0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : do_cvc5 %s %d 0.13/0.34 % Computer : n025.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 02:28:26 EDT 2022 0.13/0.34 % CPUTime : 0.19/0.50 %----Proving TF0_NAR, FOF, or CNF 1.92/2.11 ------- cvc5-fof casc J11 : /export/starexec/sandbox/benchmark/theBenchmark.p at /export/starexec/sandbox/benchmark/theBenchmark.p... 1.92/2.11 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10... 1.92/2.11 % SZS status Theorem for theBenchmark 1.92/2.11 % SZS output start Proof for theBenchmark 1.92/2.11 (let ((_let_1 (forall ((E $$unsorted) (S1 $$unsorted) (S2 $$unsorted) (T $$unsorted)) (=> (and (environment E) (subpopulation S1 E T) (subpopulation S2 E T) (= zero (cardinality_at_time S2 T)) (greater (cardinality_at_time S1 T) zero)) (selection_favors S1 S2 T))))) (let ((_let_2 (not (forall ((P $$unsorted)) (=> (and (slow_change P) (observational_period P)) (selection_favors efficient_producers first_movers P)))))) (let ((_let_3 (forall ((P $$unsorted)) (=> (and (observational_period P) (propagation_strategy first_movers) (forall ((E $$unsorted)) (=> (and (in_environment P E) (environment E)) (selection_favors efficient_producers first_movers (end_time E)))) (propagation_strategy efficient_producers)) (selection_favors efficient_producers first_movers P))))) (let ((_let_4 (forall ((E $$unsorted)) (=> (environment E) (greater_or_equal (critical_point E) (start_time E)))))) (let ((_let_5 (propagation_strategy first_movers))) (let ((_let_6 (forall ((P $$unsorted)) (=> (and (observational_period P) (slow_change P)) (forall ((E $$unsorted)) (=> (and (in_environment P E) (environment E)) (exists ((T $$unsorted)) (and (in_environment E T) (greater T (critical_point E)))))))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (= (or (greater X Y) (= Y X)) (greater_or_equal X Y))))) (let ((_let_8 (forall ((E $$unsorted) (T $$unsorted)) (=> (and (environment E) (in_environment E T)) (greater_or_equal (end_time E) T))))) (let ((_let_9 (propagation_strategy efficient_producers))) (let ((_let_10 (forall ((E $$unsorted)) (=> (environment E) (greater_or_equal (critical_point E) (appear efficient_producers E)))))) (let ((_let_11 (forall ((E $$unsorted) (T $$unsorted)) (=> (and (environment E) (greater (cardinality_at_time first_movers T) zero) (greater (cardinality_at_time efficient_producers T) zero) (in_environment E T)) (subpopulations first_movers efficient_producers E T))))) (let ((_let_12 (forall ((E $$unsorted) (T $$unsorted)) (=> (and (greater_or_equal (end_time E) T) (greater_or_equal T (start_time E)) (environment E)) (in_environment E T))))) (let ((_let_13 (forall ((E $$unsorted) (Tc $$unsorted)) (=> (and (environment E) (= (critical_point E) Tc)) (and (forall ((T $$unsorted)) (=> (and (subpopulations first_movers efficient_producers E T) (greater T Tc)) (greater (growth_rate efficient_producers T) (growth_rate first_movers T)))) (not (greater (growth_rate efficient_producers Tc) (growth_rate first_movers Tc)))))))) (let ((_let_14 (forall ((E $$unsorted) (T $$unsorted)) (=> (and (in_environment E T) (environment E)) (greater_or_equal (cardinality_at_time first_movers T) zero))))) (let ((_let_15 (forall ((E $$unsorted) (T $$unsorted)) (=> (and (greater_or_equal T (appear efficient_producers E)) (in_environment E T) (environment E)) (greater (cardinality_at_time efficient_producers T) zero))))) (let ((_let_16 (forall ((E $$unsorted) (T $$unsorted)) (=> (and (in_environment E T) (environment E)) (and (subpopulation first_movers E T) (subpopulation efficient_producers E T)))))) (let ((_let_17 (forall ((E $$unsorted) (S1 $$unsorted) (S2 $$unsorted) (T $$unsorted)) (=> (and (greater (growth_rate S2 T) (growth_rate S1 T)) (subpopulations S1 S2 E T) (environment E)) (selection_favors S2 S1 T))))) (let ((_let_18 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (greater X Y) (greater Y Z)) (greater X Z))))) (let ((_let_19 (appear efficient_producers skv_3))) (let ((_let_20 (end_time skv_3))) (let ((_let_21 (greater_or_equal _let_20 _let_19))) (let ((_let_22 (greater _let_20 _let_19))) (let ((_let_23 (or _let_22 (= _let_20 _let_19)))) (let ((_let_24 (= _let_21 _let_23))) (let ((_let_25 (greater (cardinality_at_time efficient_producers _let_20) zero))) (let ((_let_26 (environment skv_3))) (let ((_let_27 (not _let_26))) (let ((_let_28 (in_environment skv_3 _let_20))) (let ((_let_29 (not _let_28))) (let ((_let_30 (not _let_21))) (let ((_let_31 (or _let_30 _let_29 _let_27 _let_25))) (let ((_let_32 (forall ((E $$unsorted) (T $$unsorted)) (or (not (greater_or_equal T (appear efficient_producers E))) (not (in_environment E T)) (not (environment E)) (greater (cardinality_at_time efficient_producers T) zero))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (_let_32))) (let ((_let_35 (selection_favors efficient_producers first_movers _let_20))) (let ((_let_36 (subpopulation efficient_producers skv_3 _let_20))) (let ((_let_37 (subpopulation first_movers skv_3 _let_20))) (let ((_let_38 (not _let_25))) (let ((_let_39 (cardinality_at_time first_movers _let_20))) (let ((_let_40 (= zero _let_39))) (let ((_let_41 (not _let_40))) (let ((_let_42 (not _let_37))) (let ((_let_43 (not _let_36))) (let ((_let_44 (or _let_27 _let_43 _let_42 _let_41 _let_38 _let_35))) (let ((_let_45 (subpopulations first_movers efficient_producers skv_3 _let_20))) (let ((_let_46 (greater _let_39 zero))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_27 _let_47 _let_38 _let_29 _let_45))) (let ((_let_49 (or _let_46 _let_40))) (let ((_let_50 (in_environment skv_2 skv_3))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_27 _let_35))) (let ((_let_53 (forall ((E $$unsorted)) (or (not (in_environment skv_2 E)) (not (environment E)) (selection_favors efficient_producers first_movers (end_time E)))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (selection_favors efficient_producers first_movers skv_2))) (let ((_let_56 (not _let_53))) (let ((_let_57 (observational_period skv_2))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56 _let_55))) (let ((_let_60 (forall ((P $$unsorted)) (or (not (observational_period P)) (not (forall ((E $$unsorted)) (or (not (in_environment P E)) (not (environment E)) (selection_favors efficient_producers first_movers (end_time E))))) (selection_favors efficient_producers first_movers P))))) (let ((_let_61 (_let_60))) (let ((_let_62 (slow_change skv_2))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_63 _let_58 _let_55))) (let ((_let_65 (forall ((P $$unsorted)) (or (not (slow_change P)) (not (observational_period P)) (selection_favors efficient_producers first_movers P))))) (let ((_let_66 (not _let_64))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (OR))) (let ((_let_69 (not _let_65))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_67) :args (_let_69))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_65))) (REFL :args (_let_66)) :args _let_68)) _let_67 :args (_let_66 true _let_65)))) (let ((_let_71 (REFL :args (_let_64)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_64 1)) (CONG _let_71 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_68)) :args ((or _let_57 _let_64))) _let_70 :args (_let_57 true _let_64)))) (let ((_let_73 (_let_56))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_73)) :args _let_73)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_53))) (REFL :args (_let_54)) :args _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_58 _let_55 _let_56 (not _let_59)))) _let_72 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_64 2)) _let_70 :args ((not _let_55) true _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_61) :args (skv_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (observational_period P) false))))) :args _let_61)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_5)) (ASSUME :args (_let_9)) :args (_let_60 false _let_5 false _let_9)) :args (_let_59 false _let_60)) :args (_let_56 false _let_57 true _let_55 false _let_59)) :args (_let_54 true _let_53)))) (let ((_let_75 (REFL :args (_let_52)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 1)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_68)) :args ((or _let_26 _let_52))) _let_74 :args (_let_26 true _let_52)))) (let ((_let_77 (not _let_35))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_52 2)) _let_74 :args (_let_77 true _let_52)))) (let ((_let_79 (and _let_37 _let_36))) (let ((_let_80 (or _let_29 _let_27 _let_79))) (let ((_let_81 (forall ((E $$unsorted) (T $$unsorted)) (or (not (in_environment E T)) (not (environment E)) (and (subpopulation first_movers E T) (subpopulation efficient_producers E T)))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (_let_81))) (let ((_let_84 ((not (= (in_environment E T) false))))) (let ((_let_85 (greater_or_equal _let_20 _let_20))) (let ((_let_86 (start_time skv_3))) (let ((_let_87 (greater_or_equal _let_20 _let_86))) (let ((_let_88 (not _let_87))) (let ((_let_89 (not _let_85))) (let ((_let_90 (or _let_89 _let_88 _let_27 _let_28))) (let ((_let_91 (in_environment skv_3 skv_4))) (let ((_let_92 (= _let_20 skv_4))) (let ((_let_93 (greater _let_20 _let_86))) (let ((_let_94 (or _let_93 (= _let_20 _let_86)))) (let ((_let_95 (= _let_87 _let_94))) (let ((_let_96 (greater _let_20 skv_4))) (let ((_let_97 (or _let_96 _let_92))) (let ((_let_98 (critical_point skv_3))) (let ((_let_99 (greater skv_4 _let_98))) (let ((_let_100 (greater _let_20 _let_98))) (let ((_let_101 (not _let_99))) (let ((_let_102 (not _let_96))) (let ((_let_103 (or _let_102 _let_101 _let_100))) (let ((_let_104 (greater skv_4 _let_86))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_102 _let_105 _let_93))) (let ((_let_107 (or _let_100 (= _let_20 _let_98)))) (let ((_let_108 (greater _let_98 _let_86))) (let ((_let_109 (not _let_108))) (let ((_let_110 (or _let_101 _let_109 _let_104))) (let ((_let_111 (greater_or_equal _let_20 _let_98))) (let ((_let_112 (= _let_111 _let_107))) (let ((_let_113 (= _let_98 _let_86))) (let ((_let_114 (or _let_108 _let_113))) (let ((_let_115 (forall ((X $$unsorted) (Y $$unsorted)) (= (greater_or_equal X Y) (or (greater X Y) (= X Y)))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (_let_115))) (let ((_let_118 ((greater_or_equal X Y)))) (let ((_let_119 (forall ((E $$unsorted) (T $$unsorted)) (or (not (greater_or_equal (end_time E) T)) (not (greater_or_equal T (start_time E))) (not (environment E)) (in_environment E T))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (not _let_91))) (let ((_let_122 (or _let_121 _let_101))) (let ((_let_123 (forall ((T $$unsorted)) (or (not (in_environment skv_3 T)) (not (greater T (critical_point skv_3))))))) (let ((_let_124 (not _let_122))) (let ((_let_125 (not _let_123))) (let ((_let_126 (or _let_58 _let_63 _let_51 _let_27 _let_125))) (let ((_let_127 (forall ((P $$unsorted) (BOUND_VARIABLE_709 $$unsorted)) (or (not (observational_period P)) (not 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(MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (skv_3 _let_20 QUANTIFIERS_INST_E_MATCHING ((not (= (greater_or_equal T (start_time E)) false))))) :args (_let_119))) _let_120 :args (_let_90 false _let_119)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_116 :args (_let_20 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_118)) :args _let_117))) _let_116 :args (_let_85 false _let_115)) _let_76 :args (_let_28 false _let_113 false _let_114 false _let_111 false _let_112 true _let_108 false _let_110 false _let_99 false _let_107 true _let_104 false _let_106 false _let_100 false _let_103 false _let_99 true _let_93 false _let_96 false _let_97 true _let_94 false _let_95 true _let_92 false _let_91 true _let_87 false _let_90 false _let_85 false _let_26)))) (let ((_let_159 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_27 _let_29 _let_79 (not _let_80)))) _let_76 _let_158 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (skv_3 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_84)) :args _let_83)) _let_82 :args (_let_80 false _let_81)) :args (_let_79 false _let_26 false _let_28 false _let_80)))) (let ((_let_160 (not _let_79))) (let ((_let_161 (forall ((E $$unsorted) (S1 $$unsorted) (S2 $$unsorted) (T $$unsorted)) (or (not (environment E)) (not (subpopulation S1 E T)) (not (subpopulation S2 E T)) (not (= zero (cardinality_at_time S2 T))) (not (greater (cardinality_at_time S1 T) zero)) (selection_favors S1 S2 T))))) (let ((_let_162 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_163 (_let_161))) (let ((_let_164 (not (= (subpopulation S1 E T) false)))) (let ((_let_165 (greater (growth_rate efficient_producers _let_20) (growth_rate first_movers _let_20)))) (let ((_let_166 (not _let_100))) (let ((_let_167 (not _let_45))) (let ((_let_168 (or _let_167 _let_166 _let_165))) (let ((_let_169 (not 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(IMPLIES_ELIM (SCOPE (INSTANTIATE _let_233 :args (skv_3 first_movers efficient_producers _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_235)) :args _let_234)) _let_233 :args (_let_170 false _let_232)) _let_78 _let_76 (REORDERING (CNF_OR_POS :args (_let_168)) :args ((or _let_166 _let_167 _let_165 (not _let_168)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_237 0)) :args ((or _let_168 (not _let_237)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_238)) :args ((or _let_27 _let_237 (not _let_238)))) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_229 :args (skv_3 _let_20 QUANTIFIERS_INST_E_MATCHING _let_231)) :args _let_230)) _let_229 :args (_let_238 false _let_228)) :args (_let_237 false _let_26 false _let_238)) :args (_let_168 false _let_237)) (MACRO_RESOLUTION_TRUST _let_152 _let_146 _let_236 _let_151 :args (_let_100 false _let_99 false _let_96 false _let_103)) :args (_let_167 false _let_170 true _let_35 false _let_26 false _let_165 false _let_168 false _let_100)) _let_76 (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_27 _let_35 _let_38 _let_42 _let_43 _let_41 (not _let_44)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_162 :args (skv_3 efficient_producers first_movers _let_20 QUANTIFIERS_INST_E_MATCHING (_let_164 (not (= (selection_favors S1 S2 T) true))))) :args _let_163)) _let_162 :args (_let_44 false _let_161)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 0)) :args ((or _let_37 _let_160))) _let_159 :args (_let_37 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 1)) :args ((or _let_36 _let_160))) _let_159 :args (_let_36 false _let_79)) _let_78 _let_76 :args (_let_38 false _let_49 true _let_46 false _let_28 false _let_48 true _let_45 false _let_26 true _let_40 false _let_44 false _let_37 false _let_36 true _let_35 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (skv_3 _let_20 QUANTIFIERS_INST_E_MATCHING ((not (= (greater_or_equal T (appear efficient_producers E)) false))))) :args _let_34)) _let_33 :args (_let_31 false _let_32)) :args (_let_30 false _let_26 false _let_28 true _let_25 false _let_31)) :args (false false _let_24 false _let_23 true _let_21)) :args (_let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 (forall ((E $$unsorted) (T $$unsorted)) (let ((_let_1 (end_time E))) (=> (and (environment E) (greater T (start_time E)) (not (greater T _let_1))) (greater_or_equal _let_1 T)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 1.93/2.12 % SZS output end Proof for theBenchmark 1.93/2.12 EOF