%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : COM003+2 : TPTP v8.1.2. Bugfixed v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.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 : Wed Aug 30 18:36:53 EDT 2023

% Result   : Theorem 20.53s 20.94s
% Output   : Proof 20.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : COM003+2 : TPTP v8.1.2. Bugfixed v2.2.0.
% 0.14/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 29 13:06:13 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 20.53/20.94  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Oo2sltkj6W/cvc5---1.0.5_27885.p...
% 20.53/20.94  ------- get file name : TPTP file name is COM003+2
% 20.53/20.94  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27885.smt2...
% 20.53/20.94  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 20.53/20.94  --- Run --no-e-matching --full-saturate-quant at 5...
% 20.53/20.94  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.53/20.94  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 20.53/20.94  % SZS status Theorem for COM003+2
% 20.53/20.94  % SZS output start Proof for COM003+2
% 20.53/20.94  (
% 20.53/20.94  (let ((_let_1 (not (not (exists ((X $$unsorted)) (tptp.algorithm_program_decides X)))))) (let ((_let_2 (=> (exists ((V $$unsorted)) (and (tptp.program V) (forall ((Y $$unsorted)) (and (tptp.program_halts2_halts2_outputs V Y tptp.good) (tptp.program_not_halts2_halts2_outputs V Y tptp.bad))))) (exists ((U $$unsorted)) (and (tptp.program U) (forall ((Y $$unsorted)) (and (=> (tptp.program_halts2 Y Y) (not (tptp.halts2 U Y))) (tptp.program_not_halts2_halts2_outputs U Y tptp.good)))))))) (let ((_let_3 (=> (exists ((W $$unsorted)) (and (tptp.program W) (forall ((Y $$unsorted)) (and (tptp.program_halts2_halts3_outputs W Y Y tptp.good) (tptp.program_not_halts2_halts3_outputs W Y Y tptp.bad))))) (exists ((V $$unsorted)) (and (tptp.program V) (forall ((Y $$unsorted)) (and (tptp.program_halts2_halts2_outputs V Y tptp.good) (tptp.program_not_halts2_halts2_outputs V Y tptp.bad)))))))) (let ((_let_4 (forall ((W $$unsorted)) (=> (tptp.program_program_decides W) (forall ((Y $$unsorted) (Z $$unsorted)) (and (tptp.program_halts2_halts3_outputs W Y Z tptp.good) (tptp.program_not_halts2_halts3_outputs W Y Z tptp.bad))))))) (let ((_let_5 (=> (exists ((X $$unsorted)) (tptp.algorithm_program_decides X)) (exists ((W $$unsorted)) (tptp.program_program_decides W))))) (let ((_let_6 (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted)) (= (tptp.program_not_halts2_halts2_outputs X Y W) (=> (tptp.program_not_halts2 Y Y) (tptp.halts2_outputs X Y W)))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted)) (= (tptp.halts2_outputs X Y W) (and (tptp.halts2 X Y) (tptp.outputs X W)))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.program_not_halts2 X Y) (and (tptp.program X) (not (tptp.halts2 X Y))))))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.program_halts2 X Y) (and (tptp.program X) (tptp.halts2 X Y)))))) (let ((_let_10 (forall ((X $$unsorted)) (= (tptp.program_program_decides X) (and (tptp.program X) (tptp.program_decides X)))))) (let ((_let_11 (tptp.program_not_halts2_halts2_outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 tptp.good))) (let ((_let_12 (tptp.halts2_outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 tptp.good))) (let ((_let_13 (tptp.program_not_halts2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12))) (let ((_let_16 (= _let_11 _let_15))) (let ((_let_17 (forall ((BOUND_VARIABLE_943 $$unsorted)) (tptp.program_not_halts2_halts2_outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 BOUND_VARIABLE_943 tptp.good)))) (let ((_let_18 (not _let_17))) (let ((_let_19 (forall ((BOUND_VARIABLE_934 $$unsorted)) (or (not (tptp.program_halts2 BOUND_VARIABLE_934 BOUND_VARIABLE_934)) (not (tptp.halts2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 BOUND_VARIABLE_934)))))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.program SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_18))) (let ((_let_24 (forall ((U $$unsorted)) (or (not (tptp.program U)) (not (forall ((BOUND_VARIABLE_934 $$unsorted)) (or (not (tptp.program_halts2 BOUND_VARIABLE_934 BOUND_VARIABLE_934)) (not (tptp.halts2 U BOUND_VARIABLE_934))))) (not (forall ((BOUND_VARIABLE_943 $$unsorted)) (tptp.program_not_halts2_halts2_outputs U BOUND_VARIABLE_943 tptp.good))))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (forall ((V $$unsorted)) (or (not (tptp.program V)) (not (forall ((BOUND_VARIABLE_907 $$unsorted)) (tptp.program_halts2_halts2_outputs V BOUND_VARIABLE_907 tptp.good))) (not (forall ((BOUND_VARIABLE_912 $$unsorted)) (tptp.program_not_halts2_halts2_outputs V BOUND_VARIABLE_912 tptp.bad))))))) (let ((_let_27 (not _let_24))) (let ((_let_28 (forall ((V $$unsorted)) (or (not (tptp.program V)) (not (forall ((BOUND_VARIABLE_882 $$unsorted)) (tptp.program_halts2_halts2_outputs V BOUND_VARIABLE_882 tptp.good))) (not (forall ((BOUND_VARIABLE_887 $$unsorted)) (tptp.program_not_halts2_halts2_outputs V BOUND_VARIABLE_887 tptp.bad))))))) (let ((_let_29 (not _let_26))) (let ((_let_30 (forall ((W $$unsorted)) (or (not (tptp.program W)) (not (forall ((BOUND_VARIABLE_859 $$unsorted)) (tptp.program_halts2_halts3_outputs W BOUND_VARIABLE_859 BOUND_VARIABLE_859 tptp.good))) (not (forall ((BOUND_VARIABLE_864 $$unsorted)) (tptp.program_not_halts2_halts3_outputs W BOUND_VARIABLE_864 BOUND_VARIABLE_864 tptp.bad))))))) (let ((_let_31 (not _let_28))) (let ((_let_32 (forall ((BOUND_VARIABLE_864 $$unsorted)) (tptp.program_not_halts2_halts3_outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 BOUND_VARIABLE_864 BOUND_VARIABLE_864 tptp.bad)))) (let ((_let_33 (not _let_32))) (let ((_let_34 (forall ((BOUND_VARIABLE_859 $$unsorted)) (tptp.program_halts2_halts3_outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 BOUND_VARIABLE_859 BOUND_VARIABLE_859 tptp.good)))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.program SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_33))) (let ((_let_39 (not _let_30))) (let ((_let_40 (not _let_38))) (let ((_let_41 (tptp.program_not_halts2_halts3_outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 tptp.bad))) (let ((_let_42 (and (tptp.program_halts2_halts3_outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.good) _let_41))) (let ((_let_43 (tptp.program_program_decides SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42))) (let ((_let_46 (forall ((W $$unsorted) (BOUND_VARIABLE_851 $$unsorted) (BOUND_VARIABLE_849 $$unsorted) (BOUND_VARIABLE_846 $$unsorted) (BOUND_VARIABLE_844 $$unsorted)) (or (not (tptp.program_program_decides W)) (and (tptp.program_halts2_halts3_outputs W BOUND_VARIABLE_844 BOUND_VARIABLE_846 tptp.good) (tptp.program_not_halts2_halts3_outputs W BOUND_VARIABLE_849 BOUND_VARIABLE_851 tptp.bad)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (_let_46))) (let ((_let_49 (forall ((W $$unsorted)) (not (tptp.program_program_decides W))))) (let ((_let_50 (forall ((X $$unsorted)) (not (tptp.algorithm_program_decides X))))) (let ((_let_51 (not _let_49))) (let ((_let_52 (not _let_50))) (let ((_let_53 (or))) (let ((_let_54 (_let_51))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_54)) :args _let_54) (REWRITE :args ((=> _let_51 (not _let_44)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_49))) (REFL :args (_let_43)) :args _let_53)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_50))) (REFL :args _let_54) :args _let_53)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_50 (= X X)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_52 true (forall ((X $$unsorted)) (not (tptp.algorithm_program_decides X))))) :args (_let_51 true _let_50)) :args (_let_43 true _let_49)))) (let ((_let_56 (_let_33))) (let ((_let_57 (tptp.program_halts2_halts3_outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 tptp.good))) (let ((_let_58 (and _let_57 (tptp.program_not_halts2_halts3_outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.bad)))) (let ((_let_59 (or _let_44 _let_58))) (let ((_let_60 (_let_35))) (let ((_let_61 (and _let_36 (tptp.program_decides SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_62 (= _let_43 _let_61))) (let ((_let_63 (_let_10))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 (_let_30))) (let ((_let_66 (_let_27))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_24))) (REFL :args (_let_25)) :args _let_53)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_26))) (REFL :args _let_66) :args _let_53)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_28 (= BOUND_VARIABLE_882 BOUND_VARIABLE_907) (= V V) (= BOUND_VARIABLE_887 BOUND_VARIABLE_912)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_30))) (REFL :args (_let_31)) :args _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_65) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_35 _let_33 _let_40))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_61 0)) :args ((or _let_36 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_62)) :args ((or _let_44 _let_61 (not _let_62)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_63)) _let_64 :args (_let_62 false _let_10)) :args (_let_61 false _let_43 false _let_62)) :args (_let_36 false _let_61)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_60)) :args _let_60)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) (REFL :args ((not _let_57))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 0)) :args ((or _let_57 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_44 _let_58 (not _let_59)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_48)) _let_47 :args (_let_59 false _let_46)) :args (_let_58 false _let_43 false _let_59)) :args (_let_57 false _let_58)) :args (_let_34 false _let_57)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_56)) :args _let_56)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) (REFL :args ((not _let_41))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 1)) :args ((or _let_41 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_42 (not _let_45)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_48)) _let_47 :args (_let_45 false _let_46)) :args (_let_42 false _let_43 false _let_45)) :args (_let_41 false _let_42)) :args (_let_32 false _let_41)) :args (_let_40 false _let_36 false _let_34 false _let_32)) :args (_let_39 true _let_38)) :args (_let_31 true _let_30)) :args (_let_29 true _let_28)) :args (_let_27 true _let_26)) :args (_let_25 true _let_24)))) (let ((_let_68 (REFL :args (_let_23)))) (let ((_let_69 (_let_17))) (let ((_let_70 (not _let_15))) (let ((_let_71 (tptp.halts2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33))) (let ((_let_72 (and _let_71 (tptp.outputs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 tptp.good)))) (let ((_let_73 (= _let_12 _let_72))) (let ((_let_74 (not _let_12))) (let ((_let_75 (_let_7))) (let ((_let_76 (ASSUME :args _let_75))) (let ((_let_77 (not _let_72))) (let ((_let_78 (and _let_21 _let_71))) (let ((_let_79 (not _let_71))) (let ((_let_80 (tptp.program_halts2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_81 _let_79))) (let ((_let_83 (= _let_80 _let_78))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_53)) :args ((or _let_21 _let_23))) _let_67 :args (_let_21 true _let_23)))) (let ((_let_85 (_let_19))) (let ((_let_86 (_let_9))) (let ((_let_87 (ASSUME :args _let_86))) (let ((_let_88 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 QUANTIFIERS_INST_FMF_FMC_EXH))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_83)) :args ((or _let_80 (not _let_78) (not _let_83)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args _let_88) :args _let_86)) _let_87 :args (_let_83 false _let_9)) (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_79 _let_81 (not _let_82)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_85) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 1)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_53)) :args ((or _let_19 _let_23))) _let_67 :args (_let_19 true _let_23)) :args (_let_82 false _let_19)) (REORDERING (CNF_AND_NEG :args (_let_78)) :args ((or _let_22 _let_79 _let_78))) _let_84 :args (_let_79 false _let_83 true _let_80 false _let_82 false _let_78 false _let_21)))) (let ((_let_90 (and _let_21 _let_79))) (let ((_let_91 (= _let_13 _let_90))) (let ((_let_92 (_let_8))) (let ((_let_93 (ASSUME :args _let_92))) (let ((_let_94 (_let_90))) (let ((_let_95 (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted)) (= (tptp.program_not_halts2_halts2_outputs X Y W) (or (not (tptp.program_not_halts2 Y Y)) (tptp.halts2_outputs X Y W)))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_16)) :args ((or (not _let_11) _let_15 (not _let_16)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 tptp.good QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_95))) _let_96 :args (_let_16 false _let_95)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_12 _let_70))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_91)) :args ((or _let_13 (not _let_90) (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_94) (CONG (REFL :args _let_94) (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_71))) :args _let_53)) :args ((or _let_22 _let_71 _let_90))) _let_84 _let_89 :args (_let_90 false _let_21 true _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args _let_88) :args _let_92)) _let_93 :args (_let_91 false _let_8)) :args (_let_13 false _let_90 false _let_91)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_73)) :args ((or _let_72 _let_74 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_72 0)) :args ((or _let_71 _let_77))) _let_89 :args (_let_77 true _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 tptp.good QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_75)) _let_76 :args (_let_73 false _let_7)) :args (_let_74 true _let_72 false _let_73)) :args (_let_70 false _let_13 true _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_69) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 2)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_53)) :args ((or _let_17 _let_23))) _let_67 :args (_let_17 true _let_23)) :args (_let_11 false _let_17)) :args (false false _let_16 true _let_15 false _let_11)) :args ((forall ((X $$unsorted)) (= (tptp.program_decides X) (forall ((Y $$unsorted)) (=> (tptp.program Y) (forall ((Z $$unsorted)) (tptp.decides X Y Z)))))) _let_10 (forall ((X $$unsorted)) (= (tptp.algorithm_program_decides X) (and (tptp.algorithm X) (tptp.program_decides X)))) _let_9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (W $$unsorted)) (= (tptp.halts3_outputs X Y Z W) (and (tptp.halts3 X Y Z) (tptp.outputs X W)))) _let_8 _let_7 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (W $$unsorted)) (= (tptp.program_halts2_halts3_outputs X Y Z W) (=> (tptp.program_halts2 Y Z) (tptp.halts3_outputs X Y Z W)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (W $$unsorted)) (= (tptp.program_not_halts2_halts3_outputs X Y Z W) (=> (tptp.program_not_halts2 Y Z) (tptp.halts3_outputs X Y Z W)))) (forall ((X $$unsorted) (Y $$unsorted) (W $$unsorted)) (= (tptp.program_halts2_halts2_outputs X Y W) (=> (tptp.program_halts2 Y Y) (tptp.halts2_outputs X Y W)))) _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 20.53/20.94  )
% 20.53/20.94  % SZS output end Proof for COM003+2
% 20.53/20.94  % cvc5---1.0.5 exiting
% 20.53/20.95  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------