0.08/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.14/0.35	% Computer   : n029.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 1200
0.14/0.35	% DateTime   : Tue Jul 13 16:10:10 EDT 2021
0.14/0.35	% CPUTime    : 
0.47/1.09	============================== Prover9 ===============================
0.47/1.09	Prover9 (32) version 2009-11A, November 2009.
0.47/1.09	Process 6848 was started by sandbox2 on n029.cluster.edu,
0.47/1.09	Tue Jul 13 16:10:10 2021
0.47/1.09	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_6694_n029.cluster.edu".
0.47/1.09	============================== end of head ===========================
0.47/1.09	
0.47/1.09	============================== INPUT =================================
0.47/1.09	
0.47/1.09	% Reading from file /tmp/Prover9_6694_n029.cluster.edu
0.47/1.09	
0.47/1.09	set(prolog_style_variables).
0.47/1.09	set(auto2).
0.47/1.09	    % set(auto2) -> set(auto).
0.47/1.09	    % set(auto) -> set(auto_inference).
0.47/1.09	    % set(auto) -> set(auto_setup).
0.47/1.09	    % set(auto_setup) -> set(predicate_elim).
0.47/1.09	    % set(auto_setup) -> assign(eq_defs, unfold).
0.47/1.09	    % set(auto) -> set(auto_limits).
0.47/1.09	    % set(auto_limits) -> assign(max_weight, "100.000").
0.47/1.09	    % set(auto_limits) -> assign(sos_limit, 20000).
0.47/1.09	    % set(auto) -> set(auto_denials).
0.47/1.09	    % set(auto) -> set(auto_process).
0.47/1.09	    % set(auto2) -> assign(new_constants, 1).
0.47/1.09	    % set(auto2) -> assign(fold_denial_max, 3).
0.47/1.09	    % set(auto2) -> assign(max_weight, "200.000").
0.47/1.09	    % set(auto2) -> assign(max_hours, 1).
0.47/1.09	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.47/1.09	    % set(auto2) -> assign(max_seconds, 0).
0.47/1.09	    % set(auto2) -> assign(max_minutes, 5).
0.47/1.09	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.47/1.09	    % set(auto2) -> set(sort_initial_sos).
0.47/1.09	    % set(auto2) -> assign(sos_limit, -1).
0.47/1.09	    % set(auto2) -> assign(lrs_ticks, 3000).
0.47/1.09	    % set(auto2) -> assign(max_megs, 400).
0.47/1.09	    % set(auto2) -> assign(stats, some).
0.47/1.09	    % set(auto2) -> clear(echo_input).
0.47/1.09	    % set(auto2) -> set(quiet).
0.47/1.09	    % set(auto2) -> clear(print_initial_clauses).
0.47/1.09	    % set(auto2) -> clear(print_given).
0.47/1.09	assign(lrs_ticks,-1).
0.47/1.09	assign(sos_limit,10000).
0.47/1.09	assign(order,kbo).
0.47/1.09	set(lex_order_vars).
0.47/1.09	clear(print_given).
0.47/1.09	
0.47/1.09	% formulas(sos).  % not echoed (55 formulas)
0.47/1.09	
0.47/1.09	============================== end of input ==========================
0.47/1.09	
0.47/1.09	% From the command line: assign(max_seconds, 1200).
0.47/1.09	
0.47/1.09	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.47/1.09	
0.47/1.09	% Formulas that are not ordinary clauses:
0.47/1.09	1 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	2 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> --p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	3 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	4 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	5 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	6 (all V0A_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	7 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	8 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	9 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Ereal__topology_2Eball_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0)))) # label(arityeq1_2Ec_2Ereal__topology_2Eball_2E1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	10 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,V2p_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V1q_2E0)) -> p(s(tyop_2Emin_2Ebool,V0r_2E0)))) <-> (-p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0)) | -p(s(tyop_2Emin_2Ebool,V1q_2E0))) & (-p(s(tyop_2Emin_2Ebool,V0r_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0))))) # label(thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	11 (all V0B_2E0 all V1A_2E0 ((-(p(s(tyop_2Emin_2Ebool,V0B_2E0)) | -p(s(tyop_2Emin_2Ebool,V1A_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1A_2E0)) -> (-p(s(tyop_2Emin_2Ebool,V0B_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))))) # label(thm_2Esat_2EOR__DUAL3) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	12 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	13 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ereal__topology_2Ebounded__def_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ereal__topology_2Ebounded__def_2E1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	14 (all V0x_2E0 all V1e_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))))))) # label(thm_2Ereal__topology_2EBALL__SUBSET__CBALL) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	15 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	16 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2p_2E0))) <-> (-p(s(tyop_2Emin_2Ebool,V0r_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (p(s(tyop_2Emin_2Ebool,V2p_2E0)) | -p(s(tyop_2Emin_2Ebool,V1q_2E0))))) # label(thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	17 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),c_2Epair_2E_2C_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	18 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Ereal__topology_2Ecball_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0)))) # label(arityeq1_2Ec_2Ereal__topology_2Ecball_2E1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	19 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	20 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,V2p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0r_2E0)) & p(s(tyop_2Emin_2Ebool,V1q_2E0))) <-> (-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0))))) # label(thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	21 (all V0A_2E0 all V1B_2E0 all V2C_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V2C_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Ebool_2EDISJ__ASSOC) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	22 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	23 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	24 (all A_27a all V0P_2E0 ((exists V2x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) <-> -(all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2Ebool_2ENOT__FORALL__THM) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	25 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) & (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	26 (all V0A_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)))) # label(thm_2Ebool_2EDISJ__SYM) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	27 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	28 (all V0A_2E0 all V1B_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) & -p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> -(p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)))) & (-p(s(tyop_2Emin_2Ebool,V1B_2E0)) | -p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> -(p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)))))) # label(thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	29 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	30 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	31 (all V0t_2E0 ((-p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) & ((p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) & ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))))) # label(thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	32 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	33 (all V0A_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> (-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	34 (all V0q_2E0 all V1p_2E0 ((-p(s(tyop_2Emin_2Ebool,V0q_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1p_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0q_2E0)) | p(s(tyop_2Emin_2Ebool,V1p_2E0))) & (-p(s(tyop_2Emin_2Ebool,V1p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0q_2E0))))) # label(thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	35 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	36 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	37 (all A_27a all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	38 (all X0_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	39 (all V0x_2E0 all V1e_2E0 p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))))))) # label(thm_2Ereal__topology_2EBOUNDED__CBALL) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	40 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	41 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> -p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	42 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((s(tyop_2Emin_2Ebool,V0r_2E0) = s(tyop_2Emin_2Ebool,V1q_2E0) <-> p(s(tyop_2Emin_2Ebool,V2p_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V2p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0)) | -p(s(tyop_2Emin_2Ebool,V1q_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2p_2E0)) | -p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))))) # label(thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	43 (all V0B_2E0 all V1A_2E0 (((p(s(tyop_2Emin_2Ebool,V1A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> (-p(s(tyop_2Emin_2Ebool,V0B_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) <-> (-(p(s(tyop_2Emin_2Ebool,V0B_2E0)) | p(s(tyop_2Emin_2Ebool,V1A_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EOR__DUAL2) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	44 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	45 (all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Ereal__topology_2EBOUNDED__SUBSET) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	46 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.47/1.09	47 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause).  [assumption].
1.71/2.02	48 (all V0t1_2E0 all V1t2_2E0 ((p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t1_2E0))) -> s(tyop_2Emin_2Ebool,V1t2_2E0) = s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause).  [assumption].
1.71/2.02	49 (all V0t_2E0 (--p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause).  [assumption].
1.71/2.02	50 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause).  [assumption].
1.71/2.02	51 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause).  [assumption].
1.71/2.02	52 -(all V0x_2E0 all V1e_2E0 p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))))))) # label(thm_2Ereal__topology_2EBOUNDED__BALL) # label(negated_conjecture) # label(non_clause).  [assumption].
1.71/2.02	
1.71/2.02	============================== end of process non-clausal formulas ===
1.71/2.02	
1.71/2.02	============================== PROCESS INITIAL CLAUSES ===============
1.71/2.02	
1.71/2.02	============================== PREDICATE ELIMINATION =================
1.71/2.02	
1.71/2.02	============================== end predicate elimination =============
1.71/2.02	
1.71/2.02	Auto_denials:  (non-Horn, no changes).
1.71/2.02	
1.71/2.02	Term ordering decisions:
1.71/2.02	Function symbol KB weights:  tyop_2Emin_2Ebool=1. tyop_2Erealax_2Ereal=1. c_2Ebool_2ET_2E0=1. c_2Ebool_2EF_2E0=1. c_2Ebool_2E_2F_5C_2E0=1. c_2Ebool_2E_5C_2F_2E0=1. c_2Emin_2E_3D_3D_3E_2E0=1. c_2Emin_2E_3D_2E0=1. c_2Ebool_2E_21_2E0=1. c_2Ebool_2E_3F_2E0=1. c_2Ebool_2E_7E_2E0=1. c_2Epair_2E_2C_2E0=1. c_2Epred__set_2ESUBSET_2E0=1. c_2Ereal__topology_2Eball_2E0=1. c_2Ereal__topology_2Ebounded__def_2E0=1. c_2Ereal__topology_2Ecball_2E0=1. combin_i_2E0=1. combin_k_2E0=1. combin_s_2E0=1. c1=1. c2=1. s=1. tyop_2Emin_2Efun=1. app_2E2=1. tyop_2Epair_2Eprod=1. c_2Epair_2E_2C_2E2=1. c_2Ebool_2E_2F_5C_2E2=1. c_2Ebool_2E_5C_2F_2E2=1. c_2Emin_2E_3D_3D_3E_2E2=1. c_2Epred__set_2ESUBSET_2E2=1. c_2Emin_2E_3D_2E2=1. f1=1. f2=1. f3=1. f4=1. c_2Ereal__topology_2Ebounded__def_2E1=1. c_2Ebool_2E_21_2E1=1. c_2Ebool_2E_3F_2E1=1. c_2Ereal__topology_2Ecball_2E1=1. c_2Ereal__topology_2Eball_2E1=1. c_2Ebool_2E_7E_2E1=1. f5=1.
1.71/2.02	
1.71/2.02	============================== end of process initial clauses ========
1.71/2.02	
1.71/2.02	============================== CLAUSES FOR SEARCH ====================
1.71/2.02	
1.71/2.02	============================== end of clauses for search =============
1.71/2.02	
1.71/2.02	============================== SEARCH ================================
1.71/2.02	
1.71/2.02	% Starting search at 0.02 seconds.
1.71/2.02	
1.71/2.02	Low Water (keep): wt=177.000, iters=3430
1.71/2.02	
1.71/2.02	Low Water (keep): wt=151.000, iters=3624
1.71/2.02	
1.71/2.02	Low Water (keep): wt=148.000, iters=3622
1.71/2.02	
1.71/2.02	Low Water (keep): wt=143.000, iters=3615
1.71/2.02	
1.71/2.02	Low Water (keep): wt=131.000, iters=3569
1.71/2.02	
1.71/2.02	Low Water (keep): wt=103.000, iters=3333
1.71/2.02	
1.71/2.02	Low Water (keep): wt=100.000, iters=3362
1.71/2.02	
1.71/2.02	Low Water (keep): wt=99.000, iters=3487
1.71/2.02	
1.71/2.02	Low Water (keep): wt=96.000, iters=3353
1.71/2.02	
1.71/2.02	Low Water (keep): wt=95.000, iters=3396
1.71/2.02	
1.71/2.02	Low Water (keep): wt=94.000, iters=3339
1.71/2.02	
1.71/2.02	Low Water (keep): wt=92.000, iters=3402
7.16/7.42	
7.16/7.42	Low Water (keep): wt=90.000, iters=3367
7.16/7.42	
7.16/7.42	Low Water (keep): wt=88.000, iters=3364
7.16/7.42	
7.16/7.42	Low Water (keep): wt=87.000, iters=3341
7.16/7.42	
7.16/7.42	Low Water (keep): wt=84.000, iters=3355
7.16/7.42	
7.16/7.42	Low Water (keep): wt=83.000, iters=3337
7.16/7.42	
7.16/7.42	Low Water (keep): wt=82.000, iters=3367
7.16/7.42	
7.16/7.42	Low Water (keep): wt=80.000, iters=3336
7.16/7.42	
7.16/7.42	Low Water (keep): wt=77.000, iters=3373
7.16/7.42	
7.16/7.42	Low Water (keep): wt=76.000, iters=3377
7.16/7.42	
7.16/7.42	Low Water (keep): wt=74.000, iters=3352
7.16/7.42	
7.16/7.42	Low Water (keep): wt=73.000, iters=3350
7.16/7.42	
7.16/7.42	Low Water (keep): wt=70.000, iters=3349
7.16/7.42	
7.16/7.42	Low Water (keep): wt=64.000, iters=3352
7.16/7.42	
7.16/7.42	Low Water (keep): wt=58.000, iters=3413
7.16/7.42	
7.16/7.42	Low Water (keep): wt=56.000, iters=3371
7.16/7.42	
7.16/7.42	Low Water (keep): wt=54.000, iters=3389
7.16/7.42	
7.16/7.42	Low Water (keep): wt=52.000, iters=3346
7.16/7.42	
7.16/7.42	Low Water (keep): wt=51.000, iters=3348
7.16/7.42	
7.16/7.42	Low Water (keep): wt=48.000, iters=3352
7.16/7.42	
7.16/7.42	Low Water (keep): wt=47.000, iters=3400
7.16/7.42	
7.16/7.42	Low Water (keep): wt=46.000, iters=3363
7.16/7.42	
7.16/7.42	Low Water (keep): wt=44.000, iters=3355
7.16/7.42	
7.16/7.42	Low Water (keep): wt=42.000, iters=3344
7.16/7.42	
7.16/7.42	Low Water (keep): wt=41.000, iters=3397
7.16/7.42	
7.16/7.42	Low Water (keep): wt=40.000, iters=3342
7.16/7.42	
7.16/7.42	Low Water (keep): wt=39.000, iters=3362
7.16/7.42	
7.16/7.42	Low Water (keep): wt=38.000, iters=3343
7.16/7.42	
7.16/7.42	Low Water (keep): wt=37.000, iters=3336
7.16/7.42	
7.16/7.42	Low Water (keep): wt=36.000, iters=3333
7.16/7.42	
7.16/7.42	Low Water (keep): wt=35.000, iters=3343
7.16/7.42	
7.16/7.42	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 57 (0.00 of 3.48 sec).
7.16/7.42	
7.16/7.42	Low Water (keep): wt=34.000, iters=3394
7.16/7.42	
7.16/7.42	Low Water (keep): wt=33.000, iters=3382
7.16/7.42	
7.16/7.42	Low Water (keep): wt=32.000, iters=3348
7.16/7.42	
7.16/7.42	Low Water (displace): id=4015, wt=199.000
7.16/7.42	
7.16/7.42	Low Water (displace): id=9921, wt=198.000
7.16/7.42	
7.16/7.42	Low Water (displace): id=10346, wt=197.000
7.16/7.42	
7.16/7.42	Low Water (displace): id=11030, wt=196.000
7.16/7.42	
7.16/7.42	Low Water (displace): id=11128, wt=195.000
7.16/7.42	
7.16/7.42	Low Water (keep): wt=31.000, iters=3344
7.16/7.42	
7.16/7.42	Low Water (displace): id=10390, wt=194.000
7.16/7.42	
7.16/7.42	Low Water (displace): id=11379, wt=193.000
7.16/7.42	
7.16/7.42	Low Water (displace): id=11584, wt=192.000
7.16/7.42	
7.16/7.42	============================== PROOF =================================
7.16/7.42	% SZS status Theorem
7.16/7.42	% SZS output start Refutation
7.16/7.42	
7.16/7.42	% Proof 1 at 6.26 (+ 0.09) seconds.
7.16/7.42	% Length of proof is 25.
7.16/7.42	% Level of proof is 5.
7.16/7.42	% Maximum clause weight is 39.000.
7.16/7.42	% Given clauses 609.
7.16/7.42	
7.16/7.42	13 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ereal__topology_2Ebounded__def_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ereal__topology_2Ebounded__def_2E1) # label(axiom) # label(non_clause).  [assumption].
7.16/7.42	14 (all V0x_2E0 all V1e_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))))))) # label(thm_2Ereal__topology_2EBALL__SUBSET__CBALL) # label(axiom) # label(non_clause).  [assumption].
7.16/7.42	15 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause).  [assumption].
7.16/7.42	25 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) & (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
7.16/7.42	39 (all V0x_2E0 all V1e_2E0 p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))))))) # label(thm_2Ereal__topology_2EBOUNDED__CBALL) # label(axiom) # label(non_clause).  [assumption].
7.16/7.42	45 (all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Ereal__topology_2EBOUNDED__SUBSET) # label(axiom) # label(non_clause).  [assumption].
7.16/7.42	52 -(all V0x_2E0 all V1e_2E0 p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))))))) # label(thm_2Ereal__topology_2EBOUNDED__BALL) # label(negated_conjecture) # label(non_clause).  [assumption].
7.16/7.42	53 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(reserved_2Eho_2Etruth) # label(axiom).  [assumption].
7.16/7.42	55 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,A) | p(s(tyop_2Emin_2Ebool,A)) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom).  [clausify(25)].
7.16/7.42	56 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,A) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,A) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom).  [clausify(15)].
7.16/7.42	61 p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,A),s(tyop_2Erealax_2Ereal,B)))))))) # label(thm_2Ereal__topology_2EBOUNDED__CBALL) # label(axiom).  [clausify(39)].
7.16/7.42	62 s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),A))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ereal__topology_2Ebounded__def_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),A))) # label(arityeq1_2Ec_2Ereal__topology_2Ebounded__def_2E1) # label(axiom).  [clausify(13)].
7.16/7.42	63 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ereal__topology_2Ebounded__def_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),A))) = s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),A))).  [copy(62),flip(a)].
7.16/7.42	74 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,A),s(tyop_2Erealax_2Ereal,B))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,A),s(tyop_2Erealax_2Ereal,B)))))))) # label(thm_2Ereal__topology_2EBALL__SUBSET__CBALL) # label(axiom).  [clausify(14)].
7.16/7.42	81 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(reserved_2Eho_2Enotfalse) # label(axiom).  [assumption].
7.16/7.42	85 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,A) | -p(s(tyop_2Emin_2Ebool,A)) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom).  [clausify(25)].
7.16/7.42	87 -p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,c1),s(tyop_2Erealax_2Ereal,c2)))))))) # label(thm_2Ereal__topology_2EBOUNDED__BALL) # label(negated_conjecture).  [clausify(52)].
7.16/7.42	122 -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),A),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),B)))) | -p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),B)))) | p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),A)))) # label(thm_2Ereal__topology_2EBOUNDED__SUBSET) # label(axiom).  [clausify(45)].
7.16/7.42	145 s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,A),s(tyop_2Erealax_2Ereal,B))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0).  [para(56(b,2),61(a,1)),flip(a),unit_del(b,81)].
7.16/7.42	156 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,A),s(tyop_2Erealax_2Ereal,B))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,A),s(tyop_2Erealax_2Ereal,B))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0).  [para(56(b,2),74(a,1)),flip(a),unit_del(b,81)].
7.16/7.42	234 s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),A))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | -p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),A)))).  [para(63(a,1),85(b,1)),rewrite([63(17)]),flip(a)].
7.16/7.42	246 s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,c1),s(tyop_2Erealax_2Ereal,c2))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0).  [resolve(87,a,55,b),flip(a)].
7.16/7.42	3218 p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,A),s(tyop_2Erealax_2Ereal,B)))))))).  [para(156(a,1),122(a,1)),rewrite([145(21)]),merge(b),unit_del(a,53)].
7.16/7.42	12489 s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,A),s(tyop_2Erealax_2Ereal,B))))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0).  [resolve(3218,a,234,b)].
7.16/7.42	12490 $F.  [resolve(12489,a,246,a)].
7.16/7.42	
7.16/7.42	% SZS output end Refutation
7.16/7.42	============================== end of proof ==========================
7.16/7.42	
7.16/7.42	============================== STATISTICS ============================
7.16/7.42	
7.16/7.42	Given=609. Generated=130525. Kept=12426. proofs=1.
7.16/7.42	Usable=505. Sos=9999. Demods=110. Limbo=7, Disabled=1989. Hints=0.
7.16/7.42	Megabytes=59.18.
7.16/7.42	User_CPU=6.26, System_CPU=0.09, Wall_clock=7.
7.16/7.42	
7.16/7.42	============================== end of statistics =====================
7.16/7.42	
7.16/7.42	============================== end of search =========================
7.16/7.42	
7.16/7.42	THEOREM PROVED
7.16/7.42	% SZS status Theorem
7.16/7.42	
7.16/7.42	Exiting with 1 proof.
7.16/7.42	
7.16/7.42	Process 6848 exit (max_proofs) Tue Jul 13 16:10:17 2021
7.16/7.42	Prover9 interrupted
7.16/7.43	EOF