%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : MGT028+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n029.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 09:09:02 EDT 2023

% Result   : Theorem 0.19s 0.52s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : MGT028+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.12/0.34  % Computer : n029.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   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 06:37:41 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.19/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.52  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.M33tbs0XJ3/cvc5---1.0.5_2095.p...
% 0.19/0.52  ------- get file name : TPTP file name is MGT028+1
% 0.19/0.52  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2095.smt2...
% 0.19/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.52  % SZS status Theorem for MGT028+1
% 0.19/0.52  % SZS output start Proof for MGT028+1
% 0.19/0.52  (
% 0.19/0.52  (let ((_let_1 (not (forall ((E $$unsorted)) (=> (and (tptp.environment E) (tptp.stable E)) (exists ((To $$unsorted)) (and (tptp.greater To (tptp.appear tptp.efficient_producers E)) (forall ((T $$unsorted)) (=> (and (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T) (tptp.greater_or_equal T To)) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T))))))))))) (let ((_let_2 (forall ((E $$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)) (and (tptp.greater (tptp.growth_rate tptp.efficient_producers T) tptp.zero) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T))))))))))) (let ((_let_3 (forall ((E $$unsorted)) (=> (and (tptp.environment E) (tptp.stable E) (exists ((T1 $$unsorted)) (and (tptp.in_environment E T1) (forall ((T $$unsorted)) (=> (and (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T) (tptp.greater_or_equal T T1)) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T))))))) (exists ((T2 $$unsorted)) (and (tptp.greater T2 (tptp.appear tptp.efficient_producers E)) (forall ((T $$unsorted)) (=> (and (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T) (tptp.greater_or_equal T T2)) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T)))))))))) (let ((_let_4 (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_5 (tptp.greater_or_equal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_6 (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_7 (and (tptp.greater (tptp.growth_rate tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) tptp.zero) _let_6))) (let ((_let_8 (not _let_5))) (let ((_let_9 (not _let_4))) (let ((_let_10 (or _let_9 _let_8 _let_7))) (let ((_let_11 (or _let_9 _let_8 _let_6))) (let ((_let_12 (forall ((T $$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_6)) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T)))))) (let ((_let_13 (not _let_11))) (let ((_let_14 (not _let_12))) (let ((_let_15 (tptp.in_environment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_16 (not _let_15))) (let ((_let_17 (forall ((T2 $$unsorted)) (or (not (tptp.greater T2 (tptp.appear tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater_or_equal T T2)) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T))))))))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.stable SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.environment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_18 _let_16 _let_14))) (let ((_let_24 (forall ((E $$unsorted) (BOUND_VARIABLE_712 $$unsorted)) (or (not (tptp.environment E)) (not (tptp.stable E)) (not (forall ((T2 $$unsorted)) (or (not (tptp.greater T2 (tptp.appear tptp.efficient_producers E))) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T)) (not (tptp.greater_or_equal T T2)) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T)))))))) (not (tptp.in_environment E BOUND_VARIABLE_712)) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T)) (not (tptp.greater_or_equal T BOUND_VARIABLE_712)) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T))))))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (forall ((To $$unsorted)) (or (not (tptp.greater To (tptp.appear tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater_or_equal T To)) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T))))))))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_22 _let_20 _let_27))) (let ((_let_29 (forall ((E $$unsorted)) (or (not (tptp.environment E)) (not (tptp.stable E)) (not (forall ((To $$unsorted)) (or (not (tptp.greater To (tptp.appear tptp.efficient_producers E))) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers E T)) (not (tptp.greater_or_equal T To)) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T)))))))))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (or))) (let ((_let_33 (not _let_29))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_31) :args (_let_33))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_32)) _let_31 :args (_let_30 true _let_29)))) (let ((_let_35 (REFL :args (_let_28)))) (let ((_let_36 (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater_or_equal T SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (and (tptp.greater (tptp.growth_rate tptp.efficient_producers T) tptp.zero) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T))))))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_16 _let_37))) (let ((_let_39 (forall ((To $$unsorted)) (or (not (tptp.in_environment SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 To)) (not (forall ((T $$unsorted)) (or (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T)) (not (tptp.greater_or_equal T To)) (and (tptp.greater (tptp.growth_rate tptp.efficient_producers T) tptp.zero) (tptp.greater tptp.zero (tptp.growth_rate tptp.first_movers T)))))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (not _let_39))) (let ((_let_42 (or _let_22 _let_20 _let_41))) (let ((_let_43 (forall ((E $$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)) (and (tptp.greater (tptp.growth_rate tptp.efficient_producers T) tptp.zero) (tptp.greater tptp.zero (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 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 1)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_32)) :args ((or _let_19 _let_28))) _let_34 :args (_let_19 true _let_28)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_32)) :args ((or _let_21 _let_28))) _let_34 :args (_let_21 true _let_28)))) (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_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_22 _let_20 _let_41 (not _let_42)))) _let_46 _let_45 (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_21 false _let_19 false _let_42)) :args (_let_40 true _let_39)))) (let ((_let_49 (REFL :args (_let_38)))) (let ((_let_50 (_let_14))) (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_14) _let_12))) (REFL :args (_let_13)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_20 _let_16 _let_18 _let_14 (not _let_23)))) _let_46 _let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_32)) :args ((or _let_15 _let_38))) _let_48 :args (_let_15 true _let_38)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_26 (= T T) (= To T2)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 2)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_32)) :args ((or _let_26 _let_28))) _let_34 :args (_let_26 true _let_28)) :args (_let_17 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in_environment E BOUND_VARIABLE_712) false))))) :args (_let_24))) _let_25 :args (_let_23 false _let_24)) :args (_let_14 false _let_21 false _let_19 false _let_15 false _let_17 false _let_23)) :args (_let_13 true _let_12)))) (let ((_let_52 (REFL :args (_let_11)))) (let ((_let_53 (not _let_7))) (let ((_let_54 (_let_36))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_8 _let_7 (not _let_10)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_54) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subpopulations tptp.first_movers tptp.efficient_producers SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 T) false))))) :args _let_54)) (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_32)) :args ((or _let_36 _let_38))) _let_48 :args (_let_36 true _let_38)) :args (_let_10 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_7 1)) :args ((or _let_6 _let_53))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_11 2)) _let_51 :args ((not _let_6) true _let_11)) :args (_let_53 true _let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 1)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_5))) :args _let_32)) :args ((or _let_5 _let_11))) _let_51 :args (_let_5 true _let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 0)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_4))) :args _let_32)) :args ((or _let_4 _let_11))) _let_51 :args (_let_4 true _let_11)) :args (false false _let_10 true _let_7 false _let_5 false _let_4)) :args (_let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.52  )
% 0.19/0.52  % SZS output end Proof for MGT028+1
% 0.19/0.52  % cvc5---1.0.5 exiting
% 0.19/0.52  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------