0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.35	% Computer   : n005.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 960
0.13/0.35	% DateTime   : Thu Jul  2 15:19:36 EDT 2020
0.13/0.35	% CPUTime    : 
0.89/1.83	============================== Prover9 ===============================
0.89/1.83	Prover9 (32) version 2009-11A, November 2009.
0.89/1.83	Process 17278 was started by sandbox on n005.cluster.edu,
0.89/1.83	Thu Jul  2 15:19:37 2020
0.89/1.83	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_17123_n005.cluster.edu".
0.89/1.83	============================== end of head ===========================
0.89/1.83	
0.89/1.83	============================== INPUT =================================
0.89/1.83	
0.89/1.83	% Reading from file /tmp/Prover9_17123_n005.cluster.edu
0.89/1.83	
0.89/1.83	set(prolog_style_variables).
0.89/1.83	set(auto2).
0.89/1.83	    % set(auto2) -> set(auto).
0.89/1.83	    % set(auto) -> set(auto_inference).
0.89/1.83	    % set(auto) -> set(auto_setup).
0.89/1.83	    % set(auto_setup) -> set(predicate_elim).
0.89/1.83	    % set(auto_setup) -> assign(eq_defs, unfold).
0.89/1.83	    % set(auto) -> set(auto_limits).
0.89/1.83	    % set(auto_limits) -> assign(max_weight, "100.000").
0.89/1.83	    % set(auto_limits) -> assign(sos_limit, 20000).
0.89/1.83	    % set(auto) -> set(auto_denials).
0.89/1.83	    % set(auto) -> set(auto_process).
0.89/1.83	    % set(auto2) -> assign(new_constants, 1).
0.89/1.83	    % set(auto2) -> assign(fold_denial_max, 3).
0.89/1.83	    % set(auto2) -> assign(max_weight, "200.000").
0.89/1.83	    % set(auto2) -> assign(max_hours, 1).
0.89/1.83	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.89/1.83	    % set(auto2) -> assign(max_seconds, 0).
0.89/1.83	    % set(auto2) -> assign(max_minutes, 5).
0.89/1.83	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.89/1.83	    % set(auto2) -> set(sort_initial_sos).
0.89/1.83	    % set(auto2) -> assign(sos_limit, -1).
0.89/1.83	    % set(auto2) -> assign(lrs_ticks, 3000).
0.89/1.83	    % set(auto2) -> assign(max_megs, 400).
0.89/1.83	    % set(auto2) -> assign(stats, some).
0.89/1.83	    % set(auto2) -> clear(echo_input).
0.89/1.83	    % set(auto2) -> set(quiet).
0.89/1.83	    % set(auto2) -> clear(print_initial_clauses).
0.89/1.83	    % set(auto2) -> clear(print_given).
0.89/1.83	assign(lrs_ticks,-1).
0.89/1.83	assign(sos_limit,10000).
0.89/1.83	assign(order,kbo).
0.89/1.83	set(lex_order_vars).
0.89/1.83	clear(print_given).
0.89/1.83	
0.89/1.83	% formulas(sos).  % not echoed (120 formulas)
0.89/1.83	
0.89/1.83	============================== end of input ==========================
0.89/1.83	
0.89/1.83	% From the command line: assign(max_seconds, 960).
0.89/1.83	
0.89/1.83	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.89/1.83	
0.89/1.83	% Formulas that are not ordinary clauses:
0.89/1.83	1 (all A all X (mem(X,A) -> X = ap(i(A),X))) # label(ibeta) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	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].
0.89/1.83	3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	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].
0.89/1.83	5 (all A all Y all X (mem(X,A) -> Y = ap(k(A,Y),X))) # label(kbeta) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	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].
0.89/1.83	7 (all V0t (mem(V0t,bool) -> -p(V0t) | p(V0t))) # label(conj_thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	8 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) -> (all V1v (mem(V1v,A_27a) -> ((exists V2x (mem(V2x,A_27b) & ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),c_2Ebool_2ET) = ap(V0f,V2x))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f)))))))))))) # label(ax_thm_2Epred__set_2EGSPECIFICATION) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	9 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V0p) | p(V1q)) -> -p(V0p)))))) # label(conj_thm_2Esat_2Epth__no1) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	10 (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)) -> ((all V2x (mem(V2x,A_27a) -> ap(V0f,V2x) = ap(V1g,V2x))) <-> V0f = V1g))))))))) # label(conj_thm_2Ebool_2EFUN__EQ__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	11 (all V0x (mem(V0x,ty_2Eextreal_2Eextreal) -> (all V1y (mem(V1y,ty_2Eextreal_2Eextreal) -> ap(ap(c_2Eextreal_2Eextreal__div,V0x),V1y) = ap(ap(c_2Eextreal_2Eextreal__mul,V0x),ap(c_2Eextreal_2Eextreal__inv,V1y)))))) # label(ax_thm_2Eextreal_2Eextreal__div__def) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	12 (all V0A (mem(V0A,bool) -> (p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	13 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Eextreal_2Eextreal) -> (all V2z (mem(V2z,ty_2Eextreal_2Eextreal) -> (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) -> (p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__div,V2z),ap(c_2Eextreal_2ENormal,V0x)))) <-> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__mul,V1y),ap(c_2Eextreal_2ENormal,V0x))),V2z)))))))))) # label(conj_thm_2Eextreal_2Ele__rdiv) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	14 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Ecombin_2EI(A_27a),V0x) = V0x)))) # label(conj_thm_2Ecombin_2EI__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	15 (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].
0.89/1.83	16 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> ((all V1x (mem(V1x,A_27a) -> p(V0t))) <-> p(V0t)))))) # label(conj_thm_2Ebool_2EFORALL__SIMP) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	17 (all A_27a (ne(A_27a) -> mem(c_2Emeasure_2Em__space(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),ty_2Epair_2Eprod(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),ty_2Erealax_2Ereal))),arr(A_27a,bool))))) # label(mem_c_2Emeasure_2Em__space) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	18 (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].
0.89/1.83	19 (all A_27a (ne(A_27a) -> mem(c_2Elebesgue_2Epos__fn__integral(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),ty_2Epair_2Eprod(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),ty_2Erealax_2Ereal))),arr(arr(A_27a,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal))))) # label(mem_c_2Elebesgue_2Epos__fn__integral) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	20 (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].
0.89/1.83	21 (all A_27a (ne(A_27a) -> mem(c_2Emeasure_2Emeasure__space(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),ty_2Epair_2Eprod(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),ty_2Erealax_2Ereal))),bool)))) # label(mem_c_2Emeasure_2Emeasure__space) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	22 (all A_27a (ne(A_27a) -> mem(c_2Ecombin_2EI(A_27a),arr(A_27a,A_27a)))) # label(mem_c_2Ecombin_2EI) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	23 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> p(V0P) & p(ap(V1Q,V3x)))) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V1Q,V2x)))) & p(V0P)))))))) # label(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	24 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0t (mem(V0t,arr(A_27a,A_27b)) -> f31(A_27b,A_27a,V0t) = V0t)))))) # label(ax_thm_2Ebool_2EETA__AX) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	25 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V1y = V0x <-> V0x = V1y))))))) # label(conj_thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	26 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> c_2Ecombin_2EC(A_27a,A_27b,A_27c) = f74(A_27a,A_27c,A_27b))))))) # label(ax_thm_2Ecombin_2EC__DEF) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	27 (all V0v (mem(V0v,bool) -> ($T <-> p(ap(c_2Ebool_2EBOUNDED,V0v))))) # label(conj_thm_2Ebool_2EBOUNDED__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	28 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,ty_2Epair_2Eprod(arr(A_27a,bool),ty_2Epair_2Eprod(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),ty_2Erealax_2Ereal)))) -> (all V1f (mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal)) -> ap(c_2Eextreal_2Eextreal__sup,ap(c_2Epred__set_2EGSPEC(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),f4087(A_27a,V0m,V1f))) = ap(ap(c_2Elebesgue_2Epos__fn__integral(A_27a),V0m),V1f))))))) # label(ax_thm_2Elebesgue_2Epos__fn__integral__def) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	29 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (V0x = V0x <-> $T))))) # label(conj_thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	30 (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].
0.89/1.83	31 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2EC(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27c)),arr(A_27b,arr(A_27a,A_27c)))))))))) # label(mem_c_2Ecombin_2EC) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	32 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EGSPEC(A_27a,A_27b),arr(arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)),arr(A_27a,bool))))))) # label(mem_c_2Epred__set_2EGSPEC) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	33 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,ty_2Epair_2Eprod(arr(A_27a,bool),ty_2Epair_2Eprod(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),ty_2Erealax_2Ereal)))) -> (all V1f (mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal)) -> (all V2a (mem(V2a,ty_2Eextreal_2Eextreal) -> (all V3z (mem(V3z,ty_2Erealax_2Ereal) -> (p(ap(c_2Emeasure_2Emeasure__space(A_27a),V0m)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V3z)) & p(ap(ap(c_2Ebool_2EIN(ty_2Eextreal_2Eextreal),V2a),ap(ap(c_2Elebesgue_2Epsfis(A_27a),V0m),V1f))) -> p(ap(ap(c_2Ebool_2EIN(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V3z)),V2a)),ap(ap(c_2Elebesgue_2Epsfis(A_27a),V0m),f4113(A_27a,V1f,V3z))))))))))))))) # label(conj_thm_2Elebesgue_2Epsfis__cmul) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	34 (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].
0.89/1.83	35 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> ap(c_2Eextreal_2Eextreal__inv,ap(c_2Eextreal_2ENormal,V0x)) = ap(c_2Eextreal_2ENormal,ap(c_2Erealax_2Einv,V0x)))) # label(ax_thm_2Eextreal_2Eextreal__inv__def_AndRHS_AndRHS) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	36 (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].
0.89/1.83	37 (all V0t (mem(V0t,bool) -> (p(V0t) <-> --p(V0t)))) # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	38 $F <-> -$T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	39 $T <-> -$F # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	40 (all V0p (mem(V0p,arr(ty_2Eextreal_2Eextreal,bool)) -> (all V1x (mem(V1x,ty_2Eextreal_2Eextreal) -> (p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__sup,V0p)),V1x)) <-> (all V2y (mem(V2y,ty_2Eextreal_2Eextreal) -> (p(ap(V0p,V2y)) -> p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V1x)))))))))) # label(conj_thm_2Eextreal_2Esup__le) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	41 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & ($T <-> (p(V0t) -> $T)) & (($F -> p(V0t)) <-> $T) & (-p(V0t) <-> -p(V0t)) & ($T <-> (p(V0t) -> p(V0t))))) # label(conj_thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	42 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V0p) -> p(V1q)) -> -p(V1q)))))) # label(conj_thm_2Esat_2Epth__ni2) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	43 (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].
0.89/1.83	44 (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].
0.89/1.83	45 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V2r) | -p(V0p)) & (-p(V0p) | p(V1q)) & (-p(V2r) | -p(V1q) | p(V0p)) <-> (p(V0p) <-> p(V2r) & p(V1q))))))))) # label(conj_thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	46 (all V0A (mem(V0A,bool) -> (--p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	47 (all V0p (mem(V0p,arr(ty_2Eextreal_2Eextreal,bool)) -> (all V1x (mem(V1x,ty_2Eextreal_2Eextreal) -> (p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),ap(c_2Eextreal_2Eextreal__sup,V0p))) <-> (all V2y (mem(V2y,ty_2Eextreal_2Eextreal) -> ((all V3z (mem(V3z,ty_2Eextreal_2Eextreal) -> (p(ap(V0p,V3z)) -> p(ap(ap(c_2Eextreal_2Eextreal__le,V3z),V2y))))) -> p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V2y)))))))))) # label(conj_thm_2Eextreal_2Ele__sup) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	48 (all V0t (mem(V0t,bool) -> (p(V0t) <-> --p(V0t)))) # label(conj_thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	49 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V0p) -> p(V1q)) -> p(V0p)))))) # label(conj_thm_2Esat_2Epth__ni1) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	50 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	51 (all V0x (mem(V0x,ty_2Eextreal_2Eextreal) -> (all V1y (mem(V1y,ty_2Eextreal_2Eextreal) -> ap(ap(c_2Eextreal_2Eextreal__mul,V0x),V1y) = ap(ap(c_2Eextreal_2Eextreal__mul,V1y),V0x))))) # label(conj_thm_2Eextreal_2Emul__comm) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	52 (all A0 (ne(A0) -> (all A1 (ne(A1) -> ne(ty_2Epair_2Eprod(A0,A1)))))) # label(ne_ty_2Epair_2Eprod) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	53 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(R) | p(Q) <-> p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))))))) # label(ax_or_p) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	54 (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].
0.89/1.83	55 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2EIN) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	56 (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].
0.89/1.83	57 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((-p(V1q) | -p(V0p) | p(V2r)) & (-p(V2r) | p(V0p)) & (p(V0p) | p(V1q)) <-> ((p(V1q) -> p(V2r)) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	58 $T # label(conj_thm_2Ebool_2ETRUTH) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	59 (all A_27a (ne(A_27a) -> mem(c_2Elebesgue_2Epsfis(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),ty_2Epair_2Eprod(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),ty_2Erealax_2Ereal))),arr(arr(A_27a,ty_2Eextreal_2Eextreal),arr(ty_2Eextreal_2Eextreal,bool)))))) # label(mem_c_2Elebesgue_2Epsfis) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	60 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,ty_2Epair_2Eprod(arr(A_27a,bool),ty_2Epair_2Eprod(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),ty_2Erealax_2Ereal)))) -> (p(ap(c_2Emeasure_2Emeasure__space(A_27a),V0m)) -> ap(ap(c_2Elebesgue_2Epos__fn__integral(A_27a),V0m),k(A_27a,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0))) = ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)))))) # label(conj_thm_2Elebesgue_2Epos__fn__integral__zero) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	61 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),arr(arr(A_27c,A_27b),arr(arr(A_27a,A_27c),arr(A_27a,A_27b)))))))))) # label(mem_c_2Ecombin_2Eo) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	62 (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].
0.89/1.83	63 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> (((p(V1q) <-> p(V2r)) <-> p(V0p)) <-> (-p(V1q) | -p(V0p) | p(V2r)) & (p(V1q) | -p(V0p) | -p(V2r)) & (-p(V2r) | -p(V1q) | p(V0p)) & (p(V2r) | p(V1q) | p(V0p))))))))) # label(conj_thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	64 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> (p(ap(V0P,V1a)) <-> (exists V2x (V1a = V2x & p(ap(V0P,V2x)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Ebool_2EUNWIND__THM2) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	65 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) & $F <-> $F) & (p(V0t) <-> p(V0t) & p(V0t)) & ($F & p(V0t) <-> $F) & (p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	66 (all V0x (mem(V0x,ty_2Eextreal_2Eextreal) -> (all V1y (mem(V1y,ty_2Eextreal_2Eextreal) -> (all V2z (mem(V2z,ty_2Eextreal_2Eextreal) -> (p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V2z)) & p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)) -> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__mul,V2z),V0x)),ap(ap(c_2Eextreal_2Eextreal__mul,V2z),V1y)))))))))) # label(conj_thm_2Eextreal_2Ele__lmul__imp) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	67 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V1q) | p(V2r) <-> p(V0p)) <-> (-p(V1q) | p(V0p)) & (-p(V2r) | p(V0p)) & (p(V2r) | -p(V0p) | p(V1q))))))))) # label(conj_thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	68 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2a (mem(V2a,ty_2Eextreal_2Eextreal) -> (all V3v2 (mem(V3v2,ty_2Erealax_2Ereal) -> (all V4v3 (mem(V4v3,ty_2Erealax_2Ereal) -> (all V5v5 (mem(V5v5,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2ENegInf),V2a)) <-> $T) & ($T <-> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2ENormal,V3v2)),c_2Eextreal_2EPosInf))) & (p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2EPosInf),c_2Eextreal_2ENegInf)) <-> $F) & (p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2EPosInf),ap(c_2Eextreal_2ENormal,V5v5))) <-> $F) & ($F <-> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2ENormal,V4v3)),c_2Eextreal_2ENegInf))) & ($T <-> p(ap(ap(c_2Eextreal_2Eextreal__le,c_2Eextreal_2EPosInf),c_2Eextreal_2EPosInf))) & (p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) <-> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2ENormal,V0x)),ap(c_2Eextreal_2ENormal,V1y)))))))))))))))) # label(conj_thm_2Eextreal_2Eextreal__le__def) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	69 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2ES(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27c)),arr(arr(A_27a,A_27b),arr(A_27a,A_27c)))))))))) # label(mem_c_2Ecombin_2ES) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	70 (all V0x (mem(V0x,ty_2Eextreal_2Eextreal) -> ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0) = ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),V0x))) # label(conj_thm_2Eextreal_2Emul__lzero) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	71 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> V0f = ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27a),V0f),c_2Ecombin_2EI(A_27a)) & ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27b),c_2Ecombin_2EI(A_27b)),V0f) = V0f)))))) # label(conj_thm_2Ecombin_2EI__o__ID) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	72 (all Q (mem(Q,bool) -> (p(ap(c_2Ebool_2E_7E,Q)) <-> -p(Q)))) # label(ax_neg_p) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	73 (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(V3y_27) <-> p(V2y))) & (p(V1x_27) <-> p(V0x)) -> ((p(V1x_27) -> p(V3y_27)) <-> (p(V0x) -> p(V2y)))))))))))) # label(conj_thm_2Ebool_2EIMP__CONG) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	74 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (V3b = V1y & V0x = V2a <-> ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)))))))))))))) # label(conj_thm_2Epair_2ECLOSED__PAIR__EQ) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	75 (all A (ne(A) -> (all X (mem(X,A) -> (all Y (mem(Y,A) -> (X = Y <-> p(ap(ap(c_2Emin_2E_3D(A),X),Y))))))))) # label(ax_eq_p) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	76 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Eextreal_2Eextreal) -> (all V2z (mem(V2z,ty_2Eextreal_2Eextreal) -> (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) -> (p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__div,V1y),ap(c_2Eextreal_2ENormal,V0x))),V2z)) <-> p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),ap(ap(c_2Eextreal_2Eextreal__mul,V2z),ap(c_2Eextreal_2ENormal,V0x)))))))))))) # label(conj_thm_2Eextreal_2Ele__ldiv) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	77 (all V0p (mem(V0p,arr(ty_2Eextreal_2Eextreal,bool)) -> (all V1x (mem(V1x,ty_2Eextreal_2Eextreal) -> (V1x = ap(c_2Eextreal_2Eextreal__sup,V0p) <-> (all V3y (mem(V3y,ty_2Eextreal_2Eextreal) -> ((all V4z (mem(V4z,ty_2Eextreal_2Eextreal) -> (p(ap(V0p,V4z)) -> p(ap(ap(c_2Eextreal_2Eextreal__le,V4z),V3y))))) -> p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V3y))))) & (all V2y (mem(V2y,ty_2Eextreal_2Eextreal) -> (p(ap(V0p,V2y)) -> p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V1x)))))))))) # label(conj_thm_2Eextreal_2Esup__eq) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	78 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0P)) <-> p(ap(V0P,V1x))))))))) # label(conj_thm_2Epred__set_2ESPECIFICATION) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	79 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((-p(V0A) -> --p(V1B)) <-> --(p(V0A) | p(V1B))))))) # label(conj_thm_2Esat_2EOR__DUAL2) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	80 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) -> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Erealax_2Einv,V0x)))))) # label(conj_thm_2Ereal_2EREAL__LE__INV) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	81 (all V0p (mem(V0p,bool) -> (--p(V0p) -> p(V0p)))) # label(conj_thm_2Esat_2Epth__nn) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	82 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))))))) # label(mem_c_2Epair_2E_2C) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	83 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> f71(A_27c,A_27a,A_27b) = c_2Ecombin_2ES(A_27a,A_27b,A_27c))))))) # label(ax_thm_2Ecombin_2ES__DEF) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	84 (all V0t (mem(V0t,bool) -> (p(V0t) <-> ($T <-> p(V0t))) & (($F <-> p(V0t)) <-> -p(V0t)) & (-p(V0t) <-> (p(V0t) <-> $F)) & (p(V0t) <-> ($T <-> p(V0t))))) # label(conj_thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	85 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),V0f),V1g) = f77(A_27c,A_27b,A_27a,V1g,V0f))))))))))) # label(ax_thm_2Ecombin_2Eo__DEF) # label(axiom) # label(non_clause).  [assumption].
0.89/1.83	86 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V2C) & p(V1B) | p(V0A) <-> (p(V0A) | p(V1B)) & (p(V2C) | p(V0A))))))))) # label(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND) # label(axiom) # label(non_clause).  [assumption].
2.41/3.36	87 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) <-> V0x != V1y & p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y))))))) # label(conj_thm_2Ereal_2EREAL__LT__LE) # label(axiom) # label(non_clause).  [assumption].
2.41/3.36	88 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Eextreal_2ENormal,ap(c_2Ereal_2Ereal__of__num,V0n)) = ap(c_2Eextreal_2Eextreal__of__num,V0n))) # label(ax_thm_2Eextreal_2Eextreal__of__num__def) # label(axiom) # label(non_clause).  [assumption].
2.41/3.36	89 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V1q) | p(V0p)) -> -p(V1q)))))) # label(conj_thm_2Esat_2Epth__no2) # label(axiom) # label(non_clause).  [assumption].
2.41/3.36	90 -(all A_27a (ne(A_27a) -> (all V0m (mem(V0m,ty_2Epair_2Eprod(arr(A_27a,bool),ty_2Epair_2Eprod(arr(arr(A_27a,bool),bool),arr(arr(A_27a,bool),ty_2Erealax_2Ereal)))) -> (all V1f (mem(V1f,arr(A_27a,ty_2Eextreal_2Eextreal)) -> (all V2c (mem(V2c,ty_2Erealax_2Ereal) -> (p(ap(c_2Emeasure_2Emeasure__space(A_27a),V0m)) & (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Emeasure_2Em__space(A_27a),V0m))) -> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(c_2Eextreal_2Eextreal__of__num,c_2Enum_2E0)),ap(V1f,V3x)))))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2c)) -> ap(ap(c_2Eextreal_2Eextreal__mul,ap(c_2Eextreal_2ENormal,V2c)),ap(ap(c_2Elebesgue_2Epos__fn__integral(A_27a),V0m),V1f)) = ap(ap(c_2Elebesgue_2Epos__fn__integral(A_27a),V0m),f3441(A_27a,V1f,V2c))))))))))) # label(conj_thm_2Elebesgue_2Epos__fn__integral__cmul) # label(negated_conjecture) # label(non_clause).  [assumption].
2.41/3.36	
2.41/3.36	============================== end of process non-clausal formulas ===
2.41/3.36	
2.41/3.36	============================== PROCESS INITIAL CLAUSES ===============
2.41/3.36	
2.41/3.36	============================== PREDICATE ELIMINATION =================
2.41/3.36	
2.41/3.36	============================== end predicate elimination =============
2.41/3.36	
2.41/3.36	Auto_denials:  (non-Horn, no changes).
2.41/3.36	
2.41/3.36	Term ordering decisions:
2.41/3.36	Function symbol KB weights:  bool=1. ty_2Eextreal_2Eextreal=1. ty_2Erealax_2Ereal=1. c_2Eextreal_2Eextreal__le=1. c_2Eextreal_2Eextreal__sup=1. c_2Eextreal_2ENormal=1. c_2Enum_2E0=1. c_2Eextreal_2Eextreal__mul=1. c_2Ereal_2Ereal__of__num=1. c_2Ereal_2Ereal__lte=1. c_2Eextreal_2Eextreal__of__num=1. c_2Erealax_2Ereal__lt=1. c_2Eextreal_2Eextreal__div=1. c_2Eextreal_2EPosInf=1. c_2Eextreal_2Eextreal__inv=1. ty_2Enum_2Enum=1. c_2Ebool_2ET=1. c_2Ebool_2E_2F_5C=1. c_2Ebool_2E_5C_2F=1. c_2Emin_2E_3D_3D_3E=1. c_2Eextreal_2ENegInf=1. c_2Erealax_2Einv=1. c_2Ebool_2EBOUNDED=1. c_2Ebool_2E_7E=1. c_2Ebool_2EF=1. ind=1. c1=1. c2=1. c3=1. c4=1. ap=1. arr=1. ty_2Epair_2Eprod=1. c_2Epair_2E_2C=1. c_2Epred__set_2EGSPEC=1. k=1. f4=1. f7=1. f8=1. f10=1. f11=1. f14=1. f15=1. c_2Ebool_2EIN=1. c_2Ebool_2E_21=1. c_2Ebool_2E_3F=1. c_2Ecombin_2EI=1. c_2Emeasure_2Emeasure__space=1. c_2Elebesgue_2Epos__fn__integral=1. c_2Elebesgue_2Epsfis=1. c_2Emin_2E_3D=1. c_2Emeasure_2Em__space=1. i=1. c_2Ecombin_2Eo=1. c_2Ecombin_2EC=1. c_2Ecombin_2ES=1. f31=1. f4087=1. f4113=1. f71=1. f74=1. f3441=1. f5=1. f6=1. f9=1. f12=1. f13=1. f1=1. f2=1. f3=1. f77=1.
2.41/3.36	
2.41/3.36	============================== end of process initial clauses ========
2.41/3.36	
2.41/3.36	============================== CLAUSES FOR SEARCH ====================
2.41/3.36	
2.41/3.36	============================== end of clauses for search =============
2.41/3.36	
2.41/3.36	============================== SEARCH ================================
2.41/3.36	
2.41/3.36	% Starting search at 0.09 seconds.
2.41/3.36	
2.41/3.36	Low Water (keep): wt=124.000, iters=3719
2.41/3.36	
2.41/3.36	Low Water (keep): wt=54.000, iters=3348
2.41/3.36	
2.41/3.36	Low Water (keep): wt=47.000, iters=3341
2.41/3.36	
2.41/3.36	Low Water (keep): wt=44.000, iters=3490
2.41/3.36	
2.41/3.36	Low Water (keep): wt=38.000, iters=3344
2.41/3.36	
2.41/3.36	Low Water (keep): wt=36.000, iters=3361
2.41/3.36	
2.41/3.36	Low Water (keep): wt=34.000, iters=3345
2.41/3.36	
2.41/3.36	Low Water (keep): wt=27.000, iters=3677
2.41/3.36	
2.41/3.36	Low Water (keep): wt=26.000, iters=3512
2.41/3.36	
2.41/3.36	Low Water (keep): wt=24.000, iters=3348
2.41/3.36	
2.41/3.36	Low Water (keep): wt=23.000, iters=3338
2.41/3.36	
2.41/3.36	Low Water (keep): wt=22.000, iters=3409
119.06/120.01	Alarm clock 
119.06/120.01	Prover9 interrupted
119.06/120.01	EOF