0.10/0.11	% Problem    : SLH695^1 : TPTP v7.5.0. Released v7.5.0.
0.10/0.12	% Command    : do_cvc5 %s %d
0.12/0.33	% Computer : n008.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
0.12/0.33	% CPULimit   : 30
0.12/0.33	% WCLimit    : 30
0.12/0.33	% DateTime   : Tue Aug  9 03:31:23 EDT 2022
0.12/0.33	% CPUTime    : 
0.19/0.46	%----Proving TH0 SLH
0.46/0.69	------- cvc5-slh casc 28 : /export/starexec/sandbox/benchmark/theBenchmark.p at 30...
0.46/0.69	--- Run --ho-elim --full-saturate-quant at 5...
0.46/0.69	% SZS status Theorem for theBenchmark
0.46/0.69	% SZS output start Proof for theBenchmark
0.46/0.69	(let ((_let_1 (= genClo2108747023bound2 (lambda ((C4 (-> nat real real))) (forall ((P3 nat) (S3 real) (T3 real)) (let ((_let_1 (@ C4 P3))) (=> (and (@ (@ genClo1015804716orrect P3) T3) (@ (@ ord_less_eq_real S3) T3)) (@ (@ ord_less_eq_real (@ (@ times_times_real (@ (@ minus_minus_real T3) S3)) (@ (@ minus_minus_real one_one_real) genClo1144207539le_rho))) (@ (@ minus_minus_real (@ _let_1 T3)) (@ _let_1 S3)))))))))) (let ((_let_2 (= genClo2108747022bound1 (lambda ((C4 (-> nat real real))) (forall ((P3 nat) (S3 real) (T3 real)) (let ((_let_1 (@ C4 P3))) (=> (and (@ (@ genClo1015804716orrect P3) T3) (@ (@ ord_less_eq_real S3) T3)) (@ (@ ord_less_eq_real (@ (@ minus_minus_real (@ _let_1 T3)) (@ _let_1 S3))) (@ (@ times_times_real (@ (@ minus_minus_real T3) S3)) (@ (@ plus_plus_real one_one_real) genClo1144207539le_rho)))))))))) (let ((_let_3 (= genClo1087856337amma_2 (lambda ((X real)) (@ (@ plus_plus_real X) (@ (@ times_times_real (@ (@ times_times_real (@ numeral_numeral_real (@ bit0 one))) genClo1144207539le_rho)) genClo1650508560e_rmax)))))) (let ((_let_4 (= ord_less_eq_nat (lambda ((A2 nat) (B2 nat)) (exists ((C3 nat)) (= B2 (@ (@ plus_plus_nat A2) C3))))))) (let ((_let_5 (= (@ numeral_numeral_nat one) one_one_nat))) (let ((_let_6 (@ bit0 one))) (let ((_let_7 (@ numeral_numeral_real _let_6))) (let ((_let_8 (@ (@ plus_plus_nat i) one_one_nat))) (let ((_let_9 (@ (@ genClo1163638703lle_te q) _let_8))) (let ((_let_10 (@ genClo1015804716orrect q))) (let ((_let_11 (forall ((L nat)) (let ((_let_1 (@ times_times_real (@ numeral_numeral_real (@ bit0 one))))) (let ((_let_2 (@ (@ plus_plus_nat i) one_one_nat))) (let ((_let_3 (@ genClo1161277105lle_PC q))) (let ((_let_4 (@ (@ genClo1163638703lle_te p) _let_2))) (=> (@ (@ genClo1015804716orrect L) _let_4) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ (@ plus_plus_real (@ (@ (@ genClo1400225944_theta q) _let_2) L)) (@ (@ minus_minus_real (@ _let_3 _let_4)) (@ _let_3 (@ (@ genClo1163638703lle_te q) _let_2))))) (@ (@ (@ genClo1400225944_theta p) _let_2) L)))) (@ (@ plus_plus_real (@ (@ times_times_real (@ _let_1 genClo1144207539le_rho)) genClo1278781456e_beta)) (@ _let_1 genClo721845095Lambda))))))))))) (let ((_let_12 (@ times_times_real _let_7))) (let ((_let_13 (@ (@ genClo1400225944_theta p) _let_8))) (let ((_let_14 (not (@ (@ (@ (@ genClo293725282kRead2 (lambda ((N2 nat)) (let ((_let_1 (@ (@ plus_plus_nat i) one_one_nat))) (let ((_let_2 (@ genClo1161277105lle_PC q))) (@ (@ plus_plus_real (@ (@ (@ genClo1400225944_theta q) _let_1) N2)) (@ (@ minus_minus_real (@ _let_2 (@ (@ genClo1163638703lle_te p) _let_1))) (@ _let_2 (@ (@ genClo1163638703lle_te q) _let_1)))))))) _let_13) (@ (@ plus_plus_real (@ (@ times_times_real (@ _let_12 genClo1144207539le_rho)) genClo1278781456e_beta)) (@ _let_12 genClo721845095Lambda))) (lambda ((L3 nat)) (@ (@ genClo1015804716orrect L3) (@ (@ genClo1163638703lle_te p) (@ (@ plus_plus_nat i) one_one_nat)))))))) (let ((_let_15 (@ (@ genClo1163638703lle_te p) _let_8))) (let ((_let_16 (= (@ numeral_numeral_real one) one_one_real))) (let ((_let_17 (= genClo293725282kRead2 (lambda ((F (-> nat real)) (G (-> nat real)) (X real) (Ppred (-> nat Bool))) (forall ((P3 nat)) (=> (@ Ppred P3) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ F P3)) (@ G P3)))) X))))))) (let ((_let_18 (= genClo1087856336amma_1 (lambda ((X real)) (let ((_let_1 (@ times_times_real (@ numeral_numeral_real (@ bit0 one))))) (let ((_let_2 (@ times_times_real (@ _let_1 genClo1144207539le_rho)))) (let ((_let_3 (@ _let_1 genClo721845095Lambda))) (@ (@ genClo1199132825lle_pi (@ (@ plus_plus_real (@ _let_2 genClo1278781456e_beta)) _let_3)) (@ (@ plus_plus_real (@ (@ plus_plus_real _let_3) X)) (@ _let_2 (@ (@ plus_plus_real genClo1650508560e_rmax) genClo1278781456e_beta))))))))))) (let ((_let_19 (= genClo1087856338amma_3 (lambda ((X real)) (let ((_let_1 (@ times_times_real (@ numeral_numeral_real (@ bit0 one))))) (let ((_let_2 (@ times_times_real (@ _let_1 genClo1144207539le_rho)))) (@ (@ plus_plus_real (@ (@ plus_plus_real (@ genClo1586961944_alpha (@ (@ plus_plus_real (@ (@ plus_plus_real (@ _let_1 genClo721845095Lambda)) X)) (@ _let_2 (@ (@ plus_plus_real genClo1650508560e_rmax) genClo1278781456e_beta))))) genClo721845095Lambda)) (@ _let_2 genClo1278781456e_beta)))))))) (let ((_let_20 (forall ((BOUND_VARIABLE_9871 nat)) (let ((_let_1 (ho_32 k_40 (ho_45 k_44 (ho_43 k_42 one))))) (let ((_let_2 (ho_16 (ho_15 k_14 i) (ho_27 k_26 one)))) (let ((_let_3 (ho_30 k_29 q))) (let ((_let_4 (ho_25 (ho_24 k_28 p) _let_2))) (or (not (ho_49 (ho_51 k_52 BOUND_VARIABLE_9871) _let_4)) (ho_49 (ho_48 k_47 (ho_20 k_53 (ho_20 (ho_32 k_31 (ho_20 (ho_32 k_34 (ho_25 (ho_24 (ho_23 k_33 q) _let_2) BOUND_VARIABLE_9871)) (ho_20 (ho_32 k_31 (ho_20 _let_3 _let_4)) (ho_20 _let_3 (ho_25 (ho_24 k_28 q) _let_2))))) (ho_25 (ho_24 (ho_23 k_33 p) _let_2) BOUND_VARIABLE_9871)))) (ho_20 (ho_32 k_34 (ho_20 (ho_32 k_40 (ho_20 _let_1 genClo1144207539le_rho)) genClo1278781456e_beta)) (ho_20 _let_1 genClo721845095Lambda))))))))))) (let ((_let_21 (forall ((L nat)) (let ((_let_1 (ho_32 k_40 (ho_45 k_44 (ho_43 k_42 one))))) (let ((_let_2 (ho_16 (ho_15 k_14 i) (ho_27 k_26 one)))) (let ((_let_3 (ho_30 k_29 q))) (let ((_let_4 (ho_25 (ho_24 k_28 p) _let_2))) (or (not (ho_49 (ho_51 k_52 L) _let_4)) (ho_49 (ho_48 k_47 (ho_20 k_53 (ho_20 (ho_32 k_31 (ho_20 (ho_32 k_34 (ho_25 (ho_24 (ho_23 k_33 q) _let_2) L)) (ho_20 (ho_32 k_31 (ho_20 _let_3 _let_4)) (ho_20 _let_3 (ho_25 (ho_24 k_28 q) _let_2))))) (ho_25 (ho_24 (ho_23 k_33 p) _let_2) L)))) (ho_20 (ho_32 k_34 (ho_20 (ho_32 k_40 (ho_20 _let_1 genClo1144207539le_rho)) genClo1278781456e_beta)) (ho_20 _let_1 genClo721845095Lambda))))))))))) (let ((_let_22 (SYMM (ASSUME :args (_let_5))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (SYMM (ASSUME :args (_let_16))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_25 _let_24 _let_23 _let_22) :args ((= genClo2108747022bound1 (lambda ((C4 (-> nat real real))) (forall ((P3 nat) (S3 real) (T3 real)) (let ((_let_1 (@ C4 P3))) (or (not (@ (@ genClo1015804716orrect P3) T3)) (not (@ (@ ord_less_eq_real S3) T3)) (@ (@ ord_less_eq_real (@ (@ minus_minus_real (@ _let_1 T3)) (@ _let_1 S3))) (@ (@ times_times_real (@ (@ minus_minus_real T3) S3)) (@ (@ plus_plus_real one_one_real) genClo1144207539le_rho)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (AND_INTRO (ASSUME :args (_let_19)) (ASSUME :args (_let_3)) (ASSUME :args (_let_18)) (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_26 _let_25 _let_24 _let_23 _let_22) :args ((= genClo2108747023bound2 (lambda ((C4 (-> nat real real))) (forall ((P3 nat) (S3 real) (T3 real)) (let ((_let_1 (@ C4 P3))) (or (not (@ (@ genClo1015804716orrect P3) T3)) (not (@ (@ ord_less_eq_real S3) T3)) (@ (@ ord_less_eq_real (@ (@ times_times_real (@ (@ minus_minus_real T3) S3)) (@ (@ minus_minus_real one_one_real) genClo1144207539le_rho))) (@ (@ minus_minus_real (@ _let_1 T3)) (@ _let_1 S3)))))))) SB_DEFAULT SBA_FIXPOINT))) _let_26 _let_25 _let_24 _let_23 _let_22))) (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO _let_27 :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((BOUND_VARIABLE_9871 nat)) (let ((_let_1 (@ times_times_real (@ numeral_numeral_real (@ bit0 one))))) (let ((_let_2 (@ (@ plus_plus_nat i) (@ numeral_numeral_nat one)))) (let ((_let_3 (@ genClo1161277105lle_PC q))) (let ((_let_4 (@ (@ genClo1163638703lle_te p) _let_2))) (or (not (@ (@ genClo1015804716orrect BOUND_VARIABLE_9871) _let_4)) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ (@ plus_plus_real (@ (@ (@ genClo1400225944_theta q) _let_2) BOUND_VARIABLE_9871)) (@ (@ minus_minus_real (@ _let_3 _let_4)) (@ _let_3 (@ (@ genClo1163638703lle_te q) _let_2))))) (@ (@ (@ genClo1400225944_theta p) _let_2) BOUND_VARIABLE_9871)))) (@ (@ plus_plus_real (@ (@ times_times_real (@ _let_1 genClo1144207539le_rho)) genClo1278781456e_beta)) (@ _let_1 genClo721845095Lambda)))))))))) (not _let_20)))))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_21 (= L BOUND_VARIABLE_9871)))) :args ((or _let_20 (not _let_21)))) (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_27 :args ((forall ((L nat)) (let ((_let_1 (@ times_times_real (@ numeral_numeral_real (@ bit0 one))))) (let ((_let_2 (@ (@ plus_plus_nat i) one_one_nat))) (let ((_let_3 (@ genClo1161277105lle_PC q))) (let ((_let_4 (@ (@ genClo1163638703lle_te p) _let_2))) (or (not (@ (@ genClo1015804716orrect L) _let_4)) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ (@ plus_plus_real (@ (@ (@ genClo1400225944_theta q) _let_2) L)) (@ (@ minus_minus_real (@ _let_3 _let_4)) (@ _let_3 (@ (@ genClo1163638703lle_te q) _let_2))))) (@ (@ (@ genClo1400225944_theta p) _let_2) L)))) (@ (@ plus_plus_real (@ (@ times_times_real (@ _let_1 genClo1144207539le_rho)) genClo1278781456e_beta)) (@ _let_1 genClo721845095Lambda))))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((L nat)) (let ((_let_1 (@ times_times_real (@ numeral_numeral_real (@ bit0 one))))) (let ((_let_2 (@ (@ plus_plus_nat i) (@ numeral_numeral_nat one)))) (let ((_let_3 (@ genClo1161277105lle_PC q))) (let ((_let_4 (@ (@ genClo1163638703lle_te p) _let_2))) (or (not (@ (@ genClo1015804716orrect L) _let_4)) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ (@ plus_plus_real (@ (@ (@ genClo1400225944_theta q) _let_2) L)) (@ (@ minus_minus_real (@ _let_3 _let_4)) (@ _let_3 (@ (@ genClo1163638703lle_te q) _let_2))))) (@ (@ (@ genClo1400225944_theta p) _let_2) L)))) (@ (@ plus_plus_real (@ (@ times_times_real (@ _let_1 genClo1144207539le_rho)) genClo1278781456e_beta)) (@ _let_1 genClo721845095Lambda))))))))) _let_21))))) :args (_let_20 false _let_21)) :args (false false _let_20)) :args (_let_19 (forall ((K nat) (J nat) (I nat)) (=> (@ (@ ord_less_eq_nat K) J) (= (@ (@ minus_minus_nat (@ (@ plus_plus_nat J) I)) K) (@ (@ plus_plus_nat (@ (@ minus_minus_nat J) K)) I)))) (forall ((K nat) (J nat) (I nat)) (let ((_let_1 (@ plus_plus_nat I))) (=> (@ (@ ord_less_eq_nat K) J) (= (@ (@ minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ minus_minus_nat J) K)))))) (forall ((K nat) (J nat) (I nat)) (=> (@ (@ ord_less_eq_nat K) J) (= (@ (@ ord_less_eq_nat I) (@ (@ minus_minus_nat J) K)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat I) K)) J)))) (forall ((N nat)) (= (@ (@ times_times_nat N) one_one_nat) N)) (forall ((M nat) (N nat) (K nat)) (= (@ (@ times_times_nat (@ (@ plus_plus_nat M) N)) K) (@ (@ plus_plus_nat (@ (@ times_times_nat M) K)) (@ (@ times_times_nat N) K)))) (forall ((N nat) (M nat)) (= (@ (@ minus_minus_nat (@ (@ plus_plus_nat N) M)) N) M)) (forall ((I nat) (J nat) (K nat)) (=> (@ (@ ord_less_eq_nat I) J) (@ (@ ord_less_eq_nat (@ (@ times_times_nat I) K)) (@ (@ times_times_nat J) K)))) (forall ((I nat) (J nat) (K nat) (L2 nat)) (=> (@ (@ ord_less_eq_nat I) J) (=> (@ (@ ord_less_eq_nat K) L2) (@ (@ ord_less_eq_nat (@ (@ times_times_nat I) K)) (@ (@ times_times_nat J) L2))))) (forall ((M nat) (N nat) (L2 nat)) (let ((_let_1 (@ minus_minus_nat L2))) (=> (@ (@ ord_less_eq_nat M) N) (@ (@ ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))) (forall ((A nat) (C nat) (B nat)) (let ((_let_1 (@ ord_less_eq_nat B))) (let ((_let_2 (@ minus_minus_nat C))) (=> (@ (@ ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))) (forall ((K nat) (M nat) (N nat)) (let ((_let_1 (@ ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ ord_less_eq_nat (@ (@ minus_minus_nat M) K)) (@ (@ minus_minus_nat N) K)) (@ (@ ord_less_eq_nat M) N)))))) (forall ((K nat) (M nat) (N nat)) (let ((_let_1 (@ ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ minus_minus_nat M) K) (@ (@ minus_minus_nat N) K)) (= M N)))))) (forall ((M nat) (K nat) (N nat)) (=> (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat M) K)) N) (not (=> (@ (@ ord_less_eq_nat M) N) (not (@ (@ ord_less_eq_nat K) N)))))) (forall ((N nat) (M nat)) (@ (@ ord_less_eq_nat N) (@ (@ plus_plus_nat M) N))) (forall ((M nat) (K nat) (N nat)) (=> (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat M) K)) N) (@ (@ ord_less_eq_nat M) N))) (forall ((M nat) (K nat) (N nat)) (=> (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat M) K)) N) (@ (@ ord_less_eq_nat K) N))) (forall ((K nat) (L2 nat)) (=> (@ (@ ord_less_eq_nat K) L2) (exists ((N3 nat)) (= L2 (@ (@ plus_plus_nat K) N3))))) (forall ((I nat) (J nat) (K nat)) (=> (@ (@ ord_less_eq_nat I) J) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat I) K)) (@ (@ plus_plus_nat J) K)))) (forall ((I nat) (J nat) (M nat)) (let ((_let_1 (@ ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ plus_plus_nat J) M))))) (forall ((I nat) (J nat) (M nat)) (let ((_let_1 (@ ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ plus_plus_nat M) J))))) (forall ((M nat) (N nat)) (or (@ (@ ord_less_eq_nat M) N) (@ (@ ord_less_eq_nat N) M))) (forall ((M nat) (N nat)) (=> (= M N) (@ (@ ord_less_eq_nat M) N))) (forall ((M nat) (N nat)) (= (= one_one_nat (@ (@ times_times_nat M) N)) (and (= M one_one_nat) (= N one_one_nat)))) (forall ((M nat) (N nat)) (= (= (@ (@ times_times_nat M) N) one_one_nat) (and (= M one_one_nat) (= N one_one_nat)))) (forall ((I nat) (N nat)) (let ((_let_1 (@ minus_minus_nat N))) (=> (@ (@ ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))) (forall ((K nat) (M nat) (N nat)) (let ((_let_1 (@ plus_plus_nat K))) (= (@ (@ ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ ord_less_eq_nat M) N)))) (forall ((K nat) (J nat) (I nat)) (=> (@ (@ ord_less_eq_nat K) J) (= (@ (@ minus_minus_nat I) (@ (@ minus_minus_nat J) K)) (@ (@ minus_minus_nat (@ (@ plus_plus_nat I) K)) J)))) _let_18 (forall ((P2 nat) (T real) (I2 nat)) (let ((_let_1 (@ genClo1163638703lle_te P2))) (=> (and (@ (@ genClo1015804716orrect P2) T) (@ (@ ord_less_eq_real T) (@ _let_1 (@ (@ plus_plus_nat I2) one_one_nat)))) (@ (@ ord_less_eq_real (@ (@ minus_minus_real T) (@ _let_1 I2))) genClo1650508560e_rmax)))) (forall ((M nat) (N nat)) (= (@ (@ minus_minus_nat (@ (@ plus_plus_nat M) N)) N) M)) (forall ((P nat) (I nat)) (let ((_let_1 (@ genClo1163638703lle_te P))) (let ((_let_2 (@ _let_1 (@ (@ plus_plus_nat I) one_one_nat)))) (=> (@ (@ genClo1015804716orrect P) _let_2) (@ (@ ord_less_eq_real (@ (@ minus_minus_real _let_2) (@ _let_1 I))) genClo1650508560e_rmax))))) (forall ((S2 real) (T2 real) (C5 (-> nat real real)) (D2 (-> nat real real)) (Q nat) (P nat)) (let ((_let_1 (@ D2 Q))) (let ((_let_2 (@ _let_1 S2))) (let ((_let_3 (@ C5 P))) (let ((_let_4 (@ _let_3 S2))) (let ((_let_5 (@ _let_1 T2))) (let ((_let_6 (@ minus_minus_real (@ _let_3 T2)))) (=> (@ (@ ord_less_eq_real S2) T2) (=> (@ genClo2108747022bound1 C5) (=> (@ genClo2108747023bound2 D2) (=> (@ (@ ord_less_eq_real (@ (@ minus_minus_real _let_5) _let_2)) (@ _let_6 _let_4)) (=> (@ (@ genClo1015804716orrect P) T2) (=> (@ (@ genClo1015804716orrect Q) T2) (@ (@ ord_less_eq_real (@ abs_abs_real (@ _let_6 _let_5))) (@ (@ plus_plus_real (@ abs_abs_real (@ (@ minus_minus_real _let_4) _let_2))) (@ (@ times_times_real (@ (@ times_times_real (@ numeral_numeral_real (@ bit0 one))) genClo1144207539le_rho)) (@ (@ minus_minus_real T2) S2))))))))))))))))) (forall ((S2 real) (T2 real) (C5 (-> nat real real)) (D2 (-> nat real real)) (P nat) (Q nat)) (let ((_let_1 (@ D2 Q))) (let ((_let_2 (@ C5 P))) (=> (@ (@ ord_less_eq_real S2) T2) (=> (@ genClo2108747022bound1 C5) (=> (@ genClo2108747023bound2 C5) (=> (@ genClo2108747022bound1 D2) (=> (@ genClo2108747023bound2 D2) (=> (@ (@ genClo1015804716orrect P) T2) (=> (@ (@ genClo1015804716orrect Q) T2) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ _let_2 T2)) (@ _let_1 T2)))) (@ (@ plus_plus_real (@ abs_abs_real (@ (@ minus_minus_real (@ _let_2 S2)) (@ _let_1 S2)))) (@ (@ times_times_real (@ (@ times_times_real (@ numeral_numeral_real (@ bit0 one))) genClo1144207539le_rho)) (@ (@ minus_minus_real T2) S2)))))))))))))) (@ (@ ord_less_eq_real genClo1278781456e_beta) genClo1651033342e_rmin) (forall ((M nat) (N nat) (L2 nat)) (=> (@ (@ ord_less_eq_nat M) N) (@ (@ ord_less_eq_nat (@ (@ minus_minus_nat M) L2)) (@ (@ minus_minus_nat N) L2)))) (forall ((I nat)) (@ genClo2108747023bound2 (lambda ((P3 nat) (__flatten_var_0 real)) (@ (@ (@ genClo1160817912lle_IC P3) I) __flatten_var_0)))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (@ times_times_nat A))) (= (@ (@ times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ times_times_nat B) C))))) (forall ((B real) (A real) (C real)) (let ((_let_1 (@ plus_plus_real B))) (let ((_let_2 (@ plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((X2 num)) (= (@ (@ ord_less_eq_num X2) one) (= X2 one))) (forall ((B real) (A real) (C real)) (= (= (@ (@ plus_plus_real B) A) (@ (@ plus_plus_real C) A)) (= B C))) (forall ((J nat) (I nat) (U nat) (M nat) (N nat)) (=> (@ (@ ord_less_eq_nat J) I) (= (= (@ (@ plus_plus_nat (@ (@ times_times_nat I) U)) M) (@ (@ plus_plus_nat (@ (@ times_times_nat J) U)) N)) (= (@ (@ plus_plus_nat (@ (@ times_times_nat (@ (@ minus_minus_nat I) J)) U)) M) N)))) _let_17 (forall ((M num)) (not (@ (@ ord_less_eq_num (@ bit0 M)) one))) (forall ((N num)) (@ (@ ord_less_eq_num one) N)) _let_16 (forall ((A real) (B real) (C real)) (let ((_let_1 (@ plus_plus_real C))) (=> (@ (@ ord_less_eq_real A) B) (@ (@ ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))) (forall ((M num) (N num)) (= (@ (@ ord_less_eq_num (@ bit0 M)) (@ bit0 N)) (@ (@ ord_less_eq_num M) N))) (forall ((A 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K)) (@ (@ plus_plus_nat (@ (@ times_times_nat (@ (@ plus_plus_nat I) J)) U)) K))) (forall ((A nat)) (= (@ (@ times_times_nat A) one_one_nat) A)) (forall ((A real) (B real) (C real)) (= (@ (@ times_times_real (@ (@ minus_minus_real A) B)) C) (@ (@ minus_minus_real (@ (@ times_times_real A) C)) (@ (@ times_times_real B) C)))) (forall ((A real) (B real) (C real) (D real)) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ (@ plus_plus_real A) B)) (@ (@ plus_plus_real C) D)))) (@ (@ plus_plus_real (@ abs_abs_real (@ (@ minus_minus_real A) C))) (@ abs_abs_real (@ (@ minus_minus_real B) D))))) (forall ((A real) (B real)) (= (@ abs_abs_real (@ (@ minus_minus_real A) B)) (@ abs_abs_real (@ (@ minus_minus_real B) A)))) (forall ((A real) (B real) (C real)) (let ((_let_1 (@ times_times_real A))) (= (@ _let_1 (@ (@ minus_minus_real B) C)) (@ (@ minus_minus_real (@ _let_1 B)) (@ _let_1 C))))) (forall ((B nat) (C nat) (A nat)) (= (@ (@ times_times_nat (@ (@ minus_minus_nat B) C)) A) (@ (@ minus_minus_nat (@ (@ times_times_nat B) A)) (@ (@ times_times_nat C) A)))) (forall ((A real) (B real) (C real)) (let ((_let_1 (@ times_times_real A))) (= (@ _let_1 (@ (@ minus_minus_real B) C)) (@ (@ minus_minus_real (@ _let_1 B)) (@ _let_1 C))))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (@ times_times_nat A))) (= (@ _let_1 (@ (@ minus_minus_nat B) C)) (@ (@ minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))) (forall ((Q nat) (I nat) (P nat) (L2 nat)) (let ((_let_1 (@ (@ plus_plus_nat I) one_one_nat))) (let ((_let_2 (@ (@ genClo1163638703lle_te Q) _let_1))) (let ((_let_3 (@ (@ genClo1163638703lle_te P) _let_1))) (let ((_let_4 (@ genClo1161277105lle_PC L2))) (=> (@ (@ ord_less_eq_real _let_2) _let_3) (=> (@ (@ genClo1015804716orrect P) _let_3) (=> (@ (@ genClo1015804716orrect Q) _let_3) (=> (@ (@ genClo1015804716orrect L2) _let_3) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ (@ minus_minus_real (@ _let_4 _let_3)) (@ _let_4 _let_2))) (@ (@ minus_minus_real _let_3) _let_2)))) (@ (@ times_times_real genClo1278781456e_beta) genClo1144207539le_rho))))))))))) (forall ((A3 real) (K real) (A real) (B real)) (let ((_let_1 (@ plus_plus_real K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ minus_minus_real A3) B) (@ _let_1 (@ (@ minus_minus_real A) B)))))) (forall ((A real) (B real) (C real)) (= (= (@ (@ minus_minus_real A) B) C) (= A (@ (@ plus_plus_real C) B)))) (forall ((K nat) (M nat) (N nat)) (let ((_let_1 (@ plus_plus_nat K))) (= (@ (@ minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ minus_minus_nat M) N)))) _let_3 (forall ((A real) (B real) (C real)) (let ((_let_1 (@ plus_plus_real A))) (= (@ _let_1 (@ (@ minus_minus_real B) C)) (@ (@ minus_minus_real (@ _let_1 B)) C)))) (forall ((K nat) (M nat) (N nat)) (let ((_let_1 (@ times_times_nat K))) (= (@ _let_1 (@ (@ plus_plus_nat M) N)) (@ (@ plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))) (forall ((A real) (B real) (C real)) (= (@ (@ minus_minus_real A) (@ (@ minus_minus_real B) C)) (@ (@ minus_minus_real (@ (@ plus_plus_real A) C)) B))) (forall ((A real) (B real) (C real)) (= (@ (@ plus_plus_real (@ (@ minus_minus_real A) B)) C) (@ (@ minus_minus_real (@ (@ plus_plus_real A) C)) B))) (forall ((A real) (B real) (C real)) (let ((_let_1 (@ minus_minus_real A))) (= (@ _let_1 (@ (@ plus_plus_real B) C)) (@ (@ minus_minus_real (@ _let_1 C)) B)))) (forall ((A real) (B real) (C real)) (let ((_let_1 (@ minus_minus_real A))) (= (@ (@ minus_minus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ plus_plus_real B) C))))) (forall ((C real) (B real) (A real)) (=> (= (@ (@ plus_plus_real C) B) A) (= C (@ (@ minus_minus_real A) B)))) (forall ((X2 real)) (= (= one_one_real X2) (= X2 one_one_real))) (forall ((A nat)) (= (@ (@ times_times_nat A) (@ numeral_numeral_nat one)) A)) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (@ plus_plus_nat C))) (=> (@ (@ ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ minus_minus_nat B) A)) (@ (@ minus_minus_nat (@ _let_1 B)) A))))) (forall ((Q nat) (I nat) (P nat)) (let ((_let_1 (@ (@ plus_plus_nat I) one_one_nat))) (let ((_let_2 (@ (@ genClo1163638703lle_te P) _let_1))) (=> (@ (@ ord_less_eq_real (@ (@ genClo1163638703lle_te Q) _let_1)) _let_2) (=> (@ (@ genClo1015804716orrect P) _let_2) (=> (@ (@ genClo1015804716orrect Q) _let_2) (= (@ (@ (@ genClo1160817912lle_IC Q) _let_1) _let_2) (@ (@ genClo1088630061le_cfn Q) (lambda ((N2 nat)) (let ((_let_1 (@ (@ plus_plus_nat I) one_one_nat))) (let ((_let_2 (@ genClo1161277105lle_PC Q))) (@ (@ plus_plus_real (@ (@ (@ genClo1400225944_theta Q) _let_1) N2)) (@ (@ minus_minus_real (@ _let_2 (@ (@ genClo1163638703lle_te P) _let_1))) (@ _let_2 (@ (@ genClo1163638703lle_te Q) _let_1))))))))))))))) (forall ((A real)) (= (@ (@ times_times_real one_one_real) A) A)) (forall ((N num)) (= (@ (@ ord_less_eq_nat (@ numeral_numeral_nat N)) one_one_nat) (@ (@ ord_less_eq_num N) one))) (= (lambda ((X real)) X) (@ times_times_real one_one_real)) (= ord_less_eq_nat (lambda ((M2 nat) (N2 nat)) (exists ((K2 nat)) (= N2 (@ (@ plus_plus_nat M2) K2))))) (forall ((A real) (C real) (B real)) (= (@ (@ ord_less_eq_real A) (@ (@ minus_minus_real C) B)) (@ (@ ord_less_eq_real (@ (@ plus_plus_real A) B)) C))) (forall ((I real) (K real) (N real)) (=> (@ (@ ord_less_eq_real (@ (@ plus_plus_real I) K)) N) (@ (@ ord_less_eq_real I) (@ (@ minus_minus_real N) K)))) (forall ((A nat) (B nat) (C nat)) (=> (@ (@ ord_less_eq_nat A) B) (@ (@ ord_less_eq_nat C) (@ (@ minus_minus_nat (@ (@ plus_plus_nat B) C)) A)))) (forall ((A nat) (B nat) (C nat)) (=> (@ (@ ord_less_eq_nat A) B) (= (@ (@ ord_less_eq_nat C) (@ (@ minus_minus_nat B) A)) (@ (@ ord_less_eq_nat (@ (@ plus_plus_nat C) A)) B)))) _let_2 (forall ((A nat) (B nat) (C nat)) (=> (@ (@ ord_less_eq_nat A) B) (= (@ (@ minus_minus_nat C) (@ (@ minus_minus_nat B) A)) (@ (@ minus_minus_nat (@ (@ plus_plus_nat C) A)) B)))) (forall ((A nat) (B nat)) (=> (@ (@ ord_less_eq_nat A) B) (= (@ (@ plus_plus_nat A) (@ (@ minus_minus_nat B) A)) B))) (forall ((A real) (E real) (C real) (B real) (D real)) (= (= (@ (@ plus_plus_real (@ (@ times_times_real A) E)) C) (@ (@ plus_plus_real (@ (@ times_times_real B) E)) D)) (= (@ (@ plus_plus_real (@ (@ times_times_real (@ (@ minus_minus_real A) B)) E)) C) D))) (forall ((I nat) (J nat) (K nat)) (let ((_let_1 (@ times_times_nat K))) (=> (@ (@ ord_less_eq_nat I) J) (@ (@ ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))) (forall ((X2 real) (Y real)) (= (@ (@ minus_minus_real (@ (@ times_times_real X2) X2)) (@ (@ times_times_real Y) Y)) (@ (@ times_times_real (@ (@ plus_plus_real X2) Y)) (@ (@ minus_minus_real X2) Y)))) (forall ((A real) (B real)) (@ (@ ord_less_eq_real (@ (@ minus_minus_real (@ abs_abs_real A)) (@ abs_abs_real B))) (@ abs_abs_real (@ (@ minus_minus_real A) B)))) (forall ((A real) (B real)) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ abs_abs_real A)) (@ abs_abs_real B)))) (@ abs_abs_real (@ (@ minus_minus_real A) B)))) (forall ((A real) (B real)) (@ (@ ord_less_eq_real (@ (@ minus_minus_real (@ abs_abs_real A)) (@ abs_abs_real B))) (@ abs_abs_real (@ (@ minus_minus_real B) A)))) (forall ((K nat) (J nat) (I nat)) (=> (@ (@ ord_less_eq_nat K) J) (= (@ (@ plus_plus_nat (@ (@ minus_minus_nat J) K)) I) (@ (@ minus_minus_nat (@ (@ plus_plus_nat J) I)) K)))) (forall ((A real)) (let ((_let_1 (@ abs_abs_real A))) (= (@ (@ times_times_real _let_1) _let_1) (@ (@ times_times_real A) A)))) (forall ((A real) (E real) (C real) (B real) (D real)) (= (@ (@ ord_less_eq_real (@ (@ plus_plus_real (@ (@ times_times_real A) E)) C)) (@ (@ plus_plus_real (@ (@ times_times_real B) E)) D)) (@ (@ ord_less_eq_real (@ (@ plus_plus_real (@ (@ times_times_real (@ (@ minus_minus_real A) B)) E)) C)) D))) (forall ((P2 nat) (Q2 nat) (I2 nat)) (let ((_let_1 (@ (@ plus_plus_nat I2) one_one_nat))) (let ((_let_2 (@ (@ genClo1163638703lle_te P2) _let_1))) (=> (and (@ (@ genClo1015804716orrect P2) _let_2) (@ (@ genClo1015804716orrect Q2) _let_2)) (@ (@ ord_less_eq_real (@ abs_abs_real (@ (@ minus_minus_real (@ (@ (@ genClo1400225944_theta P2) _let_1) Q2)) (@ (@ (@ genClo1160817912lle_IC Q2) I2) _let_2)))) genClo721845095Lambda))))) (forall ((A real) (C real) (B real)) (= (@ (@ minus_minus_real (@ (@ plus_plus_real A) C)) (@ (@ plus_plus_real B) C)) (@ (@ minus_minus_real A) B))) (forall ((I real) (K real) (N real) (J real)) (let ((_let_1 (@ (@ ord_less_eq_real N) (@ (@ plus_plus_real J) K)))) (let ((_let_2 (@ (@ ord_less_eq_real (@ (@ plus_plus_real I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ ord_less_eq_real (@ (@ minus_minus_real N) K)) J)))))))) (forall ((P2 nat) (T real) (I2 nat)) (=> (@ (@ genClo1015804716orrect P2) T) (= (@ (@ (@ genClo1160817912lle_IC P2) I2) T) (@ (@ plus_plus_real (@ (@ genClo1161277105lle_PC P2) T)) (@ (@ genClo807607689le_Adj P2) I2))))) (forall ((P nat) (I nat) (Q nat)) (let ((_let_1 (@ (@ genClo1163638703lle_te Q) I))) (let ((_let_2 (@ (@ genClo1163638703lle_te P) (@ (@ plus_plus_nat I) one_one_nat)))) (=> (@ (@ genClo1015804716orrect P) _let_2) (=> (@ (@ genClo1015804716orrect Q) _let_1) (@ (@ ord_less_eq_real (@ (@ minus_minus_real _let_2) _let_1)) (@ (@ plus_plus_real genClo1650508560e_rmax) genClo1278781456e_beta))))))) _let_1)))))))))))))))))))))))))))))
0.46/0.69	% SZS output end Proof for theBenchmark
0.46/0.69	EOF