TSTP Solution File: ALG228+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG228+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 : Thu Jul 14 17:54:09 EDT 2022
% Result : Timeout 300.08s 300.31s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG228+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.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 : Wed Jun 8 01:14:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.79/1.05 ============================== Prover9 ===============================
% 0.79/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.05 Process 15867 was started by sandbox on n027.cluster.edu,
% 0.79/1.05 Wed Jun 8 01:14:11 2022
% 0.79/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15714_n027.cluster.edu".
% 0.79/1.05 ============================== end of head ===========================
% 0.79/1.05
% 0.79/1.05 ============================== INPUT =================================
% 0.79/1.05
% 0.79/1.05 % Reading from file /tmp/Prover9_15714_n027.cluster.edu
% 0.79/1.05
% 0.79/1.05 set(prolog_style_variables).
% 0.79/1.05 set(auto2).
% 0.79/1.05 % set(auto2) -> set(auto).
% 0.79/1.05 % set(auto) -> set(auto_inference).
% 0.79/1.05 % set(auto) -> set(auto_setup).
% 0.79/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.79/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.05 % set(auto) -> set(auto_limits).
% 0.79/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.05 % set(auto) -> set(auto_denials).
% 0.79/1.05 % set(auto) -> set(auto_process).
% 0.79/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.79/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.79/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.79/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.79/1.05 % set(auto2) -> assign(stats, some).
% 0.79/1.05 % set(auto2) -> clear(echo_input).
% 0.79/1.05 % set(auto2) -> set(quiet).
% 0.79/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.05 % set(auto2) -> clear(print_given).
% 0.79/1.05 assign(lrs_ticks,-1).
% 0.79/1.05 assign(sos_limit,10000).
% 0.79/1.05 assign(order,kbo).
% 0.79/1.05 set(lex_order_vars).
% 0.79/1.05 clear(print_given).
% 0.79/1.05
% 0.79/1.05 % formulas(sos). % not echoed (109 formulas)
% 0.79/1.05
% 0.79/1.05 ============================== end of input ==========================
% 0.79/1.05
% 0.79/1.05 % From the command line: assign(max_seconds, 300).
% 0.79/1.05
% 0.79/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.05
% 0.79/1.05 % Formulas that are not ordinary clauses:
% 0.79/1.05 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 2 (all A (v1_xboole_0(A) -> v1_fraenkel(A))) # label(cc1_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 3 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 4 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 5 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) -> v1_pre_circ(B,A)))) # label(cc1_mssubfam) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 6 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (v2_relat_1(B) -> -v3_relat_1(B)))))) # label(cc1_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 7 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v2_closure2(C,A,B) -> v1_fraenkel(C) & v1_closure2(C,A,B)))))) # label(cc2_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 8 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_finset_1(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 9 (all A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 10 (all A all B (v1_pre_circ(B,A) & m1_pboole(B,A) -> (all C (m4_pboole(C,A,B) -> v1_pre_circ(C,A))))) # label(cc2_mssubfam) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 11 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (v3_relat_1(B) -> -v2_relat_1(B)))))) # label(cc2_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 12 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v4_closure2(C,A,B) -> v1_fraenkel(C) & v3_closure2(C,A,B)))))) # label(cc3_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 13 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v4_closure2(C,A,B) -> v1_fraenkel(C) & v5_closure2(C,A,B)))))) # label(cc4_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 14 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v5_closure2(C,A,B) -> -v1_xboole_0(C) & v1_fraenkel(C)))))) # label(cc5_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 15 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v2_closure2(C,A,B) -> v1_fraenkel(C) & v6_closure2(C,A,B)))))) # label(cc6_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 16 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v6_closure2(C,A,B) -> -v1_xboole_0(C) & v1_fraenkel(C)))))) # label(cc7_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 17 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 18 (all A all B (A = B <-> r1_tarski(A,B) & r1_tarski(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 19 (all A all B (m1_pboole(B,A) -> (all C (C = k1_closure2(A,B) <-> (all D (r2_hidden(D,C) <-> m4_pboole(D,A,B))))))) # label(d1_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 20 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k1_funct_4(A,B) <-> k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) & (all D (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,D)) & (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(A,D))))))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 21 (all A all B (B = k1_tarski(A) <-> (all C (r2_hidden(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 22 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (m4_pboole(C,A,B) <-> r2_pboole(A,C,B)))))) # label(d23_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 23 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (C = k1_closure3(A,B) <-> C = a_2_0_closure3(A,B))))))) # label(d3_closure3) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 24 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (m1_pboole(B,A) <-> k1_relat_1(B) = A))) # label(d3_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 25 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(B,A) <-> (all C (r2_hidden(C,A) -> v1_finset_1(k1_funct_1(B,C))))))) # label(d3_pre_circ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 26 (all A all B (r1_tarski(A,B) <-> (all C (r2_hidden(C,A) -> r2_hidden(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 27 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d5_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 28 (all A k1_pboole(A) = k2_funcop_1(A,k1_xboole_0)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 29 $T # label(dt_k1_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 30 $T # label(dt_k1_closure3) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 31 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 32 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 33 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 34 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 35 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 36 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 37 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 38 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 39 (all A all B m1_pboole(k2_pre_circ(A,B),A)) # label(dt_k2_pre_circ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 40 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 41 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 42 (all A all B (m1_pboole(B,A) -> v1_closure2(k6_closure2(A,B),A,B) & v2_closure2(k6_closure2(A,B),A,B) & v3_closure2(k6_closure2(A,B),A,B) & v4_closure2(k6_closure2(A,B),A,B) & v5_closure2(k6_closure2(A,B),A,B) & v6_closure2(k6_closure2(A,B),A,B) & m1_subset_1(k6_closure2(A,B),k1_zfmisc_1(k1_closure2(A,B))))) # label(dt_k6_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 43 (all A all B all C (m1_pboole(B,A) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m1_closure2(D,A,B,C) -> m4_pboole(D,A,B))))) # label(dt_m1_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 44 (all A all B (m1_pboole(B,A) -> v1_relat_1(B) & v1_funct_1(B))) # label(dt_m1_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 45 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 46 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,B) -> m1_pboole(C,A))))) # label(dt_m4_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 47 (all A all B all C (m1_pboole(B,A) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (exists D m1_closure2(D,A,B,C)))) # label(existence_m1_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 48 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 49 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 50 (all A all B (m1_pboole(B,A) -> (exists C m4_pboole(C,A,B)))) # label(existence_m4_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 51 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 52 (all A (v1_relat_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)) & v1_funct_1(k1_pboole(A)) & v1_pre_circ(k1_pboole(A),A))) # label(fc1_mssubfam) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 53 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 54 (all A all B (m1_pboole(B,A) -> -v1_xboole_0(k1_closure2(A,B)) & v1_fraenkel(k1_closure2(A,B)) & v1_pralg_2(k1_closure2(A,B)))) # label(fc2_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 55 (all A all B all C (-v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) -> -v1_xboole_0(k1_funct_1(B,C)))) # label(fc2_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 56 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 57 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 58 (all A (v1_relat_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)) & v1_funct_1(k1_pboole(A)))) # label(fc3_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 59 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 60 (all A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 61 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_xboole_0(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 62 (all A all B all C (-v1_xboole_0(B) & m1_pboole(C,B) -> (r2_hidden(A,a_2_0_closure3(B,C)) <-> (exists D (m1_subset_1(D,B) & A = D & k1_funct_1(C,D) != k1_xboole_0))))) # label(fraenkel_a_2_0_closure3) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 63 (all A all B all C all D (-v1_xboole_0(B) & m1_pboole(C,B) & m1_closure2(D,B,C,k6_closure2(B,C)) -> (r2_hidden(A,a_3_1_closure3(B,C,D)) <-> (exists E (m1_subset_1(E,B) & A = E & k1_funct_1(D,E) != k1_xboole_0))))) # label(fraenkel_a_3_1_closure3) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 64 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) -> k1_funct_4(A,A) = A)) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 65 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 66 (exists A (v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_fraenkel(A))) # label(rc1_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 67 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 68 (exists A (v1_relat_1(A) & v1_funct_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 69 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,B) & v1_relat_1(C) & v3_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A))))) # label(rc1_mssubfam) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 70 (exists A (v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 71 (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].
% 0.79/1.05 72 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 73 (all A all B (m1_pboole(B,A) -> (exists C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & -v1_xboole_0(C) & v1_fraenkel(C) & v1_pralg_2(C))))) # label(rc2_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 74 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 75 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B))) # label(rc2_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 76 (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].
% 0.79/1.05 77 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 78 (all A all B (m1_pboole(B,A) -> (exists C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & v1_finset_1(C) & v1_fraenkel(C))))) # label(rc3_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 79 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & v1_finset_1(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 80 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 81 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B))) # label(rc3_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 82 (all A all B (m1_pboole(B,A) -> (exists C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & -v1_xboole_0(C) & v1_fraenkel(C) & v1_pralg_2(C) & v1_closure2(C,A,B) & v2_closure2(C,A,B) & v3_closure2(C,A,B) & v4_closure2(C,A,B) & v5_closure2(C,A,B) & v6_closure2(C,A,B))))) # label(rc4_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 83 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & v1_finset_1(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 84 (exists A (v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 85 (exists A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 86 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (exists C (m4_pboole(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.05 87 (all A all B k2_pre_circ(A,B) = k2_funcop_1(A,B)) # label(redefinition_k2_pre_circ) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 88 (all A all B (m1_pboole(B,A) -> k6_closure2(A,B) = k1_closure2(A,B))) # label(redefinition_k6_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 89 (all A all B all C (m1_pboole(B,A) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m1_closure2(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m1_closure2) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 90 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 91 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r2_pboole(A,B,B))) # label(reflexivity_r2_pboole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 92 (all A all B all C (r2_hidden(B,A) -> k1_funct_1(k2_funcop_1(A,C),B) = C)) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 93 (all A all B (A != k1_xboole_0 -> k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 94 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 95 (all A all B (k1_relat_1(k2_funcop_1(A,B)) = A & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 96 (all A k2_xboole_0(A,k1_xboole_0) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 97 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 98 (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].
% 0.79/1.06 99 (all A all B ((all C (r2_hidden(C,A) <-> r2_hidden(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 100 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 101 (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].
% 0.79/1.06 102 (all A all B (r2_hidden(A,B) -> k2_xboole_0(k1_tarski(A),B) = B)) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 103 (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].
% 0.79/1.06 104 (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].
% 0.79/1.06 105 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 106 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 107 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.06 108 -(all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_closure2(C,A,B,k6_closure2(A,B)) -> (all D (m1_subset_1(D,A) -> (all E -(r2_hidden(E,k1_funct_1(C,D)) & (all F (m1_closure2(F,A,B,k6_closure2(A,B)) -> -(r2_hidden(E,k1_funct_1(F,D)) & v1_pre_circ(F,A) & v1_finset_1(k1_closure3(A,F)) & r2_pboole(A,F,C)))))))))))))) # label(t9_closure3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.79/1.06
% 0.79/1.06 ============================== end of process non-clausal formulas ===
% 0.79/1.06
% 0.79/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.79/1.06
% 0.79/1.06 ============================== PREDICATE ELIMINATION =================
% 0.79/1.06 109 v3_relat_1(k1_pboole(A)) # label(fc1_mssubfam) # label(axiom). [clausify(52)].
% 0.79/1.06 110 -m1_pboole(A,B) | -v3_relat_1(A) | v1_pre_circ(A,B) # label(cc1_mssubfam) # label(axiom). [clausify(5)].
% 0.79/1.06 111 v1_xboole_0(A) | -m1_pboole(B,A) | -v2_relat_1(B) | -v3_relat_1(B) # label(cc1_pboole) # label(axiom). [clausify(6)].
% 0.79/1.06 112 v1_xboole_0(A) | -m1_pboole(B,A) | -v3_relat_1(B) | -v2_relat_1(B) # label(cc2_pboole) # label(axiom). [clausify(11)].
% 0.79/1.08 Derived: -m1_pboole(k1_pboole(A),B) | v1_pre_circ(k1_pboole(A),B). [resolve(109,a,110,b)].
% 0.79/1.08 Derived: v1_xboole_0(A) | -m1_pboole(k1_pboole(B),A) | -v2_relat_1(k1_pboole(B)). [resolve(109,a,111,d)].
% 0.79/1.08 113 v3_relat_1(k1_pboole(A)) # label(fc3_pboole) # label(axiom). [clausify(58)].
% 0.79/1.08 114 -m1_pboole(A,B) | v3_relat_1(f13(B,A)) # label(rc1_mssubfam) # label(axiom). [clausify(69)].
% 0.79/1.08 Derived: -m1_pboole(A,B) | -m1_pboole(f13(B,A),C) | v1_pre_circ(f13(B,A),C). [resolve(114,b,110,b)].
% 0.79/1.08 Derived: -m1_pboole(A,B) | v1_xboole_0(C) | -m1_pboole(f13(B,A),C) | -v2_relat_1(f13(B,A)). [resolve(114,b,111,d)].
% 0.79/1.08 115 v3_relat_1(c4) # label(rc1_pboole) # label(axiom). [clausify(70)].
% 0.79/1.08 Derived: -m1_pboole(c4,A) | v1_pre_circ(c4,A). [resolve(115,a,110,b)].
% 0.79/1.08 Derived: v1_xboole_0(A) | -m1_pboole(c4,A) | -v2_relat_1(c4). [resolve(115,a,111,d)].
% 0.79/1.08 116 v3_relat_1(f16(A)) # label(rc2_pboole) # label(axiom). [clausify(75)].
% 0.79/1.08 Derived: -m1_pboole(f16(A),B) | v1_pre_circ(f16(A),B). [resolve(116,a,110,b)].
% 0.79/1.08 Derived: v1_xboole_0(A) | -m1_pboole(f16(B),A) | -v2_relat_1(f16(B)). [resolve(116,a,111,d)].
% 0.79/1.08 117 v3_relat_1(c9) # label(rc4_funct_1) # label(axiom). [clausify(84)].
% 0.79/1.08 Derived: -m1_pboole(c9,A) | v1_pre_circ(c9,A). [resolve(117,a,110,b)].
% 0.79/1.08 Derived: v1_xboole_0(A) | -m1_pboole(c9,A) | -v2_relat_1(c9). [resolve(117,a,111,d)].
% 0.79/1.08 118 -m1_pboole(A,B) | v2_closure2(k6_closure2(B,A),B,A) # label(dt_k6_closure2) # label(axiom). [clausify(42)].
% 0.79/1.08 119 -m1_pboole(A,B) | -m1_subset_1(C,k1_zfmisc_1(k1_closure2(B,A))) | -v2_closure2(C,B,A) | v1_closure2(C,B,A) # label(cc2_closure2) # label(axiom). [clausify(7)].
% 0.79/1.08 120 -m1_pboole(A,B) | -m1_subset_1(C,k1_zfmisc_1(k1_closure2(B,A))) | -v2_closure2(C,B,A) | v6_closure2(C,B,A) # label(cc6_closure2) # label(axiom). [clausify(15)].
% 0.79/1.08 Derived: -m1_pboole(A,B) | -m1_pboole(A,B) | -m1_subset_1(k6_closure2(B,A),k1_zfmisc_1(k1_closure2(B,A))) | v1_closure2(k6_closure2(B,A),B,A). [resolve(118,b,119,c)].
% 0.79/1.08 121 -m1_pboole(A,B) | v2_closure2(f21(B,A),B,A) # label(rc4_closure2) # label(axiom). [clausify(82)].
% 0.79/1.08 Derived: -m1_pboole(A,B) | -m1_pboole(A,B) | -m1_subset_1(f21(B,A),k1_zfmisc_1(k1_closure2(B,A))) | v1_closure2(f21(B,A),B,A). [resolve(121,b,119,c)].
% 0.79/1.08 122 -m1_pboole(A,B) | v4_closure2(k6_closure2(B,A),B,A) # label(dt_k6_closure2) # label(axiom). [clausify(42)].
% 0.79/1.08 123 -m1_pboole(A,B) | -m1_subset_1(C,k1_zfmisc_1(k1_closure2(B,A))) | -v4_closure2(C,B,A) | v3_closure2(C,B,A) # label(cc3_closure2) # label(axiom). [clausify(12)].
% 0.79/1.08 124 -m1_pboole(A,B) | -m1_subset_1(C,k1_zfmisc_1(k1_closure2(B,A))) | -v4_closure2(C,B,A) | v5_closure2(C,B,A) # label(cc4_closure2) # label(axiom). [clausify(13)].
% 0.79/1.08 Derived: -m1_pboole(A,B) | -m1_pboole(A,B) | -m1_subset_1(k6_closure2(B,A),k1_zfmisc_1(k1_closure2(B,A))) | v3_closure2(k6_closure2(B,A),B,A). [resolve(122,b,123,c)].
% 0.79/1.08 125 -m1_pboole(A,B) | v4_closure2(f21(B,A),B,A) # label(rc4_closure2) # label(axiom). [clausify(82)].
% 0.79/1.08 Derived: -m1_pboole(A,B) | -m1_pboole(A,B) | -m1_subset_1(f21(B,A),k1_zfmisc_1(k1_closure2(B,A))) | v3_closure2(f21(B,A),B,A). [resolve(125,b,123,c)].
% 0.79/1.08 126 -m1_pboole(A,B) | v5_closure2(k6_closure2(B,A),B,A) # label(dt_k6_closure2) # label(axiom). [clausify(42)].
% 0.79/1.08 127 -m1_pboole(A,B) | -m1_subset_1(C,k1_zfmisc_1(k1_closure2(B,A))) | -v5_closure2(C,B,A) | -v1_xboole_0(C) # label(cc5_closure2) # label(axiom). [clausify(14)].
% 0.79/1.08 Derived: -m1_pboole(A,B) | -m1_pboole(A,B) | -m1_subset_1(k6_closure2(B,A),k1_zfmisc_1(k1_closure2(B,A))) | -v1_xboole_0(k6_closure2(B,A)). [resolve(126,b,127,c)].
% 0.79/1.08 128 -m1_pboole(A,B) | v5_closure2(f21(B,A),B,A) # label(rc4_closure2) # label(axiom). [clausify(82)].
% 0.79/1.08 Derived: -m1_pboole(A,B) | -m1_pboole(A,B) | -m1_subset_1(f21(B,A),k1_zfmisc_1(k1_closure2(B,A))) | -v1_xboole_0(f21(B,A)). [resolve(128,b,127,c)].
% 0.79/1.08 129 -m1_pboole(A,B) | v6_closure2(k6_closure2(B,A),B,A) # label(dt_k6_closure2) # label(axiom). [clausify(42)].
% 0.79/1.08 130 -m1_pboole(A,B) | -m1_subset_1(C,k1_zfmisc_1(k1_closure2(B,A))) | -v6_closure2(C,B,A) | -v1_xboole_0(C) # label(cc7_closure2) # label(axiom). [clausify(16)].
% 0.79/1.08 131 -m1_pboole(A,B) | v6_closure2(f21(B,A),B,A) # label(rc4_closure2) #Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------