TSTP Solution File: GRP641+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP641+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 11:20:08 EDT 2022
% Result : Theorem 0.89s 1.27s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP641+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 13:37:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.89/1.14 ============================== Prover9 ===============================
% 0.89/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.14 Process 32425 was started by sandbox2 on n015.cluster.edu,
% 0.89/1.14 Mon Jun 13 13:37:08 2022
% 0.89/1.14 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32264_n015.cluster.edu".
% 0.89/1.14 ============================== end of head ===========================
% 0.89/1.14
% 0.89/1.14 ============================== INPUT =================================
% 0.89/1.14
% 0.89/1.14 % Reading from file /tmp/Prover9_32264_n015.cluster.edu
% 0.89/1.14
% 0.89/1.14 set(prolog_style_variables).
% 0.89/1.14 set(auto2).
% 0.89/1.14 % set(auto2) -> set(auto).
% 0.89/1.14 % set(auto) -> set(auto_inference).
% 0.89/1.14 % set(auto) -> set(auto_setup).
% 0.89/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.14 % set(auto) -> set(auto_limits).
% 0.89/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.14 % set(auto) -> set(auto_denials).
% 0.89/1.14 % set(auto) -> set(auto_process).
% 0.89/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.14 % set(auto2) -> assign(stats, some).
% 0.89/1.14 % set(auto2) -> clear(echo_input).
% 0.89/1.14 % set(auto2) -> set(quiet).
% 0.89/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.14 % set(auto2) -> clear(print_given).
% 0.89/1.14 assign(lrs_ticks,-1).
% 0.89/1.14 assign(sos_limit,10000).
% 0.89/1.14 assign(order,kbo).
% 0.89/1.14 set(lex_order_vars).
% 0.89/1.14 clear(print_given).
% 0.89/1.14
% 0.89/1.14 % formulas(sos). % not echoed (55 formulas)
% 0.89/1.14
% 0.89/1.14 ============================== end of input ==========================
% 0.89/1.14
% 0.89/1.14 % From the command line: assign(max_seconds, 300).
% 0.89/1.14
% 0.89/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.14
% 0.89/1.14 % Formulas that are not ordinary clauses:
% 0.89/1.14 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].
% 0.89/1.14 2 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 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].
% 0.89/1.14 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].
% 0.89/1.14 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].
% 0.89/1.14 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].
% 0.89/1.14 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].
% 0.89/1.14 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].
% 0.89/1.14 9 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 10 $T # label(dt_k1_group_3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 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].
% 0.89/1.14 12 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 13 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 14 (all A (-v3_struct_0(A) & l1_group_1(A) -> m1_subset_1(k2_group_1(A),u1_struct_0(A)))) # label(dt_k2_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 15 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 16 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 17 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 18 (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].
% 0.89/1.14 19 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 20 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 21 (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].
% 0.89/1.14 22 (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].
% 0.89/1.14 23 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 24 (exists A l1_group_1(A)) # label(existence_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 25 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 26 (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].
% 0.89/1.14 27 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 28 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 29 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 30 (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].
% 0.89/1.14 31 (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].
% 0.89/1.14 32 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 33 (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].
% 0.89/1.14 34 (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].
% 0.89/1.14 35 (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].
% 0.89/1.14 36 (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].
% 0.89/1.14 37 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 38 (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].
% 0.89/1.14 39 (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].
% 0.89/1.14 40 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 41 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 42 (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].
% 0.89/1.14 43 (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].
% 0.89/1.14 44 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 45 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 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].
% 0.89/1.14 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].
% 0.89/1.14 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].
% 0.89/1.14 49 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> k2_group_1(B) = k2_group_1(A))))) # label(t53_group_2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 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].
% 0.89/1.14 51 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 52 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 53 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.14 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) -> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)))))) # label(t19_latsubgr) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.89/1.14
% 0.89/1.14 ============================== end of process non-clausal formulas ===
% 0.89/1.14
% 0.89/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.14
% 0.89/1.14 ============================== PREDICATE ELIMINATION =================
% 0.89/1.14 55 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(31)].
% 0.89/1.14 56 l1_struct_0(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(25)].
% 0.89/1.14 57 l1_struct_0(c5) # label(rc3_struct_0) # label(axiom). [clausify(41)].
% 0.89/1.14 58 -l1_group_1(A) | l1_struct_0(A) # label(dt_l1_group_1) # label(axiom). [clausify(16)].
% 0.89/1.14 Derived: v3_struct_0(c2) | -v1_xboole_0(u1_struct_0(c2)). [resolve(55,b,56,a)].
% 0.89/1.14 Derived: v3_struct_0(c5) | -v1_xboole_0(u1_struct_0(c5)). [resolve(55,b,57,a)].
% 0.89/1.14 Derived: v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_group_1(A). [resolve(55,b,58,b)].
% 0.89/1.14 59 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(f10(A)) # label(rc5_struct_0) # label(axiom). [clausify(42)].
% 0.89/1.14 Derived: v3_struct_0(c2) | -v1_xboole_0(f10(c2)). [resolve(59,b,56,a)].
% 0.89/1.14 Derived: v3_struct_0(c5) | -v1_xboole_0(f10(c5)). [resolve(59,b,57,a)].
% 0.89/1.14 Derived: v3_struct_0(A) | -v1_xboole_0(f10(A)) | -l1_group_1(A). [resolve(59,b,58,b)].
% 0.89/1.14 60 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(42)].
% 0.89/1.14 Derived: v3_struct_0(c2) | m1_subset_1(f10(c2),k1_zfmisc_1(u1_struct_0(c2))). [resolve(60,b,56,a)].
% 0.89/1.14 Derived: v3_struct_0(c5) | m1_subset_1(f10(c5),k1_zfmisc_1(u1_struct_0(c5))). [resolve(60,b,57,a)].
% 0.89/1.14 Derived: v3_struct_0(A) | m1_subset_1(f10(A),k1_zfmisc_1(u1_struct_0(A))) | -l1_group_1(A). [resolve(60,b,58,b)].
% 0.89/1.14 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)].
% 0.89/1.14 62 v4_group_1(c6) # label(t19_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.89/1.14 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | v1_funct_1(k1_latsubgr(c6)). [resolve(61,c,62,a)].
% 0.89/1.14 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(30)].
% 0.89/1.14 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)].
% 0.89/1.14 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)].
% 0.89/1.14 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)].
% 0.89/1.14 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)].
% 0.89/1.14 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)].
% 0.89/1.14 66 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_group_2(B,A) | k2_group_1(B) = k2_group_1(A) # label(t53_group_2) # label(axiom). [clausify(49)].
% 0.89/1.14 Derived: v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(A,c6) | k2_group_1(A) = k2_group_1(c6). [resolve(66,c,62,a)].
% 0.89/1.14 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(f1(A,B)) # label(d1_latsubgr) # label(axiom). [clausify(7)].
% 0.89/1.14 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(67,c,62,a)].
% 0.89/1.14 68 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)].
% 0.89/1.14 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(68,c,62,a)].
% 0.89/1.14 69 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)].
% 0.89/1.14 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(69,c,62,a)].
% 0.89/1.14 70 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)].
% 0.89/1.14 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(70,c,62,a)].
% 0.89/1.14 71 -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)].
% 0.89/1.15 72 v1_group_1(c7) # label(t19_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.89/1.15 Derived: -l1_group_1(c7) | g1_group_1(u1_struct_0(c7),u1_group_1(c7)) = c7. [resolve(71,b,72,a)].
% 0.89/1.15 73 -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)].
% 0.89/1.15 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(73,d,71,b)].
% 0.89/1.15 74 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(67,c,62,a)].
% 0.89/1.15 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(74,h,71,b)].
% 0.89/1.15 75 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(70,c,62,a)].
% 0.89/1.15 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(75,h,72,a)].
% 0.89/1.15 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(75,h,73,d)].
% 0.89/1.15 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(75,h,74,h)].
% 0.89/1.15 76 m1_subset_1(A,k1_zfmisc_1(B)) | -r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(47)].
% 0.89/1.15 77 r1_tarski(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(44)].
% 0.89/1.15 78 -m1_subset_1(A,k1_zfmisc_1(B)) | r1_tarski(A,B) # label(t3_subset) # label(axiom). [clausify(47)].
% 0.89/1.15 Derived: m1_subset_1(A,k1_zfmisc_1(A)). [resolve(76,b,77,a)].
% 0.89/1.15 79 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)].
% 0.89/1.15 80 -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)].
% 0.89/1.15 81 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)].
% 0.89/1.15
% 0.89/1.15 ============================== end predicate elimination =============
% 0.89/1.15
% 0.89/1.15 Auto_denials: (non-Horn, no changes).
% 0.89/1.15
% 0.89/1.15 Term ordering decisions:
% 0.89/1.15 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. k2_group_1=1. f2=1. f4=1. f7=1. f9=1. f10=1.
% 0.89/1.27
% 0.89/1.27 ============================== end of process initial clauses ========
% 0.89/1.27
% 0.89/1.27 ============================== CLAUSES FOR SEARCH ====================
% 0.89/1.27
% 0.89/1.27 ============================== end of clauses for search =============
% 0.89/1.27
% 0.89/1.27 ============================== SEARCH ================================
% 0.89/1.27
% 0.89/1.27 % Starting search at 0.03 seconds.
% 0.89/1.27
% 0.89/1.27 ============================== PROOF =================================
% 0.89/1.27 % SZS status Theorem
% 0.89/1.27 % SZS output start Refutation
% 0.89/1.27
% 0.89/1.27 % Proof 1 at 0.14 (+ 0.00) seconds.
% 0.89/1.27 % Length of proof is 47.
% 0.89/1.27 % Level of proof is 7.
% 0.89/1.27 % Maximum clause weight is 26.000.
% 0.89/1.27 % Given clauses 124.
% 0.89/1.27
% 0.89/1.27 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].
% 0.89/1.27 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].
% 0.89/1.27 14 (all A (-v3_struct_0(A) & l1_group_1(A) -> m1_subset_1(k2_group_1(A),u1_struct_0(A)))) # label(dt_k2_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.27 16 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.27 18 (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].
% 0.89/1.27 31 (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].
% 0.89/1.27 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].
% 0.89/1.27 49 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> k2_group_1(B) = k2_group_1(A))))) # label(t53_group_2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.27 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) -> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)))))) # label(t19_latsubgr) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.89/1.27 55 v3_struct_0(A) | -l1_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) # label(fc1_struct_0) # label(axiom). [clausify(31)].
% 0.89/1.27 58 -l1_group_1(A) | l1_struct_0(A) # label(dt_l1_group_1) # label(axiom). [clausify(16)].
% 0.89/1.27 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)].
% 0.89/1.27 62 v4_group_1(c6) # label(t19_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.89/1.27 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)].
% 0.89/1.27 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)].
% 0.89/1.27 66 v3_struct_0(A) | -v3_group_1(A) | -v4_group_1(A) | -l1_group_1(A) | -m1_group_2(B,A) | k2_group_1(B) = k2_group_1(A) # label(t53_group_2) # label(axiom). [clausify(49)].
% 0.89/1.27 70 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)].
% 0.89/1.27 72 v1_group_1(c7) # label(t19_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.89/1.27 75 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(70,c,62,a)].
% 0.89/1.27 85 v3_group_1(c6) # label(t19_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.89/1.27 86 l1_group_1(c6) # label(t19_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.89/1.27 88 m1_group_2(c7,c6) # label(t19_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.89/1.27 101 -v3_struct_0(c6) # label(t19_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.89/1.27 105 -r2_hidden(k2_group_1(c6),k1_funct_1(k1_latsubgr(c6),c7)) # label(t19_latsubgr) # label(negated_conjecture). [clausify(54)].
% 0.89/1.27 115 -m1_subset_1(A,B) | v1_xboole_0(B) | r2_hidden(A,B) # label(t2_subset) # label(axiom). [clausify(46)].
% 0.89/1.27 116 v3_struct_0(A) | -l1_group_1(A) | m1_subset_1(k2_group_1(A),u1_struct_0(A)) # label(dt_k2_group_1) # label(axiom). [clausify(14)].
% 0.89/1.27 120 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(18)].
% 0.89/1.27 122 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(18)].
% 0.89/1.27 132 v3_struct_0(A) | -v1_xboole_0(u1_struct_0(A)) | -l1_group_1(A). [resolve(55,b,58,b)].
% 0.89/1.27 141 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | v1_funct_1(k1_latsubgr(c6)). [resolve(61,c,62,a)].
% 0.89/1.27 142 v1_funct_1(k1_latsubgr(c6)). [copy(141),unit_del(a,101),unit_del(b,85),unit_del(c,86)].
% 0.89/1.27 145 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)].
% 0.89/1.27 146 v1_funct_2(k1_latsubgr(c6),k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))). [copy(145),unit_del(a,101),unit_del(b,85),unit_del(c,86)].
% 0.89/1.27 147 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)].
% 0.89/1.27 148 m2_relset_1(k1_latsubgr(c6),k1_group_3(c6),k1_zfmisc_1(u1_struct_0(c6))). [copy(147),unit_del(a,101),unit_del(b,85),unit_del(c,86)].
% 0.89/1.27 149 v3_struct_0(c6) | -v3_group_1(c6) | -l1_group_1(c6) | -m1_group_2(A,c6) | k2_group_1(A) = k2_group_1(c6). [resolve(66,c,62,a)].
% 0.89/1.27 150 -m1_group_2(A,c6) | k2_group_1(c6) = k2_group_1(A). [copy(149),flip(e),unit_del(a,101),unit_del(b,85),unit_del(c,86)].
% 0.89/1.27 159 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(75,h,72,a)].
% 0.89/1.27 160 -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(159),unit_del(a,101),unit_del(b,85),unit_del(c,86),unit_del(h,88)].
% 0.89/1.27 197 -v3_struct_0(c7). [resolve(120,d,88,a),unit_del(a,101),unit_del(b,85),unit_del(c,86)].
% 0.89/1.27 199 l1_group_1(c7). [resolve(122,d,88,a),unit_del(a,101),unit_del(b,85),unit_del(c,86)].
% 0.89/1.27 277 k2_group_1(c7) = k2_group_1(c6). [resolve(150,a,88,a),flip(a)].
% 0.89/1.27 284 k1_funct_1(k1_latsubgr(c6),c7) = u1_struct_0(c7). [resolve(160,c,148,a),xx(c),unit_del(a,142),unit_del(b,146)].
% 0.89/1.27 286 -r2_hidden(k2_group_1(c6),u1_struct_0(c7)). [back_rewrite(105),rewrite([284(6)])].
% 0.89/1.27 390 m1_subset_1(k2_group_1(c6),u1_struct_0(c7)). [resolve(199,a,116,b),rewrite([277(4)]),unit_del(a,197)].
% 0.89/1.27 393 -v1_xboole_0(u1_struct_0(c7)). [ur(132,a,197,a,c,199,a)].
% 0.89/1.27 1836 $F. [resolve(390,a,115,a),unit_del(a,393),unit_del(b,286)].
% 0.89/1.27
% 0.89/1.27 % SZS output end Refutation
% 0.89/1.27 ============================== end of proof ==========================
% 0.89/1.27
% 0.89/1.27 ============================== STATISTICS ============================
% 0.89/1.27
% 0.89/1.27 Given=124. Generated=1897. Kept=1740. proofs=1.
% 0.89/1.27 Usable=120. Sos=1603. Demods=7. Limbo=0, Disabled=117. Hints=0.
% 0.89/1.27 Megabytes=1.23.
% 0.89/1.27 User_CPU=0.14, System_CPU=0.00, Wall_clock=1.
% 0.89/1.27
% 0.89/1.27 ============================== end of statistics =====================
% 0.89/1.27
% 0.89/1.27 ============================== end of search =========================
% 0.89/1.27
% 0.89/1.27 THEOREM PROVED
% 0.89/1.27 % SZS status Theorem
% 0.89/1.27
% 0.89/1.27 Exiting with 1 proof.
% 0.89/1.27
% 0.89/1.27 Process 32425 exit (max_proofs) Mon Jun 13 13:37:09 2022
% 0.89/1.27 Prover9 interrupted
%------------------------------------------------------------------------------