TSTP Solution File: SEU304+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 13:30:48 EDT 2022
% Result : Theorem 1.44s 1.72s
% Output : Refutation 1.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 18:22:52 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.46/1.03 ============================== Prover9 ===============================
% 0.46/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.03 Process 16791 was started by sandbox on n012.cluster.edu,
% 0.46/1.03 Sun Jun 19 18:22:53 2022
% 0.46/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16621_n012.cluster.edu".
% 0.46/1.03 ============================== end of head ===========================
% 0.46/1.03
% 0.46/1.03 ============================== INPUT =================================
% 0.46/1.03
% 0.46/1.03 % Reading from file /tmp/Prover9_16621_n012.cluster.edu
% 0.46/1.03
% 0.46/1.03 set(prolog_style_variables).
% 0.46/1.03 set(auto2).
% 0.46/1.03 % set(auto2) -> set(auto).
% 0.46/1.03 % set(auto) -> set(auto_inference).
% 0.46/1.03 % set(auto) -> set(auto_setup).
% 0.46/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.03 % set(auto) -> set(auto_limits).
% 0.46/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.03 % set(auto) -> set(auto_denials).
% 0.46/1.03 % set(auto) -> set(auto_process).
% 0.46/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.03 % set(auto2) -> assign(stats, some).
% 0.46/1.03 % set(auto2) -> clear(echo_input).
% 0.46/1.03 % set(auto2) -> set(quiet).
% 0.46/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.03 % set(auto2) -> clear(print_given).
% 0.46/1.03 assign(lrs_ticks,-1).
% 0.46/1.03 assign(sos_limit,10000).
% 0.46/1.03 assign(order,kbo).
% 0.46/1.03 set(lex_order_vars).
% 0.46/1.03 clear(print_given).
% 0.46/1.03
% 0.46/1.03 % formulas(sos). % not echoed (50 formulas)
% 0.46/1.03
% 0.46/1.03 ============================== end of input ==========================
% 0.46/1.03
% 0.46/1.03 % From the command line: assign(max_seconds, 300).
% 0.46/1.03
% 0.46/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.03
% 0.46/1.03 % Formulas that are not ordinary clauses:
% 0.46/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 2 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 3 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 4 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> meet_commut(A,B,C) = meet_commut(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 5 (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].
% 0.46/1.03 6 (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].
% 0.46/1.03 7 (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].
% 0.46/1.03 8 (all A (-empty_carrier(A) & latt_str(A) -> (meet_absorbing(A) <-> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> join(A,meet(A,B,C),C) = C))))))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 9 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 10 (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].
% 0.46/1.03 11 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 12 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 13 (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].
% 0.46/1.03 14 (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].
% 0.46/1.03 15 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 16 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> element(meet_commut(A,B,C),the_carrier(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 17 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 18 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 19 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 20 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 21 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 22 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 23 (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].
% 0.46/1.03 24 (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].
% 0.46/1.03 25 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 26 (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].
% 0.46/1.03 27 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 28 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 29 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 30 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 31 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 32 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 33 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 34 (all A (-empty(powerset(A)) & cup_closed(powerset(A)) & diff_closed(powerset(A)) & preboolean(powerset(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 35 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 36 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 37 (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].
% 0.46/1.04 38 (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].
% 0.46/1.04 39 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> meet_commut(A,B,C) = meet(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 40 (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].
% 0.46/1.04 41 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 42 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 43 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 44 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 45 (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].
% 0.46/1.04 46 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 47 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 48 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 49 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.04 50 -(all A (-empty_carrier(A) & meet_commutative(A) & meet_absorbing(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> below(A,meet_commut(A,B,C),B))))))) # label(t23_lattices) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.04
% 0.46/1.04 ============================== end of process non-clausal formulas ===
% 0.46/1.04
% 0.46/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.04
% 0.46/1.04 ============================== PREDICATE ELIMINATION =================
% 0.46/1.04 51 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(17)].
% 0.46/1.04 52 meet_semilatt_str(c1) # label(existence_l1_lattices) # label(axiom). [clausify(27)].
% 0.46/1.04 Derived: one_sorted_str(c1). [resolve(51,a,52,a)].
% 0.46/1.04 53 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(20)].
% 0.46/1.04 Derived: -latt_str(A) | one_sorted_str(A). [resolve(53,b,51,a)].
% 0.46/1.04 54 -meet_semilatt_str(A) | function(the_L_meet(A)) # label(dt_u1_lattices) # label(axiom). [clausify(24)].
% 0.46/1.04 Derived: function(the_L_meet(c1)). [resolve(54,a,52,a)].
% 0.46/1.04 Derived: function(the_L_meet(A)) | -latt_str(A). [resolve(54,a,53,b)].
% 0.46/1.04 55 -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(24)].
% 0.46/1.04 Derived: quasi_total(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(55,a,52,a)].
% 0.46/1.04 Derived: quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(55,a,53,b)].
% 0.46/1.04 56 -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(24)].
% 0.46/1.04 Derived: relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(56,a,52,a)].
% 0.46/1.04 Derived: relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(56,a,53,b)].
% 0.46/1.04 57 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(14)].
% 0.46/1.04 Derived: empty_carrier(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | element(meet(c1,A,B),the_carrier(c1)). [resolve(57,b,52,a)].
% 0.46/1.04 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(57,b,53,b)].
% 0.46/1.04 58 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet_commut(A,B,C),the_carrier(A)) # label(dt_k4_lattices) # label(axiom). [clausify(16)].
% 0.46/1.04 Derived: empty_carrier(c1) | -meet_commutative(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | element(meet_commut(c1,A,B),the_carrier(c1)). [resolve(58,c,52,a)].
% 0.46/1.04 Derived: empty_carrier(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet_commut(A,B,C),the_carrier(A)) | -latt_str(A). [resolve(58,c,53,b)].
% 0.46/1.04 59 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet_commut(A,C,B) = meet_commut(A,B,C) # label(commutativity_k4_lattices) # label(axiom). [clausify(4)].
% 0.46/1.04 Derived: empty_carrier(c1) | -meet_commutative(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | meet_commut(c1,B,A) = meet_commut(c1,A,B). [resolve(59,c,52,a)].
% 0.46/1.04 Derived: empty_carrier(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet_commut(A,C,B) = meet_commut(A,B,C) | -latt_str(A). [resolve(59,c,53,b)].
% 0.46/1.04 60 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet(A,B,C) = meet_commut(A,B,C) # label(redefinition_k4_lattices) # label(axiom). [clausify(39)].
% 0.46/1.04 Derived: empty_carrier(c1) | -meet_commutative(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | meet(c1,A,B) = meet_commut(c1,A,B). [resolve(60,c,52,a)].
% 0.46/1.04 Derived: empty_carrier(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet(A,B,C) = meet_commut(A,B,C) | -latt_str(A). [resolve(60,c,53,b)].
% 0.46/1.04 61 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(6)].
% 0.46/1.04 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(61,b,52,a)].
% 0.46/1.04 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(61,b,53,b)].
% 0.46/1.04 62 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(35)].
% 0.46/1.04 63 one_sorted_str(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(28)].
% 0.46/1.04 64 one_sorted_str(c5) # label(rc3_struct_0) # label(axiom). [clausify(36)].
% 0.46/1.04 65 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(19)].
% 0.46/1.04 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(62,b,63,a)].
% 0.46/1.04 Derived: empty_carrier(c5) | -empty(the_carrier(c5)). [resolve(62,b,64,a)].
% 0.46/1.04 Derived: empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(62,b,65,b)].
% 0.46/1.04 66 empty_carrier(A) | -one_sorted_str(A) | -empty(f6(A)) # label(rc5_struct_0) # label(axiom). [clausify(37)].
% 0.46/1.04 Derived: empty_carrier(c2) | -empty(f6(c2)). [resolve(66,b,63,a)].
% 0.46/1.04 Derived: empty_carrier(c5) | -empty(f6(c5)). [resolve(66,b,64,a)].
% 0.46/1.04 Derived: empty_carrier(A) | -empty(f6(A)) | -join_semilatt_str(A). [resolve(66,b,65,b)].
% 0.46/1.04 67 empty_carrier(A) | -one_sorted_str(A) | element(f6(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(37)].
% 0.46/1.04 Derived: empty_carrier(c2) | element(f6(c2),powerset(the_carrier(c2))). [resolve(67,b,63,a)].
% 0.46/1.04 Derived: empty_carrier(c5) | element(f6(c5),powerset(the_carrier(c5))). [resolve(67,b,64,a)].
% 0.46/1.04 Derived: empty_carrier(A) | element(f6(A),powerset(the_carrier(A))) | -join_semilatt_str(A). [resolve(67,b,65,b)].
% 0.46/1.04 68 one_sorted_str(c1). [resolve(51,a,52,a)].
% 0.46/1.04 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(68,a,62,b)].
% 0.46/1.04 Derived: empty_carrier(c1) | -empty(f6(c1)). [resolve(68,a,66,b)].
% 0.46/1.04 Derived: empty_carrier(c1) | element(f6(c1),powerset(the_carrier(c1))). [resolve(68,a,67,b)].
% 0.46/1.04 69 -latt_str(A) | one_sorted_str(A). [resolve(53,b,51,a)].
% 0.46/1.04 Derived: -latt_str(A) | empty_carrier(A) | -empty(the_carrier(A)). [resolve(69,b,62,b)].
% 0.46/1.04 Derived: -latt_str(A) | empty_carrier(A) | -empty(f6(A)). [resolve(69,b,66,b)].
% 0.46/1.04 Derived: -latt_str(A) | empty_carrier(A) | element(f6(A),powerset(the_carrier(A))). [resolve(69,b,67,b)].
% 0.46/1.04 70 -join_semilatt_str(A) | function(the_L_join(A)) # label(dt_u2_lattices) # label(axiom). [clausify(26)].
% 0.46/1.04 71 join_semilatt_str(c3) # label(existence_l2_lattices) # label(axiom). [clausify(29)].
% 0.46/1.04 72 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(20)].
% 0.46/1.04 Derived: function(the_L_join(c3)). [resolve(70,a,71,a)].
% 0.46/1.04 Derived: function(the_L_join(A)) | -latt_str(A). [resolve(70,a,72,b)].
% 0.46/1.04 73 -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(26)].
% 0.46/1.04 Derived: quasi_total(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(73,a,71,a)].
% 0.46/1.04 Derived: quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(73,a,72,b)].
% 0.46/1.04 74 -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(26)].
% 0.46/1.04 Derived: relation_of2_as_subset(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(74,a,71,a)].
% 0.46/1.04 Derived: relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(74,a,72,b)].
% 0.46/1.04 75 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(10)].
% 0.46/1.04 Derived: empty_carrier(c3) | -element(A,the_carrier(c3)) | -element(B,the_carrier(c3)) | element(join(c3,A,B),the_carrier(c3)). [resolve(75,b,71,a)].
% 0.46/1.04 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(75,b,72,b)].
% 0.46/1.04 76 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(7)].
% 0.46/1.04 Derived: empty_carrier(c3) | -element(A,the_carrier(c3)) | -element(B,the_carrier(c3)) | -below(c3,A,B) | join(c3,A,B) = B. [resolve(76,b,71,a)].
% 0.46/1.04 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(76,b,72,b)].
% 0.46/1.04 77 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(7)].
% 0.46/1.04 Derived: empty_carrier(c3) | -element(A,the_carrier(c3)) | -element(B,the_carrier(c3)) | below(c3,A,B) | join(c3,A,B) != B. [resolve(77,b,71,a)].
% 0.46/1.04 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(77,b,72,b)].
% 0.46/1.04 78 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(5)].
% 0.46/1.04 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(78,b,71,a)].
% 0.46/1.04 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(78,b,72,b)].
% 0.46/1.04 79 empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(62,b,65,b)].
% 0.46/1.04 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(79,c,71,a)].
% 0.46/1.04 80 empty_carrier(A) | -empty(f6(A)) | -join_semilatt_str(A). [resolve(66,b,65,b)].
% 0.46/1.04 Derived: empty_carrier(c3) | -empty(f6(c3)). [resolve(80,c,71,a)].
% 0.46/1.04 81 empty_carrier(A) | element(f6(A),powerset(the_carrier(A))) | -join_semilatt_str(A). [resolve(67,b,65,b)].
% 0.46/1.04 Derived: empty_carrier(c3) | element(f6(c3),powerset(the_carrier(c3))). [resolve(81,c,71,a)].
% 0.46/1.04 82 empty_carrier(A) | -latt_str(A) | meet_absorbing(A) | element(f1(A),the_carrier(A)) # label(d8_lattices) # label(axiom). [clausify(8)].
% 0.46/1.04 83 latt_str(c4) # label(existence_l3_lattices) # label(axiom). [clausify(30)].
% 0.46/1.04 84 latt_str(c6) # label(t23_lattices) # label(negated_conjecture). [clausify(50)].
% 0.46/1.04 Derived: empty_carrier(c4) | meet_absorbing(c4) | element(f1(c4),the_carrier(c4)). [resolve(82,b,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | meet_absorbing(c6) | element(f1(c6),the_carrier(c6)). [resolve(82,b,84,a)].
% 0.46/1.04 85 empty_carrier(A) | -latt_str(A) | meet_absorbing(A) | element(f2(A),the_carrier(A)) # label(d8_lattices) # label(axiom). [clausify(8)].
% 0.46/1.04 Derived: empty_carrier(c4) | meet_absorbing(c4) | element(f2(c4),the_carrier(c4)). [resolve(85,b,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | meet_absorbing(c6) | element(f2(c6),the_carrier(c6)). [resolve(85,b,84,a)].
% 0.46/1.04 86 empty_carrier(A) | -latt_str(A) | meet_absorbing(A) | join(A,meet(A,f1(A),f2(A)),f2(A)) != f2(A) # label(d8_lattices) # label(axiom). [clausify(8)].
% 0.46/1.04 Derived: empty_carrier(c4) | meet_absorbing(c4) | join(c4,meet(c4,f1(c4),f2(c4)),f2(c4)) != f2(c4). [resolve(86,b,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | meet_absorbing(c6) | join(c6,meet(c6,f1(c6),f2(c6)),f2(c6)) != f2(c6). [resolve(86,b,84,a)].
% 0.46/1.04 87 empty_carrier(A) | -latt_str(A) | -meet_absorbing(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,meet(A,B,C),C) = C # label(d8_lattices) # label(axiom). [clausify(8)].
% 0.46/1.04 Derived: empty_carrier(c4) | -meet_absorbing(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | join(c4,meet(c4,A,B),B) = B. [resolve(87,b,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | -meet_absorbing(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | join(c6,meet(c6,A,B),B) = B. [resolve(87,b,84,a)].
% 0.46/1.04 88 function(the_L_meet(A)) | -latt_str(A). [resolve(54,a,53,b)].
% 0.46/1.04 Derived: function(the_L_meet(c4)). [resolve(88,b,83,a)].
% 0.46/1.04 Derived: function(the_L_meet(c6)). [resolve(88,b,84,a)].
% 0.46/1.04 89 quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(55,a,53,b)].
% 0.46/1.04 Derived: quasi_total(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(89,b,83,a)].
% 0.46/1.04 Derived: quasi_total(the_L_meet(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(89,b,84,a)].
% 0.46/1.04 90 relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(56,a,53,b)].
% 0.46/1.04 Derived: relation_of2_as_subset(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(90,b,83,a)].
% 0.46/1.04 Derived: relation_of2_as_subset(the_L_meet(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(90,b,84,a)].
% 0.46/1.04 91 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(57,b,53,b)].
% 0.46/1.04 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(meet(c4,A,B),the_carrier(c4)). [resolve(91,e,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | element(meet(c6,A,B),the_carrier(c6)). [resolve(91,e,84,a)].
% 0.46/1.04 92 empty_carrier(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet_commut(A,B,C),the_carrier(A)) | -latt_str(A). [resolve(58,c,53,b)].
% 0.46/1.04 Derived: empty_carrier(c4) | -meet_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(meet_commut(c4,A,B),the_carrier(c4)). [resolve(92,f,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | -meet_commutative(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | element(meet_commut(c6,A,B),the_carrier(c6)). [resolve(92,f,84,a)].
% 0.46/1.04 93 empty_carrier(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet_commut(A,C,B) = meet_commut(A,B,C) | -latt_str(A). [resolve(59,c,53,b)].
% 0.46/1.04 Derived: empty_carrier(c4) | -meet_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | meet_commut(c4,B,A) = meet_commut(c4,A,B). [resolve(93,f,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | -meet_commutative(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | meet_commut(c6,B,A) = meet_commut(c6,A,B). [resolve(93,f,84,a)].
% 0.46/1.04 94 empty_carrier(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet(A,B,C) = meet_commut(A,B,C) | -latt_str(A). [resolve(60,c,53,b)].
% 0.46/1.04 Derived: empty_carrier(c4) | -meet_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | meet(c4,A,B) = meet_commut(c4,A,B). [resolve(94,f,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | -meet_commutative(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | meet(c6,A,B) = meet_commut(c6,A,B). [resolve(94,f,84,a)].
% 0.46/1.04 95 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(61,b,53,b)].
% 0.46/1.04 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(95,e,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | meet(c6,A,B) = apply_binary_as_element(the_carrier(c6),the_carrier(c6),the_carrier(c6),the_L_meet(c6),A,B). [resolve(95,e,84,a)].
% 0.46/1.04 96 -latt_str(A) | empty_carrier(A) | -empty(the_carrier(A)). [resolve(69,b,62,b)].
% 0.46/1.04 Derived: empty_carrier(c4) | -empty(the_carrier(c4)). [resolve(96,a,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(96,a,84,a)].
% 0.46/1.04 97 -latt_str(A) | empty_carrier(A) | -empty(f6(A)). [resolve(69,b,66,b)].
% 0.46/1.04 Derived: empty_carrier(c4) | -empty(f6(c4)). [resolve(97,a,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | -empty(f6(c6)). [resolve(97,a,84,a)].
% 0.46/1.04 98 -latt_str(A) | empty_carrier(A) | element(f6(A),powerset(the_carrier(A))). [resolve(69,b,67,b)].
% 0.46/1.04 Derived: empty_carrier(c4) | element(f6(c4),powerset(the_carrier(c4))). [resolve(98,a,83,a)].
% 0.46/1.04 Derived: empty_carrier(c6) | element(f6(c6),powerset(the_carrier(c6))). [resolve(98,a,84,a)].
% 0.46/1.04 99 function(the_L_join(A)) | -latt_str(A). [resolve(70,a,72,b)].
% 0.46/1.04 Derived: function(the_L_join(c4)). [resolve(99,b,83,a)].
% 0.46/1.04 Derived: function(the_L_join(c6)). [resolve(99,b,84,a)].
% 0.46/1.04 100 quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(73,a,72,b)].
% 0.46/1.04 Derived: quasi_total(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(100,b,83,a)].
% 0.46/1.04 Derived: quasi_total(the_L_join(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(100,b,84,a)].
% 0.46/1.04 101 relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(74,a,72,b)].
% 0.46/1.04 Derived: relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(101,b,83,a)].
% 0.46/1.04 Derived: relation_of2_as_subset(the_L_join(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(101,b,84,a)].
% 0.46/1.04 102 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(75,b,72,b)].
% 0.46/1.05 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(join(c4,A,B),the_carrier(c4)). [resolve(102,e,83,a)].
% 0.46/1.05 Derived: empty_carrier(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | element(join(c6,A,B),the_carrier(c6)). [resolve(102,e,84,a)].
% 0.46/1.05 103 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(76,b,72,b)].
% 0.46/1.05 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | -below(c4,A,B) | join(c4,A,B) = B. [resolve(103,f,83,a)].
% 0.46/1.05 Derived: empty_carrier(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | -below(c6,A,B) | join(c6,A,B) = B. [resolve(103,f,84,a)].
% 0.46/1.05 104 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(77,b,72,b)].
% 0.46/1.05 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | below(c4,A,B) | join(c4,A,B) != B. [resolve(104,f,83,a)].
% 0.46/1.05 Derived: empty_carrier(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | below(c6,A,B) | join(c6,A,B) != B. [resolve(104,f,84,a)].
% 0.46/1.05 105 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(78,b,72,b)].
% 0.46/1.05 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(105,e,83,a)].
% 0.46/1.05 Derived: empty_carrier(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | apply_binary_as_element(the_carrier(c6),the_carrier(c6),the_carrier(c6),the_L_join(c6),A,B) = join(c6,A,B). [resolve(105,e,84,a)].
% 0.46/1.05 106 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(3)].
% 0.46/1.05 107 cup_closed(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(34)].
% 0.46/1.05 108 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(2)].
% 0.46/1.05 Derived: -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(106,a,107,a)].
% 0.46/1.05 109 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(2)].
% 0.46/1.05 110 preboolean(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(34)].
% 0.46/1.05 Derived: diff_closed(powerset(A)). [resolve(109,a,110,a)].
% 0.46/1.05 111 -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(106,a,107,a)].
% 0.46/1.05 112 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(44)].
% 0.46/1.05 113 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(41)].
% 0.46/1.05 114 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(44)].
% 0.46/1.05 Derived: element(A,powerset(A)). [resolve(112,b,113,a)].
% 0.46/1.05 115 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(40)].
% 0.46/1.05 116 relation_of2_as_subset(f5(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(33)].
% 0.46/1.05 Derived: relation_of2(f5(A,B),A,B). [resolve(115,a,116,a)].
% 0.46/1.05 117 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(40)].
% 0.46/1.05 118 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(23)].
% 0.46/1.05 Derived: element(f5(A,B),powerset(cartesian_product2(A,B))). [resolve(118,a,116,a)].
% 0.46/1.05 Derived: element(A,powerset(cartesian_product2(B,C))) | -relation_of2(A,B,C). [resolve(118,a,117,a)].
% 0.46/1.05 119 relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(56,a,52,a)].
% 0.46/1.05 Derived: relation_of2(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(119,a,115,a)].
% 0.46/1.05 Derived: element(the_L_meet(c1),powerset(cartesian_product2(cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)))). [resolve(119,a,118,a)].
% 0.46/1.05 120 relation_of2_as_subset(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(74,a,71,a)].
% 0.46/1.05 Derived: relation_of2(the_L_join(c3),cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)). [resolve(120,a,115,a)].
% 0.46/1.05 Derived: element(the_L_join(c3),powerset(cartesian_product2(cartesian_product2(the_carrier(c3),the_carrier(c3)),the_carrier(c3)))). [resolve(120,a,118,a)].
% 0.46/1.05 121 relation_of2_as_subset(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(90,b,83,a)].
% 0.46/1.05 Derived: relation_of2(the_L_meet(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(121,a,115,a)].
% 0.46/1.05 Derived: element(the_L_meet(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(121,a,118,a)].
% 0.46/1.05 122 relation_of2_as_subset(the_L_meet(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(90,b,84,a)].
% 0.46/1.05 Derived: relation_of2(the_L_meet(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(122,a,115,a)].
% 0.46/1.05 Derived: element(the_L_meet(c6),powerset(cartesian_product2(cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)))). [resolve(122,a,118,a)].
% 0.46/1.05 123 relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(101,b,83,a)].
% 0.46/1.05 Derived: relation_of2(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(123,a,115,a)].
% 0.46/1.05 Derived: element(the_L_join(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(123,a,118,a)].
% 0.46/1.05 124 relation_of2_as_subset(the_L_join(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(101,b,84,a)].
% 0.46/1.05 Derived: relation_of2(the_L_join(c6),cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)). [resolve(124,a,115,a)].
% 0.46/1.05 Derived: element(the_L_join(c6),powerset(cartesian_product2(cartesian_product2(the_carrier(c6),the_carrier(c6)),the_carrier(c6)))). [resolve(124,a,118,a)].
% 0.46/1.05 125 function(the_L_meet(c1)). [resolve(54,a,52,a)].
% 0.46/1.05 126 empty(A) | empty(B) | -function(C) | -quasi_total(C,cartesian_product2(A,B),D) | -relation_of2(C,cartesian_product2(A,B),D) | -element(E,A) | -element(F,B) | element(apply_binary_as_element(A,B,D,C,E,F),D) # label(dt_k2_binop_1) # label(axiom). [clausify(13)].
% 0.46/1.05 127 empty(A) | empty(B) | -function(C) | -quasi_total(C,cartesian_product2(A,B),D) | -relation_of2(C,cartesian_product2(A,B),D) | -element(E,A) | -element(F,B) | apply_binary(C,E,F) = apply_binary_as_element(A,B,D,C,E,F) # label(redefinition_k2_binop_1) # label(axiom). [clausify(38)].
% 0.46/1.05 Derived: empty(A) | empty(B) | -quasi_total(the_L_meet(c1),cartesian_product2(A,B),C) | -relation_of2(the_L_meet(c1),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | element(apply_binary_as_element(A,B,C,the_L_meet(c1),D,E),C). [resolve(125,a,126,c)].
% 0.46/1.05 Derived: empty(A) | empty(B) | -quasi_total(the_L_meet(c1),cartesian_product2(A,B),C) | -relation_of2(the_L_meet(c1),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | apply_binary(the_L_meet(c1),D,E) = apply_binary_as_element(A,B,C,the_L_meet(c1),D,E). [resolve(125,a,127,c)].
% 0.46/1.05 128 function(the_L_join(c3)). [resolve(70,a,71,a)].
% 0.46/1.05 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c3),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c3),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | element(apply_binary_as_element(A,B,C,the_L_join(c3),D,E),C). [resolve(128,a,126,c)].
% 0.46/1.05 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c3),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c3),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | apply_binary(the_L_join(c3),D,E) = apply_binary_as_element(A,B,C,the_L_join(c3),D,E). [resolve(128,a,127,c)].
% 0.46/1.05 129 function(the_L_meet(c4)). [resolve(88,b,83,a)].
% 0.46/1.05 Derived: empty(A) | empty(B) | -quasi_total(the_L_meet(c4),cartesian_product2(A,B),C) | -relation_of2(the_L_meet(c4),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | element(apply_binary_as_element(A,B,C,the_L_meet(c4),D,E),C). [resolve(129,a,126,c)].
% 1.44/1.72 Derived: empty(A) | empty(B) | -quasi_total(the_L_meet(c4),cartesian_product2(A,B),C) | -relation_of2(the_L_meet(c4),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | apply_binary(the_L_meet(c4),D,E) = apply_binary_as_element(A,B,C,the_L_meet(c4),D,E). [resolve(129,a,127,c)].
% 1.44/1.72 130 function(the_L_meet(c6)). [resolve(88,b,84,a)].
% 1.44/1.72 Derived: empty(A) | empty(B) | -quasi_total(the_L_meet(c6),cartesian_product2(A,B),C) | -relation_of2(the_L_meet(c6),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | element(apply_binary_as_element(A,B,C,the_L_meet(c6),D,E),C). [resolve(130,a,126,c)].
% 1.44/1.72 Derived: empty(A) | empty(B) | -quasi_total(the_L_meet(c6),cartesian_product2(A,B),C) | -relation_of2(the_L_meet(c6),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | apply_binary(the_L_meet(c6),D,E) = apply_binary_as_element(A,B,C,the_L_meet(c6),D,E). [resolve(130,a,127,c)].
% 1.44/1.72 131 function(the_L_join(c4)). [resolve(99,b,83,a)].
% 1.44/1.72 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c4),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c4),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | element(apply_binary_as_element(A,B,C,the_L_join(c4),D,E),C). [resolve(131,a,126,c)].
% 1.44/1.72 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c4),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c4),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | apply_binary(the_L_join(c4),D,E) = apply_binary_as_element(A,B,C,the_L_join(c4),D,E). [resolve(131,a,127,c)].
% 1.44/1.72 132 function(the_L_join(c6)). [resolve(99,b,84,a)].
% 1.44/1.72 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c6),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c6),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | element(apply_binary_as_element(A,B,C,the_L_join(c6),D,E),C). [resolve(132,a,126,c)].
% 1.44/1.72 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c6),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c6),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | apply_binary(the_L_join(c6),D,E) = apply_binary_as_element(A,B,C,the_L_join(c6),D,E). [resolve(132,a,127,c)].
% 1.44/1.72
% 1.44/1.72 ============================== end predicate elimination =============
% 1.44/1.72
% 1.44/1.72 Auto_denials: (non-Horn, no changes).
% 1.44/1.72
% 1.44/1.72 Term ordering decisions:
% 1.44/1.72 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. cartesian_product2=1. f3=1. f5=1. the_carrier=1. the_L_join=1. the_L_meet=1. powerset=1. f1=1. f2=1. f4=1. f6=1. join=1. meet=1. meet_commut=1. apply_binary=1. apply_binary_as_element=1.
% 1.44/1.72
% 1.44/1.72 ============================== end of process initial clauses ========
% 1.44/1.72
% 1.44/1.72 ============================== CLAUSES FOR SEARCH ====================
% 1.44/1.72
% 1.44/1.72 ============================== end of clauses for search =============
% 1.44/1.72
% 1.44/1.72 ============================== SEARCH ================================
% 1.44/1.72
% 1.44/1.72 % Starting search at 0.04 seconds.
% 1.44/1.72
% 1.44/1.72 Low Water (keep): wt=40.000, iters=3810
% 1.44/1.72
% 1.44/1.72 Low Water (keep): wt=33.000, iters=3566
% 1.44/1.72
% 1.44/1.72 Low Water (keep): wt=32.000, iters=3450
% 1.44/1.72
% 1.44/1.72 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.38 sec).
% 1.44/1.72
% 1.44/1.72 Low Water (keep): wt=31.000, iters=3462
% 1.44/1.72
% 1.44/1.72 Low Water (keep): wt=30.000, iters=3496
% 1.44/1.72
% 1.44/1.72 ============================== PROOF =================================
% 1.44/1.72 % SZS status Theorem
% 1.44/1.72 % SZS output start Refutation
% 1.44/1.72
% 1.44/1.72 % Proof 1 at 0.69 (+ 0.01) seconds.
% 1.44/1.72 % Length of proof is 50.
% 1.44/1.72 % Level of proof is 10.
% 1.44/1.72 % Maximum clause weight is 18.000.
% 1.44/1.72 % Given clauses 752.
% 1.44/1.72
% 1.44/1.72 4 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> meet_commut(A,B,C) = meet_commut(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.44/1.72 7 (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].
% 1.44/1.72 8 (all A (-empty_carrier(A) & latt_str(A) -> (meet_absorbing(A) <-> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> join(A,meet(A,B,C),C) = C))))))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.44/1.72 14 (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].
% 1.44/1.72 20 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.44/1.72 39 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> meet_commut(A,B,C) = meet(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.44/1.72 50 -(all A (-empty_carrier(A) & meet_commutative(A) & meet_absorbing(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> below(A,meet_commut(A,B,C),B))))))) # label(t23_lattices) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.44/1.72 53 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(20)].
% 1.44/1.72 57 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(14)].
% 1.44/1.72 59 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet_commut(A,C,B) = meet_commut(A,B,C) # label(commutativity_k4_lattices) # label(axiom). [clausify(4)].
% 1.44/1.72 60 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet(A,B,C) = meet_commut(A,B,C) # label(redefinition_k4_lattices) # label(axiom). [clausify(39)].
% 1.44/1.72 72 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(20)].
% 1.44/1.72 77 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(7)].
% 1.44/1.72 84 latt_str(c6) # label(t23_lattices) # label(negated_conjecture). [clausify(50)].
% 1.44/1.72 87 empty_carrier(A) | -latt_str(A) | -meet_absorbing(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,meet(A,B,C),C) = C # label(d8_lattices) # label(axiom). [clausify(8)].
% 1.44/1.72 91 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(57,b,53,b)].
% 1.44/1.72 93 empty_carrier(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet_commut(A,C,B) = meet_commut(A,B,C) | -latt_str(A). [resolve(59,c,53,b)].
% 1.44/1.72 94 empty_carrier(A) | -meet_commutative(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet(A,B,C) = meet_commut(A,B,C) | -latt_str(A). [resolve(60,c,53,b)].
% 1.44/1.72 104 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(77,b,72,b)].
% 1.44/1.72 133 meet_commutative(c6) # label(t23_lattices) # label(negated_conjecture). [clausify(50)].
% 1.44/1.72 134 meet_absorbing(c6) # label(t23_lattices) # label(negated_conjecture). [clausify(50)].
% 1.44/1.72 136 element(c7,the_carrier(c6)) # label(t23_lattices) # label(negated_conjecture). [clausify(50)].
% 1.44/1.72 137 element(c8,the_carrier(c6)) # label(t23_lattices) # label(negated_conjecture). [clausify(50)].
% 1.44/1.72 140 -empty_carrier(c6) # label(t23_lattices) # label(negated_conjecture). [clausify(50)].
% 1.44/1.72 144 -below(c6,meet_commut(c6,c7,c8),c7) # label(t23_lattices) # label(negated_conjecture). [clausify(50)].
% 1.44/1.72 186 empty_carrier(c6) | -meet_absorbing(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | join(c6,meet(c6,A,B),B) = B. [resolve(87,b,84,a)].
% 1.44/1.72 187 -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | join(c6,meet(c6,A,B),B) = B. [copy(186),unit_del(a,140),unit_del(b,134)].
% 1.44/1.72 191 empty_carrier(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | element(meet(c6,A,B),the_carrier(c6)). [resolve(91,e,84,a)].
% 1.44/1.72 192 -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | element(meet(c6,A,B),the_carrier(c6)). [copy(191),unit_del(a,140)].
% 1.44/1.72 197 empty_carrier(c6) | -meet_commutative(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | meet_commut(c6,B,A) = meet_commut(c6,A,B). [resolve(93,f,84,a)].
% 1.44/1.72 198 -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | meet_commut(c6,B,A) = meet_commut(c6,A,B). [copy(197),unit_del(a,140),unit_del(b,133)].
% 1.44/1.72 201 empty_carrier(c6) | -meet_commutative(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | meet(c6,A,B) = meet_commut(c6,A,B). [resolve(94,f,84,a)].
% 1.44/1.72 202 -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | meet_commut(c6,A,B) = meet(c6,A,B). [copy(201),flip(e),unit_del(a,140),unit_del(b,133)].
% 1.44/1.72 225 empty_carrier(c6) | -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | below(c6,A,B) | join(c6,A,B) != B. [resolve(104,f,84,a)].
% 1.44/1.72 226 -element(A,the_carrier(c6)) | -element(B,the_carrier(c6)) | below(c6,A,B) | join(c6,A,B) != B. [copy(225),unit_del(a,140)].
% 1.44/1.72 341 -element(A,the_carrier(c6)) | join(c6,meet(c6,c8,A),A) = A. [resolve(187,a,137,a)].
% 1.44/1.72 354 -element(A,the_carrier(c6)) | element(meet(c6,c7,A),the_carrier(c6)). [resolve(192,a,136,a)].
% 1.44/1.72 374 -element(A,the_carrier(c6)) | meet_commut(c6,c8,A) = meet_commut(c6,A,c8). [resolve(198,a,137,a),flip(b)].
% 1.44/1.72 383 -element(A,the_carrier(c6)) | meet_commut(c6,c8,A) = meet(c6,c8,A). [resolve(202,a,137,a)].
% 1.44/1.72 384 -element(A,the_carrier(c6)) | meet_commut(c6,c7,A) = meet(c6,c7,A). [resolve(202,a,136,a)].
% 1.44/1.72 425 -element(A,the_carrier(c6)) | below(c6,A,c7) | join(c6,A,c7) != c7. [resolve(226,b,136,a)].
% 1.44/1.72 1054 element(meet(c6,c7,c8),the_carrier(c6)). [resolve(354,a,137,a)].
% 1.44/1.72 1362 join(c6,meet(c6,c8,c7),c7) = c7. [resolve(341,a,136,a)].
% 1.44/1.72 4361 meet_commut(c6,c8,c7) = meet_commut(c6,c7,c8). [resolve(374,a,136,a)].
% 1.44/1.72 5473 meet_commut(c6,c7,c8) = meet(c6,c8,c7). [resolve(383,a,136,a),rewrite([4361(4)])].
% 1.44/1.72 5540 -below(c6,meet(c6,c8,c7),c7). [back_rewrite(144),rewrite([5473(5)])].
% 1.44/1.72 5607 meet(c6,c8,c7) = meet(c6,c7,c8). [resolve(384,a,137,a),rewrite([5473(4)])].
% 1.44/1.72 5656 -below(c6,meet(c6,c7,c8),c7). [back_rewrite(5540),rewrite([5607(5)])].
% 1.44/1.72 5659 join(c6,meet(c6,c7,c8),c7) = c7. [back_rewrite(1362),rewrite([5607(5)])].
% 1.44/1.72 9760 $F. [resolve(425,a,1054,a),rewrite([5659(14)]),xx(b),unit_del(a,5656)].
% 1.44/1.72
% 1.44/1.72 % SZS output end Refutation
% 1.44/1.72 ============================== end of proof ==========================
% 1.44/1.72
% 1.44/1.72 ============================== STATISTICS ============================
% 1.44/1.72
% 1.44/1.72 Given=752. Generated=14875. Kept=9598. proofs=1.
% 1.44/1.72 Usable=569. Sos=4954. Demods=1995. Limbo=54, Disabled=4210. Hints=0.
% 1.44/1.72 Megabytes=10.28.
% 1.44/1.72 User_CPU=0.69, System_CPU=0.01, Wall_clock=1.
% 1.44/1.72
% 1.44/1.72 ============================== end of statistics =====================
% 1.44/1.72
% 1.44/1.72 ============================== end of search =========================
% 1.44/1.72
% 1.44/1.72 THEOREM PROVED
% 1.44/1.72 % SZS status Theorem
% 1.44/1.72
% 1.44/1.72 Exiting with 1 proof.
% 1.44/1.72
% 1.44/1.72 Process 16791 exit (max_proofs) Sun Jun 19 18:22:54 2022
% 1.44/1.72 Prover9 interrupted
%------------------------------------------------------------------------------