0.09/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.11 % Command : do_cvc5 %s %d 0.11/0.32 % Computer : n009.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Aug 9 03:12:20 EDT 2022 0.17/0.32 % CPUTime : 0.17/0.44 %----Proving TF0_NAR, FOF, or CNF 0.17/0.54 ------- cvc5-fof casc J11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 0.17/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 0.17/0.54 % SZS status Theorem for theBenchmark 0.17/0.54 % SZS output start Proof for theBenchmark 0.17/0.54 (let ((_let_1 (succ n0))) (let ((_let_2 (succ _let_1))) (let ((_let_3 (succ _let_2))) (let ((_let_4 (succ _let_3))) (let ((_let_5 (= use (a_select2 xinit_mean_defuse n0)))) (let ((_let_6 (a_select2 xinit_mean_defuse n3))) (let ((_let_7 (= use (a_select2 xinit_mean_defuse n5)))) (let ((_let_8 (a_select2 xinit_mean_defuse n4))) (let ((_let_9 (a_select2 xinit_mean_defuse n2))) (let ((_let_10 (= use (a_select2 xinit_mean_defuse n1)))) (let ((_let_11 (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 n1 n0) use) (= use (a_select2 xinit_defuse n4)) (= (a_select2 xinit_defuse n5) use) _let_10 (= _let_9 use) (= _let_8 use) (= (a_select2 xinit_noise_defuse n0) use) (= use (a_select2 xinit_noise_defuse n1)) (= (a_select2 xinit_noise_defuse n2) use) (= (a_select2 xinit_noise_defuse n5) use) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (leq C n2) (leq D n998) (leq n0 D) (leq n0 C)) (= (a_select3 z_defuse C D) use))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (leq A n2) (leq B n998) (leq n0 B) (leq n0 A)) (= (a_select3 u_defuse A B) use))) (= (a_select2 xinit_noise_defuse n4) use) (= (a_select2 xinit_noise_defuse n3) use) _let_7 (= _let_6 use) _let_5 (= use (a_select2 xinit_defuse n3)) (= use (a_select3 u_defuse n2 n0)) (= (a_select3 u_defuse n0 n0) use) (= (a_select2 sigma_defuse n3) use) (= use (a_select2 sigma_defuse n2)) (= (a_select2 sigma_defuse n0) use) (= use (a_select2 rho_defuse n0))) (forall ((E $$unsorted)) (=> (and (leq E n5) (leq n0 E)) (= (a_select2 xinit_mean_defuse E) use))))))) (let ((_let_12 (forall ((X $$unsorted)) (=> (and (leq X n5) (leq n0 X)) (or (= n2 X) (= n3 X) (= X n5) (= X n4) (= n1 X) (= n0 X)))))) (let ((_let_13 (= use (a_select2 xinit_mean_defuse skv_2)))) (let ((_let_14 (= n0 skv_2))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_16 (NOT_IMPLIES_ELIM1 _let_15))) (let ((_let_17 (leq n0 skv_2))) (let ((_let_18 (not _let_17))) (let ((_let_19 (leq skv_2 n5))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_13))) (let ((_let_22 (forall ((E $$unsorted)) (or (not (leq E n5)) (not (leq n0 E)) (= use (a_select2 xinit_mean_defuse E)))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (OR))) (let ((_let_25 (not _let_22))) (let ((_let_26 (_let_25))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_26)) :args _let_26)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_22))) (REFL :args (_let_23)) :args _let_24)) (NOT_IMPLIES_ELIM2 _let_15) :args (_let_23 true _let_22)))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 2)) _let_27 :args ((not _let_13) true _let_21)))) (let ((_let_29 (= n1 skv_2))) (let ((_let_30 (= n4 skv_2))) (let ((_let_31 (= n5 skv_2))) (let ((_let_32 (= n3 skv_2))) (let ((_let_33 (= n2 skv_2))) (let ((_let_34 (or _let_20 _let_18 _let_33 _let_32 _let_31 _let_30 _let_29 _let_14))) (let ((_let_35 (forall ((X $$unsorted)) (or (not (leq X n5)) (not (leq n0 X)) (= n2 X) (= n3 X) (= n5 X) (= n4 X) (= n1 X) (= n0 X))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (= use _let_9))) (let ((_let_38 (not _let_33))) (let ((_let_39 (and _let_37 _let_33))) (let ((_let_40 (APPLY_UF a_select2))) (let ((_let_41 (ASSUME :args (_let_33)))) (let ((_let_42 (REFL :args (xinit_mean_defuse)))) (let ((_let_43 (ASSUME :args (_let_37)))) (let ((_let_44 (= use _let_6))) (let ((_let_45 (not _let_32))) (let ((_let_46 (and _let_44 _let_32))) (let ((_let_47 (ASSUME :args (_let_32)))) (let ((_let_48 (ASSUME :args (_let_44)))) (let ((_let_49 (= use _let_8))) (let ((_let_50 (not _let_30))) (let ((_let_51 (and _let_49 _let_30))) (let ((_let_52 (ASSUME :args (_let_30)))) (let ((_let_53 (ASSUME :args (_let_49)))) (let ((_let_54 (not _let_29))) (let ((_let_55 (and _let_10 _let_29))) (let ((_let_56 (ASSUME :args (_let_29)))) (let ((_let_57 (ASSUME :args (_let_10)))) (let ((_let_58 (not _let_31))) (let ((_let_59 (and _let_7 _let_31))) (let ((_let_60 (ASSUME :args (_let_31)))) (let ((_let_61 (ASSUME :args (_let_7)))) (let ((_let_62 (REFL :args (_let_21)))) (let ((_let_63 (and _let_5 _let_14))) (let ((_let_64 (ASSUME :args (_let_14)))) (let ((_let_65 (ASSUME :args (_let_5)))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_63)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_64 _let_65) (SCOPE (TRANS (SYMM (SYMM _let_65)) (CONG _let_42 (SYMM (SYMM _let_64)) :args _let_40)) :args (_let_14 _let_5))) :args (_let_5 _let_14))) :args (true _let_63)) :args ((or (not _let_5) _let_13 (not _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_20 _let_18 _let_14 _let_31 _let_29 _let_30 _let_32 _let_33 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG _let_62 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_24)) :args ((or _let_19 _let_21))) _let_27 :args (_let_19 true _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 1)) (CONG _let_62 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_24)) :args ((or _let_17 _let_21))) _let_27 :args (_let_17 true _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_59)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_60 _let_61) (SCOPE (TRANS (SYMM (SYMM _let_61)) (CONG _let_42 (SYMM (SYMM _let_60)) :args _let_40)) :args (_let_31 _let_7))) :args (_let_7 _let_31))) :args (true _let_59)) :args ((or (not _let_7) _let_13 _let_58))) (AND_ELIM _let_16 :args (19)) _let_28 :args (_let_58 false _let_7 true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_55)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_56 _let_57) (SCOPE (TRANS (SYMM (SYMM _let_57)) (CONG _let_42 (SYMM (SYMM _let_56)) :args _let_40)) :args (_let_29 _let_10))) :args (_let_10 _let_29))) :args (true _let_55)) :args ((or (not _let_10) _let_13 _let_54))) (AND_ELIM _let_16 :args (8)) _let_28 :args (_let_54 false _let_10 true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_51)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_52 _let_53) (SCOPE (TRANS (SYMM (SYMM _let_53)) (CONG _let_42 (SYMM (SYMM _let_52)) :args _let_40)) :args (_let_30 _let_49))) :args (_let_49 _let_30))) :args (true _let_51)) :args ((or (not _let_49) _let_13 _let_50))) (AND_ELIM _let_16 :args (10)) _let_28 :args (_let_50 false _let_49 true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_46)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_47 _let_48) (SCOPE (TRANS (SYMM (SYMM _let_48)) (CONG _let_42 (SYMM (SYMM _let_47)) :args _let_40)) :args (_let_32 _let_44))) :args (_let_44 _let_32))) :args (true _let_46)) :args ((or (not _let_44) _let_13 _let_45))) (AND_ELIM _let_16 :args (20)) _let_28 :args (_let_45 false _let_44 true _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_39)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_41 _let_43) (SCOPE (TRANS (SYMM (SYMM _let_43)) (CONG _let_42 (SYMM (SYMM _let_41)) :args _let_40)) :args (_let_33 _let_37))) :args (_let_37 _let_33))) :args (true _let_39)) :args ((or (not _let_37) _let_13 _let_38))) (AND_ELIM _let_16 :args (9)) _let_28 :args (_let_38 false _let_37 true _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (skv_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (leq X n5) false))))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_14 false _let_19 false _let_17 true _let_31 true _let_29 true _let_30 true _let_32 true _let_33 false _let_34)) _let_28 (AND_ELIM _let_16 :args (21)) :args (false false _let_14 true _let_13 false _let_5)) :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 $$unsorted)) (=> (and (not (= I U)) (= VAL (a_select2 X U))) (= VAL (a_select2 (tptp_update2 X I VAL2) U)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (leq X Y) (not (= Y X))) (gt Y X))) (forall ((X $$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 $$unsorted)) (= (succ (succ (succ X))) (plus X n3))) (forall ((X $$unsorted) (Y $$unsorted)) (= (leq X (pred Y)) (gt Y X))) (forall ((A $$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 n3 tptp_minus_1) (gt n5 n1) (gt n998 n4) (gt n998 n2) (= _let_2 n2) (gt n4 n2) (= n1 _let_1) (gt n2 n1) (= (succ _let_4) n5) (gt n0 tptp_minus_1) (gt n4 tptp_minus_1) (forall ((X $$unsorted)) (=> (and (leq n0 X) (leq X n4)) (or (= n0 X) (= X n1) (= n4 X) (= X n3) (= X n2)))) _let_12 _let_11 (gt n4 n1) (gt n3 n2) (= _let_4 n4) (gt n3 n1) (gt n1 tptp_minus_1) (gt n3 n0) (gt n4 n3) (gt n5 n3) (forall ((X $$unsorted)) (=> (and (leq n0 X) (leq X n0)) (= n0 X))) (gt n998 n1) (gt n998 n5) (gt n5 n2) (gt n2 tptp_minus_1) (gt n998 n3) (gt n5 tptp_minus_1) (forall ((X $$unsorted)) (=> (and (leq n0 X) (leq X n3)) (or (= n0 X) (= X n3) (= n2 X) (= n1 X)))) (gt n4 n0) (gt n5 n4) (forall ((X $$unsorted)) (=> (and (leq X n1) (leq n0 X)) (or (= n1 X) (= n0 X)))) (= n3 _let_3) (gt n5 n0) (gt n2 n0) (gt n998 tptp_minus_1) (gt n1 n0) (gt n998 n0) (forall ((X $$unsorted)) (=> (and (leq n0 X) (leq X n2)) (or (= X n1) (= X n2) (= X n0)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.17/0.54 % SZS output end Proof for theBenchmark 0.17/0.54 EOF