TSTP Solution File: GRP639+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP639+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 : Sat Jul 16 11:20:07 EDT 2022
% Result : Theorem 1.55s 1.85s
% Output : Refutation 1.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP639+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 11:50:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.73/1.00 ============================== Prover9 ===============================
% 0.73/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.00 Process 28717 was started by sandbox2 on n022.cluster.edu,
% 0.73/1.00 Mon Jun 13 11:50:34 2022
% 0.73/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28563_n022.cluster.edu".
% 0.73/1.00 ============================== end of head ===========================
% 0.73/1.00
% 0.73/1.00 ============================== INPUT =================================
% 0.73/1.00
% 0.73/1.00 % Reading from file /tmp/Prover9_28563_n022.cluster.edu
% 0.73/1.00
% 0.73/1.00 set(prolog_style_variables).
% 0.73/1.00 set(auto2).
% 0.73/1.00 % set(auto2) -> set(auto).
% 0.73/1.00 % set(auto) -> set(auto_inference).
% 0.73/1.00 % set(auto) -> set(auto_setup).
% 0.73/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.00 % set(auto) -> set(auto_limits).
% 0.73/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.00 % set(auto) -> set(auto_denials).
% 0.73/1.00 % set(auto) -> set(auto_process).
% 0.73/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.00 % set(auto2) -> assign(stats, some).
% 0.73/1.00 % set(auto2) -> clear(echo_input).
% 0.73/1.00 % set(auto2) -> set(quiet).
% 0.73/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.00 % set(auto2) -> clear(print_given).
% 0.73/1.00 assign(lrs_ticks,-1).
% 0.73/1.00 assign(sos_limit,10000).
% 0.73/1.00 assign(order,kbo).
% 0.73/1.00 set(lex_order_vars).
% 0.73/1.00 clear(print_given).
% 0.73/1.00
% 0.73/1.00 % formulas(sos). % not echoed (54 formulas)
% 0.73/1.00
% 0.73/1.00 ============================== end of input ==========================
% 0.73/1.00
% 0.73/1.00 % From the command line: assign(max_seconds, 300).
% 0.73/1.00
% 0.73/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.00
% 0.73/1.00 % Formulas that are not ordinary clauses:
% 0.73/1.00 1 (all A (l1_group_1(A) -> (v1_group_1(A) -> A = g1_group_1(u1_struct_0(A),u1_group_1(A))))) # label(abstractness_v1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 2 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 3 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_partfun1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 4 (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].
% 0.73/1.00 5 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 6 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_funct_1(C) & -v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 7 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> (C = k5_group_4(A,B) <-> r1_tarski(B,u1_struct_0(C)) & (all D (v1_group_1(D) & m1_group_2(D,A) -> (r1_tarski(B,u1_struct_0(D)) -> m1_group_2(C,D))))))))))) # label(d5_group_4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 8 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> v1_group_1(g1_group_1(A,B)) & l1_group_1(g1_group_1(A,B)))) # label(dt_g1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 9 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 10 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 11 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 12 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 13 (all A all B (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_group_1(k5_group_4(A,B)) & m1_group_2(k5_group_4(A,B),A))) # label(dt_k5_group_4) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 14 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 15 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 16 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 17 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> -v3_struct_0(B) & v3_group_1(B) & l1_group_1(B))))) # label(dt_m1_group_2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 18 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 19 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 20 (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].
% 0.73/1.00 21 (all A (l1_group_1(A) -> v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 22 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 23 (exists A l1_group_1(A)) # label(existence_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 24 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 25 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) -> (exists B m1_group_2(B,A)))) # label(existence_m1_group_2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 26 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 27 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 28 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 29 (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].
% 0.73/1.00 30 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 31 (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].
% 0.73/1.00 32 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C all D (g1_group_1(A,B) = g1_group_1(C,D) -> A = C & B = D)))) # label(free_g1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 33 (all A all B exists C (m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 34 (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].
% 0.73/1.00 35 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 36 (all A all B exists C (m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 37 (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].
% 0.73/1.00 38 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 39 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 40 (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].
% 0.73/1.00 41 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) -> k2_funct_2(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 42 (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].
% 0.73/1.00 43 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 44 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t156_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 45 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 46 (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].
% 0.73/1.00 47 (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].
% 0.73/1.00 48 (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].
% 0.73/1.00 49 (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].
% 0.73/1.00 50 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 51 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 52 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 53 -(all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(k5_group_4(A,D)))))))))))) # label(t12_latsubgr) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.00
% 0.73/1.00 ============================== end of process non-clausal formulas ===
% 0.73/1.00
% 0.73/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.00
% 0.73/1.00 ============================== PREDICATE ELIMINATION =================
% 0.73/1.00 54 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(29)].
% 0.73/1.00 55 l1_struct_0(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(24)].
% 0.73/1.00 56 l1_struct_0(c5) # label(rc3_struct_0) # label(axiom). [clausify(39)].
% 0.73/1.00 57 -l1_group_1(A) | l1_struct_0(A) # label(dt_l1_group_1) # label(axiom). [clausify(15)].
% 0.73/1.00 Derived: v3_struct_0(c2) | -v1_xboole_0(u1_struct_0(c2)). [resolve(54,b,55,a)].
% 0.73/1.00 Derived: v3_struct_0(c5) | -v1_xboole_0(u1_struct_0(c5)). [resolve(54,b,56,a)].
% 0.73/1.00 Derived: v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_group_1(A). [resolve(54,b,57,b)].
% 0.73/1.00 58 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(f10(A)) # label(rc5_struct_0) # label(axiom). [clausify(40)].
% 0.73/1.00 Derived: v3_struct_0(c2) | -v1_xboole_0(f10(c2)). [resolve(58,b,55,a)].
% 0.73/1.00 Derived: v3_struct_0(c5) | -v1_xboole_0(f10(c5)). [resolve(58,b,56,a)].
% 0.73/1.00 Derived: v3_struct_0(A) | -v1_xboole_0(f10(A)) | -l1_group_1(A). [resolve(58,b,57,b)].
% 0.73/1.00 59 v3_struct_0(A) | -l1_struct_0(A) | m1_subset_1(f10(A),k1_zfmisc_1(u1_struct_0(A))) # label(rc5_struct_0) # label(axiom). [clausify(40)].
% 0.73/1.00 Derived: v3_struct_0(c2) | m1_subset_1(f10(c2),k1_zfmisc_1(u1_struct_0(c2))). [resolve(59,b,55,a)].
% 0.73/1.00 Derived: v3_struct_0(c5) | m1_subset_1(f10(c5),k1_zfmisc_1(u1_struct_0(c5))). [resolve(59,b,56,a)].
% 0.73/1.00 Derived: v3_struct_0(A) | m1_subset_1(f10(A),k1_zfmisc_1(u1_struct_0(A))) | -l1_group_1(A). [resolve(59,b,57,b)].
% 0.73/1.00 60 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | v1_group_1(k5_group_4(A,B)) # label(dt_k5_group_4) # label(axiom). [clausify(13)].
% 0.73/1.00 61 v4_group_1(c6) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 0.73/1.00 62 v4_group_1(c7) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 0.73/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | v1_group_1(k5_group_4(c6,A)). [resolve(60,c,61,a)].
% 0.73/1.00 Derived: v3_struct_0(c7) | -v3_group_1(c7) | -l1_group_1(c7) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c7))) | v1_group_1(k5_group_4(c7,A)). [resolve(60,c,62,a)].
% 0.73/1.00 63 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m1_group_2(k5_group_4(A,B),A) # label(dt_k5_group_4) # label(axiom). [clausify(13)].
% 0.73/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | m1_group_2(k5_group_4(c6,A),c6). [resolve(63,c,61,a)].
% 0.73/1.00 Derived: v3_struct_0(c7) | -v3_group_1(c7) | -l1_group_1(c7) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c7))) | m1_group_2(k5_group_4(c7,A),c7). [resolve(63,c,62,a)].
% 0.73/1.00 64 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v1_group_1(C) | -m1_group_2(C,A) | k5_group_4(A,B) != C | r1_tarski(B,u1_struct_0(C)) # label(d5_group_4) # label(axiom). [clausify(7)].
% 0.73/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | -v1_group_1(B) | -m1_group_2(B,c6) | k5_group_4(c6,A) != B | r1_tarski(A,u1_struct_0(B)). [resolve(64,c,61,a)].
% 0.73/1.00 Derived: v3_struct_0(c7) | -v3_group_1(c7) | -l1_group_1(c7) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c7))) | -v1_group_1(B) | -m1_group_2(B,c7) | k5_group_4(c7,A) != B | r1_tarski(A,u1_struct_0(B)). [resolve(64,c,62,a)].
% 0.73/1.00 65 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v1_group_1(C) | -m1_group_2(C,A) | k5_group_4(A,B) = C | -r1_tarski(B,u1_struct_0(C)) | v1_group_1(f1(A,B,C)) # label(d5_group_4) # label(axiom). [clausify(7)].
% 0.73/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | -v1_group_1(B) | -m1_group_2(B,c6) | k5_group_4(c6,A) = B | -r1_tarski(A,u1_struct_0(B)) | v1_group_1(f1(c6,A,B)). [resolve(65,c,61,a)].
% 0.73/1.00 Derived: v3_struct_0(c7) | -v3_group_1(c7) | -l1_group_1(c7) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c7))) | -v1_group_1(B) | -m1_group_2(B,c7) | k5_group_4(c7,A) = B | -r1_tarski(A,u1_struct_0(B)) | v1_group_1(f1(c7,A,B)). [resolve(65,c,62,a)].
% 0.73/1.00 66 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v1_group_1(C) | -m1_group_2(C,A) | k5_group_4(A,B) = C | -r1_tarski(B,u1_struct_0(C)) | m1_group_2(f1(A,B,C),A) # label(d5_group_4) # label(axiom). [clausify(7)].
% 0.73/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | -v1_group_1(B) | -m1_group_2(B,c6) | k5_group_4(c6,A) = B | -r1_tarski(A,u1_struct_0(B)) | m1_group_2(f1(c6,A,B),c6). [resolve(66,c,61,a)].
% 0.73/1.00 Derived: v3_struct_0(c7) | -v3_group_1(c7) | -l1_group_1(c7) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c7))) | -v1_group_1(B) | -m1_group_2(B,c7) | k5_group_4(c7,A) = B | -r1_tarski(A,u1_struct_0(B)) | m1_group_2(f1(c7,A,B),c7). [resolve(66,c,62,a)].
% 0.73/1.00 67 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v1_group_1(C) | -m1_group_2(C,A) | k5_group_4(A,B) = C | -r1_tarski(B,u1_struct_0(C)) | -m1_group_2(C,f1(A,B,C)) # label(d5_group_4) # label(axiom). [clausify(7)].
% 0.73/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | -v1_group_1(B) | -m1_group_2(B,c6) | k5_group_4(c6,A) = B | -r1_tarski(A,u1_struct_0(B)) | -m1_group_2(B,f1(c6,A,B)). [resolve(67,c,61,a)].
% 0.73/1.01 Derived: v3_struct_0(c7) | -v3_group_1(c7) | -l1_group_1(c7) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c7))) | -v1_group_1(B) | -m1_group_2(B,c7) | k5_group_4(c7,A) = B | -r1_tarski(A,u1_struct_0(B)) | -m1_group_2(B,f1(c7,A,B)). [resolve(67,c,62,a)].
% 0.73/1.01 68 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v1_group_1(C) | -m1_group_2(C,A) | k5_group_4(A,B) = C | -r1_tarski(B,u1_struct_0(C)) | r1_tarski(B,u1_struct_0(f1(A,B,C))) # label(d5_group_4) # label(axiom). [clausify(7)].
% 0.73/1.01 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | -v1_group_1(B) | -m1_group_2(B,c6) | k5_group_4(c6,A) = B | -r1_tarski(A,u1_struct_0(B)) | r1_tarski(A,u1_struct_0(f1(c6,A,B))). [resolve(68,c,61,a)].
% 0.73/1.01 Derived: v3_struct_0(c7) | -v3_group_1(c7) | -l1_group_1(c7) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c7))) | -v1_group_1(B) | -m1_group_2(B,c7) | k5_group_4(c7,A) = B | -r1_tarski(A,u1_struct_0(B)) | r1_tarski(A,u1_struct_0(f1(c7,A,B))). [resolve(68,c,62,a)].
% 0.73/1.01 69 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v1_group_1(C) | -m1_group_2(C,A) | k5_group_4(A,B) != C | -v1_group_1(D) | -m1_group_2(D,A) | -r1_tarski(B,u1_struct_0(D)) | m1_group_2(C,D) # label(d5_group_4) # label(axiom). [clausify(7)].
% 0.73/1.01 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | -v1_group_1(B) | -m1_group_2(B,c6) | k5_group_4(c6,A) != B | -v1_group_1(C) | -m1_group_2(C,c6) | -r1_tarski(A,u1_struct_0(C)) | m1_group_2(B,C). [resolve(69,c,61,a)].
% 0.73/1.01 Derived: v3_struct_0(c7) | -v3_group_1(c7) | -l1_group_1(c7) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c7))) | -v1_group_1(B) | -m1_group_2(B,c7) | k5_group_4(c7,A) != B | -v1_group_1(C) | -m1_group_2(C,c7) | -r1_tarski(A,u1_struct_0(C)) | m1_group_2(B,C). [resolve(69,c,62,a)].
% 0.73/1.01 70 -m1_relset_1(A,B,C) | -v1_funct_1(A) | -v1_partfun1(A,B,C) | v1_funct_2(A,B,C) # label(cc1_funct_2) # label(axiom). [clausify(3)].
% 0.73/1.01 71 v1_funct_1(c8) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 0.73/1.01 72 v1_funct_1(f6(A,B)) # label(rc1_funct_2) # label(axiom). [clausify(33)].
% 0.73/1.01 73 v1_funct_1(f8(A,B)) # label(rc2_partfun1) # label(axiom). [clausify(36)].
% 0.73/1.01 74 -l1_group_1(A) | v1_funct_1(u1_group_1(A)) # label(dt_u1_group_1) # label(axiom). [clausify(21)].
% 0.73/1.01 Derived: -m1_relset_1(c8,A,B) | -v1_partfun1(c8,A,B) | v1_funct_2(c8,A,B). [resolve(70,b,71,a)].
% 0.73/1.01 Derived: -m1_relset_1(f6(A,B),C,D) | -v1_partfun1(f6(A,B),C,D) | v1_funct_2(f6(A,B),C,D). [resolve(70,b,72,a)].
% 0.73/1.01 Derived: -m1_relset_1(f8(A,B),C,D) | -v1_partfun1(f8(A,B),C,D) | v1_funct_2(f8(A,B),C,D). [resolve(70,b,73,a)].
% 0.73/1.01 Derived: -m1_relset_1(u1_group_1(A),B,C) | -v1_partfun1(u1_group_1(A),B,C) | v1_funct_2(u1_group_1(A),B,C) | -l1_group_1(A). [resolve(70,b,74,b)].
% 0.73/1.01 75 v1_xboole_0(A) | -m1_relset_1(B,C,A) | -v1_funct_1(B) | -v1_funct_2(B,C,A) | v1_partfun1(B,C,A) # label(cc5_funct_2) # label(axiom). [clausify(5)].
% 0.73/1.01 Derived: v1_xboole_0(A) | -m1_relset_1(c8,B,A) | -v1_funct_2(c8,B,A) | v1_partfun1(c8,B,A). [resolve(75,c,71,a)].
% 0.73/1.01 Derived: v1_xboole_0(A) | -m1_relset_1(f6(B,C),D,A) | -v1_funct_2(f6(B,C),D,A) | v1_partfun1(f6(B,C),D,A). [resolve(75,c,72,a)].
% 0.73/1.01 Derived: v1_xboole_0(A) | -m1_relset_1(f8(B,C),D,A) | -v1_funct_2(f8(B,C),D,A) | v1_partfun1(f8(B,C),D,A). [resolve(75,c,73,a)].
% 0.73/1.01 Derived: v1_xboole_0(A) | -m1_relset_1(u1_group_1(B),C,A) | -v1_funct_2(u1_group_1(B),C,A) | v1_partfun1(u1_group_1(B),C,A) | -l1_group_1(B). [resolve(75,c,74,b)].
% 0.73/1.01 76 v1_xboole_0(A) | v1_xboole_0(B) | -m1_relset_1(C,A,B) | -v1_funct_1(C) | -v1_funct_2(C,A,B) | -v1_xboole_0(C) # label(cc6_funct_2) # label(axiom). [clausify(6)].
% 0.73/1.01 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -m1_relset_1(c8,A,B) | -v1_funct_2(c8,A,B) | -v1_xboole_0(c8). [resolve(76,d,71,a)].
% 0.73/1.01 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -m1_relset_1(f6(C,D),A,B) | -v1_funct_2(f6(C,D),A,B) | -v1_xboole_0(f6(C,D)). [resolve(76,d,72,a)].
% 0.73/1.01 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -m1_relset_1(f8(C,D),A,B) | -v1_funct_2(f8(C,D),A,B) | -v1_xboole_0(f8(C,D)). [resolve(76,d,73,a)].
% 0.73/1.01 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -m1_relset_1(u1_group_1(C),A,B) | -v1_funct_2(u1_group_1(C),A,B) | -v1_xboole_0(u1_group_1(C)) | -l1_group_1(C). [resolve(76,d,74,b)].
% 0.73/1.01 77 v1_xboole_0(A) | v1_xboole_0(B) | -m1_relset_1(C,A,B) | -v1_funct_1(C) | -v1_funct_2(C,A,B) | v1_partfun1(C,A,B) # label(cc6_funct_2) # label(axiom). [clausify(6)].
% 0.73/1.01 78 -v1_funct_1(A) | -v1_funct_2(A,k2_zfmisc_1(B,B),B) | -m1_relset_1(A,k2_zfmisc_1(B,B),B) | v1_group_1(g1_group_1(B,A)) # label(dt_g1_group_1) # label(axiom). [clausify(8)].
% 0.73/1.01 Derived: -v1_funct_2(c8,k2_zfmisc_1(A,A),A) | -m1_relset_1(c8,k2_zfmisc_1(A,A),A) | v1_group_1(g1_group_1(A,c8)). [resolve(78,a,71,a)].
% 0.73/1.01 Derived: -v1_funct_2(f6(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f6(A,B),k2_zfmisc_1(C,C),C) | v1_group_1(g1_group_1(C,f6(A,B))). [resolve(78,a,72,a)].
% 0.73/1.01 Derived: -v1_funct_2(f8(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f8(A,B),k2_zfmisc_1(C,C),C) | v1_group_1(g1_group_1(C,f8(A,B))). [resolve(78,a,73,a)].
% 0.73/1.01 Derived: -v1_funct_2(u1_group_1(A),k2_zfmisc_1(B,B),B) | -m1_relset_1(u1_group_1(A),k2_zfmisc_1(B,B),B) | v1_group_1(g1_group_1(B,u1_group_1(A))) | -l1_group_1(A). [resolve(78,a,74,b)].
% 0.73/1.01 79 -v1_funct_1(A) | -v1_funct_2(A,k2_zfmisc_1(B,B),B) | -m1_relset_1(A,k2_zfmisc_1(B,B),B) | l1_group_1(g1_group_1(B,A)) # label(dt_g1_group_1) # label(axiom). [clausify(8)].
% 0.73/1.01 Derived: -v1_funct_2(c8,k2_zfmisc_1(A,A),A) | -m1_relset_1(c8,k2_zfmisc_1(A,A),A) | l1_group_1(g1_group_1(A,c8)). [resolve(79,a,71,a)].
% 0.73/1.01 Derived: -v1_funct_2(f6(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f6(A,B),k2_zfmisc_1(C,C),C) | l1_group_1(g1_group_1(C,f6(A,B))). [resolve(79,a,72,a)].
% 0.73/1.01 Derived: -v1_funct_2(f8(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f8(A,B),k2_zfmisc_1(C,C),C) | l1_group_1(g1_group_1(C,f8(A,B))). [resolve(79,a,73,a)].
% 0.73/1.01 Derived: -v1_funct_2(u1_group_1(A),k2_zfmisc_1(B,B),B) | -m1_relset_1(u1_group_1(A),k2_zfmisc_1(B,B),B) | l1_group_1(g1_group_1(B,u1_group_1(A))) | -l1_group_1(A). [resolve(79,a,74,b)].
% 0.73/1.01 80 -v1_funct_1(A) | -v1_funct_2(A,B,C) | -m1_relset_1(A,B,C) | m1_subset_1(k2_funct_2(B,C,A,D),k1_zfmisc_1(C)) # label(dt_k2_funct_2) # label(axiom). [clausify(11)].
% 0.73/1.01 Derived: -v1_funct_2(c8,A,B) | -m1_relset_1(c8,A,B) | m1_subset_1(k2_funct_2(A,B,c8,C),k1_zfmisc_1(B)). [resolve(80,a,71,a)].
% 0.73/1.01 Derived: -v1_funct_2(f6(A,B),C,D) | -m1_relset_1(f6(A,B),C,D) | m1_subset_1(k2_funct_2(C,D,f6(A,B),E),k1_zfmisc_1(D)). [resolve(80,a,72,a)].
% 0.73/1.01 Derived: -v1_funct_2(f8(A,B),C,D) | -m1_relset_1(f8(A,B),C,D) | m1_subset_1(k2_funct_2(C,D,f8(A,B),E),k1_zfmisc_1(D)). [resolve(80,a,73,a)].
% 0.73/1.01 Derived: -v1_funct_2(u1_group_1(A),B,C) | -m1_relset_1(u1_group_1(A),B,C) | m1_subset_1(k2_funct_2(B,C,u1_group_1(A),D),k1_zfmisc_1(C)) | -l1_group_1(A). [resolve(80,a,74,b)].
% 0.73/1.01 81 -v1_funct_1(A) | -v1_funct_2(A,B,C) | -m1_relset_1(A,B,C) | k9_relat_1(A,D) = k2_funct_2(B,C,A,D) # label(redefinition_k2_funct_2) # label(axiom). [clausify(41)].
% 0.73/1.01 Derived: -v1_funct_2(c8,A,B) | -m1_relset_1(c8,A,B) | k9_relat_1(c8,C) = k2_funct_2(A,B,c8,C). [resolve(81,a,71,a)].
% 0.73/1.01 Derived: -v1_funct_2(f6(A,B),C,D) | -m1_relset_1(f6(A,B),C,D) | k9_relat_1(f6(A,B),E) = k2_funct_2(C,D,f6(A,B),E). [resolve(81,a,72,a)].
% 0.73/1.01 Derived: -v1_funct_2(f8(A,B),C,D) | -m1_relset_1(f8(A,B),C,D) | k9_relat_1(f8(A,B),E) = k2_funct_2(C,D,f8(A,B),E). [resolve(81,a,73,a)].
% 0.73/1.01 Derived: -v1_funct_2(u1_group_1(A),B,C) | -m1_relset_1(u1_group_1(A),B,C) | k9_relat_1(u1_group_1(A),D) = k2_funct_2(B,C,u1_group_1(A),D) | -l1_group_1(A). [resolve(81,a,74,b)].
% 0.73/1.01 82 -v1_funct_1(A) | -v1_funct_2(A,k2_zfmisc_1(B,B),B) | -m1_relset_1(A,k2_zfmisc_1(B,B),B) | g1_group_1(C,D) != g1_group_1(B,A) | C = B # label(free_g1_group_1) # label(axiom). [clausify(32)].
% 0.73/1.01 Derived: -v1_funct_2(c8,k2_zfmisc_1(A,A),A) | -m1_relset_1(c8,k2_zfmisc_1(A,A),A) | g1_group_1(B,C) != g1_group_1(A,c8) | B = A. [resolve(82,a,71,a)].
% 0.73/1.01 Derived: -v1_funct_2(f6(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f6(A,B),k2_zfmisc_1(C,C),C) | g1_group_1(D,E) != g1_group_1(C,f6(A,B)) | D = C. [resolve(82,a,72,a)].
% 0.73/1.01 Derived: -v1_funct_2(f8(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f8(A,B),k2_zfmisc_1(C,C),C) | g1_group_1(D,E) != g1_group_1(C,f8(A,B)) | D = C. [resolve(82,a,73,a)].
% 0.73/1.02 Derived: -v1_funct_2(u1_group_1(A),k2_zfmisc_1(B,B),B) | -m1_relset_1(u1_group_1(A),k2_zfmisc_1(B,B),B) | g1_group_1(C,D) != g1_group_1(B,u1_group_1(A)) | C = B | -l1_group_1(A). [resolve(82,a,74,b)].
% 0.73/1.02 83 -v1_funct_1(A) | -v1_funct_2(A,k2_zfmisc_1(B,B),B) | -m1_relset_1(A,k2_zfmisc_1(B,B),B) | g1_group_1(C,D) != g1_group_1(B,A) | D = A # label(free_g1_group_1) # label(axiom). [clausify(32)].
% 0.73/1.02 Derived: -v1_funct_2(c8,k2_zfmisc_1(A,A),A) | -m1_relset_1(c8,k2_zfmisc_1(A,A),A) | g1_group_1(B,C) != g1_group_1(A,c8) | C = c8. [resolve(83,a,71,a)].
% 0.73/1.02 Derived: -v1_funct_2(f6(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f6(A,B),k2_zfmisc_1(C,C),C) | g1_group_1(D,E) != g1_group_1(C,f6(A,B)) | E = f6(A,B). [resolve(83,a,72,a)].
% 0.73/1.02 Derived: -v1_funct_2(f8(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f8(A,B),k2_zfmisc_1(C,C),C) | g1_group_1(D,E) != g1_group_1(C,f8(A,B)) | E = f8(A,B). [resolve(83,a,73,a)].
% 0.73/1.02 Derived: -v1_funct_2(u1_group_1(A),k2_zfmisc_1(B,B),B) | -m1_relset_1(u1_group_1(A),k2_zfmisc_1(B,B),B) | g1_group_1(C,D) != g1_group_1(B,u1_group_1(A)) | D = u1_group_1(A) | -l1_group_1(A). [resolve(83,a,74,b)].
% 0.73/1.02 84 -v1_relat_1(A) | -r1_tarski(B,C) | r1_tarski(k9_relat_1(A,B),k9_relat_1(A,C)) # label(t156_relat_1) # label(axiom). [clausify(44)].
% 0.73/1.02 85 v1_relat_1(f6(A,B)) # label(rc1_funct_2) # label(axiom). [clausify(33)].
% 0.73/1.02 86 v1_relat_1(f8(A,B)) # label(rc2_partfun1) # label(axiom). [clausify(36)].
% 0.73/1.02 87 -m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) | v1_relat_1(A) # label(cc1_relset_1) # label(axiom). [clausify(4)].
% 0.73/1.02 Derived: -r1_tarski(A,B) | r1_tarski(k9_relat_1(f6(C,D),A),k9_relat_1(f6(C,D),B)). [resolve(84,a,85,a)].
% 0.73/1.02 Derived: -r1_tarski(A,B) | r1_tarski(k9_relat_1(f8(C,D),A),k9_relat_1(f8(C,D),B)). [resolve(84,a,86,a)].
% 0.73/1.02 Derived: -r1_tarski(A,B) | r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) | -m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(D,E))). [resolve(84,a,87,b)].
% 0.73/1.02 88 -m2_relset_1(A,B,C) | m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(42)].
% 0.73/1.02 89 m2_relset_1(f5(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(28)].
% 0.73/1.02 90 m2_relset_1(c8,u1_struct_0(c6),u1_struct_0(c7)) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 0.73/1.02 Derived: m1_relset_1(f5(A,B),A,B). [resolve(88,a,89,a)].
% 0.73/1.02 Derived: m1_relset_1(c8,u1_struct_0(c6),u1_struct_0(c7)). [resolve(88,a,90,a)].
% 0.73/1.02 91 m2_relset_1(A,B,C) | -m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(42)].
% 0.73/1.02 92 -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(20)].
% 0.73/1.02 Derived: m1_subset_1(f5(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))). [resolve(92,a,89,a)].
% 0.73/1.02 Derived: m1_subset_1(c8,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(c6),u1_struct_0(c7)))). [resolve(92,a,90,a)].
% 0.73/1.02 Derived: m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) | -m1_relset_1(A,B,C). [resolve(92,a,91,a)].
% 0.73/1.02 93 -l1_group_1(A) | m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) # label(dt_u1_group_1) # label(axiom). [clausify(21)].
% 0.73/1.02 Derived: -l1_group_1(A) | m1_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)). [resolve(93,b,88,a)].
% 0.73/1.02 Derived: -l1_group_1(A) | m1_subset_1(u1_group_1(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))). [resolve(93,b,92,a)].
% 0.73/1.02
% 0.73/1.02 ============================== end predicate elimination =============
% 0.73/1.02
% 0.73/1.02 Auto_denials: (non-Horn, no changes).
% 0.73/1.02
% 0.73/1.02 Term ordering decisions:
% 0.73/1.02 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. k2_zfmisc_1=1. g1_group_1=1. k5_group_4=1. k9_relat_1=1. f3=1. f5=1. f6=1. f8=1. u1_struct_0=1. k1_zfmisc_1=1. u1_group_1=1. f2=1. f4=1. f7=1. f9=1. f10=1. f1=1. k2_funct_2=1.
% 0.73/1.02
% 0.73/1.02 ============================== end of process initial clauses ========
% 0.73/1.02
% 0.73/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.02
% 0.73/1.02 ============================== end of clauses for search =============
% 1.55/1.85
% 1.55/1.85 ============================== SEARCH ================================
% 1.55/1.85
% 1.55/1.85 % Starting search at 0.04 seconds.
% 1.55/1.85
% 1.55/1.85 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 81 (0.00 of 0.16 sec).
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=86.000, iters=3758
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=67.000, iters=3735
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=55.000, iters=3638
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=49.000, iters=3513
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=46.000, iters=3422
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=39.000, iters=3424
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=38.000, iters=3470
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=36.000, iters=3720
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=34.000, iters=3567
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=31.000, iters=3447
% 1.55/1.85
% 1.55/1.85 Low Water (keep): wt=30.000, iters=3378
% 1.55/1.85
% 1.55/1.85 ============================== PROOF =================================
% 1.55/1.85 % SZS status Theorem
% 1.55/1.85 % SZS output start Refutation
% 1.55/1.85
% 1.55/1.85 % Proof 1 at 0.86 (+ 0.01) seconds.
% 1.55/1.85 % Length of proof is 44.
% 1.55/1.85 % Level of proof is 8.
% 1.55/1.85 % Maximum clause weight is 19.000.
% 1.55/1.85 % Given clauses 2473.
% 1.55/1.85
% 1.55/1.85 4 (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].
% 1.55/1.85 7 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> (C = k5_group_4(A,B) <-> r1_tarski(B,u1_struct_0(C)) & (all D (v1_group_1(D) & m1_group_2(D,A) -> (r1_tarski(B,u1_struct_0(D)) -> m1_group_2(C,D))))))))))) # label(d5_group_4) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.85 13 (all A all B (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_group_1(k5_group_4(A,B)) & m1_group_2(k5_group_4(A,B),A))) # label(dt_k5_group_4) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.85 20 (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].
% 1.55/1.85 41 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) -> k2_funct_2(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.85 42 (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].
% 1.55/1.85 44 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t156_relat_1) # label(axiom) # label(non_clause). [assumption].
% 1.55/1.85 53 -(all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(k5_group_4(A,D)))))))))))) # label(t12_latsubgr) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.55/1.85 60 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | v1_group_1(k5_group_4(A,B)) # label(dt_k5_group_4) # label(axiom). [clausify(13)].
% 1.55/1.85 61 v4_group_1(c6) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 1.55/1.85 63 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | m1_group_2(k5_group_4(A,B),A) # label(dt_k5_group_4) # label(axiom). [clausify(13)].
% 1.55/1.85 64 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) | -v1_group_1(C) | -m1_group_2(C,A) | k5_group_4(A,B) != C | r1_tarski(B,u1_struct_0(C)) # label(d5_group_4) # label(axiom). [clausify(7)].
% 1.55/1.85 71 v1_funct_1(c8) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 1.55/1.85 81 -v1_funct_1(A) | -v1_funct_2(A,B,C) | -m1_relset_1(A,B,C) | k9_relat_1(A,D) = k2_funct_2(B,C,A,D) # label(redefinition_k2_funct_2) # label(axiom). [clausify(41)].
% 1.55/1.85 84 -v1_relat_1(A) | -r1_tarski(B,C) | r1_tarski(k9_relat_1(A,B),k9_relat_1(A,C)) # label(t156_relat_1) # label(axiom). [clausify(44)].
% 1.55/1.85 87 -m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) | v1_relat_1(A) # label(cc1_relset_1) # label(axiom). [clausify(4)].
% 1.55/1.85 88 -m2_relset_1(A,B,C) | m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(42)].
% 1.55/1.85 90 m2_relset_1(c8,u1_struct_0(c6),u1_struct_0(c7)) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 1.55/1.85 92 -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(20)].
% 1.55/1.85 97 v3_group_1(c6) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 1.55/1.85 98 l1_group_1(c6) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 1.55/1.85 105 m1_subset_1(c9,k1_zfmisc_1(u1_struct_0(c6))) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 1.55/1.85 110 v1_funct_2(c8,u1_struct_0(c6),u1_struct_0(c7)) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 1.55/1.85 114 -v3_struct_0(c6) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 1.55/1.85 120 -r1_tarski(k2_funct_2(u1_struct_0(c6),u1_struct_0(c7),c8,c9),k2_funct_2(u1_struct_0(c6),u1_struct_0(c7),c8,u1_struct_0(k5_group_4(c6,c9)))) # label(t12_latsubgr) # label(negated_conjecture). [clausify(53)].
% 1.55/1.85 148 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | v1_group_1(k5_group_4(c6,A)). [resolve(60,c,61,a)].
% 1.55/1.85 149 -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | v1_group_1(k5_group_4(c6,A)). [copy(148),unit_del(a,114),unit_del(b,97),unit_del(c,98)].
% 1.55/1.85 152 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | m1_group_2(k5_group_4(c6,A),c6). [resolve(63,c,61,a)].
% 1.55/1.85 153 -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | m1_group_2(k5_group_4(c6,A),c6). [copy(152),unit_del(a,114),unit_del(b,97),unit_del(c,98)].
% 1.55/1.85 156 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | -v1_group_1(B) | -m1_group_2(B,c6) | k5_group_4(c6,A) != B | r1_tarski(A,u1_struct_0(B)). [resolve(64,c,61,a)].
% 1.55/1.85 157 -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | -v1_group_1(B) | -m1_group_2(B,c6) | k5_group_4(c6,A) != B | r1_tarski(A,u1_struct_0(B)). [copy(156),unit_del(a,114),unit_del(b,97),unit_del(c,98)].
% 1.55/1.85 204 -v1_funct_2(c8,A,B) | -m1_relset_1(c8,A,B) | k9_relat_1(c8,C) = k2_funct_2(A,B,c8,C). [resolve(81,a,71,a)].
% 1.55/1.85 205 -v1_funct_2(c8,A,B) | -m1_relset_1(c8,A,B) | k2_funct_2(A,B,c8,C) = k9_relat_1(c8,C). [copy(204),flip(c)].
% 1.55/1.85 230 -r1_tarski(A,B) | r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) | -m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(D,E))). [resolve(84,a,87,b)].
% 1.55/1.85 232 m1_relset_1(c8,u1_struct_0(c6),u1_struct_0(c7)). [resolve(88,a,90,a)].
% 1.55/1.85 234 m1_subset_1(c8,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(c6),u1_struct_0(c7)))). [resolve(92,a,90,a)].
% 1.55/1.85 269 v1_group_1(k5_group_4(c6,c9)). [resolve(149,a,105,a)].
% 1.55/1.85 274 m1_group_2(k5_group_4(c6,c9),c6). [resolve(153,a,105,a)].
% 1.55/1.85 299 k2_funct_2(u1_struct_0(c6),u1_struct_0(c7),c8,A) = k9_relat_1(c8,A). [resolve(205,a,110,a),unit_del(a,232)].
% 1.55/1.85 301 -r1_tarski(k9_relat_1(c8,c9),k9_relat_1(c8,u1_struct_0(k5_group_4(c6,c9)))). [back_rewrite(120),rewrite([299(7),299(13)])].
% 1.55/1.85 432 -m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c6))) | k5_group_4(c6,c9) != k5_group_4(c6,A) | r1_tarski(A,u1_struct_0(k5_group_4(c6,c9))). [resolve(274,a,157,c),flip(c),unit_del(b,269)].
% 1.55/1.85 2478 r1_tarski(c9,u1_struct_0(k5_group_4(c6,c9))). [resolve(432,a,105,a),xx(a)].
% 1.55/1.85 2482 r1_tarski(k9_relat_1(A,c9),k9_relat_1(A,u1_struct_0(k5_group_4(c6,c9)))) | -m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))). [resolve(2478,a,230,a)].
% 1.55/1.85 7912 $F. [resolve(2482,b,234,a),unit_del(a,301)].
% 1.55/1.85
% 1.55/1.85 % SZS output end Refutation
% 1.55/1.85 ============================== end of proof ==========================
% 1.55/1.85
% 1.55/1.85 ============================== STATISTICS ============================
% 1.55/1.85
% 1.55/1.85 Given=2473. Generated=10759. Kept=7787. proofs=1.
% 1.55/1.85 Usable=2447. Sos=5160. Demods=55. Limbo=29, Disabled=304. Hints=0.
% 1.55/1.85 Megabytes=14.31.
% 1.55/1.85 User_CPU=0.86, System_CPU=0.01, Wall_clock=1.
% 1.55/1.85
% 1.55/1.85 ============================== end of statistics =====================
% 1.55/1.85
% 1.55/1.85 ============================== end of search =========================
% 1.55/1.85
% 1.55/1.85 THEOREM PROVED
% 1.55/1.85 % SZS status Theorem
% 1.55/1.85
% 1.55/1.85 Exiting with 1 proof.
% 1.55/1.85
% 1.55/1.85 Process 28717 exit (max_proofs) Mon Jun 13 11:50:35 2022
% 1.55/1.85 Prover9 interrupted
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