TSTP Solution File: SEU343+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU343+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 13:31:07 EDT 2022
% Result : Timeout 300.03s 300.28s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU343+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 04:55:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.04 ============================== Prover9 ===============================
% 0.44/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.04 Process 24163 was started by sandbox2 on n029.cluster.edu,
% 0.44/1.04 Mon Jun 20 04:55:16 2022
% 0.44/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24009_n029.cluster.edu".
% 0.44/1.04 ============================== end of head ===========================
% 0.44/1.04
% 0.44/1.04 ============================== INPUT =================================
% 0.44/1.04
% 0.44/1.04 % Reading from file /tmp/Prover9_24009_n029.cluster.edu
% 0.44/1.04
% 0.44/1.04 set(prolog_style_variables).
% 0.44/1.04 set(auto2).
% 0.44/1.04 % set(auto2) -> set(auto).
% 0.44/1.04 % set(auto) -> set(auto_inference).
% 0.44/1.04 % set(auto) -> set(auto_setup).
% 0.44/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.04 % set(auto) -> set(auto_limits).
% 0.44/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.04 % set(auto) -> set(auto_denials).
% 0.44/1.04 % set(auto) -> set(auto_process).
% 0.44/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.04 % set(auto2) -> assign(stats, some).
% 0.44/1.04 % set(auto2) -> clear(echo_input).
% 0.44/1.04 % set(auto2) -> set(quiet).
% 0.44/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.04 % set(auto2) -> clear(print_given).
% 0.44/1.04 assign(lrs_ticks,-1).
% 0.44/1.04 assign(sos_limit,10000).
% 0.44/1.04 assign(order,kbo).
% 0.44/1.04 set(lex_order_vars).
% 0.44/1.04 clear(print_given).
% 0.44/1.04
% 0.44/1.04 % formulas(sos). % not echoed (86 formulas)
% 0.44/1.04
% 0.44/1.04 ============================== end of input ==========================
% 0.44/1.04
% 0.44/1.04 % From the command line: assign(max_seconds, 300).
% 0.44/1.04
% 0.44/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.04
% 0.44/1.04 % Formulas that are not ordinary clauses:
% 0.44/1.04 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].
% 0.44/1.04 2 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 3 (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].
% 0.44/1.04 4 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 5 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 6 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 7 (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].
% 0.44/1.04 8 (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].
% 0.44/1.04 9 (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].
% 0.44/1.04 10 (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].
% 0.44/1.04 11 (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].
% 0.78/1.04 12 (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].
% 0.78/1.04 13 (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].
% 0.78/1.04 14 (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].
% 0.78/1.04 15 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 16 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 17 (all A (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 18 (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].
% 0.78/1.04 19 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 20 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 21 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 22 (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].
% 0.78/1.04 23 (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].
% 0.78/1.04 24 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 25 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 26 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 27 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 28 (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].
% 0.78/1.04 29 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 30 (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].
% 0.78/1.04 31 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 32 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 33 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 34 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 35 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 36 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 37 (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].
% 0.78/1.04 38 (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].
% 0.78/1.04 39 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 40 (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].
% 0.78/1.04 41 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 42 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 43 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 44 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 45 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 46 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 47 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 48 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 49 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 50 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 51 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 52 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 53 (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].
% 0.78/1.04 54 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 55 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 56 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 57 (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].
% 0.78/1.04 58 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 59 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 60 (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].
% 0.78/1.04 61 (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].
% 0.78/1.04 62 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 63 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 64 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 65 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 66 (exists A (latt_str(A) & strict_latt_str(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 67 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 68 (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].
% 0.78/1.05 69 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 70 (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].
% 0.78/1.05 71 (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].
% 0.78/1.05 72 (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].
% 0.78/1.05 73 (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].
% 0.78/1.05 74 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 75 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 76 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 77 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 78 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 79 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 80 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 81 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 82 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 83 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 84 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.05 85 -(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(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.05
% 0.78/1.05 ============================== end of process non-clausal formulas ===
% 0.78/1.05
% 0.78/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.78/1.05
% 0.78/1.05 ============================== PREDICATE ELIMINATION =================
% 0.78/1.05 86 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(31)].
% 0.78/1.05 87 meet_semilatt_str(c1) # label(existence_l1_lattices) # label(axiom). [clausify(41)].
% 0.78/1.05 Derived: one_sorted_str(c1). [resolve(86,a,87,a)].
% 0.78/1.05 88 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(34)].
% 0.78/1.05 Derived: -latt_str(A) | one_sorted_str(A). [resolve(88,b,86,a)].
% 0.78/1.05 89 -meet_semilatt_str(A) | function(the_L_meet(A)) # label(dt_u1_lattices) # label(axiom). [clausify(38)].
% 0.78/1.05 Derived: function(the_L_meet(c1)). [resolve(89,a,87,a)].
% 0.78/1.05 Derived: function(the_L_meet(A)) | -latt_str(A). [resolve(89,a,88,b)].
% 0.78/1.05 90 -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(38)].
% 0.78/1.05 Derived: quasi_total(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(90,a,87,a)].
% 0.78/1.05 Derived: quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(90,a,88,b)].
% 0.78/1.05 91 -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(38)].
% 0.78/1.05 Derived: relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(91,a,87,a)].
% 0.78/1.05 Derived: relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(91,a,88,b)].
% 0.78/1.05 92 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(23)].
% 0.78/1.05 Derived: empty_carrier(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | element(meet(c1,A,B),the_carrier(c1)). [resolve(92,b,87,a)].
% 0.78/1.05 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet(A,B,C),the_carrier(A)) | -latt_str(A). [resolve(92,b,88,b)].
% 0.78/1.05 93 empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -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). [clausify(12)].
% 0.78/1.05 Derived: empty_carrier(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | meet(c1,A,B) = apply_binary_as_element(the_carrier(c1),the_carrier(c1),the_carrier(c1),the_L_meet(c1),A,B). [resolve(93,b,87,a)].
% 0.78/1.05 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -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) | -latt_str(A). [resolve(93,b,88,b)].
% 0.78/1.05 94 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(49)].
% 0.78/1.05 95 one_sorted_str(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(42)].
% 0.78/1.05 96 one_sorted_str(c8) # label(rc3_struct_0) # label(axiom). [clausify(67)].
% 0.78/1.05 97 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(33)].
% 0.78/1.05 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(94,b,95,a)].
% 0.78/1.05 Derived: empty_carrier(c8) | -empty(the_carrier(c8)). [resolve(94,b,96,a)].
% 0.78/1.05 Derived: empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(94,b,97,b)].
% 0.78/1.05 98 empty_carrier(A) | -one_sorted_str(A) | -empty(f8(A)) # label(rc5_struct_0) # label(axiom). [clausify(68)].
% 0.78/1.05 Derived: empty_carrier(c2) | -empty(f8(c2)). [resolve(98,b,95,a)].
% 0.78/1.05 Derived: empty_carrier(c8) | -empty(f8(c8)). [resolve(98,b,96,a)].
% 0.78/1.05 Derived: empty_carrier(A) | -empty(f8(A)) | -join_semilatt_str(A). [resolve(98,b,97,b)].
% 0.78/1.05 99 empty_carrier(A) | -one_sorted_str(A) | element(f8(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(68)].
% 0.78/1.05 Derived: empty_carrier(c2) | element(f8(c2),powerset(the_carrier(c2))). [resolve(99,b,95,a)].
% 0.78/1.05 Derived: empty_carrier(c8) | element(f8(c8),powerset(the_carrier(c8))). [resolve(99,b,96,a)].
% 0.78/1.05 Derived: empty_carrier(A) | element(f8(A),powerset(the_carrier(A))) | -join_semilatt_str(A). [resolve(99,b,97,b)].
% 0.78/1.05 100 one_sorted_str(c1). [resolve(86,a,87,a)].
% 0.78/1.05 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(100,a,94,b)].
% 0.78/1.05 Derived: empty_carrier(c1) | -empty(f8(c1)). [resolve(100,a,98,b)].
% 0.78/1.05 Derived: empty_carrier(c1) | element(f8(c1),powerset(the_carrier(c1))). [resolve(100,a,99,b)].
% 0.78/1.05 101 -latt_str(A) | one_sorted_str(A). [resolve(88,b,86,a)].
% 0.78/1.05 Derived: -latt_str(A) | empty_carrier(A) | -empty(the_carrier(A)). [resolve(101,b,94,b)].
% 0.78/1.05 Derived: -latt_str(A) | empty_carrier(A) | -empty(f8(A)). [resolve(101,b,98,b)].
% 0.78/1.05 Derived: -latt_str(A) | empty_carrier(A) | element(f8(A),powerset(the_carrier(A))). [resolve(101,b,99,b)].
% 0.78/1.05 102 -join_semilatt_str(A) | function(the_L_join(A)) # label(dt_u2_lattices) # label(axiom). [clausify(40)].
% 0.78/1.05 103 join_semilatt_str(c3) # label(existence_l2_lattices) # label(axiom). [clausify(43)].
% 0.78/1.05 104 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(34)].
% 0.78/1.05 Derived: function(the_L_join(c3)). [resolve(102,a,103,a)].
% 0.78/1.05 Derived: function(the_L_join(A)) | -latt_str(A). [resolve(102,a,104,b)].
% 0.78/1.05 105 -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(40)].
% 0.78/1.05 Derived: quasi_total(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(105,a,103,a)].
% 0.78/1.05 Derived: quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(105,a,104,b)].
% 0.78/1.05 106 -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(40)].
% 0.78/1.05 Derived: relation_of2_as_subset(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(106,a,103,a)].
% 0.78/1.05 Derived: relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(106,a,104,b)].
% 0.78/1.05 107 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(18)].
% 0.78/1.05 Derived: empty_carrier(c3) | -element(A,the_carrier(c3)) | -element(B,the_carrier(c3)) | element(join(c3,A,B),the_carrier(c3)). [resolve(107,b,103,a)].
% 0.78/1.05 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(join(A,B,C),the_carrier(A)) | -latt_str(A). [resolve(107,b,104,b)].
% 0.78/1.05 108 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(11)].
% 0.78/1.05 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(108,b,103,a)].
% 0.78/1.05 Derived: empty_carrier(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) | -latt_str(A). [resolve(108,b,104,b)].
% 0.78/1.05 109 empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(94,b,97,b)].
% 0.78/1.05 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(109,c,103,a)].
% 0.78/1.05 110 empty_carrier(A) | -empty(f8(A)) | -join_semilatt_str(A). [resolve(98,b,97,b)].
% 0.78/1.05 Derived: empty_carrier(c3) | -empty(f8(c3)). [resolve(110,c,103,a)].
% 0.78/1.05 111 empty_carrier(A) | element(f8(A),powerset(the_carrier(A))) | -join_semilatt_str(A). [resolve(99,b,97,b)].
% 0.78/1.05 Derived: empty_carrier(c3) | element(f8(c3),powerset(the_carrier(c3))). [resolve(111,c,103,a)].
% 0.78/1.05 112 -latt_str(A) | -strict_latt_str(A) | latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)) = A # label(abstractness_v3_lattices) # label(axiom). [clausify(1)].
% 0.78/1.05 113 latt_str(c4) # label(existence_l3_lattices) # label(axiom). [clausify(44)].
% 0.78/1.05 114 latt_str(c7) # label(rc3_lattices) # label(axiom). [clausify(66)].
% 0.78/1.05 115 latt_str(c9) # label(rc6_lattices) # label(axiom). [clausify(69)].
% 0.78/1.05 116 latt_str(boole_lattice(A)) # label(dt_k1_lattice3) # label(axiom). [clausify(17)].
% 0.78/1.05 Derived: -strict_latt_str(c4) | latt_str_of(the_carrier(c4),the_L_join(c4),the_L_meet(c4)) = c4. [resolve(112,a,113,a)].
% 0.78/1.05 Derived: -strict_latt_str(c7) | latt_str_of(the_carrier(c7),the_L_join(c7),the_L_meet(c7)) = c7. [resolve(112,a,114,a)].
% 0.78/1.05 Derived: -strict_latt_str(c9) | latt_str_of(the_carrier(c9),the_L_join(c9),the_L_meet(c9)) = c9. [resolve(112,a,115,a)].
% 0.78/1.05 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(112,a,116,a)].
% 0.78/1.05 117 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) != A | powerset(B) = the_carrier(A) # label(d1_lattice3) # label(axiom). [clausify(10)].
% 0.78/1.05 Derived: -strict_latt_str(c4) | boole_lattice(A) != c4 | powerset(A) = the_carrier(c4). [resolve(117,b,113,a)].
% 0.78/1.05 Derived: -strict_latt_str(c7) | boole_lattice(A) != c7 | powerset(A) = the_carrier(c7). [resolve(117,b,114,a)].
% 0.78/1.05 Derived: -strict_latt_str(c9) | boole_lattice(A) != c9 | powerset(A) = the_carrier(c9). [resolve(117,b,115,a)].
% 0.78/1.05 Derived: -strict_latt_str(boole_lattice(A)) | boole_lattice(B) != boole_lattice(A) | powerset(B) = the_carrier(boole_lattice(A)). [resolve(117,b,116,a)].
% 0.78/1.05 118 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) = A | powerset(B) != the_carrier(A) | element(f1(B,A),powerset(B)) # label(d1_lattice3) # label(axiom). [clausify(10)].
% 0.78/1.05 Derived: -strict_latt_str(c4) | boole_lattice(A) = c4 | powerset(A) != the_carrier(c4) | element(f1(A,c4),powerset(A)). [resolve(118,b,113,a)].
% 0.78/1.05 Derived: -strict_latt_str(c7) | boole_lattice(A) = c7 | powerset(A) != the_carrier(c7) | element(f1(A,c7),powerset(A)). [resolve(118,b,114,a)].
% 0.78/1.05 Derived: -strict_latt_str(c9) | boole_lattice(A) = c9 | powerset(A) != the_carrier(c9) | element(f1(A,c9),powerset(A)). [resolve(118,b,115,a)].
% 0.78/1.05 Derived: -strict_latt_str(boole_lattice(A)) | boole_lattice(B) = boole_lattice(A) | powerset(B) != the_carrier(boole_lattice(A)) | element(f1(B,boole_lattice(A)),powerset(B)). [resolve(118,b,116,a)].
% 0.78/1.05 119 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) = A | powerset(B) != the_carrier(A) | element(f2(B,A),powerset(B)) # label(d1_lattice3) # label(axiom). [clausify(10)].
% 0.78/1.05 Derived: -strict_latt_str(c4) | boole_lattice(A) = c4 | powerset(A) != the_carrier(c4) | element(f2(A,c4),powerset(A)). [resolve(119,b,113,a)].
% 0.78/1.05 Derived: -strict_latt_str(c7) | boole_lattice(A) = c7 | powerset(A) != the_carrier(c7) | element(f2(A,c7),powerset(A)). [resolve(119,b,114,a)].
% 0.78/1.05 Derived: -strict_latt_str(c9) | boole_lattice(A) = c9 | powerset(A) != the_carrier(c9) | element(f2(A,c9),powerset(A)). [resolve(119,b,115,a)].
% 0.78/1.05 Derived: -strict_latt_str(boole_lattice(A)) | boole_lattice(B) = boole_lattice(A) | powerset(B) != the_carrier(boole_lattice(A)) | element(f2(B,boole_lattice(A)),powerset(B)). [resolve(119,b,116,a)].
% 0.78/1.05 120 -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(10)].
% 0.78/1.05 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,b,113,a)].
% 0.78/1.05 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(120,b,114,a)].
% 0.78/1.05 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(120,b,115,a)].
% 0.78/1.05 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(120,b,116,a)].
% 0.78/1.05 121 -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(10)].
% 0.78/1.05 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(121,b,113,a)].
% 0.78/1.05 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,b,114,a)].
% 0.78/1.05 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(121,b,115,a)].
% 0.78/1.05 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(121,b,116,a)].
% 0.78/1.05 122 -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(14)].
% 0.78/1.05 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(122,g,112,a)].
% 0.78/1.05 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(122,g,117,b)].
% 0.78/1.05 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(f1(D,latt_str_of(B,A,C)),powerset(D)). [resolve(122,g,118,b)].
% 0.78/1.05 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(f2(D,latt_str_of(B,A,C)),powerset(D)). [resolve(122,g,119,b)].
% 0.78/1.05 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(122,g,120,b)].
% 0.78/1.05 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(122,g,121,b)].
% 0.78/1.05 123 -strict_latt_str(A) | -latt_str(A) | boole_lattice(B) = A | powerset(B) != the_carrier(A) | apply_binary(the_L_join(A),f1(B,A),f2(B,A)) != subset_union2(B,f1(B,A),f2(B,A)) | apply_binary(the_L_meet(A),f1(B,A),f2(B,A)) != subset_intersection2(B,f1(B,A),f2(B,A)) # label(d1_lattice3) # label(axiom). [clausify(10)].
% 0.78/1.05 Derived: -strict_latt_str(c4) | boole_lattice(A) = c4 | powerset(A) != the_carrier(c4) | apply_binary(the_L_join(c4),f1(A,c4),f2(A,c4)) != subset_union2(A,f1(A,c4),f2(A,c4)) | apply_binary(the_L_meet(c4),f1(A,c4),f2(A,c4)) != subset_intersection2(A,f1(A,c4),f2(A,c4)). [resolve(123,b,113,a)].
% 0.78/1.05 Derived: -strict_latt_str(c7) | boole_lattice(A) = c7 | powerset(A) != the_carrier(c7) | apply_binary(the_L_join(c7),f1(A,c7),f2(A,c7)) != subset_union2(A,f1(A,c7),f2(A,c7)) | apply_binary(the_L_meet(c7),f1(A,c7),f2(A,c7)) != subset_intersection2(A,f1(A,c7),f2(A,c7)). [resolve(123,b,114,a)].
% 0.78/1.05 Derived: -strict_latt_str(c9) | boole_lattice(A) = c9 | powerset(A) != the_carrier(c9) | apply_binary(the_L_join(c9),f1(A,c9),f2(A,c9)) != subset_union2(A,f1(A,c9),f2(A,c9)) | apply_binary(the_L_meet(c9),f1(A,c9),f2(A,c9)) != subset_intersection2(A,f1(A,c9),f2(A,c9)). [resolve(123,b,115,a)].
% 0.78/1.05 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)),f1(B,boole_lattice(A)),f2(B,boole_lattice(A))) != subset_union2(B,f1(B,boole_lattice(A)),f2(B,boole_lattice(A))) | apply_binary(the_L_meet(boole_lattice(A)),f1(B,boole_lattice(A)),f2(B,boole_lattice(A))) != subset_intersection2(B,f1(B,boole_lattice(A)),f2(B,boole_lattice(A))). [resolve(123,b,116,a)].
% 0.78/1.05 Derived: -strict_latt_str(latt_str_of(A,B,C)) | boole_lattice(D) = latt_str_of(A,B,C) | powerset(D) != the_carrier(latt_str_of(A,B,C)) | apply_binary(the_L_join(latt_str_of(A,B,C)),f1(D,latt_str_of(A,B,C)),f2(D,latt_str_of(A,B,C))) != subset_union2(D,f1(D,latt_str_of(A,B,C)),f2(D,latt_str_of(A,B,C))) | apply_binary(the_L_meet(latt_str_of(A,B,C)),f1(D,latt_str_of(A,B,C)),f2(D,latt_str_of(A,B,C))) != subset_intersection2(D,f1(D,latt_str_of(A,B,C)),f2(D,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(123,b,122,g)].
% 0.78/1.05 124 function(the_L_meet(A)) | -latt_str(A). [resolve(89,a,88,b)].
% 0.78/1.05 Derived: function(the_L_meet(c4)). [resolve(124,b,113,a)].
% 0.78/1.05 Derived: function(the_L_meet(c7)). [resolve(124,b,114,a)].
% 0.78/1.05 Derived: function(the_L_meet(c9)). [resolve(124,b,115,a)].
% 0.78/1.05 Derived: function(the_L_meet(boole_lattice(A))). [resolve(124,b,116,a)].
% 0.78/1.05 Derived: function(the_L_meet(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(124,b,122,g)].
% 0.78/1.05 125 quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(90,a,88,b)].
% 0.78/1.05 Derived: quasi_total(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(125,b,113,a)].
% 0.78/1.05 Derived: quasi_total(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(125,b,114,a)].
% 0.78/1.05 Derived: quasi_total(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(125,b,115,a)].
% 0.78/1.05 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(125,b,116,a)].
% 0.78/1.05 Derived: quasi_total(the_L_meet(latt_str_of(A,B,C)),cartesian_product2(the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))),the_carrier(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(125,b,122,g)].
% 0.78/1.05 126 relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(91,a,88,b)].
% 0.78/1.05 Derived: relation_of2_as_subset(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(126,b,113,a)].
% 0.78/1.05 Derived: relation_of2_as_subset(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(126,b,114,a)].
% 0.78/1.05 Derived: relation_of2_as_subset(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(126,b,115,a)].
% 0.78/1.05 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(126,b,116,a)].
% 0.78/1.06 Derived: relation_of2_as_subset(the_L_meet(latt_str_of(A,B,C)),cartesian_product2(the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))),the_carrier(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(126,b,122,g)].
% 0.78/1.06 127 empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet(A,B,C),the_carrier(A)) | -latt_str(A). [resolve(92,b,88,b)].
% 0.78/1.06 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(meet(c4,A,B),the_carrier(c4)). [resolve(127,e,113,a)].
% 0.78/1.06 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | element(meet(c7,A,B),the_carrier(c7)). [resolve(127,e,114,a)].
% 0.78/1.06 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | element(meet(c9,A,B),the_carrier(c9)). [resolve(127,e,115,a)].
% 0.78/1.06 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(127,e,116,a)].
% 0.78/1.06 Derived: empty_carrier(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | -element(E,the_carrier(latt_str_of(A,B,C))) | element(meet(latt_str_of(A,B,C),D,E),the_carrier(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(127,e,122,g)].
% 0.78/1.06 128 empty_carrier(A) | -element(B,the_carrier(A)) | -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) | -latt_str(A). [resolve(93,b,88,b)].
% 0.78/1.06 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | meet(c4,A,B) = apply_binary_as_element(the_carrier(c4),the_carrier(c4),the_carrier(c4),the_L_meet(c4),A,B). [resolve(128,e,113,a)].
% 0.78/1.06 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | meet(c7,A,B) = apply_binary_as_element(the_carrier(c7),the_carrier(c7),the_carrier(c7),the_L_meet(c7),A,B). [resolve(128,e,114,a)].
% 0.78/1.06 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | meet(c9,A,B) = apply_binary_as_element(the_carrier(c9),the_carrier(c9),the_carrier(c9),the_L_meet(c9),A,B). [resolve(128,e,115,a)].
% 0.78/1.06 Derived: empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | meet(boole_lattice(A),B,C) = 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). [resolve(128,e,116,a)].
% 0.78/1.06 Derived: empty_carrier(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | -element(E,the_carrier(latt_str_of(A,B,C))) | meet(latt_str_of(A,B,C),D,E) = apply_binary_as_element(the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C)),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(128,e,122,g)].
% 0.78/1.06 129 -latt_str(A) | empty_carrier(A) | -empty(the_carrier(A)). [resolve(101,b,94,b)].
% 0.78/1.06 Derived: empty_carrier(c4) | -empty(the_carrier(c4)). [resolve(129,a,113,a)].
% 0.78/1.06 Derived: empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(129,a,114,a)].
% 0.78/1.06 Derived: empty_carrier(c9) | -empty(the_carrier(c9)). [resolve(129,a,115,a)].
% 0.78/1.06 Derived: empty_carrier(boole_lattice(A)) | -empty(the_carrier(boole_lattice(A))). [resolve(129,a,116,a)].
% 0.78/1.06 Derived: empty_carrier(latt_str_of(A,B,C)) | -empty(the_carrier(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(129,a,122,g)].
% 0.78/1.06 130 -latt_str(A) | empty_carrier(A) | -empty(f8(A)). [resolve(101,b,98,b)].
% 0.78/1.06 Derived: empty_carrier(c4) | -empty(f8(c4)). [resolve(130,a,113,a)].
% 0.78/1.06 Derived: empty_carrier(c7) | -empty(f8(c7)). [resolve(130,a,114,a)].
% 0.78/1.06 Derived: empty_carrier(c9) | -empty(f8(c9)). [resolve(130,a,115,a)].
% 0.78/1.06 Derived: empty_carrier(boole_lattice(A)) | -empty(f8(boole_lattice(A))). [resolve(130,a,116,a)].
% 0.78/1.06 Derived: empty_carrier(latt_str_of(A,B,C)) | -empty(f8(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(130,a,122,g)].
% 0.78/1.06 131 -latt_str(A) | empty_carrier(A) | element(f8(A),powerset(the_carrier(A))). [resolve(101,b,99,b)].
% 0.78/1.06 Derived: empty_carrier(c4) | element(f8(c4),powerset(the_carrier(c4))). [resolve(131,a,113,a)].
% 0.78/1.06 Derived: empty_carrier(c7) | element(f8(c7),powerset(the_carrier(c7))). [resolve(131,a,114,a)].
% 0.78/1.06 Derived: empty_carrier(c9) | element(f8(c9),powerset(the_carrier(c9))). [resolve(131,a,115,a)].
% 0.78/1.06 Derived: empty_carrier(boole_lattice(A)) | element(f8(boole_lattice(A)),powerset(the_carrier(boole_lattice(A)))). [resolve(131,a,116,a)].
% 0.78/1.06 Derived: empty_carrier(latt_str_of(A,B,C)) | element(f8(latt_str_of(A,B,C)),powerset(the_carrier(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(131,a,122,g)].
% 0.78/1.06 132 function(the_L_join(A)) | -latt_str(A). [resolve(102,a,104,b)].
% 0.78/1.06 Derived: function(the_L_join(c4)). [resolve(132,b,113,a)].
% 0.78/1.06 Derived: function(the_L_join(c7)). [resolve(132,b,114,a)].
% 0.78/1.06 Derived: function(the_L_join(c9)). [resolve(132,b,115,a)].
% 0.78/1.06 Derived: function(the_L_join(boole_lattice(A))). [resolve(132,b,116,a)].
% 0.78/1.06 Derived: function(the_L_join(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(132,b,122,g)].
% 0.78/1.06 133 quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(105,a,104,b)].
% 0.78/1.06 Derived: quasi_total(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(133,b,113,a)].
% 0.78/1.06 Derived: quasi_total(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(133,b,114,a)].
% 0.78/1.06 Derived: quasi_total(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(133,b,115,a)].
% 0.78/1.06 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(133,b,116,a)].
% 0.78/1.06 Derived: quasi_total(the_L_join(latt_str_of(A,B,C)),cartesian_product2(the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))),the_carrier(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(133,b,122,g)].
% 0.78/1.06 134 relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(106,a,104,b)].
% 0.78/1.06 Derived: relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(134,b,113,a)].
% 0.78/1.06 Derived: relation_of2_as_subset(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(134,b,114,a)].
% 0.78/1.06 Derived: relation_of2_as_subset(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(134,b,115,a)].
% 0.78/1.06 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(134,b,116,a)].
% 0.78/1.06 Derived: relation_of2_as_subset(the_L_join(latt_str_of(A,B,C)),cartesian_product2(the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))),the_carrier(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(134,b,122,g)].
% 0.78/1.06 135 empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(join(A,B,C),the_carrier(A)) | -latt_str(A). [resolve(107,b,104,b)].
% 0.78/1.06 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(join(c4,A,B),the_carrier(c4)). [resolve(135,e,113,a)].
% 0.78/1.06 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | element(join(c7,A,B),the_carrier(c7)). [resolve(135,e,114,a)].
% 0.78/1.06 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | element(join(c9,A,B),the_carrier(c9)). [resolve(135,e,115,a)].
% 0.78/1.06 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(135,e,116,a)].
% 0.78/1.06 Derived: empty_carrier(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | -element(E,the_carrier(latt_str_of(A,B,C))) | element(join(latt_str_of(A,B,C),D,E),the_carrier(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(135,e,122,g)].
% 0.78/1.06 136 empty_carrier(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) | -latt_str(A). [resolve(108,b,104,b)].
% 0.78/1.06 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(136,e,113,a)].
% 0.78/1.06 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(136,e,114,a)].
% 0.78/1.06 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(136,e,115,a)].
% 0.78/1.06 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(136,e,116,a)].
% 0.78/1.06 Derived: empty_carrier(latt_str_of(A,B,C)) | -element(D,the_carrier(latt_str_of(A,B,C))) | -element(E,the_carrier(latt_str_of(A,B,C))) | apply_binary_as_element(the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C)),the_L_join(latt_str_of(A,B,C)),D,E) = 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(136,e,122,g)].
% 0.78/1.06 137 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(79)].
% 0.78/1.06 138 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(74)].
% 0.78/1.06 139 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(79)].
% 0.78/1.06 Derived: element(A,powerset(A)). [resolve(137,b,138,a)].
% 0.78/1.06 140 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(73)].
% 0.78/1.07 141 relation_of2_as_subset(f5(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(47)].
% 0.78/1.07 Derived: relation_of2(f5(A,B),A,B). [resolve(140,a,141,a)].
% 0.78/1.07 142 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(73)].
% 0.78/1.07 143 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(37)].
% 0.78/1.07 Derived: element(f5(A,B),powerset(cartesian_product2(A,B))). [resolve(143,a,141,a)].
% 0.78/1.07 Derived: element(A,powerset(cartesian_product2(B,C))) | -relation_of2(A,B,C). [resolve(143,a,142,a)].
% 0.78/1.07 144 relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(91,a,87,a)].
% 0.78/1.07 Derived: relation_of2(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(144,a,140,a)].
% 0.78/1.07 Derived: element(the_L_meet(c1),powerset(cartesian_product2(cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)))). [resolve(144,a,143,a)].
% 0.78/1.07 145 relation_of2_as_subset(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(106,a,103,a)].
% 0.78/1.07 Derived: relation_of2(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(145,a,140,a)].
% 0.78/1.07 Derived: element(the_L_join(c3),powerset(cartesian_product2(cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)))). [resolve(145,a,143,a)].
% 0.78/1.07 146 relation_of2_as_subset(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(126,b,113,a)].
% 0.78/1.07 Derived: relation_of2(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(146,a,140,a)].
% 0.78/1.07 Derived: element(the_L_meet(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(146,a,143,a)].
% 0.78/1.07 147 relation_of2_as_subset(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(126,b,114,a)].
% 0.78/1.07 Derived: relation_of2(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(147,a,140,a)].
% 0.78/1.07 Derived: element(the_L_meet(c7),powerset(cartesian_product2(cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)))). [resolve(147,a,143,a)].
% 0.78/1.07 148 relation_of2_as_subset(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(126,b,115,a)].
% 0.78/1.07 Derived: relation_of2(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(148,a,140,a)].
% 0.78/1.07 Derived: element(the_L_meet(c9),powerset(cartesian_product2(cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)))). [resolve(148,a,143,a)].
% 0.78/1.07 149 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(126,b,116,a)].
% 0.78/1.07 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(149,a,140,a)].
% 0.78/1.07 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(149,a,143,a)].
% 0.78/1.07 150 relation_of2_as_subset(the_L_meet(latt_str_of(A,B,C)),cartesian_product2(the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))),the_carrier(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(126,b,122,g)].
% 0.78/1.07 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(150,a,140,a)].
% 0.78/1.07 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(150,a,143,a)].
% 0.78/1.07 151 relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(134,b,113,a)].
% 0.78/1.07 Derived: relation_of2(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(151,a,140,a)].
% 0.78/1.07 Derived: element(the_L_join(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(151,a,143,a)].
% 0.78/1.07 152 relation_of2_as_subset(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(134,b,114,a)].
% 0.78/1.07 Derived: relation_of2(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(152,a,140,a)].
% 0.78/1.07 Derived: element(the_L_join(c7),powerset(cartesian_product2(cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)))). [resolve(152,a,143,a)].
% 0.78/1.07 153 relation_of2_as_subset(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(134,b,115,a)].
% 0.78/1.07 Derived: relation_of2(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(153,a,140,a)].
% 0.78/1.07 Derived: element(the_L_join(c9),powerset(cartesian_product2(cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)))). [resolve(153,a,143,a)].
% 0.78/1.07 154 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(134,b,116,a)].
% 0.78/1.07 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(154,a,140,a)].
% 0.78/1.07 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(154,a,143,a)].
% 0.78/1.07 155 relation_of2_as_subset(the_L_join(latt_str_of(A,B,C)),cartesian_product2(the_carrier(latt_str_of(A,B,C)),the_carrier(latt_str_of(A,B,C))),the_carrier(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(134,b,122,g)].
% 0.78/1.07 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(155,a,140,a)].
% 0.78/1.07 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(155,a,143,a)].
% 0.78/1.07 156 -relation(A) | -function(A) | apply(A,ordered_pair(B,C)) = apply_binary(A,B,C) # label(d1_binop_1) # label(axiom). [clausify(9)].
% 0.78/1.07 157 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(3)].
% 0.78/1.07 Derived: -function(A) | apply(A,ordered_pair(B,C)) = apply_binary(A,B,C) | -element(A,powerset(cartesian_product2(D,E))). [resolve(156,a,15Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------