TSTP Solution File: SEU305+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU305+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 13:30:49 EDT 2022
% Result : Theorem 1.28s 1.55s
% Output : Refutation 1.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU305+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.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 : Sat Jun 18 19:17:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.99 ============================== Prover9 ===============================
% 0.41/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.99 Process 3976 was started by sandbox2 on n028.cluster.edu,
% 0.41/0.99 Sat Jun 18 19:17:45 2022
% 0.41/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3823_n028.cluster.edu".
% 0.41/0.99 ============================== end of head ===========================
% 0.41/0.99
% 0.41/0.99 ============================== INPUT =================================
% 0.41/0.99
% 0.41/0.99 % Reading from file /tmp/Prover9_3823_n028.cluster.edu
% 0.41/0.99
% 0.41/0.99 set(prolog_style_variables).
% 0.41/0.99 set(auto2).
% 0.41/0.99 % set(auto2) -> set(auto).
% 0.41/0.99 % set(auto) -> set(auto_inference).
% 0.41/0.99 % set(auto) -> set(auto_setup).
% 0.41/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.99 % set(auto) -> set(auto_limits).
% 0.41/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.99 % set(auto) -> set(auto_denials).
% 0.41/0.99 % set(auto) -> set(auto_process).
% 0.41/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.99 % set(auto2) -> assign(stats, some).
% 0.41/0.99 % set(auto2) -> clear(echo_input).
% 0.41/0.99 % set(auto2) -> set(quiet).
% 0.41/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.99 % set(auto2) -> clear(print_given).
% 0.41/0.99 assign(lrs_ticks,-1).
% 0.41/0.99 assign(sos_limit,10000).
% 0.41/0.99 assign(order,kbo).
% 0.41/0.99 set(lex_order_vars).
% 0.41/0.99 clear(print_given).
% 0.41/0.99
% 0.41/0.99 % formulas(sos). % not echoed (42 formulas)
% 0.41/0.99
% 0.41/0.99 ============================== end of input ==========================
% 0.41/0.99
% 0.41/0.99 % From the command line: assign(max_seconds, 300).
% 0.41/0.99
% 0.41/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.99
% 0.41/0.99 % Formulas that are not ordinary clauses:
% 0.41/0.99 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 2 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 3 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 4 (all A all B all C (-empty_carrier(A) & join_commutative(A) & join_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> join_commut(A,B,C) = join_commut(A,C,B))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 5 (all A (-empty_carrier(A) & join_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> join(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 6 (all A (-empty_carrier(A) & join_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below(A,B,C) <-> join(A,B,C) = C))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 7 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 8 (all A all B all C (-empty_carrier(A) & join_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> element(join(A,B,C),the_carrier(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 9 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 10 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 11 (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].
% 0.41/0.99 12 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 13 (all A all B all C (-empty_carrier(A) & join_commutative(A) & join_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> element(join_commut(A,B,C),the_carrier(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 14 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 15 (all A (join_semilatt_str(A) -> one_sorted_str(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 16 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 17 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 18 (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].
% 0.41/0.99 19 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 20 (all A (join_semilatt_str(A) -> function(the_L_join(A)) & quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) & relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 21 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 22 (exists A join_semilatt_str(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 23 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 24 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 25 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 26 (all A (-empty(powerset(A)) & cup_closed(powerset(A)) & diff_closed(powerset(A)) & preboolean(powerset(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 27 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 28 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 29 (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].
% 0.41/0.99 30 (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].
% 0.41/0.99 31 (all A all B all C (-empty_carrier(A) & join_commutative(A) & join_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> join_commut(A,B,C) = join(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 32 (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].
% 0.41/0.99 33 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 34 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 35 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 36 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 37 (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].
% 0.41/0.99 38 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 39 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 40 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 41 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.99 42 -(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(negated_conjecture) # label(non_clause). [assumption].
% 0.41/0.99
% 0.41/0.99 ============================== end of process non-clausal formulas ===
% 0.41/0.99
% 0.41/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.99
% 0.41/0.99 ============================== PREDICATE ELIMINATION =================
% 0.41/0.99 43 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(27)].
% 0.41/0.99 44 one_sorted_str(c1) # label(existence_l1_struct_0) # label(axiom). [clausify(21)].
% 0.41/0.99 45 one_sorted_str(c3) # label(rc3_struct_0) # label(axiom). [clausify(28)].
% 0.41/0.99 46 -join_semilatt_str(A) | one_sorted_str(A) # label(dt_l2_lattices) # label(axiom). [clausify(15)].
% 0.41/0.99 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(43,b,44,a)].
% 0.41/0.99 Derived: empty_carrier(c3) | -empty(the_carrier(c3)). [resolve(43,b,45,a)].
% 0.41/0.99 Derived: empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(43,b,46,b)].
% 0.41/0.99 47 empty_carrier(A) | -one_sorted_str(A) | -empty(f4(A)) # label(rc5_struct_0) # label(axiom). [clausify(29)].
% 0.41/0.99 Derived: empty_carrier(c1) | -empty(f4(c1)). [resolve(47,b,44,a)].
% 0.41/0.99 Derived: empty_carrier(c3) | -empty(f4(c3)). [resolve(47,b,45,a)].
% 0.41/0.99 Derived: empty_carrier(A) | -empty(f4(A)) | -join_semilatt_str(A). [resolve(47,b,46,b)].
% 0.41/0.99 48 empty_carrier(A) | -one_sorted_str(A) | element(f4(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(29)].
% 0.41/0.99 Derived: empty_carrier(c1) | element(f4(c1),powerset(the_carrier(c1))). [resolve(48,b,44,a)].
% 0.41/0.99 Derived: empty_carrier(c3) | element(f4(c3),powerset(the_carrier(c3))). [resolve(48,b,45,a)].
% 0.41/0.99 Derived: empty_carrier(A) | element(f4(A),powerset(the_carrier(A))) | -join_semilatt_str(A). [resolve(48,b,46,b)].
% 0.41/0.99 49 -join_semilatt_str(A) | function(the_L_join(A)) # label(dt_u2_lattices) # label(axiom). [clausify(20)].
% 0.41/0.99 50 join_semilatt_str(c2) # label(existence_l2_lattices) # label(axiom). [clausify(22)].
% 0.41/0.99 51 join_semilatt_str(c4) # label(t26_lattices) # label(negated_conjecture). [clausify(42)].
% 0.41/0.99 Derived: function(the_L_join(c2)). [resolve(49,a,50,a)].
% 0.41/0.99 Derived: function(the_L_join(c4)). [resolve(49,a,51,a)].
% 0.41/0.99 52 -join_semilatt_str(A) | quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u2_lattices) # label(axiom). [clausify(20)].
% 0.41/0.99 Derived: quasi_total(the_L_join(c2),cartesian_product2(the_carrier(c2),the_carrier(c2)),the_carrier(c2)). [resolve(52,a,50,a)].
% 0.41/0.99 Derived: quasi_total(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(52,a,51,a)].
% 0.41/0.99 53 -join_semilatt_str(A) | relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A)) # label(dt_u2_lattices) # label(axiom). [clausify(20)].
% 0.41/0.99 Derived: relation_of2_as_subset(the_L_join(c2),cartesian_product2(the_carrier(c2),the_carrier(c2)),the_carrier(c2)). [resolve(53,a,50,a)].
% 0.41/0.99 Derived: relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(53,a,51,a)].
% 0.41/0.99 54 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(join(A,B,C),the_carrier(A)) # label(dt_k1_lattices) # label(axiom). [clausify(8)].
% 0.41/0.99 Derived: empty_carrier(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | element(join(c2,A,B),the_carrier(c2)). [resolve(54,b,50,a)].
% 0.41/0.99 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(join(c4,A,B),the_carrier(c4)). [resolve(54,b,51,a)].
% 0.41/0.99 55 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | element(join_commut(A,B,C),the_carrier(A)) # label(dt_k3_lattices) # label(axiom). [clausify(13)].
% 0.41/0.99 Derived: empty_carrier(c2) | -join_commutative(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | element(join_commut(c2,A,B),the_carrier(c2)). [resolve(55,c,50,a)].
% 0.41/0.99 Derived: empty_carrier(c4) | -join_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | element(join_commut(c4,A,B),the_carrier(c4)). [resolve(55,c,51,a)].
% 0.41/0.99 56 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | join(A,B,C) = C # label(d3_lattices) # label(axiom). [clausify(6)].
% 0.41/0.99 Derived: empty_carrier(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | -below(c2,A,B) | join(c2,A,B) = B. [resolve(56,b,50,a)].
% 0.41/0.99 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | -below(c4,A,B) | join(c4,A,B) = B. [resolve(56,b,51,a)].
% 0.41/0.99 57 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | below(A,B,C) | join(A,B,C) != C # label(d3_lattices) # label(axiom). [clausify(6)].
% 0.41/0.99 Derived: empty_carrier(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | below(c2,A,B) | join(c2,A,B) != B. [resolve(57,b,50,a)].
% 0.41/0.99 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | below(c4,A,B) | join(c4,A,B) != B. [resolve(57,b,51,a)].
% 0.41/0.99 58 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join_commut(A,C,B) = join_commut(A,B,C) # label(commutativity_k3_lattices) # label(axiom). [clausify(4)].
% 0.41/0.99 Derived: empty_carrier(c2) | -join_commutative(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | join_commut(c2,B,A) = join_commut(c2,A,B). [resolve(58,c,50,a)].
% 0.41/0.99 Derived: empty_carrier(c4) | -join_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | join_commut(c4,B,A) = join_commut(c4,A,B). [resolve(58,c,51,a)].
% 0.41/0.99 59 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,B,C) = join_commut(A,B,C) # label(redefinition_k3_lattices) # label(axiom). [clausify(31)].
% 0.41/0.99 Derived: empty_carrier(c2) | -join_commutative(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | join(c2,A,B) = join_commut(c2,A,B). [resolve(59,c,50,a)].
% 0.41/0.99 Derived: empty_carrier(c4) | -join_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | join(c4,A,B) = join_commut(c4,A,B). [resolve(59,c,51,a)].
% 0.41/0.99 60 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C) = join(A,B,C) # label(d1_lattices) # label(axiom). [clausify(5)].
% 0.41/0.99 Derived: empty_carrier(c2) | -element(A,the_carrier(c2)) | -element(B,the_carrier(c2)) | apply_binary_as_element(the_carrier(c2),the_carrier(c2),the_carrier(c2),the_L_join(c2),A,B) = join(c2,A,B). [resolve(60,b,50,a)].
% 0.41/0.99 Derived: empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | apply_binary_as_element(the_carrier(c4),the_carrier(c4),the_carrier(c4),the_L_join(c4),A,B) = join(c4,A,B). [resolve(60,b,51,a)].
% 0.41/0.99 61 empty_carrier(A) | -empty(the_carrier(A)) | -join_semilatt_str(A). [resolve(43,b,46,b)].
% 0.41/0.99 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(61,c,50,a)].
% 0.41/0.99 Derived: empty_carrier(c4) | -empty(the_carrier(c4)). [resolve(61,c,51,a)].
% 0.41/0.99 62 empty_carrier(A) | -empty(f4(A)) | -join_semilatt_str(A). [resolve(47,b,46,b)].
% 0.41/0.99 Derived: empty_carrier(c2) | -empty(f4(c2)). [resolve(62,c,50,a)].
% 0.41/0.99 Derived: empty_carrier(c4) | -empty(f4(c4)). [resolve(62,c,51,a)].
% 0.41/0.99 63 empty_carrier(A) | element(f4(A),powerset(the_carrier(A))) | -join_semilatt_str(A). [resolve(48,b,46,b)].
% 0.41/0.99 Derived: empty_carrier(c2) | element(f4(c2),powerset(the_carrier(c2))). [resolve(63,c,50,a)].
% 0.41/1.00 Derived: empty_carrier(c4) | element(f4(c4),powerset(the_carrier(c4))). [resolve(63,c,51,a)].
% 0.41/1.00 64 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(3)].
% 0.41/1.00 65 cup_closed(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(26)].
% 0.41/1.00 66 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(2)].
% 0.41/1.00 Derived: -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(64,a,65,a)].
% 0.41/1.00 67 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(2)].
% 0.41/1.00 68 preboolean(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(26)].
% 0.41/1.00 Derived: diff_closed(powerset(A)). [resolve(67,a,68,a)].
% 0.41/1.00 69 -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(64,a,65,a)].
% 0.41/1.00 70 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(36)].
% 0.41/1.00 71 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(33)].
% 0.41/1.00 72 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(36)].
% 0.41/1.00 Derived: element(A,powerset(A)). [resolve(70,b,71,a)].
% 0.41/1.00 73 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(32)].
% 0.41/1.00 74 relation_of2_as_subset(f3(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(25)].
% 0.41/1.00 Derived: relation_of2(f3(A,B),A,B). [resolve(73,a,74,a)].
% 0.41/1.00 75 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(32)].
% 0.41/1.00 76 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(18)].
% 0.41/1.00 Derived: element(f3(A,B),powerset(cartesian_product2(A,B))). [resolve(76,a,74,a)].
% 0.41/1.00 Derived: element(A,powerset(cartesian_product2(B,C))) | -relation_of2(A,B,C). [resolve(76,a,75,a)].
% 0.41/1.00 77 relation_of2_as_subset(the_L_join(c2),cartesian_product2(the_carrier(c2),the_carrier(c2)),the_carrier(c2)). [resolve(53,a,50,a)].
% 0.41/1.00 Derived: relation_of2(the_L_join(c2),cartesian_product2(the_carrier(c2),the_carrier(c2)),the_carrier(c2)). [resolve(77,a,73,a)].
% 0.41/1.00 Derived: element(the_L_join(c2),powerset(cartesian_product2(cartesian_product2(the_carrier(c2),the_carrier(c2)),the_carrier(c2)))). [resolve(77,a,76,a)].
% 0.41/1.00 78 relation_of2_as_subset(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(53,a,51,a)].
% 0.41/1.00 Derived: relation_of2(the_L_join(c4),cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)). [resolve(78,a,73,a)].
% 0.41/1.00 Derived: element(the_L_join(c4),powerset(cartesian_product2(cartesian_product2(the_carrier(c4),the_carrier(c4)),the_carrier(c4)))). [resolve(78,a,76,a)].
% 0.41/1.00 79 function(the_L_join(c2)). [resolve(49,a,50,a)].
% 0.41/1.00 80 empty(A) | empty(B) | -function(C) | -quasi_total(C,cartesian_product2(A,B),D) | -relation_of2(C,cartesian_product2(A,B),D) | -element(E,A) | -element(F,B) | element(apply_binary_as_element(A,B,D,C,E,F),D) # label(dt_k2_binop_1) # label(axiom). [clausify(11)].
% 0.41/1.00 81 empty(A) | empty(B) | -function(C) | -quasi_total(C,cartesian_product2(A,B),D) | -relation_of2(C,cartesian_product2(A,B),D) | -element(E,A) | -element(F,B) | apply_binary(C,E,F) = apply_binary_as_element(A,B,D,C,E,F) # label(redefinition_k2_binop_1) # label(axiom). [clausify(30)].
% 0.41/1.00 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c2),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c2),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | element(apply_binary_as_element(A,B,C,the_L_join(c2),D,E),C). [resolve(79,a,80,c)].
% 0.41/1.00 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c2),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c2),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | apply_binary(the_L_join(c2),D,E) = apply_binary_as_element(A,B,C,the_L_join(c2),D,E). [resolve(79,a,81,c)].
% 0.41/1.00 82 function(the_L_join(c4)). [resolve(49,a,51,a)].
% 0.41/1.00 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c4),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c4),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | element(apply_binary_as_element(A,B,C,the_L_join(c4),D,E),C). [resolve(82,a,80,c)].
% 1.28/1.55 Derived: empty(A) | empty(B) | -quasi_total(the_L_join(c4),cartesian_product2(A,B),C) | -relation_of2(the_L_join(c4),cartesian_product2(A,B),C) | -element(D,A) | -element(E,B) | apply_binary(the_L_join(c4),D,E) = apply_binary_as_element(A,B,C,the_L_join(c4),D,E). [resolve(82,a,81,c)].
% 1.28/1.55
% 1.28/1.55 ============================== end predicate elimination =============
% 1.28/1.55
% 1.28/1.55 Auto_denials: (non-Horn, no changes).
% 1.28/1.55
% 1.28/1.55 Term ordering decisions:
% 1.28/1.55 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. cartesian_product2=1. f1=1. f3=1. the_carrier=1. the_L_join=1. powerset=1. f2=1. f4=1. join=1. join_commut=1. apply_binary=1. apply_binary_as_element=1.
% 1.28/1.55
% 1.28/1.55 ============================== end of process initial clauses ========
% 1.28/1.55
% 1.28/1.55 ============================== CLAUSES FOR SEARCH ====================
% 1.28/1.55
% 1.28/1.55 ============================== end of clauses for search =============
% 1.28/1.55
% 1.28/1.55 ============================== SEARCH ================================
% 1.28/1.55
% 1.28/1.55 % Starting search at 0.03 seconds.
% 1.28/1.55
% 1.28/1.55 ============================== PROOF =================================
% 1.28/1.55 % SZS status Theorem
% 1.28/1.55 % SZS output start Refutation
% 1.28/1.55
% 1.28/1.55 % Proof 1 at 0.57 (+ 0.01) seconds.
% 1.28/1.55 % Length of proof is 29.
% 1.28/1.55 % Level of proof is 7.
% 1.28/1.55 % Maximum clause weight is 18.000.
% 1.28/1.55 % Given clauses 378.
% 1.28/1.55
% 1.28/1.55 4 (all A all B all C (-empty_carrier(A) & join_commutative(A) & join_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> join_commut(A,B,C) = join_commut(A,C,B))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 6 (all A (-empty_carrier(A) & join_semilatt_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (below(A,B,C) <-> join(A,B,C) = C))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 31 (all A all B all C (-empty_carrier(A) & join_commutative(A) & join_semilatt_str(A) & element(B,the_carrier(A)) & element(C,the_carrier(A)) -> join_commut(A,B,C) = join(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.55 42 -(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(negated_conjecture) # label(non_clause). [assumption].
% 1.28/1.55 51 join_semilatt_str(c4) # label(t26_lattices) # label(negated_conjecture). [clausify(42)].
% 1.28/1.55 56 empty_carrier(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -below(A,B,C) | join(A,B,C) = C # label(d3_lattices) # label(axiom). [clausify(6)].
% 1.28/1.55 58 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join_commut(A,C,B) = join_commut(A,B,C) # label(commutativity_k3_lattices) # label(axiom). [clausify(4)].
% 1.28/1.55 59 empty_carrier(A) | -join_commutative(A) | -join_semilatt_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | join(A,B,C) = join_commut(A,B,C) # label(redefinition_k3_lattices) # label(axiom). [clausify(31)].
% 1.28/1.55 83 join_commutative(c4) # label(t26_lattices) # label(negated_conjecture). [clausify(42)].
% 1.28/1.55 85 element(c5,the_carrier(c4)) # label(t26_lattices) # label(negated_conjecture). [clausify(42)].
% 1.28/1.55 86 element(c6,the_carrier(c4)) # label(t26_lattices) # label(negated_conjecture). [clausify(42)].
% 1.28/1.55 87 below(c4,c5,c6) # label(t26_lattices) # label(negated_conjecture). [clausify(42)].
% 1.28/1.55 88 below(c4,c6,c5) # label(t26_lattices) # label(negated_conjecture). [clausify(42)].
% 1.28/1.55 91 -empty_carrier(c4) # label(t26_lattices) # label(negated_conjecture). [clausify(42)].
% 1.28/1.55 93 c6 != c5 # label(t26_lattices) # label(negated_conjecture). [clausify(42)].
% 1.28/1.55 120 empty_carrier(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | -below(c4,A,B) | join(c4,A,B) = B. [resolve(56,b,51,a)].
% 1.28/1.55 121 -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | -below(c4,A,B) | join(c4,A,B) = B. [copy(120),unit_del(a,91)].
% 1.28/1.55 126 empty_carrier(c4) | -join_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | join_commut(c4,B,A) = join_commut(c4,A,B). [resolve(58,c,51,a)].
% 1.28/1.55 127 -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | join_commut(c4,B,A) = join_commut(c4,A,B). [copy(126),unit_del(a,91),unit_del(b,83)].
% 1.28/1.55 130 empty_carrier(c4) | -join_commutative(c4) | -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | join(c4,A,B) = join_commut(c4,A,B). [resolve(59,c,51,a)].
% 1.28/1.55 131 -element(A,the_carrier(c4)) | -element(B,the_carrier(c4)) | join_commut(c4,A,B) = join(c4,A,B). [copy(130),flip(e),unit_del(a,91),unit_del(b,83)].
% 1.28/1.55 200 join(c4,c6,c5) = c5. [resolve(121,c,88,a),unit_del(a,86),unit_del(b,85)].
% 1.28/1.55 201 join(c4,c5,c6) = c6. [resolve(121,c,87,a),unit_del(a,85),unit_del(b,86)].
% 1.28/1.55 211 -element(A,the_carrier(c4)) | join_commut(c4,c6,A) = join_commut(c4,A,c6). [resolve(127,a,86,a),flip(b)].
% 1.28/1.55 216 -element(A,the_carrier(c4)) | join_commut(c4,c6,A) = join(c4,c6,A). [resolve(131,a,86,a)].
% 1.28/1.55 217 -element(A,the_carrier(c4)) | join_commut(c4,c5,A) = join(c4,c5,A). [resolve(131,a,85,a)].
% 1.28/1.55 2365 join_commut(c4,c6,c5) = join_commut(c4,c5,c6). [resolve(211,a,85,a)].
% 1.28/1.55 2555 join_commut(c4,c5,c6) = c5. [resolve(216,a,85,a),rewrite([2365(4),200(8)])].
% 1.28/1.55 2637 $F. [resolve(217,a,86,a),rewrite([2555(4),201(5)]),flip(a),unit_del(a,93)].
% 1.28/1.55
% 1.28/1.55 % SZS output end Refutation
% 1.28/1.55 ============================== end of proof ==========================
% 1.28/1.55
% 1.28/1.55 ============================== STATISTICS ============================
% 1.28/1.55
% 1.28/1.55 Given=378. Generated=4490. Kept=2538. proofs=1.
% 1.28/1.55 Usable=317. Sos=949. Demods=181. Limbo=25, Disabled=1348. Hints=0.
% 1.28/1.55 Megabytes=2.80.
% 1.28/1.55 User_CPU=0.57, System_CPU=0.01, Wall_clock=0.
% 1.28/1.55
% 1.28/1.55 ============================== end of statistics =====================
% 1.28/1.55
% 1.28/1.55 ============================== end of search =========================
% 1.28/1.55
% 1.28/1.55 THEOREM PROVED
% 1.28/1.55 % SZS status Theorem
% 1.28/1.55
% 1.28/1.55 Exiting with 1 proof.
% 1.28/1.55
% 1.28/1.55 Process 3976 exit (max_proofs) Sat Jun 18 19:17:45 2022
% 1.28/1.55 Prover9 interrupted
%------------------------------------------------------------------------------