TSTP Solution File: LAT305+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT305+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 : Sun Jul 17 06:27:13 EDT 2022
% Result : Theorem 1.28s 1.56s
% Output : Refutation 1.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT305+1 : TPTP v8.1.0. Released v3.4.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 29 16:39:41 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.45/1.07 ============================== Prover9 ===============================
% 0.45/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.07 Process 25984 was started by sandbox2 on n015.cluster.edu,
% 0.45/1.07 Wed Jun 29 16:39:41 2022
% 0.45/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25830_n015.cluster.edu".
% 0.45/1.07 ============================== end of head ===========================
% 0.45/1.07
% 0.45/1.07 ============================== INPUT =================================
% 0.45/1.07
% 0.45/1.07 % Reading from file /tmp/Prover9_25830_n015.cluster.edu
% 0.45/1.07
% 0.45/1.07 set(prolog_style_variables).
% 0.45/1.07 set(auto2).
% 0.45/1.07 % set(auto2) -> set(auto).
% 0.45/1.07 % set(auto) -> set(auto_inference).
% 0.45/1.07 % set(auto) -> set(auto_setup).
% 0.45/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.07 % set(auto) -> set(auto_limits).
% 0.45/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.07 % set(auto) -> set(auto_denials).
% 0.45/1.07 % set(auto) -> set(auto_process).
% 0.45/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.07 % set(auto2) -> assign(stats, some).
% 0.45/1.07 % set(auto2) -> clear(echo_input).
% 0.45/1.07 % set(auto2) -> set(quiet).
% 0.45/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.07 % set(auto2) -> clear(print_given).
% 0.45/1.07 assign(lrs_ticks,-1).
% 0.45/1.07 assign(sos_limit,10000).
% 0.45/1.07 assign(order,kbo).
% 0.45/1.07 set(lex_order_vars).
% 0.45/1.07 clear(print_given).
% 0.45/1.07
% 0.45/1.07 % formulas(sos). % not echoed (84 formulas)
% 0.45/1.07
% 0.45/1.07 ============================== end of input ==========================
% 0.45/1.07
% 0.45/1.07 % From the command line: assign(max_seconds, 300).
% 0.45/1.07
% 0.45/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.07
% 0.45/1.07 % Formulas that are not ordinary clauses:
% 0.45/1.07 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 2 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 3 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) -> -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 4 (all A (-v1_realset1(A) -> -v1_xboole_0(A))) # label(cc1_realset1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 5 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> v1_relat_1(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 6 (all A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 7 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) -> -v3_struct_0(A) & v10_lattices(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 8 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 9 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,C) = k4_lattices(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 10 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C))))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 11 (all A (-v3_struct_0(A) & l1_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C))))))) # label(d2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 12 (all A all B k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 13 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k18_filter_2(A,B) = a_2_0_filter_2(A,B))))) # label(d9_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 14 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) -> m2_filter_2(k18_filter_2(A,B),A))) # label(dt_k18_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 15 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 16 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 17 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 18 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 19 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 20 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) -> m1_subset_1(k2_binop_1(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 21 (all A all B all C (-v3_struct_0(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 22 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 23 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 24 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 25 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 26 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 27 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 28 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 29 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 30 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 31 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 32 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m2_filter_2(B,A) -> -v1_xboole_0(B) & m2_lattice4(B,A))))) # label(dt_m2_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 33 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m2_lattice4(B,A) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_lattice4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 34 (all A all B all C (m2_relset_1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 35 (all A (l1_lattices(A) -> v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 36 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 37 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 38 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 39 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 40 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 41 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 42 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 43 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (exists B m2_filter_2(B,A)))) # label(existence_m2_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 44 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (exists B m2_lattice4(B,A)))) # label(existence_m2_lattice4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 45 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.07 46 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 47 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 48 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 49 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)))) # label(fc3_realset1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 50 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 51 (all A (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) -> v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_binop_1(u1_lattices(A),u1_struct_0(A)) & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(fc4_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 52 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 53 (all A (-v3_struct_0(A) & v7_lattices(A) & l1_lattices(A) -> v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v2_binop_1(u1_lattices(A),u1_struct_0(A)) & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(fc5_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 54 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) -> (r2_hidden(A,a_2_0_filter_2(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,D,C)))))) # label(fraenkel_a_2_0_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 55 (exists A (v1_relat_1(A) & v1_funct_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 56 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (exists B (m2_lattice4(B,A) & -v1_xboole_0(B))))) # label(rc1_lattice4) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 57 (exists A (-v1_xboole_0(A) & v1_realset1(A))) # label(rc1_realset1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 58 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 59 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 60 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 61 (exists A (-v1_xboole_0(A) & -v1_realset1(A))) # label(rc2_realset1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 62 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 63 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 64 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 65 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 66 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 67 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) -> k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 68 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,C) = k2_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 69 (all A all B all C (m2_relset_1(C,A,B) <-> m1_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 70 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) <-> r1_lattices(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 71 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 72 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 73 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 74 (all A (-v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k4_lattices(A,B,C),B))))))) # label(t23_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 75 (all A all B (m1_subset_1(A,B) -> v1_xboole_0(B) | r2_hidden(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 76 (all A all B ((all C (r2_hidden(C,A) <-> r2_hidden(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 77 (all A all B (m1_subset_1(A,k1_zfmisc_1(B)) <-> r1_tarski(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 78 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 79 (all A all B all C -(r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 80 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 81 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 82 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.08 83 -(all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(B,k18_filter_2(A,B)) & r2_hidden(k4_lattices(A,B,C),k18_filter_2(A,B)) & r2_hidden(k4_lattices(A,C,B),k18_filter_2(A,B)))))))) # label(t31_filter_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.08
% 0.45/1.08 ============================== end of process non-clausal formulas ===
% 0.45/1.08
% 0.45/1.08 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.08
% 0.45/1.08 ============================== PREDICATE ELIMINATION =================
% 0.45/1.08 84 -v1_relat_1(A) | -v1_xboole_0(A) | -v1_funct_1(A) | v2_funct_1(A) # label(cc2_funct_1) # label(axiom). [clausify(6)].
% 0.45/1.08 85 -v1_xboole_0(A) | v1_funct_1(A) # label(cc1_funct_1) # label(axiom). [clausify(2)].
% 0.45/1.08 Derived: -v1_relat_1(A) | -v1_xboole_0(A) | v2_funct_1(A) | -v1_xboole_0(A). [resolve(84,c,85,b)].
% 0.45/1.08 86 -v1_relat_1(A) | -v1_funct_1(A) | k1_funct_1(A,k4_tarski(B,C)) = k1_binop_1(A,B,C) # label(d1_binop_1) # label(axiom). [clausify(10)].
% 0.45/1.08 Derived: -v1_relat_1(A) | k1_funct_1(A,k4_tarski(B,C)) = k1_binop_1(A,B,C) | -v1_xboole_0(A). [resolve(86,b,85,b)].
% 0.45/1.08 87 v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_1(C) | -v1_funct_2(C,k2_zfmisc_1(A,B),D) | -m1_relset_1(C,k2_zfmisc_1(A,B),D) | -m1_subset_1(E,A) | -m1_subset_1(F,B) | m1_subset_1(k2_binop_1(A,B,D,C,E,F),D) # label(dt_k2_binop_1) # label(axiom). [clausify(20)].
% 0.45/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(C,k2_zfmisc_1(A,B),D) | -m1_relset_1(C,k2_zfmisc_1(A,B),D) | -m1_subset_1(E,A) | -m1_subset_1(F,B) | m1_subset_1(k2_binop_1(A,B,D,C,E,F),D) | -v1_xboole_0(C). [resolve(87,c,85,b)].
% 0.45/1.08 88 -l1_lattices(A) | v1_funct_1(u1_lattices(A)) # label(dt_u1_lattices) # label(axiom). [clausify(35)].
% 0.45/1.08 Derived: -l1_lattices(A) | -v1_relat_1(u1_lattices(A)) | k1_funct_1(u1_lattices(A),k4_tarski(B,C)) = k1_binop_1(u1_lattices(A),B,C). [resolve(88,b,86,b)].
% 0.45/1.08 Derived: -l1_lattices(A) | v1_xboole_0(B) | v1_xboole_0(C) | -v1_funct_2(u1_lattices(A),k2_zfmisc_1(B,C),D) | -m1_relset_1(u1_lattices(A),k2_zfmisc_1(B,C),D) | -m1_subset_1(E,B) | -m1_subset_1(F,C) | m1_subset_1(k2_binop_1(B,C,D,u1_lattices(A),E,F),D). [resolve(88,b,87,c)].
% 0.45/1.08 89 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | v1_funct_1(u1_lattices(A)) # label(fc4_lattice2) # label(axiom). [clausify(51)].
% 0.45/1.08 90 v3_struct_0(A) | -v7_lattices(A) | -l1_lattices(A) | v1_funct_1(u1_lattices(A)) # label(fc5_lattice2) # label(axiom). [clausify(53)].
% 0.45/1.08 91 v1_funct_1(c5) # label(rc1_funct_1) # label(axiom). [clausify(55)].
% 0.45/1.08 Derived: -v1_relat_1(c5) | k1_funct_1(c5,k4_tarski(A,B)) = k1_binop_1(c5,A,B). [resolve(91,a,86,b)].
% 0.45/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(c5,k2_zfmisc_1(A,B),C) | -m1_relset_1(c5,k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | m1_subset_1(k2_binop_1(A,B,C,c5,D,E),C). [resolve(91,a,87,c)].
% 0.45/1.08 92 v1_funct_1(c8) # label(rc2_funct_1) # label(axiom). [clausify(60)].
% 0.45/1.08 Derived: -v1_relat_1(c8) | k1_funct_1(c8,k4_tarski(A,B)) = k1_binop_1(c8,A,B). [resolve(92,a,86,b)].
% 0.45/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(c8,k2_zfmisc_1(A,B),C) | -m1_relset_1(c8,k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | m1_subset_1(k2_binop_1(A,B,C,c8,D,E),C). [resolve(92,a,87,c)].
% 0.45/1.08 93 v1_funct_1(c11) # label(rc3_funct_1) # label(axiom). [clausify(64)].
% 0.45/1.08 Derived: -v1_relat_1(c11) | k1_funct_1(c11,k4_tarski(A,B)) = k1_binop_1(c11,A,B). [resolve(93,a,86,b)].
% 0.45/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(c11,k2_zfmisc_1(A,B),C) | -m1_relset_1(c11,k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | m1_subset_1(k2_binop_1(A,B,C,c11,D,E),C). [resolve(93,a,87,c)].
% 0.45/1.08 94 v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_1(C) | -v1_funct_2(C,k2_zfmisc_1(A,B),D) | -m1_relset_1(C,k2_zfmisc_1(A,B),D) | -m1_subset_1(E,A) | -m1_subset_1(F,B) | k2_binop_1(A,B,D,C,E,F) = k1_binop_1(C,E,F) # label(redefinition_k2_binop_1) # label(axiom). [clausify(67)].
% 0.45/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(C,k2_zfmisc_1(A,B),D) | -m1_relset_1(C,k2_zfmisc_1(A,B),D) | -m1_subset_1(E,A) | -m1_subset_1(F,B) | k2_binop_1(A,B,D,C,E,F) = k1_binop_1(C,E,F) | -v1_xboole_0(C). [resolve(94,c,85,b)].
% 0.45/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u1_lattices(C),k2_zfmisc_1(A,B),D) | -m1_relset_1(u1_lattices(C),k2_zfmisc_1(A,B),D) | -m1_subset_1(E,A) | -m1_subset_1(F,B) | k2_binop_1(A,B,D,u1_lattices(C),E,F) = k1_binop_1(u1_lattices(C),E,F) | -l1_lattices(C). [resolve(94,c,88,b)].
% 0.45/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(c5,k2_zfmisc_1(A,B),C) | -m1_relset_1(c5,k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | k2_binop_1(A,B,C,c5,D,E) = k1_binop_1(c5,D,E). [resolve(94,c,91,a)].
% 0.45/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(c8,k2_zfmisc_1(A,B),C) | -m1_relset_1(c8,k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | k2_binop_1(A,B,C,c8,D,E) = k1_binop_1(c8,D,E). [resolve(94,c,92,a)].
% 0.45/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(c11,k2_zfmisc_1(A,B),C) | -m1_relset_1(c11,k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | k2_binop_1(A,B,C,c11,D,E) = k1_binop_1(c11,D,E). [resolve(94,c,93,a)].
% 0.45/1.08 95 l3_lattices(c4) # label(existence_l3_lattices) # label(axiom). [clausify(40)].
% 0.45/1.08 96 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v4_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.08 97 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v5_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.08 98 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v6_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.08 99 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v7_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.08 100 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v8_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.08 101 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v9_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.45/1.08 102 -l3_lattices(A) | v3_struct_0(A) | -v4_lattices(A) | -v5_lattices(A) | -v6_lattices(A) | -v7_lattices(A) | -v8_lattices(A) | -v9_lattices(A) | v10_lattices(A) # label(cc2_lattices) # label(axiom). [clausify(7)].
% 0.45/1.08 103 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | a_2_0_filter_2(A,B) = k18_filter_2(A,B) # label(d9_filter_2) # label(axiom). [clausify(13)].
% 0.45/1.08 104 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | m2_filter_2(k18_filter_2(A,B),A) # label(dt_k18_filter_2) # label(axiom). [clausify(14)].
% 0.45/1.08 105 -l3_lattices(A) | l1_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(29)].
% 0.45/1.08 106 -l3_lattices(A) | l2_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(29)].
% 0.45/1.08 107 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m2_filter_2(B,A) | -v1_xboole_0(B) # label(dt_m2_filter_2) # label(axiom). [clausify(32)].
% 0.45/1.08 108 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m2_filter_2(B,A) | m2_lattice4(B,A) # label(dt_m2_filter_2) # label(axiom). [clausify(32)].
% 0.45/1.08 109 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m2_lattice4(B,A) | m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) # label(dt_m2_lattice4) # label(axiom). [clausify(33)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v4_lattices(c4). [resolve(95,a,96,a)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v5_lattices(c4). [resolve(95,a,97,a)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v6_lattices(c4). [resolve(95,a,98,a)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v7_lattices(c4). [resolve(95,a,99,a)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v8_lattices(c4). [resolve(95,a,100,a)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v9_lattices(c4). [resolve(95,a,101,a)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v4_lattices(c4) | -v5_lattices(c4) | -v6_lattices(c4) | -v7_lattices(c4) | -v8_lattices(c4) | -v9_lattices(c4) | v10_lattices(c4). [resolve(95,a,102,a)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | a_2_0_filter_2(c4,A) = k18_filter_2(c4,A). [resolve(95,a,103,c)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | m2_filter_2(k18_filter_2(c4,A),c4). [resolve(95,a,104,c)].
% 0.45/1.08 Derived: l1_lattices(c4). [resolve(95,a,105,a)].
% 0.45/1.08 Derived: l2_lattices(c4). [resolve(95,a,106,a)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m2_filter_2(A,c4) | -v1_xboole_0(A). [resolve(95,a,107,c)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m2_filter_2(A,c4) | m2_lattice4(A,c4). [resolve(95,a,108,c)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m2_lattice4(A,c4) | m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))). [resolve(95,a,109,c)].
% 0.45/1.08 110 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | m2_filter_2(f3(A),A) # label(existence_m2_filter_2) # label(axiom). [clausify(43)].
% 0.45/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | m2_filter_2(f3(c4),c4). [resolve(110,c,95,a)].
% 0.82/1.08 111 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | m2_lattice4(f4(A),A) # label(existence_m2_lattice4) # label(axiom). [clausify(44)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | m2_lattice4(f4(c4),c4). [resolve(111,c,95,a)].
% 0.82/1.08 112 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -r2_hidden(C,a_2_0_filter_2(A,B)) | m1_subset_1(f6(C,A,B),u1_struct_0(A)) # label(fraenkel_a_2_0_filter_2) # label(axiom). [clausify(54)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -r2_hidden(B,a_2_0_filter_2(c4,A)) | m1_subset_1(f6(B,c4,A),u1_struct_0(c4)). [resolve(112,c,95,a)].
% 0.82/1.08 113 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -r2_hidden(C,a_2_0_filter_2(A,B)) | f6(C,A,B) = C # label(fraenkel_a_2_0_filter_2) # label(axiom). [clausify(54)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -r2_hidden(B,a_2_0_filter_2(c4,A)) | f6(B,c4,A) = B. [resolve(113,c,95,a)].
% 0.82/1.08 114 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -r2_hidden(C,a_2_0_filter_2(A,B)) | r3_lattices(A,f6(C,A,B),B) # label(fraenkel_a_2_0_filter_2) # label(axiom). [clausify(54)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -r2_hidden(B,a_2_0_filter_2(c4,A)) | r3_lattices(c4,f6(B,c4,A),A). [resolve(114,c,95,a)].
% 0.82/1.08 115 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | r2_hidden(C,a_2_0_filter_2(A,B)) | -m1_subset_1(D,u1_struct_0(A)) | D != C | -r3_lattices(A,D,B) # label(fraenkel_a_2_0_filter_2) # label(axiom). [clausify(54)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | r2_hidden(B,a_2_0_filter_2(c4,A)) | -m1_subset_1(C,u1_struct_0(c4)) | C != B | -r3_lattices(c4,C,A). [resolve(115,c,95,a)].
% 0.82/1.08 116 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | m2_lattice4(f7(A),A) # label(rc1_lattice4) # label(axiom). [clausify(56)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | m2_lattice4(f7(c4),c4). [resolve(116,c,95,a)].
% 0.82/1.08 117 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -v1_xboole_0(f7(A)) # label(rc1_lattice4) # label(axiom). [clausify(56)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -v1_xboole_0(f7(c4)). [resolve(117,c,95,a)].
% 0.82/1.08 118 v3_struct_0(A) | -v6_lattices(A) | -v8_lattices(A) | -v9_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | -r3_lattices(A,B,C) | r1_lattices(A,B,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(70)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | -v8_lattices(c4) | -v9_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | -r3_lattices(c4,A,B) | r1_lattices(c4,A,B). [resolve(118,e,95,a)].
% 0.82/1.08 119 v3_struct_0(A) | -v6_lattices(A) | -v8_lattices(A) | -v9_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | r3_lattices(A,B,C) | -r1_lattices(A,B,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(70)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | -v8_lattices(c4) | -v9_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | r3_lattices(c4,A,B) | -r1_lattices(c4,A,B). [resolve(119,e,95,a)].
% 0.82/1.08 120 v3_struct_0(A) | -v6_lattices(A) | -v8_lattices(A) | -v9_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | r3_lattices(A,B,B) # label(reflexivity_r3_lattices) # label(axiom). [clausify(72)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | -v8_lattices(c4) | -v9_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | r3_lattices(c4,A,A). [resolve(120,e,95,a)].
% 0.82/1.08 121 v3_struct_0(A) | -v6_lattices(A) | -v8_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | r1_lattices(A,k4_lattices(A,B,C),B) # label(t23_lattices) # label(axiom). [clausify(74)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | -v8_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | r1_lattices(c4,k4_lattices(c4,A,B),A). [resolve(121,d,95,a)].
% 0.82/1.08 122 l3_lattices(c13) # label(t31_filter_2) # label(negated_conjecture). [clausify(83)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v4_lattices(c13). [resolve(122,a,96,a)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v5_lattices(c13). [resolve(122,a,97,a)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v6_lattices(c13). [resolve(122,a,98,a)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v7_lattices(c13). [resolve(122,a,99,a)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v8_lattices(c13). [resolve(122,a,100,a)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v9_lattices(c13). [resolve(122,a,101,a)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v4_lattices(c13) | -v5_lattices(c13) | -v6_lattices(c13) | -v7_lattices(c13) | -v8_lattices(c13) | -v9_lattices(c13) | v10_lattices(c13). [resolve(122,a,102,a)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | a_2_0_filter_2(c13,A) = k18_filter_2(c13,A). [resolve(122,a,103,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | m2_filter_2(k18_filter_2(c13,A),c13). [resolve(122,a,104,c)].
% 0.82/1.08 Derived: l1_lattices(c13). [resolve(122,a,105,a)].
% 0.82/1.08 Derived: l2_lattices(c13). [resolve(122,a,106,a)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m2_filter_2(A,c13) | -v1_xboole_0(A). [resolve(122,a,107,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m2_filter_2(A,c13) | m2_lattice4(A,c13). [resolve(122,a,108,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m2_lattice4(A,c13) | m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))). [resolve(122,a,109,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | m2_filter_2(f3(c13),c13). [resolve(122,a,110,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | m2_lattice4(f4(c13),c13). [resolve(122,a,111,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -r2_hidden(B,a_2_0_filter_2(c13,A)) | m1_subset_1(f6(B,c13,A),u1_struct_0(c13)). [resolve(122,a,112,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -r2_hidden(B,a_2_0_filter_2(c13,A)) | f6(B,c13,A) = B. [resolve(122,a,113,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -r2_hidden(B,a_2_0_filter_2(c13,A)) | r3_lattices(c13,f6(B,c13,A),A). [resolve(122,a,114,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | r2_hidden(B,a_2_0_filter_2(c13,A)) | -m1_subset_1(C,u1_struct_0(c13)) | C != B | -r3_lattices(c13,C,A). [resolve(122,a,115,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | m2_lattice4(f7(c13),c13). [resolve(122,a,116,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -v1_xboole_0(f7(c13)). [resolve(122,a,117,c)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v6_lattices(c13) | -v8_lattices(c13) | -v9_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | -r3_lattices(c13,A,B) | r1_lattices(c13,A,B). [resolve(122,a,118,e)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v6_lattices(c13) | -v8_lattices(c13) | -v9_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r3_lattices(c13,A,B) | -r1_lattices(c13,A,B). [resolve(122,a,119,e)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v6_lattices(c13) | -v8_lattices(c13) | -v9_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r3_lattices(c13,A,A). [resolve(122,a,120,e)].
% 0.82/1.08 Derived: v3_struct_0(c13) | -v6_lattices(c13) | -v8_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r1_lattices(c13,k4_lattices(c13,A,B),A). [resolve(122,a,121,d)].
% 0.82/1.08 123 l1_lattices(c1) # label(existence_l1_lattices) # label(axiom). [clausify(37)].
% 0.82/1.08 124 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k4_lattices(A,C,B) = k4_lattices(A,B,C) # label(commutativity_k4_lattices) # label(axiom). [clausify(9)].
% 0.82/1.08 125 v3_struct_0(A) | -l1_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) = k2_lattices(A,B,C) # label(d2_lattices) # label(axiom). [clausify(11)].
% 0.82/1.08 126 v3_struct_0(A) | -l1_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)) # label(dt_k2_lattices) # label(axiom). [clausify(21)].
% 0.82/1.08 127 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)) # label(dt_k4_lattices) # label(axiom). [clausify(24)].
% 0.82/1.08 128 -l1_lattices(A) | l1_struct_0(A) # label(dt_l1_lattices) # label(axiom). [clausify(26)].
% 0.82/1.08 129 -l1_lattices(A) | v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(dt_u1_lattices) # label(axiom). [clausify(35)].
% 0.82/1.08 130 -l1_lattices(A) | m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(dt_u1_lattices) # label(axiom). [clausify(35)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -v6_lattices(c1) | -m1_subset_1(A,u1_struct_0(c1)) | -m1_subset_1(B,u1_struct_0(c1)) | k4_lattices(c1,B,A) = k4_lattices(c1,A,B). [resolve(123,a,124,c)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -m1_subset_1(A,u1_struct_0(c1)) | -m1_subset_1(B,u1_struct_0(c1)) | k2_binop_1(u1_struct_0(c1),u1_struct_0(c1),u1_struct_0(c1),u1_lattices(c1),A,B) = k2_lattices(c1,A,B). [resolve(123,a,125,b)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -m1_subset_1(A,u1_struct_0(c1)) | -m1_subset_1(B,u1_struct_0(c1)) | m1_subset_1(k2_lattices(c1,A,B),u1_struct_0(c1)). [resolve(123,a,126,b)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -v6_lattices(c1) | -m1_subset_1(A,u1_struct_0(c1)) | -m1_subset_1(B,u1_struct_0(c1)) | m1_subset_1(k4_lattices(c1,A,B),u1_struct_0(c1)). [resolve(123,a,127,c)].
% 0.82/1.08 Derived: l1_struct_0(c1). [resolve(123,a,128,a)].
% 0.82/1.08 Derived: v1_funct_2(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(123,a,129,a)].
% 0.82/1.08 Derived: m2_relset_1(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(123,a,130,a)].
% 0.82/1.08 131 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | v1_relat_1(u1_lattices(A)) # label(fc4_lattice2) # label(axiom). [clausify(51)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -v6_lattices(c1) | v1_relat_1(u1_lattices(c1)). [resolve(131,c,123,a)].
% 0.82/1.08 132 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(fc4_lattice2) # label(axiom). [clausify(51)].
% 0.82/1.08 133 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | v1_binop_1(u1_lattices(A),u1_struct_0(A)) # label(fc4_lattice2) # label(axiom). [clausify(51)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -v6_lattices(c1) | v1_binop_1(u1_lattices(c1),u1_struct_0(c1)). [resolve(133,c,123,a)].
% 0.82/1.08 134 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(fc4_lattice2) # label(axiom). [clausify(51)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -v6_lattices(c1) | v1_partfun1(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(134,c,123,a)].
% 0.82/1.08 135 v3_struct_0(A) | -v7_lattices(A) | -l1_lattices(A) | v1_relat_1(u1_lattices(A)) # label(fc5_lattice2) # label(axiom). [clausify(53)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -v7_lattices(c1) | v1_relat_1(u1_lattices(c1)). [resolve(135,c,123,a)].
% 0.82/1.08 136 v3_struct_0(A) | -v7_lattices(A) | -l1_lattices(A) | v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(fc5_lattice2) # label(axiom). [clausify(53)].
% 0.82/1.08 137 v3_struct_0(A) | -v7_lattices(A) | -l1_lattices(A) | v2_binop_1(u1_lattices(A),u1_struct_0(A)) # label(fc5_lattice2) # label(axiom). [clausify(53)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -v7_lattices(c1) | v2_binop_1(u1_lattices(c1),u1_struct_0(c1)). [resolve(137,c,123,a)].
% 0.82/1.08 138 v3_struct_0(A) | -v7_lattices(A) | -l1_lattices(A) | v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(fc5_lattice2) # label(axiom). [clausify(53)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -v7_lattices(c1) | v1_partfun1(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(138,c,123,a)].
% 0.82/1.08 139 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k2_lattices(A,B,C) = k4_lattices(A,B,C) # label(redefinition_k4_lattices) # label(axiom). [clausify(68)].
% 0.82/1.08 Derived: v3_struct_0(c1) | -v6_lattices(c1) | -m1_subset_1(A,u1_struct_0(c1)) | -m1_subset_1(B,u1_struct_0(c1)) | k2_lattices(c1,A,B) = k4_lattices(c1,A,B). [resolve(139,c,123,a)].
% 0.82/1.08 140 -l1_lattices(A) | -v1_relat_1(u1_lattices(A)) | k1_funct_1(u1_lattices(A),k4_tarski(B,C)) = k1_binop_1(u1_lattices(A),B,C). [resolve(88,b,86,b)].
% 0.82/1.08 Derived: -v1_relat_1(u1_lattices(c1)) | k1_funct_1(u1_lattices(c1),k4_tarski(A,B)) = k1_binop_1(u1_lattices(c1),A,B). [resolve(140,a,123,a)].
% 0.82/1.08 141 -l1_lattices(A) | v1_xboole_0(B) | v1_xboole_0(C) | -v1_funct_2(u1_lattices(A),k2_zfmisc_1(B,C),D) | -m1_relset_1(u1_lattices(A),k2_zfmisc_1(B,C),D) | -m1_subset_1(E,B) | -m1_subset_1(F,C) | m1_subset_1(k2_binop_1(B,C,D,u1_lattices(A),E,F),D). [resolve(88,b,87,c)].
% 0.82/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u1_lattices(c1),k2_zfmisc_1(A,B),C) | -m1_relset_1(u1_lattices(c1),k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | m1_subset_1(k2_binop_1(A,B,C,u1_lattices(c1),D,E),C). [resolve(141,a,123,a)].
% 0.82/1.08 142 v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u1_lattices(C),k2_zfmisc_1(A,B),D) | -m1_relset_1(u1_lattices(C),k2_zfmisc_1(A,B),D) | -m1_subset_1(E,A) | -m1_subset_1(F,B) | k2_binop_1(A,B,D,u1_lattices(C),E,F) = k1_binop_1(u1_lattices(C),E,F) | -l1_lattices(C). [resolve(94,c,88,b)].
% 0.82/1.08 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u1_lattices(c1),k2_zfmisc_1(A,B),C) | -m1_relset_1(u1_lattices(c1),k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | k2_binop_1(A,B,C,u1_lattices(c1),D,E) = k1_binop_1(u1_lattices(c1),D,E). [resolve(142,h,123,a)].
% 0.82/1.08 143 l1_lattices(c4). [resolve(95,a,105,a)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | k4_lattices(c4,B,A) = k4_lattices(c4,A,B). [resolve(143,a,124,c)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | k2_binop_1(u1_struct_0(c4),u1_struct_0(c4),u1_struct_0(c4),u1_lattices(c4),A,B) = k2_lattices(c4,A,B). [resolve(143,a,125,b)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | m1_subset_1(k2_lattices(c4,A,B),u1_struct_0(c4)). [resolve(143,a,126,b)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | m1_subset_1(k4_lattices(c4,A,B),u1_struct_0(c4)). [resolve(143,a,127,c)].
% 0.82/1.08 Derived: l1_struct_0(c4). [resolve(143,a,128,a)].
% 0.82/1.08 Derived: v1_funct_2(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(143,a,129,a)].
% 0.82/1.08 Derived: m2_relset_1(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(143,a,130,a)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | v1_relat_1(u1_lattices(c4)). [resolve(143,a,131,c)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | v1_binop_1(u1_lattices(c4),u1_struct_0(c4)). [resolve(143,a,133,c)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | v1_partfun1(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(143,a,134,c)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v7_lattices(c4) | v1_relat_1(u1_lattices(c4)). [resolve(143,a,135,c)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v7_lattices(c4) | v2_binop_1(u1_lattices(c4),u1_struct_0(c4)). [resolve(143,a,137,c)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v7_lattices(c4) | v1_partfun1(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(143,a,138,c)].
% 0.82/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | k2_lattices(c4,A,B) = k4_lattices(c4,A,B). [resolve(143,a,139,c)].
% 0.82/1.08 Derived: -v1_relat_1(u1_lattices(c4)) | k1_funct_1(u1_lattices(c4),k4_tarski(A,B)) = k1_binop_1(u1_lattices(c4),A,B). [resolve(143,a,140,a)].
% 0.82/1.09 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u1_lattices(c4),k2_zfmisc_1(A,B),C) | -m1_relset_1(u1_lattices(c4),k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | m1_subset_1(k2_binop_1(A,B,C,u1_lattices(c4),D,E),C). [resolve(143,a,141,a)].
% 0.82/1.09 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u1_lattices(c4),k2_zfmisc_1(A,B),C) | -m1_relset_1(u1_lattices(c4),k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | k2_binop_1(A,B,C,u1_lattices(c4),D,E) = k1_binop_1(u1_lattices(c4),D,E). [resolve(143,a,142,h)].
% 0.82/1.09 144 l1_lattices(c13). [resolve(122,a,105,a)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v6_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k4_lattices(c13,B,A) = k4_lattices(c13,A,B). [resolve(144,a,124,c)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k2_binop_1(u1_struct_0(c13),u1_struct_0(c13),u1_struct_0(c13),u1_lattices(c13),A,B) = k2_lattices(c13,A,B). [resolve(144,a,125,b)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | m1_subset_1(k2_lattices(c13,A,B),u1_struct_0(c13)). [resolve(144,a,126,b)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v6_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | m1_subset_1(k4_lattices(c13,A,B),u1_struct_0(c13)). [resolve(144,a,127,c)].
% 0.82/1.09 Derived: l1_struct_0(c13). [resolve(144,a,128,a)].
% 0.82/1.09 Derived: v1_funct_2(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(144,a,129,a)].
% 0.82/1.09 Derived: m2_relset_1(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(144,a,130,a)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v6_lattices(c13) | v1_relat_1(u1_lattices(c13)). [resolve(144,a,131,c)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v6_lattices(c13) | v1_binop_1(u1_lattices(c13),u1_struct_0(c13)). [resolve(144,a,133,c)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v6_lattices(c13) | v1_partfun1(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(144,a,134,c)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v7_lattices(c13) | v1_relat_1(u1_lattices(c13)). [resolve(144,a,135,c)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v7_lattices(c13) | v2_binop_1(u1_lattices(c13),u1_struct_0(c13)). [resolve(144,a,137,c)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v7_lattices(c13) | v1_partfun1(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(144,a,138,c)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v6_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k2_lattices(c13,A,B) = k4_lattices(c13,A,B). [resolve(144,a,139,c)].
% 0.82/1.09 Derived: -v1_relat_1(u1_lattices(c13)) | k1_funct_1(u1_lattices(c13),k4_tarski(A,B)) = k1_binop_1(u1_lattices(c13),A,B). [resolve(144,a,140,a)].
% 0.82/1.09 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u1_lattices(c13),k2_zfmisc_1(A,B),C) | -m1_relset_1(u1_lattices(c13),k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | m1_subset_1(k2_binop_1(A,B,C,u1_lattices(c13),D,E),C). [resolve(144,a,141,a)].
% 0.82/1.09 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u1_lattices(c13),k2_zfmisc_1(A,B),C) | -m1_relset_1(u1_lattices(c13),k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | k2_binop_1(A,B,C,u1_lattices(c13),D,E) = k1_binop_1(u1_lattices(c13),D,E). [resolve(144,a,142,h)].
% 0.82/1.09 145 l2_lattices(c3) # label(existence_l2_lattices) # label(axiom). [clausify(39)].
% 0.82/1.09 146 -l2_lattices(A) | l1_struct_0(A) # label(dt_l2_lattices) # label(axiom). [clausify(28)].
% 0.82/1.09 Derived: l1_struct_0(c3). [resolve(145,a,146,a)].
% 0.82/1.09 147 l2_lattices(c4). [resolve(95,a,106,a)].
% 0.82/1.09 148 l2_lattices(c13). [resolve(122,a,106,a)].
% 0.82/1.09 149 m2_relset_1(f5(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(45)].
% 0.82/1.09 150 -m2_relset_1(A,B,C) | m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(34)].
% 0.82/1.09 Derived: m1_subset_1(f5(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))). [resolve(149,a,150,a)].
% 0.82/1.09 151 -m2_relset_1(A,B,C) | m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(69)].
% 0.82/1.09 Derived: m1_relset_1(f5(A,B),A,B). [resolve(151,a,149,a)].
% 0.82/1.09 152 m2_relset_1(A,B,C) | -m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(69)].
% 0.82/1.09 Derived: -m1_relset_1(A,B,C) | m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))). [resolve(152,a,150,a)].
% 0.82/1.09 153 m2_relset_1(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(123,a,130,a)].
% 0.82/1.09 Derived: m1_subset_1(u1_lattices(c1),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)))). [resolve(153,a,150,a)].
% 0.82/1.09 Derived: m1_relset_1(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(153,a,151,a)].
% 0.82/1.09 154 m2_relset_1(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(143,a,130,a)].
% 0.82/1.09 Derived: m1_subset_1(u1_lattices(c4),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)))). [resolve(154,a,150,a)].
% 0.82/1.09 Derived: m1_relset_1(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(154,a,151,a)].
% 0.82/1.09 155 m2_relset_1(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(144,a,130,a)].
% 0.82/1.09 Derived: m1_subset_1(u1_lattices(c13),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)))). [resolve(155,a,150,a)].
% 0.82/1.09 Derived: m1_relset_1(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(155,a,151,a)].
% 0.82/1.09 156 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(46)].
% 0.82/1.09 157 l1_struct_0(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(38)].
% 0.82/1.09 Derived: v3_struct_0(c2) | -v1_xboole_0(u1_struct_0(c2)). [resolve(156,b,157,a)].
% 0.82/1.09 158 l1_struct_0(c12) # label(rc3_struct_0) # label(axiom). [clausify(65)].
% 0.82/1.09 Derived: v3_struct_0(c12) | -v1_xboole_0(u1_struct_0(c12)). [resolve(158,a,156,b)].
% 0.82/1.09 159 v3_struct_0(A) | -l1_struct_0(A) | m1_subset_1(f10(A),k1_zfmisc_1(u1_struct_0(A))) # label(rc5_struct_0) # label(axiom). [clausify(66)].
% 0.82/1.09 Derived: v3_struct_0(c2) | m1_subset_1(f10(c2),k1_zfmisc_1(u1_struct_0(c2))). [resolve(159,b,157,a)].
% 0.82/1.09 Derived: v3_struct_0(c12) | m1_subset_1(f10(c12),k1_zfmisc_1(u1_struct_0(c12))). [resolve(159,b,158,a)].
% 0.82/1.09 160 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(f10(A)) # label(rc5_struct_0) # label(axiom). [clausify(66)].
% 0.82/1.09 Derived: v3_struct_0(c2) | -v1_xboole_0(f10(c2)). [resolve(160,b,157,a)].
% 0.82/1.09 Derived: v3_struct_0(c12) | -v1_xboole_0(f10(c12)). [resolve(160,b,158,a)].
% 0.82/1.09 161 l1_struct_0(c1). [resolve(123,a,128,a)].
% 0.82/1.09 Derived: v3_struct_0(c1) | -v1_xboole_0(u1_struct_0(c1)). [resolve(161,a,156,b)].
% 0.82/1.09 Derived: v3_struct_0(c1) | m1_subset_1(f10(c1),k1_zfmisc_1(u1_struct_0(c1))). [resolve(161,a,159,b)].
% 0.82/1.09 Derived: v3_struct_0(c1) | -v1_xboole_0(f10(c1)). [resolve(161,a,160,b)].
% 0.82/1.09 162 l1_struct_0(c4). [resolve(143,a,128,a)].
% 0.82/1.09 Derived: v3_struct_0(c4) | -v1_xboole_0(u1_struct_0(c4)). [resolve(162,a,156,b)].
% 0.82/1.09 Derived: v3_struct_0(c4) | m1_subset_1(f10(c4),k1_zfmisc_1(u1_struct_0(c4))). [resolve(162,a,159,b)].
% 0.82/1.09 Derived: v3_struct_0(c4) | -v1_xboole_0(f10(c4)). [resolve(162,a,160,b)].
% 0.82/1.09 163 l1_struct_0(c13). [resolve(144,a,128,a)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v1_xboole_0(u1_struct_0(c13)). [resolve(163,a,156,b)].
% 0.82/1.09 Derived: v3_struct_0(c13) | m1_subset_1(f10(c13),k1_zfmisc_1(u1_struct_0(c13))). [resolve(163,a,159,b)].
% 0.82/1.09 Derived: v3_struct_0(c13) | -v1_xboole_0(f10(c13)). [resolve(163,a,160,b)].
% 0.82/1.09 164 l1_struct_0(c3). [resolve(145,a,146,a)].
% 0.82/1.09 Derived: v3_struct_0(c3) | -v1_xboole_0(u1_struct_0(c3)). [resolve(164,a,156,b)].
% 0.82/1.09 Derived: v3_struct_0(c3) | m1_subset_1(f10(c3),k1_zfmisc_1(u1_struct_0(c3))). [resolve(164,a,159,b)].
% 0.82/1.09 Derived: v3_struct_0(c3) | -v1_xboole_0(f10(c3)). [resolve(164,a,160,b)].
% 0.82/1.09 165 m1_subset_1(A,k1_zfmisc_1(B)) | -r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(77)].
% 0.82/1.09 166 r1_tarski(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(71)].
% 0.82/1.09 167 -m1_subset_1(A,k1_zfmisc_1(B)) | r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(77)].
% 1.28/1.56 Derived: m1_subset_1(A,k1_zfmisc_1(A)). [resolve(165,b,166,a)].
% 1.28/1.56
% 1.28/1.56 ============================== end predicate elimination =============
% 1.28/1.56
% 1.28/1.56 Auto_denials: (non-Horn, no changes).
% 1.28/1.56
% 1.28/1.56 Term ordering decisions:
% 1.28/1.56 Function symbol KB weights: k1_xboole_0=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. c14=1. c15=1. k2_zfmisc_1=1. a_2_0_filter_2=1. k4_tarski=1. k1_funct_1=1. k18_filter_2=1. k2_tarski=1. f1=1. f5=1. f11=1. u1_struct_0=1. u1_lattices=1. k1_zfmisc_1=1. k1_tarski=1. f2=1. f3=1. f4=1. f7=1. f8=1. f9=1. f10=1. k1_binop_1=1. k4_lattices=1. k2_lattices=1. f6=1. k2_binop_1=1.
% 1.28/1.56
% 1.28/1.56 ============================== end of process initial clauses ========
% 1.28/1.56
% 1.28/1.56 ============================== CLAUSES FOR SEARCH ====================
% 1.28/1.56
% 1.28/1.56 ============================== end of clauses for search =============
% 1.28/1.56
% 1.28/1.56 ============================== SEARCH ================================
% 1.28/1.56
% 1.28/1.56 % Starting search at 0.04 seconds.
% 1.28/1.56
% 1.28/1.56 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 62 (0.00 of 0.13 sec).
% 1.28/1.56
% 1.28/1.56 Low Water (keep): wt=48.000, iters=3597
% 1.28/1.56
% 1.28/1.56 Low Water (keep): wt=43.000, iters=3478
% 1.28/1.56
% 1.28/1.56 Low Water (keep): wt=36.000, iters=3337
% 1.28/1.56
% 1.28/1.56 Low Water (keep): wt=32.000, iters=3604
% 1.28/1.56
% 1.28/1.56 ============================== PROOF =================================
% 1.28/1.56 % SZS status Theorem
% 1.28/1.56 % SZS output start Refutation
% 1.28/1.56
% 1.28/1.56 % Proof 1 at 0.49 (+ 0.01) seconds.
% 1.28/1.56 % Length of proof is 73.
% 1.28/1.56 % Level of proof is 11.
% 1.28/1.56 % Maximum clause weight is 21.000.
% 1.28/1.56 % Given clauses 964.
% 1.28/1.56
% 1.28/1.56 3 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) -> -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.56 9 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,C) = k4_lattices(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.56 13 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k18_filter_2(A,B) = a_2_0_filter_2(A,B))))) # label(d9_filter_2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.57 24 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.57 29 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.57 54 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) -> (r2_hidden(A,a_2_0_filter_2(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,D,C)))))) # label(fraenkel_a_2_0_filter_2) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.57 68 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,C) = k2_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.57 70 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) <-> r1_lattices(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.57 72 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.57 74 (all A (-v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k4_lattices(A,B,C),B))))))) # label(t23_lattices) # label(axiom) # label(non_clause). [assumption].
% 1.28/1.57 83 -(all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(B,k18_filter_2(A,B)) & r2_hidden(k4_lattices(A,B,C),k18_filter_2(A,B)) & r2_hidden(k4_lattices(A,C,B),k18_filter_2(A,B)))))))) # label(t31_filter_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.28/1.57 98 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v6_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 1.28/1.57 100 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v8_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 1.28/1.57 101 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v9_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 1.28/1.57 103 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | a_2_0_filter_2(A,B) = k18_filter_2(A,B) # label(d9_filter_2) # label(axiom). [clausify(13)].
% 1.28/1.57 105 -l3_lattices(A) | l1_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(29)].
% 1.28/1.57 115 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | r2_hidden(C,a_2_0_filter_2(A,B)) | -m1_subset_1(D,u1_struct_0(A)) | D != C | -r3_lattices(A,D,B) # label(fraenkel_a_2_0_filter_2) # label(axiom). [clausify(54)].
% 1.28/1.57 119 v3_struct_0(A) | -v6_lattices(A) | -v8_lattices(A) | -v9_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | r3_lattices(A,B,C) | -r1_lattices(A,B,C) # label(redefinition_r3_lattices) # label(axiom). [clausify(70)].
% 1.28/1.57 120 v3_struct_0(A) | -v6_lattices(A) | -v8_lattices(A) | -v9_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | r3_lattices(A,B,B) # label(reflexivity_r3_lattices) # label(axiom). [clausify(72)].
% 1.28/1.57 121 v3_struct_0(A) | -v6_lattices(A) | -v8_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | r1_lattices(A,k4_lattices(A,B,C),B) # label(t23_lattices) # label(axiom). [clausify(74)].
% 1.28/1.57 122 l3_lattices(c13) # label(t31_filter_2) # label(negated_conjecture). [clausify(83)].
% 1.28/1.57 124 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k4_lattices(A,C,B) = k4_lattices(A,B,C) # label(commutativity_k4_lattices) # label(axiom). [clausify(9)].
% 1.28/1.57 127 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)) # label(dt_k4_lattices) # label(axiom). [clausify(24)].
% 1.28/1.57 139 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k2_lattices(A,B,C) = k4_lattices(A,B,C) # label(redefinition_k4_lattices) # label(axiom). [clausify(68)].
% 1.28/1.57 144 l1_lattices(c13). [resolve(122,a,105,a)].
% 1.28/1.57 206 -v3_struct_0(c13) # label(t31_filter_2) # label(negated_conjecture). [clausify(83)].
% 1.28/1.57 207 v10_lattices(c13) # label(t31_filter_2) # label(negated_conjecture). [clausify(83)].
% 1.28/1.57 208 m1_subset_1(c14,u1_struct_0(c13)) # label(t31_filter_2) # label(negated_conjecture). [clausify(83)].
% 1.28/1.57 209 m1_subset_1(c15,u1_struct_0(c13)) # label(t31_filter_2) # label(negated_conjecture). [clausify(83)].
% 1.28/1.57 210 -r2_hidden(c14,k18_filter_2(c13,c14)) | -r2_hidden(k4_lattices(c13,c14,c15),k18_filter_2(c13,c14)) | -r2_hidden(k4_lattices(c13,c15,c14),k18_filter_2(c13,c14)) # label(t31_filter_2) # label(negated_conjecture). [clausify(83)].
% 1.28/1.57 256 v3_struct_0(c13) | -v10_lattices(c13) | v6_lattices(c13). [resolve(122,a,98,a)].
% 1.28/1.57 257 v6_lattices(c13). [copy(256),unit_del(a,206),unit_del(b,207)].
% 1.28/1.57 260 v3_struct_0(c13) | -v10_lattices(c13) | v8_lattices(c13). [resolve(122,a,100,a)].
% 1.28/1.57 261 v8_lattices(c13). [copy(260),unit_del(a,206),unit_del(b,207)].
% 1.28/1.57 262 v3_struct_0(c13) | -v10_lattices(c13) | v9_lattices(c13). [resolve(122,a,101,a)].
% 1.28/1.57 263 v9_lattices(c13). [copy(262),unit_del(a,206),unit_del(b,207)].
% 1.28/1.57 265 v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | a_2_0_filter_2(c13,A) = k18_filter_2(c13,A). [resolve(122,a,103,c)].
% 1.28/1.57 266 -m1_subset_1(A,u1_struct_0(c13)) | k18_filter_2(c13,A) = a_2_0_filter_2(c13,A). [copy(265),flip(d),unit_del(a,206),unit_del(b,207)].
% 1.28/1.57 285 v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | r2_hidden(B,a_2_0_filter_2(c13,A)) | -m1_subset_1(C,u1_struct_0(c13)) | C != B | -r3_lattices(c13,C,A). [resolve(122,a,115,c)].
% 1.28/1.57 286 -m1_subset_1(A,u1_struct_0(c13)) | r2_hidden(B,a_2_0_filter_2(c13,A)) | -m1_subset_1(C,u1_struct_0(c13)) | C != B | -r3_lattices(c13,C,A). [copy(285),unit_del(a,206),unit_del(b,207)].
% 1.28/1.57 293 v3_struct_0(c13) | -v6_lattices(c13) | -v8_lattices(c13) | -v9_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r3_lattices(c13,A,B) | -r1_lattices(c13,A,B). [resolve(122,a,119,e)].
% 1.28/1.57 294 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r3_lattices(c13,A,B) | -r1_lattices(c13,A,B). [copy(293),unit_del(a,206),unit_del(b,257),unit_del(c,261),unit_del(d,263)].
% 1.28/1.57 295 v3_struct_0(c13) | -v6_lattices(c13) | -v8_lattices(c13) | -v9_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r3_lattices(c13,A,A). [resolve(122,a,120,e)].
% 1.28/1.57 296 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r3_lattices(c13,A,A). [copy(295),unit_del(a,206),unit_del(b,257),unit_del(c,261),unit_del(d,263)].
% 1.28/1.57 297 v3_struct_0(c13) | -v6_lattices(c13) | -v8_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r1_lattices(c13,k4_lattices(c13,A,B),A). [resolve(122,a,121,d)].
% 1.28/1.57 298 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r1_lattices(c13,k4_lattices(c13,A,B),A). [copy(297),unit_del(a,206),unit_del(b,257),unit_del(c,261)].
% 1.28/1.57 323 v3_struct_0(c13) | -v6_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k4_lattices(c13,B,A) = k4_lattices(c13,A,B). [resolve(144,a,124,c)].
% 1.28/1.57 324 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k4_lattices(c13,B,A) = k4_lattices(c13,A,B). [copy(323),unit_del(a,206),unit_del(b,257)].
% 1.28/1.57 329 v3_struct_0(c13) | -v6_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | m1_subset_1(k4_lattices(c13,A,B),u1_struct_0(c13)). [resolve(144,a,127,c)].
% 1.28/1.57 330 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | m1_subset_1(k4_lattices(c13,A,B),u1_struct_0(c13)). [copy(329),unit_del(a,206),unit_del(b,257)].
% 1.28/1.57 335 v3_struct_0(c13) | -v6_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k2_lattices(c13,A,B) = k4_lattices(c13,A,B). [resolve(144,a,139,c)].
% 1.28/1.57 336 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k2_lattices(c13,A,B) = k4_lattices(c13,A,B). [copy(335),unit_del(a,206),unit_del(b,257)].
% 1.28/1.57 398 -m1_subset_1(A,u1_struct_0(c13)) | r2_hidden(B,a_2_0_filter_2(c13,A)) | A != B | -r3_lattices(c13,A,A). [factor(286,a,c)].
% 1.28/1.57 401 -m1_subset_1(A,u1_struct_0(c13)) | r3_lattices(c13,A,A). [factor(296,a,b)].
% 1.28/1.57 473 k18_filter_2(c13,c14) = a_2_0_filter_2(c13,c14). [resolve(266,a,208,a)].
% 1.28/1.57 475 -r2_hidden(c14,a_2_0_filter_2(c13,c14)) | -r2_hidden(k4_lattices(c13,c14,c15),a_2_0_filter_2(c13,c14)) | -r2_hidden(k4_lattices(c13,c15,c14),a_2_0_filter_2(c13,c14)). [back_rewrite(210),rewrite([473(4),473(12),473(20)])].
% 1.28/1.57 490 -m1_subset_1(A,u1_struct_0(c13)) | r1_lattices(c13,k4_lattices(c13,c14,A),c14). [resolve(298,a,208,a)].
% 1.28/1.57 529 -m1_subset_1(A,u1_struct_0(c13)) | k4_lattices(c13,c15,A) = k4_lattices(c13,A,c15). [resolve(324,a,209,a),flip(b)].
% 1.28/1.57 544 -m1_subset_1(A,u1_struct_0(c13)) | m1_subset_1(k4_lattices(c13,c15,A),u1_struct_0(c13)). [resolve(330,a,209,a)].
% 1.28/1.57 555 -m1_subset_1(A,u1_struct_0(c13)) | k2_lattices(c13,c14,A) = k4_lattices(c13,c14,A). [resolve(336,a,208,a)].
% 1.28/1.57 585 r3_lattices(c13,c14,c14). [resolve(401,a,208,a)].
% 1.28/1.57 653 r2_hidden(A,a_2_0_filter_2(c13,c14)) | c14 != A. [resolve(585,a,398,d),unit_del(a,208)].
% 1.28/1.57 825 r2_hidden(c14,a_2_0_filter_2(c13,c14)). [xx_res(653,b)].
% 1.28/1.57 826 -r2_hidden(k4_lattices(c13,c14,c15),a_2_0_filter_2(c13,c14)) | -r2_hidden(k4_lattices(c13,c15,c14),a_2_0_filter_2(c13,c14)). [back_unit_del(475),unit_del(a,825)].
% 1.28/1.57 1433 r1_lattices(c13,k4_lattices(c13,c14,c15),c14). [resolve(490,a,209,a)].
% 1.28/1.57 1435 -m1_subset_1(k4_lattices(c13,c14,c15),u1_struct_0(c13)) | r3_lattices(c13,k4_lattices(c13,c14,c15),c14). [resolve(1433,a,294,d),unit_del(b,208)].
% 1.28/1.57 2927 k4_lattices(c13,c15,c14) = k4_lattices(c13,c14,c15). [resolve(529,a,208,a)].
% 1.28/1.57 2969 -r2_hidden(k4_lattices(c13,c14,c15),a_2_0_filter_2(c13,c14)). [back_rewrite(826),rewrite([2927(12)]),merge(b)].
% 1.28/1.57 4390 m1_subset_1(k4_lattices(c13,c14,c15),u1_struct_0(c13)). [resolve(544,a,208,a),rewrite([2927(4)])].
% 1.28/1.57 4402 r3_lattices(c13,k4_lattices(c13,c14,c15),c14). [back_unit_del(1435),unit_del(a,4390)].
% 1.28/1.57 4453 r2_hidden(A,a_2_0_filter_2(c13,c14)) | k4_lattices(c13,c14,c15) != A. [resolve(4402,a,286,e),unit_del(a,208),unit_del(c,4390)].
% 1.28/1.57 5636 k2_lattices(c13,c14,c15) = k4_lattices(c13,c14,c15). [resolve(555,a,209,a)].
% 1.28/1.57 7509 $F. [resolve(4453,b,5636,a(flip)),rewrite([5636(4)]),unit_del(a,2969)].
% 1.28/1.57
% 1.28/1.57 % SZS output end Refutation
% 1.28/1.57 ============================== end of proof ==========================
% 1.28/1.57
% 1.28/1.57 ============================== STATISTICS ============================
% 1.28/1.57
% 1.28/1.57 Given=964. Generated=11312. Kept=7295. proofs=1.
% 1.28/1.57 Usable=781. Sos=3224. Demods=813. Limbo=0, Disabled=3553. Hints=0.
% 1.28/1.57 Megabytes=8.90.
% 1.28/1.57 User_CPU=0.49, System_CPU=0.01, Wall_clock=1.
% 1.28/1.57
% 1.28/1.57 ============================== end of statistics =====================
% 1.28/1.57
% 1.28/1.57 ============================== end of search =========================
% 1.28/1.57
% 1.28/1.57 THEOREM PROVED
% 1.28/1.57 % SZS status Theorem
% 1.28/1.57
% 1.28/1.57 Exiting with 1 proof.
% 1.28/1.57
% 1.28/1.57 Process 25984 exit (max_proofs) Wed Jun 29 16:39:42 2022
% 1.28/1.57 Prover9 interrupted
%------------------------------------------------------------------------------