TSTP Solution File: GRP643+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP643+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 11:20:10 EDT 2022
% Result : Theorem 7.95s 8.24s
% Output : Refutation 7.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP643+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 : n008.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 : Mon Jun 13 17:43:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/0.99 ============================== Prover9 ===============================
% 0.70/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.70/0.99 Process 4274 was started by sandbox2 on n008.cluster.edu,
% 0.70/0.99 Mon Jun 13 17:43:23 2022
% 0.70/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4121_n008.cluster.edu".
% 0.70/0.99 ============================== end of head ===========================
% 0.70/0.99
% 0.70/0.99 ============================== INPUT =================================
% 0.70/0.99
% 0.70/0.99 % Reading from file /tmp/Prover9_4121_n008.cluster.edu
% 0.70/0.99
% 0.70/0.99 set(prolog_style_variables).
% 0.70/0.99 set(auto2).
% 0.70/0.99 % set(auto2) -> set(auto).
% 0.70/0.99 % set(auto) -> set(auto_inference).
% 0.70/0.99 % set(auto) -> set(auto_setup).
% 0.70/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.70/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/0.99 % set(auto) -> set(auto_limits).
% 0.70/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/0.99 % set(auto) -> set(auto_denials).
% 0.70/0.99 % set(auto) -> set(auto_process).
% 0.70/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.70/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.70/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.70/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.70/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.70/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.70/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.70/0.99 % set(auto2) -> assign(stats, some).
% 0.70/0.99 % set(auto2) -> clear(echo_input).
% 0.70/0.99 % set(auto2) -> set(quiet).
% 0.70/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.70/0.99 % set(auto2) -> clear(print_given).
% 0.70/0.99 assign(lrs_ticks,-1).
% 0.70/0.99 assign(sos_limit,10000).
% 0.70/0.99 assign(order,kbo).
% 0.70/0.99 set(lex_order_vars).
% 0.70/0.99 clear(print_given).
% 0.70/0.99
% 0.70/0.99 % formulas(sos). % not echoed (55 formulas)
% 0.70/0.99
% 0.70/0.99 ============================== end of input ==========================
% 0.70/0.99
% 0.70/0.99 % From the command line: assign(max_seconds, 300).
% 0.70/0.99
% 0.70/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/0.99
% 0.70/0.99 % Formulas that are not ordinary clauses:
% 0.70/0.99 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].
% 0.70/0.99 2 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 0.70/0.99 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].
% 0.70/0.99 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].
% 0.70/0.99 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].
% 0.70/0.99 7 (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].
% 0.70/0.99 8 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 9 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 10 $T # label(dt_k1_group_3) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 11 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> v1_funct_1(k1_latsubgr(A)) & v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_latsubgr) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 12 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 13 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 14 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 15 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 16 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 0.70/0.99 18 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 19 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 0.70/0.99 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].
% 0.70/0.99 22 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 23 (exists A l1_group_1(A)) # label(existence_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 24 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 0.70/0.99 26 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 27 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 28 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 29 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> -v1_xboole_0(k1_group_3(A)))) # label(fc1_group_3) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 30 (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].
% 0.70/0.99 31 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 32 (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].
% 0.70/0.99 33 (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].
% 0.70/0.99 34 (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].
% 0.70/0.99 35 (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].
% 0.70/0.99 36 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 37 (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].
% 0.70/0.99 38 (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].
% 0.70/0.99 39 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 40 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 41 (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].
% 0.70/0.99 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].
% 0.70/0.99 43 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 44 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) <-> r1_rlvect_1(B,C)))))))) # label(t18_latsubgr) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 45 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 0.70/0.99 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].
% 0.70/0.99 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].
% 0.70/0.99 49 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (r1_rlvect_1(D,B) & r1_rlvect_1(D,C) -> r1_rlvect_1(D,k1_group_1(A,B,C))))))))))) # label(t59_group_2) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 50 (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].
% 0.70/0.99 51 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 52 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 53 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 54 -(all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(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,k1_funct_1(k1_latsubgr(A),B)) & r2_hidden(D,k1_funct_1(k1_latsubgr(A),B)) -> r2_hidden(k1_group_1(A,C,D),k1_funct_1(k1_latsubgr(A),B))))))))))) # label(t21_latsubgr) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.70/0.99
% 0.70/0.99 ============================== end of process non-clausal formulas ===
% 0.70/0.99
% 0.70/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/0.99
% 0.70/0.99 ============================== PREDICATE ELIMINATION =================
% 0.70/0.99 55 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(30)].
% 0.70/0.99 56 l1_struct_0(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(24)].
% 0.70/0.99 57 l1_struct_0(c5) # label(rc3_struct_0) # label(axiom). [clausify(40)].
% 0.70/0.99 58 -l1_group_1(A) | l1_struct_0(A) # label(dt_l1_group_1) # label(axiom). [clausify(15)].
% 0.70/0.99 Derived: v3_struct_0(c2) | -v1_xboole_0(u1_struct_0(c2)). [resolve(55,b,56,a)].
% 0.70/0.99 Derived: v3_struct_0(c5) | -v1_xboole_0(u1_struct_0(c5)). [resolve(55,b,57,a)].
% 0.70/0.99 Derived: v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_group_1(A). [resolve(55,b,58,b)].
% 0.70/0.99 59 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(f9(A)) # label(rc5_struct_0) # label(axiom). [clausify(41)].
% 0.70/0.99 Derived: v3_struct_0(c2) | -v1_xboole_0(f9(c2)). [resolve(59,b,56,a)].
% 0.70/0.99 Derived: v3_struct_0(c5) | -v1_xboole_0(f9(c5)). [resolve(59,b,57,a)].
% 0.70/0.99 Derived: v3_struct_0(A) | -v1_xboole_0(f9(A)) | -l1_group_1(A). [resolve(59,b,58,b)].
% 0.70/0.99 60 v3_struct_0(A) | -l1_struct_0(A) | m1_subset_1(f9(A),k1_zfmisc_1(u1_struct_0(A))) # label(rc5_struct_0) # label(axiom). [clausify(41)].
% 0.70/0.99 Derived: v3_struct_0(c2) | m1_subset_1(f9(c2),k1_zfmisc_1(u1_struct_0(c2))). [resolve(60,b,56,a)].
% 0.70/1.00 Derived: v3_struct_0(c5) | m1_subset_1(f9(c5),k1_zfmisc_1(u1_struct_0(c5))). [resolve(60,b,57,a)].
% 0.70/1.00 Derived: v3_struct_0(A) | m1_subset_1(f9(A),k1_zfmisc_1(u1_struct_0(A))) | -l1_group_1(A). [resolve(60,b,58,b)].
% 0.70/1.00 61 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | v1_funct_1(k1_latsubgr(A)) # label(dt_k1_latsubgr) # label(axiom). [clausify(11)].
% 0.70/1.00 62 v4_group_1(c6) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | v1_funct_1(k1_latsubgr(c6)). [resolve(61,c,62,a)].
% 0.70/1.00 63 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_xboole_0(k1_group_3(A)) # label(fc1_group_3) # label(axiom). [clausify(29)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_xboole_0(k1_group_3(c6)). [resolve(63,c,62,a)].
% 0.70/1.00 64 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) # label(dt_k1_latsubgr) # label(axiom). [clausify(11)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | v1_funct_2(k1_latsubgr(c6),k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))). [resolve(64,c,62,a)].
% 0.70/1.00 65 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) # label(dt_k1_latsubgr) # label(axiom). [clausify(11)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | m2_relset_1(k1_latsubgr(c6),k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))). [resolve(65,c,62,a)].
% 0.70/1.00 66 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_group_1(B) | -m1_group_2(B,A) | -m1_subset_1(C,u1_struct_0(A)) | -r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) | r1_rlvect_1(B,C) # label(t18_latsubgr) # label(axiom). [clausify(44)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_group_1(A) | -m1_group_2(A,c6) | -m1_subset_1(B,u1_struct_0(c6)) | -r2_hidden(B,k1_funct_1(k1_latsubgr(c6),A)) | r1_rlvect_1(A,B). [resolve(66,c,62,a)].
% 0.70/1.00 67 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_group_1(B) | -m1_group_2(B,A) | -m1_subset_1(C,u1_struct_0(A)) | r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) | -r1_rlvect_1(B,C) # label(t18_latsubgr) # label(axiom). [clausify(44)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_group_1(A) | -m1_group_2(A,c6) | -m1_subset_1(B,u1_struct_0(c6)) | r2_hidden(B,k1_funct_1(k1_latsubgr(c6),A)) | -r1_rlvect_1(A,B). [resolve(67,c,62,a)].
% 0.70/1.00 68 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | -m1_group_2(D,A) | -r1_rlvect_1(D,B) | -r1_rlvect_1(D,C) | r1_rlvect_1(D,k1_group_1(A,B,C)) # label(t59_group_2) # label(axiom). [clausify(49)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,u1_struct_0(c6)) | -m1_subset_1(B,u1_struct_0(c6)) | -m1_group_2(C,c6) | -r1_rlvect_1(C,A) | -r1_rlvect_1(C,B) | r1_rlvect_1(C,k1_group_1(c6,A,B)). [resolve(68,c,62,a)].
% 0.70/1.00 69 -l1_group_1(A) | -v1_group_1(A) | g1_group_1(u1_struct_0(A),u1_group_1(A)) = A # label(abstractness_v1_group_1) # label(axiom). [clausify(1)].
% 0.70/1.00 70 v1_group_1(c7) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.70/1.00 Derived: -l1_group_1(c7) | g1_group_1(u1_struct_0(c7),u1_group_1(c7)) = c7. [resolve(69,b,70,a)].
% 0.70/1.00 71 -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(7)].
% 0.70/1.00 Derived: -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)) | g1_group_1(u1_struct_0(g1_group_1(B,A)),u1_group_1(g1_group_1(B,A))) = g1_group_1(B,A). [resolve(71,d,69,b)].
% 0.70/1.00 72 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_group_1(A) | -m1_group_2(A,c6) | -m1_subset_1(B,u1_struct_0(c6)) | -r2_hidden(B,k1_funct_1(k1_latsubgr(c6),A)) | r1_rlvect_1(A,B). [resolve(66,c,62,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(c7,c6) | -m1_subset_1(A,u1_struct_0(c6)) | -r2_hidden(A,k1_funct_1(k1_latsubgr(c6),c7)) | r1_rlvect_1(c7,A). [resolve(72,d,70,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,B),c6) | -m1_subset_1(C,u1_struct_0(c6)) | -r2_hidden(C,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,B))) | r1_rlvect_1(g1_group_1(A,B),C) | -v1_funct_1(B) | -v1_funct_2(B,k2_zfmisc_1(A,A),A) | -m1_relset_1(B,k2_zfmisc_1(A,A),A). [resolve(72,d,71,d)].
% 0.70/1.00 73 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_group_1(A) | -m1_group_2(A,c6) | -m1_subset_1(B,u1_struct_0(c6)) | r2_hidden(B,k1_funct_1(k1_latsubgr(c6),A)) | -r1_rlvect_1(A,B). [resolve(67,c,62,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(c7,c6) | -m1_subset_1(A,u1_struct_0(c6)) | r2_hidden(A,k1_funct_1(k1_latsubgr(c6),c7)) | -r1_rlvect_1(c7,A). [resolve(73,d,70,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,B),c6) | -m1_subset_1(C,u1_struct_0(c6)) | r2_hidden(C,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,B))) | -r1_rlvect_1(g1_group_1(A,B),C) | -v1_funct_1(B) | -v1_funct_2(B,k2_zfmisc_1(A,A),A) | -m1_relset_1(B,k2_zfmisc_1(A,A),A). [resolve(73,d,71,d)].
% 0.70/1.00 74 m1_subset_1(A,k1_zfmisc_1(B)) | -r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(47)].
% 0.70/1.00 75 r1_tarski(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(43)].
% 0.70/1.00 76 -m1_subset_1(A,k1_zfmisc_1(B)) | r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(47)].
% 0.70/1.00 Derived: m1_subset_1(A,k1_zfmisc_1(A)). [resolve(74,b,75,a)].
% 0.70/1.00 77 -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)].
% 0.70/1.00 78 v1_funct_1(f5(A,B)) # label(rc1_funct_2) # label(axiom). [clausify(34)].
% 0.70/1.00 79 v1_funct_1(f7(A,B)) # label(rc2_partfun1) # label(axiom). [clausify(37)].
% 0.70/1.00 80 -l1_group_1(A) | v1_funct_1(u1_group_1(A)) # label(dt_u1_group_1) # label(axiom). [clausify(21)].
% 0.70/1.00 Derived: -m1_relset_1(f5(A,B),C,D) | -v1_partfun1(f5(A,B),C,D) | v1_funct_2(f5(A,B),C,D). [resolve(77,b,78,a)].
% 0.70/1.00 Derived: -m1_relset_1(f7(A,B),C,D) | -v1_partfun1(f7(A,B),C,D) | v1_funct_2(f7(A,B),C,D). [resolve(77,b,79,a)].
% 0.70/1.00 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(77,b,80,b)].
% 0.70/1.00 81 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)].
% 0.70/1.00 Derived: v1_xboole_0(A) | -m1_relset_1(f5(B,C),D,A) | -v1_funct_2(f5(B,C),D,A) | v1_partfun1(f5(B,C),D,A). [resolve(81,c,78,a)].
% 0.70/1.00 Derived: v1_xboole_0(A) | -m1_relset_1(f7(B,C),D,A) | -v1_funct_2(f7(B,C),D,A) | v1_partfun1(f7(B,C),D,A). [resolve(81,c,79,a)].
% 0.70/1.00 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(81,c,80,b)].
% 0.70/1.00 82 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)].
% 0.70/1.00 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -m1_relset_1(f5(C,D),A,B) | -v1_funct_2(f5(C,D),A,B) | -v1_xboole_0(f5(C,D)). [resolve(82,d,78,a)].
% 0.70/1.00 Derived: v1_xboole_0(A) | v1_xboole_0(B) | -m1_relset_1(f7(C,D),A,B) | -v1_funct_2(f7(C,D),A,B) | -v1_xboole_0(f7(C,D)). [resolve(82,d,79,a)].
% 0.70/1.00 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(82,d,80,b)].
% 0.70/1.00 83 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)].
% 0.70/1.00 84 -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(7)].
% 0.70/1.00 Derived: -v1_funct_2(f5(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f5(A,B),k2_zfmisc_1(C,C),C) | l1_group_1(g1_group_1(C,f5(A,B))). [resolve(84,a,78,a)].
% 0.70/1.00 Derived: -v1_funct_2(f7(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f7(A,B),k2_zfmisc_1(C,C),C) | l1_group_1(g1_group_1(C,f7(A,B))). [resolve(84,a,79,a)].
% 0.70/1.00 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(84,a,80,b)].
% 0.70/1.00 85 -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(33)].
% 0.70/1.00 Derived: -v1_funct_2(f5(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f5(A,B),k2_zfmisc_1(C,C),C) | g1_group_1(D,E) != g1_group_1(C,f5(A,B)) | D = C. [resolve(85,a,78,a)].
% 0.70/1.00 Derived: -v1_funct_2(f7(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f7(A,B),k2_zfmisc_1(C,C),C) | g1_group_1(D,E) != g1_group_1(C,f7(A,B)) | D = C. [resolve(85,a,79,a)].
% 0.70/1.00 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(85,a,80,b)].
% 0.70/1.00 86 -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(33)].
% 0.70/1.00 Derived: -v1_funct_2(f5(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f5(A,B),k2_zfmisc_1(C,C),C) | g1_group_1(D,E) != g1_group_1(C,f5(A,B)) | E = f5(A,B). [resolve(86,a,78,a)].
% 0.70/1.00 Derived: -v1_funct_2(f7(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f7(A,B),k2_zfmisc_1(C,C),C) | g1_group_1(D,E) != g1_group_1(C,f7(A,B)) | E = f7(A,B). [resolve(86,a,79,a)].
% 0.70/1.00 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(86,a,80,b)].
% 0.70/1.00 87 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | v1_funct_1(k1_latsubgr(c6)). [resolve(61,c,62,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_relset_1(k1_latsubgr(c6),A,B) | -v1_partfun1(k1_latsubgr(c6),A,B) | v1_funct_2(k1_latsubgr(c6),A,B). [resolve(87,d,77,b)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | v1_xboole_0(A) | -m1_relset_1(k1_latsubgr(c6),B,A) | -v1_funct_2(k1_latsubgr(c6),B,A) | v1_partfun1(k1_latsubgr(c6),B,A). [resolve(87,d,81,c)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | v1_xboole_0(A) | v1_xboole_0(B) | -m1_relset_1(k1_latsubgr(c6),A,B) | -v1_funct_2(k1_latsubgr(c6),A,B) | -v1_xboole_0(k1_latsubgr(c6)). [resolve(87,d,82,d)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_2(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | -m1_relset_1(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | l1_group_1(g1_group_1(A,k1_latsubgr(c6))). [resolve(87,d,84,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_2(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | -m1_relset_1(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | g1_group_1(B,C) != g1_group_1(A,k1_latsubgr(c6)) | B = A. [resolve(87,d,85,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_2(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | -m1_relset_1(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | g1_group_1(B,C) != g1_group_1(A,k1_latsubgr(c6)) | C = k1_latsubgr(c6). [resolve(87,d,86,a)].
% 0.70/1.00 88 -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)) | g1_group_1(u1_struct_0(g1_group_1(B,A)),u1_group_1(g1_group_1(B,A))) = g1_group_1(B,A). [resolve(71,d,69,b)].
% 0.70/1.00 Derived: -v1_funct_2(f5(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f5(A,B),k2_zfmisc_1(C,C),C) | -l1_group_1(g1_group_1(C,f5(A,B))) | g1_group_1(u1_struct_0(g1_group_1(C,f5(A,B))),u1_group_1(g1_group_1(C,f5(A,B)))) = g1_group_1(C,f5(A,B)). [resolve(88,a,78,a)].
% 0.70/1.00 Derived: -v1_funct_2(f7(A,B),k2_zfmisc_1(C,C),C) | -m1_relset_1(f7(A,B),k2_zfmisc_1(C,C),C) | -l1_group_1(g1_group_1(C,f7(A,B))) | g1_group_1(u1_struct_0(g1_group_1(C,f7(A,B))),u1_group_1(g1_group_1(C,f7(A,B)))) = g1_group_1(C,f7(A,B)). [resolve(88,a,79,a)].
% 0.70/1.00 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))) | g1_group_1(u1_struct_0(g1_group_1(B,u1_group_1(A))),u1_group_1(g1_group_1(B,u1_group_1(A)))) = g1_group_1(B,u1_group_1(A)) | -l1_group_1(A). [resolve(88,a,80,b)].
% 0.70/1.00 Derived: -v1_funct_2(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | -m1_relset_1(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | -l1_group_1(g1_group_1(A,k1_latsubgr(c6))) | g1_group_1(u1_struct_0(g1_group_1(A,k1_latsubgr(c6))),u1_group_1(g1_group_1(A,k1_latsubgr(c6)))) = g1_group_1(A,k1_latsubgr(c6)) | v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6). [resolve(88,a,87,d)].
% 0.70/1.00 89 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,B),c6) | -m1_subset_1(C,u1_struct_0(c6)) | -r2_hidden(C,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,B))) | r1_rlvect_1(g1_group_1(A,B),C) | -v1_funct_1(B) | -v1_funct_2(B,k2_zfmisc_1(A,A),A) | -m1_relset_1(B,k2_zfmisc_1(A,A),A). [resolve(72,d,71,d)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,f5(B,C)),c6) | -m1_subset_1(D,u1_struct_0(c6)) | -r2_hidden(D,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,f5(B,C)))) | r1_rlvect_1(g1_group_1(A,f5(B,C)),D) | -v1_funct_2(f5(B,C),k2_zfmisc_1(A,A),A) | -m1_relset_1(f5(B,C),k2_zfmisc_1(A,A),A). [resolve(89,h,78,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,f7(B,C)),c6) | -m1_subset_1(D,u1_struct_0(c6)) | -r2_hidden(D,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,f7(B,C)))) | r1_rlvect_1(g1_group_1(A,f7(B,C)),D) | -v1_funct_2(f7(B,C),k2_zfmisc_1(A,A),A) | -m1_relset_1(f7(B,C),k2_zfmisc_1(A,A),A). [resolve(89,h,79,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,u1_group_1(B)),c6) | -m1_subset_1(C,u1_struct_0(c6)) | -r2_hidden(C,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,u1_group_1(B)))) | r1_rlvect_1(g1_group_1(A,u1_group_1(B)),C) | -v1_funct_2(u1_group_1(B),k2_zfmisc_1(A,A),A) | -m1_relset_1(u1_group_1(B),k2_zfmisc_1(A,A),A) | -l1_group_1(B). [resolve(89,h,80,b)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,k1_latsubgr(c6)),c6) | -m1_subset_1(B,u1_struct_0(c6)) | -r2_hidden(B,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,k1_latsubgr(c6)))) | r1_rlvect_1(g1_group_1(A,k1_latsubgr(c6)),B) | -v1_funct_2(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | -m1_relset_1(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6). [resolve(89,h,87,d)].
% 0.70/1.00 90 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,B),c6) | -m1_subset_1(C,u1_struct_0(c6)) | r2_hidden(C,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,B))) | -r1_rlvect_1(g1_group_1(A,B),C) | -v1_funct_1(B) | -v1_funct_2(B,k2_zfmisc_1(A,A),A) | -m1_relset_1(B,k2_zfmisc_1(A,A),A). [resolve(73,d,71,d)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,f5(B,C)),c6) | -m1_subset_1(D,u1_struct_0(c6)) | r2_hidden(D,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,f5(B,C)))) | -r1_rlvect_1(g1_group_1(A,f5(B,C)),D) | -v1_funct_2(f5(B,C),k2_zfmisc_1(A,A),A) | -m1_relset_1(f5(B,C),k2_zfmisc_1(A,A),A). [resolve(90,h,78,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,f7(B,C)),c6) | -m1_subset_1(D,u1_struct_0(c6)) | r2_hidden(D,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,f7(B,C)))) | -r1_rlvect_1(g1_group_1(A,f7(B,C)),D) | -v1_funct_2(f7(B,C),k2_zfmisc_1(A,A),A) | -m1_relset_1(f7(B,C),k2_zfmisc_1(A,A),A). [resolve(90,h,79,a)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,u1_group_1(B)),c6) | -m1_subset_1(C,u1_struct_0(c6)) | r2_hidden(C,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,u1_group_1(B)))) | -r1_rlvect_1(g1_group_1(A,u1_group_1(B)),C) | -v1_funct_2(u1_group_1(B),k2_zfmisc_1(A,A),A) | -m1_relset_1(u1_group_1(B),k2_zfmisc_1(A,A),A) | -l1_group_1(B). [resolve(90,h,80,b)].
% 0.70/1.00 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(g1_group_1(A,k1_latsubgr(c6)),c6) | -m1_subset_1(B,u1_struct_0(c6)) | r2_hidden(B,k1_funct_1(k1_latsubgr(c6),g1_group_1(A,k1_latsubgr(c6)))) | -r1_rlvect_1(g1_group_1(A,k1_latsubgr(c6)),B) | -v1_funct_2(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | -m1_relset_1(k1_latsubgr(c6),k2_zfmisc_1(A,A),A) | v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6). [resolve(90,h,87,d)].
% 7.95/8.24 91 -m2_relset_1(A,B,C) | m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(42)].
% 7.95/8.24 92 m2_relset_1(f4(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(28)].
% 7.95/8.24 Derived: m1_relset_1(f4(A,B),A,B). [resolve(91,a,92,a)].
% 7.95/8.24 93 m2_relset_1(A,B,C) | -m1_relset_1(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(42)].
% 7.95/8.24 94 -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)].
% 7.95/8.24 Derived: m1_subset_1(f4(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))). [resolve(94,a,92,a)].
% 7.95/8.24 Derived: m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) | -m1_relset_1(A,B,C). [resolve(94,a,93,a)].
% 7.95/8.24 95 -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)].
% 7.95/8.24 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(95,b,91,a)].
% 7.95/8.24 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(95,b,94,a)].
% 7.95/8.24 96 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | m2_relset_1(k1_latsubgr(c6),k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))). [resolve(65,c,62,a)].
% 7.95/8.24 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | m1_relset_1(k1_latsubgr(c6),k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))). [resolve(96,d,91,a)].
% 7.95/8.24 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | m1_subset_1(k1_latsubgr(c6),k1_zfmisc_1(k2_zfmisc_1(k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))))). [resolve(96,d,94,a)].
% 7.95/8.24
% 7.95/8.24 ============================== end predicate elimination =============
% 7.95/8.24
% 7.95/8.24 Auto_denials: (non-Horn, no changes).
% 7.95/8.24
% 7.95/8.24 Term ordering decisions:
% 7.95/8.24 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. g1_group_1=1. k2_zfmisc_1=1. k1_funct_1=1. f2=1. f4=1. f5=1. f7=1. k1_latsubgr=1. u1_group_1=1. u1_struct_0=1. k1_zfmisc_1=1. k1_group_3=1. f1=1. f3=1. f6=1. f8=1. f9=1. k1_group_1=1.
% 7.95/8.24
% 7.95/8.24 ============================== end of process initial clauses ========
% 7.95/8.24
% 7.95/8.24 ============================== CLAUSES FOR SEARCH ====================
% 7.95/8.24
% 7.95/8.24 ============================== end of clauses for search =============
% 7.95/8.24
% 7.95/8.24 ============================== SEARCH ================================
% 7.95/8.24
% 7.95/8.24 % Starting search at 0.03 seconds.
% 7.95/8.24
% 7.95/8.24 Low Water (keep): wt=11.000, iters=3763
% 7.95/8.24
% 7.95/8.24 Low Water (keep): wt=9.000, iters=3504
% 7.95/8.24
% 7.95/8.24 Low Water (keep): wt=8.000, iters=3344
% 7.95/8.24
% 7.95/8.24 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 516 (0.00 of 1.59 sec).
% 7.95/8.24
% 7.95/8.24 ============================== PROOF =================================
% 7.95/8.24 % SZS status Theorem
% 7.95/8.24 % SZS output start Refutation
% 7.95/8.24
% 7.95/8.24 % Proof 1 at 7.09 (+ 0.17) seconds.
% 7.95/8.24 % Length of proof is 34.
% 7.95/8.24 % Level of proof is 7.
% 7.95/8.24 % Maximum clause weight is 23.000.
% 7.95/8.24 % Given clauses 843.
% 7.95/8.24
% 7.95/8.24 9 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k1_group_1) # label(axiom) # label(non_clause). [assumption].
% 7.95/8.24 44 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) <-> r1_rlvect_1(B,C)))))))) # label(t18_latsubgr) # label(axiom) # label(non_clause). [assumption].
% 7.95/8.24 49 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (r1_rlvect_1(D,B) & r1_rlvect_1(D,C) -> r1_rlvect_1(D,k1_group_1(A,B,C))))))))))) # label(t59_group_2) # label(axiom) # label(non_clause). [assumption].
% 7.95/8.24 54 -(all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(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,k1_funct_1(k1_latsubgr(A),B)) & r2_hidden(D,k1_funct_1(k1_latsubgr(A),B)) -> r2_hidden(k1_group_1(A,C,D),k1_funct_1(k1_latsubgr(A),B))))))))))) # label(t21_latsubgr) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.95/8.24 62 v4_group_1(c6) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 66 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_group_1(B) | -m1_group_2(B,A) | -m1_subset_1(C,u1_struct_0(A)) | -r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) | r1_rlvect_1(B,C) # label(t18_latsubgr) # label(axiom). [clausify(44)].
% 7.95/8.24 67 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_group_1(B) | -m1_group_2(B,A) | -m1_subset_1(C,u1_struct_0(A)) | r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) | -r1_rlvect_1(B,C) # label(t18_latsubgr) # label(axiom). [clausify(44)].
% 7.95/8.24 68 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | -m1_group_2(D,A) | -r1_rlvect_1(D,B) | -r1_rlvect_1(D,C) | r1_rlvect_1(D,k1_group_1(A,B,C)) # label(t59_group_2) # label(axiom). [clausify(49)].
% 7.95/8.24 70 v1_group_1(c7) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 72 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_group_1(A) | -m1_group_2(A,c6) | -m1_subset_1(B,u1_struct_0(c6)) | -r2_hidden(B,k1_funct_1(k1_latsubgr(c6),A)) | r1_rlvect_1(A,B). [resolve(66,c,62,a)].
% 7.95/8.24 73 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_group_1(A) | -m1_group_2(A,c6) | -m1_subset_1(B,u1_struct_0(c6)) | r2_hidden(B,k1_funct_1(k1_latsubgr(c6),A)) | -r1_rlvect_1(A,B). [resolve(67,c,62,a)].
% 7.95/8.24 100 v3_group_1(c6) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 101 l1_group_1(c6) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 103 m1_group_2(c7,c6) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 105 m1_subset_1(c8,u1_struct_0(c6)) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 106 m1_subset_1(c9,u1_struct_0(c6)) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 112 r2_hidden(c8,k1_funct_1(k1_latsubgr(c6),c7)) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 113 r2_hidden(c9,k1_funct_1(k1_latsubgr(c6),c7)) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 117 -v3_struct_0(c6) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 122 -r2_hidden(k1_group_1(c6,c8,c9),k1_funct_1(k1_latsubgr(c6),c7)) # label(t21_latsubgr) # label(negated_conjecture). [clausify(54)].
% 7.95/8.24 135 v3_struct_0(A) | -l1_group_1(A) | -m1_subset_1(B,u1_struct_0(A)) | -m1_subset_1(C,u1_struct_0(A)) | m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) # label(dt_k1_group_1) # label(axiom). [clausify(9)].
% 7.95/8.24 152 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_subset_1(A,u1_struct_0(c6)) | -m1_subset_1(B,u1_struct_0(c6)) | -m1_group_2(C,c6) | -r1_rlvect_1(C,A) | -r1_rlvect_1(C,B) | r1_rlvect_1(C,k1_group_1(c6,A,B)). [resolve(68,c,62,a)].
% 7.95/8.24 153 -m1_subset_1(A,u1_struct_0(c6)) | -m1_subset_1(B,u1_struct_0(c6)) | -m1_group_2(C,c6) | -r1_rlvect_1(C,A) | -r1_rlvect_1(C,B) | r1_rlvect_1(C,k1_group_1(c6,A,B)). [copy(152),unit_del(a,117),unit_del(b,100),unit_del(c,101)].
% 7.95/8.24 155 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(c7,c6) | -m1_subset_1(A,u1_struct_0(c6)) | -r2_hidden(A,k1_funct_1(k1_latsubgr(c6),c7)) | r1_rlvect_1(c7,A). [resolve(72,d,70,a)].
% 7.95/8.24 156 -m1_subset_1(A,u1_struct_0(c6)) | -r2_hidden(A,k1_funct_1(k1_latsubgr(c6),c7)) | r1_rlvect_1(c7,A). [copy(155),unit_del(a,117),unit_del(b,100),unit_del(c,101),unit_del(d,103)].
% 7.95/8.24 157 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(c7,c6) | -m1_subset_1(A,u1_struct_0(c6)) | r2_hidden(A,k1_funct_1(k1_latsubgr(c6),c7)) | -r1_rlvect_1(c7,A). [resolve(73,d,70,a)].
% 7.95/8.24 158 -m1_subset_1(A,u1_struct_0(c6)) | r2_hidden(A,k1_funct_1(k1_latsubgr(c6),c7)) | -r1_rlvect_1(c7,A). [copy(157),unit_del(a,117),unit_del(b,100),unit_del(c,101),unit_del(d,103)].
% 7.95/8.24 272 -m1_subset_1(A,u1_struct_0(c6)) | m1_subset_1(k1_group_1(c6,c8,A),u1_struct_0(c6)). [resolve(135,c,105,a),unit_del(a,117),unit_del(b,101)].
% 7.95/8.24 309 r1_rlvect_1(c7,c9). [resolve(156,b,113,a),unit_del(a,106)].
% 7.95/8.24 310 r1_rlvect_1(c7,c8). [resolve(156,b,112,a),unit_del(a,105)].
% 7.95/8.24 458 -m1_subset_1(A,u1_struct_0(c6)) | -r1_rlvect_1(c7,A) | r1_rlvect_1(c7,k1_group_1(c6,A,c9)). [resolve(309,a,153,e),unit_del(b,106),unit_del(c,103)].
% 7.95/8.24 4445 m1_subset_1(k1_group_1(c6,c8,c9),u1_struct_0(c6)). [resolve(272,a,106,a)].
% 7.95/8.24 4601 -r1_rlvect_1(c7,k1_group_1(c6,c8,c9)). [ur(158,a,4445,a,b,122,a)].
% 7.95/8.24 6647 $F. [resolve(458,b,310,a),unit_del(a,105),unit_del(b,4601)].
% 7.95/8.24
% 7.95/8.24 % SZS output end Refutation
% 7.95/8.24 ============================== end of proof ==========================
% 7.95/8.24
% 7.95/8.24 ============================== STATISTICS ============================
% 7.95/8.24
% 7.95/8.24 Given=843. Generated=328361. Kept=6519. proofs=1.
% 7.95/8.24 Usable=835. Sos=5643. Demods=9. Limbo=4, Disabled=180. Hints=0.
% 7.95/8.24 Megabytes=4.38.
% 7.95/8.24 User_CPU=7.09, System_CPU=0.17, Wall_clock=7.
% 7.95/8.24
% 7.95/8.24 ============================== end of statistics =====================
% 7.95/8.24
% 7.95/8.24 ============================== end of search =========================
% 7.95/8.24
% 7.95/8.24 THEOREM PROVED
% 7.95/8.24 % SZS status Theorem
% 7.95/8.24
% 7.95/8.24 Exiting with 1 proof.
% 7.95/8.24
% 7.95/8.24 Process 4274 exit (max_proofs) Mon Jun 13 17:43:30 2022
% 7.95/8.24 Prover9 interrupted
%------------------------------------------------------------------------------