TSTP Solution File: SEU350+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU350+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 13:31:10 EDT 2022
% Result : Theorem 0.83s 1.14s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU350+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 11:53:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/1.05 ============================== Prover9 ===============================
% 0.45/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.05 Process 28387 was started by sandbox on n009.cluster.edu,
% 0.45/1.05 Sun Jun 19 11:53:08 2022
% 0.45/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28227_n009.cluster.edu".
% 0.45/1.05 ============================== end of head ===========================
% 0.45/1.05
% 0.45/1.05 ============================== INPUT =================================
% 0.45/1.05
% 0.45/1.05 % Reading from file /tmp/Prover9_28227_n009.cluster.edu
% 0.45/1.05
% 0.45/1.05 set(prolog_style_variables).
% 0.45/1.05 set(auto2).
% 0.45/1.05 % set(auto2) -> set(auto).
% 0.45/1.05 % set(auto) -> set(auto_inference).
% 0.45/1.05 % set(auto) -> set(auto_setup).
% 0.45/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.05 % set(auto) -> set(auto_limits).
% 0.45/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.05 % set(auto) -> set(auto_denials).
% 0.45/1.05 % set(auto) -> set(auto_process).
% 0.45/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.05 % set(auto2) -> assign(stats, some).
% 0.45/1.05 % set(auto2) -> clear(echo_input).
% 0.45/1.05 % set(auto2) -> set(quiet).
% 0.45/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.05 % set(auto2) -> clear(print_given).
% 0.45/1.05 assign(lrs_ticks,-1).
% 0.45/1.05 assign(sos_limit,10000).
% 0.45/1.05 assign(order,kbo).
% 0.45/1.05 set(lex_order_vars).
% 0.45/1.05 clear(print_given).
% 0.45/1.05
% 0.45/1.05 % formulas(sos). % not echoed (65 formulas)
% 0.45/1.05
% 0.45/1.05 ============================== end of input ==========================
% 0.45/1.05
% 0.45/1.05 % From the command line: assign(max_seconds, 300).
% 0.45/1.05
% 0.45/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.05
% 0.45/1.05 % Formulas that are not ordinary clauses:
% 0.45/1.05 1 (all A (rel_str(A) -> (strict_rel_str(A) -> A = rel_str_of(the_carrier(A),the_InternalRel(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 2 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 3 (all A (latt_str(A) -> (-empty_carrier(A) & lattice(A) -> -empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 4 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 5 (all A (latt_str(A) -> (-empty_carrier(A) & join_commutative(A) & join_associative(A) & meet_commutative(A) & meet_associative(A) & meet_absorbing(A) & join_absorbing(A) -> -empty_carrier(A) & lattice(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 6 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)))) # label(d2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 7 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> cast_to_el_of_LattPOSet(A,B) = B)))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 8 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(poset_of_lattice(A))) -> cast_to_el_of_lattice(A,B) = B)))) # label(d4_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 9 (all A all B (relation_of2(B,A,A) -> strict_rel_str(rel_str_of(A,B)) & rel_str(rel_str_of(A,B)))) # label(dt_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 10 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 11 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 12 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> reflexive(k2_lattice3(A)) & antisymmetric(k2_lattice3(A)) & transitive(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A)) & relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A)))) # label(dt_k2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 13 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 14 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)) & rel_str(poset_of_lattice(A)))) # label(dt_k3_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 15 (all A all B (-empty_carrier(A) & lattice(A) & latt_str(A) & element(B,the_carrier(A)) -> element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A))))) # label(dt_k4_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 16 (all A all B (-empty_carrier(A) & lattice(A) & latt_str(A) & element(B,the_carrier(poset_of_lattice(A))) -> element(cast_to_el_of_lattice(A,B),the_carrier(A)))) # label(dt_k5_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 17 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> relation(relation_of_lattice(A)))) # label(dt_k9_filter_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 18 (all A (meet_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 19 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 20 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 21 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 22 (all A (latt_str(A) -> meet_semilatt_str(A) & join_semilatt_str(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 23 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 24 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 25 (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].
% 0.45/1.05 26 (all A (rel_str(A) -> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 27 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 28 (exists A meet_semilatt_str(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 29 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 30 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 31 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 32 (exists A latt_str(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 33 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 34 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 35 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 36 (all A all B (-empty(A) & relation_of2(B,A,A) -> -empty_carrier(rel_str_of(A,B)) & strict_rel_str(rel_str_of(A,B)))) # label(fc1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 37 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 38 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.05 39 (all A (reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & rel_str(A) -> relation(the_InternalRel(A)) & reflexive(the_InternalRel(A)) & antisymmetric(the_InternalRel(A)) & transitive(the_InternalRel(A)) & v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(fc2_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 40 (all A all B (reflexive(B) & antisymmetric(B) & transitive(B) & v1_partfun1(B,A,A) & relation_of2(B,A,A) -> strict_rel_str(rel_str_of(A,B)) & reflexive_relstr(rel_str_of(A,B)) & transitive_relstr(rel_str_of(A,B)) & antisymmetric_relstr(rel_str_of(A,B)))) # label(fc3_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 41 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> -empty_carrier(poset_of_lattice(A)) & strict_rel_str(poset_of_lattice(A)) & reflexive_relstr(poset_of_lattice(A)) & transitive_relstr(poset_of_lattice(A)) & antisymmetric_relstr(poset_of_lattice(A)))) # label(fc4_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 42 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 43 (all A all B (relation_of2(B,A,A) -> (all C all D (rel_str_of(A,B) = rel_str_of(C,D) -> A = C & B = D)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 44 (exists A (rel_str(A) & strict_rel_str(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 45 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 46 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 47 (exists A (rel_str(A) & -empty_carrier(A) & strict_rel_str(A) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A))) # label(rc2_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 48 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 49 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 50 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 51 (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].
% 0.45/1.06 52 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> k2_lattice3(A) = relation_of_lattice(A))) # label(redefinition_k2_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 53 (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].
% 0.45/1.06 54 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 55 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 56 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 57 (all A all B (-empty_carrier(B) & lattice(B) & latt_str(B) -> (all C (element(C,the_carrier(B)) -> (latt_element_smaller(B,C,A) <-> relstr_set_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))))))) # label(t30_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 58 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 59 (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].
% 0.45/1.06 60 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 61 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 62 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 63 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.06 64 -(all A all B (-empty_carrier(B) & lattice(B) & latt_str(B) -> (all C (element(C,the_carrier(poset_of_lattice(B))) -> (relstr_set_smaller(poset_of_lattice(B),A,C) <-> latt_element_smaller(B,cast_to_el_of_lattice(B,C),A)))))) # label(t31_lattice3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.06
% 0.45/1.06 ============================== end of process non-clausal formulas ===
% 0.45/1.06
% 0.45/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.06
% 0.45/1.06 ============================== PREDICATE ELIMINATION =================
% 0.45/1.06 65 -relation_of2(A,B,B) | rel_str(rel_str_of(B,A)) # label(dt_g1_orders_2) # label(axiom). [clausify(9)].
% 0.45/1.06 66 -rel_str(A) | -strict_rel_str(A) | rel_str_of(the_carrier(A),the_InternalRel(A)) = A # label(abstractness_v1_orders_2) # label(axiom). [clausify(1)].
% 0.45/1.06 Derived: -relation_of2(A,B,B) | -strict_rel_str(rel_str_of(B,A)) | rel_str_of(the_carrier(rel_str_of(B,A)),the_InternalRel(rel_str_of(B,A))) = rel_str_of(B,A). [resolve(65,b,66,a)].
% 0.45/1.06 67 empty_carrier(A) | -lattice(A) | -latt_str(A) | rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(14)].
% 0.45/1.06 Derived: empty_carrier(A) | -lattice(A) | -latt_str(A) | -strict_rel_str(poset_of_lattice(A)) | rel_str_of(the_carrier(poset_of_lattice(A)),the_InternalRel(poset_of_lattice(A))) = poset_of_lattice(A). [resolve(67,d,66,a)].
% 0.45/1.06 68 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(19)].
% 0.45/1.06 Derived: one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(68,a,65,b)].
% 0.45/1.06 Derived: one_sorted_str(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(68,a,67,d)].
% 0.45/1.06 69 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(26)].
% 0.45/1.06 Derived: relation_of2_as_subset(the_InternalRel(rel_str_of(A,B)),the_carrier(rel_str_of(A,B)),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(69,a,65,b)].
% 0.45/1.06 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(69,a,67,d)].
% 0.45/1.06 70 rel_str(c2) # label(existence_l1_orders_2) # label(axiom). [clausify(29)].
% 0.45/1.06 Derived: -strict_rel_str(c2) | rel_str_of(the_carrier(c2),the_InternalRel(c2)) = c2. [resolve(70,a,66,a)].
% 0.45/1.06 Derived: one_sorted_str(c2). [resolve(70,a,68,a)].
% 0.45/1.06 Derived: relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(70,a,69,a)].
% 0.45/1.06 71 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | relation(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(39)].
% 0.45/1.06 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | relation(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(71,d,65,b)].
% 0.45/1.06 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | relation(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(71,d,67,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | relation(the_InternalRel(c2)). [resolve(71,d,70,a)].
% 0.45/1.06 72 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | reflexive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(39)].
% 0.45/1.06 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | reflexive(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(72,d,65,b)].
% 0.45/1.06 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | reflexive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(72,d,67,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(72,d,70,a)].
% 0.45/1.06 73 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | antisymmetric(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(39)].
% 0.45/1.06 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | antisymmetric(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(73,d,65,b)].
% 0.45/1.06 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | antisymmetric(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(73,d,67,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | antisymmetric(the_InternalRel(c2)). [resolve(73,d,70,a)].
% 0.45/1.06 74 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | transitive(the_InternalRel(A)) # label(fc2_orders_2) # label(axiom). [clausify(39)].
% 0.45/1.06 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | transitive(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(74,d,65,b)].
% 0.45/1.06 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | transitive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(74,d,67,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | transitive(the_InternalRel(c2)). [resolve(74,d,70,a)].
% 0.45/1.06 75 -reflexive_relstr(A) | -transitive_relstr(A) | -antisymmetric_relstr(A) | -rel_str(A) | v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(fc2_orders_2) # label(axiom). [clausify(39)].
% 0.45/1.06 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | v1_partfun1(the_InternalRel(rel_str_of(A,B)),the_carrier(rel_str_of(A,B)),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(75,d,65,b)].
% 0.45/1.06 Derived: -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | v1_partfun1(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(75,d,67,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | v1_partfun1(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(75,d,70,a)].
% 0.45/1.06 76 rel_str(c6) # label(rc1_orders_2) # label(axiom). [clausify(44)].
% 0.45/1.06 Derived: -strict_rel_str(c6) | rel_str_of(the_carrier(c6),the_InternalRel(c6)) = c6. [resolve(76,a,66,a)].
% 0.45/1.06 Derived: one_sorted_str(c6). [resolve(76,a,68,a)].
% 0.45/1.06 Derived: relation_of2_as_subset(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(76,a,69,a)].
% 0.45/1.06 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | relation(the_InternalRel(c6)). [resolve(76,a,71,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | reflexive(the_InternalRel(c6)). [resolve(76,a,72,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | antisymmetric(the_InternalRel(c6)). [resolve(76,a,73,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | transitive(the_InternalRel(c6)). [resolve(76,a,74,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | v1_partfun1(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(76,a,75,d)].
% 0.45/1.06 77 rel_str(c8) # label(rc2_orders_2) # label(axiom). [clausify(47)].
% 0.45/1.06 Derived: -strict_rel_str(c8) | rel_str_of(the_carrier(c8),the_InternalRel(c8)) = c8. [resolve(77,a,66,a)].
% 0.45/1.06 Derived: one_sorted_str(c8). [resolve(77,a,68,a)].
% 0.45/1.06 Derived: relation_of2_as_subset(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(77,a,69,a)].
% 0.45/1.06 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | relation(the_InternalRel(c8)). [resolve(77,a,71,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | reflexive(the_InternalRel(c8)). [resolve(77,a,72,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | antisymmetric(the_InternalRel(c8)). [resolve(77,a,73,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | transitive(the_InternalRel(c8)). [resolve(77,a,74,d)].
% 0.45/1.06 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | v1_partfun1(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(77,a,75,d)].
% 0.45/1.06 78 latt_str(c5) # label(existence_l3_lattices) # label(axiom). [clausify(32)].
% 0.45/1.06 79 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.06 80 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_associative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.06 81 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_commutative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.06 82 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_associative(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.06 83 -latt_str(A) | empty_carrier(A) | -lattice(A) | meet_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.06 84 -latt_str(A) | empty_carrier(A) | -lattice(A) | join_absorbing(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.06 85 -latt_str(A) | empty_carrier(A) | -join_commutative(A) | -join_associative(A) | -meet_commutative(A) | -meet_associative(A) | -meet_absorbing(A) | -join_absorbing(A) | lattice(A) # label(cc2_lattices) # label(axiom). [clausify(5)].
% 0.45/1.06 86 empty_carrier(A) | -lattice(A) | -latt_str(A) | poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)) # label(d2_lattice3) # label(axiom). [clausify(6)].
% 0.45/1.06 87 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | cast_to_el_of_LattPOSet(A,B) = B # label(d3_lattice3) # label(axiom). [clausify(7)].
% 0.45/1.06 88 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | cast_to_el_of_lattice(A,B) = B # label(d4_lattice3) # label(axiom). [clausify(8)].
% 0.45/1.06 89 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(12)].
% 0.45/1.06 90 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(12)].
% 0.45/1.06 91 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive(k2_lattice3(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(12)].
% 0.45/1.06 92 empty_carrier(A) | -lattice(A) | -latt_str(A) | v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(12)].
% 0.45/1.06 93 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A)) # label(dt_k2_lattice3) # label(axiom). [clausify(12)].
% 0.45/1.06 94 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(14)].
% 0.45/1.06 95 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(14)].
% 0.45/1.06 96 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(14)].
% 0.45/1.06 97 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(dt_k3_lattice3) # label(axiom). [clausify(14)].
% 0.45/1.06 98 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A))) # label(dt_k4_lattice3) # label(axiom). [clausify(15)].
% 0.45/1.06 99 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | element(cast_to_el_of_lattice(A,B),the_carrier(A)) # label(dt_k5_lattice3) # label(axiom). [clausify(16)].
% 0.45/1.06 100 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation(relation_of_lattice(A)) # label(dt_k9_filter_1) # label(axiom). [clausify(17)].
% 0.45/1.06 101 -latt_str(A) | meet_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(22)].
% 0.45/1.06 102 -latt_str(A) | join_semilatt_str(A) # label(dt_l3_lattices) # label(axiom). [clausify(22)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | join_commutative(c5). [resolve(78,a,79,a)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | join_associative(c5). [resolve(78,a,80,a)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | meet_commutative(c5). [resolve(78,a,81,a)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | meet_associative(c5). [resolve(78,a,82,a)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | meet_absorbing(c5). [resolve(78,a,83,a)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | join_absorbing(c5). [resolve(78,a,84,a)].
% 0.45/1.06 Derived: empty_carrier(c5) | -join_commutative(c5) | -join_associative(c5) | -meet_commutative(c5) | -meet_associative(c5) | -meet_absorbing(c5) | -join_absorbing(c5) | lattice(c5). [resolve(78,a,85,a)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | poset_of_lattice(c5) = rel_str_of(the_carrier(c5),k2_lattice3(c5)). [resolve(78,a,86,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | cast_to_el_of_LattPOSet(c5,A) = A. [resolve(78,a,87,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | cast_to_el_of_lattice(c5,A) = A. [resolve(78,a,88,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | reflexive(k2_lattice3(c5)). [resolve(78,a,89,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | antisymmetric(k2_lattice3(c5)). [resolve(78,a,90,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | transitive(k2_lattice3(c5)). [resolve(78,a,91,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | v1_partfun1(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(78,a,92,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(78,a,93,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | strict_rel_str(poset_of_lattice(c5)). [resolve(78,a,94,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | reflexive_relstr(poset_of_lattice(c5)). [resolve(78,a,95,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | transitive_relstr(poset_of_lattice(c5)). [resolve(78,a,96,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | antisymmetric_relstr(poset_of_lattice(c5)). [resolve(78,a,97,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | element(cast_to_el_of_LattPOSet(c5,A),the_carrier(poset_of_lattice(c5))). [resolve(78,a,98,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(poset_of_lattice(c5))) | element(cast_to_el_of_lattice(c5,A),the_carrier(c5)). [resolve(78,a,99,c)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | relation(relation_of_lattice(c5)). [resolve(78,a,100,c)].
% 0.45/1.06 Derived: meet_semilatt_str(c5). [resolve(78,a,101,a)].
% 0.45/1.06 Derived: join_semilatt_str(c5). [resolve(78,a,102,a)].
% 0.45/1.06 103 empty_carrier(A) | -lattice(A) | -latt_str(A) | -empty_carrier(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(41)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | -empty_carrier(poset_of_lattice(c5)). [resolve(103,c,78,a)].
% 0.45/1.06 104 empty_carrier(A) | -lattice(A) | -latt_str(A) | strict_rel_str(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(41)].
% 0.45/1.06 105 empty_carrier(A) | -lattice(A) | -latt_str(A) | reflexive_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(41)].
% 0.45/1.06 106 empty_carrier(A) | -lattice(A) | -latt_str(A) | transitive_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(41)].
% 0.45/1.06 107 empty_carrier(A) | -lattice(A) | -latt_str(A) | antisymmetric_relstr(poset_of_lattice(A)) # label(fc4_lattice3) # label(axiom). [clausify(41)].
% 0.45/1.06 108 empty_carrier(A) | -lattice(A) | -latt_str(A) | relation_of_lattice(A) = k2_lattice3(A) # label(redefinition_k2_lattice3) # label(axiom). [clausify(52)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | relation_of_lattice(c5) = k2_lattice3(c5). [resolve(108,c,78,a)].
% 0.45/1.06 109 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -latt_element_smaller(A,B,C) | relstr_set_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B)) # label(t30_lattice3) # label(axiom). [clausify(57)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | -latt_element_smaller(c5,A,B) | relstr_set_smaller(poset_of_lattice(c5),B,cast_to_el_of_LattPOSet(c5,A)). [resolve(109,c,78,a)].
% 0.45/1.06 110 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | latt_element_smaller(A,B,C) | -relstr_set_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B)) # label(t30_lattice3) # label(axiom). [clausify(57)].
% 0.45/1.06 Derived: empty_carrier(c5) | -lattice(c5) | -element(A,the_carrier(c5)) | latt_element_smaller(c5,A,B) | -relstr_set_smaller(poset_of_lattice(c5),B,cast_to_el_of_LattPOSet(c5,A)). [resolve(110,c,78,a)].
% 0.45/1.06 111 latt_str(c12) # label(t31_lattice3) # label(negated_conjecture). [clausify(64)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | join_commutative(c12). [resolve(111,a,79,a)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | join_associative(c12). [resolve(111,a,80,a)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | meet_commutative(c12). [resolve(111,a,81,a)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | meet_associative(c12). [resolve(111,a,82,a)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | meet_absorbing(c12). [resolve(111,a,83,a)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | join_absorbing(c12). [resolve(111,a,84,a)].
% 0.45/1.06 Derived: empty_carrier(c12) | -join_commutative(c12) | -join_associative(c12) | -meet_commutative(c12) | -meet_associative(c12) | -meet_absorbing(c12) | -join_absorbing(c12) | lattice(c12). [resolve(111,a,85,a)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | poset_of_lattice(c12) = rel_str_of(the_carrier(c12),k2_lattice3(c12)). [resolve(111,a,86,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | cast_to_el_of_LattPOSet(c12,A) = A. [resolve(111,a,87,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | cast_to_el_of_lattice(c12,A) = A. [resolve(111,a,88,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | reflexive(k2_lattice3(c12)). [resolve(111,a,89,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | antisymmetric(k2_lattice3(c12)). [resolve(111,a,90,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | transitive(k2_lattice3(c12)). [resolve(111,a,91,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | v1_partfun1(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(111,a,92,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | relation_of2_as_subset(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(111,a,93,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | strict_rel_str(poset_of_lattice(c12)). [resolve(111,a,94,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | reflexive_relstr(poset_of_lattice(c12)). [resolve(111,a,95,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | transitive_relstr(poset_of_lattice(c12)). [resolve(111,a,96,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | antisymmetric_relstr(poset_of_lattice(c12)). [resolve(111,a,97,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | element(cast_to_el_of_LattPOSet(c12,A),the_carrier(poset_of_lattice(c12))). [resolve(111,a,98,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | element(cast_to_el_of_lattice(c12,A),the_carrier(c12)). [resolve(111,a,99,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | relation(relation_of_lattice(c12)). [resolve(111,a,100,c)].
% 0.45/1.06 Derived: meet_semilatt_str(c12). [resolve(111,a,101,a)].
% 0.45/1.06 Derived: join_semilatt_str(c12). [resolve(111,a,102,a)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | -empty_carrier(poset_of_lattice(c12)). [resolve(111,a,103,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | relation_of_lattice(c12) = k2_lattice3(c12). [resolve(111,a,108,c)].
% 0.45/1.06 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | -latt_element_smaller(c12,A,B) | relstr_set_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [resolve(111,a,109,c)].
% 0.45/1.07 Derived: empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | latt_element_smaller(c12,A,B) | -relstr_set_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [resolve(111,a,110,c)].
% 0.45/1.07 112 empty_carrier(A) | -lattice(A) | -latt_str(A) | -strict_rel_str(poset_of_lattice(A)) | rel_str_of(the_carrier(poset_of_lattice(A)),the_InternalRel(poset_of_lattice(A))) = poset_of_lattice(A). [resolve(67,d,66,a)].
% 0.45/1.07 Derived: empty_carrier(c5) | -lattice(c5) | -strict_rel_str(poset_of_lattice(c5)) | rel_str_of(the_carrier(poset_of_lattice(c5)),the_InternalRel(poset_of_lattice(c5))) = poset_of_lattice(c5). [resolve(112,c,78,a)].
% 0.45/1.07 Derived: empty_carrier(c12) | -lattice(c12) | -strict_rel_str(poset_of_lattice(c12)) | rel_str_of(the_carrier(poset_of_lattice(c12)),the_InternalRel(poset_of_lattice(c12))) = poset_of_lattice(c12). [resolve(112,c,111,a)].
% 0.45/1.07 113 one_sorted_str(poset_of_lattice(A)) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(68,a,67,d)].
% 0.45/1.07 Derived: one_sorted_str(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5). [resolve(113,d,78,a)].
% 0.45/1.07 Derived: one_sorted_str(poset_of_lattice(c12)) | empty_carrier(c12) | -lattice(c12). [resolve(113,d,111,a)].
% 0.45/1.07 114 relation_of2_as_subset(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(69,a,67,d)].
% 0.45/1.07 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(114,d,78,a)].
% 0.45/1.07 Derived: relation_of2_as_subset(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(114,d,111,a)].
% 0.45/1.07 115 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | relation(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(71,d,67,d)].
% 0.45/1.07 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | relation(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(115,g,78,a)].
% 0.45/1.07 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | relation(the_InternalRel(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(115,g,111,a)].
% 0.45/1.07 116 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | reflexive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(72,d,67,d)].
% 0.45/1.07 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | reflexive(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(116,g,78,a)].
% 0.45/1.07 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | reflexive(the_InternalRel(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(116,g,111,a)].
% 0.45/1.07 117 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | antisymmetric(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(73,d,67,d)].
% 0.45/1.07 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | antisymmetric(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(117,g,78,a)].
% 0.45/1.07 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | antisymmetric(the_InternalRel(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(117,g,111,a)].
% 0.45/1.08 118 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | transitive(the_InternalRel(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(74,d,67,d)].
% 0.45/1.08 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | transitive(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(118,g,78,a)].
% 0.45/1.08 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | transitive(the_InternalRel(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(118,g,111,a)].
% 0.45/1.08 119 -reflexive_relstr(poset_of_lattice(A)) | -transitive_relstr(poset_of_lattice(A)) | -antisymmetric_relstr(poset_of_lattice(A)) | v1_partfun1(the_InternalRel(poset_of_lattice(A)),the_carrier(poset_of_lattice(A)),the_carrier(poset_of_lattice(A))) | empty_carrier(A) | -lattice(A) | -latt_str(A). [resolve(75,d,67,d)].
% 0.45/1.08 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | v1_partfun1(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(119,g,78,a)].
% 0.45/1.08 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | v1_partfun1(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(119,g,111,a)].
% 0.45/1.08 120 meet_semilatt_str(c1) # label(existence_l1_lattices) # label(axiom). [clausify(28)].
% 0.45/1.08 121 -meet_semilatt_str(A) | one_sorted_str(A) # label(dt_l1_lattices) # label(axiom). [clausify(18)].
% 0.45/1.08 Derived: one_sorted_str(c1). [resolve(120,a,121,a)].
% 0.45/1.08 122 meet_semilatt_str(c5). [resolve(78,a,101,a)].
% 0.45/1.08 Derived: one_sorted_str(c5). [resolve(122,a,121,a)].
% 0.45/1.08 123 meet_semilatt_str(c12). [resolve(111,a,101,a)].
% 0.45/1.08 Derived: one_sorted_str(c12). [resolve(123,a,121,a)].
% 0.45/1.08 124 join_semilatt_str(c4) # label(existence_l2_lattices) # label(axiom). [clausify(31)].
% 0.45/1.08 125 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(21)].
% 0.45/1.08 Derived: one_sorted_str(c4). [resolve(124,a,125,a)].
% 0.45/1.08 126 join_semilatt_str(c5). [resolve(78,a,102,a)].
% 0.45/1.08 127 join_semilatt_str(c12). [resolve(111,a,102,a)].
% 0.45/1.08 128 relation_of2_as_subset(f3(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(35)].
% 0.45/1.08 129 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(25)].
% 0.45/1.08 Derived: element(f3(A,B),powerset(cartesian_product2(A,B))). [resolve(128,a,129,a)].
% 0.45/1.08 130 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(53)].
% 0.45/1.08 Derived: relation_of2(f3(A,B),A,B). [resolve(130,a,128,a)].
% 0.45/1.08 131 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(53)].
% 0.45/1.08 Derived: -relation_of2(A,B,C) | element(A,powerset(cartesian_product2(B,C))). [resolve(131,a,129,a)].
% 0.45/1.08 132 relation_of2_as_subset(the_InternalRel(rel_str_of(A,B)),the_carrier(rel_str_of(A,B)),the_carrier(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(69,a,65,b)].
% 0.45/1.08 Derived: -relation_of2(A,B,B) | element(the_InternalRel(rel_str_of(B,A)),powerset(cartesian_product2(the_carrier(rel_str_of(B,A)),the_carrier(rel_str_of(B,A))))). [resolve(132,a,129,a)].
% 0.45/1.08 Derived: -relation_of2(A,B,B) | relation_of2(the_InternalRel(rel_str_of(B,A)),the_carrier(rel_str_of(B,A)),the_carrier(rel_str_of(B,A))). [resolve(132,a,130,a)].
% 0.45/1.08 133 relation_of2_as_subset(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(70,a,69,a)].
% 0.45/1.08 Derived: element(the_InternalRel(c2),powerset(cartesian_product2(the_carrier(c2),the_carrier(c2)))). [resolve(133,a,129,a)].
% 0.45/1.08 Derived: relation_of2(the_InternalRel(c2),the_carrier(c2),the_carrier(c2)). [resolve(133,a,130,a)].
% 0.83/1.08 134 relation_of2_as_subset(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(76,a,69,a)].
% 0.83/1.08 Derived: element(the_InternalRel(c6),powerset(cartesian_product2(the_carrier(c6),the_carrier(c6)))). [resolve(134,a,129,a)].
% 0.83/1.08 Derived: relation_of2(the_InternalRel(c6),the_carrier(c6),the_carrier(c6)). [resolve(134,a,130,a)].
% 0.83/1.08 135 relation_of2_as_subset(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(77,a,69,a)].
% 0.83/1.08 Derived: element(the_InternalRel(c8),powerset(cartesian_product2(the_carrier(c8),the_carrier(c8)))). [resolve(135,a,129,a)].
% 0.83/1.08 Derived: relation_of2(the_InternalRel(c8),the_carrier(c8),the_carrier(c8)). [resolve(135,a,130,a)].
% 0.83/1.08 136 empty_carrier(c5) | -lattice(c5) | relation_of2_as_subset(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(78,a,93,c)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | element(k2_lattice3(c5),powerset(cartesian_product2(the_carrier(c5),the_carrier(c5)))). [resolve(136,c,129,a)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2(k2_lattice3(c5),the_carrier(c5),the_carrier(c5)). [resolve(136,c,130,a)].
% 0.83/1.08 137 empty_carrier(c12) | -lattice(c12) | relation_of2_as_subset(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(111,a,93,c)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | element(k2_lattice3(c12),powerset(cartesian_product2(the_carrier(c12),the_carrier(c12)))). [resolve(137,c,129,a)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | relation_of2(k2_lattice3(c12),the_carrier(c12),the_carrier(c12)). [resolve(137,c,130,a)].
% 0.83/1.08 138 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(114,d,78,a)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | element(the_InternalRel(poset_of_lattice(c5)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))))). [resolve(138,a,129,a)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | relation_of2(the_InternalRel(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5)),the_carrier(poset_of_lattice(c5))). [resolve(138,a,130,a)].
% 0.83/1.08 139 relation_of2_as_subset(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(114,d,111,a)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | element(the_InternalRel(poset_of_lattice(c12)),powerset(cartesian_product2(the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))))). [resolve(139,a,129,a)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | relation_of2(the_InternalRel(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12)),the_carrier(poset_of_lattice(c12))). [resolve(139,a,130,a)].
% 0.83/1.08 140 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(37)].
% 0.83/1.08 141 one_sorted_str(c3) # label(existence_l1_struct_0) # label(axiom). [clausify(30)].
% 0.83/1.08 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(140,b,141,a)].
% 0.83/1.08 142 one_sorted_str(c10) # label(rc3_struct_0) # label(axiom). [clausify(50)].
% 0.83/1.08 Derived: empty_carrier(c10) | -empty(the_carrier(c10)). [resolve(142,a,140,b)].
% 0.83/1.08 143 empty_carrier(A) | -one_sorted_str(A) | element(f6(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(51)].
% 0.83/1.08 Derived: empty_carrier(c3) | element(f6(c3),powerset(the_carrier(c3))). [resolve(143,b,141,a)].
% 0.83/1.08 Derived: empty_carrier(c10) | element(f6(c10),powerset(the_carrier(c10))). [resolve(143,b,142,a)].
% 0.83/1.08 144 empty_carrier(A) | -one_sorted_str(A) | -empty(f6(A)) # label(rc5_struct_0) # label(axiom). [clausify(51)].
% 0.83/1.08 Derived: empty_carrier(c3) | -empty(f6(c3)). [resolve(144,b,141,a)].
% 0.83/1.08 Derived: empty_carrier(c10) | -empty(f6(c10)). [resolve(144,b,142,a)].
% 0.83/1.08 145 one_sorted_str(rel_str_of(A,B)) | -relation_of2(B,A,A). [resolve(68,a,65,b)].
% 0.83/1.08 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(the_carrier(rel_str_of(B,A))). [resolve(145,a,140,b)].
% 0.83/1.08 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | element(f6(rel_str_of(B,A)),powerset(the_carrier(rel_str_of(B,A)))). [resolve(145,a,143,b)].
% 0.83/1.08 Derived: -relation_of2(A,B,B) | empty_carrier(rel_str_of(B,A)) | -empty(f6(rel_str_of(B,A))). [resolve(145,a,144,b)].
% 0.83/1.08 146 one_sorted_str(c2). [resolve(70,a,68,a)].
% 0.83/1.08 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(146,a,140,b)].
% 0.83/1.08 Derived: empty_carrier(c2) | element(f6(c2),powerset(the_carrier(c2))). [resolve(146,a,143,b)].
% 0.83/1.08 Derived: empty_carrier(c2) | -empty(f6(c2)). [resolve(146,a,144,b)].
% 0.83/1.08 147 one_sorted_str(c6). [resolve(76,a,68,a)].
% 0.83/1.08 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(147,a,140,b)].
% 0.83/1.08 Derived: empty_carrier(c6) | element(f6(c6),powerset(the_carrier(c6))). [resolve(147,a,143,b)].
% 0.83/1.08 Derived: empty_carrier(c6) | -empty(f6(c6)). [resolve(147,a,144,b)].
% 0.83/1.08 148 one_sorted_str(c8). [resolve(77,a,68,a)].
% 0.83/1.08 Derived: empty_carrier(c8) | -empty(the_carrier(c8)). [resolve(148,a,140,b)].
% 0.83/1.08 Derived: empty_carrier(c8) | element(f6(c8),powerset(the_carrier(c8))). [resolve(148,a,143,b)].
% 0.83/1.08 Derived: empty_carrier(c8) | -empty(f6(c8)). [resolve(148,a,144,b)].
% 0.83/1.08 149 one_sorted_str(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5). [resolve(113,d,78,a)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -empty(the_carrier(poset_of_lattice(c5))). [resolve(149,a,140,b)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | element(f6(poset_of_lattice(c5)),powerset(the_carrier(poset_of_lattice(c5)))). [resolve(149,a,143,b)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | empty_carrier(poset_of_lattice(c5)) | -empty(f6(poset_of_lattice(c5))). [resolve(149,a,144,b)].
% 0.83/1.08 150 one_sorted_str(poset_of_lattice(c12)) | empty_carrier(c12) | -lattice(c12). [resolve(113,d,111,a)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | -empty(the_carrier(poset_of_lattice(c12))). [resolve(150,a,140,b)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | element(f6(poset_of_lattice(c12)),powerset(the_carrier(poset_of_lattice(c12)))). [resolve(150,a,143,b)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | empty_carrier(poset_of_lattice(c12)) | -empty(f6(poset_of_lattice(c12))). [resolve(150,a,144,b)].
% 0.83/1.08 151 one_sorted_str(c1). [resolve(120,a,121,a)].
% 0.83/1.08 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(151,a,140,b)].
% 0.83/1.08 Derived: empty_carrier(c1) | element(f6(c1),powerset(the_carrier(c1))). [resolve(151,a,143,b)].
% 0.83/1.08 Derived: empty_carrier(c1) | -empty(f6(c1)). [resolve(151,a,144,b)].
% 0.83/1.08 152 one_sorted_str(c5). [resolve(122,a,121,a)].
% 0.83/1.08 Derived: empty_carrier(c5) | -empty(the_carrier(c5)). [resolve(152,a,140,b)].
% 0.83/1.08 Derived: empty_carrier(c5) | element(f6(c5),powerset(the_carrier(c5))). [resolve(152,a,143,b)].
% 0.83/1.08 Derived: empty_carrier(c5) | -empty(f6(c5)). [resolve(152,a,144,b)].
% 0.83/1.08 153 one_sorted_str(c12). [resolve(123,a,121,a)].
% 0.83/1.08 Derived: empty_carrier(c12) | -empty(the_carrier(c12)). [resolve(153,a,140,b)].
% 0.83/1.08 Derived: empty_carrier(c12) | element(f6(c12),powerset(the_carrier(c12))). [resolve(153,a,143,b)].
% 0.83/1.08 Derived: empty_carrier(c12) | -empty(f6(c12)). [resolve(153,a,144,b)].
% 0.83/1.08 154 one_sorted_str(c4). [resolve(124,a,125,a)].
% 0.83/1.08 Derived: empty_carrier(c4) | -empty(the_carrier(c4)). [resolve(154,a,140,b)].
% 0.83/1.08 Derived: empty_carrier(c4) | element(f6(c4),powerset(the_carrier(c4))). [resolve(154,a,143,b)].
% 0.83/1.08 Derived: empty_carrier(c4) | -empty(f6(c4)). [resolve(154,a,144,b)].
% 0.83/1.08 155 -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | reflexive(the_InternalRel(rel_str_of(A,B))) | -relation_of2(B,A,A). [resolve(72,d,65,b)].
% 0.83/1.08 156 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | strict_rel_str(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(40)].
% 0.83/1.08 157 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | reflexive_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(40)].
% 0.83/1.08 158 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | transitive_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(40)].
% 0.83/1.08 159 -reflexive(A) | -antisymmetric(A) | -transitive(A) | -v1_partfun1(A,B,B) | -relation_of2(A,B,B) | antisymmetric_relstr(rel_str_of(B,A)) # label(fc3_orders_2) # label(axiom). [clausify(40)].
% 0.83/1.08 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | strict_rel_str(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(155,d,156,a)].
% 0.83/1.08 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | reflexive_relstr(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(155,d,157,a)].
% 0.83/1.08 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | transitive_relstr(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(155,d,158,a)].
% 0.83/1.08 Derived: -reflexive_relstr(rel_str_of(A,B)) | -transitive_relstr(rel_str_of(A,B)) | -antisymmetric_relstr(rel_str_of(A,B)) | -relation_of2(B,A,A) | -antisymmetric(the_InternalRel(rel_str_of(A,B))) | -transitive(the_InternalRel(rel_str_of(A,B))) | -v1_partfun1(the_InternalRel(rel_str_of(A,B)),C,C) | -relation_of2(the_InternalRel(rel_str_of(A,B)),C,C) | antisymmetric_relstr(rel_str_of(C,the_InternalRel(rel_str_of(A,B)))). [resolve(155,d,159,a)].
% 0.83/1.08 160 -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | reflexive(the_InternalRel(c2)). [resolve(72,d,70,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c2))). [resolve(160,d,156,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c2))). [resolve(160,d,157,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c2))). [resolve(160,d,158,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c2) | -transitive_relstr(c2) | -antisymmetric_relstr(c2) | -antisymmetric(the_InternalRel(c2)) | -transitive(the_InternalRel(c2)) | -v1_partfun1(the_InternalRel(c2),A,A) | -relation_of2(the_InternalRel(c2),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c2))). [resolve(160,d,159,a)].
% 0.83/1.08 161 -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | reflexive(the_InternalRel(c6)). [resolve(76,a,72,d)].
% 0.83/1.08 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | -antisymmetric(the_InternalRel(c6)) | -transitive(the_InternalRel(c6)) | -v1_partfun1(the_InternalRel(c6),A,A) | -relation_of2(the_InternalRel(c6),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c6))). [resolve(161,d,156,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | -antisymmetric(the_InternalRel(c6)) | -transitive(the_InternalRel(c6)) | -v1_partfun1(the_InternalRel(c6),A,A) | -relation_of2(the_InternalRel(c6),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c6))). [resolve(161,d,157,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | -antisymmetric(the_InternalRel(c6)) | -transitive(the_InternalRel(c6)) | -v1_partfun1(the_InternalRel(c6),A,A) | -relation_of2(the_InternalRel(c6),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c6))). [resolve(161,d,158,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c6) | -transitive_relstr(c6) | -antisymmetric_relstr(c6) | -antisymmetric(the_InternalRel(c6)) | -transitive(the_InternalRel(c6)) | -v1_partfun1(the_InternalRel(c6),A,A) | -relation_of2(the_InternalRel(c6),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c6))). [resolve(161,d,159,a)].
% 0.83/1.08 162 -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | reflexive(the_InternalRel(c8)). [resolve(77,a,72,d)].
% 0.83/1.08 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -antisymmetric(the_InternalRel(c8)) | -transitive(the_InternalRel(c8)) | -v1_partfun1(the_InternalRel(c8),A,A) | -relation_of2(the_InternalRel(c8),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(c8))). [resolve(162,d,156,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -antisymmetric(the_InternalRel(c8)) | -transitive(the_InternalRel(c8)) | -v1_partfun1(the_InternalRel(c8),A,A) | -relation_of2(the_InternalRel(c8),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(c8))). [resolve(162,d,157,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -antisymmetric(the_InternalRel(c8)) | -transitive(the_InternalRel(c8)) | -v1_partfun1(the_InternalRel(c8),A,A) | -relation_of2(the_InternalRel(c8),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(c8))). [resolve(162,d,158,a)].
% 0.83/1.08 Derived: -reflexive_relstr(c8) | -transitive_relstr(c8) | -antisymmetric_relstr(c8) | -antisymmetric(the_InternalRel(c8)) | -transitive(the_InternalRel(c8)) | -v1_partfun1(the_InternalRel(c8),A,A) | -relation_of2(the_InternalRel(c8),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(c8))). [resolve(162,d,159,a)].
% 0.83/1.08 163 empty_carrier(c5) | -lattice(c5) | reflexive(k2_lattice3(c5)). [resolve(78,a,89,c)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric(k2_lattice3(c5)) | -transitive(k2_lattice3(c5)) | -v1_partfun1(k2_lattice3(c5),A,A) | -relation_of2(k2_lattice3(c5),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c5))). [resolve(163,c,156,a)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric(k2_lattice3(c5)) | -transitive(k2_lattice3(c5)) | -v1_partfun1(k2_lattice3(c5),A,A) | -relation_of2(k2_lattice3(c5),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c5))). [resolve(163,c,157,a)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric(k2_lattice3(c5)) | -transitive(k2_lattice3(c5)) | -v1_partfun1(k2_lattice3(c5),A,A) | -relation_of2(k2_lattice3(c5),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c5))). [resolve(163,c,158,a)].
% 0.83/1.08 Derived: empty_carrier(c5) | -lattice(c5) | -antisymmetric(k2_lattice3(c5)) | -transitive(k2_lattice3(c5)) | -v1_partfun1(k2_lattice3(c5),A,A) | -relation_of2(k2_lattice3(c5),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c5))). [resolve(163,c,159,a)].
% 0.83/1.08 164 empty_carrier(c12) | -lattice(c12) | reflexive(k2_lattice3(c12)). [resolve(111,a,89,c)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric(k2_lattice3(c12)) | -transitive(k2_lattice3(c12)) | -v1_partfun1(k2_lattice3(c12),A,A) | -relation_of2(k2_lattice3(c12),A,A) | strict_rel_str(rel_str_of(A,k2_lattice3(c12))). [resolve(164,c,156,a)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric(k2_lattice3(c12)) | -transitive(k2_lattice3(c12)) | -v1_partfun1(k2_lattice3(c12),A,A) | -relation_of2(k2_lattice3(c12),A,A) | reflexive_relstr(rel_str_of(A,k2_lattice3(c12))). [resolve(164,c,157,a)].
% 0.83/1.08 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric(k2_lattice3(c12)) | -transitive(k2_lattice3(c12)) | -v1_partfun1(k2_lattice3(c12),A,A) | -relation_of2(k2_lattice3(c12),A,A) | transitive_relstr(rel_str_of(A,k2_lattice3(c12))). [resolve(164,c,158,a)].
% 0.83/1.09 Derived: empty_carrier(c12) | -lattice(c12) | -antisymmetric(k2_lattice3(c12)) | -transitive(k2_lattice3(c12)) | -v1_partfun1(k2_lattice3(c12),A,A) | -relation_of2(k2_lattice3(c12),A,A) | antisymmetric_relstr(rel_str_of(A,k2_lattice3(c12))). [resolve(164,c,159,a)].
% 0.83/1.09 165 -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | reflexive(the_InternalRel(poset_of_lattice(c5))) | empty_carrier(c5) | -lattice(c5). [resolve(116,g,78,a)].
% 0.83/1.09 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(165,d,156,a)].
% 0.83/1.09 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(165,d,157,a)].
% 0.83/1.09 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(165,d,158,a)].
% 0.83/1.09 Derived: -reflexive_relstr(poset_of_lattice(c5)) | -transitive_relstr(poset_of_lattice(c5)) | -antisymmetric_relstr(poset_of_lattice(c5)) | empty_carrier(c5) | -lattice(c5) | -antisymmetric(the_InternalRel(poset_of_lattice(c5))) | -transitive(the_InternalRel(poset_of_lattice(c5))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c5)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c5)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c5)))). [resolve(165,d,159,a)].
% 0.83/1.09 166 -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | reflexive(the_InternalRel(poset_of_lattice(c12))) | empty_carrier(c12) | -lattice(c12). [resolve(116,g,111,a)].
% 0.83/1.09 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | empty_carrier(c12) | -lattice(c12) | -antisymmetric(the_InternalRel(poset_of_lattice(c12))) | -transitive(the_InternalRel(poset_of_lattice(c12))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c12)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c12)),A,A) | strict_rel_str(rel_str_of(A,the_InternalRel(poset_of_lattice(c12)))). [resolve(166,d,156,a)].
% 0.83/1.09 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | empty_carrier(c12) | -lattice(c12) | -antisymmetric(the_InternalRel(poset_of_lattice(c12))) | -transitive(the_InternalRel(poset_of_lattice(c12))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c12)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c12)),A,A) | reflexive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c12)))). [resolve(166,d,157,a)].
% 0.83/1.09 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | empty_carrier(c12) | -lattice(c12) | -antisymmetric(the_InternalRel(poset_of_lattice(c12))) | -transitive(the_InternalRel(poset_of_lattice(c12))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c12)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c12)),A,A) | transitive_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c12)))). [resolve(166,d,158,a)].
% 0.83/1.14 Derived: -reflexive_relstr(poset_of_lattice(c12)) | -transitive_relstr(poset_of_lattice(c12)) | -antisymmetric_relstr(poset_of_lattice(c12)) | empty_carrier(c12) | -lattice(c12) | -antisymmetric(the_InternalRel(poset_of_lattice(c12))) | -transitive(the_InternalRel(poset_of_lattice(c12))) | -v1_partfun1(the_InternalRel(poset_of_lattice(c12)),A,A) | -relation_of2(the_InternalRel(poset_of_lattice(c12)),A,A) | antisymmetric_relstr(rel_str_of(A,the_InternalRel(poset_of_lattice(c12)))). [resolve(166,d,159,a)].
% 0.83/1.14 167 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(58)].
% 0.83/1.14 168 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(54)].
% 0.83/1.14 169 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(58)].
% 0.83/1.14 Derived: element(A,powerset(A)). [resolve(167,b,168,a)].
% 0.83/1.14
% 0.83/1.14 ============================== end predicate elimination =============
% 0.83/1.14
% 0.83/1.14 Auto_denials: (non-Horn, no changes).
% 0.83/1.14
% 0.83/1.14 Term ordering decisions:
% 0.83/1.14 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. rel_str_of=1. cartesian_product2=1. cast_to_el_of_LattPOSet=1. cast_to_el_of_lattice=1. f1=1. f3=1. the_InternalRel=1. poset_of_lattice=1. the_carrier=1. k2_lattice3=1. powerset=1. relation_of_lattice=1. f2=1. f4=1. f5=1. f6=1.
% 0.83/1.14
% 0.83/1.14 ============================== end of process initial clauses ========
% 0.83/1.14
% 0.83/1.14 ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.14
% 0.83/1.14 ============================== end of clauses for search =============
% 0.83/1.14
% 0.83/1.14 ============================== SEARCH ================================
% 0.83/1.14
% 0.83/1.14 % Starting search at 0.07 seconds.
% 0.83/1.14
% 0.83/1.14 ============================== PROOF =================================
% 0.83/1.14 % SZS status Theorem
% 0.83/1.14 % SZS output start Refutation
% 0.83/1.14
% 0.83/1.14 % Proof 1 at 0.10 (+ 0.00) seconds.
% 0.83/1.14 % Length of proof is 35.
% 0.83/1.14 % Level of proof is 10.
% 0.83/1.14 % Maximum clause weight is 15.000.
% 0.83/1.14 % Given clauses 289.
% 0.83/1.14
% 0.83/1.14 7 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(A)) -> cast_to_el_of_LattPOSet(A,B) = B)))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 8 (all A (-empty_carrier(A) & lattice(A) & latt_str(A) -> (all B (element(B,the_carrier(poset_of_lattice(A))) -> cast_to_el_of_lattice(A,B) = B)))) # label(d4_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 16 (all A all B (-empty_carrier(A) & lattice(A) & latt_str(A) & element(B,the_carrier(poset_of_lattice(A))) -> element(cast_to_el_of_lattice(A,B),the_carrier(A)))) # label(dt_k5_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 57 (all A all B (-empty_carrier(B) & lattice(B) & latt_str(B) -> (all C (element(C,the_carrier(B)) -> (latt_element_smaller(B,C,A) <-> relstr_set_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))))))) # label(t30_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 64 -(all A all B (-empty_carrier(B) & lattice(B) & latt_str(B) -> (all C (element(C,the_carrier(poset_of_lattice(B))) -> (relstr_set_smaller(poset_of_lattice(B),A,C) <-> latt_element_smaller(B,cast_to_el_of_lattice(B,C),A)))))) # label(t31_lattice3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.83/1.14 87 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | cast_to_el_of_LattPOSet(A,B) = B # label(d3_lattice3) # label(axiom). [clausify(7)].
% 0.83/1.14 88 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | cast_to_el_of_lattice(A,B) = B # label(d4_lattice3) # label(axiom). [clausify(8)].
% 0.83/1.14 99 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(poset_of_lattice(A))) | element(cast_to_el_of_lattice(A,B),the_carrier(A)) # label(dt_k5_lattice3) # label(axiom). [clausify(16)].
% 0.83/1.14 109 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | -latt_element_smaller(A,B,C) | relstr_set_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B)) # label(t30_lattice3) # label(axiom). [clausify(57)].
% 0.83/1.14 110 empty_carrier(A) | -lattice(A) | -latt_str(A) | -element(B,the_carrier(A)) | latt_element_smaller(A,B,C) | -relstr_set_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B)) # label(t30_lattice3) # label(axiom). [clausify(57)].
% 0.83/1.14 111 latt_str(c12) # label(t31_lattice3) # label(negated_conjecture). [clausify(64)].
% 0.83/1.14 200 -empty_carrier(c12) # label(t31_lattice3) # label(negated_conjecture). [clausify(64)].
% 0.83/1.14 201 lattice(c12) # label(t31_lattice3) # label(negated_conjecture). [clausify(64)].
% 0.83/1.14 202 element(c13,the_carrier(poset_of_lattice(c12))) # label(t31_lattice3) # label(negated_conjecture). [clausify(64)].
% 0.83/1.14 203 relstr_set_smaller(poset_of_lattice(c12),c11,c13) | latt_element_smaller(c12,cast_to_el_of_lattice(c12,c13),c11) # label(t31_lattice3) # label(negated_conjecture). [clausify(64)].
% 0.83/1.14 204 -relstr_set_smaller(poset_of_lattice(c12),c11,c13) | -latt_element_smaller(c12,cast_to_el_of_lattice(c12,c13),c11) # label(t31_lattice3) # label(negated_conjecture). [clausify(64)].
% 0.83/1.14 265 empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | cast_to_el_of_LattPOSet(c12,A) = A. [resolve(111,a,87,c)].
% 0.83/1.14 266 -element(A,the_carrier(c12)) | cast_to_el_of_LattPOSet(c12,A) = A. [copy(265),unit_del(a,200),unit_del(b,201)].
% 0.83/1.14 267 empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | cast_to_el_of_lattice(c12,A) = A. [resolve(111,a,88,c)].
% 0.83/1.14 268 -element(A,the_carrier(poset_of_lattice(c12))) | cast_to_el_of_lattice(c12,A) = A. [copy(267),unit_del(a,200),unit_del(b,201)].
% 0.83/1.14 285 empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(poset_of_lattice(c12))) | element(cast_to_el_of_lattice(c12,A),the_carrier(c12)). [resolve(111,a,99,c)].
% 0.83/1.14 286 -element(A,the_carrier(poset_of_lattice(c12))) | element(cast_to_el_of_lattice(c12,A),the_carrier(c12)). [copy(285),unit_del(a,200),unit_del(b,201)].
% 0.83/1.14 291 empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | -latt_element_smaller(c12,A,B) | relstr_set_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [resolve(111,a,109,c)].
% 0.83/1.14 292 -element(A,the_carrier(c12)) | -latt_element_smaller(c12,A,B) | relstr_set_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [copy(291),unit_del(a,200),unit_del(b,201)].
% 0.83/1.14 293 empty_carrier(c12) | -lattice(c12) | -element(A,the_carrier(c12)) | latt_element_smaller(c12,A,B) | -relstr_set_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [resolve(111,a,110,c)].
% 0.83/1.14 294 -element(A,the_carrier(c12)) | latt_element_smaller(c12,A,B) | -relstr_set_smaller(poset_of_lattice(c12),B,cast_to_el_of_LattPOSet(c12,A)). [copy(293),unit_del(a,200),unit_del(b,201)].
% 0.83/1.14 438 cast_to_el_of_lattice(c12,c13) = c13. [resolve(268,a,202,a)].
% 0.83/1.14 440 -relstr_set_smaller(poset_of_lattice(c12),c11,c13) | -latt_element_smaller(c12,c13,c11). [back_rewrite(204),rewrite([438(9)])].
% 0.83/1.14 441 relstr_set_smaller(poset_of_lattice(c12),c11,c13) | latt_element_smaller(c12,c13,c11). [back_rewrite(203),rewrite([438(9)])].
% 0.83/1.14 443 element(c13,the_carrier(c12)). [resolve(286,a,202,a),rewrite([438(3)])].
% 0.83/1.14 509 cast_to_el_of_LattPOSet(c12,c13) = c13. [resolve(443,a,266,a)].
% 0.83/1.14 519 latt_element_smaller(c12,c13,A) | -relstr_set_smaller(poset_of_lattice(c12),A,c13). [para(509(a,1),294(c,3)),unit_del(a,443)].
% 0.83/1.14 610 latt_element_smaller(c12,c13,c11). [resolve(519,b,441,a),merge(b)].
% 0.83/1.14 611 -relstr_set_smaller(poset_of_lattice(c12),c11,c13). [back_unit_del(440),unit_del(b,610)].
% 0.83/1.14 612 $F. [resolve(610,a,292,b),rewrite([509(10)]),unit_del(a,443),unit_del(b,611)].
% 0.83/1.14
% 0.83/1.14 % SZS output end Refutation
% 0.83/1.14 ============================== end of proof ==========================
% 0.83/1.14
% 0.83/1.14 ============================== STATISTICS ============================
% 0.83/1.14
% 0.83/1.14 Given=289. Generated=630. Kept=381. proofs=1.
% 0.83/1.14 Usable=280. Sos=77. Demods=18. Limbo=0, Disabled=332. Hints=0.
% 0.83/1.14 Megabytes=0.83.
% 0.83/1.14 User_CPU=0.10, System_CPU=0.00, Wall_clock=0.
% 0.83/1.14
% 0.83/1.14 ============================== end of statistics =====================
% 0.83/1.14
% 0.83/1.14 ============================== end of search =========================
% 0.83/1.14
% 0.83/1.14 THEOREM PROVED
% 0.83/1.14 % SZS status Theorem
% 0.83/1.14
% 0.83/1.14 Exiting with 1 proof.
% 0.83/1.14
% 0.83/1.14 Process 28387 exit (max_proofs) Sun Jun 19 11:53:08 2022
% 0.83/1.14 Prover9 interrupted
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