TSTP Solution File: LAT297+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT297+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 06:27:04 EDT 2022
% Result : Theorem 19.96s 20.30s
% Output : Refutation 19.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT297+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n011.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 : Wed Jun 29 08:58:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.73/1.05 ============================== Prover9 ===============================
% 0.73/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.05 Process 29931 was started by sandbox on n011.cluster.edu,
% 0.73/1.05 Wed Jun 29 08:58:47 2022
% 0.73/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29778_n011.cluster.edu".
% 0.73/1.05 ============================== end of head ===========================
% 0.73/1.05
% 0.73/1.05 ============================== INPUT =================================
% 0.73/1.05
% 0.73/1.05 % Reading from file /tmp/Prover9_29778_n011.cluster.edu
% 0.73/1.05
% 0.73/1.05 set(prolog_style_variables).
% 0.73/1.05 set(auto2).
% 0.73/1.05 % set(auto2) -> set(auto).
% 0.73/1.05 % set(auto) -> set(auto_inference).
% 0.73/1.05 % set(auto) -> set(auto_setup).
% 0.73/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.05 % set(auto) -> set(auto_limits).
% 0.73/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.05 % set(auto) -> set(auto_denials).
% 0.73/1.05 % set(auto) -> set(auto_process).
% 0.73/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.05 % set(auto2) -> assign(stats, some).
% 0.73/1.05 % set(auto2) -> clear(echo_input).
% 0.73/1.05 % set(auto2) -> set(quiet).
% 0.73/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.05 % set(auto2) -> clear(print_given).
% 0.73/1.05 assign(lrs_ticks,-1).
% 0.73/1.05 assign(sos_limit,10000).
% 0.73/1.05 assign(order,kbo).
% 0.73/1.05 set(lex_order_vars).
% 0.73/1.05 clear(print_given).
% 0.73/1.05
% 0.73/1.05 % formulas(sos). % not echoed (85 formulas)
% 0.73/1.05
% 0.73/1.05 ============================== end of input ==========================
% 0.73/1.05
% 0.73/1.05 % From the command line: assign(max_seconds, 300).
% 0.73/1.05
% 0.73/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.05
% 0.73/1.05 % Formulas that are not ordinary clauses:
% 0.73/1.05 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 2 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 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].
% 0.73/1.05 4 (all A (-v1_realset1(A) -> -v1_xboole_0(A))) # label(cc1_realset1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 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].
% 0.73/1.05 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].
% 0.73/1.05 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].
% 0.73/1.05 8 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 9 (all A all B all C (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,B,C) = k3_lattices(A,C,B))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 10 (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].
% 0.73/1.05 11 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m2_lattice4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k4_lattices(A,C,D),B) & r2_hidden(k3_lattices(A,C,D),B))))))))))) # label(d10_lattice4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 12 (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].
% 0.73/1.05 13 (all A (-v3_struct_0(A) & l2_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 14 (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].
% 0.73/1.05 15 (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].
% 0.73/1.05 16 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v9_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,k1_lattices(A,B,C)) = B))))))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 17 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 18 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 19 (all A all B all C (-v3_struct_0(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 20 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 21 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 22 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 23 (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].
% 0.73/1.05 24 (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].
% 0.73/1.05 25 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 26 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 27 (all A all B all C (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 28 (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].
% 0.73/1.05 29 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 30 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 31 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 32 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 33 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 34 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 35 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 36 (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].
% 0.73/1.05 37 (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].
% 0.73/1.05 38 (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].
% 0.73/1.05 39 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 40 (all A (l2_lattices(A) -> v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 41 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 42 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 43 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 44 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 45 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 46 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 47 (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].
% 0.73/1.05 48 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 49 (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].
% 0.73/1.05 50 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 51 (all A (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) -> v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_binop_1(u2_lattices(A),u1_struct_0(A)) & v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(fc2_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 52 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 53 (all A (-v3_struct_0(A) & v5_lattices(A) & l2_lattices(A) -> v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v2_binop_1(u2_lattices(A),u1_struct_0(A)) & v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(fc3_lattice2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 54 (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].
% 0.73/1.05 55 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 56 (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].
% 0.73/1.05 57 (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].
% 0.73/1.05 58 (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].
% 0.73/1.05 59 (exists A (v1_relat_1(A) & v1_funct_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 60 (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].
% 0.73/1.05 61 (exists A (-v1_xboole_0(A) & v1_realset1(A))) # label(rc1_realset1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 62 (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].
% 0.73/1.05 63 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 64 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 65 (exists A (-v1_xboole_0(A) & -v1_realset1(A))) # label(rc2_realset1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 66 (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].
% 0.73/1.05 67 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 68 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 69 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 70 (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].
% 0.73/1.05 71 (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].
% 0.73/1.05 72 (all A all B all C (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,B,C) = k1_lattices(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 73 (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].
% 0.73/1.05 74 (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].
% 0.73/1.05 75 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 76 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 77 (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].
% 0.73/1.05 78 (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].
% 0.73/1.05 79 (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].
% 0.73/1.05 80 (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].
% 0.73/1.05 81 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 82 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 83 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.06 84 -(all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) <-> r2_hidden(k4_lattices(A,C,D),B)))))) -> m2_lattice4(B,A)))))) # label(t13_filter_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.06
% 0.73/1.06 ============================== end of process non-clausal formulas ===
% 0.73/1.06
% 0.73/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.06
% 0.73/1.06 ============================== PREDICATE ELIMINATION =================
% 0.73/1.06 85 -v1_relat_1(A) | -v1_xboole_0(A) | -v1_funct_1(A) | v2_funct_1(A) # label(cc2_funct_1) # label(axiom). [clausify(6)].
% 0.73/1.06 86 -v1_xboole_0(A) | v1_funct_1(A) # label(cc1_funct_1) # label(axiom). [clausify(2)].
% 0.73/1.06 Derived: -v1_relat_1(A) | -v1_xboole_0(A) | v2_funct_1(A) | -v1_xboole_0(A). [resolve(85,c,86,b)].
% 0.73/1.06 87 -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(12)].
% 0.73/1.06 Derived: -v1_relat_1(A) | k1_funct_1(A,k4_tarski(B,C)) = k1_binop_1(A,B,C) | -v1_xboole_0(A). [resolve(87,b,86,b)].
% 0.73/1.06 88 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(23)].
% 0.73/1.06 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(88,c,86,b)].
% 0.73/1.06 89 -l1_lattices(A) | v1_funct_1(u1_lattices(A)) # label(dt_u1_lattices) # label(axiom). [clausify(38)].
% 0.73/1.06 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(89,b,87,b)].
% 0.73/1.06 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(89,b,88,c)].
% 0.73/1.06 90 -l2_lattices(A) | v1_funct_1(u2_lattices(A)) # label(dt_u2_lattices) # label(axiom). [clausify(40)].
% 0.73/1.06 Derived: -l2_lattices(A) | -v1_relat_1(u2_lattices(A)) | k1_funct_1(u2_lattices(A),k4_tarski(B,C)) = k1_binop_1(u2_lattices(A),B,C). [resolve(90,b,87,b)].
% 0.73/1.06 Derived: -l2_lattices(A) | v1_xboole_0(B) | v1_xboole_0(C) | -v1_funct_2(u2_lattices(A),k2_zfmisc_1(B,C),D) | -m1_relset_1(u2_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,u2_lattices(A),E,F),D). [resolve(90,b,88,c)].
% 0.73/1.06 91 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | v1_funct_1(u2_lattices(A)) # label(fc2_lattice2) # label(axiom). [clausify(51)].
% 0.73/1.06 92 v3_struct_0(A) | -v5_lattices(A) | -l2_lattices(A) | v1_funct_1(u2_lattices(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.73/1.06 93 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | v1_funct_1(u1_lattices(A)) # label(fc4_lattice2) # label(axiom). [clausify(56)].
% 0.73/1.06 94 v3_struct_0(A) | -v7_lattices(A) | -l1_lattices(A) | v1_funct_1(u1_lattices(A)) # label(fc5_lattice2) # label(axiom). [clausify(58)].
% 0.73/1.06 95 v1_funct_1(c5) # label(rc1_funct_1) # label(axiom). [clausify(59)].
% 0.73/1.06 Derived: -v1_relat_1(c5) | k1_funct_1(c5,k4_tarski(A,B)) = k1_binop_1(c5,A,B). [resolve(95,a,87,b)].
% 0.73/1.06 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(95,a,88,c)].
% 0.73/1.06 96 v1_funct_1(c8) # label(rc2_funct_1) # label(axiom). [clausify(64)].
% 0.73/1.06 Derived: -v1_relat_1(c8) | k1_funct_1(c8,k4_tarski(A,B)) = k1_binop_1(c8,A,B). [resolve(96,a,87,b)].
% 0.73/1.06 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(96,a,88,c)].
% 0.73/1.06 97 v1_funct_1(c11) # label(rc3_funct_1) # label(axiom). [clausify(68)].
% 0.73/1.06 Derived: -v1_relat_1(c11) | k1_funct_1(c11,k4_tarski(A,B)) = k1_binop_1(c11,A,B). [resolve(97,a,87,b)].
% 0.73/1.06 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(97,a,88,c)].
% 0.73/1.06 98 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(71)].
% 0.73/1.06 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(98,c,86,b)].
% 0.73/1.06 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(98,c,89,b)].
% 0.73/1.06 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u2_lattices(C),k2_zfmisc_1(A,B),D) | -m1_relset_1(u2_lattices(C),k2_zfmisc_1(A,B),D) | -m1_subset_1(E,A) | -m1_subset_1(F,B) | k2_binop_1(A,B,D,u2_lattices(C),E,F) = k1_binop_1(u2_lattices(C),E,F) | -l2_lattices(C). [resolve(98,c,90,b)].
% 0.73/1.06 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(98,c,95,a)].
% 0.73/1.06 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(98,c,96,a)].
% 0.73/1.06 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(98,c,97,a)].
% 0.73/1.06 99 l3_lattices(c4) # label(existence_l3_lattices) # label(axiom). [clausify(44)].
% 0.73/1.06 100 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v4_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.73/1.06 101 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v5_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.73/1.06 102 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v6_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.73/1.06 103 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v7_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.73/1.06 104 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v8_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.73/1.06 105 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v9_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.73/1.06 106 -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)].
% 0.73/1.06 107 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -m2_lattice4(B,A) | -m1_subset_1(C,u1_struct_0(A)) | -m1_subset_1(D,u1_struct_0(A)) | -r2_hidden(C,B) | -r2_hidden(D,B) | r2_hidden(k4_lattices(A,C,D),B) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 0.73/1.06 108 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -m2_lattice4(B,A) | -m1_subset_1(C,u1_struct_0(A)) | -m1_subset_1(D,u1_struct_0(A)) | -r2_hidden(C,B) | -r2_hidden(D,B) | r2_hidden(k3_lattices(A,C,D),B) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 0.73/1.06 109 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | m1_subset_1(f1(A,B),u1_struct_0(A)) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 0.73/1.06 110 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | m1_subset_1(f2(A,B),u1_struct_0(A)) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 0.73/1.06 111 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | r2_hidden(f1(A,B),B) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 0.73/1.06 112 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | r2_hidden(f2(A,B),B) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 0.73/1.06 113 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | -r2_hidden(k4_lattices(A,f1(A,B),f2(A,B)),B) | -r2_hidden(k3_lattices(A,f1(A,B),f2(A,B)),B) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 0.73/1.06 114 v3_struct_0(A) | -l3_lattices(A) | -v9_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k2_lattices(A,B,k1_lattices(A,B,C)) = B # label(d9_lattices) # label(axiom). [clausify(16)].
% 0.73/1.06 115 v3_struct_0(A) | -l3_lattices(A) | v9_lattices(A) | m1_subset_1(f3(A),u1_struct_0(A)) # label(d9_lattices) # label(axiom). [clausify(16)].
% 0.73/1.06 116 v3_struct_0(A) | -l3_lattices(A) | v9_lattices(A) | m1_subset_1(f4(A),u1_struct_0(A)) # label(d9_lattices) # label(axiom). [clausify(16)].
% 0.73/1.06 117 v3_struct_0(A) | -l3_lattices(A) | v9_lattices(A) | k2_lattices(A,f3(A),k1_lattices(A,f3(A),f4(A))) != f3(A) # label(d9_lattices) # label(axiom). [clausify(16)].
% 0.73/1.06 118 -l3_lattices(A) | l1_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(33)].
% 0.73/1.06 119 -l3_lattices(A) | l2_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(33)].
% 0.73/1.06 120 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(36)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v4_lattices(c4). [resolve(99,a,100,a)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v5_lattices(c4). [resolve(99,a,101,a)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v6_lattices(c4). [resolve(99,a,102,a)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v7_lattices(c4). [resolve(99,a,103,a)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v8_lattices(c4). [resolve(99,a,104,a)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v9_lattices(c4). [resolve(99,a,105,a)].
% 0.73/1.06 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(99,a,106,a)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | -m2_lattice4(A,c4) | -m1_subset_1(B,u1_struct_0(c4)) | -m1_subset_1(C,u1_struct_0(c4)) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(k4_lattices(c4,B,C),A). [resolve(99,a,107,c)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | -m2_lattice4(A,c4) | -m1_subset_1(B,u1_struct_0(c4)) | -m1_subset_1(C,u1_struct_0(c4)) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(k3_lattices(c4,B,C),A). [resolve(99,a,108,c)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | m2_lattice4(A,c4) | m1_subset_1(f1(c4,A),u1_struct_0(c4)). [resolve(99,a,109,c)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | m2_lattice4(A,c4) | m1_subset_1(f2(c4,A),u1_struct_0(c4)). [resolve(99,a,110,c)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | m2_lattice4(A,c4) | r2_hidden(f1(c4,A),A). [resolve(99,a,111,c)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | m2_lattice4(A,c4) | r2_hidden(f2(c4,A),A). [resolve(99,a,112,c)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | m2_lattice4(A,c4) | -r2_hidden(k4_lattices(c4,f1(c4,A),f2(c4,A)),A) | -r2_hidden(k3_lattices(c4,f1(c4,A),f2(c4,A)),A). [resolve(99,a,113,c)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v9_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | k2_lattices(c4,A,k1_lattices(c4,A,B)) = A. [resolve(99,a,114,b)].
% 0.73/1.06 Derived: v3_struct_0(c4) | v9_lattices(c4) | m1_subset_1(f3(c4),u1_struct_0(c4)). [resolve(99,a,115,b)].
% 0.73/1.06 Derived: v3_struct_0(c4) | v9_lattices(c4) | m1_subset_1(f4(c4),u1_struct_0(c4)). [resolve(99,a,116,b)].
% 0.73/1.06 Derived: v3_struct_0(c4) | v9_lattices(c4) | k2_lattices(c4,f3(c4),k1_lattices(c4,f3(c4),f4(c4))) != f3(c4). [resolve(99,a,117,b)].
% 0.73/1.06 Derived: l1_lattices(c4). [resolve(99,a,118,a)].
% 0.73/1.06 Derived: l2_lattices(c4). [resolve(99,a,119,a)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m2_lattice4(A,c4) | m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))). [resolve(99,a,120,c)].
% 0.73/1.06 121 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | m2_lattice4(f7(A),A) # label(existence_m2_lattice4) # label(axiom). [clausify(47)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | m2_lattice4(f7(c4),c4). [resolve(121,c,99,a)].
% 0.73/1.06 122 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | m2_lattice4(f9(A),A) # label(rc1_lattice4) # label(axiom). [clausify(60)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | m2_lattice4(f9(c4),c4). [resolve(122,c,99,a)].
% 0.73/1.06 123 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -v1_xboole_0(f9(A)) # label(rc1_lattice4) # label(axiom). [clausify(60)].
% 0.73/1.06 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -v1_xboole_0(f9(c4)). [resolve(123,c,99,a)].
% 0.73/1.06 124 l3_lattices(c13) # label(t13_filter_2) # label(negated_conjecture). [clausify(84)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v4_lattices(c13). [resolve(124,a,100,a)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v5_lattices(c13). [resolve(124,a,101,a)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v6_lattices(c13). [resolve(124,a,102,a)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v7_lattices(c13). [resolve(124,a,103,a)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v8_lattices(c13). [resolve(124,a,104,a)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | v9_lattices(c13). [resolve(124,a,105,a)].
% 0.73/1.06 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(124,a,106,a)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | -m2_lattice4(A,c13) | -m1_subset_1(B,u1_struct_0(c13)) | -m1_subset_1(C,u1_struct_0(c13)) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(k4_lattices(c13,B,C),A). [resolve(124,a,107,c)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | -m2_lattice4(A,c13) | -m1_subset_1(B,u1_struct_0(c13)) | -m1_subset_1(C,u1_struct_0(c13)) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(k3_lattices(c13,B,C),A). [resolve(124,a,108,c)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | m1_subset_1(f1(c13,A),u1_struct_0(c13)). [resolve(124,a,109,c)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | m1_subset_1(f2(c13,A),u1_struct_0(c13)). [resolve(124,a,110,c)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | r2_hidden(f1(c13,A),A). [resolve(124,a,111,c)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | r2_hidden(f2(c13,A),A). [resolve(124,a,112,c)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | -r2_hidden(k4_lattices(c13,f1(c13,A),f2(c13,A)),A) | -r2_hidden(k3_lattices(c13,f1(c13,A),f2(c13,A)),A). [resolve(124,a,113,c)].
% 0.73/1.06 Derived: v3_struct_0(c13) | -v9_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k2_lattices(c13,A,k1_lattices(c13,A,B)) = A. [resolve(124,a,114,b)].
% 0.73/1.07 Derived: v3_struct_0(c13) | v9_lattices(c13) | m1_subset_1(f3(c13),u1_struct_0(c13)). [resolve(124,a,115,b)].
% 0.73/1.07 Derived: v3_struct_0(c13) | v9_lattices(c13) | m1_subset_1(f4(c13),u1_struct_0(c13)). [resolve(124,a,116,b)].
% 0.73/1.07 Derived: v3_struct_0(c13) | v9_lattices(c13) | k2_lattices(c13,f3(c13),k1_lattices(c13,f3(c13),f4(c13))) != f3(c13). [resolve(124,a,117,b)].
% 0.73/1.07 Derived: l1_lattices(c13). [resolve(124,a,118,a)].
% 0.73/1.07 Derived: l2_lattices(c13). [resolve(124,a,119,a)].
% 0.73/1.07 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -m2_lattice4(A,c13) | m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))). [resolve(124,a,120,c)].
% 0.73/1.07 Derived: v3_struct_0(c13) | -v10_lattices(c13) | m2_lattice4(f7(c13),c13). [resolve(124,a,121,c)].
% 0.73/1.07 Derived: v3_struct_0(c13) | -v10_lattices(c13) | m2_lattice4(f9(c13),c13). [resolve(124,a,122,c)].
% 0.73/1.07 Derived: v3_struct_0(c13) | -v10_lattices(c13) | -v1_xboole_0(f9(c13)). [resolve(124,a,123,c)].
% 0.73/1.07 125 l2_lattices(c3) # label(existence_l2_lattices) # label(axiom). [clausify(43)].
% 0.73/1.07 126 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k3_lattices(A,C,B) = k3_lattices(A,B,C) # label(commutativity_k3_lattices) # label(axiom). [clausify(9)].
% 0.73/1.07 127 v3_struct_0(A) | -l2_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),u2_lattices(A),B,C) = k1_lattices(A,B,C) # label(d1_lattices) # label(axiom). [clausify(13)].
% 0.73/1.07 128 v3_struct_0(A) | -l2_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)) # label(dt_k1_lattices) # label(axiom). [clausify(19)].
% 0.73/1.07 129 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)) # label(dt_k3_lattices) # label(axiom). [clausify(27)].
% 0.73/1.07 130 -l2_lattices(A) | l1_struct_0(A) # label(dt_l2_lattices) # label(axiom). [clausify(32)].
% 0.73/1.07 131 -l2_lattices(A) | v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(dt_u2_lattices) # label(axiom). [clausify(40)].
% 0.73/1.07 132 -l2_lattices(A) | m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(dt_u2_lattices) # label(axiom). [clausify(40)].
% 0.73/1.07 Derived: v3_struct_0(c3) | -v4_lattices(c3) | -m1_subset_1(A,u1_struct_0(c3)) | -m1_subset_1(B,u1_struct_0(c3)) | k3_lattices(c3,B,A) = k3_lattices(c3,A,B). [resolve(125,a,126,c)].
% 0.73/1.07 Derived: v3_struct_0(c3) | -m1_subset_1(A,u1_struct_0(c3)) | -m1_subset_1(B,u1_struct_0(c3)) | k2_binop_1(u1_struct_0(c3),u1_struct_0(c3),u1_struct_0(c3),u2_lattices(c3),A,B) = k1_lattices(c3,A,B). [resolve(125,a,127,b)].
% 0.73/1.07 Derived: v3_struct_0(c3) | -m1_subset_1(A,u1_struct_0(c3)) | -m1_subset_1(B,u1_struct_0(c3)) | m1_subset_1(k1_lattices(c3,A,B),u1_struct_0(c3)). [resolve(125,a,128,b)].
% 0.73/1.07 Derived: v3_struct_0(c3) | -v4_lattices(c3) | -m1_subset_1(A,u1_struct_0(c3)) | -m1_subset_1(B,u1_struct_0(c3)) | m1_subset_1(k3_lattices(c3,A,B),u1_struct_0(c3)). [resolve(125,a,129,c)].
% 0.73/1.07 Derived: l1_struct_0(c3). [resolve(125,a,130,a)].
% 0.73/1.07 Derived: v1_funct_2(u2_lattices(c3),k2_zfmisc_1(u1_struct_0(c3),u1_struct_0(c3)),u1_struct_0(c3)). [resolve(125,a,131,a)].
% 0.73/1.07 Derived: m2_relset_1(u2_lattices(c3),k2_zfmisc_1(u1_struct_0(c3),u1_struct_0(c3)),u1_struct_0(c3)). [resolve(125,a,132,a)].
% 0.73/1.07 133 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | v1_relat_1(u2_lattices(A)) # label(fc2_lattice2) # label(axiom). [clausify(51)].
% 0.73/1.07 Derived: v3_struct_0(c3) | -v4_lattices(c3) | v1_relat_1(u2_lattices(c3)). [resolve(133,c,125,a)].
% 0.73/1.07 134 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(fc2_lattice2) # label(axiom). [clausify(51)].
% 0.73/1.07 135 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | v1_binop_1(u2_lattices(A),u1_struct_0(A)) # label(fc2_lattice2) # label(axiom). [clausify(51)].
% 0.78/1.07 Derived: v3_struct_0(c3) | -v4_lattices(c3) | v1_binop_1(u2_lattices(c3),u1_struct_0(c3)). [resolve(135,c,125,a)].
% 0.78/1.07 136 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(fc2_lattice2) # label(axiom). [clausify(51)].
% 0.78/1.07 Derived: v3_struct_0(c3) | -v4_lattices(c3) | v1_partfun1(u2_lattices(c3),k2_zfmisc_1(u1_struct_0(c3),u1_struct_0(c3)),u1_struct_0(c3)). [resolve(136,c,125,a)].
% 0.78/1.07 137 v3_struct_0(A) | -v5_lattices(A) | -l2_lattices(A) | v1_relat_1(u2_lattices(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.78/1.07 Derived: v3_struct_0(c3) | -v5_lattices(c3) | v1_relat_1(u2_lattices(c3)). [resolve(137,c,125,a)].
% 0.78/1.07 138 v3_struct_0(A) | -v5_lattices(A) | -l2_lattices(A) | v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.78/1.07 139 v3_struct_0(A) | -v5_lattices(A) | -l2_lattices(A) | v2_binop_1(u2_lattices(A),u1_struct_0(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.78/1.07 Derived: v3_struct_0(c3) | -v5_lattices(c3) | v2_binop_1(u2_lattices(c3),u1_struct_0(c3)). [resolve(139,c,125,a)].
% 0.78/1.07 140 v3_struct_0(A) | -v5_lattices(A) | -l2_lattices(A) | v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(fc3_lattice2) # label(axiom). [clausify(53)].
% 0.78/1.07 Derived: v3_struct_0(c3) | -v5_lattices(c3) | v1_partfun1(u2_lattices(c3),k2_zfmisc_1(u1_struct_0(c3),u1_struct_0(c3)),u1_struct_0(c3)). [resolve(140,c,125,a)].
% 0.78/1.07 141 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k1_lattices(A,B,C) = k3_lattices(A,B,C) # label(redefinition_k3_lattices) # label(axiom). [clausify(72)].
% 0.78/1.07 Derived: v3_struct_0(c3) | -v4_lattices(c3) | -m1_subset_1(A,u1_struct_0(c3)) | -m1_subset_1(B,u1_struct_0(c3)) | k1_lattices(c3,A,B) = k3_lattices(c3,A,B). [resolve(141,c,125,a)].
% 0.78/1.07 142 -l2_lattices(A) | -v1_relat_1(u2_lattices(A)) | k1_funct_1(u2_lattices(A),k4_tarski(B,C)) = k1_binop_1(u2_lattices(A),B,C). [resolve(90,b,87,b)].
% 0.78/1.07 Derived: -v1_relat_1(u2_lattices(c3)) | k1_funct_1(u2_lattices(c3),k4_tarski(A,B)) = k1_binop_1(u2_lattices(c3),A,B). [resolve(142,a,125,a)].
% 0.78/1.07 143 -l2_lattices(A) | v1_xboole_0(B) | v1_xboole_0(C) | -v1_funct_2(u2_lattices(A),k2_zfmisc_1(B,C),D) | -m1_relset_1(u2_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,u2_lattices(A),E,F),D). [resolve(90,b,88,c)].
% 0.78/1.07 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u2_lattices(c3),k2_zfmisc_1(A,B),C) | -m1_relset_1(u2_lattices(c3),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,u2_lattices(c3),D,E),C). [resolve(143,a,125,a)].
% 0.78/1.07 144 v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u2_lattices(C),k2_zfmisc_1(A,B),D) | -m1_relset_1(u2_lattices(C),k2_zfmisc_1(A,B),D) | -m1_subset_1(E,A) | -m1_subset_1(F,B) | k2_binop_1(A,B,D,u2_lattices(C),E,F) = k1_binop_1(u2_lattices(C),E,F) | -l2_lattices(C). [resolve(98,c,90,b)].
% 0.78/1.07 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u2_lattices(c3),k2_zfmisc_1(A,B),C) | -m1_relset_1(u2_lattices(c3),k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | k2_binop_1(A,B,C,u2_lattices(c3),D,E) = k1_binop_1(u2_lattices(c3),D,E). [resolve(144,h,125,a)].
% 0.78/1.07 145 l2_lattices(c4). [resolve(99,a,119,a)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -v4_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | k3_lattices(c4,B,A) = k3_lattices(c4,A,B). [resolve(145,a,126,c)].
% 0.78/1.07 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),u2_lattices(c4),A,B) = k1_lattices(c4,A,B). [resolve(145,a,127,b)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | m1_subset_1(k1_lattices(c4,A,B),u1_struct_0(c4)). [resolve(145,a,128,b)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -v4_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | m1_subset_1(k3_lattices(c4,A,B),u1_struct_0(c4)). [resolve(145,a,129,c)].
% 0.78/1.07 Derived: l1_struct_0(c4). [resolve(145,a,130,a)].
% 0.78/1.07 Derived: v1_funct_2(u2_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(145,a,131,a)].
% 0.78/1.07 Derived: m2_relset_1(u2_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(145,a,132,a)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -v4_lattices(c4) | v1_relat_1(u2_lattices(c4)). [resolve(145,a,133,c)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -v4_lattices(c4) | v1_binop_1(u2_lattices(c4),u1_struct_0(c4)). [resolve(145,a,135,c)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -v4_lattices(c4) | v1_partfun1(u2_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(145,a,136,c)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -v5_lattices(c4) | v1_relat_1(u2_lattices(c4)). [resolve(145,a,137,c)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -v5_lattices(c4) | v2_binop_1(u2_lattices(c4),u1_struct_0(c4)). [resolve(145,a,139,c)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -v5_lattices(c4) | v1_partfun1(u2_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(145,a,140,c)].
% 0.78/1.07 Derived: v3_struct_0(c4) | -v4_lattices(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | k1_lattices(c4,A,B) = k3_lattices(c4,A,B). [resolve(145,a,141,c)].
% 0.78/1.07 Derived: -v1_relat_1(u2_lattices(c4)) | k1_funct_1(u2_lattices(c4),k4_tarski(A,B)) = k1_binop_1(u2_lattices(c4),A,B). [resolve(145,a,142,a)].
% 0.78/1.07 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u2_lattices(c4),k2_zfmisc_1(A,B),C) | -m1_relset_1(u2_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,u2_lattices(c4),D,E),C). [resolve(145,a,143,a)].
% 0.78/1.07 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u2_lattices(c4),k2_zfmisc_1(A,B),C) | -m1_relset_1(u2_lattices(c4),k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | k2_binop_1(A,B,C,u2_lattices(c4),D,E) = k1_binop_1(u2_lattices(c4),D,E). [resolve(145,a,144,h)].
% 0.78/1.07 146 l2_lattices(c13). [resolve(124,a,119,a)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -v4_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k3_lattices(c13,B,A) = k3_lattices(c13,A,B). [resolve(146,a,126,c)].
% 0.78/1.07 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),u2_lattices(c13),A,B) = k1_lattices(c13,A,B). [resolve(146,a,127,b)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | m1_subset_1(k1_lattices(c13,A,B),u1_struct_0(c13)). [resolve(146,a,128,b)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -v4_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | m1_subset_1(k3_lattices(c13,A,B),u1_struct_0(c13)). [resolve(146,a,129,c)].
% 0.78/1.07 Derived: l1_struct_0(c13). [resolve(146,a,130,a)].
% 0.78/1.07 Derived: v1_funct_2(u2_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(146,a,131,a)].
% 0.78/1.07 Derived: m2_relset_1(u2_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(146,a,132,a)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -v4_lattices(c13) | v1_relat_1(u2_lattices(c13)). [resolve(146,a,133,c)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -v4_lattices(c13) | v1_binop_1(u2_lattices(c13),u1_struct_0(c13)). [resolve(146,a,135,c)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -v4_lattices(c13) | v1_partfun1(u2_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(146,a,136,c)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -v5_lattices(c13) | v1_relat_1(u2_lattices(c13)). [resolve(146,a,137,c)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -v5_lattices(c13) | v2_binop_1(u2_lattices(c13),u1_struct_0(c13)). [resolve(146,a,139,c)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -v5_lattices(c13) | v1_partfun1(u2_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(146,a,140,c)].
% 0.78/1.07 Derived: v3_struct_0(c13) | -v4_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k1_lattices(c13,A,B) = k3_lattices(c13,A,B). [resolve(146,a,141,c)].
% 0.78/1.07 Derived: -v1_relat_1(u2_lattices(c13)) | k1_funct_1(u2_lattices(c13),k4_tarski(A,B)) = k1_binop_1(u2_lattices(c13),A,B). [resolve(146,a,142,a)].
% 0.78/1.07 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u2_lattices(c13),k2_zfmisc_1(A,B),C) | -m1_relset_1(u2_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,u2_lattices(c13),D,E),C). [resolve(146,a,143,a)].
% 0.78/1.07 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(u2_lattices(c13),k2_zfmisc_1(A,B),C) | -m1_relset_1(u2_lattices(c13),k2_zfmisc_1(A,B),C) | -m1_subset_1(D,A) | -m1_subset_1(E,B) | k2_binop_1(A,B,C,u2_lattices(c13),D,E) = k1_binop_1(u2_lattices(c13),D,E). [resolve(146,a,144,h)].
% 0.78/1.07 147 l1_lattices(c1) # label(existence_l1_lattices) # label(axiom). [clausify(41)].
% 0.78/1.07 148 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(10)].
% 0.78/1.07 149 v3_struct_0(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) = 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). [clausify(14)].
% 0.78/1.07 150 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(24)].
% 0.78/1.07 151 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(28)].
% 0.78/1.07 152 -l1_lattices(A) | l1_struct_0(A) # label(dt_l1_lattices) # label(axiom). [clausify(30)].
% 0.78/1.07 153 -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(38)].
% 0.78/1.07 154 -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(38)].
% 0.78/1.07 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(147,a,148,c)].
% 0.78/1.07 Derived: v3_struct_0(c1) | -m1_subset_1(A,u1_struct_0(c1)) | -m1_subset_1(B,u1_struct_0(c1)) | k2_lattices(c1,A,B) = k2_binop_1(u1_struct_0(c1),u1_struct_0(c1),u1_struct_0(c1),u1_lattices(c1),A,B). [resolve(147,a,149,b)].
% 0.78/1.07 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(147,a,150,b)].
% 0.78/1.07 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(147,a,151,c)].
% 0.78/1.07 Derived: l1_struct_0(c1). [resolve(147,a,152,a)].
% 0.78/1.07 Derived: v1_funct_2(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(147,a,153,a)].
% 0.78/1.07 Derived: m2_relset_1(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(147,a,154,a)].
% 0.78/1.07 155 v3_struct_0(A) | -v6_lattices(A) | -l1_lattices(A) | v1_relat_1(u1_lattices(A)) # label(fc4_lattice2) # label(axiom). [clausify(56)].
% 0.78/1.07 Derived: v3_struct_0(c1) | -v6_lattices(c1) | v1_relat_1(u1_lattices(c1)). [resolve(155,c,147,a)].
% 0.78/1.07 156 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(56)].
% 0.78/1.07 157 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(56)].
% 0.78/1.07 Derived: v3_struct_0(c1) | -v6_lattices(c1) | v1_binop_1(u1_lattices(c1),u1_struct_0(c1)). [resolve(157,c,147,a)].
% 0.78/1.07 158 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(56)].
% 0.78/1.08 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(158,c,147,a)].
% 0.78/1.08 159 v3_struct_0(A) | -v7_lattices(A) | -l1_lattices(A) | v1_relat_1(u1_lattices(A)) # label(fc5_lattice2) # label(axiom). [clausify(58)].
% 0.78/1.08 Derived: v3_struct_0(c1) | -v7_lattices(c1) | v1_relat_1(u1_lattices(c1)). [resolve(159,c,147,a)].
% 0.78/1.08 160 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(58)].
% 0.78/1.08 161 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(58)].
% 0.78/1.08 Derived: v3_struct_0(c1) | -v7_lattices(c1) | v2_binop_1(u1_lattices(c1),u1_struct_0(c1)). [resolve(161,c,147,a)].
% 0.78/1.08 162 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(58)].
% 0.78/1.08 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(162,c,147,a)].
% 0.78/1.08 163 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(73)].
% 0.78/1.08 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(163,c,147,a)].
% 0.78/1.08 164 -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(89,b,87,b)].
% 0.78/1.08 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(164,a,147,a)].
% 0.78/1.08 165 -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(89,b,88,c)].
% 0.78/1.08 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(165,a,147,a)].
% 0.78/1.08 166 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(98,c,89,b)].
% 0.78/1.08 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(166,h,147,a)].
% 0.78/1.08 167 l1_lattices(c4). [resolve(99,a,118,a)].
% 0.78/1.08 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(167,a,148,c)].
% 0.78/1.08 Derived: v3_struct_0(c4) | -m1_subset_1(A,u1_struct_0(c4)) | -m1_subset_1(B,u1_struct_0(c4)) | k2_lattices(c4,A,B) = k2_binop_1(u1_struct_0(c4),u1_struct_0(c4),u1_struct_0(c4),u1_lattices(c4),A,B). [resolve(167,a,149,b)].
% 0.78/1.08 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(167,a,150,b)].
% 0.78/1.08 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(167,a,151,c)].
% 0.78/1.08 Derived: v1_funct_2(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(167,a,153,a)].
% 0.78/1.08 Derived: m2_relset_1(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(167,a,154,a)].
% 0.78/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | v1_relat_1(u1_lattices(c4)). [resolve(167,a,155,c)].
% 0.78/1.08 Derived: v3_struct_0(c4) | -v6_lattices(c4) | v1_binop_1(u1_lattices(c4),u1_struct_0(c4)). [resolve(167,a,157,c)].
% 0.78/1.08 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(167,a,158,c)].
% 0.78/1.08 Derived: v3_struct_0(c4) | -v7_lattices(c4) | v1_relat_1(u1_lattices(c4)). [resolve(167,a,159,c)].
% 0.78/1.08 Derived: v3_struct_0(c4) | -v7_lattices(c4) | v2_binop_1(u1_lattices(c4),u1_struct_0(c4)). [resolve(167,a,161,c)].
% 0.78/1.08 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(167,a,162,c)].
% 0.78/1.08 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(167,a,163,c)].
% 0.78/1.08 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(167,a,164,a)].
% 0.78/1.08 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(167,a,165,a)].
% 0.78/1.08 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(167,a,166,h)].
% 0.78/1.08 168 l1_lattices(c13). [resolve(124,a,118,a)].
% 0.78/1.08 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(168,a,148,c)].
% 0.78/1.08 Derived: v3_struct_0(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k2_lattices(c13,A,B) = k2_binop_1(u1_struct_0(c13),u1_struct_0(c13),u1_struct_0(c13),u1_lattices(c13),A,B). [resolve(168,a,149,b)].
% 0.78/1.08 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(168,a,150,b)].
% 0.78/1.08 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(168,a,151,c)].
% 0.78/1.08 Derived: v1_funct_2(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(168,a,153,a)].
% 0.78/1.08 Derived: m2_relset_1(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(168,a,154,a)].
% 0.78/1.08 Derived: v3_struct_0(c13) | -v6_lattices(c13) | v1_relat_1(u1_lattices(c13)). [resolve(168,a,155,c)].
% 0.78/1.08 Derived: v3_struct_0(c13) | -v6_lattices(c13) | v1_binop_1(u1_lattices(c13),u1_struct_0(c13)). [resolve(168,a,157,c)].
% 0.78/1.08 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(168,a,158,c)].
% 0.78/1.08 Derived: v3_struct_0(c13) | -v7_lattices(c13) | v1_relat_1(u1_lattices(c13)). [resolve(168,a,159,c)].
% 0.78/1.08 Derived: v3_struct_0(c13) | -v7_lattices(c13) | v2_binop_1(u1_lattices(c13),u1_struct_0(c13)). [resolve(168,a,161,c)].
% 0.78/1.08 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(168,a,162,c)].
% 0.78/1.08 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(168,a,163,c)].
% 0.78/1.08 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(168,a,164,a)].
% 0.78/1.08 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(168,a,165,a)].
% 0.78/1.09 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(168,a,166,h)].
% 0.78/1.09 169 m2_relset_1(f8(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(48)].
% 0.78/1.09 170 -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(37)].
% 0.78/1.09 Derived: m1_subset_1(f8(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))). [resolve(169,a,170,a)].
% 0.78/1.09 171 -m2_relset_1(A,B,C) | m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(74)].
% 0.78/1.09 Derived: m1_relset_1(f8(A,B),A,B). [resolve(171,a,169,a)].
% 0.78/1.09 172 m2_relset_1(A,B,C) | -m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(74)].
% 0.78/1.09 Derived: -m1_relset_1(A,B,C) | m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))). [resolve(172,a,170,a)].
% 0.78/1.09 173 m2_relset_1(u2_lattices(c3),k2_zfmisc_1(u1_struct_0(c3),u1_struct_0(c3)),u1_struct_0(c3)). [resolve(125,a,132,a)].
% 0.78/1.09 Derived: m1_subset_1(u2_lattices(c3),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(c3),u1_struct_0(c3)),u1_struct_0(c3)))). [resolve(173,a,170,a)].
% 0.78/1.09 Derived: m1_relset_1(u2_lattices(c3),k2_zfmisc_1(u1_struct_0(c3),u1_struct_0(c3)),u1_struct_0(c3)). [resolve(173,a,171,a)].
% 0.78/1.09 174 m2_relset_1(u2_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(145,a,132,a)].
% 0.78/1.09 Derived: m1_subset_1(u2_lattices(c4),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)))). [resolve(174,a,170,a)].
% 0.78/1.09 Derived: m1_relset_1(u2_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(174,a,171,a)].
% 0.78/1.09 175 m2_relset_1(u2_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(146,a,132,a)].
% 0.78/1.09 Derived: m1_subset_1(u2_lattices(c13),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)))). [resolve(175,a,170,a)].
% 0.78/1.09 Derived: m1_relset_1(u2_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(175,a,171,a)].
% 0.78/1.09 176 m2_relset_1(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(147,a,154,a)].
% 0.78/1.09 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(176,a,170,a)].
% 0.78/1.09 Derived: m1_relset_1(u1_lattices(c1),k2_zfmisc_1(u1_struct_0(c1),u1_struct_0(c1)),u1_struct_0(c1)). [resolve(176,a,171,a)].
% 0.78/1.09 177 m2_relset_1(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(167,a,154,a)].
% 0.78/1.09 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(177,a,170,a)].
% 0.78/1.09 Derived: m1_relset_1(u1_lattices(c4),k2_zfmisc_1(u1_struct_0(c4),u1_struct_0(c4)),u1_struct_0(c4)). [resolve(177,a,171,a)].
% 0.78/1.09 178 m2_relset_1(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(168,a,154,a)].
% 0.78/1.09 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(178,a,170,a)].
% 0.78/1.09 Derived: m1_relset_1(u1_lattices(c13),k2_zfmisc_1(u1_struct_0(c13),u1_struct_0(c13)),u1_struct_0(c13)). [resolve(178,a,171,a)].
% 0.78/1.09 179 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(49)].
% 0.78/1.09 180 l1_struct_0(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(42)].
% 0.78/1.09 Derived: v3_struct_0(c2) | -v1_xboole_0(u1_struct_0(c2)). [resolve(179,b,180,a)].
% 0.78/1.09 181 l1_struct_0(c12) # label(rc3_struct_0) # label(axiom). [clausify(69)].
% 0.78/1.09 Derived: v3_struct_0(c12) | -v1_xboole_0(u1_struct_0(c12)). [resolve(181,a,179,b)].
% 0.78/1.09 182 v3_struct_0(A) | -l1_struct_0(A) | m1_subset_1(f12(A),k1_zfmisc_1(u1_struct_0(A))) # label(rc5_struct_0) # label(axiom). [clausify(70)].
% 0.78/1.09 Derived: v3_struct_0(c2) | m1_subset_1(f12(c2),k1_zfmisc_1(u1_struct_0(c2))). [resolve(182,b,180,a)].
% 19.96/20.30 Derived: v3_struct_0(c12) | m1_subset_1(f12(c12),k1_zfmisc_1(u1_struct_0(c12))). [resolve(182,b,181,a)].
% 19.96/20.30 183 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(f12(A)) # label(rc5_struct_0) # label(axiom). [clausify(70)].
% 19.96/20.30 Derived: v3_struct_0(c2) | -v1_xboole_0(f12(c2)). [resolve(183,b,180,a)].
% 19.96/20.30 Derived: v3_struct_0(c12) | -v1_xboole_0(f12(c12)). [resolve(183,b,181,a)].
% 19.96/20.30 184 l1_struct_0(c3). [resolve(125,a,130,a)].
% 19.96/20.30 Derived: v3_struct_0(c3) | -v1_xboole_0(u1_struct_0(c3)). [resolve(184,a,179,b)].
% 19.96/20.30 Derived: v3_struct_0(c3) | m1_subset_1(f12(c3),k1_zfmisc_1(u1_struct_0(c3))). [resolve(184,a,182,b)].
% 19.96/20.30 Derived: v3_struct_0(c3) | -v1_xboole_0(f12(c3)). [resolve(184,a,183,b)].
% 19.96/20.30 185 l1_struct_0(c4). [resolve(145,a,130,a)].
% 19.96/20.30 Derived: v3_struct_0(c4) | -v1_xboole_0(u1_struct_0(c4)). [resolve(185,a,179,b)].
% 19.96/20.30 Derived: v3_struct_0(c4) | m1_subset_1(f12(c4),k1_zfmisc_1(u1_struct_0(c4))). [resolve(185,a,182,b)].
% 19.96/20.30 Derived: v3_struct_0(c4) | -v1_xboole_0(f12(c4)). [resolve(185,a,183,b)].
% 19.96/20.30 186 l1_struct_0(c13). [resolve(146,a,130,a)].
% 19.96/20.30 Derived: v3_struct_0(c13) | -v1_xboole_0(u1_struct_0(c13)). [resolve(186,a,179,b)].
% 19.96/20.30 Derived: v3_struct_0(c13) | m1_subset_1(f12(c13),k1_zfmisc_1(u1_struct_0(c13))). [resolve(186,a,182,b)].
% 19.96/20.30 Derived: v3_struct_0(c13) | -v1_xboole_0(f12(c13)). [resolve(186,a,183,b)].
% 19.96/20.30 187 l1_struct_0(c1). [resolve(147,a,152,a)].
% 19.96/20.30 Derived: v3_struct_0(c1) | -v1_xboole_0(u1_struct_0(c1)). [resolve(187,a,179,b)].
% 19.96/20.30 Derived: v3_struct_0(c1) | m1_subset_1(f12(c1),k1_zfmisc_1(u1_struct_0(c1))). [resolve(187,a,182,b)].
% 19.96/20.30 Derived: v3_struct_0(c1) | -v1_xboole_0(f12(c1)). [resolve(187,a,183,b)].
% 19.96/20.30 188 m1_subset_1(A,k1_zfmisc_1(B)) | -r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(78)].
% 19.96/20.30 189 r1_tarski(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(75)].
% 19.96/20.30 190 -m1_subset_1(A,k1_zfmisc_1(B)) | r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(78)].
% 19.96/20.30 Derived: m1_subset_1(A,k1_zfmisc_1(A)). [resolve(188,b,189,a)].
% 19.96/20.30
% 19.96/20.30 ============================== end predicate elimination =============
% 19.96/20.30
% 19.96/20.30 Auto_denials: (non-Horn, no changes).
% 19.96/20.30
% 19.96/20.30 Term ordering decisions:
% 19.96/20.30 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. k2_zfmisc_1=1. k4_tarski=1. k1_funct_1=1. k2_tarski=1. f1=1. f2=1. f5=1. f8=1. u1_struct_0=1. u1_lattices=1. u2_lattices=1. k1_zfmisc_1=1. k1_tarski=1. f3=1. f4=1. f6=1. f7=1. f9=1. f10=1. f11=1. f12=1. k1_binop_1=1. k4_lattices=1. k3_lattices=1. k1_lattices=1. k2_lattices=1. k2_binop_1=1.
% 19.96/20.30
% 19.96/20.30 ============================== end of process initial clauses ========
% 19.96/20.30
% 19.96/20.30 ============================== CLAUSES FOR SEARCH ====================
% 19.96/20.30
% 19.96/20.30 ============================== end of clauses for search =============
% 19.96/20.30
% 19.96/20.30 ============================== SEARCH ================================
% 19.96/20.30
% 19.96/20.30 % Starting search at 0.11 seconds.
% 19.96/20.30
% 19.96/20.30 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 0.25 sec).
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=37.000, iters=3598
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=34.000, iters=3483
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=30.000, iters=3533
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=27.000, iters=3430
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=26.000, iters=3783
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=22.000, iters=3385
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=21.000, iters=3336
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=20.000, iters=3498
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=18.000, iters=3450
% 19.96/20.30
% 19.96/20.30 Low Water (keep): wt=16.000, iters=3423
% 19.96/20.30
% 19.96/20.30 ============================== PROOF =================================
% 19.96/20.30 % SZS status Theorem
% 19.96/20.30 % SZS output start Refutation
% 19.96/20.30
% 19.96/20.30 % Proof 1 at 18.37 (+ 0.90) seconds.
% 19.96/20.30 % Length of proof is 78.
% 19.96/20.30 % Level of proof is 11.
% 19.96/20.30 % Maximum clause weight is 28.000.
% 19.96/20.30 % Given clauses 9226.
% 19.96/20.30
% 19.96/20.30 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].
% 19.96/20.30 9 (all A all B all C (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,B,C) = k3_lattices(A,C,B))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 19.96/20.30 11 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m2_lattice4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k4_lattices(A,C,D),B) & r2_hidden(k3_lattices(A,C,D),B))))))))))) # label(d10_lattice4) # label(axiom) # label(non_clause). [assumption].
% 19.96/20.30 16 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v9_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,k1_lattices(A,B,C)) = B))))))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption].
% 19.96/20.30 27 (all A all B all C (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 19.96/20.30 33 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 19.96/20.30 72 (all A all B all C (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,B,C) = k1_lattices(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption].
% 19.96/20.30 73 (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].
% 19.96/20.30 84 -(all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) <-> r2_hidden(k4_lattices(A,C,D),B)))))) -> m2_lattice4(B,A)))))) # label(t13_filter_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 19.96/20.30 100 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v4_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 19.96/20.30 102 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v6_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 19.96/20.30 105 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v9_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 19.96/20.30 109 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | m1_subset_1(f1(A,B),u1_struct_0(A)) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 19.96/20.30 110 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | m1_subset_1(f2(A,B),u1_struct_0(A)) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 19.96/20.30 111 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | r2_hidden(f1(A,B),B) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 19.96/20.30 112 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | r2_hidden(f2(A,B),B) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 19.96/20.30 113 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_lattice4(B,A) | -r2_hidden(k4_lattices(A,f1(A,B),f2(A,B)),B) | -r2_hidden(k3_lattices(A,f1(A,B),f2(A,B)),B) # label(d10_lattice4) # label(axiom). [clausify(11)].
% 19.96/20.30 114 v3_struct_0(A) | -l3_lattices(A) | -v9_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k2_lattices(A,B,k1_lattices(A,B,C)) = B # label(d9_lattices) # label(axiom). [clausify(16)].
% 19.96/20.30 118 -l3_lattices(A) | l1_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(33)].
% 19.96/20.30 119 -l3_lattices(A) | l2_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(33)].
% 19.96/20.30 124 l3_lattices(c13) # label(t13_filter_2) # label(negated_conjecture). [clausify(84)].
% 19.96/20.30 126 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k3_lattices(A,C,B) = k3_lattices(A,B,C) # label(commutativity_k3_lattices) # label(axiom). [clausify(9)].
% 19.96/20.30 129 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)) # label(dt_k3_lattices) # label(axiom). [clausify(27)].
% 19.96/20.30 141 v3_struct_0(A) | -v4_lattices(A) | -l2_lattices(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | k1_lattices(A,B,C) = k3_lattices(A,B,C) # label(redefinition_k3_lattices) # label(axiom). [clausify(72)].
% 19.96/20.30 146 l2_lattices(c13). [resolve(124,a,119,a)].
% 19.96/20.30 163 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(73)].
% 19.96/20.30 168 l1_lattices(c13). [resolve(124,a,118,a)].
% 19.96/20.30 227 -v3_struct_0(c13) # label(t13_filter_2) # label(negated_conjecture). [clausify(84)].
% 19.96/20.30 228 v10_lattices(c13) # label(t13_filter_2) # label(negated_conjecture). [clausify(84)].
% 19.96/20.30 229 m1_subset_1(c14,k1_zfmisc_1(u1_struct_0(c13))) # label(t13_filter_2) # label(negated_conjecture). [clausify(84)].
% 19.96/20.30 230 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | -r2_hidden(A,c14) | -r2_hidden(B,c14) | r2_hidden(k4_lattices(c13,A,B),c14) # label(t13_filter_2) # label(negated_conjecture). [clausify(84)].
% 19.96/20.30 232 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | r2_hidden(B,c14) | -r2_hidden(k4_lattices(c13,A,B),c14) # label(t13_filter_2) # label(negated_conjecture). [clausify(84)].
% 19.96/20.30 233 -m2_lattice4(c14,c13) # label(t13_filter_2) # label(negated_conjecture). [clausify(84)].
% 19.96/20.30 272 v3_struct_0(c13) | -v10_lattices(c13) | v4_lattices(c13). [resolve(124,a,100,a)].
% 19.96/20.30 273 v4_lattices(c13). [copy(272),unit_del(a,227),unit_del(b,228)].
% 19.96/20.30 276 v3_struct_0(c13) | -v10_lattices(c13) | v6_lattices(c13). [resolve(124,a,102,a)].
% 19.96/20.30 277 v6_lattices(c13). [copy(276),unit_del(a,227),unit_del(b,228)].
% 19.96/20.30 282 v3_struct_0(c13) | -v10_lattices(c13) | v9_lattices(c13). [resolve(124,a,105,a)].
% 19.96/20.30 283 v9_lattices(c13). [copy(282),unit_del(a,227),unit_del(b,228)].
% 19.96/20.30 289 v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | m1_subset_1(f1(c13,A),u1_struct_0(c13)). [resolve(124,a,109,c)].
% 19.96/20.30 290 -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | m1_subset_1(f1(c13,A),u1_struct_0(c13)). [copy(289),unit_del(a,227),unit_del(b,228)].
% 19.96/20.30 291 v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | m1_subset_1(f2(c13,A),u1_struct_0(c13)). [resolve(124,a,110,c)].
% 19.96/20.30 292 -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | m1_subset_1(f2(c13,A),u1_struct_0(c13)). [copy(291),unit_del(a,227),unit_del(b,228)].
% 19.96/20.30 293 v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | r2_hidden(f1(c13,A),A). [resolve(124,a,111,c)].
% 19.96/20.30 294 -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | r2_hidden(f1(c13,A),A). [copy(293),unit_del(a,227),unit_del(b,228)].
% 19.96/20.30 295 v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | r2_hidden(f2(c13,A),A). [resolve(124,a,112,c)].
% 19.96/20.30 296 -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | r2_hidden(f2(c13,A),A). [copy(295),unit_del(a,227),unit_del(b,228)].
% 19.96/20.30 297 v3_struct_0(c13) | -v10_lattices(c13) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | -r2_hidden(k4_lattices(c13,f1(c13,A),f2(c13,A)),A) | -r2_hidden(k3_lattices(c13,f1(c13,A),f2(c13,A)),A). [resolve(124,a,113,c)].
% 19.96/20.30 298 -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c13))) | m2_lattice4(A,c13) | -r2_hidden(k4_lattices(c13,f1(c13,A),f2(c13,A)),A) | -r2_hidden(k3_lattices(c13,f1(c13,A),f2(c13,A)),A). [copy(297),unit_del(a,227),unit_del(b,228)].
% 19.96/20.30 299 v3_struct_0(c13) | -v9_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k2_lattices(c13,A,k1_lattices(c13,A,B)) = A. [resolve(124,a,114,b)].
% 19.96/20.30 300 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k2_lattices(c13,A,k1_lattices(c13,A,B)) = A. [copy(299),unit_del(a,227),unit_del(b,283)].
% 19.96/20.30 336 v3_struct_0(c13) | -v4_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k3_lattices(c13,B,A) = k3_lattices(c13,A,B). [resolve(146,a,126,c)].
% 19.96/20.30 337 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k3_lattices(c13,B,A) = k3_lattices(c13,A,B). [copy(336),unit_del(a,227),unit_del(b,273)].
% 19.96/20.30 342 v3_struct_0(c13) | -v4_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | m1_subset_1(k3_lattices(c13,A,B),u1_struct_0(c13)). [resolve(146,a,129,c)].
% 19.96/20.30 343 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | m1_subset_1(k3_lattices(c13,A,B),u1_struct_0(c13)). [copy(342),unit_del(a,227),unit_del(b,273)].
% 19.96/20.30 348 v3_struct_0(c13) | -v4_lattices(c13) | -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k1_lattices(c13,A,B) = k3_lattices(c13,A,B). [resolve(146,a,141,c)].
% 19.96/20.30 349 -m1_subset_1(A,u1_struct_0(c13)) | -m1_subset_1(B,u1_struct_0(c13)) | k1_lattices(c13,A,B) = k3_lattices(c13,A,B). [copy(348),unit_del(a,227),unit_del(b,273)].
% 19.96/20.30 392 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(168,a,163,c)].
% 19.96/20.30 393 -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(392),unit_del(a,227),unit_del(b,277)].
% 19.96/20.30 548 m1_subset_1(f1(c13,c14),u1_struct_0(c13)). [resolve(290,a,229,a),unit_del(a,233)].
% 19.96/20.30 551 m1_subset_1(f2(c13,c14),u1_struct_0(c13)). [resolve(292,a,229,a),unit_del(a,233)].
% 19.96/20.30 554 r2_hidden(f1(c13,c14),c14). [resolve(294,a,229,a),unit_del(a,233)].
% 19.96/20.30 557 r2_hidden(f2(c13,c14),c14). [resolve(296,a,229,a),unit_del(a,233)].
% 19.96/20.30 825 -m1_subset_1(A,u1_struct_0(c13)) | -r2_hidden(A,c14) | r2_hidden(k4_lattices(c13,f1(c13,c14),A),c14). [resolve(554,a,230,c),unit_del(a,548)].
% 19.96/20.30 856 -m1_subset_1(A,u1_struct_0(c13)) | k1_lattices(c13,A,f1(c13,c14)) = k3_lattices(c13,A,f1(c13,c14)). [resolve(548,a,349,b)].
% 19.96/20.30 859 -m1_subset_1(A,u1_struct_0(c13)) | m1_subset_1(k3_lattices(c13,f1(c13,c14),A),u1_struct_0(c13)). [resolve(548,a,343,a)].
% 19.96/20.30 864 -m1_subset_1(A,u1_struct_0(c13)) | k3_lattices(c13,f1(c13,c14),A) = k3_lattices(c13,A,f1(c13,c14)). [resolve(548,a,337,b)].
% 19.96/20.30 865 -m1_subset_1(A,u1_struct_0(c13)) | k2_lattices(c13,A,k1_lattices(c13,A,f1(c13,c14))) = A. [resolve(548,a,300,b)].
% 19.96/20.30 876 -m1_subset_1(A,u1_struct_0(c13)) | k2_lattices(c13,f2(c13,c14),A) = k4_lattices(c13,f2(c13,c14),A). [resolve(551,a,393,a)].
% 19.96/20.30 7830 m1_subset_1(k3_lattices(c13,f1(c13,c14),f2(c13,c14)),u1_struct_0(c13)). [resolve(859,a,551,a)].
% 19.96/20.30 11920 r2_hidden(k4_lattices(c13,f1(c13,c14),f2(c13,c14)),c14). [resolve(825,b,557,a),unit_del(a,551)].
% 19.96/20.30 12062 k1_lattices(c13,f2(c13,c14),f1(c13,c14)) = k3_lattices(c13,f2(c13,c14),f1(c13,c14)). [resolve(856,a,551,a)].
% 19.96/20.30 12457 k3_lattices(c13,f2(c13,c14),f1(c13,c14)) = k3_lattices(c13,f1(c13,c14),f2(c13,c14)). [resolve(864,a,551,a),flip(a)].
% 19.96/20.30 12472 k1_lattices(c13,f2(c13,c14),f1(c13,c14)) = k3_lattices(c13,f1(c13,c14),f2(c13,c14)). [back_rewrite(12062),rewrite([12457(16)])].
% 19.96/20.30 12632 k2_lattices(c13,f2(c13,c14),k3_lattices(c13,f1(c13,c14),f2(c13,c14))) = f2(c13,c14). [resolve(865,a,551,a),rewrite([12472(12)])].
% 19.96/20.30 12909 k4_lattices(c13,f2(c13,c14),k3_lattices(c13,f1(c13,c14),f2(c13,c14))) = f2(c13,c14). [resolve(876,a,7830,a),rewrite([12632(13)]),flip(a)].
% 19.96/20.30 23800 r2_hidden(k3_lattices(c13,f1(c13,c14),f2(c13,c14)),c14). [para(12909(a,1),232(d,1)),unit_del(a,551),unit_del(b,7830),unit_del(d,557)].
% 19.96/20.30 23812 $F. [resolve(23800,a,298,d),unit_del(a,229),unit_del(b,233),unit_del(c,11920)].
% 19.96/20.30
% 19.96/20.30 % SZS output end Refutation
% 19.96/20.30 ============================== end of proof ==========================
% 19.96/20.30
% 19.96/20.30 ============================== STATISTICS ============================
% 19.96/20.30
% 19.96/20.30 Given=9226. Generated=1570759. Kept=23566. proofs=1.
% 19.96/20.30 Usable=8664. Sos=6619. Demods=574. Limbo=11, Disabled=8604. Hints=0.
% 19.96/20.30 Megabytes=22.71.
% 19.96/20.30 User_CPU=18.37, System_CPU=0.90, Wall_clock=20.
% 19.96/20.30
% 19.96/20.30 ============================== end of statistics =====================
% 19.96/20.30
% 19.96/20.30 ============================== end of search =========================
% 19.96/20.30
% 19.96/20.30 THEOREM PROVED
% 19.96/20.30 % SZS status Theorem
% 19.96/20.30
% 19.96/20.30 Exiting with 1 proof.
% 19.96/20.30
% 19.96/20.30 Process 29931 exit (max_proofs) Wed Jun 29 08:59:07 2022
% 19.96/20.30 Prover9 interrupted
%------------------------------------------------------------------------------