%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : MGT023+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 09:09:00 EDT 2023

% Result   : Theorem 0.20s 0.53s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : MGT023+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon Aug 28 06:18:47 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.53  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8Pci317ev4/cvc5---1.0.5_25200.p...
% 0.20/0.53  ------- get file name : TPTP file name is MGT023+2
% 0.20/0.53  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25200.smt2...
% 0.20/0.53  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.53  % SZS status Theorem for MGT023+2
% 0.20/0.53  % SZS output start Proof for MGT023+2
% 0.20/0.53  (
% 0.20/0.53  (let ((_let_1 (not (forall ((E $$unsorted)) (=> (and (tptp.environment E) (tptp.stable E)) (tptp.in_environment E (tptp.critical_point E))))))) (let ((_let_2 (forall ((E $$unsorted)) (=> (and (tptp.environment E) (tptp.stable E)) (exists ((To $$unsorted)) (and (tptp.in_environment E To) (forall ((T $$unsorted)) (=> (and (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T) (tptp.greater_or_equal T To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T)))))))))) (let ((_let_3 (forall ((E $$unsorted) (To $$unsorted)) (=> (and (tptp.environment E) (not (tptp.greater (tptp.growth_rate tptp.efficient_producers To) (tptp.growth_rate tptp.first_movers To))) (tptp.in_environment E To) (forall ((T $$unsorted)) (=> (and (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T) (tptp.greater T To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T))))) (= To (tptp.critical_point E)))))) (let ((_let_4 (forall ((E $$unsorted)) (=> (and (tptp.environment E) (exists ((To $$unsorted)) (and (tptp.in_environment E To) (forall ((T $$unsorted)) (=> (and (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T) (tptp.greater_or_equal T To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T))))))) (exists ((To $$unsorted)) (and (tptp.in_environment E To) (not (tptp.greater (tptp.growth_rate tptp.efficient_producers To) (tptp.growth_rate tptp.first_movers To))) (forall ((T $$unsorted)) (=> (and (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T) (tptp.greater T To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T)))))))))) (let ((_let_5 (tptp.critical_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_6 (tptp.in_environment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_5))) (let ((_let_7 (tptp.in_environment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_8 (= _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (tptp.stable SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.environment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10 _let_6))) (let ((_let_14 (not _let_6))) (let ((_let_15 (forall ((E $$unsorted)) (or (not (tptp.environment E)) (not (tptp.stable E)) (tptp.in_environment E (tptp.critical_point E)))))) (let ((_let_16 (not _let_13))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_18 (or))) (let ((_let_19 (not _let_15))) (let ((_let_20 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_17) :args (_let_19))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_15))) (REFL :args (_let_16)) :args _let_18)) _let_17 :args (_let_16 true _let_15)))) (let ((_let_21 (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater T SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T)))))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.greater (tptp.growth_rate tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.growth_rate tptp.first_movers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_24 (not _let_7))) (let ((_let_25 (or _let_24 _let_23 _let_22))) (let ((_let_26 (forall ((To $$unsorted)) (or (not (tptp.in_environment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers To) (tptp.growth_rate tptp.first_movers To)) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater T To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T))))))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater_or_equal T SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T)))))) (let ((_let_29 (not _let_28))) (let ((_let_30 (tptp.in_environment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_31 (not _let_30))) (let ((_let_32 (not _let_26))) (let ((_let_33 (or _let_12 _let_32 _let_31 _let_29))) (let ((_let_34 (forall ((E $$unsorted) (BOUND_VARIABLE_724 $$unsorted)) (or (not (tptp.environment E)) (not (forall ((To $$unsorted)) (or (not (tptp.in_environment E To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers To) (tptp.growth_rate tptp.first_movers To)) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T)) (not (tptp.greater T To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T)))))))) (not (tptp.in_environment E BOUND_VARIABLE_724)) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T)) (not (tptp.greater_or_equal T BOUND_VARIABLE_724)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T))))))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater_or_equal T SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T)))))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_31 _let_37))) (let ((_let_39 (forall ((To $$unsorted)) (or (not (tptp.in_environment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 To)) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater_or_equal T To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T))))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (not _let_39))) (let ((_let_42 (or _let_12 _let_10 _let_41))) (let ((_let_43 (forall ((E $$unsorted)) (or (not (tptp.environment E)) (not (tptp.stable E)) (not (forall ((To $$unsorted)) (or (not (tptp.in_environment E To)) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T)) (not (tptp.greater_or_equal T To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T)))))))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (REFL :args (_let_13)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 0)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_18)) :args ((or _let_11 _let_13))) _let_20 :args (_let_11 true _let_13)))) (let ((_let_47 (_let_41))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_47)) :args _let_47)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_39))) (REFL :args (_let_40)) :args _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_12 _let_10 _let_41 (not _let_42)))) _let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 1)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_18)) :args ((or _let_9 _let_13))) _let_20 :args (_let_9 true _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.environment E) false))))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_41 false _let_11 false _let_9 false _let_42)) :args (_let_40 true _let_39)))) (let ((_let_49 (REFL :args (_let_38)))) (let ((_let_50 (_let_32))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_50)) :args _let_50)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_26))) (REFL :args (_let_27)) :args _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_12 _let_31 _let_32 _let_29 (not _let_33)))) _let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_18)) :args ((or _let_30 _let_38))) _let_48 :args (_let_30 true _let_38)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_36 (= T T)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_18)) :args ((or _let_36 _let_38))) _let_48 :args (_let_36 true _let_38)) :args (_let_28 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in_environment E BOUND_VARIABLE_724) false))))) :args (_let_34))) _let_35 :args (_let_33 false _let_34)) :args (_let_32 false _let_11 false _let_30 false _let_28 false _let_33)) :args (_let_27 true _let_26)))) (let ((_let_52 (REFL :args (_let_25)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_7))) :args _let_18)) :args ((or _let_7 _let_25))) _let_51 :args (_let_7 true _let_25)))) (let ((_let_54 (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater T SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T)))))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_12 _let_23 _let_24 _let_55 _let_8))) (let ((_let_57 (forall ((E $$unsorted) (To $$unsorted)) (or (not (tptp.environment E)) (tptp.greater (tptp.growth_rate tptp.efficient_producers To) (tptp.growth_rate tptp.first_movers To)) (not (tptp.in_environment E To)) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T)) (not (tptp.greater T To)) (tptp.greater (tptp.growth_rate tptp.efficient_producers T) (tptp.growth_rate tptp.first_movers T))))) (= To (tptp.critical_point E)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (ASSUME :args (_let_14)))) (let ((_let_60 (ASSUME :args (_let_8)))) (let ((_let_61 (ASSUME :args (_let_7)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_59 _let_60 _let_61) :args (_let_14 _let_7 _let_8)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_61)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (SYMM _let_60) :args (APPLY_UF tptp.in_environment)) (FALSE_INTRO _let_59))) :args (_let_14 _let_8 _let_7)) :args ((not (and _let_14 _let_7 _let_8)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_6))) (REFL :args (_let_24)) (REFL :args ((not _let_8))) :args _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_12 _let_24 _let_23 _let_55 _let_8 (not _let_56)))) _let_46 _let_53 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 1)) _let_51 :args ((not _let_23) true _let_25)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_21 (= T T)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_18)) :args ((or _let_21 _let_25))) _let_51 :args (_let_21 true _let_25)) :args (_let_54 false _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in_environment E To) false))))) :args (_let_57)))) _let_58 :args (_let_56 false _let_57)) :args (_let_8 false _let_11 false _let_7 true _let_23 false _let_54 false _let_56)) _let_53 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_13 2)) _let_20 :args (_let_14 true _let_13)) :args (false false _let_8 false _let_7 true _let_6)) :args (_let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.53  )
% 0.20/0.53  % SZS output end Proof for MGT023+2
% 0.20/0.53  % cvc5---1.0.5 exiting
% 0.20/0.54  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------