TSTP Solution File: SEU344+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 13:31:08 EDT 2022
% Result : Theorem 3.41s 3.67s
% Output : Refutation 3.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n004.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 11:21:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.02 ============================== Prover9 ===============================
% 0.43/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.02 Process 4343 was started by sandbox on n004.cluster.edu,
% 0.43/1.02 Mon Jun 20 11:21:24 2022
% 0.43/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4190_n004.cluster.edu".
% 0.43/1.02 ============================== end of head ===========================
% 0.43/1.02
% 0.43/1.02 ============================== INPUT =================================
% 0.43/1.02
% 0.43/1.02 % Reading from file /tmp/Prover9_4190_n004.cluster.edu
% 0.43/1.02
% 0.43/1.02 set(prolog_style_variables).
% 0.43/1.02 set(auto2).
% 0.43/1.02 % set(auto2) -> set(auto).
% 0.43/1.02 % set(auto) -> set(auto_inference).
% 0.43/1.02 % set(auto) -> set(auto_setup).
% 0.43/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.02 % set(auto) -> set(auto_limits).
% 0.43/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.02 % set(auto) -> set(auto_denials).
% 0.43/1.02 % set(auto) -> set(auto_process).
% 0.43/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.02 % set(auto2) -> assign(stats, some).
% 0.43/1.02 % set(auto2) -> clear(echo_input).
% 0.43/1.02 % set(auto2) -> set(quiet).
% 0.43/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.02 % set(auto2) -> clear(print_given).
% 0.43/1.02 assign(lrs_ticks,-1).
% 0.43/1.02 assign(sos_limit,10000).
% 0.43/1.02 assign(order,kbo).
% 0.43/1.02 set(lex_order_vars).
% 0.43/1.02 clear(print_given).
% 0.43/1.02
% 0.43/1.02 % formulas(sos). % not echoed (81 formulas)
% 0.43/1.02
% 0.43/1.02 ============================== end of input ==========================
% 0.43/1.02
% 0.43/1.02 % From the command line: assign(max_seconds, 300).
% 0.43/1.02
% 0.43/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.02
% 0.43/1.02 % Formulas that are not ordinary clauses:
% 0.43/1.02 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].
% 0.43/1.02 2 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 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].
% 0.43/1.02 4 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 5 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 6 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 7 (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].
% 0.43/1.02 8 (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].
% 0.43/1.02 9 (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].
% 0.43/1.02 10 (all A (-empty_carrier(A) & join_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below(A,B,C) <-> join(A,B,C) = C))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 11 (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].
% 0.43/1.02 12 (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].
% 0.43/1.02 13 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 14 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 15 (all A (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 16 (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].
% 0.43/1.02 17 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 18 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 19 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 20 (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].
% 0.43/1.02 21 (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].
% 0.43/1.02 22 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 23 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 24 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 25 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 26 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 27 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 28 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 29 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 30 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 31 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 32 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 33 (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].
% 0.43/1.02 34 (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].
% 0.43/1.02 35 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 36 (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].
% 0.43/1.02 37 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 38 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.02 39 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 40 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 41 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 42 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 43 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 44 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 45 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 46 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 47 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 48 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 49 (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].
% 0.43/1.03 50 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 51 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 52 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 53 (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].
% 0.43/1.03 54 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 55 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 56 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 57 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 58 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 59 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 60 (exists A (latt_str(A) & strict_latt_str(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 61 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 62 (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].
% 0.43/1.03 63 (exists A (latt_str(A) & -empty_carrier(A) & strict_latt_str(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 64 (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].
% 0.43/1.03 65 (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].
% 0.43/1.03 66 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 67 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 68 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 69 (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].
% 0.43/1.03 70 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 71 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 72 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 73 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 74 (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].
% 0.43/1.03 75 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 76 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 77 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 78 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 79 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.03 80 -(all A all B (element(B,the_carrier(boole_lattice(A))) -> (all C (element(C,the_carrier(boole_lattice(A))) -> (below(boole_lattice(A),B,C) <-> subset(B,C)))))) # label(t2_lattice3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.03
% 0.43/1.03 ============================== end of process non-clausal formulas ===
% 0.43/1.03
% 0.43/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.03
% 0.43/1.03 ============================== PREDICATE ELIMINATION =================
% 0.43/1.03 81 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(27)].
% 0.43/1.03 82 meet_semilatt_str(c1) # label(existence_l1_lattices) # label(axiom). [clausify(37)].
% 0.43/1.03 Derived: one_sorted_str(c1). [resolve(81,a,82,a)].
% 0.43/1.03 83 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(30)].
% 0.43/1.03 Derived: -latt_str(A) | one_sorted_str(A). [resolve(83,b,81,a)].
% 0.43/1.03 84 -meet_semilatt_str(A) | function(the_L_meet(A)) # label(dt_u1_lattices) # label(axiom). [clausify(34)].
% 0.43/1.03 Derived: function(the_L_meet(c1)). [resolve(84,a,82,a)].
% 0.43/1.03 Derived: function(the_L_meet(A)) | -latt_str(A). [resolve(84,a,83,b)].
% 0.43/1.03 85 -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(34)].
% 0.43/1.03 Derived: quasi_total(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(85,a,82,a)].
% 0.43/1.03 Derived: quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(85,a,83,b)].
% 0.43/1.03 86 -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(34)].
% 0.43/1.03 Derived: relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(86,a,82,a)].
% 0.43/1.03 Derived: relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(86,a,83,b)].
% 0.43/1.03 87 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(21)].
% 0.43/1.03 Derived: empty_carrier(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | element(meet(c1,A,B),the_carrier(c1)). [resolve(87,b,82,a)].
% 0.43/1.03 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(87,b,83,b)].
% 0.43/1.03 88 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(9)].
% 0.43/1.03 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(88,b,82,a)].
% 0.43/1.03 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(88,b,83,b)].
% 0.43/1.03 89 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(45)].
% 0.43/1.03 90 one_sorted_str(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(38)].
% 0.43/1.03 91 one_sorted_str(c8) # label(rc3_struct_0) # label(axiom). [clausify(61)].
% 0.43/1.03 92 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(29)].
% 0.43/1.03 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(89,b,90,a)].
% 0.43/1.03 Derived: empty_carrier(c8) | -empty(the_carrier(c8)). [resolve(89,b,91,a)].
% 0.43/1.03 Derived: empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(89,b,92,b)].
% 0.43/1.03 93 empty_carrier(A) | -one_sorted_str(A) | -empty(f6(A)) # label(rc5_struct_0) # label(axiom). [clausify(62)].
% 0.43/1.03 Derived: empty_carrier(c2) | -empty(f6(c2)). [resolve(93,b,90,a)].
% 0.43/1.03 Derived: empty_carrier(c8) | -empty(f6(c8)). [resolve(93,b,91,a)].
% 0.43/1.03 Derived: empty_carrier(A) | -empty(f6(A)) | -join_semilatt_str(A). [resolve(93,b,92,b)].
% 0.43/1.03 94 empty_carrier(A) | -one_sorted_str(A) | element(f6(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(62)].
% 0.43/1.03 Derived: empty_carrier(c2) | element(f6(c2),powerset(the_carrier(c2))). [resolve(94,b,90,a)].
% 0.43/1.03 Derived: empty_carrier(c8) | element(f6(c8),powerset(the_carrier(c8))). [resolve(94,b,91,a)].
% 0.43/1.03 Derived: empty_carrier(A) | element(f6(A),powerset(the_carrier(A))) | -join_semilatt_str(A). [resolve(94,b,92,b)].
% 0.43/1.03 95 one_sorted_str(c1). [resolve(81,a,82,a)].
% 0.43/1.03 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(95,a,89,b)].
% 0.43/1.03 Derived: empty_carrier(c1) | -empty(f6(c1)). [resolve(95,a,93,b)].
% 0.43/1.03 Derived: empty_carrier(c1) | element(f6(c1),powerset(the_carrier(c1))). [resolve(95,a,94,b)].
% 0.43/1.03 96 -latt_str(A) | one_sorted_str(A). [resolve(83,b,81,a)].
% 0.43/1.03 Derived: -latt_str(A) | empty_carrier(A) | -empty(the_carrier(A)). [resolve(96,b,89,b)].
% 0.43/1.03 Derived: -latt_str(A) | empty_carrier(A) | -empty(f6(A)). [resolve(96,b,93,b)].
% 0.43/1.03 Derived: -latt_str(A) | empty_carrier(A) | element(f6(A),powerset(the_carrier(A))). [resolve(96,b,94,b)].
% 0.43/1.03 97 -join_semilatt_str(A) | function(the_L_join(A)) # label(dt_u2_lattices) # label(axiom). [clausify(36)].
% 0.43/1.03 98 join_semilatt_str(c3) # label(existence_l2_lattices) # label(axiom). [clausify(39)].
% 0.43/1.03 99 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(30)].
% 0.43/1.03 Derived: function(the_L_join(c3)). [resolve(97,a,98,a)].
% 0.43/1.03 Derived: function(the_L_join(A)) | -latt_str(A). [resolve(97,a,99,b)].
% 0.43/1.03 100 -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(36)].
% 0.43/1.03 Derived: quasi_total(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(100,a,98,a)].
% 0.43/1.03 Derived: quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(100,a,99,b)].
% 0.43/1.03 101 -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(36)].
% 0.43/1.03 Derived: relation_of2_as_subset(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(101,a,98,a)].
% 0.43/1.03 Derived: relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(101,a,99,b)].
% 0.43/1.03 102 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(16)].
% 0.43/1.03 Derived: empty_carrier(c3) | -element(A,the_carrier(c3)) | -element(B,the_carrier(c3)) | element(join(c3,A,B),the_carrier(c3)). [resolve(102,b,98,a)].
% 0.43/1.03 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(102,b,99,b)].
% 0.43/1.03 103 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | join(A,B,C) = C # label(d3_lattices) # label(axiom). [clausify(10)].
% 0.43/1.03 Derived: empty_carrier(c3) | -element(A,the_carrier(c3)) | -element(B,the_carrier(c3)) | -below(c3,A,B) | join(c3,A,B) = B. [resolve(103,b,98,a)].
% 0.43/1.03 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | join(A,B,C) = C | -latt_str(A). [resolve(103,b,99,b)].
% 0.43/1.03 104 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,B,C) | join(A,B,C) != C # label(d3_lattices) # label(axiom). [clausify(10)].
% 0.43/1.03 Derived: empty_carrier(c3) | -element(A,the_carrier(c3)) | -element(B,the_carrier(c3)) | below(c3,A,B) | join(c3,A,B) != B. [resolve(104,b,98,a)].
% 0.43/1.03 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,B,C) | join(A,B,C) != C | -latt_str(A). [resolve(104,b,99,b)].
% 0.43/1.03 105 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(8)].
% 0.43/1.03 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(105,b,98,a)].
% 0.43/1.03 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(105,b,99,b)].
% 0.43/1.03 106 empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(89,b,92,b)].
% 0.43/1.03 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(106,c,98,a)].
% 0.43/1.03 107 empty_carrier(A) | -empty(f6(A)) | -join_semilatt_str(A). [resolve(93,b,92,b)].
% 0.43/1.03 Derived: empty_carrier(c3) | -empty(f6(c3)). [resolve(107,c,98,a)].
% 0.43/1.03 108 empty_carrier(A) | element(f6(A),powerset(the_carrier(A))) | -join_semilatt_str(A). [resolve(94,b,92,b)].
% 0.43/1.03 Derived: empty_carrier(c3) | element(f6(c3),powerset(the_carrier(c3))). [resolve(108,c,98,a)].
% 0.43/1.03 109 -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)].
% 0.43/1.03 110 latt_str(c4) # label(existence_l3_lattices) # label(axiom). [clausify(40)].
% 0.43/1.03 111 latt_str(c7) # label(rc3_lattices) # label(axiom). [clausify(60)].
% 0.43/1.03 112 latt_str(c9) # label(rc6_lattices) # label(axiom). [clausify(63)].
% 0.43/1.03 113 latt_str(boole_lattice(A)) # label(dt_k1_lattice3) # label(axiom). [clausify(15)].
% 0.43/1.03 Derived: -strict_latt_str(c4) | latt_str_of(the_carrier(c4),the_L_join(c4),the_L_meet(c4)) = c4. [resolve(109,a,110,a)].
% 0.43/1.03 Derived: -strict_latt_str(c7) | latt_str_of(the_carrier(c7),the_L_join(c7),the_L_meet(c7)) = c7. [resolve(109,a,111,a)].
% 0.43/1.03 Derived: -strict_latt_str(c9) | latt_str_of(the_carrier(c9),the_L_join(c9),the_L_meet(c9)) = c9. [resolve(109,a,112,a)].
% 0.43/1.03 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(109,a,113,a)].
% 0.43/1.03 114 -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(12)].
% 0.43/1.03 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(114,g,109,a)].
% 0.43/1.03 115 function(the_L_meet(A)) | -latt_str(A). [resolve(84,a,83,b)].
% 0.43/1.03 Derived: function(the_L_meet(c4)). [resolve(115,b,110,a)].
% 0.43/1.03 Derived: function(the_L_meet(c7)). [resolve(115,b,111,a)].
% 0.43/1.03 Derived: function(the_L_meet(c9)). [resolve(115,b,112,a)].
% 0.43/1.03 Derived: function(the_L_meet(boole_lattice(A))). [resolve(115,b,113,a)].
% 0.43/1.03 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(115,b,114,g)].
% 0.43/1.03 116 quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(85,a,83,b)].
% 0.43/1.03 Derived: quasi_total(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(116,b,110,a)].
% 0.43/1.03 Derived: quasi_total(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(116,b,111,a)].
% 0.43/1.03 Derived: quasi_total(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(116,b,112,a)].
% 0.43/1.03 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(116,b,113,a)].
% 0.43/1.03 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(116,b,114,g)].
% 0.43/1.03 117 relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(86,a,83,b)].
% 0.43/1.03 Derived: relation_of2_as_subset(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(117,b,110,a)].
% 0.43/1.03 Derived: relation_of2_as_subset(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(117,b,111,a)].
% 0.43/1.03 Derived: relation_of2_as_subset(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(117,b,112,a)].
% 0.43/1.03 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(117,b,113,a)].
% 0.43/1.03 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(117,b,114,g)].
% 0.43/1.03 118 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(87,b,83,b)].
% 0.43/1.03 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(meet(c4,A,B),the_carrier(c4)). [resolve(118,e,110,a)].
% 0.43/1.03 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | element(meet(c7,A,B),the_carrier(c7)). [resolve(118,e,111,a)].
% 0.76/1.04 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | element(meet(c9,A,B),the_carrier(c9)). [resolve(118,e,112,a)].
% 0.76/1.04 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(118,e,113,a)].
% 0.76/1.04 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(118,e,114,g)].
% 0.76/1.04 119 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(88,b,83,b)].
% 0.76/1.04 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(119,e,110,a)].
% 0.76/1.04 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(119,e,111,a)].
% 0.76/1.04 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(119,e,112,a)].
% 0.76/1.04 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(119,e,113,a)].
% 0.76/1.04 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(119,e,114,g)].
% 0.76/1.04 120 -latt_str(A) | empty_carrier(A) | -empty(the_carrier(A)). [resolve(96,b,89,b)].
% 0.76/1.04 Derived: empty_carrier(c4) | -empty(the_carrier(c4)). [resolve(120,a,110,a)].
% 0.76/1.04 Derived: empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(120,a,111,a)].
% 0.76/1.04 Derived: empty_carrier(c9) | -empty(the_carrier(c9)). [resolve(120,a,112,a)].
% 0.76/1.04 Derived: empty_carrier(boole_lattice(A)) | -empty(the_carrier(boole_lattice(A))). [resolve(120,a,113,a)].
% 0.76/1.04 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(120,a,114,g)].
% 0.76/1.04 121 -latt_str(A) | empty_carrier(A) | -empty(f6(A)). [resolve(96,b,93,b)].
% 0.76/1.04 Derived: empty_carrier(c4) | -empty(f6(c4)). [resolve(121,a,110,a)].
% 0.76/1.04 Derived: empty_carrier(c7) | -empty(f6(c7)). [resolve(121,a,111,a)].
% 0.76/1.04 Derived: empty_carrier(c9) | -empty(f6(c9)). [resolve(121,a,112,a)].
% 0.76/1.04 Derived: empty_carrier(boole_lattice(A)) | -empty(f6(boole_lattice(A))). [resolve(121,a,113,a)].
% 0.76/1.04 Derived: empty_carrier(latt_str_of(A,B,C)) | -empty(f6(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(121,a,114,g)].
% 0.76/1.04 122 -latt_str(A) | empty_carrier(A) | element(f6(A),powerset(the_carrier(A))). [resolve(96,b,94,b)].
% 0.76/1.04 Derived: empty_carrier(c4) | element(f6(c4),powerset(the_carrier(c4))). [resolve(122,a,110,a)].
% 0.76/1.04 Derived: empty_carrier(c7) | element(f6(c7),powerset(the_carrier(c7))). [resolve(122,a,111,a)].
% 0.76/1.04 Derived: empty_carrier(c9) | element(f6(c9),powerset(the_carrier(c9))). [resolve(122,a,112,a)].
% 0.76/1.04 Derived: empty_carrier(boole_lattice(A)) | element(f6(boole_lattice(A)),powerset(the_carrier(boole_lattice(A)))). [resolve(122,a,113,a)].
% 0.76/1.04 Derived: empty_carrier(latt_str_of(A,B,C)) | element(f6(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(122,a,114,g)].
% 0.76/1.04 123 function(the_L_join(A)) | -latt_str(A). [resolve(97,a,99,b)].
% 0.76/1.04 Derived: function(the_L_join(c4)). [resolve(123,b,110,a)].
% 0.76/1.04 Derived: function(the_L_join(c7)). [resolve(123,b,111,a)].
% 0.76/1.04 Derived: function(the_L_join(c9)). [resolve(123,b,112,a)].
% 0.76/1.04 Derived: function(the_L_join(boole_lattice(A))). [resolve(123,b,113,a)].
% 0.76/1.04 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(123,b,114,g)].
% 0.76/1.04 124 quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(100,a,99,b)].
% 0.76/1.04 Derived: quasi_total(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(124,b,110,a)].
% 0.76/1.04 Derived: quasi_total(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(124,b,111,a)].
% 0.76/1.04 Derived: quasi_total(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(124,b,112,a)].
% 0.76/1.04 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(124,b,113,a)].
% 0.76/1.04 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(124,b,114,g)].
% 0.76/1.04 125 relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(101,a,99,b)].
% 0.76/1.04 Derived: relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(125,b,110,a)].
% 0.76/1.04 Derived: relation_of2_as_subset(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(125,b,111,a)].
% 0.76/1.04 Derived: relation_of2_as_subset(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(125,b,112,a)].
% 0.76/1.04 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(125,b,113,a)].
% 0.76/1.04 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(125,b,114,g)].
% 0.76/1.04 126 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(102,b,99,b)].
% 0.76/1.04 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(join(c4,A,B),the_carrier(c4)). [resolve(126,e,110,a)].
% 0.76/1.04 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | element(join(c7,A,B),the_carrier(c7)). [resolve(126,e,111,a)].
% 0.76/1.04 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | element(join(c9,A,B),the_carrier(c9)). [resolve(126,e,112,a)].
% 0.76/1.04 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(126,e,113,a)].
% 0.76/1.04 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(126,e,114,g)].
% 0.76/1.04 127 empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | join(A,B,C) = C | -latt_str(A). [resolve(103,b,99,b)].
% 0.76/1.04 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | -below(c4,A,B) | join(c4,A,B) = B. [resolve(127,f,110,a)].
% 0.76/1.04 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | -below(c7,A,B) | join(c7,A,B) = B. [resolve(127,f,111,a)].
% 0.76/1.04 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | -below(c9,A,B) | join(c9,A,B) = B. [resolve(127,f,112,a)].
% 0.76/1.04 Derived: empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | -below(boole_lattice(A),B,C) | join(boole_lattice(A),B,C) = C. [resolve(127,f,113,a)].
% 0.76/1.04 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))) | -below(latt_str_of(A,B,C),D,E) | join(latt_str_of(A,B,C),D,E) = 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(127,f,114,g)].
% 0.76/1.04 128 empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,B,C) | join(A,B,C) != C | -latt_str(A). [resolve(104,b,99,b)].
% 0.76/1.04 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | below(c4,A,B) | join(c4,A,B) != B. [resolve(128,f,110,a)].
% 0.76/1.04 Derived: empty_carrier(c7) | -element(A,the_carrier(c7)) | -element(B,the_carrier(c7)) | below(c7,A,B) | join(c7,A,B) != B. [resolve(128,f,111,a)].
% 0.76/1.04 Derived: empty_carrier(c9) | -element(A,the_carrier(c9)) | -element(B,the_carrier(c9)) | below(c9,A,B) | join(c9,A,B) != B. [resolve(128,f,112,a)].
% 0.76/1.04 Derived: empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | below(boole_lattice(A),B,C) | join(boole_lattice(A),B,C) != C. [resolve(128,f,113,a)].
% 0.76/1.04 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))) | below(latt_str_of(A,B,C),D,E) | join(latt_str_of(A,B,C),D,E) != 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,f,114,g)].
% 0.76/1.04 129 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(105,b,99,b)].
% 0.76/1.04 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(129,e,110,a)].
% 0.76/1.04 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(129,e,111,a)].
% 0.76/1.04 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(129,e,112,a)].
% 0.76/1.04 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(129,e,113,a)].
% 0.76/1.04 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(129,e,114,g)].
% 0.76/1.04 130 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(65)].
% 0.76/1.04 131 relation_of2_as_subset(f3(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(43)].
% 0.76/1.04 Derived: relation_of2(f3(A,B),A,B). [resolve(130,a,131,a)].
% 0.76/1.04 132 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(65)].
% 0.76/1.04 133 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(33)].
% 0.76/1.04 Derived: element(f3(A,B),powerset(cartesian_product2(A,B))). [resolve(133,a,131,a)].
% 0.76/1.04 Derived: element(A,powerset(cartesian_product2(B,C))) | -relation_of2(A,B,C). [resolve(133,a,132,a)].
% 0.76/1.04 134 relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(86,a,82,a)].
% 0.76/1.04 Derived: relation_of2(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(134,a,130,a)].
% 0.76/1.04 Derived: element(the_L_meet(c1),powerset(cartesian_product2(cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)))). [resolve(134,a,133,a)].
% 0.76/1.04 135 relation_of2_as_subset(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(101,a,98,a)].
% 0.76/1.04 Derived: relation_of2(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(135,a,130,a)].
% 0.76/1.04 Derived: element(the_L_join(c3),powerset(cartesian_product2(cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)))). [resolve(135,a,133,a)].
% 0.76/1.04 136 relation_of2_as_subset(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(117,b,110,a)].
% 0.76/1.04 Derived: relation_of2(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(136,a,130,a)].
% 0.76/1.04 Derived: element(the_L_meet(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(136,a,133,a)].
% 0.76/1.04 137 relation_of2_as_subset(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(117,b,111,a)].
% 0.76/1.04 Derived: relation_of2(the_L_meet(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(137,a,130,a)].
% 0.76/1.04 Derived: element(the_L_meet(c7),powerset(cartesian_product2(cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)))). [resolve(137,a,133,a)].
% 0.76/1.04 138 relation_of2_as_subset(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(117,b,112,a)].
% 0.76/1.04 Derived: relation_of2(the_L_meet(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(138,a,130,a)].
% 0.76/1.04 Derived: element(the_L_meet(c9),powerset(cartesian_product2(cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)))). [resolve(138,a,133,a)].
% 0.76/1.04 139 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(117,b,113,a)].
% 0.76/1.04 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(139,a,130,a)].
% 0.76/1.04 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(139,a,133,a)].
% 0.76/1.04 140 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(117,b,114,g)].
% 0.76/1.04 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(140,a,130,a)].
% 0.76/1.04 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(140,a,133,a)].
% 0.76/1.04 141 relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(125,b,110,a)].
% 0.76/1.04 Derived: relation_of2(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(141,a,130,a)].
% 0.76/1.04 Derived: element(the_L_join(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(141,a,133,a)].
% 0.76/1.04 142 relation_of2_as_subset(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(125,b,111,a)].
% 0.76/1.04 Derived: relation_of2(the_L_join(c7),cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)). [resolve(142,a,130,a)].
% 0.76/1.04 Derived: element(the_L_join(c7),powerset(cartesian_product2(cartesian_product2(the_carrier(c7),the_carrier(c7)),the_carrier(c7)))). [resolve(142,a,133,a)].
% 0.76/1.04 143 relation_of2_as_subset(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(125,b,112,a)].
% 0.76/1.04 Derived: relation_of2(the_L_join(c9),cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)). [resolve(143,a,130,a)].
% 0.76/1.04 Derived: element(the_L_join(c9),powerset(cartesian_product2(cartesian_product2(the_carrier(c9),the_carrier(c9)),the_carrier(c9)))). [resolve(143,a,133,a)].
% 0.76/1.04 144 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(125,b,113,a)].
% 0.76/1.04 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(144,a,130,a)].
% 0.76/1.04 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(144,a,133,a)].
% 0.76/1.04 145 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(125,b,114,g)].
% 0.76/1.04 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(145,a,130,a)].
% 3.41/3.67 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(145,a,133,a)].
% 3.41/3.67 146 -relation(A) | -function(A) | apply(A,ordered_pair(B,C)) = apply_binary(A,B,C) # label(d1_binop_1) # label(axiom). [clausify(7)].
% 3.41/3.67 147 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(3)].
% 3.41/3.67 Derived: -function(A) | apply(A,ordered_pair(B,C)) = apply_binary(A,B,C) | -element(A,powerset(cartesian_product2(D,E))). [resolve(146,a,147,b)].
% 3.41/3.67
% 3.41/3.67 ============================== end predicate elimination =============
% 3.41/3.67
% 3.41/3.67 Auto_denials: (non-Horn, no changes).
% 3.41/3.67
% 3.41/3.67 Term ordering decisions:
% 3.41/3.67 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. cartesian_product2=1. set_union2=1. set_intersection2=1. unordered_pair=1. ordered_pair=1. apply=1. f1=1. f3=1. the_carrier=1. boole_lattice=1. the_L_join=1. the_L_meet=1. powerset=1. singleton=1. f2=1. f4=1. f5=1. f6=1. latt_str_of=1. join=1. meet=1. apply_binary=1. apply_binary_as_element=1.
% 3.41/3.67
% 3.41/3.67 ============================== end of process initial clauses ========
% 3.41/3.67
% 3.41/3.67 ============================== CLAUSES FOR SEARCH ====================
% 3.41/3.67
% 3.41/3.67 ============================== end of clauses for search =============
% 3.41/3.67
% 3.41/3.67 ============================== SEARCH ================================
% 3.41/3.67
% 3.41/3.67 % Starting search at 0.06 seconds.
% 3.41/3.67
% 3.41/3.67 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 318 (0.00 of 0.23 sec).
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=43.000, iters=3367
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=42.000, iters=3335
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=38.000, iters=3497
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=37.000, iters=3399
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=36.000, iters=3368
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=35.000, iters=3360
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=33.000, iters=3434
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=32.000, iters=3394
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=31.000, iters=3333
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=26.000, iters=3690
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=24.000, iters=3378
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=23.000, iters=3394
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=22.000, iters=4047
% 3.41/3.67
% 3.41/3.67 Low Water (keep): wt=21.000, iters=3639
% 3.41/3.67
% 3.41/3.67 Low Water (displace): id=15460, wt=24.000
% 3.41/3.67
% 3.41/3.67 Low Water (displace): id=15461, wt=22.000
% 3.41/3.67
% 3.41/3.67 Low Water (displace): id=15505, wt=20.000
% 3.41/3.67
% 3.41/3.67 Low Water (displace): id=15525, wt=16.000
% 3.41/3.67
% 3.41/3.67 Low Water (displace): id=15526, wt=15.000
% 3.41/3.67
% 3.41/3.67 ============================== PROOF =================================
% 3.41/3.67 % SZS status Theorem
% 3.41/3.67 % SZS output start Refutation
% 3.41/3.67
% 3.41/3.67 % Proof 1 at 2.60 (+ 0.06) seconds.
% 3.41/3.67 % Length of proof is 38.
% 3.41/3.67 % Level of proof is 10.
% 3.41/3.67 % Maximum clause weight is 22.000.
% 3.41/3.67 % Given clauses 3220.
% 3.41/3.67
% 3.41/3.67 5 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.67 10 (all A (-empty_carrier(A) & join_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below(A,B,C) <-> join(A,B,C) = C))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.67 15 (all A (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.67 30 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.67 44 (all A (-empty_carrier(boole_lattice(A)) & strict_latt_str(boole_lattice(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.67 67 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.67 69 (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].
% 3.41/3.67 78 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.67 80 -(all A all B (element(B,the_carrier(boole_lattice(A))) -> (all C (element(C,the_carrier(boole_lattice(A))) -> (below(boole_lattice(A),B,C) <-> subset(B,C)))))) # label(t2_lattice3) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.41/3.67 99 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(30)].
% 3.41/3.67 103 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | join(A,B,C) = C # label(d3_lattices) # label(axiom). [clausify(10)].
% 3.41/3.67 104 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,B,C) | join(A,B,C) != C # label(d3_lattices) # label(axiom). [clausify(10)].
% 3.41/3.67 113 latt_str(boole_lattice(A)) # label(dt_k1_lattice3) # label(axiom). [clausify(15)].
% 3.41/3.67 127 empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | join(A,B,C) = C | -latt_str(A). [resolve(103,b,99,b)].
% 3.41/3.67 128 empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,B,C) | join(A,B,C) != C | -latt_str(A). [resolve(104,b,99,b)].
% 3.41/3.67 161 subset(A,set_union2(A,B)) # label(t7_xboole_1) # label(axiom). [clausify(78)].
% 3.41/3.67 162 element(c11,the_carrier(boole_lattice(c10))) # label(t2_lattice3) # label(negated_conjecture). [clausify(80)].
% 3.41/3.67 163 element(c12,the_carrier(boole_lattice(c10))) # label(t2_lattice3) # label(negated_conjecture). [clausify(80)].
% 3.41/3.67 166 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(5)].
% 3.41/3.67 169 below(boole_lattice(c10),c11,c12) | subset(c11,c12) # label(t2_lattice3) # label(negated_conjecture). [clausify(80)].
% 3.41/3.67 175 -empty_carrier(boole_lattice(A)) # label(fc1_lattice3) # label(axiom). [clausify(44)].
% 3.41/3.67 181 -below(boole_lattice(c10),c11,c12) | -subset(c11,c12) # label(t2_lattice3) # label(negated_conjecture). [clausify(80)].
% 3.41/3.67 192 -subset(A,B) | set_union2(A,B) = B # label(t12_xboole_1) # label(axiom). [clausify(67)].
% 3.41/3.67 195 -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | join(boole_lattice(B),A,C) = set_union2(A,C) # label(t1_lattice3) # label(axiom). [clausify(69)].
% 3.41/3.67 307 empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | -below(boole_lattice(A),B,C) | join(boole_lattice(A),B,C) = C. [resolve(127,f,113,a)].
% 3.41/3.67 308 -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | -below(boole_lattice(B),A,C) | join(boole_lattice(B),A,C) = C. [copy(307),unit_del(a,175)].
% 3.41/3.67 314 empty_carrier(boole_lattice(A)) | -element(B,the_carrier(boole_lattice(A))) | -element(C,the_carrier(boole_lattice(A))) | below(boole_lattice(A),B,C) | join(boole_lattice(A),B,C) != C. [resolve(128,f,113,a)].
% 3.41/3.67 315 -element(A,the_carrier(boole_lattice(B))) | -element(C,the_carrier(boole_lattice(B))) | below(boole_lattice(B),A,C) | join(boole_lattice(B),A,C) != C. [copy(314),unit_del(a,175)].
% 3.41/3.67 438 -element(A,the_carrier(boole_lattice(c10))) | join(boole_lattice(c10),c11,A) = set_union2(A,c11). [resolve(195,a,162,a),rewrite([166(10)])].
% 3.41/3.67 931 join(boole_lattice(c10),c11,c12) = c12 | subset(c11,c12). [resolve(308,c,169,a),unit_del(a,162),unit_del(b,163)].
% 3.41/3.67 939 -element(A,the_carrier(boole_lattice(c10))) | below(boole_lattice(c10),c11,A) | join(boole_lattice(c10),c11,A) != A. [resolve(315,a,162,a)].
% 3.41/3.67 1499 join(boole_lattice(c10),c11,c12) = set_union2(c11,c12). [resolve(438,a,163,a),rewrite([166(8)])].
% 3.41/3.67 1501 set_union2(c11,c12) = c12 | subset(c11,c12). [back_rewrite(931),rewrite([1499(5)])].
% 3.41/3.67 1600 set_union2(c11,c12) = c12. [resolve(1501,b,192,a),merge(b)].
% 3.41/3.67 1601 join(boole_lattice(c10),c11,c12) = c12. [back_rewrite(1499),rewrite([1600(8)])].
% 3.41/3.67 1603 subset(c11,c12). [para(1600(a,1),161(a,2))].
% 3.41/3.67 1608 -below(boole_lattice(c10),c11,c12). [back_unit_del(181),unit_del(b,1603)].
% 3.41/3.67 18313 $F. [resolve(939,a,163,a),rewrite([1601(10)]),xx(b),unit_del(a,1608)].
% 3.41/3.67
% 3.41/3.67 % SZS output end Refutation
% 3.41/3.67 ============================== end of proof ==========================
% 3.41/3.67
% 3.41/3.67 ============================== STATISTICS ============================
% 3.41/3.67
% 3.41/3.67 Given=3220. Generated=86409. Kept=18134. proofs=1.
% 3.41/3.67 Usable=3208. Sos=9994. Demods=2986. Limbo=48, Disabled=5128. Hints=0.
% 3.41/3.67 Megabytes=26.47.
% 3.41/3.67 User_CPU=2.60, System_CPU=0.06, Wall_clock=2.
% 3.41/3.67
% 3.41/3.67 ============================== end of statistics =====================
% 3.41/3.67
% 3.41/3.67 ============================== end of search =========================
% 3.41/3.67
% 3.41/3.67 THEOREM PROVED
% 3.41/3.67 % SZS status Theorem
% 3.41/3.67
% 3.41/3.67 Exiting with 1 proof.
% 3.41/3.67
% 3.41/3.67 Process 4343 exit (max_proofs) Mon Jun 20 11:21:26 2022
% 3.41/3.67 Prover9 interrupted
%------------------------------------------------------------------------------