0.02/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.10	% Command    : tptp2X_and_run_prover9 %d %s
0.10/0.30	% Computer   : n012.cluster.edu
0.10/0.30	% Model      : x86_64 x86_64
0.10/0.30	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.30	% Memory     : 8042.1875MB
0.10/0.30	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.30	% CPULimit   : 960
0.10/0.30	% DateTime   : Thu Jul  2 15:14:06 EDT 2020
0.10/0.30	% CPUTime    : 
0.82/1.15	============================== Prover9 ===============================
0.82/1.15	Prover9 (32) version 2009-11A, November 2009.
0.82/1.15	Process 21169 was started by sandbox2 on n012.cluster.edu,
0.82/1.15	Thu Jul  2 15:14:07 2020
0.82/1.15	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_21007_n012.cluster.edu".
0.82/1.15	============================== end of head ===========================
0.82/1.15	
0.82/1.15	============================== INPUT =================================
0.82/1.15	
0.82/1.15	% Reading from file /tmp/Prover9_21007_n012.cluster.edu
0.82/1.15	
0.82/1.15	set(prolog_style_variables).
0.82/1.15	set(auto2).
0.82/1.15	    % set(auto2) -> set(auto).
0.82/1.15	    % set(auto) -> set(auto_inference).
0.82/1.15	    % set(auto) -> set(auto_setup).
0.82/1.15	    % set(auto_setup) -> set(predicate_elim).
0.82/1.15	    % set(auto_setup) -> assign(eq_defs, unfold).
0.82/1.15	    % set(auto) -> set(auto_limits).
0.82/1.15	    % set(auto_limits) -> assign(max_weight, "100.000").
0.82/1.15	    % set(auto_limits) -> assign(sos_limit, 20000).
0.82/1.15	    % set(auto) -> set(auto_denials).
0.82/1.15	    % set(auto) -> set(auto_process).
0.82/1.15	    % set(auto2) -> assign(new_constants, 1).
0.82/1.15	    % set(auto2) -> assign(fold_denial_max, 3).
0.82/1.15	    % set(auto2) -> assign(max_weight, "200.000").
0.82/1.15	    % set(auto2) -> assign(max_hours, 1).
0.82/1.15	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.82/1.15	    % set(auto2) -> assign(max_seconds, 0).
0.82/1.15	    % set(auto2) -> assign(max_minutes, 5).
0.82/1.15	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.82/1.15	    % set(auto2) -> set(sort_initial_sos).
0.82/1.15	    % set(auto2) -> assign(sos_limit, -1).
0.82/1.15	    % set(auto2) -> assign(lrs_ticks, 3000).
0.82/1.15	    % set(auto2) -> assign(max_megs, 400).
0.82/1.15	    % set(auto2) -> assign(stats, some).
0.82/1.15	    % set(auto2) -> clear(echo_input).
0.82/1.15	    % set(auto2) -> set(quiet).
0.82/1.15	    % set(auto2) -> clear(print_initial_clauses).
0.82/1.15	    % set(auto2) -> clear(print_given).
0.82/1.15	assign(lrs_ticks,-1).
0.82/1.15	assign(sos_limit,10000).
0.82/1.15	assign(order,kbo).
0.82/1.15	set(lex_order_vars).
0.82/1.15	clear(print_given).
0.82/1.15	
0.82/1.15	% formulas(sos).  % not echoed (88 formulas)
0.82/1.15	
0.82/1.15	============================== end of input ==========================
0.82/1.15	
0.82/1.15	% From the command line: assign(max_seconds, 960).
0.82/1.15	
0.82/1.15	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.82/1.15	
0.82/1.15	% Formulas that are not ordinary clauses:
0.82/1.15	1 (all A all X (mem(X,A) -> X = ap(i(A),X))) # label(ibeta) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	2 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) <-> p(R)) -> R = Q))))) # label(boolext) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	4 (all A all B all F (mem(F,arr(A,B)) -> (all G (mem(G,arr(A,B)) -> ((all X (mem(X,A) -> ap(F,X) = ap(G,X))) -> F = G))))) # label(funcext) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	5 (all A all Y all X (mem(X,A) -> Y = ap(k(A,Y),X))) # label(kbeta) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	6 (all A all B all F (mem(F,arr(A,B)) -> (all X (mem(X,A) -> mem(ap(F,X),B))))) # label(ap_tp) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	7 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t3 (mem(V2t3,bool) -> ((p(V1t2) & p(V0t1) -> p(V2t3)) <-> (p(V0t1) -> (p(V1t2) -> p(V2t3)))))))))) # label(conj_thm_2Ebool_2EAND__IMP__INTRO) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	8 (all Q (mem(Q,bool) -> (p(ap(c_2Ebool_2E_7E,Q)) <-> -p(Q)))) # label(ax_neg_p) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	9 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V0A) | p(V1B) <-> p(V1B) | p(V0A)))))) # label(conj_thm_2Ebool_2EDISJ__SYM) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	10 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V0A) | p(V2C) | p(V1B) <-> p(V0A) | p(V2C) | p(V1B)))))))) # label(conj_thm_2Ebool_2EDISJ__ASSOC) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	11 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((exists V2x (mem(V2x,A_27a) & -p(ap(V0P,V2x)))) <-> -(all V1x (mem(V1x,A_27a) -> p(ap(V0P,V1x))))))))) # label(conj_thm_2Ebool_2ENOT__FORALL__THM) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	12 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_3F) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	13 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),ap(c_2Eoption_2ESOME(A_27a),V1x)) = ap(c_2Eoption_2ESOME(A_27b),ap(V0f,V1x)))))) & (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f),c_2Eoption_2ENONE(A_27a)) = c_2Eoption_2ENONE(A_27b))))))) # label(ax_thm_2Eoption_2EOPTION__MAP__DEF) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	14 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V0x = V1y <-> V1y = V0x))))))) # label(conj_thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	15 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> (((p(V1q) <-> p(V2r)) <-> p(V0p)) <-> (-p(V2r) | -p(V1q) | p(V0p)) & (-p(V0p) | -p(V2r) | p(V1q)) & (-p(V1q) | -p(V0p) | p(V2r)) & (p(V1q) | p(V2r) | p(V0p))))))))) # label(conj_thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	16 (all V0A (mem(V0A,bool) -> (p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	17 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2Esome(A_27a),arr(arr(A_27a,bool),ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2Esome) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	18 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(Q) & p(R) <-> p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))))))) # label(ax_and_p) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	19 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((-p(V0A) -> --p(V1B)) <-> --(p(V1B) | p(V0A))))))) # label(conj_thm_2Esat_2EOR__DUAL2) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	20 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ENONE(A_27a),ty_2Eoption_2Eoption(A_27a)))) # label(mem_c_2Eoption_2ENONE) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	21 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (--(p(V1B) | -p(V0A)) <-> (p(V0A) -> --p(V1B))))))) # label(conj_thm_2Esat_2EOR__DUAL3) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	22 (all V0t (mem(V0t,bool) -> (-p(V0t) <-> -p(V0t)) & ($T <-> (p(V0t) -> p(V0t))) & ($T <-> ($F -> p(V0t))) & ($T <-> (p(V0t) -> $T)) & (p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	23 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> ((all X (mem(X,A) -> p(ap(Q,X)))) <-> p(ap(c_2Ebool_2E_21(A),Q))))))) # label(ax_all_p) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	24 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2EpatternMatches_2EPMATCH__ROW(A_27a,A_27b,A_27c),arr(arr(A_27b,A_27c),arr(arr(A_27b,bool),arr(arr(A_27b,A_27a),arr(A_27c,ty_2Eoption_2Eoption(A_27a)))))))))))) # label(mem_c_2EpatternMatches_2EPMATCH__ROW) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	25 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0pat (mem(V0pat,arr(A_27b,A_27c)) -> (all V1guard (mem(V1guard,arr(A_27b,bool)) -> (all V2rhs (mem(V2rhs,arr(A_27b,A_27a)) -> (all V3i (mem(V3i,A_27c) -> ap(ap(ap(ap(c_2EpatternMatches_2EPMATCH__ROW(A_27a,A_27b,A_27c),V0pat),V1guard),V2rhs),V3i) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V2rhs),ap(c_2Eoption_2Esome(A_27b),f822(A_27c,A_27b,V3i,V0pat,V1guard))))))))))))))))) # label(ax_thm_2EpatternMatches_2EPMATCH__ROW__def) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	26 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0p (mem(V0p,arr(A_27b,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,bool)) -> (all V2row (mem(V2row,arr(A_27b,arr(A_27b,ty_2Eoption_2Eoption(A_27a)))) -> (all V3v (mem(V3v,A_27c) -> ap(ap(ap(ap(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN(A_27a,A_27b,A_27c),V0p),V1g),V2row),V3v) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27b,ty_2Eoption_2Eoption(A_27a)),ap(c_2Eoption_2Esome(A_27b),f850(A_27c,A_27b,V3v,V0p,V1g))),c_2Eoption_2ENONE(A_27a)),f851(A_27a,A_27b,V2row)))))))))))))))) # label(ax_thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__def) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	27 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) <-> p(V0x)) & (p(V1x_27) -> (p(V2y) <-> p(V3y_27))) -> ((p(V0x) -> p(V2y)) <-> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2Ebool_2EIMP__CONG) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	28 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V2r) | -p(V0p)) & (p(V1q) | -p(V0p)) & (p(V0p) | -p(V1q) | -p(V2r)) <-> (p(V1q) & p(V2r) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	29 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	30 (all V0P (mem(V0P,bool) -> (all V1P_27 (mem(V1P_27,bool) -> (all V2Q (mem(V2Q,bool) -> (all V3Q_27 (mem(V3Q_27,bool) -> ((p(V1P_27) -> (p(V3Q_27) <-> p(V2Q))) & (p(V2Q) -> (p(V1P_27) <-> p(V0P))) -> (p(V2Q) & p(V0P) <-> p(V1P_27) & p(V3Q_27))))))))))) # label(conj_thm_2Ebool_2EAND__CONG) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	31 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))))) # label(mem_c_2Ebool_2ECOND) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	32 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (-p(V0P) <-> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),ap(c_2Eoption_2ESOME(A_27a),V1x)),c_2Eoption_2ENONE(A_27a)) = c_2Eoption_2ENONE(A_27a)) & (p(V0P) <-> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1x)) = c_2Eoption_2ENONE(A_27a)) & (ap(c_2Eoption_2ESOME(A_27a),V2y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),ap(c_2Eoption_2ESOME(A_27a),V1x)),c_2Eoption_2ENONE(A_27a)) <-> V1x = V2y & p(V0P)) & (V2y = V1x & -p(V0P) <-> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1x)) = ap(c_2Eoption_2ESOME(A_27a),V2y)))))))))) # label(conj_thm_2Eoption_2EIF__EQUALS__OPTION) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	33 (all V0t (mem(V0t,bool) -> ($F <-> p(V0t) & $F) & ($F & p(V0t) <-> $F) & (p(V0t) <-> p(V0t) & p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	34 (all V0A (mem(V0A,bool) -> (--p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	35 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN(A_27a,A_27b,A_27c),arr(arr(A_27b,A_27c),arr(arr(A_27b,bool),arr(arr(A_27b,arr(A_27b,ty_2Eoption_2Eoption(A_27a))),arr(A_27c,ty_2Eoption_2Eoption(A_27a)))))))))))) # label(mem_c_2EpatternMatches_2EPMATCH__FLATTEN__FUN) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	36 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	37 (all A (ne(A) -> (all X (mem(X,A) -> (all Y (mem(Y,A) -> (p(ap(ap(c_2Emin_2E_3D(A),X),Y)) <-> X = Y))))))) # label(ax_eq_p) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	38 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	39 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Ebool_2E_3F(A_27a),f49(A_27a,V0P))),ap(c_2Eoption_2ESOME(A_27a),ap(c_2Emin_2E_40(A_27a),f108(A_27a,V0P)))),c_2Eoption_2ENONE(A_27a)) = ap(c_2Eoption_2Esome(A_27a),V0P))))) # label(ax_thm_2Eoption_2Esome__def) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	40 (all A0 (ne(A0) -> ne(ty_2Eoption_2Eoption(A0)))) # label(ne_ty_2Eoption_2Eoption) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	41 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2Eoption__CASE(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27a),arr(A_27b,arr(arr(A_27a,A_27b),A_27b)))))))) # label(mem_c_2Eoption_2Eoption__CASE) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	42 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V0x = V1y <-> ap(c_2Eoption_2ESOME(A_27a),V0x) = ap(c_2Eoption_2ESOME(A_27a),V1y)))))))) # label(conj_thm_2Eoption_2ESOME__11) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	43 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <-> p(R) | p(Q)))))) # label(ax_or_p) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	44 (all A_27a (ne(A_27a) -> mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2Emin_2E_40) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	45 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V0p) | -p(V2r)) & (p(V2r) | -p(V0p) | -p(V1q)) & (p(V0p) | p(V1q)) <-> (p(V0p) <-> (p(V1q) -> p(V2r)))))))))) # label(conj_thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	46 (all V0t (mem(V0t,bool) -> (($T <-> p(V0t)) <-> p(V0t)) & (p(V0t) <-> ($T <-> p(V0t))) & ((p(V0t) <-> $F) <-> -p(V0t)) & (-p(V0t) <-> (p(V0t) <-> $F)))) # label(conj_thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	47 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0pat (mem(V0pat,arr(A_27a,A_27b)) -> (all V1guard (mem(V1guard,arr(A_27a,bool)) -> (all V2inp (mem(V2inp,A_27b) -> (all V3v (mem(V3v,A_27a) -> (p(ap(ap(ap(ap(c_2EpatternMatches_2EPMATCH__ROW__COND(A_27a,A_27b),V0pat),V1guard),V2inp),V3v)) <-> p(ap(V1guard,V3v)) & ap(V0pat,V3v) = V2inp))))))))))))) # label(ax_thm_2EpatternMatches_2EPMATCH__ROW__COND__def) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	48 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V0A) | p(V1B) <-> p(V1B) | p(V0A)))))) # label(conj_thm_2Ebool_2EDISJ__COMM) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	49 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	50 $F <-> -$T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	51 -$F <-> $T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	52 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> c_2Eoption_2ENONE(A_27a) = V0opt | (exists V1x (V0opt = ap(c_2Eoption_2ESOME(A_27a),V1x) & mem(V1x,A_27a))))))) # label(conj_thm_2Eoption_2Eoption__nchotomy) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	53 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((p(V0A) -> p(V1B)) <-> -p(V0A) | p(V1B)))))) # label(conj_thm_2Ebool_2EIMP__DISJ__THM) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	54 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	55 (all A_27a (ne(A_27a) -> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))))) # label(mem_c_2Emin_2E_3D) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	56 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V2x (p(ap(V0P,V2x)) & mem(V2x,A_27a))) & (all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(ap(V1Q,V3x))))) -> p(ap(V1Q,ap(c_2Emin_2E_40(A_27a),V0P)))))))))) # label(conj_thm_2Ebool_2ESELECT__ELIM__THM) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	57 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ESOME(A_27a),arr(A_27a,ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2ESOME) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	58 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) <-> (p(Q) -> p(R))))))) # label(ax_imp_p) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	59 $T # label(conj_thm_2Ebool_2ETRUTH) # label(axiom) # label(non_clause).  [assumption].
0.82/1.15	60 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (V1g = V0f <-> (all V2x (mem(V2x,A_27a) -> ap(V1g,V2x) = ap(V0f,V2x)))))))))))) # label(conj_thm_2Ebool_2EFUN__EQ__THM) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	61 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27b)) -> (V1x = c_2Eoption_2ENONE(A_27b) <-> ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V0f),V1x) = c_2Eoption_2ENONE(A_27a)) & (c_2Eoption_2ENONE(A_27b) = V1x <-> c_2Eoption_2ENONE(A_27a) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V0f),V1x)))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	62 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (-p(V1B) & -p(V0A) <-> -(p(V0A) | p(V1B))) & (-(p(V1B) & p(V0A)) <-> -p(V0A) | -p(V1B)))))) # label(conj_thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	63 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0v (mem(V0v,A_27b) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> V0v = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),c_2Eoption_2ENONE(A_27a)),V0v),V1f))))) & (all V2x (mem(V2x,A_27a) -> (all V3v (mem(V3v,A_27b) -> (all V4f (mem(V4f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27a),V2x)),V3v),V4f) = ap(V4f,V2x))))))))))) # label(ax_thm_2Eoption_2Eoption__case__def) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	64 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> ((all V2x (mem(V2x,A_27a) -> (V1v = V2x -> p(ap(V0f,V2x))))) <-> p(ap(V0f,V1v))))))))) # label(conj_thm_2Ebool_2EUNWIND__FORALL__THM2) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	65 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (-(exists V1x (mem(V1x,A_27a) & p(ap(V0P,V1x)))) <-> (all V2x (mem(V2x,A_27a) -> -p(ap(V0P,V2x))))))))) # label(conj_thm_2Ebool_2ENOT__EXISTS__THM) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	66 (all V0t (mem(V0t,bool) -> -p(V0t) | p(V0t))) # label(conj_thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	67 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((-p(V1q) | p(V0p)) & (p(V2r) | -p(V0p) | p(V1q)) & (-p(V2r) | p(V0p)) <-> (p(V1q) | p(V2r) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	68 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> ((-p(V1q) | -p(V0p)) & (p(V1q) | p(V0p)) <-> (-p(V1q) <-> p(V0p))))))) # label(conj_thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	69 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> ((exists X (p(ap(Q,X)) & mem(X,A))) <-> p(ap(c_2Ebool_2E_3F(A),Q))))))) # label(ax_ex_p) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	70 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> V0x = V0x))))) # label(conj_thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	71 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EpatternMatches_2EPMATCH__ROW__COND(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,arr(A_27a,bool))))))))) # label(mem_c_2EpatternMatches_2EPMATCH__ROW__COND) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	72 (all V0t (mem(V0t,bool) -> ($F <-> p(V0t)) | (p(V0t) <-> $T))) # label(ax_thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	73 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)))))))) # label(mem_c_2Eoption_2EOPTION__MAP) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	74 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> (p(V0t) <-> (all V1x (mem(V1x,A_27a) -> p(V0t)))))))) # label(conj_thm_2Ebool_2EFORALL__SIMP) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	75 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_21) # label(axiom) # label(non_clause).  [assumption].
0.86/1.15	76 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> ((p(V0t1) -> p(V1t2)) -> ((p(V1t2) -> p(V0t1)) -> (p(V0t1) <-> p(V1t2)))))))) # label(conj_thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause).  [assumption].
2.46/2.79	77 (all V0t (mem(V0t,bool) -> ($T <-> p(V0t) | $T) & (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t) | p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) | $T <-> $T))) # label(conj_thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
2.46/2.79	78 -(all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0p (mem(V0p,arr(A_27a,A_27b)) -> ((all V1x1 (mem(V1x1,A_27a) -> (all V2x2 (mem(V2x2,A_27a) -> (ap(V0p,V2x2) = ap(V0p,V1x1) -> V2x2 = V1x1))))) -> (all V3g (mem(V3g,arr(A_27a,bool)) -> (all V4p_27 (mem(V4p_27,arr(A_27c,A_27a)) -> (all V5g_27 (mem(V5g_27,arr(A_27a,arr(A_27c,bool))) -> (all V6r_27 (mem(V6r_27,arr(A_27a,arr(A_27c,A_27d))) -> ap(ap(ap(c_2EpatternMatches_2EPMATCH__ROW(A_27d,A_27c,A_27b),f860(A_27a,A_27b,A_27c,V4p_27,V0p)),f861(A_27a,A_27c,V3g,V5g_27,V4p_27)),f862(A_27d,A_27a,A_27c,V6r_27,V4p_27)) = ap(ap(ap(c_2EpatternMatches_2EPMATCH__FLATTEN__FUN(A_27d,A_27a,A_27b),V0p),V3g),f859(A_27d,A_27c,A_27a,V4p_27,V5g_27,V6r_27))))))))))))))))))))) # label(conj_thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW) # label(negated_conjecture) # label(non_clause).  [assumption].
2.46/2.79	
2.46/2.79	============================== end of process non-clausal formulas ===
2.46/2.79	
2.46/2.79	============================== PROCESS INITIAL CLAUSES ===============
2.46/2.79	
2.46/2.79	============================== PREDICATE ELIMINATION =================
2.46/2.79	
2.46/2.79	============================== end predicate elimination =============
2.46/2.79	
2.46/2.79	Auto_denials:  (non-Horn, no changes).
2.46/2.79	
2.46/2.79	Term ordering decisions:
2.46/2.79	Function symbol KB weights:  bool=1. c_2Ebool_2E_2F_5C=1. c_2Ebool_2E_5C_2F=1. c_2Emin_2E_3D_3D_3E=1. c_2Ebool_2ET=1. c_2Ebool_2E_7E=1. c_2Ebool_2EF=1. ind=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. ap=1. arr=1. c_2Eoption_2EOPTION__MAP=1. c_2Eoption_2Eoption__CASE=1. c_2EpatternMatches_2EPMATCH__ROW__COND=1. f108=1. f49=1. k=1. f2=1. f3=1. f4=1. f5=1. f9=1. f10=1. f11=1. f12=1. ty_2Eoption_2Eoption=1. c_2Eoption_2ENONE=1. c_2Eoption_2ESOME=1. c_2Ebool_2ECOND=1. c_2Ebool_2E_3F=1. c_2Emin_2E_40=1. c_2Ebool_2E_21=1. c_2Eoption_2Esome=1. c_2Emin_2E_3D=1. i=1. c_2EpatternMatches_2EPMATCH__FLATTEN__FUN=1. c_2EpatternMatches_2EPMATCH__ROW=1. f851=1. f6=1. f8=1. f1=1. f7=1. f822=1. f850=1. f860=1. f861=1. f862=1. f859=1.
2.46/2.79	
2.46/2.79	============================== end of process initial clauses ========
2.46/2.79	
2.46/2.79	============================== CLAUSES FOR SEARCH ====================
2.46/2.79	
2.46/2.79	============================== end of clauses for search =============
2.46/2.79	
2.46/2.79	============================== SEARCH ================================
2.46/2.79	
2.46/2.79	% Starting search at 0.05 seconds.
2.46/2.79	
2.46/2.79	Low Water (keep): wt=147.000, iters=3727
2.46/2.79	
2.46/2.79	Low Water (keep): wt=92.000, iters=3692
2.46/2.79	
2.46/2.79	Low Water (keep): wt=62.000, iters=3511
2.46/2.79	
2.46/2.79	Low Water (keep): wt=56.000, iters=3404
2.46/2.79	
2.46/2.79	Low Water (keep): wt=55.000, iters=3388
2.46/2.79	
2.46/2.79	Low Water (keep): wt=51.000, iters=3525
2.46/2.79	
2.46/2.79	Low Water (keep): wt=49.000, iters=3436
2.46/2.79	
2.46/2.79	Low Water (keep): wt=48.000, iters=3395
2.46/2.79	
2.46/2.79	Low Water (keep): wt=46.000, iters=3370
2.46/2.79	
2.46/2.79	Low Water (keep): wt=42.000, iters=3354
2.46/2.79	
2.46/2.79	Low Water (keep): wt=41.000, iters=3357
2.46/2.79	
2.46/2.79	Low Water (keep): wt=40.000, iters=3390
2.46/2.79	
2.46/2.79	Low Water (keep): wt=38.000, iters=3348
2.46/2.79	
2.46/2.79	Low Water (keep): wt=37.000, iters=3336
2.46/2.79	
2.46/2.79	Low Water (keep): wt=36.000, iters=3355
2.46/2.79	
2.46/2.79	Low Water (keep): wt=35.000, iters=3334
2.46/2.79	
2.46/2.79	Low Water (keep): wt=34.000, iters=3344
2.46/2.79	
2.46/2.79	Low Water (keep): wt=32.000, iters=3358
2.46/2.79	
2.46/2.79	Low Water (keep): wt=31.000, iters=3352
2.46/2.79	
2.46/2.79	Low Water (keep): wt=29.000, iters=3579
2.46/2.79	
2.46/2.79	Low Water (keep): wt=28.000, iters=3346
2.46/2.79	
2.46/2.79	Low Water (keep): wt=27.000, iters=3367
2.46/2.79	
2.46/2.79	Low Water (keep): wt=26.000, iters=3369
2.46/2.79	
2.46/2.79	Low Water (keep): wt=25.000, iters=3463
2.46/2.79	
2.46/2.79	Low Water (keep): wt=24.000, iters=3359
2.46/2.79	
2.46/2.79	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 106 (0.00 of 1.51 sec).
2.46/2.79	
2.46/2.79	Low Water (keep): wt=23.000, iters=3377
2.46/2.79	
2.46/2.79	Low Water (keep): wt=22.000, iters=3340
2.46/2.79	
2.46/2.79	Low Water (keep): wt=21.000, iters=3368
2.46/2.79	
2.46/2.79	Low Water (keep): wt=18.000, iters=3339
2.46/2.79	
2.46/2.79	Low Water (keep): wtAlarm clock 
119.61/120.08	Prover9 interrupted
119.61/120.08	EOF