TSTP Solution File: SEU352+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU352+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 13:31:11 EDT 2022
% Result : Timeout 300.05s 300.35s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU352+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 17:22:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/1.03 ============================== Prover9 ===============================
% 0.41/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.03 Process 9462 was started by sandbox on n026.cluster.edu,
% 0.41/1.03 Sun Jun 19 17:22:26 2022
% 0.41/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9307_n026.cluster.edu".
% 0.41/1.03 ============================== end of head ===========================
% 0.41/1.03
% 0.41/1.03 ============================== INPUT =================================
% 0.41/1.03
% 0.41/1.03 % Reading from file /tmp/Prover9_9307_n026.cluster.edu
% 0.41/1.03
% 0.41/1.03 set(prolog_style_variables).
% 0.41/1.03 set(auto2).
% 0.41/1.03 % set(auto2) -> set(auto).
% 0.41/1.03 % set(auto) -> set(auto_inference).
% 0.41/1.03 % set(auto) -> set(auto_setup).
% 0.41/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.03 % set(auto) -> set(auto_limits).
% 0.41/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.03 % set(auto) -> set(auto_denials).
% 0.41/1.03 % set(auto) -> set(auto_process).
% 0.41/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.03 % set(auto2) -> assign(stats, some).
% 0.41/1.03 % set(auto2) -> clear(echo_input).
% 0.41/1.03 % set(auto2) -> set(quiet).
% 0.41/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.03 % set(auto2) -> clear(print_given).
% 0.41/1.03 assign(lrs_ticks,-1).
% 0.41/1.03 assign(sos_limit,10000).
% 0.41/1.03 assign(order,kbo).
% 0.41/1.03 set(lex_order_vars).
% 0.41/1.03 clear(print_given).
% 0.41/1.03
% 0.41/1.03 % formulas(sos). % not echoed (73 formulas)
% 0.41/1.03
% 0.41/1.03 ============================== end of input ==========================
% 0.41/1.03
% 0.41/1.03 % From the command line: assign(max_seconds, 300).
% 0.41/1.03
% 0.41/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.03
% 0.41/1.03 % Formulas that are not ordinary clauses:
% 0.41/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 2 (all A (latt_str(A) -> (-empty_carrier(A) & lattice(A) -> -empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 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].
% 0.41/1.03 4 (all A (latt_str(A) -> (-empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) -> -empty_carrier(A) & lattice(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 5 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 6 (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].
% 0.41/1.03 7 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (lower_bounded_semilattstr(A) <-> (exists B (element(B,the_carrier(A)) & (all C (element(C,the_carrier(A)) -> meet(A,B,C) = B & meet(A,C,B) = B))))))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 8 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (lower_bounded_semilattstr(A) -> (all B (element(B,the_carrier(A)) -> (B = bottom_of_semilattstr(A) <-> (all C (element(C,the_carrier(A)) -> meet(A,B,C) = B & meet(A,C,B) = B)))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 9 (all A (-empty_carrier(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (latt_element_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,C) -> below(A,D,B)))))))))) # label(d17_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 10 (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].
% 0.41/1.03 11 (all A (-empty_carrier(A) & latt_str(A) -> (-empty_carrier(A) & lattice(A) & complete_latt_str(A) & latt_str(A) -> (all B all C (element(C,the_carrier(A)) -> (C = join_of_latt_set(A,B) <-> latt_element_smaller(A,C,B) & (all D (element(D,the_carrier(A)) -> (latt_element_smaller(A,D,B) -> below(A,C,D)))))))))) # label(d21_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 12 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> meet(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C))))))) # label(d2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 13 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 14 (all A all B (-empty_carrier(A) & latt_str(A) -> element(join_of_latt_set(A,B),the_carrier(A)))) # label(dt_k15_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 15 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 16 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 17 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 18 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 19 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 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].
% 0.41/1.03 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].
% 0.41/1.03 22 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 23 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 24 (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].
% 0.41/1.03 25 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 26 (all A (-empty_carrier(A) & meet_semilatt_str(A) -> element(bottom_of_semilattstr(A),the_carrier(A)))) # label(dt_k5_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 27 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 28 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 29 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 30 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 31 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 32 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 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].
% 0.41/1.03 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].
% 0.41/1.03 35 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 36 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 37 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 38 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 39 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 40 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 41 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 42 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 43 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 44 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 45 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 46 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 47 (all A (-empty_carrier(A) & meet_commutative(A) & meet_semilatt_str(A) -> relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v1_binop_1(the_L_meet(A),the_carrier(A)) & v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc4_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 48 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 49 (all A (-empty_carrier(A) & meet_associative(A) & meet_semilatt_str(A) -> relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & v2_binop_1(the_L_meet(A),the_carrier(A)) & v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(fc5_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 50 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 51 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 52 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 53 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 54 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 55 (all A (-empty_carrier(A) & one_sorted_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & -empty(B))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 56 (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].
% 0.41/1.03 57 (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].
% 0.41/1.03 58 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.03 59 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> (below_refl(A,B,C) <-> below(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 60 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 61 (all A all B all C (-empty_carrier(A) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> below_refl(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 62 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 63 (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(axiom) # label(non_clause). [assumption].
% 0.41/1.04 64 (all A (-empty_carrier(A) & join_commutative(A) & join_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below(A,B,C) & below(A,C,B) -> B = C))))))) # label(t26_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 65 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 66 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 67 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 68 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 69 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 70 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 71 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.04 72 -(all A (-empty_carrier(A) & lattice(A) & complete_latt_str(A) & latt_str(A) -> -empty_carrier(A) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & bottom_of_semilattstr(A) = join_of_latt_set(A,empty_set))) # label(t50_lattice3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/1.04
% 0.41/1.04 ============================== end of process non-clausal formulas ===
% 0.41/1.04
% 0.41/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/1.04
% 0.41/1.04 ============================== PREDICATE ELIMINATION =================
% 0.41/1.04 73 -latt_str(A) | empty_carrier(A) | -join_commutative(A) | -join_associative(A) | -meet_commutative(A) | -meet_associative(A) | -meet_absorbing(A) | -join_absorbing(A) | lattice(A) # label(cc2_lattices) # label(axiom). [clausify(4)].
% 0.41/1.04 74 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(2)].
% 0.41/1.04 75 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | -below(A,C,B) | C = B # label(t26_lattices) # label(axiom). [clausify(64)].
% 0.41/1.04 Derived: empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | -below(A,C,B) | C = B | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(75,b,74,d)].
% 0.41/1.04 76 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(6)].
% 0.41/1.04 77 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(2)].
% 0.41/1.04 Derived: empty_carrier(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) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(76,b,77,d)].
% 0.41/1.04 78 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(24)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet_commut(A,B,C),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(78,b,77,d)].
% 0.41/1.04 79 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | relation(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(47)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_semilatt_str(A) | relation(the_L_meet(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(79,b,77,d)].
% 0.41/1.04 80 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | function(the_L_meet(A)) # label(fc4_lattice2) # label(axiom). [clausify(47)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_semilatt_str(A) | function(the_L_meet(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(80,b,77,d)].
% 0.41/1.04 81 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(47)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(81,b,77,d)].
% 0.41/1.04 82 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | v1_binop_1(the_L_meet(A),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(47)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_semilatt_str(A) | v1_binop_1(the_L_meet(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(82,b,77,d)].
% 0.41/1.04 83 empty_carrier(A) | -meet_commutative(A) | -meet_semilatt_str(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc4_lattice2) # label(axiom). [clausify(47)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_semilatt_str(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(83,b,77,d)].
% 0.41/1.04 84 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(57)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet(A,B,C) = meet_commut(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(84,b,77,d)].
% 0.41/1.04 85 empty_carrier(A) | -meet_commutative(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | below(A,B,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(59)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(85,b,77,d)].
% 0.41/1.04 86 empty_carrier(A) | -meet_commutative(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -below(A,B,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(59)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(86,b,77,d)].
% 0.41/1.04 87 empty_carrier(A) | -meet_commutative(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,B) # label(reflexivity_r3_lattices) # label(axiom). [clausify(61)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,B) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(87,b,77,d)].
% 0.41/1.04 88 empty_carrier(A) | -meet_commutative(A) | -meet_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,meet_commut(A,B,C),B) # label(t23_lattices) # label(axiom). [clausify(63)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,meet_commut(A,B,C),B) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(88,b,77,d)].
% 0.41/1.04 89 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | relation(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(49)].
% 0.41/1.04 90 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_associative(A) # label(cc1_lattices) # label(axiom). [clausify(2)].
% 0.41/1.04 91 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | function(the_L_meet(A)) # label(fc5_lattice2) # label(axiom). [clausify(49)].
% 0.41/1.04 92 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(49)].
% 0.41/1.04 93 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(49)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_semilatt_str(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(93,b,90,d)].
% 0.41/1.04 94 empty_carrier(A) | -meet_associative(A) | -meet_semilatt_str(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(fc5_lattice2) # label(axiom). [clausify(49)].
% 0.41/1.04 95 empty_carrier(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(85,b,77,d)].
% 0.41/1.04 96 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(2)].
% 0.41/1.04 Derived: empty_carrier(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(95,b,96,d)].
% 0.41/1.04 97 empty_carrier(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(86,b,77,d)].
% 0.41/1.04 Derived: empty_carrier(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(97,b,96,d)].
% 0.41/1.04 98 empty_carrier(A) | -meet_absorbing(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,B) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(87,b,77,d)].
% 0.41/1.04 Derived: empty_carrier(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,B) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(98,b,96,d)].
% 0.41/1.04 99 empty_carrier(A) | -meet_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,meet_commut(A,B,C),B) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(88,b,77,d)].
% 0.41/1.04 Derived: empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,meet_commut(A,B,C),B) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(99,b,96,d)].
% 0.41/1.04 100 empty_carrier(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(95,b,96,d)].
% 0.41/1.04 101 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(2)].
% 0.41/1.04 Derived: empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below_refl(A,B,C) | below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(100,b,101,d)].
% 0.41/1.04 102 empty_carrier(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(97,b,96,d)].
% 0.41/1.04 Derived: empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,C) | -below(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(102,b,101,d)].
% 0.41/1.04 103 empty_carrier(A) | -join_absorbing(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,B) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(98,b,96,d)].
% 0.41/1.04 Derived: empty_carrier(A) | -latt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below_refl(A,B,B) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(103,b,101,d)].
% 0.41/1.04 104 -relation(A) | -function(A) | apply(A,ordered_pair(B,C)) = apply_binary(A,B,C) # label(d1_binop_1) # label(axiom). [clausify(10)].
% 0.41/1.04 105 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(3)].
% 0.41/1.04 Derived: -function(A) | apply(A,ordered_pair(B,C)) = apply_binary(A,B,C) | -element(A,powerset(cartesian_product2(D,E))). [resolve(104,a,105,b)].
% 0.41/1.04 106 empty_carrier(A) | -meet_semilatt_str(A) | relation(the_L_meet(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(79,b,77,d)].
% 0.41/1.04 Derived: empty_carrier(A) | -meet_semilatt_str(A) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -function(the_L_meet(A)) | apply(the_L_meet(A),ordered_pair(B,C)) = apply_binary(the_L_meet(A),B,C). [resolve(106,c,104,a)].
% 0.41/1.04 107 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(30)].
% 0.41/1.04 108 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | element(f1(A),the_carrier(A)) # label(d13_lattices) # label(axiom). [clausify(7)].
% 0.41/1.04 109 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,f1(A),B) = f1(A) # label(d13_lattices) # label(axiom). [clausify(7)].
% 0.41/1.04 110 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f1(A)) = f1(A) # label(d13_lattices) # label(axiom). [clausify(7)].
% 0.41/1.04 111 empty_carrier(A) | -meet_semilatt_str(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | element(f2(A,B),the_carrier(A)) # label(d13_lattices) # label(axiom). [clausify(7)].
% 0.41/1.04 112 empty_carrier(A) | -meet_semilatt_str(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f2(A,B)) != B | meet(A,f2(A,B),B) != B # label(d13_lattices) # label(axiom). [clausify(7)].
% 0.41/1.04 113 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,B,C) = B # label(d16_lattices) # label(axiom). [clausify(8)].
% 0.41/1.04 114 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,C,B) = B # label(d16_lattices) # label(axiom). [clausify(8)].
% 0.41/1.04 115 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | element(f3(A,B),the_carrier(A)) # label(d16_lattices) # label(axiom). [clausify(8)].
% 0.41/1.04 116 empty_carrier(A) | -meet_semilatt_str(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | meet(A,B,f3(A,B)) != B | meet(A,f3(A,B),B) != B # label(d16_lattices) # label(axiom). [clausify(8)].
% 0.76/1.05 117 empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C) = meet(A,B,C) # label(d2_lattices) # label(axiom). [clausify(12)].
% 0.76/1.05 118 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)].
% 0.76/1.05 119 empty_carrier(A) | -meet_semilatt_str(A) | element(bottom_of_semilattstr(A),the_carrier(A)) # label(dt_k5_lattices) # label(axiom). [clausify(26)].
% 0.76/1.05 120 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(27)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | element(f1(A),the_carrier(A)). [resolve(107,b,108,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,f1(A),B) = f1(A). [resolve(107,b,109,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f1(A)) = f1(A). [resolve(107,b,110,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | element(f2(A,B),the_carrier(A)). [resolve(107,b,111,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | meet(A,B,f2(A,B)) != B | meet(A,f2(A,B),B) != B. [resolve(107,b,112,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,B,C) = B. [resolve(107,b,113,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) != B | -element(C,the_carrier(A)) | meet(A,C,B) = B. [resolve(107,b,114,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | element(f3(A,B),the_carrier(A)). [resolve(107,b,115,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | -lower_bounded_semilattstr(A) | -element(B,the_carrier(A)) | bottom_of_semilattstr(A) = B | meet(A,B,f3(A,B)) != B | meet(A,f3(A,B),B) != B. [resolve(107,b,116,b)].
% 0.76/1.05 Derived: -latt_str(A) | 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_meet(A),B,C) = meet(A,B,C). [resolve(107,b,117,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet(A,B,C),the_carrier(A)). [resolve(107,b,118,b)].
% 0.76/1.05 Derived: -latt_str(A) | empty_carrier(A) | element(bottom_of_semilattstr(A),the_carrier(A)). [resolve(107,b,119,b)].
% 0.76/1.05 Derived: -latt_str(A) | one_sorted_str(A). [resolve(107,b,120,a)].
% 0.76/1.05 121 -meet_semilatt_str(A) | function(the_L_meet(A)) # label(dt_u1_lattices) # label(axiom). [clausify(34)].
% 0.76/1.05 Derived: function(the_L_meet(A)) | -latt_str(A). [resolve(121,a,107,b)].
% 0.76/1.05 122 -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)].
% 0.76/1.05 Derived: quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(122,a,107,b)].
% 0.76/1.05 123 -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)].
% 0.76/1.05 Derived: relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(123,a,107,b)].
% 0.76/1.05 124 meet_semilatt_str(c1) # label(existence_l1_lattices) # label(axiom). [clausify(36)].
% 0.76/1.05 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | element(f1(c1),the_carrier(c1)). [resolve(124,a,108,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | meet(c1,f1(c1),A) = f1(c1). [resolve(124,a,109,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | meet(c1,A,f1(c1)) = f1(c1). [resolve(124,a,110,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | element(f2(c1,A),the_carrier(c1)). [resolve(124,a,111,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | meet(c1,A,f2(c1,A)) != A | meet(c1,f2(c1,A),A) != A. [resolve(124,a,112,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | bottom_of_semilattstr(c1) != A | -element(B,the_carrier(c1)) | meet(c1,A,B) = A. [resolve(124,a,113,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | bottom_of_semilattstr(c1) != A | -element(B,the_carrier(c1)) | meet(c1,B,A) = A. [resolve(124,a,114,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | bottom_of_semilattstr(c1) = A | element(f3(c1,A),the_carrier(c1)). [resolve(124,a,115,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | -lower_bounded_semilattstr(c1) | -element(A,the_carrier(c1)) | bottom_of_semilattstr(c1) = A | meet(c1,A,f3(c1,A)) != A | meet(c1,f3(c1,A),A) != A. [resolve(124,a,116,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | apply_binary_as_element(the_carrier(c1),the_carrier(c1),the_carrier(c1),the_L_meet(c1),A,B) = meet(c1,A,B). [resolve(124,a,117,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | element(meet(c1,A,B),the_carrier(c1)). [resolve(124,a,118,b)].
% 0.76/1.05 Derived: empty_carrier(c1) | element(bottom_of_semilattstr(c1),the_carrier(c1)). [resolve(124,a,119,b)].
% 0.76/1.05 Derived: one_sorted_str(c1). [resolve(124,a,120,a)].
% 0.76/1.05 Derived: function(the_L_meet(c1)). [resolve(124,a,121,a)].
% 0.76/1.05 Derived: quasi_total(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(124,a,122,a)].
% 0.76/1.05 Derived: relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(124,a,123,a)].
% 0.76/1.05 125 empty_carrier(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) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(76,b,77,d)].
% 0.76/1.05 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet_commut(A,C,B) = meet_commut(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(125,b,107,b)].
% 0.76/1.05 126 empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet_commut(A,B,C),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(78,b,77,d)].
% 0.76/1.05 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(meet_commut(A,B,C),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(126,b,107,b)].
% 0.76/1.05 127 empty_carrier(A) | -meet_semilatt_str(A) | function(the_L_meet(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(80,b,77,d)].
% 0.76/1.05 128 empty_carrier(A) | -meet_semilatt_str(A) | quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(81,b,77,d)].
% 0.76/1.05 129 empty_carrier(A) | -meet_semilatt_str(A) | v1_binop_1(the_L_meet(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(82,b,77,d)].
% 0.76/1.05 Derived: empty_carrier(A) | v1_binop_1(the_L_meet(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(129,b,107,b)].
% 0.76/1.05 130 empty_carrier(A) | -meet_semilatt_str(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(83,b,77,d)].
% 0.76/1.05 Derived: empty_carrier(A) | v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(130,b,107,b)].
% 0.76/1.05 131 empty_carrier(A) | -meet_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet(A,B,C) = meet_commut(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(84,b,77,d)].
% 0.76/1.05 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | meet(A,B,C) = meet_commut(A,B,C) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(131,b,107,b)].
% 0.76/1.05 132 empty_carrier(A) | -meet_semilatt_str(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(93,b,90,d)].
% 0.76/1.05 Derived: empty_carrier(A) | v2_binop_1(the_L_meet(A),the_carrier(A)) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(132,b,107,b)].
% 0.76/1.05 133 empty_carrier(A) | -meet_semilatt_str(A) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -function(the_L_meet(A)) | apply(the_L_meet(A),ordered_pair(B,C)) = apply_binary(the_L_meet(A),B,C). [resolve(106,c,104,a)].
% 0.76/1.05 Derived: empty_carrier(A) | -latt_str(A) | empty_carrier(A) | -lattice(A) | -function(the_L_meet(A)) | apply(the_L_meet(A),ordered_pair(B,C)) = apply_binary(the_L_meet(A),B,C) | -latt_str(A). [resolve(133,b,107,b)].
% 0.76/1.05 134 complete_latt_str(c8) # label(t50_lattice3) # label(negated_conjecture). [clausify(72)].
% 0.76/1.05 135 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) != B | latt_element_smaller(A,B,C) # label(d21_lattice3) # label(axiom). [clausify(11)].
% 0.76/1.05 136 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) != B | -element(D,the_carrier(A)) | -latt_element_smaller(A,D,C) | below(A,B,D) # label(d21_lattice3) # label(axiom). [clausify(11)].
% 0.76/1.05 137 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) = B | -latt_element_smaller(A,B,C) | element(f5(A,C,B),the_carrier(A)) # label(d21_lattice3) # label(axiom). [clausify(11)].
% 0.76/1.05 138 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) = B | -latt_element_smaller(A,B,C) | latt_element_smaller(A,f5(A,C,B),C) # label(d21_lattice3) # label(axiom). [clausify(11)].
% 0.76/1.05 139 empty_carrier(A) | -latt_str(A) | -lattice(A) | -complete_latt_str(A) | -element(B,the_carrier(A)) | join_of_latt_set(A,C) = B | -latt_element_smaller(A,B,C) | -below(A,B,f5(A,C,B)) # label(d21_lattice3) # label(axiom). [clausify(11)].
% 0.76/1.05 Derived: empty_carrier(c8) | -latt_str(c8) | -lattice(c8) | -element(A,the_carrier(c8)) | join_of_latt_set(c8,B) != A | latt_element_smaller(c8,A,B). [resolve(134,a,135,d)].
% 0.76/1.05 Derived: empty_carrier(c8) | -latt_str(c8) | -lattice(c8) | -element(A,the_carrier(c8)) | join_of_latt_set(c8,B) != A | -element(C,the_carrier(c8)) | -latt_element_smaller(c8,C,B) | below(c8,A,C). [resolve(134,a,136,d)].
% 0.76/1.05 Derived: empty_carrier(c8) | -latt_str(c8) | -lattice(c8) | -element(A,the_carrier(c8)) | join_of_latt_set(c8,B) = A | -latt_element_smaller(c8,A,B) | element(f5(c8,B,A),the_carrier(c8)). [resolve(134,a,137,d)].
% 0.76/1.05 Derived: empty_carrier(c8) | -latt_str(c8) | -lattice(c8) | -element(A,the_carrier(c8)) | join_of_latt_set(c8,B) = A | -latt_element_smaller(c8,A,B) | latt_element_smaller(c8,f5(c8,B,A),B). [resolve(134,a,138,d)].
% 0.76/1.05 Derived: empty_carrier(c8) | -latt_str(c8) | -lattice(c8) | -element(A,the_carrier(c8)) | join_of_latt_set(c8,B) = A | -latt_element_smaller(c8,A,B) | -below(c8,A,f5(c8,B,A)). [resolve(134,a,139,d)].
% 0.76/1.05 140 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(30)].
% 0.76/1.05 141 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(29)].
% 0.76/1.05 142 join_semilatt_str(c3) # label(existence_l2_lattices) # label(axiom). [clausify(38)].
% 0.76/1.05 Derived: one_sorted_str(c3). [resolve(142,a,141,a)].
% 0.76/1.05 143 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | -below(A,C,B) | C = B | -latt_str(A) | empty_carrier(A) | -lattice(A). [resolve(75,b,74,d)].
% 0.76/1.06 Derived: empty_carrier(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | -below(A,C,B) | C = B | -latt_str(A) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(143,b,140,b)].
% 0.76/1.06 144 relation_of2_as_subset(f8(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(42)].
% 0.76/1.06 145 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(33)].
% 0.76/1.06 Derived: element(f8(A,B),powerset(cartesian_product2(A,B))). [resolve(144,a,145,a)].
% 0.76/1.06 146 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(58)].
% 0.76/1.06 Derived: relation_of2(f8(A,B),A,B). [resolve(146,a,144,a)].
% 0.76/1.06 147 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(58)].
% 0.76/1.06 Derived: -relation_of2(A,B,C) | element(A,powerset(cartesian_product2(B,C))). [resolve(147,a,145,a)].
% 0.76/1.06 148 relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) | -latt_str(A). [resolve(123,a,107,b)].
% 0.76/1.06 Derived: -latt_str(A) | element(the_L_meet(A),powerset(cartesian_product2(cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))). [resolve(148,a,145,a)].
% 0.76/1.06 Derived: -latt_str(A) | relation_of2(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)). [resolve(148,a,146,a)].
% 0.76/1.06 149 relation_of2_as_subset(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(124,a,123,a)].
% 0.76/1.06 Derived: element(the_L_meet(c1),powerset(cartesian_product2(cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)))). [resolve(149,a,145,a)].
% 0.76/1.06 Derived: relation_of2(the_L_meet(c1),cartesian_product2(the_carrier(c1),the_carrier(c1)),the_carrier(c1)). [resolve(149,a,146,a)].
% 0.76/1.06 150 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(43)].
% 0.76/1.06 151 one_sorted_str(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(37)].
% 0.76/1.06 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(150,b,151,a)].
% 0.76/1.06 152 one_sorted_str(c7) # label(rc3_struct_0) # label(axiom). [clausify(54)].
% 0.76/1.06 Derived: empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(152,a,150,b)].
% 0.76/1.06 153 empty_carrier(A) | -one_sorted_str(A) | element(f11(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(55)].
% 0.76/1.06 Derived: empty_carrier(c2) | element(f11(c2),powerset(the_carrier(c2))). [resolve(153,b,151,a)].
% 0.76/1.06 Derived: empty_carrier(c7) | element(f11(c7),powerset(the_carrier(c7))). [resolve(153,b,152,a)].
% 0.76/1.06 154 empty_carrier(A) | -one_sorted_str(A) | -empty(f11(A)) # label(rc5_struct_0) # label(axiom). [clausify(55)].
% 0.76/1.06 Derived: empty_carrier(c2) | -empty(f11(c2)). [resolve(154,b,151,a)].
% 0.76/1.06 Derived: empty_carrier(c7) | -empty(f11(c7)). [resolve(154,b,152,a)].
% 0.76/1.06 155 -latt_str(A) | one_sorted_str(A). [resolve(107,b,120,a)].
% 0.76/1.06 Derived: -latt_str(A) | empty_carrier(A) | -empty(the_carrier(A)). [resolve(155,b,150,b)].
% 0.76/1.06 Derived: -latt_str(A) | empty_carrier(A) | element(f11(A),powerset(the_carrier(A))). [resolve(155,b,153,b)].
% 0.76/1.06 Derived: -latt_str(A) | empty_carrier(A) | -empty(f11(A)). [resolve(155,b,154,b)].
% 0.76/1.06 156 one_sorted_str(c1). [resolve(124,a,120,a)].
% 0.76/1.06 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(156,a,150,b)].
% 0.76/1.06 Derived: empty_carrier(c1) | element(f11(c1),powerset(the_carrier(c1))). [resolve(156,a,153,b)].
% 0.76/1.06 Derived: empty_carrier(c1) | -empty(f11(c1)). [resolve(156,a,154,b)].
% 0.76/1.06 157 one_sorted_str(c3). [resolve(142,a,141,a)].
% 0.76/1.06 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(157,a,150,b)].
% 0.76/1.06 Derived: empty_carrier(c3) | element(f11(c3),powerset(the_carrier(c3))). [resolve(157,a,153,b)].
% 0.76/1.06 Derived: empty_carrier(c3) | -empty(f11(c3)). [resolve(157,a,154,b)].
% 0.76/1.06 158 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(66)].
% 0.76/1.06 159 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(6Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------