0.04/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.33	% Computer   : n020.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 1200
0.13/0.33	% DateTime   : Tue Jul 13 15:35:36 EDT 2021
0.13/0.33	% CPUTime    : 
0.42/1.02	============================== Prover9 ===============================
0.42/1.02	Prover9 (32) version 2009-11A, November 2009.
0.42/1.02	Process 29873 was started by sandbox2 on n020.cluster.edu,
0.42/1.02	Tue Jul 13 15:35:36 2021
0.42/1.02	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_29720_n020.cluster.edu".
0.42/1.02	============================== end of head ===========================
0.42/1.02	
0.42/1.02	============================== INPUT =================================
0.42/1.02	
0.42/1.02	% Reading from file /tmp/Prover9_29720_n020.cluster.edu
0.42/1.02	
0.42/1.02	set(prolog_style_variables).
0.42/1.02	set(auto2).
0.42/1.02	    % set(auto2) -> set(auto).
0.42/1.02	    % set(auto) -> set(auto_inference).
0.42/1.02	    % set(auto) -> set(auto_setup).
0.42/1.02	    % set(auto_setup) -> set(predicate_elim).
0.42/1.02	    % set(auto_setup) -> assign(eq_defs, unfold).
0.42/1.02	    % set(auto) -> set(auto_limits).
0.42/1.02	    % set(auto_limits) -> assign(max_weight, "100.000").
0.42/1.02	    % set(auto_limits) -> assign(sos_limit, 20000).
0.42/1.02	    % set(auto) -> set(auto_denials).
0.42/1.02	    % set(auto) -> set(auto_process).
0.42/1.02	    % set(auto2) -> assign(new_constants, 1).
0.42/1.02	    % set(auto2) -> assign(fold_denial_max, 3).
0.42/1.02	    % set(auto2) -> assign(max_weight, "200.000").
0.42/1.02	    % set(auto2) -> assign(max_hours, 1).
0.42/1.02	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.42/1.02	    % set(auto2) -> assign(max_seconds, 0).
0.42/1.02	    % set(auto2) -> assign(max_minutes, 5).
0.42/1.02	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.42/1.02	    % set(auto2) -> set(sort_initial_sos).
0.42/1.02	    % set(auto2) -> assign(sos_limit, -1).
0.42/1.02	    % set(auto2) -> assign(lrs_ticks, 3000).
0.42/1.02	    % set(auto2) -> assign(max_megs, 400).
0.42/1.02	    % set(auto2) -> assign(stats, some).
0.42/1.02	    % set(auto2) -> clear(echo_input).
0.42/1.02	    % set(auto2) -> set(quiet).
0.42/1.02	    % set(auto2) -> clear(print_initial_clauses).
0.42/1.02	    % set(auto2) -> clear(print_given).
0.42/1.02	assign(lrs_ticks,-1).
0.42/1.02	assign(sos_limit,10000).
0.42/1.02	assign(order,kbo).
0.42/1.02	set(lex_order_vars).
0.42/1.02	clear(print_given).
0.42/1.02	
0.42/1.02	% formulas(sos).  % not echoed (48 formulas)
0.42/1.02	
0.42/1.02	============================== end of input ==========================
0.42/1.02	
0.42/1.02	% From the command line: assign(max_seconds, 1200).
0.42/1.02	
0.42/1.02	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.42/1.02	
0.42/1.02	% Formulas that are not ordinary clauses:
0.42/1.02	1 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	2 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> s(A_27a,V0x_2E0) = s(A_27a,V0x_2E0))) # label(thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	3 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	4 (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].
0.42/1.02	5 (all 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,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_2EF_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_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))))) # label(thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	6 (all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	7 (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].
0.42/1.02	8 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__JOIN_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	9 (all X0_2E0 all X1_2E0 ((p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	10 (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].
0.42/1.02	11 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),c_2Eoption_2EOPTREL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	12 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	13 (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].
0.42/1.02	14 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_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].
0.42/1.02	15 (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].
0.42/1.02	16 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	17 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	18 (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_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	19 (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].
0.42/1.02	20 (all V0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	21 (all X0_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),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	22 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	23 -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].
0.42/1.02	24 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> --p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	25 (all V0t_2E0 ((s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = 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_2ET_2E0) <-> p(s(tyop_2Emin_2Ebool,V0t_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)))) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	26 (all V0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	27 (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].
0.42/1.02	28 (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].
0.42/1.02	29 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool))),c_2Eoption_2EOPTREL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	30 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	31 (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_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	32 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(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].
0.42/1.02	33 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2e_2E0 ((all V5x_2E0 s(A_27a,V5x_2E0) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5x_2E0)))))) & (all V7x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7x_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) & (all V10x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0)))) <-> s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) & (all V16x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0)))) -> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0))) & (all V22f_2E0 all V23x_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V22f_2E0),s(A_27a,V23x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V22f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V23x_2E0)))))) & (all V24f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V24f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0)) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ENONE_2E0))) & (all V25x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V25x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V25x_2E0)))))) & (all V19x_2E0 all V20v_2E0 all V21f_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V21f_2E0),s(A_27a,V19x_2E0))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V19x_2E0))),s(A_27b,V20v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V21f_2E0)))) & (all V17v_2E0 all V18f_2E0 s(A_27b,V17v_2E0) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(A_27b,V17v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V18f_2E0)))) & (all V15x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0))))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) & (all V14x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V14x_2E0)))) -> s(A_27b,V2e_2E0) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V14x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) & (all V13x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0)))) & (all V12x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V12x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V12x_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0)))) & (all V11x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0)))) -> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0))) & (all V9x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V9x_2E0)))) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V9x_2E0))) & s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) & (all V8x_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V8x_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & (all V6x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0)))) & (all V3x_2E0 all V4y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) <-> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0))))) # label(thm_2Eoption_2Eoption__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	34 (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].
0.42/1.02	35 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2Eoption_2EIS__NONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	36 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	37 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	38 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	39 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EEXISTS__SIMP) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	40 (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,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	41 (all V0t_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_2EF_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,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_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,V0t_2E0))))) # label(thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.42/1.02	42 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0)))) <-> (exists V3x0_2E0 exists V4y0_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x0_2E0))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x0_2E0))),s(A_27b,V4y0_2E0)))) & s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V4y0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0))) | s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))) # label(thm_2Eoption_2EOPTREL__def) # label(axiom) # label(non_clause).  [assumption].
0.76/1.03	43 (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),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(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause).  [assumption].
0.76/1.03	44 (all A_27a all X0_2E0 s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause).  [assumption].
0.76/1.03	45 -(all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 (s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) & s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) & 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)),V2R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V0y_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))))) & s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) # label(thm_2Equotient__option_2EOPTION__REL__def) # label(negated_conjecture) # label(non_clause).  [assumption].
0.76/1.03	
0.76/1.03	============================== end of process non-clausal formulas ===
0.76/1.03	
0.76/1.03	============================== PROCESS INITIAL CLAUSES ===============
0.76/1.03	
0.76/1.03	============================== PREDICATE ELIMINATION =================
0.76/1.03	
0.76/1.03	============================== end predicate elimination =============
0.76/1.03	
0.76/1.03	Auto_denials:  (non-Horn, no changes).
0.76/1.03	
0.76/1.03	Term ordering decisions:
0.76/1.03	Function symbol KB weights:  tyop_2Emin_2Ebool=1. c_2Eoption_2ENONE_2E0=1. c_2Ebool_2ET_2E0=1. c_2Ebool_2EF_2E0=1. c_2Eoption_2ESOME_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_2Eoption_2EOPTREL_2E0=1. c_2Eoption_2Eoption__CASE_2E0=1. c_2Ebool_2E_21_2E0=1. c_2Ebool_2E_3F_2E0=1. c_2Ebool_2E_7E_2E0=1. c_2Eoption_2EIS__NONE_2E0=1. c_2Eoption_2EIS__SOME_2E0=1. c_2Eoption_2EOPTION__JOIN_2E0=1. c_2Eoption_2EOPTION__MAP_2E0=1. c_2Eoption_2ETHE_2E0=1. combin_i_2E0=1. combin_k_2E0=1. combin_s_2E0=1. c1=1. c2=1. c3=1. c4=1. s=1. tyop_2Emin_2Efun=1. app_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_2Eoption_2EOPTION__MAP_2E2=1. c_2Emin_2E_3D_2E2=1. f1=1. f2=1. tyop_2Eoption_2Eoption=1. c_2Eoption_2ESOME_2E1=1. c_2Eoption_2EIS__SOME_2E1=1. c_2Eoption_2EIS__NONE_2E1=1. c_2Eoption_2ETHE_2E1=1. c_2Ebool_2E_21_2E1=1. c_2Ebool_2E_3F_2E1=1. c_2Eoption_2EOPTION__JOIN_2E1=1. c_2Ebool_2E_7E_2E1=1. c_2Eoption_2EOPTREL_2E3=1. c_2Eoption_2Eoption__CASE_2E3=1. f6=1. f4=1. f5=1.
8.24/8.49	
8.24/8.49	============================== end of process initial clauses ========
8.24/8.49	
8.24/8.49	============================== CLAUSES FOR SEARCH ====================
8.24/8.49	
8.24/8.49	============================== end of clauses for search =============
8.24/8.49	
8.24/8.49	============================== SEARCH ================================
8.24/8.49	
8.24/8.49	% Starting search at 0.02 seconds.
8.24/8.49	
8.24/8.49	Low Water (keep): wt=127.000, iters=3444
8.24/8.49	
8.24/8.49	Low Water (keep): wt=112.000, iters=3351
8.24/8.49	
8.24/8.49	Low Water (keep): wt=111.000, iters=3345
8.24/8.49	
8.24/8.49	Low Water (keep): wt=99.000, iters=3475
8.24/8.49	
8.24/8.49	Low Water (keep): wt=98.000, iters=3432
8.24/8.49	
8.24/8.49	Low Water (keep): wt=97.000, iters=3424
8.24/8.49	
8.24/8.49	Low Water (keep): wt=94.000, iters=3381
8.24/8.49	
8.24/8.49	Low Water (keep): wt=92.000, iters=3354
8.24/8.49	
8.24/8.49	Low Water (keep): wt=87.000, iters=3375
8.24/8.49	
8.24/8.49	Low Water (keep): wt=81.000, iters=3350
8.24/8.49	
8.24/8.49	Low Water (keep): wt=79.000, iters=3391
8.24/8.49	
8.24/8.49	Low Water (keep): wt=78.000, iters=3367
8.24/8.49	
8.24/8.49	Low Water (keep): wt=77.000, iters=3345
8.24/8.49	
8.24/8.49	Low Water (keep): wt=75.000, iters=3418
8.24/8.49	
8.24/8.49	Low Water (keep): wt=74.000, iters=3391
8.24/8.49	
8.24/8.49	Low Water (keep): wt=73.000, iters=3349
8.24/8.49	
8.24/8.49	Low Water (keep): wt=71.000, iters=3333
8.24/8.49	
8.24/8.49	Low Water (keep): wt=70.000, iters=3340
8.24/8.49	
8.24/8.49	Low Water (keep): wt=67.000, iters=3357
8.24/8.49	
8.24/8.49	Low Water (keep): wt=66.000, iters=3479
8.24/8.49	
8.24/8.49	Low Water (keep): wt=65.000, iters=3453
8.24/8.49	
8.24/8.49	Low Water (keep): wt=64.000, iters=3430
8.24/8.49	
8.24/8.49	Low Water (keep): wt=61.000, iters=3422
8.24/8.49	
8.24/8.49	Low Water (keep): wt=58.000, iters=3475
8.24/8.49	
8.24/8.49	Low Water (keep): wt=55.000, iters=3367
8.24/8.49	
8.24/8.49	Low Water (keep): wt=54.000, iters=3337
8.24/8.49	
8.24/8.49	Low Water (keep): wt=48.000, iters=3343
8.24/8.49	
8.24/8.49	Low Water (keep): wt=47.000, iters=3344
8.24/8.49	
8.24/8.49	Low Water (keep): wt=45.000, iters=3351
8.24/8.49	
8.24/8.49	Low Water (keep): wt=43.000, iters=3373
8.24/8.49	
8.24/8.49	Low Water (keep): wt=42.000, iters=3343
8.24/8.49	
8.24/8.49	Low Water (keep): wt=41.000, iters=3443
8.24/8.49	
8.24/8.49	Low Water (keep): wt=40.000, iters=3373
8.24/8.49	
8.24/8.49	Low Water (keep): wt=39.000, iters=3344
8.24/8.49	
8.24/8.49	Low Water (keep): wt=38.000, iters=3380
8.24/8.49	
8.24/8.49	Low Water (keep): wt=36.000, iters=3340
8.24/8.49	
8.24/8.49	Low Water (keep): wt=35.000, iters=3333
8.24/8.49	
8.24/8.49	Low Water (displace): id=9677, wt=199.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=7651, wt=198.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=9680, wt=197.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10642, wt=195.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=7654, wt=190.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=8302, wt=188.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=7069, wt=187.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=9357, wt=186.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=8394, wt=185.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10473, wt=184.000
8.24/8.49	
8.24/8.49	Low Water (keep): wt=34.000, iters=3384
8.24/8.49	
8.24/8.49	Low Water (displace): id=10820, wt=182.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10570, wt=181.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10824, wt=180.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10866, wt=179.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10710, wt=178.000
8.24/8.49	
8.24/8.49	Low Water (keep): wt=33.000, iters=3353
8.24/8.49	
8.24/8.49	Low Water (displace): id=10395, wt=177.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10861, wt=176.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10739, wt=175.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10849, wt=174.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10332, wt=173.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10099, wt=172.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10445, wt=171.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10697, wt=170.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10862, wt=169.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10822, wt=168.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10851, wt=167.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=10895, wt=166.000
8.24/8.49	
8.24/8.49	Low Water (keep): wt=32.000, iters=3336
8.24/8.49	
8.24/8.49	Low Water (displace): id=11058, wt=165.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=11091, wt=164.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=11623, wt=163.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=11980, wt=162.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=12273, wt=161.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=12573, wt=160.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=12555, wt=159.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=12603, wt=158.000
8.24/8.49	
8.24/8.49	Low Water (keep): wt=31.000, iters=3348
8.24/8.49	
8.24/8.49	Low Water (displace): id=12788, wt=157.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=12983, wt=156.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=13146, wt=155.000
8.24/8.49	
8.24/8.49	Low Water (keep): wt=30.000, iters=3349
8.24/8.49	
8.24/8.49	Low Water (displace): id=13283, wt=154.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=13725, wt=153.000
8.24/8.49	
8.24/8.49	Low Water (displace): id=Alarm clock 
119.79/120.05	Prover9 interrupted
119.79/120.05	EOF