0.08/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : do_cvc5 %s %d 0.12/0.34 % Computer : n025.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 02:09:56 EDT 2022 0.12/0.34 % CPUTime : 0.31/0.53 %----Proving TF0_NAR, FOF, or CNF 0.31/0.58 ------- cvc5-fof casc J11 : /export/starexec/sandbox2/benchmark/theBenchmark.p at /export/starexec/sandbox2/benchmark/theBenchmark.p... 0.31/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 0.31/0.58 % SZS status Theorem for theBenchmark 0.31/0.58 % SZS output start Proof for theBenchmark 0.31/0.58 (let ((_let_1 (not (= pv64 pv63)))) (let ((_let_2 (leq pv5 n998))) (let ((_let_3 (leq pv64 n5))) (let ((_let_4 (leq pv63 n5))) (let ((_let_5 (leq n0 pv64))) (let ((_let_6 (leq n0 pv63))) (let ((_let_7 (leq n0 pv5))) (let ((_let_8 (not (not (not (=> (and _let_7 _let_6 _let_5 _let_4 _let_3 (forall ((X3 $$unsorted) (X4 $$unsorted)) (=> (and (leq n0 X3) (leq n0 X4) (leq X3 n5) (leq X4 n5)) (= init (a_select3 phi_ds1_filter_init X3 X4)))) (forall ((X5 $$unsorted) (X6 $$unsorted)) (=> (and (leq n0 X6) (leq X5 n5) (leq X6 n0) (leq n0 X5)) (= init (a_select3 dv_ds1_filter_init X5 X6)))) (forall ((X7 $$unsorted) (X8 $$unsorted)) (=> (and (leq n0 X8) (leq X7 n5) (leq X8 n5) (leq n0 X7)) (= (a_select3 q_ds1_filter_init X7 X8) init))) (forall ((X9 $$unsorted) (X10 $$unsorted)) (=> (and (leq n0 X9) (leq n0 X10) (leq X9 n2) (leq X10 n2)) (= (a_select3 r_ds1_filter_init X9 X10) init))) (forall ((X11 $$unsorted) (X12 $$unsorted)) (=> (and (leq n0 X11) (leq n0 X12) (leq X11 n5) (leq X12 n0)) (= (a_select3 xhatmin_ds1_filter_init X11 X12) init))) (forall ((X13 $$unsorted) (X14 $$unsorted)) (=> (and (leq n0 X13) (leq n0 X14) (leq X13 n5) (leq X14 n5)) (= (a_select3 pminus_ds1_filter_init X13 X14) init))) (forall ((X15 $$unsorted) (X16 $$unsorted)) (=> (and (leq n0 X15) (leq n0 X16) (leq X16 n5) (leq X15 n5)) (=> (and (gt pv64 X16) (= pv63 X15)) (= (a_select3 id_ds1_filter_init X15 X16) init)))) (forall ((X17 $$unsorted) (X18 $$unsorted)) (=> (and (leq X18 n5) (leq X17 n5) (leq n0 X18) (leq n0 X17)) (=> (gt pv63 X17) (= (a_select3 id_ds1_filter_init X17 X18) init)))) (forall ((X19 $$unsorted)) (=> (and (leq n0 X19) (leq X19 (pred pv63))) (forall ((X20 $$unsorted)) (=> (and (leq X20 n5) (leq n0 X20)) (= (a_select3 id_ds1_filter_init X19 X20) init))))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (=> (and (leq n0 X1) (leq n0 X2) (leq X1 n2) (leq X2 n5)) (= (a_select3 h_ds1_filter_init X1 X2) init))) _let_2 _let_1) (forall ((X21 $$unsorted) (X22 $$unsorted)) (=> (and (leq n0 X22) (leq X22 n5) (leq X21 n5) (leq n0 X21)) (=> (and (= pv63 X21) (leq X22 pv64) (not (= pv64 X22))) (= init (a_select3 id_ds1_filter_init X21 X22))))))))))) (let ((_let_9 (=> (and _let_1 _let_2 _let_4 _let_3 (forall ((X3 $$unsorted) (X4 $$unsorted)) (=> (and (leq n0 X3) (leq n0 X4) (leq X4 n5) (leq X3 n5)) (= (a_select3 phi_ds1_filter_init X3 X4) init))) (forall ((X9 $$unsorted) (X10 $$unsorted)) (=> (and (leq n0 X9) (leq X9 n2) (leq X10 n2) (leq n0 X10)) (= (a_select3 r_ds1_filter_init X9 X10) init))) (forall ((X11 $$unsorted) (X12 $$unsorted)) (=> (and (leq n0 X12) (leq X12 n0) (leq X11 n5) (leq n0 X11)) (= init (a_select3 xhatmin_ds1_filter_init X11 X12)))) (forall ((X13 $$unsorted) (X14 $$unsorted)) (=> (and (leq n0 X13) (leq n0 X14) (leq X13 n5) (leq X14 n5)) (= (a_select3 pminus_ds1_filter_init X13 X14) init))) (forall ((X17 $$unsorted) (X18 $$unsorted)) (=> (and (leq n0 X18) (leq X18 n5) (leq X17 n5) (leq n0 X17)) (=> (gt pv63 X17) (= init (a_select3 id_ds1_filter_init X17 X18))))) (forall ((X19 $$unsorted)) (=> (and (leq n0 X19) (leq X19 (pred pv63))) (forall ((X20 $$unsorted)) (=> (and (leq n0 X20) (leq X20 n5)) (= (a_select3 id_ds1_filter_init X19 X20) init))))) (forall ((X15 $$unsorted) (X16 $$unsorted)) (=> (and (leq X16 n5) (leq X15 n5) (leq n0 X16) (leq n0 X15)) (=> (and (gt pv64 X16) (= pv63 X15)) (= (a_select3 id_ds1_filter_init X15 X16) init)))) (forall ((X7 $$unsorted) (X8 $$unsorted)) (=> (and (leq n0 X8) (leq X8 n5) (leq X7 n5) (leq n0 X7)) (= init (a_select3 q_ds1_filter_init X7 X8)))) (forall ((X5 $$unsorted) (X6 $$unsorted)) (=> (and (leq n0 X6) (leq X6 n0) (leq X5 n5) (leq n0 X5)) (= (a_select3 dv_ds1_filter_init X5 X6) init))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (=> (and (leq n0 X1) (leq X2 n5) (leq X1 n2) (leq n0 X2)) (= init (a_select3 h_ds1_filter_init X1 X2)))) _let_5 _let_6 _let_7) (forall ((X21 $$unsorted) (X22 $$unsorted)) (=> (and (leq n0 X21) (leq X22 n5) (leq X21 n5) (leq n0 X22)) (=> (and (not (= X22 pv64)) (= X21 pv63) (leq X22 pv64)) (= init (a_select3 id_ds1_filter_init X21 X22)))))))) (let ((_let_10 (leq n0 skv_12))) (let ((_let_11 (leq skv_12 n0))) (let ((_let_12 (leq skv_11 n5))) (let ((_let_13 (= init (a_select3 xhatmin_ds1_filter_init skv_11 skv_12)))) (let ((_let_14 (not _let_11))) (let ((_let_15 (not _let_12))) (let ((_let_16 (not _let_10))) (let ((_let_17 (leq n0 skv_11))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16 _let_15 _let_14 _let_13))) (let ((_let_20 (or _let_16 _let_14 _let_15 _let_18 _let_13))) (let ((_let_21 (forall ((X11 $$unsorted) (X12 $$unsorted)) (or (not (leq n0 X12)) (not (leq X12 n0)) (not (leq X11 n5)) (not (leq n0 X11)) (= init (a_select3 xhatmin_ds1_filter_init X11 X12)))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (forall ((X1 $$unsorted) (X2 $$unsorted)) (or (not (leq n0 X1)) (not (leq X2 n5)) (not (leq X1 n2)) (not (leq n0 X2)) (= init (a_select3 h_ds1_filter_init X1 X2)))))) (let ((_let_24 (forall ((X5 $$unsorted) (X6 $$unsorted)) (or (not (leq n0 X6)) (not (leq X6 n0)) (not (leq X5 n5)) (not (leq n0 X5)) (= init (a_select3 dv_ds1_filter_init X5 X6)))))) (let ((_let_25 (forall ((X7 $$unsorted) (X8 $$unsorted)) (or (not (leq n0 X8)) (not (leq X8 n5)) (not (leq X7 n5)) (not (leq n0 X7)) (= init (a_select3 q_ds1_filter_init X7 X8)))))) (let ((_let_26 (forall ((X16 $$unsorted)) (or (not (leq X16 n5)) (not (leq n0 X16)) (not (gt pv64 X16)) (= init (a_select3 id_ds1_filter_init pv63 X16)))))) (let ((_let_27 (not _let_6))) (let ((_let_28 (not _let_4))) (let ((_let_29 (or _let_28 _let_27 _let_26))) (let ((_let_30 (forall ((X19 $$unsorted) (BOUND_VARIABLE_728 $$unsorted)) (or (not (leq n0 X19)) (not (leq X19 (pred pv63))) (not (leq n0 BOUND_VARIABLE_728)) (not (leq BOUND_VARIABLE_728 n5)) (= init (a_select3 id_ds1_filter_init X19 BOUND_VARIABLE_728)))))) (let ((_let_31 (forall ((X17 $$unsorted) (X18 $$unsorted)) (or (not (leq n0 X18)) (not (leq X18 n5)) (not (leq X17 n5)) (not (leq n0 X17)) (not (gt pv63 X17)) (= init (a_select3 id_ds1_filter_init X17 X18)))))) (let ((_let_32 (forall ((X13 $$unsorted) (X14 $$unsorted)) (or (not (leq n0 X13)) (not (leq n0 X14)) (not (leq X13 n5)) (not (leq X14 n5)) (= init (a_select3 pminus_ds1_filter_init X13 X14)))))) (let ((_let_33 (forall ((X9 $$unsorted) (X10 $$unsorted)) (or (not (leq n0 X9)) (not (leq X9 n2)) (not (leq X10 n2)) (not (leq n0 X10)) (= init (a_select3 r_ds1_filter_init X9 X10)))))) (let ((_let_34 (forall ((X3 $$unsorted) (X4 $$unsorted)) (or (not (leq n0 X3)) (not (leq n0 X4)) (not (leq X4 n5)) (not (leq X3 n5)) (= init (a_select3 phi_ds1_filter_init X3 X4)))))) (let ((_let_35 (= pv63 pv64))) (let ((_let_36 (not _let_35))) (let ((_let_37 (and _let_36 _let_2 _let_4 _let_3 _let_34 _let_33 _let_21 _let_32 _let_31 _let_30 _let_29 _let_25 _let_24 _let_23 _let_5 _let_6 _let_7))) (let ((_let_38 (not _let_21))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (NOT_IMPLIES_ELIM1 _let_39))) (let ((_let_41 (2))) (let ((_let_42 (= init (a_select3 h_ds1_filter_init skv_5 skv_6)))) (let ((_let_43 (leq n0 skv_6))) (let ((_let_44 (not _let_43))) (let ((_let_45 (leq skv_5 n2))) (let ((_let_46 (not _let_45))) (let ((_let_47 (leq skv_6 n5))) (let ((_let_48 (not _let_47))) (let ((_let_49 (leq n0 skv_5))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48 _let_46 _let_44 _let_42))) (let ((_let_52 (or _let_50 _let_44 _let_46 _let_48 _let_42))) (let ((_let_53 (OR))) (let ((_let_54 (REFL :args (_let_51)))) (let ((_let_55 (forall ((X1 $$unsorted) (X2 $$unsorted)) (or (not (leq n0 X1)) (not (leq n0 X2)) (not (leq X1 n2)) (not (leq X2 n5)) (= init (a_select3 h_ds1_filter_init X1 X2)))))) (let ((_let_56 (_let_55))) (let ((_let_57 (not _let_23))) (let ((_let_58 (_let_57))) (let ((_let_59 (= init (a_select3 dv_ds1_filter_init skv_7 skv_8)))) (let ((_let_60 (leq n0 skv_7))) (let ((_let_61 (not _let_60))) (let ((_let_62 (leq skv_7 n5))) (let ((_let_63 (not _let_62))) (let ((_let_64 (leq skv_8 n0))) (let ((_let_65 (not _let_64))) (let ((_let_66 (leq n0 skv_8))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_65 _let_63 _let_61 _let_59))) (let ((_let_69 (or _let_67 _let_63 _let_65 _let_61 _let_59))) (let ((_let_70 (REFL :args (_let_68)))) (let ((_let_71 (forall ((X5 $$unsorted) (X6 $$unsorted)) (or (not (leq n0 X6)) (not (leq X5 n5)) (not (leq X6 n0)) (not (leq n0 X5)) (= init (a_select3 dv_ds1_filter_init X5 X6)))))) (let ((_let_72 (_let_71))) (let ((_let_73 (not _let_24))) (let ((_let_74 (_let_73))) (let ((_let_75 (= init (a_select3 q_ds1_filter_init skv_9 skv_10)))) (let ((_let_76 (leq n0 skv_9))) (let ((_let_77 (not _let_76))) (let ((_let_78 (leq skv_9 n5))) (let ((_let_79 (not _let_78))) (let ((_let_80 (leq skv_10 n5))) (let ((_let_81 (not _let_80))) (let ((_let_82 (leq n0 skv_10))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_83 _let_81 _let_79 _let_77 _let_75))) (let ((_let_85 (or _let_83 _let_79 _let_81 _let_77 _let_75))) (let ((_let_86 (REFL :args (_let_84)))) (let ((_let_87 (forall ((X7 $$unsorted) (X8 $$unsorted)) (or (not (leq n0 X8)) (not (leq X7 n5)) (not (leq X8 n5)) (not (leq n0 X7)) (= init (a_select3 q_ds1_filter_init X7 X8)))))) (let ((_let_88 (_let_87))) (let ((_let_89 (not _let_25))) (let ((_let_90 (_let_89))) (let ((_let_91 (forall ((X16 $$unsorted)) (or (not (leq n0 X16)) (not (leq X16 n5)) (not (gt pv64 X16)) (= init (a_select3 id_ds1_filter_init pv63 X16)))))) (let ((_let_92 (AND_ELIM _let_40 :args (1)))) (let ((_let_93 (AND_ELIM _let_40 :args (3)))) (let ((_let_94 (forall ((X19 $$unsorted) (BOUND_VARIABLE_954 $$unsorted)) (or (not (leq n0 X19)) (not (leq X19 (pred pv63))) (not (leq BOUND_VARIABLE_954 n5)) (not (leq n0 BOUND_VARIABLE_954)) (= init (a_select3 id_ds1_filter_init X19 BOUND_VARIABLE_954)))))) (let ((_let_95 (forall ((X17 $$unsorted) (X18 $$unsorted)) (or (not (leq X18 n5)) (not (leq X17 n5)) (not (leq n0 X18)) (not (leq n0 X17)) (not (gt pv63 X17)) (= init (a_select3 id_ds1_filter_init X17 X18)))))) (let ((_let_96 (forall ((X9 $$unsorted) (X10 $$unsorted)) (or (not (leq n0 X9)) (not (leq n0 X10)) (not (leq X9 n2)) (not (leq X10 n2)) (= init (a_select3 r_ds1_filter_init X9 X10)))))) (let ((_let_97 (= init (a_select3 phi_ds1_filter_init skv_3 skv_4)))) (let ((_let_98 (leq skv_3 n5))) (let ((_let_99 (not _let_98))) (let ((_let_100 (leq skv_4 n5))) (let ((_let_101 (not _let_100))) (let ((_let_102 (leq n0 skv_4))) (let ((_let_103 (not _let_102))) (let ((_let_104 (leq n0 skv_3))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_105 _let_103 _let_101 _let_99 _let_97))) (let ((_let_107 (or _let_105 _let_103 _let_99 _let_101 _let_97))) (let ((_let_108 (REFL :args (_let_106)))) (let ((_let_109 (forall ((X3 $$unsorted) (X4 $$unsorted)) (or (not (leq n0 X3)) (not (leq n0 X4)) (not (leq X3 n5)) (not (leq X4 n5)) (= init (a_select3 phi_ds1_filter_init X3 X4)))))) (let ((_let_110 (_let_109))) (let ((_let_111 (not _let_34))) (let ((_let_112 (_let_111))) (let ((_let_113 (forall ((X22 $$unsorted)) (or (not (leq X22 n5)) (not (leq n0 X22)) (= pv64 X22) (not (leq X22 pv64)) (= init (a_select3 id_ds1_filter_init pv63 X22)))))) (let ((_let_114 (or _let_27 _let_28 _let_113))) (let ((_let_115 (not _let_37))) (let ((_let_116 (not _let_114))) (let ((_let_117 (forall ((X22 $$unsorted)) (or (not (leq n0 X22)) (not (leq X22 n5)) (not (leq X22 pv64)) (= pv64 X22) (= init (a_select3 id_ds1_filter_init pv63 X22)))))) (let ((_let_118 (not _let_113))) (let ((_let_119 (not _let_7))) (let ((_let_120 (not _let_5))) (let ((_let_121 (not _let_29))) (let ((_let_122 (not _let_30))) (let ((_let_123 (not _let_31))) (let ((_let_124 (not _let_32))) (let ((_let_125 (not _let_33))) (let ((_let_126 (not _let_3))) (let ((_let_127 (not _let_2))) (let ((_let_128 (_let_38))) (let ((_let_129 (_let_37))) (let ((_let_130 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_128)) :args _let_128)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_21))) (REFL :args (_let_22)) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_129) (CONG (REFL :args _let_129) (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) (REFL :args (_let_127)) (REFL :args (_let_28)) (REFL :args (_let_126)) (REFL :args _let_112) (REFL :args (_let_125)) (REFL :args _let_128) (REFL :args (_let_124)) (REFL :args (_let_123)) (REFL :args (_let_122)) (REFL :args (_let_121)) (REFL :args _let_90) (REFL :args _let_74) (REFL :args _let_58) (REFL :args (_let_120)) (REFL :args (_let_27)) (REFL :args (_let_119)) :args _let_53)) :args ((or _let_35 _let_28 _let_27 _let_37 _let_127 _let_126 _let_111 _let_125 _let_38 _let_124 _let_123 _let_122 _let_121 _let_89 _let_73 _let_57 _let_120 _let_119))) (AND_ELIM _let_40 :args (16)) _let_93 _let_92 (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_114 _let_115))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_28 _let_27 _let_113 _let_116))) _let_93 _let_92 (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_113 (= X22 X22))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X22 $$unsorted)) (or (not (leq X22 n5)) (not (leq n0 X22)) (= pv64 X22) (not (leq X22 pv64)) (= init (a_select3 id_ds1_filter_init pv63 X22)))) _let_117) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) :args ((or _let_117 _let_118))) (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 _let_39) :args _let_41) :args (_let_118 true _let_117)) :args (_let_116 false _let_4 false _let_6 true _let_113)) :args (_let_115 true _let_114)) (AND_ELIM _let_40 :args (15)) (AND_ELIM _let_40 :args (4)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_112)) :args _let_112)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_111) _let_34))) (REFL :args ((not _let_106))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_105 _let_99 _let_103 _let_101 _let_97 (not _let_107)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_110) :args (skv_3 skv_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (a_select3 phi_ds1_filter_init X3 X4) init))))) :args _let_110)) (AND_ELIM _let_40 :args (5)) :args (_let_107 false _let_109)) (CNF_OR_NEG :args (_let_106 4)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_106 3)) (CONG _let_108 (MACRO_SR_PRED_INTRO :args ((= (not _let_99) _let_98))) :args _let_53)) :args ((or _let_98 _let_106))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_106 2)) (CONG _let_108 (MACRO_SR_PRED_INTRO :args ((= (not _let_101) _let_100))) :args _let_53)) :args ((or _let_100 _let_106))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_106 1)) (CONG _let_108 (MACRO_SR_PRED_INTRO :args ((= (not _let_103) _let_102))) :args _let_53)) :args ((or _let_102 _let_106))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_106 0)) (CONG _let_108 (MACRO_SR_PRED_INTRO :args ((= (not _let_105) _let_104))) :args _let_53)) :args ((or _let_104 _let_106))) :args (_let_106 false _let_107 true _let_97 false _let_98 false _let_100 false _let_102 false _let_104)) :args (_let_34 false _let_106)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_33 (= X9 X9) (= X10 X10))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X9 $$unsorted) (X10 $$unsorted)) (or (not (leq n0 X9)) (not (leq X9 n2)) (not (leq X10 n2)) (not (leq n0 X10)) (= init (a_select3 r_ds1_filter_init X9 X10)))) _let_96) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (AND_ELIM _let_40 :args (8)) :args (_let_33 false _let_96)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_32 (= X13 X13) (= X14 X14)))) (AND_ELIM _let_40 :args (10)) :args (_let_32 false (forall ((X13 $$unsorted) (X14 $$unsorted)) (or (not (leq n0 X13)) (not (leq n0 X14)) (not (leq X13 n5)) (not (leq X14 n5)) (= init (a_select3 pminus_ds1_filter_init X13 X14)))))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_31 (= X17 X17) (= X18 X18))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X17 $$unsorted) (X18 $$unsorted)) (or (not (leq n0 X18)) (not (leq X18 n5)) (not (leq X17 n5)) (not (leq n0 X17)) (not (gt pv63 X17)) (= init (a_select3 id_ds1_filter_init X17 X18)))) _let_95) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (AND_ELIM _let_40 :args (12)) :args (_let_31 false _let_95)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_30 (= X19 X19) (= BOUND_VARIABLE_728 BOUND_VARIABLE_954))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X19 $$unsorted) (BOUND_VARIABLE_954 $$unsorted)) (or (not (leq n0 X19)) (not (leq X19 (pred pv63))) (not (leq n0 BOUND_VARIABLE_954)) (not (leq BOUND_VARIABLE_954 n5)) (= init (a_select3 id_ds1_filter_init X19 BOUND_VARIABLE_954)))) _let_94) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (AND_ELIM _let_40 :args (13)) :args (_let_30 false _let_94)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 2)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_26 (= X16 X16))) (MACRO_SR_PRED_INTRO :args ((= (forall ((X16 $$unsorted)) (or (not (leq X16 n5)) (not (leq n0 X16)) (not (gt pv64 X16)) (= init (a_select3 id_ds1_filter_init pv63 X16)))) _let_91) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (MACRO_RESOLUTION_TRUST (REORDERING (AND_ELIM _let_40 :args (11)) :args ((or _let_28 _let_27 _let_91))) _let_93 _let_92 :args (_let_91 false _let_4 false _let_6)) :args (_let_26 false _let_91)) :args (_let_29 false _let_26)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_90)) :args _let_90)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_25))) (REFL :args ((not _let_84))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_79 _let_77 _let_83 _let_81 _let_75 (not _let_85)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_88) :args (skv_9 skv_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (a_select3 q_ds1_filter_init X7 X8) init))))) :args _let_88)) (AND_ELIM _let_40 :args (7)) :args (_let_85 false _let_87)) (CNF_OR_NEG :args (_let_84 4)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 3)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_76))) :args _let_53)) :args ((or _let_76 _let_84))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 2)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_78))) :args _let_53)) :args ((or _let_78 _let_84))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 1)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_80))) :args _let_53)) :args ((or _let_80 _let_84))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 0)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_82))) :args _let_53)) :args ((or _let_82 _let_84))) :args (_let_84 false _let_85 true _let_75 false _let_76 false _let_78 false _let_80 false _let_82)) :args (_let_25 false _let_84)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_74)) :args _let_74)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_24))) (REFL :args ((not _let_68))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_63 _let_61 _let_67 _let_65 _let_59 (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_72) :args (skv_7 skv_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (a_select3 dv_ds1_filter_init X5 X6) init))))) :args _let_72)) (AND_ELIM _let_40 :args (6)) :args (_let_69 false _let_71)) (CNF_OR_NEG :args (_let_68 4)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 3)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_53)) :args ((or _let_60 _let_68))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 2)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_62))) :args _let_53)) :args ((or _let_62 _let_68))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 1)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_64))) :args _let_53)) :args ((or _let_64 _let_68))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 0)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_53)) :args ((or _let_66 _let_68))) :args (_let_68 false _let_69 true _let_59 false _let_60 false _let_62 false _let_64 false _let_66)) :args (_let_24 false _let_68)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_23))) (REFL :args ((not _let_51))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_50 _let_46 _let_48 _let_44 _let_42 (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_56) :args (skv_5 skv_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (a_select3 h_ds1_filter_init X1 X2) init))))) :args _let_56)) (AND_ELIM _let_40 :args (14)) :args (_let_52 false _let_55)) (CNF_OR_NEG :args (_let_51 4)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 3)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_53)) :args ((or _let_43 _let_51))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 2)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_53)) :args ((or _let_45 _let_51))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 1)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_53)) :args ((or _let_47 _let_51))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_53)) :args ((or _let_49 _let_51))) :args (_let_51 false _let_52 true _let_42 false _let_43 false _let_45 false _let_47 false _let_49)) :args (_let_23 false _let_51)) (AND_ELIM _let_40 :args _let_41) (AND_ELIM _let_40 :args (0)) :args (_let_38 true _let_35 false _let_4 false _let_6 true _let_37 false _let_2 false _let_3 false _let_34 false _let_33 false _let_32 false _let_31 false _let_30 false _let_29 false _let_25 false _let_24 false _let_23 false _let_5 false _let_7)) :args (_let_22 true _let_21)))) (let ((_let_131 (REFL :args (_let_20)))) (let ((_let_132 (forall ((X11 $$unsorted) (X12 $$unsorted)) (or (not (leq n0 X11)) (not (leq n0 X12)) (not (leq X11 n5)) (not (leq X12 n0)) (= init (a_select3 xhatmin_ds1_filter_init X11 X12)))))) (let ((_let_133 (_let_132))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_15 _let_18 _let_16 _let_14 _let_13 (not _let_19)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 4)) _let_130 :args ((not _let_13) true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 3)) (CONG _let_131 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_53)) :args ((or _let_17 _let_20))) _let_130 :args (_let_17 true _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_133) :args (skv_11 skv_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (a_select3 xhatmin_ds1_filter_init X11 X12) init))))) :args _let_133)) (AND_ELIM _let_40 :args (9)) :args (_let_19 false _let_132)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 2)) (CONG _let_131 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_12))) :args _let_53)) :args ((or _let_12 _let_20))) _let_130 :args (_let_12 true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 1)) (CONG _let_131 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_11))) :args _let_53)) :args ((or _let_11 _let_20))) _let_130 :args (_let_11 true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 0)) (CONG _let_131 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_10))) :args _let_53)) :args ((or _let_10 _let_20))) _let_130 :args (_let_10 true _let_20)) :args (false true _let_13 false _let_17 false _let_19 false _let_12 false _let_11 false _let_10)) :args (_let_9 _let_8 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.31/0.59 % SZS output end Proof for theBenchmark 0.31/0.59 EOF