10). [resolve(163,a,145,a)].
% 0.78/1.09 Derived: function(the_L_meet(c10)). [resolve(163,a,146,a)].
% 0.78/1.09 Derived: quasi_total(the_L_meet(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(163,a,147,a)].
% 0.78/1.09 Derived: relation_of2_as_subset(the_L_meet(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(163,a,148,a)].
% 0.78/1.09 Derived: empty_carrier(c10) | -meet_commutative(c10) | v1_binop_1(the_L_meet(c10),the_carrier(c10)). [resolve(163,a,151,c)].
% 0.78/1.09 Derived: empty_carrier(c10) | -meet_commutative(c10) | v1_partfun1(the_L_meet(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(163,a,152,c)].
% 0.78/1.09 Derived: empty_carrier(c10) | -meet_associative(c10) | v2_binop_1(the_L_meet(c10),the_carrier(c10)). [resolve(163,a,155,c)].
% 0.78/1.09 Derived: empty_carrier(c10) | -meet_associative(c10) | v1_partfun1(the_L_meet(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(163,a,156,c)].
% 0.78/1.09 Derived: empty_carrier(c10) | -meet_commutative(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | meet(c10,A,B) = meet_commut(c10,A,B). [resolve(163,a,157,c)].
% 0.78/1.09 164 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -function(the_L_meet(A)) | apply(the_L_meet(A),ordered_pair(B,C)) = apply_binary(the_L_meet(A),B,C). [resolve(128,d,124,a)].
% 0.78/1.09 Derived: empty_carrier(c1) | -meet_commutative(c1) | -function(the_L_meet(c1)) | apply(the_L_meet(c1),ordered_pair(A,B)) = apply_binary(the_L_meet(c1),A,B). [resolve(164,c,130,a)].
% 0.78/1.09 Derived: empty_carrier(latt_str_of(A,B,C)) | -meet_commutative(latt_str_of(A,B,C)) | -function(the_L_meet(latt_str_of(A,B,C))) | apply(the_L_meet(latt_str_of(A,B,C)),ordered_pair(D,E)) = apply_binary(the_L_meet(latt_str_of(A,B,C)),D,E) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(164,c,158,a)].
% 0.78/1.09 Derived: empty_carrier(boole_lattice(A)) | -meet_commutative(boole_lattice(A)) | -function(the_L_meet(boole_lattice(A))) | apply(the_L_meet(boole_lattice(A)),ordered_pair(B,C)) = apply_binary(the_L_meet(boole_lattice(A)),B,C). [resolve(164,c,159,a)].
% 0.78/1.09 Derived: empty_carrier(c4) | -meet_commutative(c4) | -function(the_L_meet(c4)) | apply(the_L_meet(c4),ordered_pair(A,B)) = apply_binary(the_L_meet(c4),A,B). [resolve(164,c,160,a)].
% 0.78/1.11 Derived: empty_carrier(c7) | -meet_commutative(c7) | -function(the_L_meet(c7)) | apply(the_L_meet(c7),ordered_pair(A,B)) = apply_binary(the_L_meet(c7),A,B). [resolve(164,c,161,a)].
% 0.78/1.11 Derived: empty_carrier(c9) | -meet_commutative(c9) | -function(the_L_meet(c9)) | apply(the_L_meet(c9),ordered_pair(A,B)) = apply_binary(the_L_meet(c9),A,B). [resolve(164,c,162,a)].
% 0.78/1.11 Derived: empty_carrier(c10) | -meet_commutative(c10) | -function(the_L_meet(c10)) | apply(the_L_meet(c10),ordered_pair(A,B)) = apply_binary(the_L_meet(c10),A,B). [resolve(164,c,163,a)].
% 0.78/1.11 165 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | -function(the_L_meet(A)) | apply(the_L_meet(A),ordered_pair(B,C)) = apply_binary(the_L_meet(A),B,C). [resolve(129,d,124,a)].
% 0.78/1.11 Derived: empty_carrier(c1) | -meet_associative(c1) | -function(the_L_meet(c1)) | apply(the_L_meet(c1),ordered_pair(A,B)) = apply_binary(the_L_meet(c1),A,B). [resolve(165,c,130,a)].
% 0.78/1.11 Derived: empty_carrier(latt_str_of(A,B,C)) | -meet_associative(latt_str_of(A,B,C)) | -function(the_L_meet(latt_str_of(A,B,C))) | apply(the_L_meet(latt_str_of(A,B,C)),ordered_pair(D,E)) = apply_binary(the_L_meet(latt_str_of(A,B,C)),D,E) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(165,c,158,a)].
% 0.78/1.11 Derived: empty_carrier(boole_lattice(A)) | -meet_associative(boole_lattice(A)) | -function(the_L_meet(boole_lattice(A))) | apply(the_L_meet(boole_lattice(A)),ordered_pair(B,C)) = apply_binary(the_L_meet(boole_lattice(A)),B,C). [resolve(165,c,159,a)].
% 0.78/1.11 Derived: empty_carrier(c4) | -meet_associative(c4) | -function(the_L_meet(c4)) | apply(the_L_meet(c4),ordered_pair(A,B)) = apply_binary(the_L_meet(c4),A,B). [resolve(165,c,160,a)].
% 0.78/1.11 Derived: empty_carrier(c7) | -meet_associative(c7) | -function(the_L_meet(c7)) | apply(the_L_meet(c7),ordered_pair(A,B)) = apply_binary(the_L_meet(c7),A,B). [resolve(165,c,161,a)].
% 0.78/1.11 Derived: empty_carrier(c9) | -meet_associative(c9) | -function(the_L_meet(c9)) | apply(the_L_meet(c9),ordered_pair(A,B)) = apply_binary(the_L_meet(c9),A,B). [resolve(165,c,162,a)].
% 0.78/1.11 Derived: empty_carrier(c10) | -meet_associative(c10) | -function(the_L_meet(c10)) | apply(the_L_meet(c10),ordered_pair(A,B)) = apply_binary(the_L_meet(c10),A,B). [resolve(165,c,163,a)].
% 0.78/1.11 166 join_semilatt_str(c3) # label(existence_l2_lattices) # label(axiom). [clausify(50)].
% 0.78/1.11 167 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C) = join(A,B,C) # label(d1_lattices) # label(axiom). [clausify(16)].
% 0.78/1.11 168 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(join(A,B,C),the_carrier(A)) # label(dt_k1_lattices) # label(axiom). [clausify(23)].
% 0.78/1.11 169 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(40)].
% 0.78/1.11 170 -join_semilatt_str(A) | function(the_L_join(A)) # label(dt_u2_lattices) # label(axiom). [clausify(47)].
% 0.78/1.11 171 -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u2_lattices) # label(axiom). [clausify(47)].
% 0.78/1.11 172 -join_semilatt_str(A) | relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u2_lattices) # label(axiom). [clausify(47)].
% 0.78/1.11 Derived: empty_carrier(c3) | -element(A,the_carrier(c3)) | -element(B,the_carrier(c3)) | apply_binary_as_element(the_carrier(c3),the_carrier(c3),the_carrier(c3),the_L_join(c3),A,B) = join(c3,A,B). [resolve(166,a,167,b)].
% 0.78/1.11 Derived: empty_carrier(c3) | -element(A,the_carrier(c3)) | -element(B,the_carrier(c3)) | element(join(c3,A,B),the_carrier(c3)). [resolve(166,a,168,b)].
% 0.78/1.11 Derived: one_sorted_str(c3). [resolve(166,a,169,a)].
% 0.78/1.11 Derived: function(the_L_join(c3)). [resolve(166,a,170,a)].
% 0.78/1.11 Derived: quasi_total(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(166,a,171,a)].
% 0.78/1.11 Derived: relation_of2_as_subset(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(166,a,172,a)].
% 0.78/1.11 173 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | function(the_L_join(A)) # label(fc2_lattice2) # label(axiom). [clausify(58)].
% 0.78/1.11 174 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(58)].
% 0.78/1.11 175 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | v1_binop_1(the_L_join(A),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(58)].
% 0.78/1.11 Derived: empty_carrier(c3) | -join_commutative(c3) | v1_binop_1(the_L_join(c3),the_carrier(c3)). [resolve(175,c,166,a)].
% 0.78/1.11 176 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc2_lattice2) # label(axiom). [clausify(58)].
% 0.78/1.11 Derived: empty_carrier(c3) | -join_commutative(c3) | v1_partfun1(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(176,c,166,a)].
% 0.78/1.11 177 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | function(the_L_join(A)) # label(fc3_lattice2) # label(axiom). [clausify(62)].
% 0.78/1.11 178 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc3_lattice2) # label(axiom). [clausify(62)].
% 0.78/1.11 179 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | v2_binop_1(the_L_join(A),the_carrier(A)) # label(fc3_lattice2) # label(axiom). [clausify(62)].
% 0.78/1.11 Derived: empty_carrier(c3) | -join_associative(c3) | v2_binop_1(the_L_join(c3),the_carrier(c3)). [resolve(179,c,166,a)].
% 0.78/1.11 180 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc3_lattice2) # label(axiom). [clausify(62)].
% 0.78/1.11 Derived: empty_carrier(c3) | -join_associative(c3) | v1_partfun1(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(180,c,166,a)].
% 0.78/1.11 181 join_semilatt_str(latt_str_of(A,B,C)) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(119,a,102,g)].
% 0.78/1.11 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | -element(E,the_carrier(latt_str_of(B,A,C))) | apply_binary_as_element(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C)),the_L_join(latt_str_of(B,A,C)),D,E) = join(latt_str_of(B,A,C),D,E). [resolve(181,a,167,b)].
% 0.78/1.11 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -element(D,the_carrier(latt_str_of(B,A,C))) | -element(E,the_carrier(latt_str_of(B,A,C))) | element(join(latt_str_of(B,A,C),D,E),the_carrier(latt_str_of(B,A,C))). [resolve(181,a,168,b)].
% 0.78/1.11 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | function(the_L_join(latt_str_of(B,A,C))). [resolve(181,a,170,a)].
% 0.78/1.11 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | quasi_total(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(181,a,171,a)].
% 0.78/1.11 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2_as_subset(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(181,a,172,a)].
% 0.78/1.11 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -join_commutative(latt_str_of(B,A,C)) | v1_binop_1(the_L_join(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))). [resolve(181,a,175,c)].
% 0.78/1.11 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -join_commutative(latt_str_of(B,A,C)) | v1_partfun1(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(181,a,176,c)].
% 0.78/1.11 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -join_associative(latt_str_of(B,A,C)) | v2_binop_1(the_L_join(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))). [resolve(181,a,179,c)].
% 0.78/1.11 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -join_associative(latt_str_of(B,A,C)) | v1_partfun1(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(181,a,180,c)].
% 0.78/1.11 182 join_semilatt_str(boole_lattice(A)). [resolve(119,a,117,a)].
% 0.78/1.11 Derived: empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | apply_binary_as_element(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A)),the_L_join(boole_lattice(A)),B,C) = join(boole_lattice(A),B,C). [resolve(182,a,167,b)].
% 0.78/1.11 Derived: empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | element(join(boole_lattice(A),B,C),the_carrier(boole_lattice(A))). [resolve(182,a,168,b)].
% 0.78/1.11 Derived: function(the_L_join(boole_lattice(A))). [resolve(182,a,170,a)].
% 0.78/1.11 Derived: quasi_total(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(182,a,171,a)].
% 0.78/1.11 Derived: relation_of2_as_subset(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(182,a,172,a)].
% 0.78/1.11 Derived: empty_carrier(boole_lattice(A)) | -join_commutative(boole_lattice(A)) | v1_binop_1(the_L_join(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(182,a,175,c)].
% 0.78/1.11 Derived: empty_carrier(boole_lattice(A)) | -join_commutative(boole_lattice(A)) | v1_partfun1(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(182,a,176,c)].
% 0.78/1.11 Derived: empty_carrier(boole_lattice(A)) | -join_associative(boole_lattice(A)) | v2_binop_1(the_L_join(boole_lattice(A)),the_carrier(boole_lattice(A))). [resolve(182,a,179,c)].
% 0.78/1.11 Derived: empty_carrier(boole_lattice(A)) | -join_associative(boole_lattice(A)) | v1_partfun1(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(182,a,180,c)].
% 0.78/1.12 183 join_semilatt_str(c4). [resolve(120,a,119,a)].
% 0.78/1.12 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | apply_binary_as_element(the_carrier(c4),the_carrier(c4),the_carrier(c4),the_L_join(c4),A,B) = join(c4,A,B). [resolve(183,a,167,b)].
% 0.78/1.12 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(join(c4,A,B),the_carrier(c4)). [resolve(183,a,168,b)].
% 0.78/1.12 Derived: function(the_L_join(c4)). [resolve(183,a,170,a)].
% 0.78/1.12 Derived: quasi_total(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(183,a,171,a)].
% 0.78/1.12 Derived: relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(183,a,172,a)].
% 0.78/1.12 Derived: empty_carrier(c4) | -join_commutative(c4) | v1_binop_1(the_L_join(c4),the_carrier(c4)). [resolve(183,a,175,c)].
% 0.78/1.12 Derived: empty_carrier(c4) | -join_commutative(c4) | v1_partfun1(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(183,a,176,c)].
% 0.78/1.12 Derived: empty_carrier(c4) | -join_associative(c4) | v2_binop_1(the_L_join(c4),the_carrier(c4)). [resolve(183,a,179,c)].
% 0.78/1.12 Derived: empty_carrier(c4) | -join_associative(c4) | v1_partfun1(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(183,a,180,c)].
% 0.78/1.12 184 join_semilatt_str(c7). [resolve(121,a,119,a)].
% 0.78/1.12 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | apply_binary_as_element(the_carrier(c7),the_carrier(c7),the_carrier(c7),the_L_join(c7),A,B) = join(c7,A,B). [resolve(184,a,167,b)].
% 0.78/1.12 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | element(join(c7,A,B),the_carrier(c7)). [resolve(184,a,168,b)].
% 0.78/1.12 Derived: function(the_L_join(c7)). [resolve(184,a,170,a)].
% 0.78/1.12 Derived: quasi_total(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(184,a,171,a)].
% 0.78/1.12 Derived: relation_of2_as_subset(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(184,a,172,a)].
% 0.78/1.12 Derived: empty_carrier(c7) | -join_commutative(c7) | v1_binop_1(the_L_join(c7),the_carrier(c7)). [resolve(184,a,175,c)].
% 0.78/1.12 Derived: empty_carrier(c7) | -join_commutative(c7) | v1_partfun1(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(184,a,176,c)].
% 0.78/1.12 Derived: empty_carrier(c7) | -join_associative(c7) | v2_binop_1(the_L_join(c7),the_carrier(c7)). [resolve(184,a,179,c)].
% 0.78/1.12 Derived: empty_carrier(c7) | -join_associative(c7) | v1_partfun1(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(184,a,180,c)].
% 0.78/1.12 185 join_semilatt_str(c9). [resolve(122,a,119,a)].
% 0.78/1.12 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | apply_binary_as_element(the_carrier(c9),the_carrier(c9),the_carrier(c9),the_L_join(c9),A,B) = join(c9,A,B). [resolve(185,a,167,b)].
% 0.78/1.12 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | element(join(c9,A,B),the_carrier(c9)). [resolve(185,a,168,b)].
% 0.78/1.12 Derived: function(the_L_join(c9)). [resolve(185,a,170,a)].
% 0.78/1.12 Derived: quasi_total(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(185,a,171,a)].
% 0.78/1.12 Derived: relation_of2_as_subset(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(185,a,172,a)].
% 0.78/1.12 Derived: empty_carrier(c9) | -join_commutative(c9) | v1_binop_1(the_L_join(c9),the_carrier(c9)). [resolve(185,a,175,c)].
% 0.78/1.12 Derived: empty_carrier(c9) | -join_commutative(c9) | v1_partfun1(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(185,a,176,c)].
% 0.78/1.12 Derived: empty_carrier(c9) | -join_associative(c9) | v2_binop_1(the_L_join(c9),the_carrier(c9)). [resolve(185,a,179,c)].
% 0.78/1.12 Derived: empty_carrier(c9) | -join_associative(c9) | v1_partfun1(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(185,a,180,c)].
% 0.78/1.12 186 join_semilatt_str(c10). [resolve(123,a,119,a)].
% 0.78/1.12 Derived: empty_carrier(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | apply_binary_as_element(the_carrier(c10),the_carrier(c10),the_carrier(c10),the_L_join(c10),A,B) = join(c10,A,B). [resolve(186,a,167,b)].
% 0.78/1.12 Derived: empty_carrier(c10) | -element(A,the_carrier(c10)) | -element(B,the_carrier(c10)) | element(join(c10,A,B),the_carrier(c10)). [resolve(186,a,168,b)].
% 0.78/1.12 Derived: function(the_L_join(c10)). [resolve(186,a,170,a)].
% 0.78/1.12 Derived: quasi_total(the_L_join(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(186,a,171,a)].
% 0.78/1.12 Derived: relation_of2_as_subset(the_L_join(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(186,a,172,a)].
% 0.78/1.12 Derived: empty_carrier(c10) | -join_commutative(c10) | v1_binop_1(the_L_join(c10),the_carrier(c10)). [resolve(186,a,175,c)].
% 0.78/1.12 Derived: empty_carrier(c10) | -join_commutative(c10) | v1_partfun1(the_L_join(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(186,a,176,c)].
% 0.78/1.12 Derived: empty_carrier(c10) | -join_associative(c10) | v2_binop_1(the_L_join(c10),the_carrier(c10)). [resolve(186,a,179,c)].
% 0.78/1.12 Derived: empty_carrier(c10) | -join_associative(c10) | v1_partfun1(the_L_join(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(186,a,180,c)].
% 0.78/1.12 187 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | -function(the_L_join(A)) | apply(the_L_join(A),ordered_pair(B,C)) = apply_binary(the_L_join(A),B,C). [resolve(126,d,124,a)].
% 0.78/1.12 Derived: empty_carrier(c3) | -join_commutative(c3) | -function(the_L_join(c3)) | apply(the_L_join(c3),ordered_pair(A,B)) = apply_binary(the_L_join(c3),A,B). [resolve(187,c,166,a)].
% 0.78/1.12 Derived: empty_carrier(latt_str_of(A,B,C)) | -join_commutative(latt_str_of(A,B,C)) | -function(the_L_join(latt_str_of(A,B,C))) | apply(the_L_join(latt_str_of(A,B,C)),ordered_pair(D,E)) = apply_binary(the_L_join(latt_str_of(A,B,C)),D,E) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(187,c,181,a)].
% 0.78/1.12 Derived: empty_carrier(boole_lattice(A)) | -join_commutative(boole_lattice(A)) | -function(the_L_join(boole_lattice(A))) | apply(the_L_join(boole_lattice(A)),ordered_pair(B,C)) = apply_binary(the_L_join(boole_lattice(A)),B,C). [resolve(187,c,182,a)].
% 0.78/1.12 Derived: empty_carrier(c4) | -join_commutative(c4) | -function(the_L_join(c4)) | apply(the_L_join(c4),ordered_pair(A,B)) = apply_binary(the_L_join(c4),A,B). [resolve(187,c,183,a)].
% 0.78/1.12 Derived: empty_carrier(c7) | -join_commutative(c7) | -function(the_L_join(c7)) | apply(the_L_join(c7),ordered_pair(A,B)) = apply_binary(the_L_join(c7),A,B). [resolve(187,c,184,a)].
% 0.78/1.12 Derived: empty_carrier(c9) | -join_commutative(c9) | -function(the_L_join(c9)) | apply(the_L_join(c9),ordered_pair(A,B)) = apply_binary(the_L_join(c9),A,B). [resolve(187,c,185,a)].
% 0.78/1.12 Derived: empty_carrier(c10) | -join_commutative(c10) | -function(the_L_join(c10)) | apply(the_L_join(c10),ordered_pair(A,B)) = apply_binary(the_L_join(c10),A,B). [resolve(187,c,186,a)].
% 0.78/1.12 188 empty_carrier(A) | -join_associative(A) | -join_semilatt_str(A) | -function(the_L_join(A)) | apply(the_L_join(A),ordered_pair(B,C)) = apply_binary(the_L_join(A),B,C). [resolve(127,d,124,a)].
% 0.78/1.12 Derived: empty_carrier(c3) | -join_associative(c3) | -function(the_L_join(c3)) | apply(the_L_join(c3),ordered_pair(A,B)) = apply_binary(the_L_join(c3),A,B). [resolve(188,c,166,a)].
% 0.78/1.12 Derived: empty_carrier(latt_str_of(A,B,C)) | -join_associative(latt_str_of(A,B,C)) | -function(the_L_join(latt_str_of(A,B,C))) | apply(the_L_join(latt_str_of(A,B,C)),ordered_pair(D,E)) = apply_binary(the_L_join(latt_str_of(A,B,C)),D,E) | -function(B) | -quasi_total(B,cartesian_product2(A,A),A) | -relation_of2(B,cartesian_product2(A,A),A) | -function(C) | -quasi_total(C,cartesian_product2(A,A),A) | -relation_of2(C,cartesian_product2(A,A),A). [resolve(188,c,181,a)].
% 0.78/1.14 Derived: empty_carrier(boole_lattice(A)) | -join_associative(boole_lattice(A)) | -function(the_L_join(boole_lattice(A))) | apply(the_L_join(boole_lattice(A)),ordered_pair(B,C)) = apply_binary(the_L_join(boole_lattice(A)),B,C). [resolve(188,c,182,a)].
% 0.78/1.14 Derived: empty_carrier(c4) | -join_associative(c4) | -function(the_L_join(c4)) | apply(the_L_join(c4),ordered_pair(A,B)) = apply_binary(the_L_join(c4),A,B). [resolve(188,c,183,a)].
% 0.78/1.14 Derived: empty_carrier(c7) | -join_associative(c7) | -function(the_L_join(c7)) | apply(the_L_join(c7),ordered_pair(A,B)) = apply_binary(the_L_join(c7),A,B). [resolve(188,c,184,a)].
% 0.78/1.14 Derived: empty_carrier(c9) | -join_associative(c9) | -function(the_L_join(c9)) | apply(the_L_join(c9),ordered_pair(A,B)) = apply_binary(the_L_join(c9),A,B). [resolve(188,c,185,a)].
% 0.78/1.14 Derived: empty_carrier(c10) | -join_associative(c10) | -function(the_L_join(c10)) | apply(the_L_join(c10),ordered_pair(A,B)) = apply_binary(the_L_join(c10),A,B). [resolve(188,c,186,a)].
% 0.78/1.14 189 relation_of2_as_subset(f8(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(54)].
% 0.78/1.14 190 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(44)].
% 0.78/1.14 Derived: element(f8(A,B),powerset(cartesian_product2(A,B))). [resolve(189,a,190,a)].
% 0.78/1.14 191 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(87)].
% 0.78/1.14 Derived: relation_of2(f8(A,B),A,B). [resolve(191,a,189,a)].
% 0.78/1.14 192 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(87)].
% 0.78/1.14 Derived: -relation_of2(A,B,C) | element(A,powerset(cartesian_product2(B,C))). [resolve(192,a,190,a)].
% 0.78/1.14 193 relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(130,a,148,a)].
% 0.78/1.14 Derived: element(the_L_meet(c1),powerset(cartesian_product2(cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)))). [resolve(193,a,190,a)].
% 0.78/1.14 Derived: relation_of2(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(193,a,191,a)].
% 0.78/1.14 194 -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2_as_subset(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(158,a,148,a)].
% 0.78/1.14 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | element(the_L_meet(latt_str_of(B,A,C)),powerset(cartesian_product2(cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))))). [resolve(194,g,190,a)].
% 0.78/1.14 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2(the_L_meet(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(194,g,191,a)].
% 0.78/1.14 195 relation_of2_as_subset(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(159,a,148,a)].
% 0.78/1.14 Derived: element(the_L_meet(boole_lattice(A)),powerset(cartesian_product2(cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))))). [resolve(195,a,190,a)].
% 0.78/1.14 Derived: relation_of2(the_L_meet(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(195,a,191,a)].
% 0.78/1.15 196 relation_of2_as_subset(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(160,a,148,a)].
% 0.78/1.15 Derived: element(the_L_meet(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(196,a,190,a)].
% 0.78/1.15 Derived: relation_of2(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(196,a,191,a)].
% 0.78/1.15 197 relation_of2_as_subset(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(161,a,148,a)].
% 0.78/1.15 Derived: element(the_L_meet(c7),powerset(cartesian_product2(cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)))). [resolve(197,a,190,a)].
% 0.78/1.15 Derived: relation_of2(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(197,a,191,a)].
% 0.78/1.15 198 relation_of2_as_subset(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(162,a,148,a)].
% 0.78/1.15 Derived: element(the_L_meet(c9),powerset(cartesian_product2(cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)))). [resolve(198,a,190,a)].
% 0.78/1.15 Derived: relation_of2(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(198,a,191,a)].
% 0.78/1.15 199 relation_of2_as_subset(the_L_meet(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(163,a,148,a)].
% 0.78/1.15 Derived: element(the_L_meet(c10),powerset(cartesian_product2(cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)))). [resolve(199,a,190,a)].
% 0.78/1.15 Derived: relation_of2(the_L_meet(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(199,a,191,a)].
% 0.78/1.15 200 relation_of2_as_subset(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(166,a,172,a)].
% 0.78/1.15 Derived: element(the_L_join(c3),powerset(cartesian_product2(cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)))). [resolve(200,a,190,a)].
% 0.78/1.15 Derived: relation_of2(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(200,a,191,a)].
% 0.78/1.15 201 -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2_as_subset(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(181,a,172,a)].
% 0.78/1.15 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | element(the_L_join(latt_str_of(B,A,C)),powerset(cartesian_product2(cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))))). [resolve(201,g,190,a)].
% 0.78/1.15 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | relation_of2(the_L_join(latt_str_of(B,A,C)),cartesian_product2(the_carrier(latt_str_of(B,A,C)),the_carrier(latt_str_of(B,A,C))),the_carrier(latt_str_of(B,A,C))). [resolve(201,g,191,a)].
% 0.78/1.15 202 relation_of2_as_subset(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(182,a,172,a)].
% 0.78/1.15 Derived: element(the_L_join(boole_lattice(A)),powerset(cartesian_product2(cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))))). [resolve(202,a,190,a)].
% 0.78/1.15 Derived: relation_of2(the_L_join(boole_lattice(A)),cartesian_product2(the_carrier(boole_lattice(A)),the_carrier(boole_lattice(A))),the_carrier(boole_lattice(A))). [resolve(202,a,191,a)].
% 0.78/1.15 203 relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(183,a,172,a)].
% 0.78/1.16 Derived: element(the_L_join(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(203,a,190,a)].
% 0.78/1.16 Derived: relation_of2(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(203,a,191,a)].
% 0.78/1.16 204 relation_of2_as_subset(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(184,a,172,a)].
% 0.78/1.16 Derived: element(the_L_join(c7),powerset(cartesian_product2(cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)))). [resolve(204,a,190,a)].
% 0.78/1.16 Derived: relation_of2(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(204,a,191,a)].
% 0.78/1.16 205 relation_of2_as_subset(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(185,a,172,a)].
% 0.78/1.16 Derived: element(the_L_join(c9),powerset(cartesian_product2(cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)))). [resolve(205,a,190,a)].
% 0.78/1.16 Derived: relation_of2(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(205,a,191,a)].
% 0.78/1.16 206 relation_of2_as_subset(the_L_join(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(186,a,172,a)].
% 0.78/1.16 Derived: element(the_L_join(c10),powerset(cartesian_product2(cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)))). [resolve(206,a,190,a)].
% 0.78/1.16 Derived: relation_of2(the_L_join(c10),cartesian_product2(the_carrier(c10),the_carrier(c10)),the_carrier(c10)). [resolve(206,a,191,a)].
% 0.78/1.16 207 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(56)].
% 0.78/1.16 208 one_sorted_str(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(49)].
% 0.78/1.16 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(207,b,208,a)].
% 0.78/1.16 209 one_sorted_str(c8) # label(rc3_struct_0) # label(axiom). [clausify(79)].
% 0.78/1.16 Derived: empty_carrier(c8) | -empty(the_carrier(c8)). [resolve(209,a,207,b)].
% 0.78/1.16 210 empty_carrier(A) | -one_sorted_str(A) | element(f11(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(80)].
% 0.78/1.16 Derived: empty_carrier(c2) | element(f11(c2),powerset(the_carrier(c2))). [resolve(210,b,208,a)].
% 0.78/1.16 Derived: empty_carrier(c8) | element(f11(c8),powerset(the_carrier(c8))). [resolve(210,b,209,a)].
% 0.78/1.16 211 empty_carrier(A) | -one_sorted_str(A) | -empty(f11(A)) # label(rc5_struct_0) # label(axiom). [clausify(80)].
% 0.78/1.16 Derived: empty_carrier(c2) | -empty(f11(c2)). [resolve(211,b,208,a)].
% 0.78/1.16 Derived: empty_carrier(c8) | -empty(f11(c8)). [resolve(211,b,209,a)].
% 0.78/1.16 212 one_sorted_str(c1). [resolve(130,a,145,a)].
% 0.78/1.16 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(212,a,207,b)].
% 0.78/1.16 Derived: empty_carrier(c1) | element(f11(c1),powerset(the_carrier(c1))). [resolve(212,a,210,b)].
% 0.78/1.16 Derived: empty_carrier(c1) | -empty(f11(c1)). [resolve(212,a,211,b)].
% 0.78/1.16 213 -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | one_sorted_str(latt_str_of(B,A,C)). [resolve(158,a,145,a)].
% 0.78/1.16 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -empty(the_carrier(latt_str_of(B,A,C))). [resolve(213,g,207,b)].
% 0.78/1.16 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | element(f11(latt_str_of(B,A,C)),powerset(the_carrier(latt_str_of(B,A,C)))). [resolve(213,g,210,b)].
% 0.78/1.16 Derived: -function(A) | -quasi_total(A,cartesian_product2(B,B),B) | -relation_of2(A,cartesian_product2(B,B),B) | -function(C) | -quasi_total(C,cartesian_product2(B,B),B) | -relation_of2(C,cartesian_product2(B,B),B) | empty_carrier(latt_str_of(B,A,C)) | -empty(f11(latt_str_of(B,A,C))). [resolve(213,g,211,b)].
% 1.82/2.10 214 one_sorted_str(boole_lattice(A)). [resolve(159,a,145,a)].
% 1.82/2.10 Derived: empty_carrier(boole_lattice(A)) | -empty(the_carrier(boole_lattice(A))). [resolve(214,a,207,b)].
% 1.82/2.10 Derived: empty_carrier(boole_lattice(A)) | element(f11(boole_lattice(A)),powerset(the_carrier(boole_lattice(A)))). [resolve(214,a,210,b)].
% 1.82/2.10 Derived: empty_carrier(boole_lattice(A)) | -empty(f11(boole_lattice(A))). [resolve(214,a,211,b)].
% 1.82/2.10 215 one_sorted_str(c4). [resolve(160,a,145,a)].
% 1.82/2.10 Derived: empty_carrier(c4) | -empty(the_carrier(c4)). [resolve(215,a,207,b)].
% 1.82/2.10 Derived: empty_carrier(c4) | element(f11(c4),powerset(the_carrier(c4))). [resolve(215,a,210,b)].
% 1.82/2.10 Derived: empty_carrier(c4) | -empty(f11(c4)). [resolve(215,a,211,b)].
% 1.82/2.10 216 one_sorted_str(c7). [resolve(161,a,145,a)].
% 1.82/2.10 Derived: empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(216,a,207,b)].
% 1.82/2.10 Derived: empty_carrier(c7) | element(f11(c7),powerset(the_carrier(c7))). [resolve(216,a,210,b)].
% 1.82/2.10 Derived: empty_carrier(c7) | -empty(f11(c7)). [resolve(216,a,211,b)].
% 1.82/2.10 217 one_sorted_str(c9). [resolve(162,a,145,a)].
% 1.82/2.10 Derived: empty_carrier(c9) | -empty(the_carrier(c9)). [resolve(217,a,207,b)].
% 1.82/2.10 Derived: empty_carrier(c9) | element(f11(c9),powerset(the_carrier(c9))). [resolve(217,a,210,b)].
% 1.82/2.10 Derived: empty_carrier(c9) | -empty(f11(c9)). [resolve(217,a,211,b)].
% 1.82/2.10 218 one_sorted_str(c10). [resolve(163,a,145,a)].
% 1.82/2.10 Derived: empty_carrier(c10) | -empty(the_carrier(c10)). [resolve(218,a,207,b)].
% 1.82/2.10 Derived: empty_carrier(c10) | element(f11(c10),powerset(the_carrier(c10))). [resolve(218,a,210,b)].
% 1.82/2.10 Derived: empty_carrier(c10) | -empty(f11(c10)). [resolve(218,a,211,b)].
% 1.82/2.10 219 one_sorted_str(c3). [resolve(166,a,169,a)].
% 1.82/2.10 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(219,a,207,b)].
% 1.82/2.10 Derived: empty_carrier(c3) | element(f11(c3),powerset(the_carrier(c3))). [resolve(219,a,210,b)].
% 1.82/2.10 Derived: empty_carrier(c3) | -empty(f11(c3)). [resolve(219,a,211,b)].
% 1.82/2.10 220 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(95)].
% 1.82/2.10 221 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(88)].
% 1.82/2.10 222 subset(empty_set,A) # label(t2_xboole_1) # label(axiom). [clausify(94)].
% 1.82/2.10 223 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(95)].
% 1.82/2.10 Derived: element(A,powerset(A)). [resolve(220,b,221,a)].
% 1.82/2.10 Derived: element(empty_set,powerset(A)). [resolve(220,b,222,a)].
% 1.82/2.10
% 1.82/2.10 ============================== end predicate elimination =============
% 1.82/2.10
% 1.82/2.10 Auto_denials: (non-Horn, no changes).
% 1.82/2.10
% 1.82/2.10 Term ordering decisions:
% 1.82/2.10 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. cartesian_product2=1. ordered_pair=1. apply=1. set_union2=1. set_intersection2=1. unordered_pair=1. f2=1. f3=1. f4=1. f5=1. f6=1. f8=1. the_carrier=1. boole_lattice=1. powerset=1. the_L_join=1. the_L_meet=1. bottom_of_semilattstr=1. singleton=1. f1=1. f7=1. f9=1. f10=1. f11=1. latt_str_of=1. meet=1. apply_binary=1. meet_commut=1. subset_intersection2=1. subset_union2=1. join=1. apply_binary_as_element=1.
% 1.82/2.10
% 1.82/2.10 ============================== end of process initial clauses ========
% 1.82/2.10
% 1.82/2.10 ============================== CLAUSES FOR SEARCH ====================
% 1.82/2.10
% 1.82/2.10 ============================== end of clauses for search =============
% 1.82/2.10
% 1.82/2.10 ============================== SEARCH ================================
% 1.82/2.10
% 1.82/2.10 % Starting search at 0.23 seconds.
% 1.82/2.10
% 1.82/2.10 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 217 (0.00 of 0.54 sec).
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=36.000, iters=3381
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=35.000, iters=3425
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=34.000, iters=3351
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=27.000, iters=4146
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=25.000, iters=3858
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=24.000, iters=4297
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=22.000, iters=3569
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=21.000, iters=3498
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=20.000, iters=3354
% 1.82/2.10
% 1.82/2.10 Low Water (keep): wt=19.000, iters=3363
% 1.82/2.10
% 1.82/2.10 Low Water (displace): id=6695, wt=145.000
% 1.82/2.10
% 1.82/2.10 Low Water (displace): id=2222, wt=132.000
% 1.82/2.10
% 1.82/2.10 Low Water (displaCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------