0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n016.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 960
0.12/0.34	% DateTime   : Thu Jul  2 15:22:05 EDT 2020
0.12/0.34	% CPUTime    : 
0.79/1.10	============================== Prover9 ===============================
0.79/1.10	Prover9 (32) version 2009-11A, November 2009.
0.79/1.10	Process 14409 was started by sandbox2 on n016.cluster.edu,
0.79/1.10	Thu Jul  2 15:22:05 2020
0.79/1.10	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_14256_n016.cluster.edu".
0.79/1.10	============================== end of head ===========================
0.79/1.10	
0.79/1.10	============================== INPUT =================================
0.79/1.10	
0.79/1.10	% Reading from file /tmp/Prover9_14256_n016.cluster.edu
0.79/1.10	
0.79/1.10	set(prolog_style_variables).
0.79/1.10	set(auto2).
0.79/1.10	    % set(auto2) -> set(auto).
0.79/1.10	    % set(auto) -> set(auto_inference).
0.79/1.10	    % set(auto) -> set(auto_setup).
0.79/1.10	    % set(auto_setup) -> set(predicate_elim).
0.79/1.10	    % set(auto_setup) -> assign(eq_defs, unfold).
0.79/1.10	    % set(auto) -> set(auto_limits).
0.79/1.10	    % set(auto_limits) -> assign(max_weight, "100.000").
0.79/1.10	    % set(auto_limits) -> assign(sos_limit, 20000).
0.79/1.10	    % set(auto) -> set(auto_denials).
0.79/1.10	    % set(auto) -> set(auto_process).
0.79/1.10	    % set(auto2) -> assign(new_constants, 1).
0.79/1.10	    % set(auto2) -> assign(fold_denial_max, 3).
0.79/1.10	    % set(auto2) -> assign(max_weight, "200.000").
0.79/1.10	    % set(auto2) -> assign(max_hours, 1).
0.79/1.10	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.79/1.10	    % set(auto2) -> assign(max_seconds, 0).
0.79/1.10	    % set(auto2) -> assign(max_minutes, 5).
0.79/1.10	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.79/1.10	    % set(auto2) -> set(sort_initial_sos).
0.79/1.10	    % set(auto2) -> assign(sos_limit, -1).
0.79/1.10	    % set(auto2) -> assign(lrs_ticks, 3000).
0.79/1.10	    % set(auto2) -> assign(max_megs, 400).
0.79/1.10	    % set(auto2) -> assign(stats, some).
0.79/1.10	    % set(auto2) -> clear(echo_input).
0.79/1.10	    % set(auto2) -> set(quiet).
0.79/1.10	    % set(auto2) -> clear(print_initial_clauses).
0.79/1.10	    % set(auto2) -> clear(print_given).
0.79/1.10	assign(lrs_ticks,-1).
0.79/1.10	assign(sos_limit,10000).
0.79/1.10	assign(order,kbo).
0.79/1.10	set(lex_order_vars).
0.79/1.10	clear(print_given).
0.79/1.10	
0.79/1.10	% formulas(sos).  % not echoed (112 formulas)
0.79/1.10	
0.79/1.10	============================== end of input ==========================
0.79/1.10	
0.79/1.10	% From the command line: assign(max_seconds, 960).
0.79/1.10	
0.79/1.10	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.79/1.10	
0.79/1.10	% Formulas that are not ordinary clauses:
0.79/1.10	1 (all A all X (mem(X,A) -> X = ap(i(A),X))) # label(ibeta) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	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].
0.79/1.10	3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	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].
0.79/1.10	5 (all A all Y all X (mem(X,A) -> Y = ap(k(A,Y),X))) # label(kbeta) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	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].
0.79/1.10	7 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V1y),V0x))))) # label(conj_thm_2Ereal_2EREAL__ADD__SYM) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	8 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> ((p(V0t1) -> p(V1t2)) -> ((p(V1t2) -> p(V0t1)) -> (p(V1t2) <-> p(V0t1)))))))) # label(conj_thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	9 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((-p(V2r) | p(V0p)) & (p(V1q) | -p(V0p) | p(V2r)) & (p(V0p) | -p(V1q)) <-> (p(V1q) | p(V2r) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	10 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (V1y != ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) -> V0x = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,V0x),V1y)),V1y)))))) # label(conj_thm_2Ereal_2EREAL__DIV__RMUL) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	11 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	12 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n)))))) # label(conj_thm_2Ereal_2EREAL__ADD) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	13 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) -> p(R)) <-> p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))))))) # label(ax_imp_p) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	14 (all V0y (mem(V0y,ty_2Erealax_2Ereal) -> (all V1x (mem(V1x,ty_2Erealax_2Ereal) -> (-p(ap(ap(c_2Ereal_2Ereal__lte,V0y),V1x)) <-> p(ap(ap(c_2Erealax_2Ereal__lt,V1x),V0y))))))) # label(conj_thm_2Ereal_2Ereal__lt) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	15 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	16 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V0p) | -p(V1q) | -p(V2r)) & (p(V1q) | -p(V0p)) & (p(V2r) | -p(V0p)) <-> (p(V2r) & p(V1q) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	17 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Erealax_2Ereal__neg,V1y)))))) # label(ax_thm_2Ereal_2Ereal__sub) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	18 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2z (mem(V2z,ty_2Erealax_2Ereal) -> (ap(ap(c_2Erealax_2Ereal__add,V0x),V2z) = ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) <-> V2z = V1y))))))) # label(conj_thm_2Ereal_2EREAL__EQ__LADD) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	19 (all V0t (mem(V0t,bool) -> -p(V0t) | p(V0t))) # label(conj_thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	20 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V1y = V0x <-> V1y = V0x))))))) # label(conj_thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	21 (all V0r (mem(V0r,ty_2Erealax_2Ereal) -> (exists V1n (mem(V1n,ty_2Enum_2Enum) & p(ap(ap(c_2Erealax_2Ereal__lt,V0r),ap(c_2Ereal_2Ereal__of__num,V1n))))))) # label(conj_thm_2Ereal_2EREAL__BIGNUM) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	22 (all Q (mem(Q,bool) -> (-p(Q) <-> p(ap(c_2Ebool_2E_7E,Q))))) # label(ax_neg_p) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	23 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> (((p(V1q) -> p(V2r)) <-> p(V0p)) <-> (p(V0p) | p(V1q)) & (-p(V2r) | p(V0p)) & (-p(V1q) | p(V2r) | -p(V0p))))))))) # label(conj_thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	24 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2z (mem(V2z,ty_2Erealax_2Ereal) -> ap(ap(c_2Erealax_2Ereal__add,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z))))))) # label(conj_thm_2Ereal_2EREAL__ADD__ASSOC) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	25 (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(V0x) <-> p(V1x_27)) & (p(V1x_27) -> (p(V3y_27) <-> p(V2y))) -> ((p(V0x) -> p(V2y)) <-> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2Ebool_2EIMP__CONG) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	26 (all V0m (mem(V0m,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(c_2Enum_2ESUC,V0m))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__SUC__REFL) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	27 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <-> p(Q) | p(R)))))) # label(ax_or_p) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	28 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,V0m) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EADD1) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	29 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2z (mem(V2z,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Erealax_2Ereal__add,V2z),V1y))) <-> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)),V2z))))))))) # label(conj_thm_2Ereal_2EREAL__LE__SUB__RADD) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	30 $T # label(conj_thm_2Ebool_2ETRUTH) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	31 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (exists V1n (mem(V1n,ty_2Enum_2Enum) & V0m = ap(c_2Enum_2ESUC,V1n))) | c_2Enum_2E0 = V0m)) # label(conj_thm_2Earithmetic_2Enum__CASES) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	32 (all V0t (mem(V0t,bool) -> (($T <-> p(V0t)) <-> p(V0t)) & ((p(V0t) <-> $F) <-> -p(V0t)) & (-p(V0t) <-> (p(V0t) <-> $F)) & ((p(V0t) <-> $T) <-> p(V0t)))) # label(conj_thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	33 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2z (mem(V2z,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) -> (p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) <-> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z))))))))))) # label(conj_thm_2Ereal_2EREAL__LE__RMUL) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	34 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) & p(V0t) <-> p(V0t)) & ($F <-> $F & p(V0t)) & ($F & p(V0t) <-> $F))) # label(conj_thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	35 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> ap(ap(c_2Ereal_2Ereal__sub,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = V0x)) # label(conj_thm_2Ereal_2EREAL__SUB__RZERO) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	36 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> (p(ap(c_2Ebool_2E_3F(A),Q)) <-> (exists X (mem(X,A) & p(ap(Q,X))))))))) # label(ax_ex_p) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	37 (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].
0.79/1.10	38 (all V0p (mem(V0p,arr(ty_2Enum_2Enum,bool)) -> ((exists V1n (p(ap(V0p,V1n)) & mem(V1n,ty_2Enum_2Enum))) -> p(ap(V0p,ap(c_2Ewhile_2ELEAST,V0p))) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Ewhile_2ELEAST,V0p))) -> -p(ap(V0p,V2n)))))))) # label(conj_thm_2Ewhile_2ELEAST__EXISTS__IMP) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	39 (all V0A (mem(V0A,bool) -> (p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	40 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (V0x = V1y <-> ap(c_2Erealax_2Ereal__neg,V1y) = ap(c_2Erealax_2Ereal__neg,V0x)))))) # label(conj_thm_2Ereal_2EREAL__EQ__NEG) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	41 (all V0t (mem(V0t,bool) -> (p(V0t) <-> $F) | ($T <-> p(V0t)))) # label(ax_thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	42 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) <-> V1y != V0x & p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y))))))) # label(conj_thm_2Ereal_2EREAL__LT__LE) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	43 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,V0x)),V1y) = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)))))) # label(conj_thm_2Ereal_2EREAL__MUL__LNEG) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	44 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t3 (mem(V2t3,bool) -> ((p(V0t1) -> (p(V1t2) -> p(V2t3))) <-> (p(V1t2) & p(V0t1) -> p(V2t3))))))))) # label(conj_thm_2Ebool_2EAND__IMP__INTRO) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	45 (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].
0.79/1.10	46 (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].
0.79/1.10	47 (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].
0.79/1.10	48 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Ereal_2EREAL__LE) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	49 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	50 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2z (mem(V2z,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) & p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) -> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V2z))))))))) # label(conj_thm_2Ereal_2EREAL__LE__TRANS) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	51 (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].
0.79/1.10	52 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (-p(V0A) & -p(V1B) <-> -(p(V1B) | p(V0A))) & (-p(V0A) | -p(V1B) <-> -(p(V0A) & p(V1B))))))) # label(conj_thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	53 (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].
0.79/1.10	54 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) <-> -p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y))))))) # label(conj_thm_2Ereal_2EREAL__NOT__LT) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	55 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V1B) | p(V0A) <-> p(V0A) | p(V1B)))))) # label(conj_thm_2Ebool_2EDISJ__SYM) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	56 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2z (mem(V2z,ty_2Erealax_2Ereal) -> (V1y = ap(ap(c_2Erealax_2Ereal__add,V0x),V2z) <-> ap(ap(c_2Ereal_2Ereal__sub,V1y),V2z) = V0x))))))) # label(conj_thm_2Ereal_2EREAL__EQ__SUB__LADD) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	57 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2z (mem(V2z,ty_2Erealax_2Ereal) -> (ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) = V2z | V1y = V0x <-> ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z) = ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)))))))) # label(conj_thm_2Ereal_2EREAL__EQ__RMUL) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	58 (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].
0.79/1.10	59 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enum_2ESUC,V0n))))) # label(conj_thm_2Eprim__rec_2ELESS__SUC__REFL) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	60 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Ereal_2Ereal__of__num,V1n) = ap(c_2Ereal_2Ereal__of__num,V0m) <-> V1n = V0m))))) # label(conj_thm_2Ereal_2EREAL__INJ) # label(axiom) # label(non_clause).  [assumption].
0.79/1.10	61 (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].
0.79/1.11	62 (all V0t (mem(V0t,bool) -> (($F -> p(V0t)) <-> $T) & ($T <-> (p(V0t) -> p(V0t))) & (-p(V0t) <-> -p(V0t)) & ((p(V0t) -> $T) <-> $T) & (p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	63 (all V0A (mem(V0A,bool) -> (--p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	64 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_2F_5C,Q),R)) <-> p(R) & p(Q)))))) # label(ax_and_p) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	65 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) # label(conj_thm_2Ereal_2EREAL__MUL__LZERO) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	66 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2z (mem(V2z,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z))) <-> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y))))))))) # label(conj_thm_2Ereal_2EREAL__LE__RADD) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	67 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	68 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V2r) | p(V1q) | p(V0p)) & (-p(V2r) | -p(V0p) | p(V1q)) & (-p(V1q) | -p(V0p) | p(V2r)) & (p(V0p) | -p(V2r) | -p(V1q)) <-> ((p(V1q) <-> p(V2r)) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	69 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> (all V2z (mem(V2z,ty_2Erealax_2Ereal) -> ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)))))))) # label(conj_thm_2Ereal_2EREAL__ADD__RDISTRIB) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	70 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) | p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & ($T <-> p(V0t) | $T) & (p(V0t) | $T <-> $T))) # label(conj_thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	71 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> V0x = ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Ereal__neg,V0x)))) # label(conj_thm_2Ereal_2EREAL__NEGNEG) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	72 (all V0x (mem(V0x,ty_2Erealax_2Ereal) -> (all V1y (mem(V1y,ty_2Erealax_2Ereal) -> ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y)))))) # label(conj_thm_2Ereal_2EREAL__NEG__ADD) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	73 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> ((p(V0p) <-> -p(V1q)) <-> (p(V1q) | p(V0p)) & (-p(V0p) | -p(V1q))))))) # label(conj_thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	74 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	75 -$F <-> $T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	76 -$T <-> $F # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause).  [assumption].
0.79/1.11	77 (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].
0.79/1.11	78 (all V0P (mem(V0P,arr(ty_2Erealax_2Ereal,bool)) -> ((exists V2z (mem(V2z,ty_2Erealax_2Ereal) & (all V3x (mem(V3x,ty_2Erealax_2Ereal) -> (p(ap(V0P,V3x)) -> p(ap(ap(c_2Ereal_2Ereal__lte,V3x),V2z))))))) & (exists V1x (mem(V1x,ty_2Erealax_2Ereal) & p(ap(V0P,V1x)))) -> (all V4y (mem(V4y,ty_2Erealax_2Ereal) -> (p(ap(ap(c_2Erealax_2Ereal__lt,V4y),ap(c_2Ereal_2Esup,V0P))) <-> (exists V5x (mem(V5x,ty_2Erealax_2Ereal) & p(ap(ap(cAlarm clock 
119.61/120.02	Prover9 interrupted
119.61/120.03	EOF