0.09/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.09/0.11	% Command    : tptp2X_and_run_prover9 %d %s
0.10/0.31	% Computer   : n024.cluster.edu
0.10/0.31	% Model      : x86_64 x86_64
0.10/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory     : 8042.1875MB
0.10/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 960
0.10/0.31	% DateTime   : Thu Jul  2 14:53:43 EDT 2020
0.10/0.32	% CPUTime    : 
0.89/1.20	============================== Prover9 ===============================
0.89/1.20	Prover9 (32) version 2009-11A, November 2009.
0.89/1.20	Process 17222 was started by sandbox2 on n024.cluster.edu,
0.89/1.20	Thu Jul  2 14:53:44 2020
0.89/1.20	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_17064_n024.cluster.edu".
0.89/1.20	============================== end of head ===========================
0.89/1.20	
0.89/1.20	============================== INPUT =================================
0.89/1.20	
0.89/1.20	% Reading from file /tmp/Prover9_17064_n024.cluster.edu
0.89/1.20	
0.89/1.20	set(prolog_style_variables).
0.89/1.20	set(auto2).
0.89/1.20	    % set(auto2) -> set(auto).
0.89/1.20	    % set(auto) -> set(auto_inference).
0.89/1.20	    % set(auto) -> set(auto_setup).
0.89/1.20	    % set(auto_setup) -> set(predicate_elim).
0.89/1.20	    % set(auto_setup) -> assign(eq_defs, unfold).
0.89/1.20	    % set(auto) -> set(auto_limits).
0.89/1.20	    % set(auto_limits) -> assign(max_weight, "100.000").
0.89/1.20	    % set(auto_limits) -> assign(sos_limit, 20000).
0.89/1.20	    % set(auto) -> set(auto_denials).
0.89/1.20	    % set(auto) -> set(auto_process).
0.89/1.20	    % set(auto2) -> assign(new_constants, 1).
0.89/1.20	    % set(auto2) -> assign(fold_denial_max, 3).
0.89/1.20	    % set(auto2) -> assign(max_weight, "200.000").
0.89/1.20	    % set(auto2) -> assign(max_hours, 1).
0.89/1.20	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.89/1.20	    % set(auto2) -> assign(max_seconds, 0).
0.89/1.20	    % set(auto2) -> assign(max_minutes, 5).
0.89/1.20	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.89/1.20	    % set(auto2) -> set(sort_initial_sos).
0.89/1.20	    % set(auto2) -> assign(sos_limit, -1).
0.89/1.20	    % set(auto2) -> assign(lrs_ticks, 3000).
0.89/1.20	    % set(auto2) -> assign(max_megs, 400).
0.89/1.20	    % set(auto2) -> assign(stats, some).
0.89/1.20	    % set(auto2) -> clear(echo_input).
0.89/1.20	    % set(auto2) -> set(quiet).
0.89/1.20	    % set(auto2) -> clear(print_initial_clauses).
0.89/1.20	    % set(auto2) -> clear(print_given).
0.89/1.20	assign(lrs_ticks,-1).
0.89/1.20	assign(sos_limit,10000).
0.89/1.20	assign(order,kbo).
0.89/1.20	set(lex_order_vars).
0.89/1.20	clear(print_given).
0.89/1.20	
0.89/1.20	% formulas(sos).  % not echoed (100 formulas)
0.89/1.20	
0.89/1.20	============================== end of input ==========================
0.89/1.20	
0.89/1.20	% From the command line: assign(max_seconds, 960).
0.89/1.20	
0.89/1.20	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.89/1.20	
0.89/1.20	% Formulas that are not ordinary clauses:
0.89/1.20	1 (all A all X (mem(X,A) -> X = ap(i(A),X))) # label(ibeta) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	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].
0.89/1.20	3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	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].
0.89/1.20	5 (all A all Y all X (mem(X,A) -> Y = ap(k(A,Y),X))) # label(kbeta) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	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].
0.89/1.20	7 (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].
0.89/1.20	8 (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].
0.89/1.20	9 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V1q) | p(V0p)) -> -p(V0p)))))) # label(conj_thm_2Esat_2Epth__no1) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	10 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x (mem(V2x,A_27a) & p(V1Q) & p(ap(V0P,V2x)))) <-> (exists V3x (p(ap(V0P,V3x)) & mem(V3x,A_27a))) & p(V1Q)))))))) # label(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	11 (all V0t (mem(V0t,bool) -> ($T <-> (p(V0t) -> $T)) & (($F -> p(V0t)) <-> $T) & ((p(V0t) -> p(V0t)) <-> $T) & (-p(V0t) <-> -p(V0t)) & (p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	12 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V0x = V1y <-> V0x = V1y))))))) # label(conj_thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	13 (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].
0.89/1.20	14 (all A (ne(A) -> (all X (mem(X,A) -> (all Y (mem(Y,A) -> (p(ap(ap(c_2Emin_2E_3D(A),X),Y)) <-> Y = X))))))) # label(ax_eq_p) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	15 (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(ap(V1Q,V3x)))) | p(V0P) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V1Q,V2x)) | p(V0P)))))))))) # label(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	16 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V2x (p(V0P) & p(ap(V1Q,V2x)) & mem(V2x,A_27a))) <-> (exists V3x (mem(V3x,A_27a) & p(ap(V1Q,V3x)))) & p(V0P)))))))) # label(conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	17 (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].
0.89/1.20	18 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> ((p(V0p) <-> -p(V1q)) <-> (p(V1q) | p(V0p)) & (-p(V0p) | -p(V1q))))))) # label(conj_thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	19 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V0n)) <-> -p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(conj_thm_2Earithmetic_2EODD__EVEN) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	20 (all V0A (mem(V0A,bool) -> (p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	21 $F <-> -$T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	22 -$F <-> $T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	23 (all V0t (mem(V0t,bool) -> (p(V0t) <-> --p(V0t)))) # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	24 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	25 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),V0m))))) # label(conj_thm_2Earithmetic_2EMULT__COMM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	26 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	27 (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].
0.89/1.20	28 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Enum_2ESUC,V0m))) # label(conj_thm_2Earithmetic_2EADD1) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	29 (all V0b (mem(V0b,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> ((p(V2t2) | p(V0b)) & (-p(V0b) | p(V1t1)) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0b),V1t1),V2t2))))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	30 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V4x (p(ap(V1Q,V4x)) & mem(V4x,A_27a))) | (exists V3x (p(ap(V0P,V3x)) & mem(V3x,A_27a))) <-> (exists V2x (mem(V2x,A_27a) & (p(ap(V0P,V2x)) | p(ap(V1Q,V2x)))))))))))) # label(conj_thm_2Ebool_2EEXISTS__OR__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	31 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((all V1x (mem(V1x,A_27a) -> (exists V2y (p(ap(ap(V0P,V1x),V2y)) & mem(V2y,A_27b))))) <-> (exists V3f ((all V4x (mem(V4x,A_27a) -> p(ap(ap(V0P,V4x),ap(V3f,V4x))))) & mem(V3f,arr(A_27a,A_27b))))))))))) # label(conj_thm_2Ebool_2ESKOLEM__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	32 (all V0t (mem(V0t,bool) -> p(V0t) | -p(V0t))) # label(conj_thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	33 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V2r) & p(V1q) <-> p(V0p)) <-> (p(V0p) | -p(V2r) | -p(V1q)) & (-p(V0p) | p(V1q)) & (-p(V0p) | p(V2r))))))))) # label(conj_thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	34 (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].
0.89/1.20	35 (all V0A (mem(V0A,bool) -> (--p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	36 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> ((exists V3q (mem(V3q,ty_2Enum_2Enum) & V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V0n)),V2r) & p(ap(ap(c_2Eprim__rec_2E_3C,V2r),V0n)))) -> ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = V2r))))))) # label(conj_thm_2Earithmetic_2EMOD__UNIQUE) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	37 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1b (mem(V1b,bool) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27b),V1b),ap(V0f,V2x)),ap(V0f,V3y)) = ap(V0f,ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1b),V2x),V3y)))))))))))))) # label(conj_thm_2Ebool_2ECOND__RAND) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	38 (all V0t (mem(V0t,bool) -> ($T | p(V0t) <-> $T) & (p(V0t) | $T <-> $T) & (p(V0t) | p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	39 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> V0x = V0x))))) # label(conj_thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	40 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) & $F <-> $F) & (p(V0t) & p(V0t) <-> p(V0t)) & ($F <-> $F & p(V0t)) & (p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	41 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> -p(ap(V0P,V2x)))) <-> -(exists V1x (p(ap(V0P,V1x)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Ebool_2ENOT__EXISTS__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	42 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V1B) | p(V0A) <-> p(V1B) | p(V0A)))))) # label(conj_thm_2Ebool_2EDISJ__SYM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	43 (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].
0.89/1.20	44 (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(V2r) | -p(V1q) | -p(V0p)) & (p(V0p) | -p(V1q) | -p(V2r)) <-> ((p(V2r) <-> p(V1q)) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	45 (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].
0.89/1.20	46 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V0n)) <-> (exists V1m (V0n = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)) & mem(V1m,ty_2Enum_2Enum)))))) # label(conj_thm_2Earithmetic_2EODD__EXISTS) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	47 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> (p(V1Q) & (all V2x (mem(V2x,A_27a) -> p(ap(V0P,V2x)))) <-> (all V3x (mem(V3x,A_27a) -> p(ap(V0P,V3x)) & p(V1Q)))))))))) # label(conj_thm_2Ebool_2ELEFT__AND__FORALL__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	48 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m)) # label(conj_thm_2Earithmetic_2EADD__0) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	49 (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(V0p) <-> p(V2r) | p(V1q))))))))) # label(conj_thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	50 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0b (mem(V0b,bool) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2g (mem(V2g,arr(A_27a,A_27b)) -> (all V3x (mem(V3x,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27b),V0b),ap(V1f,V3x)),ap(V2g,V3x)) = ap(ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,A_27b)),V0b),V1f),V2g),V3x))))))))))))) # label(conj_thm_2Ebool_2ECOND__RATOR) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	51 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> V0t1 = ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) & V1t2 = ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2))))))) # label(conj_thm_2Ebool_2ECOND__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	52 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V3x ((p(V1Q) | p(ap(V0P,V3x))) & mem(V3x,A_27a))) <-> (exists V2x (p(ap(V0P,V2x)) & mem(V2x,A_27a))) | p(V1Q)))))))) # label(conj_thm_2Ebool_2ELEFT__OR__EXISTS__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	53 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__EQ) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	54 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V1q) | p(V0p)) & (p(V0p) | -p(V2r)) & (-p(V1q) | p(V2r) | -p(V0p)) <-> ((p(V1q) -> p(V2r)) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	55 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (-(p(V0A) | p(V1B)) <-> -p(V1B) & -p(V0A)) & (-(p(V1B) & p(V0A)) <-> -p(V1B) | -p(V0A)))))) # label(conj_thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	56 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_2F_5C,Q),R)) <-> p(Q) & p(R)))))) # label(ax_and_p) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	57 (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].
0.89/1.20	58 (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].
0.89/1.20	59 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	60 (all V0t (mem(V0t,bool) -> ($T <-> p(V0t)) | ($F <-> p(V0t)))) # label(ax_thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	61 (all V0p (mem(V0p,bool) -> (--p(V0p) -> p(V0p)))) # label(conj_thm_2Esat_2Epth__nn) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	62 (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].
0.89/1.20	63 (all V0t (mem(V0t,bool) -> (($T <-> p(V0t)) <-> p(V0t)) & (-p(V0t) <-> ($F <-> p(V0t))) & (($F <-> p(V0t)) <-> -p(V0t)) & (p(V0t) <-> (p(V0t) <-> $T)))) # label(conj_thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	64 (all Q (mem(Q,bool) -> (-p(Q) <-> p(ap(c_2Ebool_2E_7E,Q))))) # label(ax_neg_p) # label(axiom) # label(non_clause).  [assumption].
0.89/1.20	65 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> (p(ap(c_2Ebool_2E_21(A),Q)) <-> (all X (mem(X,A) -> p(ap(Q,X))))))))) # label(ax_all_p) # label(axiom) # label(non_clause).  [assumption].
1.68/1.97	66 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (p(V0P) | (exists V2x (p(ap(V1Q,V2x)) & mem(V2x,A_27a))) <-> (exists V3x (mem(V3x,A_27a) & (p(ap(V1Q,V3x)) | p(V0P))))))))))) # label(conj_thm_2Ebool_2ERIGHT__OR__EXISTS__THM) # label(axiom) # label(non_clause).  [assumption].
1.68/1.97	67 (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].
1.68/1.97	68 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ((exists V1m (mem(V1m,ty_2Enum_2Enum) & V0n = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) <-> p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__EXISTS) # label(axiom) # label(non_clause).  [assumption].
1.68/1.97	69 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Enum_2ESUC,V0n))))) # label(conj_thm_2Eprim__rec_2ELESS__0) # label(axiom) # label(non_clause).  [assumption].
1.68/1.97	70 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((p(V0A) -> --p(V1B)) <-> --(-p(V0A) | p(V1B))))))) # label(conj_thm_2Esat_2EOR__DUAL3) # label(axiom) # label(non_clause).  [assumption].
1.68/1.97	71 (all V0t (mem(V0t,bool) -> (p(V0t) <-> --p(V0t)))) # label(conj_thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause).  [assumption].
1.68/1.97	72 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (-p(ap(c_2Earithmetic_2EODD,V0n)) <-> p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__ODD) # label(axiom) # label(non_clause).  [assumption].
1.68/1.97	73 $T # label(conj_thm_2Ebool_2ETRUTH) # label(axiom) # label(non_clause).  [assumption].
1.68/1.97	74 (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].
1.68/1.97	75 -(all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,V0n)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EMOD__2) # label(negated_conjecture) # label(non_clause).  [assumption].
1.68/1.97	
1.68/1.97	============================== end of process non-clausal formulas ===
1.68/1.97	
1.68/1.97	============================== PROCESS INITIAL CLAUSES ===============
1.68/1.97	
1.68/1.97	============================== PREDICATE ELIMINATION =================
1.68/1.97	
1.68/1.97	============================== end predicate elimination =============
1.68/1.97	
1.68/1.97	Auto_denials:  (non-Horn, no changes).
1.68/1.97	
1.68/1.97	Term ordering decisions:
1.68/1.97	Function symbol KB weights:  bool=1. ty_2Enum_2Enum=1. c_2Enum_2ESUC=1. c_2Earithmetic_2ENUMERAL=1. c_2Earithmetic_2EZERO=1. c_2Earithmetic_2E_2A=1. c_2Eprim__rec_2E_3C=1. c_2Earithmetic_2EBIT2=1. c_2Earithmetic_2EEVEN=1. c_2Earithmetic_2EODD=1. c_2Earithmetic_2EBIT1=1. c_2Earithmetic_2E_2B=1. c_2Ebool_2E_2F_5C=1. c_2Ebool_2E_5C_2F=1. c_2Emin_2E_3D_3D_3E=1. c_2Enum_2E0=1. c_2Ebool_2ET=1. c_2Earithmetic_2EMOD=1. c_2Ebool_2EF=1. c_2Ebool_2E_7E=1. ind=1. c1=1. ap=1. arr=1. k=1. f15=1. f16=1. f17=1. f23=1. c_2Ebool_2ECOND=1. c_2Ebool_2E_21=1. c_2Ebool_2E_3F=1. c_2Emin_2E_3D=1. i=1. f18=1. f26=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f19=1. f20=1. f21=1. f22=1. f24=1. f25=1. f1=1. f13=1. f14=1.
1.68/1.97	
1.68/1.97	============================== end of process initial clauses ========
1.68/1.97	
1.68/1.97	============================== CLAUSES FOR SEARCH ====================
1.68/1.97	
1.68/1.97	============================== end of clauses for search =============
1.68/1.97	
1.68/1.97	============================== SEARCH ================================
1.68/1.97	
1.68/1.97	% Starting search at 0.04 seconds.
1.68/1.97	
1.68/1.97	Low Water (keep): wt=42.000, iters=3405
1.68/1.97	
1.68/1.97	Low Water (keep): wt=41.000, iters=3488
1.68/1.97	
1.68/1.97	Low Water (keep): wt=40.000, iters=3477
1.68/1.97	
1.68/1.97	Low Water (keep): wt=39.000, iters=3443
1.68/1.97	
1.68/1.97	Low Water (keep): wt=37.000, iters=3407
1.68/1.97	
1.68/1.97	Low Water (keep): wAlarm clock 
119.63/120.06	Prover9 interrupted
119.63/120.06	EOF