TSTP Solution File: GRP642+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:20:09 EDT 2022
% Result : Theorem 0.76s 1.06s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 16:18:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.44/1.03 ============================== Prover9 ===============================
% 0.44/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.03 Process 32104 was started by sandbox on n011.cluster.edu,
% 0.44/1.03 Mon Jun 13 16:18:49 2022
% 0.44/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31947_n011.cluster.edu".
% 0.44/1.03 ============================== end of head ===========================
% 0.44/1.03
% 0.44/1.03 ============================== INPUT =================================
% 0.44/1.03
% 0.44/1.03 % Reading from file /tmp/Prover9_31947_n011.cluster.edu
% 0.44/1.03
% 0.44/1.03 set(prolog_style_variables).
% 0.44/1.03 set(auto2).
% 0.44/1.03 % set(auto2) -> set(auto).
% 0.44/1.03 % set(auto) -> set(auto_inference).
% 0.44/1.03 % set(auto) -> set(auto_setup).
% 0.44/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.03 % set(auto) -> set(auto_limits).
% 0.44/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.03 % set(auto) -> set(auto_denials).
% 0.44/1.03 % set(auto) -> set(auto_process).
% 0.44/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.03 % set(auto2) -> assign(stats, some).
% 0.44/1.03 % set(auto2) -> clear(echo_input).
% 0.44/1.03 % set(auto2) -> set(quiet).
% 0.44/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.03 % set(auto2) -> clear(print_given).
% 0.44/1.03 assign(lrs_ticks,-1).
% 0.44/1.03 assign(sos_limit,10000).
% 0.44/1.03 assign(order,kbo).
% 0.44/1.03 set(lex_order_vars).
% 0.44/1.03 clear(print_given).
% 0.44/1.03
% 0.44/1.03 % formulas(sos). % not echoed (53 formulas)
% 0.44/1.03
% 0.44/1.03 ============================== end of input ==========================
% 0.44/1.03
% 0.44/1.03 % From the command line: assign(max_seconds, 300).
% 0.44/1.03
% 0.44/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.03
% 0.44/1.03 % Formulas that are not ordinary clauses:
% 0.44/1.03 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].
% 0.44/1.03 2 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 7 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) -> (B = k1_latsubgr(A) <-> (all C (v1_group_1(C) & m1_group_2(C,A) -> k1_funct_1(B,C) = u1_struct_0(C)))))))) # label(d1_latsubgr) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 9 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 10 $T # label(dt_k1_group_3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 12 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 13 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 14 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 15 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 16 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 18 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 19 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 22 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 23 (exists A l1_group_1(A)) # label(existence_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 24 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 26 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 27 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 28 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 31 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 36 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 39 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 40 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 43 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 44 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 45 (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].
% 0.44/1.03 46 (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].
% 0.44/1.03 47 (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].
% 0.44/1.03 48 (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].
% 0.44/1.03 49 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 50 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 51 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 52 -(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) -> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0)))) # label(t20_latsubgr) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.03
% 0.44/1.03 ============================== end of process non-clausal formulas ===
% 0.44/1.03
% 0.44/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.03
% 0.44/1.03 ============================== PREDICATE ELIMINATION =================
% 0.44/1.03 53 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(30)].
% 0.44/1.03 54 l1_struct_0(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(24)].
% 0.44/1.03 55 l1_struct_0(c5) # label(rc3_struct_0) # label(axiom). [clausify(40)].
% 0.44/1.03 56 -l1_group_1(A) | l1_struct_0(A) # label(dt_l1_group_1) # label(axiom). [clausify(15)].
% 0.44/1.03 Derived: v3_struct_0(c2) | -v1_xboole_0(u1_struct_0(c2)). [resolve(53,b,54,a)].
% 0.44/1.03 Derived: v3_struct_0(c5) | -v1_xboole_0(u1_struct_0(c5)). [resolve(53,b,55,a)].
% 0.44/1.03 Derived: v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_group_1(A). [resolve(53,b,56,b)].
% 0.44/1.03 57 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(f10(A)) # label(rc5_struct_0) # label(axiom). [clausify(41)].
% 0.44/1.03 Derived: v3_struct_0(c2) | -v1_xboole_0(f10(c2)). [resolve(57,b,54,a)].
% 0.44/1.03 Derived: v3_struct_0(c5) | -v1_xboole_0(f10(c5)). [resolve(57,b,55,a)].
% 0.44/1.03 Derived: v3_struct_0(A) | -v1_xboole_0(f10(A)) | -l1_group_1(A). [resolve(57,b,56,b)].
% 0.44/1.03 58 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(41)].
% 0.44/1.03 Derived: v3_struct_0(c2) | m1_subset_1(f10(c2),k1_zfmisc_1(u1_struct_0(c2))). [resolve(58,b,54,a)].
% 0.44/1.03 Derived: v3_struct_0(c5) | m1_subset_1(f10(c5),k1_zfmisc_1(u1_struct_0(c5))). [resolve(58,b,55,a)].
% 0.44/1.03 Derived: v3_struct_0(A) | m1_subset_1(f10(A),k1_zfmisc_1(u1_struct_0(A))) | -l1_group_1(A). [resolve(58,b,56,b)].
% 0.44/1.03 59 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)].
% 0.44/1.03 60 v4_group_1(c6) # label(t20_latsubgr) # label(negated_conjecture). [clausify(52)].
% 0.44/1.03 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | v1_funct_1(k1_latsubgr(c6)). [resolve(59,c,60,a)].
% 0.44/1.03 61 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)].
% 0.44/1.03 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_xboole_0(k1_group_3(c6)). [resolve(61,c,60,a)].
% 0.44/1.03 62 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)].
% 0.44/1.03 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(62,c,60,a)].
% 0.44/1.03 63 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)].
% 0.44/1.03 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(63,c,60,a)].
% 0.44/1.03 64 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_funct_1(B) | -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | k1_latsubgr(A) = B | v1_group_1(f1(A,B)) # label(d1_latsubgr) # label(axiom). [clausify(7)].
% 0.44/1.03 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) = A | v1_group_1(f1(c6,A)). [resolve(64,c,60,a)].
% 0.44/1.03 65 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_funct_1(B) | -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | k1_latsubgr(A) = B | m1_group_2(f1(A,B),A) # label(d1_latsubgr) # label(axiom). [clausify(7)].
% 0.44/1.03 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) = A | m1_group_2(f1(c6,A),c6). [resolve(65,c,60,a)].
% 0.44/1.03 66 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_funct_1(B) | -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | k1_latsubgr(A) = B | k1_funct_1(B,f1(A,B)) != u1_struct_0(f1(A,B)) # label(d1_latsubgr) # label(axiom). [clausify(7)].
% 0.44/1.03 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) = A | k1_funct_1(A,f1(c6,A)) != u1_struct_0(f1(c6,A)). [resolve(66,c,60,a)].
% 0.44/1.03 67 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_funct_1(B) | -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | k1_latsubgr(A) != B | -v1_group_1(C) | -m1_group_2(C,A) | k1_funct_1(B,C) = u1_struct_0(C) # label(d1_latsubgr) # label(axiom). [clausify(7)].
% 0.44/1.03 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) != A | -v1_group_1(B) | -m1_group_2(B,c6) | k1_funct_1(A,B) = u1_struct_0(B). [resolve(67,c,60,a)].
% 0.44/1.03 68 -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)].
% 0.44/1.03 69 v1_group_1(c7) # label(t20_latsubgr) # label(negated_conjecture). [clausify(52)].
% 0.44/1.03 Derived: -l1_group_1(c7) | g1_group_1(u1_struct_0(c7),u1_group_1(c7)) = c7. [resolve(68,b,69,a)].
% 0.44/1.03 70 -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)].
% 0.44/1.03 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(70,d,68,b)].
% 0.44/1.03 71 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) = A | v1_group_1(f1(c6,A)). [resolve(64,c,60,a)].
% 0.76/1.06 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) = A | -l1_group_1(f1(c6,A)) | g1_group_1(u1_struct_0(f1(c6,A)),u1_group_1(f1(c6,A))) = f1(c6,A). [resolve(71,h,68,b)].
% 0.76/1.06 72 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) != A | -v1_group_1(B) | -m1_group_2(B,c6) | k1_funct_1(A,B) = u1_struct_0(B). [resolve(67,c,60,a)].
% 0.76/1.06 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) != A | -m1_group_2(c7,c6) | k1_funct_1(A,c7) = u1_struct_0(c7). [resolve(72,h,69,a)].
% 0.76/1.06 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) != A | -m1_group_2(g1_group_1(B,C),c6) | k1_funct_1(A,g1_group_1(B,C)) = u1_struct_0(g1_group_1(B,C)) | -v1_funct_1(C) | -v1_funct_2(C,k2_zfmisc_1(B,B),B) | -m1_relset_1(C,k2_zfmisc_1(B,B),B). [resolve(72,h,70,d)].
% 0.76/1.06 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) != A | -m1_group_2(f1(c6,B),c6) | k1_funct_1(A,f1(c6,B)) = u1_struct_0(f1(c6,B)) | v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(B) | -v1_funct_2(B,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(B,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) = B. [resolve(72,h,71,h)].
% 0.76/1.06 73 m1_subset_1(A,k1_zfmisc_1(B)) | -r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(46)].
% 0.76/1.06 74 r1_tarski(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(43)].
% 0.76/1.06 75 -m1_subset_1(A,k1_zfmisc_1(B)) | r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(46)].
% 0.76/1.06 Derived: m1_subset_1(A,k1_zfmisc_1(A)). [resolve(73,b,74,a)].
% 0.76/1.06 76 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)].
% 0.76/1.06 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)].
% 0.76/1.06 78 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)].
% 0.76/1.06
% 0.76/1.06 ============================== end predicate elimination =============
% 0.76/1.06
% 0.76/1.06 Auto_denials: (non-Horn, no changes).
% 0.76/1.06
% 0.76/1.06 Term ordering decisions:
% 0.76/1.06 Function symbol KB weights: k1_xboole_0=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. g1_group_1=1. k2_zfmisc_1=1. k1_funct_1=1. f1=1. f3=1. f5=1. f6=1. f8=1. u1_struct_0=1. k1_zfmisc_1=1. k1_group_3=1. k1_latsubgr=1. u1_group_1=1. f2=1. f4=1. f7=1. f9=1. f10=1.
% 0.76/1.06
% 0.76/1.06 ============================== end of process initial clauses ========
% 0.76/1.06
% 0.76/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.06
% 0.76/1.06 ============================== end of clauses for search =============
% 0.76/1.06
% 0.76/1.06 ============================== SEARCH ================================
% 0.76/1.06
% 0.76/1.06 % Starting search at 0.03 seconds.
% 0.76/1.06
% 0.76/1.06 ============================== PROOF =================================
% 0.76/1.06 % SZS status Theorem
% 0.76/1.06 % SZS output start Refutation
% 0.76/1.06
% 0.76/1.06 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.76/1.06 % Length of proof is 36.
% 0.76/1.06 % Level of proof is 6.
% 0.76/1.06 % Maximum clause weight is 26.000.
% 0.76/1.06 % Given clauses 78.
% 0.76/1.06
% 0.76/1.06 7 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) & m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) -> (B = k1_latsubgr(A) <-> (all C (v1_group_1(C) & m1_group_2(C,A) -> k1_funct_1(B,C) = u1_struct_0(C)))))))) # label(d1_latsubgr) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 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].
% 0.76/1.06 15 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 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].
% 0.76/1.06 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].
% 0.76/1.06 52 -(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) -> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0)))) # label(t20_latsubgr) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.06 53 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(30)].
% 0.76/1.06 56 -l1_group_1(A) | l1_struct_0(A) # label(dt_l1_group_1) # label(axiom). [clausify(15)].
% 0.76/1.06 59 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)].
% 0.76/1.06 60 v4_group_1(c6) # label(t20_latsubgr) # label(negated_conjecture). [clausify(52)].
% 0.76/1.06 62 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)].
% 0.76/1.06 63 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)].
% 0.76/1.06 67 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -v1_funct_1(B) | -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) | k1_latsubgr(A) != B | -v1_group_1(C) | -m1_group_2(C,A) | k1_funct_1(B,C) = u1_struct_0(C) # label(d1_latsubgr) # label(axiom). [clausify(7)].
% 0.76/1.06 69 v1_group_1(c7) # label(t20_latsubgr) # label(negated_conjecture). [clausify(52)].
% 0.76/1.06 72 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) != A | -v1_group_1(B) | -m1_group_2(B,c6) | k1_funct_1(A,B) = u1_struct_0(B). [resolve(67,c,60,a)].
% 0.76/1.06 80 v1_xboole_0(k1_xboole_0) # label(fc1_xboole_0) # label(axiom). [assumption].
% 0.76/1.06 82 v3_group_1(c6) # label(t20_latsubgr) # label(negated_conjecture). [clausify(52)].
% 0.76/1.06 83 l1_group_1(c6) # label(t20_latsubgr) # label(negated_conjecture). [clausify(52)].
% 0.76/1.06 85 m1_group_2(c7,c6) # label(t20_latsubgr) # label(negated_conjecture). [clausify(52)].
% 0.76/1.06 95 k1_funct_1(k1_latsubgr(c6),c7) = k1_xboole_0 # label(t20_latsubgr) # label(negated_conjecture). [clausify(52)].
% 0.76/1.06 99 -v3_struct_0(c6) # label(t20_latsubgr) # label(negated_conjecture). [clausify(52)].
% 0.76/1.06 116 v3_struct_0(A) | -v3_group_1(A) | -l1_group_1(A) | -m1_group_2(B,A) | -v3_struct_0(B) # label(dt_m1_group_2) # label(axiom). [clausify(17)].
% 0.76/1.06 118 v3_struct_0(A) | -v3_group_1(A) | -l1_group_1(A) | -m1_group_2(B,A) | l1_group_1(B) # label(dt_m1_group_2) # label(axiom). [clausify(17)].
% 0.76/1.06 128 v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_group_1(A). [resolve(53,b,56,b)].
% 0.76/1.06 137 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | v1_funct_1(k1_latsubgr(c6)). [resolve(59,c,60,a)].
% 0.76/1.06 138 v1_funct_1(k1_latsubgr(c6)). [copy(137),unit_del(a,99),unit_del(b,82),unit_del(c,83)].
% 0.76/1.06 141 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(62,c,60,a)].
% 0.76/1.06 142 v1_funct_2(k1_latsubgr(c6),k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))). [copy(141),unit_del(a,99),unit_del(b,82),unit_del(c,83)].
% 0.76/1.06 143 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(63,c,60,a)].
% 0.76/1.06 144 m2_relset_1(k1_latsubgr(c6),k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))). [copy(143),unit_del(a,99),unit_del(b,82),unit_del(c,83)].
% 0.76/1.06 153 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) != A | -m1_group_2(c7,c6) | k1_funct_1(A,c7) = u1_struct_0(c7). [resolve(72,h,69,a)].
% 0.76/1.06 154 -v1_funct_1(A) | -v1_funct_2(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | -m2_relset_1(A,k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))) | k1_latsubgr(c6) != A | k1_funct_1(A,c7) = u1_struct_0(c7). [copy(153),unit_del(a,99),unit_del(b,82),unit_del(c,83),unit_del(h,85)].
% 0.76/1.06 189 -v3_struct_0(c7). [resolve(116,d,85,a),unit_del(a,99),unit_del(b,82),unit_del(c,83)].
% 0.76/1.06 191 l1_group_1(c7). [resolve(118,d,85,a),unit_del(a,99),unit_del(b,82),unit_del(c,83)].
% 0.76/1.06 275 u1_struct_0(c7) = k1_xboole_0. [resolve(154,c,144,a),rewrite([95(20)]),flip(d),xx(c),unit_del(a,138),unit_del(b,142)].
% 0.76/1.06 384 $F. [ur(128,a,189,a,c,191,a),rewrite([275(2)]),unit_del(a,80)].
% 0.76/1.06
% 0.76/1.06 % SZS output end Refutation
% 0.76/1.06 ============================== end of proof ==========================
% 0.76/1.06
% 0.76/1.06 ============================== STATISTICS ============================
% 0.76/1.06
% 0.76/1.06 Given=78. Generated=352. Kept=292. proofs=1.
% 0.76/1.06 Usable=74. Sos=203. Demods=6. Limbo=5, Disabled=107. Hints=0.
% 0.76/1.06 Megabytes=0.45.
% 0.76/1.06 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.76/1.06
% 0.76/1.06 ============================== end of statistics =====================
% 0.76/1.06
% 0.76/1.06 ============================== end of search =========================
% 0.76/1.06
% 0.76/1.06 THEOREM PROVED
% 0.76/1.06 % SZS status Theorem
% 0.76/1.06
% 0.76/1.06 Exiting with 1 proof.
% 0.76/1.06
% 0.76/1.06 Process 32104 exit (max_proofs) Mon Jun 13 16:18:49 2022
% 0.76/1.06 Prover9 interrupted
%------------------------------------------------------------------------------