0.10/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.12 % Command : do_cvc5 %s %d 0.12/0.33 % Computer : n010.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 : 960 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Tue Aug 9 02:48:05 EDT 2022 0.12/0.33 % CPUTime : 0.20/0.46 %----Proving TF0_NAR, FOF, or CNF 0.48/0.64 ------- cvc5-fof casc J11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 0.48/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 0.48/0.64 % SZS status Theorem for theBenchmark 0.48/0.64 % SZS output start Proof for theBenchmark 0.48/0.64 (let ((_let_1 (succ n0))) (let ((_let_2 (succ _let_1))) (let ((_let_3 (succ _let_2))) (let ((_let_4 (not (=> (and (= use (a_select2 rho_defuse n1)) (= use (a_select2 rho_defuse n2)) (= use (a_select2 sigma_defuse n1)) (= (a_select2 sigma_defuse n4) use) (= (a_select2 sigma_defuse n5) use) (= (a_select3 u_defuse n0 n0) use) (= (a_select2 xinit_defuse n4) use) (= use (a_select2 xinit_mean_defuse n2)) (= use (a_select2 xinit_mean_defuse n4)) (= use (a_select2 xinit_noise_defuse n0)) (= use (a_select2 xinit_noise_defuse n2)) (= (a_select2 xinit_noise_defuse n3) use) (= (a_select2 xinit_noise_defuse n4) use) (= use (a_select2 xinit_noise_defuse n5)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (leq B (pred pv5)) (leq A n2) (leq n0 B) (leq n0 A)) (= use (a_select3 u_defuse A B)))) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (leq n0 C) (leq n0 D) (leq C n2) (leq D (pred pv5))) (= use (a_select3 z_defuse C D)))) (gt pv5 n0) (leq pv5 n998) (leq n0 pv5) (= (a_select2 xinit_noise_defuse n1) use) (= use (a_select2 xinit_mean_defuse n5)) (= use (a_select2 xinit_mean_defuse n3)) (= use (a_select2 xinit_mean_defuse n1)) (= (a_select2 xinit_mean_defuse n0) use) (= (a_select2 xinit_defuse n5) use) (= use (a_select2 xinit_defuse n3)) (= use (a_select3 u_defuse n2 n0)) (= (a_select3 u_defuse n1 n0) use) (= (a_select2 sigma_defuse n3) use) (= use (a_select2 sigma_defuse n2)) (= use (a_select2 sigma_defuse n0)) (= (a_select2 rho_defuse n0) use)) (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (= F pv5))) (=> (and (leq n0 E) (leq E n2) (leq F pv5) (leq n0 F)) (=> (and (not (and _let_1 (= E n0))) (not (and (= n2 E) _let_1)) (not (and (= E n1) (= pv5 F)))) (= use (a_select3 z_defuse E F)))))))))) (let ((_let_5 (forall ((X $$unsorted)) (=> (and (leq n0 X) (leq X n2)) (or (= n0 X) (= n1 X) (= X n2)))))) (let ((_let_6 (succ _let_3))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (= (leq X (pred Y)) (gt Y X))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (leq X Y) (not (= Y X))) (gt Y X))))) (let ((_let_9 (leq n0 skv_2))) (let ((_let_10 (leq skv_2 n2))) (let ((_let_11 (= n2 skv_2))) (let ((_let_12 (= n1 skv_2))) (let ((_let_13 (= n0 skv_2))) (let ((_let_14 (not _let_10))) (let ((_let_15 (not _let_9))) (let ((_let_16 (or _let_15 _let_14 _let_13 _let_12 _let_11))) (let ((_let_17 (= use (a_select3 z_defuse skv_2 skv_3)))) (let ((_let_18 (= pv5 skv_3))) (let ((_let_19 (and _let_12 _let_18))) (let ((_let_20 (and _let_11 _let_18))) (let ((_let_21 (and _let_18 _let_13))) (let ((_let_22 (leq n0 skv_3))) (let ((_let_23 (not _let_22))) (let ((_let_24 (leq skv_3 pv5))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_15 _let_14 _let_25 _let_23 _let_21 _let_20 _let_19 _let_17))) (let ((_let_27 (forall ((E $$unsorted) (F $$unsorted)) (let ((_let_1 (= pv5 F))) (or (not (leq n0 E)) (not (leq E n2)) (not (leq F pv5)) (not (leq n0 F)) (and _let_1 (= n0 E)) (and (= n2 E) _let_1) (and (= n1 E) _let_1) (= use (a_select3 z_defuse E F))))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (OR))) (let ((_let_31 (not _let_27))) (let ((_let_32 (_let_31))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_32)) :args _let_32)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_27))) (REFL :args (_let_28)) :args _let_30)) (NOT_IMPLIES_ELIM2 _let_29) :args (_let_28 true _let_27)))) (let ((_let_34 (REFL :args (_let_26)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_9))) :args _let_30)) :args ((or _let_9 _let_26))) _let_33 :args (_let_9 true _let_26)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 1)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_10))) :args _let_30)) :args ((or _let_10 _let_26))) _let_33 :args (_let_10 true _let_26)))) (let ((_let_37 (not _let_11))) (let ((_let_38 (gt pv5 skv_3))) (let ((_let_39 (or _let_25 _let_18 _let_38))) (let ((_let_40 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (leq X Y)) (= X Y) (gt Y X))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (leq skv_3 (pred pv5)))) (let ((_let_43 (= _let_38 _let_42))) (let ((_let_44 (not _let_38))) (let ((_let_45 (_let_7))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (not _let_42))) (let ((_let_48 (or _let_15 _let_23 _let_14 _let_47 _let_17))) (let ((_let_49 (forall ((C $$unsorted) (D $$unsorted)) (or (not (leq n0 C)) (not (leq n0 D)) (not (leq C n2)) (not (leq D (pred pv5))) (= use (a_select3 z_defuse C D)))))) (let ((_let_50 (_let_49))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_25 _let_18 _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 2)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_30)) :args ((or _let_24 _let_26))) _let_33 :args (_let_24 true _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_43)) :args ((or _let_42 _let_44 (not _let_43)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_15 _let_14 _let_23 _let_17 _let_47 (not _let_48)))) _let_35 _let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 3)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_30)) :args ((or _let_22 _let_26))) _let_33 :args (_let_22 true _let_26)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 7)) _let_33 :args ((not _let_17) true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_50) :args (skv_2 skv_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (a_select3 z_defuse C D) use))))) :args _let_50)) (AND_ELIM (NOT_IMPLIES_ELIM1 _let_29) :args (15)) :args (_let_48 false _let_49)) :args (_let_47 false _let_9 false _let_10 false _let_22 true _let_17 false _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (skv_3 pv5 QUANTIFIERS_INST_E_MATCHING ((leq X (pred Y))))) :args _let_45))) _let_46 :args (_let_43 false _let_7)) :args (_let_44 true _let_42 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (skv_3 pv5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (leq X Y) false))))) :args (_let_40)))) _let_41 :args (_let_39 false _let_40)) :args (_let_18 false _let_24 true _let_38 false _let_39)))) (let ((_let_52 (not _let_18))) (let ((_let_53 (forall ((X $$unsorted)) (or (not (leq n0 X)) (not (leq X n2)) (= n0 X) (= n1 X) (= n2 X))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (not _let_12))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_14 _let_13 _let_11 _let_12 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_19)) :args ((or _let_19 _let_52 _let_55))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 6)) _let_33 :args ((not _let_19) true _let_26)) _let_51 :args (_let_55 true _let_19 false _let_18)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_21)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 4)) _let_33 :args ((not _let_21) true _let_26)) _let_51 :args ((not _let_13) true _let_21 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (skv_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (leq n0 X) false))))) :args (_let_53))) _let_54 :args (_let_16 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_20)) :args ((or _let_20 _let_52 _let_37))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 5)) _let_33 :args ((not _let_20) true _let_26)) _let_51 :args (_let_37 true _let_20 false _let_18)) _let_36 _let_35 :args (false true _let_12 true _let_13 false _let_16 true _let_11 false _let_10 false _let_9)) :args ((forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq n0 I) (leq I N) (leq J N) (leq n0 J)) (= (a_select3 A I J) (a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq n0 I) (leq n0 J) (leq J N) (leq I N)) (= (a_select3 F J I) (a_select3 F I J)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq n0 I) (leq I M) (leq n0 J) (leq J M)) (= (a_select3 D J I) (a_select3 D I J))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp_madd A (tptp_mmul B (tptp_mmul (tptp_madd (tptp_mmul C (tptp_mmul D (trans C))) (tptp_mmul E (tptp_mmul F (trans E)))) (trans B)))))) (=> (and (leq n0 I) (leq n0 J) (leq J N) (leq I N)) (= (a_select3 _let_1 J I) (a_select3 _let_1 I J))))))) true (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq n0 I) (leq I N) (leq J N) (leq n0 J)) (= (a_select3 A I J) (a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted) (VAL $$unsorted)) (let ((_let_1 (tptp_update3 A K K VAL))) (=> (and (leq n0 I) (leq n0 J) (leq K N) (leq n0 K) (leq J N) (leq I N)) (= (a_select3 _let_1 I J) (a_select3 _let_1 J I))))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (gt Y X) (leq X Y))) (forall ((I $$unsorted) (L $$unsorted) (U $$unsorted) (Val $$unsorted)) (=> (and (leq L I) (leq I U)) (= (a_select2 (tptp_const_array1 (dim L U) Val) I) Val))) (forall ((X $$unsorted) (U $$unsorted) (VAL $$unsorted)) (= VAL (a_select2 (tptp_update2 X U VAL) U))) (forall ((X $$unsorted)) (= (minus X n1) (pred X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (leq Y Z) (leq X Y)) (leq X Z))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (VAL $$unsorted)) (= VAL (a_select3 (tptp_update3 X U V VAL) U V))) (forall ((X $$unsorted)) (= (pred (succ X)) X)) (forall ((X $$unsorted)) (= (succ (succ X)) (plus X n2))) (forall ((X $$unsorted) (Y $$unsorted)) (= (leq X Y) (leq (succ X) (succ Y)))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq I N) (leq J N) (leq n0 J) (leq n0 I)) (= (a_select3 A I J) (a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (trans A))) (=> (and (leq n0 I) (leq n0 J) (leq J N) (leq I N)) (= (a_select3 _let_1 I J) (a_select3 _let_1 J I))))))) (forall ((A $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq J N) (leq n0 J) (leq I N) (leq n0 I)) (= (a_select3 A I J) (a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (inv A))) (=> (and (leq I N) (leq n0 J) (leq J N) (leq n0 I)) (= (a_select3 _let_1 I J) (a_select3 _let_1 J I))))))) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= (a_select3 X U V) VAL) (= V J)) (= VAL (a_select3 (tptp_update3 X I J VAL2) U V)))) (forall ((X $$unsorted)) (leq X X)) (forall ((Body $$unsorted)) (= n0 (sum n0 tptp_minus_1 Body))) (forall ((X $$unsorted)) (not (gt X X))) (= (succ tptp_minus_1) n0) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (leq I U) (leq n0 I) (forall ((I0 $$unsorted)) (=> (and (leq n0 I0) (leq I0 U)) (= VAL (a_select2 X I0))))) (= (a_select2 (tptp_update2 X U VAL) I) VAL))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (leq (succ X) Y) (gt Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (gt Y X) (= X Y) (gt X Y))) (forall ((X $$unsorted) (C $$unsorted)) (=> (leq n0 X) (leq n0 (uniform_int_rnd C X)))) (forall ((X $$unsorted)) (= (succ X) (plus n1 X))) (forall ((I $$unsorted) (L1 $$unsorted) (U1 $$unsorted) (J $$unsorted) (L2 $$unsorted) (U2 $$unsorted) (Val $$unsorted)) (=> (and (leq L1 I) (leq I U1) (leq J U2) (leq L2 J)) (= Val (a_select3 (tptp_const_array2 (dim L1 U1) (dim L2 U2) Val) I J)))) (forall ((X $$unsorted)) (gt (succ X) X)) (not (= use def)) (forall ((X $$unsorted) (Y $$unsorted)) (=> (leq X Y) (leq X (succ Y)))) (forall ((X $$unsorted)) (= (succ (succ (succ (succ (succ X))))) (plus X n5))) (forall ((X $$unsorted)) (= (plus n3 X) (succ (succ (succ X))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq n0 I) (leq J N) (leq n0 J) (leq I N)) (= (a_select3 A I J) (a_select3 A J I)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq n0 J) (leq J N) (leq I N) (leq n0 I)) (= (a_select3 B I J) (a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp_msub A B))) (=> (and (leq n0 I) (leq n0 J) (leq J N) (leq I N)) (= (a_select3 _let_1 I J) (a_select3 _let_1 J I))))))) (forall ((X $$unsorted)) (= (succ (succ (succ (succ (succ X))))) (plus n5 X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (gt (succ Y) X) (leq X Y))) (forall ((X $$unsorted)) (= (succ (succ X)) (plus n2 X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (leq (minus X Y) X) (leq n0 Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (lt X Y) (gt Y X))) (forall ((I $$unsorted) (U $$unsorted) (X $$unsorted) (VAL $$unsorted) (VAL2 $$unsorted)) (=> (and (not (= I U)) (= VAL (a_select2 X U))) (= VAL (a_select2 (tptp_update2 X I VAL2) U)))) _let_8 (forall ((X $$unsorted) (C $$unsorted)) (=> (leq n0 X) (leq (uniform_int_rnd C X) X))) (forall ((X $$unsorted)) (= (succ (succ (succ (succ X)))) (plus n4 X))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq I N) (leq J N) (leq n0 J) (leq n0 I)) (= (a_select3 B I J) (a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp_mmul A (tptp_mmul B (trans A))))) (=> (and (leq J N) (leq n0 J) (leq I N) (leq n0 I)) (= (a_select3 _let_1 J I) (a_select3 _let_1 I J))))))) (forall ((X $$unsorted)) (= (plus X n4) (succ (succ (succ (succ X)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (geq X Y) (leq Y X))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted)) (=> (and (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq n0 I) (leq n0 J) (leq J N) (leq I N)) (= (a_select3 A J I) (a_select3 A I J)))) (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq I N) (leq J N) (leq n0 J) (leq n0 I)) (= (a_select3 B I J) (a_select3 B J I))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp_madd A B))) (=> (and (leq I N) (leq J N) (leq n0 J) (leq n0 I)) (= (a_select3 _let_1 I J) (a_select3 _let_1 J I))))))) (forall ((X $$unsorted)) (= (succ X) (plus X n1))) (forall ((X $$unsorted)) (= (succ (succ (succ X))) (plus X n3))) _let_7 (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted) (M $$unsorted)) (=> (forall ((I $$unsorted) (J $$unsorted)) (=> (and (leq n0 I) (leq J M) (leq n0 J) (leq I M)) (= (a_select3 B I J) (a_select3 B J I)))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp_mmul A (tptp_mmul B (trans A))))) (=> (and (leq J N) (leq n0 J) (leq I N) (leq n0 I)) (= (a_select3 _let_1 J I) (a_select3 _let_1 I J))))))) (forall ((X $$unsorted)) (= X (succ (pred X)))) (forall ((I $$unsorted) (J $$unsorted) (U $$unsorted) (V $$unsorted) (X $$unsorted) (VAL $$unsorted)) (=> (and (leq n0 I) (leq n0 J) (leq J V) (leq I U) (forall ((I0 $$unsorted) (J0 $$unsorted)) (=> (and (leq n0 I0) (leq I0 U) (leq J0 V) (leq n0 J0)) (= VAL (a_select3 X I0 J0))))) (= VAL (a_select3 (tptp_update3 X U V VAL) I J)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (gt Y Z) (gt X Y)) (gt X Z))) (forall ((Body $$unsorted)) (= tptp_float_0_0 (sum n0 tptp_minus_1 Body))) (gt n4 n1) (gt n5 n4) (gt n998 n5) (gt n5 n1) (gt n2 n1) (= n5 (succ _let_6)) (gt n4 n3) (gt n2 tptp_minus_1) (= _let_6 n4) (forall ((X $$unsorted)) (=> (and (leq n0 X) (leq X n0)) (= X n0))) (gt n998 n2) (gt n998 n1) (gt n3 n2) (gt n1 n0) (forall ((X $$unsorted)) (=> (and (leq n0 X) (leq X n1)) (or (= X n1) (= X n0)))) (gt n2 n0) (gt n998 n0) _let_5 (gt n0 tptp_minus_1) (= _let_1 n1) (= _let_2 n2) (gt n5 tptp_minus_1) (gt n998 n3) (gt n5 n2) (gt n4 n2) (gt n998 n4) (forall ((X $$unsorted)) (=> (and (leq X n3) (leq n0 X)) (or (= n0 X) (= X n1) (= X n3) (= X n2)))) (gt n1 tptp_minus_1) (gt n3 tptp_minus_1) (gt n998 tptp_minus_1) _let_4 (gt n3 n1) (= n3 _let_3) (gt n3 n0) (forall ((X $$unsorted)) (=> (and (leq n0 X) (leq X n4)) (or (= n0 X) (= n2 X) (= X n3) (= n4 X) (= X n1)))) (gt n4 n0) (gt n5 n0) (gt n4 tptp_minus_1) (gt n5 n3) (forall ((X $$unsorted)) (=> (and (leq n0 X) (leq X n5)) (or (= X n1) (= n4 X) (= n5 X) (= X n3) (= X n2) (= n0 X)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.48/0.64 % SZS output end Proof for theBenchmark 0.48/0.65 EOF