TSTP Solution File: LAT313+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT313+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 06:27:22 EDT 2022
% Result : Theorem 0.74s 1.05s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT313+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n021.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 : Tue Jun 28 20:32:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/1.01 ============================== Prover9 ===============================
% 0.42/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.01 Process 27664 was started by sandbox2 on n021.cluster.edu,
% 0.42/1.01 Tue Jun 28 20:32:27 2022
% 0.42/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27511_n021.cluster.edu".
% 0.42/1.01 ============================== end of head ===========================
% 0.42/1.01
% 0.42/1.01 ============================== INPUT =================================
% 0.42/1.01
% 0.42/1.01 % Reading from file /tmp/Prover9_27511_n021.cluster.edu
% 0.42/1.01
% 0.42/1.01 set(prolog_style_variables).
% 0.42/1.01 set(auto2).
% 0.42/1.01 % set(auto2) -> set(auto).
% 0.42/1.01 % set(auto) -> set(auto_inference).
% 0.42/1.01 % set(auto) -> set(auto_setup).
% 0.42/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.01 % set(auto) -> set(auto_limits).
% 0.42/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.01 % set(auto) -> set(auto_denials).
% 0.42/1.01 % set(auto) -> set(auto_process).
% 0.42/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.01 % set(auto2) -> assign(stats, some).
% 0.42/1.01 % set(auto2) -> clear(echo_input).
% 0.42/1.01 % set(auto2) -> set(quiet).
% 0.42/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.01 % set(auto2) -> clear(print_given).
% 0.42/1.01 assign(lrs_ticks,-1).
% 0.42/1.01 assign(sos_limit,10000).
% 0.42/1.01 assign(order,kbo).
% 0.42/1.01 set(lex_order_vars).
% 0.42/1.01 clear(print_given).
% 0.42/1.01
% 0.42/1.01 % formulas(sos). % not echoed (50 formulas)
% 0.42/1.01
% 0.42/1.01 ============================== end of input ==========================
% 0.42/1.01
% 0.42/1.01 % From the command line: assign(max_seconds, 300).
% 0.42/1.01
% 0.42/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.01
% 0.42/1.01 % Formulas that are not ordinary clauses:
% 0.42/1.01 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 2 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 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].
% 0.42/1.01 4 (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].
% 0.42/1.01 5 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> k17_filter_2(A) = u1_struct_0(A))) # label(d8_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 6 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> m2_filter_2(k17_filter_2(A),A))) # label(dt_k17_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 7 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m2_filter_2(k19_filter_2(A,B),A))) # label(dt_k19_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 8 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 9 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 10 (all A (-v3_struct_0(A) & l2_lattices(A) -> m1_subset_1(k6_lattices(A),u1_struct_0(A)))) # label(dt_k6_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 11 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 12 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.01 13 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 14 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 15 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 16 (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].
% 0.74/1.01 17 (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].
% 0.74/1.01 18 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 19 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 20 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 21 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 22 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 23 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 24 (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].
% 0.74/1.01 25 (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].
% 0.74/1.01 26 (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].
% 0.74/1.01 27 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 28 (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].
% 0.74/1.01 29 (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].
% 0.74/1.01 30 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 31 (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].
% 0.74/1.01 32 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 33 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 34 (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].
% 0.74/1.01 35 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_filter_2(A,B,C) <-> B = C))) # label(redefinition_r1_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 36 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> r1_filter_2(A,B,B))) # label(reflexivity_r1_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 37 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 38 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_filter_2(A,B,C) -> r1_filter_2(A,C,B)))) # label(symmetry_r1_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 39 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 40 (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].
% 0.74/1.01 41 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m2_filter_2(B,A) -> r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B))))) # label(t38_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 42 (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].
% 0.74/1.01 43 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v14_lattices(A) & r2_hidden(k6_lattices(A),B) -> r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) & k19_filter_2(A,B) = u1_struct_0(A)))))) # label(t42_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 44 (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].
% 0.74/1.01 45 (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].
% 0.74/1.01 46 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 47 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 48 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 49 -(all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m2_filter_2(B,A) -> (v14_lattices(A) & r2_hidden(k6_lattices(A),B) -> r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) & B = u1_struct_0(A)))))) # label(t43_filter_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.01
% 0.74/1.01 ============================== end of process non-clausal formulas ===
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.01
% 0.74/1.01 ============================== PREDICATE ELIMINATION =================
% 0.74/1.01 50 -l1_lattices(A) | l1_struct_0(A) # label(dt_l1_lattices) # label(axiom). [clausify(11)].
% 0.74/1.01 51 l1_lattices(c1) # label(existence_l1_lattices) # label(axiom). [clausify(19)].
% 0.74/1.01 Derived: l1_struct_0(c1). [resolve(50,a,51,a)].
% 0.74/1.01 52 -l3_lattices(A) | l1_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(14)].
% 0.74/1.01 Derived: -l3_lattices(A) | l1_struct_0(A). [resolve(52,b,50,a)].
% 0.74/1.01 53 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(26)].
% 0.74/1.01 54 l1_struct_0(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(20)].
% 0.74/1.01 55 l1_struct_0(c7) # label(rc3_struct_0) # label(axiom). [clausify(33)].
% 0.74/1.01 56 -l2_lattices(A) | l1_struct_0(A) # label(dt_l2_lattices) # label(axiom). [clausify(13)].
% 0.74/1.01 Derived: v3_struct_0(c2) | -v1_xboole_0(u1_struct_0(c2)). [resolve(53,b,54,a)].
% 0.74/1.01 Derived: v3_struct_0(c7) | -v1_xboole_0(u1_struct_0(c7)). [resolve(53,b,55,a)].
% 0.74/1.01 Derived: v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l2_lattices(A). [resolve(53,b,56,b)].
% 0.74/1.01 57 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(f7(A)) # label(rc5_struct_0) # label(axiom). [clausify(34)].
% 0.74/1.01 Derived: v3_struct_0(c2) | -v1_xboole_0(f7(c2)). [resolve(57,b,54,a)].
% 0.74/1.01 Derived: v3_struct_0(c7) | -v1_xboole_0(f7(c7)). [resolve(57,b,55,a)].
% 0.74/1.01 Derived: v3_struct_0(A) | -v1_xboole_0(f7(A)) | -l2_lattices(A). [resolve(57,b,56,b)].
% 0.74/1.01 58 v3_struct_0(A) | -l1_struct_0(A) | m1_subset_1(f7(A),k1_zfmisc_1(u1_struct_0(A))) # label(rc5_struct_0) # label(axiom). [clausify(34)].
% 0.74/1.01 Derived: v3_struct_0(c2) | m1_subset_1(f7(c2),k1_zfmisc_1(u1_struct_0(c2))). [resolve(58,b,54,a)].
% 0.74/1.01 Derived: v3_struct_0(c7) | m1_subset_1(f7(c7),k1_zfmisc_1(u1_struct_0(c7))). [resolve(58,b,55,a)].
% 0.74/1.01 Derived: v3_struct_0(A) | m1_subset_1(f7(A),k1_zfmisc_1(u1_struct_0(A))) | -l2_lattices(A). [resolve(58,b,56,b)].
% 0.74/1.01 59 l1_struct_0(c1). [resolve(50,a,51,a)].
% 0.74/1.01 Derived: v3_struct_0(c1) | -v1_xboole_0(u1_struct_0(c1)). [resolve(59,a,53,b)].
% 0.74/1.01 Derived: v3_struct_0(c1) | -v1_xboole_0(f7(c1)). [resolve(59,a,57,b)].
% 0.74/1.01 Derived: v3_struct_0(c1) | m1_subset_1(f7(c1),k1_zfmisc_1(u1_struct_0(c1))). [resolve(59,a,58,b)].
% 0.74/1.01 60 -l3_lattices(A) | l1_struct_0(A). [resolve(52,b,50,a)].
% 0.74/1.01 Derived: -l3_lattices(A) | v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)). [resolve(60,b,53,b)].
% 0.74/1.01 Derived: -l3_lattices(A) | v3_struct_0(A) | -v1_xboole_0(f7(A)). [resolve(60,b,57,b)].
% 0.74/1.01 Derived: -l3_lattices(A) | v3_struct_0(A) | m1_subset_1(f7(A),k1_zfmisc_1(u1_struct_0(A))). [resolve(60,b,58,b)].
% 0.74/1.01 61 v3_struct_0(A) | -l2_lattices(A) | m1_subset_1(k6_lattices(A),u1_struct_0(A)) # label(dt_k6_lattices) # label(axiom). [clausify(10)].
% 0.74/1.01 62 l2_lattices(c3) # label(existence_l2_lattices) # label(axiom). [clausify(21)].
% 0.74/1.01 63 -l3_lattices(A) | l2_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(14)].
% 0.74/1.01 Derived: v3_struct_0(c3) | m1_subset_1(k6_lattices(c3),u1_struct_0(c3)). [resolve(61,b,62,a)].
% 0.74/1.01 Derived: v3_struct_0(A) | m1_subset_1(k6_lattices(A),u1_struct_0(A)) | -l3_lattices(A). [resolve(61,b,63,b)].
% 0.74/1.01 64 v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l2_lattices(A). [resolve(53,b,56,b)].
% 0.74/1.01 Derived: v3_struct_0(c3) | -v1_xboole_0(u1_struct_0(c3)). [resolve(64,c,62,a)].
% 0.74/1.01 65 v3_struct_0(A) | -v1_xboole_0(f7(A)) | -l2_lattices(A). [resolve(57,b,56,b)].
% 0.74/1.01 Derived: v3_struct_0(c3) | -v1_xboole_0(f7(c3)). [resolve(65,c,62,a)].
% 0.74/1.01 66 v3_struct_0(A) | m1_subset_1(f7(A),k1_zfmisc_1(u1_struct_0(A))) | -l2_lattices(A). [resolve(58,b,56,b)].
% 0.74/1.01 Derived: v3_struct_0(c3) | m1_subset_1(f7(c3),k1_zfmisc_1(u1_struct_0(c3))). [resolve(66,c,62,a)].
% 0.74/1.01 67 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v4_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.74/1.01 68 l3_lattices(c4) # label(existence_l3_lattices) # label(axiom). [clausify(22)].
% 0.74/1.01 69 l3_lattices(c8) # label(t43_filter_2) # label(negated_conjecture). [clausify(49)].
% 0.74/1.01 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v4_lattices(c4). [resolve(67,a,68,a)].
% 0.74/1.01 Derived: v3_struct_0(c8) | -v10_lattices(c8) | v4_lattices(c8). [resolve(67,a,69,a)].
% 0.74/1.01 70 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v5_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.74/1.01 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v5_lattices(c4). [resolve(70,a,68,a)].
% 0.74/1.01 Derived: v3_struct_0(c8) | -v10_lattices(c8) | v5_lattices(c8). [resolve(70,a,69,a)].
% 0.74/1.01 71 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v6_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.74/1.01 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v6_lattices(c4). [resolve(71,a,68,a)].
% 0.74/1.01 Derived: v3_struct_0(c8) | -v10_lattices(c8) | v6_lattices(c8). [resolve(71,a,69,a)].
% 0.74/1.01 72 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v7_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.74/1.01 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v7_lattices(c4). [resolve(72,a,68,a)].
% 0.74/1.01 Derived: v3_struct_0(c8) | -v10_lattices(c8) | v7_lattices(c8). [resolve(72,a,69,a)].
% 0.74/1.01 73 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v8_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.74/1.01 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v8_lattices(c4). [resolve(73,a,68,a)].
% 0.74/1.01 Derived: v3_struct_0(c8) | -v10_lattices(c8) | v8_lattices(c8). [resolve(73,a,69,a)].
% 0.74/1.01 74 -l3_lattices(A) | v3_struct_0(A) | -v10_lattices(A) | v9_lattices(A) # label(cc1_lattices) # label(axiom). [clausify(3)].
% 0.74/1.01 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v9_lattices(c4). [resolve(74,a,68,a)].
% 0.74/1.01 Derived: v3_struct_0(c8) | -v10_lattices(c8) | v9_lattices(c8). [resolve(74,a,69,a)].
% 0.74/1.01 75 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -v1_xboole_0(f4(A)) # label(rc1_lattice4) # label(axiom). [clausify(28)].
% 0.74/1.01 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -v1_xboole_0(f4(c4)). [resolve(75,c,68,a)].
% 0.74/1.01 Derived: v3_struct_0(c8) | -v10_lattices(c8) | -v1_xboole_0(f4(c8)). [resolve(75,c,69,a)].
% 0.74/1.01 76 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | m2_filter_2(k17_filter_2(A),A) # label(dt_k17_filter_2) # label(axiom). [clausify(6)].
% 0.74/1.01 Derived: v3_struct_0(c4) | -v10_lattices(c4) | m2_filter_2(k17_filter_2(c4),c4). [resolve(76,c,68,a)].
% 0.74/1.01 Derived: v3_struct_0(c8) | -v10_lattices(c8) | m2_filter_2(k17_filter_2(c8),c8). [resolve(76,c,69,a)].
% 0.74/1.01 77 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | m2_filter_2(f2(A),A) # label(existence_m2_filter_2) # label(axiom). [clausify(24)].
% 0.74/1.01 Derived: v3_struct_0(c4) | -v10_lattices(c4) | m2_filter_2(f2(c4),c4). [resolve(77,c,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v10_lattices(c8) | m2_filter_2(f2(c8),c8). [resolve(77,c,69,a)].
% 0.74/1.02 78 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | m2_lattice4(f3(A),A) # label(existence_m2_lattice4) # label(axiom). [clausify(25)].
% 0.74/1.02 Derived: v3_struct_0(c4) | -v10_lattices(c4) | m2_lattice4(f3(c4),c4). [resolve(78,c,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v10_lattices(c8) | m2_lattice4(f3(c8),c8). [resolve(78,c,69,a)].
% 0.74/1.02 79 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | m2_lattice4(f4(A),A) # label(rc1_lattice4) # label(axiom). [clausify(28)].
% 0.74/1.02 Derived: v3_struct_0(c4) | -v10_lattices(c4) | m2_lattice4(f4(c4),c4). [resolve(79,c,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v10_lattices(c8) | m2_lattice4(f4(c8),c8). [resolve(79,c,69,a)].
% 0.74/1.02 80 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | u1_struct_0(A) = k17_filter_2(A) # label(d8_filter_2) # label(axiom). [clausify(5)].
% 0.74/1.02 Derived: v3_struct_0(c4) | -v10_lattices(c4) | u1_struct_0(c4) = k17_filter_2(c4). [resolve(80,c,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v10_lattices(c8) | u1_struct_0(c8) = k17_filter_2(c8). [resolve(80,c,69,a)].
% 0.74/1.02 81 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(16)].
% 0.74/1.02 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m2_filter_2(A,c4) | -v1_xboole_0(A). [resolve(81,c,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v10_lattices(c8) | -m2_filter_2(A,c8) | -v1_xboole_0(A). [resolve(81,c,69,a)].
% 0.74/1.02 82 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(16)].
% 0.74/1.02 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m2_filter_2(A,c4) | m2_lattice4(A,c4). [resolve(82,c,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v10_lattices(c8) | -m2_filter_2(A,c8) | m2_lattice4(A,c8). [resolve(82,c,69,a)].
% 0.74/1.02 83 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(17)].
% 0.74/1.02 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m2_lattice4(A,c4) | m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))). [resolve(83,c,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v10_lattices(c8) | -m2_lattice4(A,c8) | m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c8))). [resolve(83,c,69,a)].
% 0.74/1.02 84 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m2_filter_2(B,A) | r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B) # label(t38_filter_2) # label(axiom). [clausify(41)].
% 0.74/1.02 Derived: v3_struct_0(c4) | -v10_lattices(c4) | -m2_filter_2(A,c4) | r1_filter_2(u1_struct_0(c4),k19_filter_2(c4,A),A). [resolve(84,c,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v10_lattices(c8) | -m2_filter_2(A,c8) | r1_filter_2(u1_struct_0(c8),k19_filter_2(c8,A),A). [resolve(84,c,69,a)].
% 0.74/1.02 85 -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(4)].
% 0.74/1.02 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(85,a,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v4_lattices(c8) | -v5_lattices(c8) | -v6_lattices(c8) | -v7_lattices(c8) | -v8_lattices(c8) | -v9_lattices(c8) | v10_lattices(c8). [resolve(85,a,69,a)].
% 0.74/1.02 86 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | v1_xboole_0(B) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m2_filter_2(k19_filter_2(A,B),A) # label(dt_k19_filter_2) # label(axiom). [clausify(7)].
% 0.74/1.02 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v1_xboole_0(A) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | m2_filter_2(k19_filter_2(c4,A),c4). [resolve(86,c,68,a)].
% 0.74/1.02 Derived: v3_struct_0(c8) | -v10_lattices(c8) | v1_xboole_0(A) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c8))) | m2_filter_2(k19_filter_2(c8,A),c8). [resolve(86,c,69,a)].
% 0.74/1.02 87 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | v1_xboole_0(B) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v14_lattices(A) | -r2_hidden(k6_lattices(A),B) | k19_filter_2(A,B) = u1_struct_0(A) # label(t42_filter_2) # label(axiom). [clausify(43)].
% 0.74/1.05 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v1_xboole_0(A) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | -v14_lattices(c4) | -r2_hidden(k6_lattices(c4),A) | k19_filter_2(c4,A) = u1_struct_0(c4). [resolve(87,c,68,a)].
% 0.74/1.05 Derived: v3_struct_0(c8) | -v10_lattices(c8) | v1_xboole_0(A) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c8))) | -v14_lattices(c8) | -r2_hidden(k6_lattices(c8),A) | k19_filter_2(c8,A) = u1_struct_0(c8). [resolve(87,c,69,a)].
% 0.74/1.05 88 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | v1_xboole_0(B) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v14_lattices(A) | -r2_hidden(k6_lattices(A),B) | r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) # label(t42_filter_2) # label(axiom). [clausify(43)].
% 0.74/1.05 Derived: v3_struct_0(c4) | -v10_lattices(c4) | v1_xboole_0(A) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c4))) | -v14_lattices(c4) | -r2_hidden(k6_lattices(c4),A) | r1_filter_2(u1_struct_0(c4),k19_filter_2(c4,A),k17_filter_2(c4)). [resolve(88,c,68,a)].
% 0.74/1.05 Derived: v3_struct_0(c8) | -v10_lattices(c8) | v1_xboole_0(A) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c8))) | -v14_lattices(c8) | -r2_hidden(k6_lattices(c8),A) | r1_filter_2(u1_struct_0(c8),k19_filter_2(c8,A),k17_filter_2(c8)). [resolve(88,c,69,a)].
% 0.74/1.05 89 -l3_lattices(A) | v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)). [resolve(60,b,53,b)].
% 0.74/1.05 Derived: v3_struct_0(c4) | -v1_xboole_0(u1_struct_0(c4)). [resolve(89,a,68,a)].
% 0.74/1.05 Derived: v3_struct_0(c8) | -v1_xboole_0(u1_struct_0(c8)). [resolve(89,a,69,a)].
% 0.74/1.05 90 -l3_lattices(A) | v3_struct_0(A) | -v1_xboole_0(f7(A)). [resolve(60,b,57,b)].
% 0.74/1.05 Derived: v3_struct_0(c4) | -v1_xboole_0(f7(c4)). [resolve(90,a,68,a)].
% 0.74/1.05 Derived: v3_struct_0(c8) | -v1_xboole_0(f7(c8)). [resolve(90,a,69,a)].
% 0.74/1.05 91 -l3_lattices(A) | v3_struct_0(A) | m1_subset_1(f7(A),k1_zfmisc_1(u1_struct_0(A))). [resolve(60,b,58,b)].
% 0.74/1.05 Derived: v3_struct_0(c4) | m1_subset_1(f7(c4),k1_zfmisc_1(u1_struct_0(c4))). [resolve(91,a,68,a)].
% 0.74/1.05 Derived: v3_struct_0(c8) | m1_subset_1(f7(c8),k1_zfmisc_1(u1_struct_0(c8))). [resolve(91,a,69,a)].
% 0.74/1.05 92 v3_struct_0(A) | m1_subset_1(k6_lattices(A),u1_struct_0(A)) | -l3_lattices(A). [resolve(61,b,63,b)].
% 0.74/1.05 Derived: v3_struct_0(c4) | m1_subset_1(k6_lattices(c4),u1_struct_0(c4)). [resolve(92,c,68,a)].
% 0.74/1.05 Derived: v3_struct_0(c8) | m1_subset_1(k6_lattices(c8),u1_struct_0(c8)). [resolve(92,c,69,a)].
% 0.74/1.05 93 m1_subset_1(A,k1_zfmisc_1(B)) | -r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(42)].
% 0.74/1.05 94 r1_tarski(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(37)].
% 0.74/1.05 95 -m1_subset_1(A,k1_zfmisc_1(B)) | r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(42)].
% 0.74/1.05 Derived: m1_subset_1(A,k1_zfmisc_1(A)). [resolve(93,b,94,a)].
% 0.74/1.05
% 0.74/1.05 ============================== end predicate elimination =============
% 0.74/1.05
% 0.74/1.05 Auto_denials: (non-Horn, no changes).
% 0.74/1.05
% 0.74/1.05 Term ordering decisions:
% 0.74/1.05 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. k19_filter_2=1. u1_struct_0=1. k1_zfmisc_1=1. k6_lattices=1. k17_filter_2=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1.
% 0.74/1.05
% 0.74/1.05 ============================== end of process initial clauses ========
% 0.74/1.05
% 0.74/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.05
% 0.74/1.05 ============================== end of clauses for search =============
% 0.74/1.05
% 0.74/1.05 ============================== SEARCH ================================
% 0.74/1.05
% 0.74/1.05 % Starting search at 0.03 seconds.
% 0.74/1.05
% 0.74/1.05 ============================== PROOF =================================
% 0.74/1.05 % SZS status Theorem
% 0.74/1.05 % SZS output start Refutation
% 0.74/1.05
% 0.74/1.05 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.74/1.05 % Length of proof is 61.
% 0.74/1.05 % Level of proof is 10.
% 0.74/1.05 % Maximum clause weight is 18.000.
% 0.74/1.05 % Given clauses 144.
% 0.74/1.05
% 0.74/1.05 5 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> k17_filter_2(A) = u1_struct_0(A))) # label(d8_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 11 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 14 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 16 (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].
% 0.74/1.05 17 (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].
% 0.74/1.05 26 (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].
% 0.74/1.05 35 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_filter_2(A,B,C) <-> B = C))) # label(redefinition_r1_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 37 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 38 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_filter_2(A,B,C) -> r1_filter_2(A,C,B)))) # label(symmetry_r1_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 41 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m2_filter_2(B,A) -> r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B))))) # label(t38_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 42 (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].
% 0.74/1.05 43 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v14_lattices(A) & r2_hidden(k6_lattices(A),B) -> r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) & k19_filter_2(A,B) = u1_struct_0(A)))))) # label(t42_filter_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 47 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 49 -(all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m2_filter_2(B,A) -> (v14_lattices(A) & r2_hidden(k6_lattices(A),B) -> r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) & B = u1_struct_0(A)))))) # label(t43_filter_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.05 50 -l1_lattices(A) | l1_struct_0(A) # label(dt_l1_lattices) # label(axiom). [clausify(11)].
% 0.74/1.05 52 -l3_lattices(A) | l1_lattices(A) # label(dt_l3_lattices) # label(axiom). [clausify(14)].
% 0.74/1.05 53 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(26)].
% 0.74/1.05 60 -l3_lattices(A) | l1_struct_0(A). [resolve(52,b,50,a)].
% 0.74/1.05 69 l3_lattices(c8) # label(t43_filter_2) # label(negated_conjecture). [clausify(49)].
% 0.74/1.05 80 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | u1_struct_0(A) = k17_filter_2(A) # label(d8_filter_2) # label(axiom). [clausify(5)].
% 0.74/1.05 82 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(16)].
% 0.74/1.05 83 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(17)].
% 0.74/1.05 84 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | -m2_filter_2(B,A) | r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B) # label(t38_filter_2) # label(axiom). [clausify(41)].
% 0.74/1.05 87 v3_struct_0(A) | -v10_lattices(A) | -l3_lattices(A) | v1_xboole_0(B) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v14_lattices(A) | -r2_hidden(k6_lattices(A),B) | k19_filter_2(A,B) = u1_struct_0(A) # label(t42_filter_2) # label(axiom). [clausify(43)].
% 0.74/1.05 89 -l3_lattices(A) | v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)). [resolve(60,b,53,b)].
% 0.74/1.05 93 m1_subset_1(A,k1_zfmisc_1(B)) | -r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(42)].
% 0.74/1.05 94 r1_tarski(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(37)].
% 0.74/1.05 98 v10_lattices(c8) # label(t43_filter_2) # label(negated_conjecture). [clausify(49)].
% 0.74/1.05 99 v14_lattices(c8) # label(t43_filter_2) # label(negated_conjecture). [clausify(49)].
% 0.74/1.05 101 m2_filter_2(c9,c8) # label(t43_filter_2) # label(negated_conjecture). [clausify(49)].
% 0.74/1.05 103 r2_hidden(k6_lattices(c8),c9) # label(t43_filter_2) # label(negated_conjecture). [clausify(49)].
% 0.74/1.05 108 -v3_struct_0(c8) # label(t43_filter_2) # label(negated_conjecture). [clausify(49)].
% 0.74/1.05 110 -r2_hidden(A,B) | -v1_xboole_0(B) # label(t7_boole) # label(axiom). [clausify(47)].
% 0.74/1.05 113 -r1_filter_2(u1_struct_0(c8),c9,k17_filter_2(c8)) | u1_struct_0(c8) != c9 # label(t43_filter_2) # label(negated_conjecture). [clausify(49)].
% 0.74/1.05 121 v1_xboole_0(A) | -m1_subset_1(B,k1_zfmisc_1(A)) | -m1_subset_1(C,k1_zfmisc_1(A)) | -r1_filter_2(A,B,C) | C = B # label(redefinition_r1_filter_2) # label(axiom). [clausify(35)].
% 0.74/1.05 123 v1_xboole_0(A) | -m1_subset_1(B,k1_zfmisc_1(A)) | -m1_subset_1(C,k1_zfmisc_1(A)) | -r1_filter_2(A,B,C) | r1_filter_2(A,C,B) # label(symmetry_r1_filter_2) # label(axiom). [clausify(38)].
% 0.74/1.05 175 v3_struct_0(c8) | -v10_lattices(c8) | u1_struct_0(c8) = k17_filter_2(c8). [resolve(80,c,69,a)].
% 0.74/1.05 176 k17_filter_2(c8) = u1_struct_0(c8). [copy(175),flip(c),unit_del(a,108),unit_del(b,98)].
% 0.74/1.05 181 v3_struct_0(c8) | -v10_lattices(c8) | -m2_filter_2(A,c8) | m2_lattice4(A,c8). [resolve(82,c,69,a)].
% 0.74/1.05 182 -m2_filter_2(A,c8) | m2_lattice4(A,c8). [copy(181),unit_del(a,108),unit_del(b,98)].
% 0.74/1.05 184 v3_struct_0(c8) | -v10_lattices(c8) | -m2_lattice4(A,c8) | m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c8))). [resolve(83,c,69,a)].
% 0.74/1.05 185 -m2_lattice4(A,c8) | m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c8))). [copy(184),unit_del(a,108),unit_del(b,98)].
% 0.74/1.05 187 v3_struct_0(c8) | -v10_lattices(c8) | -m2_filter_2(A,c8) | r1_filter_2(u1_struct_0(c8),k19_filter_2(c8,A),A). [resolve(84,c,69,a)].
% 0.74/1.05 188 -m2_filter_2(A,c8) | r1_filter_2(u1_struct_0(c8),k19_filter_2(c8,A),A). [copy(187),unit_del(a,108),unit_del(b,98)].
% 0.74/1.05 195 v3_struct_0(c8) | -v10_lattices(c8) | v1_xboole_0(A) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c8))) | -v14_lattices(c8) | -r2_hidden(k6_lattices(c8),A) | k19_filter_2(c8,A) = u1_struct_0(c8). [resolve(87,c,69,a)].
% 0.74/1.05 196 v1_xboole_0(A) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c8))) | -r2_hidden(k6_lattices(c8),A) | k19_filter_2(c8,A) = u1_struct_0(c8). [copy(195),unit_del(a,108),unit_del(b,98),unit_del(e,99)].
% 0.74/1.05 201 v3_struct_0(c8) | -v1_xboole_0(u1_struct_0(c8)). [resolve(89,a,69,a)].
% 0.74/1.05 202 -v1_xboole_0(u1_struct_0(c8)). [copy(201),unit_del(a,108)].
% 0.74/1.05 212 m1_subset_1(A,k1_zfmisc_1(A)). [resolve(93,b,94,a)].
% 0.74/1.05 216 -r1_filter_2(u1_struct_0(c8),c9,u1_struct_0(c8)) | u1_struct_0(c8) != c9. [back_rewrite(113),rewrite([176(5)])].
% 0.74/1.05 217 -v1_xboole_0(c9). [resolve(110,a,103,a)].
% 0.74/1.05 261 m2_lattice4(c9,c8). [resolve(182,a,101,a)].
% 0.74/1.05 265 r1_filter_2(u1_struct_0(c8),k19_filter_2(c8,c9),c9). [resolve(188,a,101,a)].
% 0.74/1.05 270 -m1_subset_1(c9,k1_zfmisc_1(u1_struct_0(c8))) | k19_filter_2(c8,c9) = u1_struct_0(c8). [resolve(196,c,103,a),unit_del(a,217)].
% 0.74/1.05 314 m1_subset_1(c9,k1_zfmisc_1(u1_struct_0(c8))). [resolve(261,a,185,a)].
% 0.74/1.05 316 k19_filter_2(c8,c9) = u1_struct_0(c8). [back_unit_del(270),unit_del(a,314)].
% 0.74/1.05 318 r1_filter_2(u1_struct_0(c8),u1_struct_0(c8),c9). [back_rewrite(265),rewrite([316(5)])].
% 0.74/1.05 426 r1_filter_2(u1_struct_0(c8),c9,u1_struct_0(c8)). [resolve(318,a,123,d),unit_del(a,202),unit_del(b,212),unit_del(c,314)].
% 0.74/1.05 427 u1_struct_0(c8) = c9. [resolve(318,a,121,d),flip(d),unit_del(a,202),unit_del(b,212),unit_del(c,314)].
% 0.74/1.05 428 -r1_filter_2(c9,c9,c9). [back_unit_del(216),rewrite([427(2),427(4),427(6)]),xx(b)].
% 0.74/1.05 429 $F. [back_rewrite(426),rewrite([427(2),427(4)]),unit_del(a,428)].
% 0.74/1.05
% 0.74/1.05 % SZS output end Refutation
% 0.74/1.05 ============================== end of proof ==========================
% 0.74/1.05
% 0.74/1.05 ============================== STATISTICS ============================
% 0.74/1.05
% 0.74/1.05 Given=144. Generated=466. Kept=305. proofs=1.
% 0.74/1.05 Usable=138. Sos=141. Demods=7. Limbo=2, Disabled=161. Hints=0.
% 0.74/1.05 Megabytes=0.42.
% 0.74/1.05 User_CPU=0.05, System_CPU=0.01, Wall_clock=0.
% 0.74/1.05
% 0.74/1.05 ============================== end of statistics =====================
% 0.74/1.05
% 0.74/1.05 ============================== end of search =========================
% 0.74/1.05
% 0.74/1.05 THEOREM PROVED
% 0.74/1.05 % SZS status Theorem
% 0.74/1.05
% 0.74/1.05 Exiting with 1 proof.
% 0.74/1.05
% 0.74/1.05 Process 27664 exit (max_proofs) Tue Jun 28 20:32:27 2022
% 0.74/1.05 Prover9 interrupted
%------------------------------------------------------------------------------