%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : COM123+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 18:37:14 EDT 2023

% Result   : Theorem 0.95s 1.18s
% Output   : Proof 0.95s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem    : COM123+1 : TPTP v8.1.2. Released v6.4.0.
% 0.12/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Aug 29 13:07:41 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.95/1.18  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.alKLAg34I3/cvc5---1.0.5_10266.p...
% 0.95/1.18  ------- get file name : TPTP file name is COM123+1
% 0.95/1.18  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10266.smt2...
% 0.95/1.18  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.95/1.18  % SZS status Theorem for COM123+1
% 0.95/1.18  % SZS output start Proof for COM123+1
% 0.95/1.18  (
% 0.95/1.18  (let ((_let_1 (not (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Vy $$unsorted) (VS1 $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS1 tptp.veabs))) (=> (and (not (= Vx Vy)) (not (tptp.visFreeVar Vx _let_1)) (tptp.vtcheck VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT))))))) (let ((_let_2 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (VT $$unsorted)) (=> (and (not (tptp.visFreeVar Vx tptp.veabs)) (tptp.vtcheck VC tptp.veabs VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) tptp.veabs VT))))) (let ((_let_3 (forall ((Ve $$unsorted) (VT $$unsorted) (VC $$unsorted)) (=> (tptp.vtcheck VC Ve VT) (or (exists ((Vx $$unsorted)) (and (= Ve (tptp.vvar Vx)) (= (tptp.vlookup Vx VC) (tptp.vsomeType VT)))) (exists ((Vx $$unsorted) (Ve2 $$unsorted) (VT1 $$unsorted) (VT2 $$unsorted)) (and (= Ve (tptp.vabs Vx VT1 Ve2)) (= VT (tptp.varrow VT1 VT2)) (tptp.vtcheck (tptp.vbind Vx VT1 VC) Ve2 VT2))) (exists ((Ve1 $$unsorted) (Ve2 $$unsorted) (VS $$unsorted)) (and (= Ve (tptp.vapp Ve1 Ve2)) (tptp.vtcheck VC Ve1 (tptp.varrow VS VT)) (tptp.vtcheck VC Ve2 VS)))))))) (let ((_let_4 (forall ((VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VS $$unsorted) (VT $$unsorted)) (=> (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT) (tptp.vtcheck VC (tptp.vabs Vx VS Ve) (tptp.varrow VS VT)))))) (let ((_let_5 (= tptp.vnoExp tptp.vnoExp))) (let ((_let_6 (forall ((Vy $$unsorted) (VTy $$unsorted) (Vx $$unsorted) (VTx $$unsorted) (VC $$unsorted) (Ve $$unsorted) (VT $$unsorted)) (=> (and (not (= Vx Vy)) (tptp.vtcheck (tptp.vbind Vx VTx (tptp.vbind Vy VTy VC)) Ve VT)) (tptp.vtcheck (tptp.vbind Vy VTy (tptp.vbind Vx VTx VC)) Ve VT))))) (let ((_let_7 (= tptp.vnoType tptp.vnoType))) (let ((_let_8 (= tptp.vempty tptp.vempty))) (let ((_let_9 (forall ((VT $$unsorted) (VVar0 $$unsorted) (VExp0 $$unsorted) (Vx $$unsorted) (Vv $$unsorted) (Ve $$unsorted)) (let ((_let_1 (and (not (= Vx Vv)) (tptp.visFreeVar Vv Ve)))) (let ((_let_2 (tptp.visFreeVar VVar0 VExp0))) (=> (and (= VVar0 Vv) (= VExp0 (tptp.vabs Vx VT Ve))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))))) (let ((_let_10 (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (VExp2 $$unsorted)) (not (= (tptp.vabs VVar0 VTyp0 VExp0) (tptp.vapp VExp1 VExp2)))))) (let ((_let_11 (forall ((VVar0 $$unsorted) (VVar1 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vabs VVar1 VTyp0 VExp0)))))) (let ((_let_12 (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted) (VVar1 $$unsorted) (VTyp1 $$unsorted) (VExp1 $$unsorted)) (let ((_let_1 (= (tptp.vabs VVar0 VTyp0 VExp0) (tptp.vabs VVar1 VTyp1 VExp1)))) (let ((_let_2 (and (= VVar0 VVar1) (= VTyp0 VTyp1) (= VExp0 VExp1)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))))) (let ((_let_13 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.veabs))) (let ((_let_14 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14))) (let ((_let_16 (tptp.vtcheck _let_15 tptp.veabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_17 (tptp.vtcheck _let_14 tptp.veabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_13 _let_18 _let_16))) (let ((_let_20 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.veabs))) (let ((_let_21 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_20))) (let ((_let_22 (not _let_13))) (let ((_let_23 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (or _let_23 _let_22 _let_21))) (let ((_let_25 (forall ((BOUND_VARIABLE_2046 $$unsorted) (BOUND_VARIABLE_2048 $$unsorted) (BOUND_VARIABLE_2050 $$unsorted) (BOUND_VARIABLE_2052 $$unsorted)) (or (= BOUND_VARIABLE_2048 BOUND_VARIABLE_2050) (not (tptp.visFreeVar BOUND_VARIABLE_2050 BOUND_VARIABLE_2052)) (tptp.visFreeVar BOUND_VARIABLE_2050 (tptp.vabs BOUND_VARIABLE_2048 BOUND_VARIABLE_2046 BOUND_VARIABLE_2052)))))) (let ((_let_26 (_let_25))) (let ((_let_27 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_28 (tptp.vtcheck _let_27 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_29 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_23 _let_21 _let_30 _let_28))) (let ((_let_32 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Vy $$unsorted) (VS1 $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS1 tptp.veabs))) (or (= Vx Vy) (tptp.visFreeVar Vx _let_1) (not (tptp.vtcheck VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT)))))) (let ((_let_33 (not _let_31))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (or))) (let ((_let_36 (not _let_32))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_34) :args (_let_36))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_32))) (REFL :args (_let_33)) :args _let_35)) _let_34 :args (_let_33 true _let_32)))) (let ((_let_38 (not _let_23))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 0)) _let_37 :args (_let_38 true _let_31)))) (let ((_let_40 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (VT $$unsorted)) (or (tptp.visFreeVar Vx tptp.veabs) (not (tptp.vtcheck VC tptp.veabs VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) tptp.veabs VT))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (tptp.vtcheck _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_43 (= tptp.veabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_44 (not _let_16))) (let ((_let_45 (tptp.vtcheck (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_27) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_46 (not _let_42))) (let ((_let_47 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_48 (or _let_47 _let_46 _let_45))) (let ((_let_49 (forall ((Vy $$unsorted) (VTy $$unsorted) (Vx $$unsorted) (VTx $$unsorted) (VC $$unsorted) (Ve $$unsorted) (VT $$unsorted)) (or (= Vy Vx) (not (tptp.vtcheck (tptp.vbind Vx VTx (tptp.vbind Vy VTy VC)) Ve VT)) (tptp.vtcheck (tptp.vbind Vy VTy (tptp.vbind Vx VTx VC)) Ve VT))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_52 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_53 (tptp.vtcheck _let_27 _let_52 _let_51))) (let ((_let_54 (not _let_45))) (let ((_let_55 (or _let_54 _let_53))) (let ((_let_56 (forall ((VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VS $$unsorted) (VT $$unsorted)) (or (not (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT)) (tptp.vtcheck VC (tptp.vabs Vx VS Ve) (tptp.varrow VS VT)))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_51))) (let ((_let_59 (= _let_20 _let_52))) (let ((_let_60 (not _let_53))) (let ((_let_61 (tptp.vtcheck _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_62 (not _let_61))) (let ((_let_63 (not _let_58))) (let ((_let_64 (not _let_59))) (let ((_let_65 (or _let_64 _let_63 _let_62))) (let ((_let_66 (forall ((Vx $$unsorted) (Ve2 $$unsorted) (VT1 $$unsorted) (VT2 $$unsorted)) (or (not (= (tptp.vabs Vx VT1 Ve2) (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.veabs))) (not (= (tptp.varrow VT1 VT2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.vtcheck (tptp.vbind Vx VT1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) Ve2 VT2)))))) (let ((_let_67 (not _let_65))) (let ((_let_68 (forall ((Ve1 $$unsorted) (Ve2 $$unsorted) (VS $$unsorted)) (or (not (= (tptp.vapp Ve1 Ve2) (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.veabs))) (not (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Ve1 (tptp.varrow VS SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (not (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Ve2 VS)))))) (let ((_let_69 (not _let_68))) (let ((_let_70 (not _let_66))) (let ((_let_71 (forall ((Vx $$unsorted)) (or (not (= (tptp.vvar Vx) (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.veabs))) (not (= (tptp.vlookup Vx SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.vsomeType SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_30 _let_72 _let_70 _let_69))) (let ((_let_74 (forall ((Ve $$unsorted) (VT $$unsorted) (VC $$unsorted)) (or (not (tptp.vtcheck VC Ve VT)) (not (forall ((Vx $$unsorted)) (or (not (= Ve (tptp.vvar Vx))) (not (= (tptp.vlookup Vx VC) (tptp.vsomeType VT)))))) (not (forall ((Vx $$unsorted) (Ve2 $$unsorted) (VT1 $$unsorted) (VT2 $$unsorted)) (or (not (= Ve (tptp.vabs Vx VT1 Ve2))) (not (= VT (tptp.varrow VT1 VT2))) (not (tptp.vtcheck (tptp.vbind Vx VT1 VC) Ve2 VT2))))) (not (forall ((Ve1 $$unsorted) (Ve2 $$unsorted) (VS $$unsorted)) (or (not (= Ve (tptp.vapp Ve1 Ve2))) (not (tptp.vtcheck VC Ve1 (tptp.varrow VS VT))) (not (tptp.vtcheck VC Ve2 VS))))))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (not (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_77 (not (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_78 (tptp.vapp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_79 (= _let_20 _let_78))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_80 _let_77 _let_76))) (let ((_let_82 (_let_10))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 (_let_69))) (let ((_let_85 (tptp.vlookup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_86 (tptp.vsomeType SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_87 (tptp.vvar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_88 (= _let_20 _let_87))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_89 (not (= _let_86 _let_85))))) (let ((_let_91 (_let_11))) (let ((_let_92 (ASSUME :args _let_91))) (let ((_let_93 (_let_72))) (let ((_let_94 (_let_70))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_94)) :args _let_94) (REWRITE :args ((=> _let_70 (not (or (not (= _let_52 _let_20)) (not (= _let_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_62))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_66))) (REFL :args (_let_67)) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_30 _let_72 _let_70 _let_69 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 2)) (CONG (REFL :args (_let_31)) (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_35)) :args ((or _let_29 _let_31))) _let_37 :args (_let_29 true _let_31)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_93)) :args _let_93) (REWRITE :args ((=> _let_72 (not (or (not (= _let_87 _let_20)) (not (= _let_85 _let_86))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_71))) (REFL :args ((not _let_90))) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_90 0)) (CONG (REFL :args (_let_90)) (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_88))) :args _let_35)) :args ((or _let_88 _let_90))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_92 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.veabs QUANTIFIERS_INST_E_MATCHING ((tptp.vvar VVar0) (tptp.vabs VVar1 VTyp0 VExp0)))) :args _let_91))) _let_92 :args (_let_89 false _let_11)) :args (_let_90 true _let_88)) :args (_let_71 false _let_90)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84) (REWRITE :args ((=> _let_69 (not (or (not (= _let_78 _let_20)) _let_77 _let_76))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) (REFL :args ((not _let_81))) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_81 0)) (CONG (REFL :args (_let_81)) (MACRO_SR_PRED_INTRO :args ((= (not _let_80) _let_79))) :args _let_35)) :args ((or _let_79 _let_81))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.veabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING ((tptp.vabs VVar0 VTyp0 VExp0) (tptp.vapp VExp1 VExp2)))) :args _let_82)) _let_83 :args (_let_80 false _let_10)) :args (_let_81 true _let_79)) :args (_let_68 false _let_81)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_75 :args (_let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.vtcheck VC Ve VT) false))))) :args (_let_74)))) _let_75 :args (_let_73 false _let_74)) :args (_let_70 false _let_29 false _let_71 false _let_68 false _let_73)) :args (_let_67 true _let_66)))) (let ((_let_96 (REFL :args (_let_65)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 0)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_59))) :args _let_35)) :args ((or _let_59 _let_65))) _let_95 :args (_let_59 true _let_65)))) (let ((_let_98 (not _let_28))) (let ((_let_99 (and _let_98 _let_59 _let_58))) (let ((_let_100 (_let_98 _let_59 _let_58))) (let ((_let_101 (ASSUME :args (_let_98)))) (let ((_let_102 (APPLY_UF tptp.vtcheck))) (let ((_let_103 (ASSUME :args (_let_58)))) (let ((_let_104 (ASSUME :args (_let_59)))) (let ((_let_105 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_106 (not _let_47))) (let ((_let_107 (and _let_105 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) _let_43))) (let ((_let_108 (or _let_64 _let_107))) (let ((_let_109 (forall ((BOUND_VARIABLE_1781 $$unsorted) (BOUND_VARIABLE_1783 $$unsorted) (BOUND_VARIABLE_1785 $$unsorted) (BOUND_VARIABLE_1787 $$unsorted) (BOUND_VARIABLE_1789 $$unsorted) (BOUND_VARIABLE_1791 $$unsorted)) (or (not (= (tptp.vabs BOUND_VARIABLE_1781 BOUND_VARIABLE_1783 BOUND_VARIABLE_1785) (tptp.vabs BOUND_VARIABLE_1787 BOUND_VARIABLE_1789 BOUND_VARIABLE_1791))) (and (= BOUND_VARIABLE_1781 BOUND_VARIABLE_1787) (= BOUND_VARIABLE_1783 BOUND_VARIABLE_1789) (= BOUND_VARIABLE_1785 BOUND_VARIABLE_1791)))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_64 _let_107 (not _let_108)))) _let_97 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.veabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING ((tptp.vabs BOUND_VARIABLE_1781 BOUND_VARIABLE_1783 BOUND_VARIABLE_1785) (tptp.vabs BOUND_VARIABLE_1787 BOUND_VARIABLE_1789 BOUND_VARIABLE_1791)))) :args (_let_109))) _let_110 :args (_let_108 false _let_109)) :args (_let_107 false _let_59 false _let_108)))) (let ((_let_112 (not _let_107))) (let ((_let_113 (and _let_38 _let_105))) (let ((_let_114 (_let_38 _let_105))) (let ((_let_115 (ASSUME :args (_let_38)))) (let ((_let_116 (ASSUME :args (_let_105)))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_107 2)) :args ((or _let_43 _let_112))) _let_111 :args (_let_43 false _let_107)))) (let ((_let_118 (and _let_43 _let_46))) (let ((_let_119 (ASSUME :args (_let_46)))) (let ((_let_120 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))) (let ((_let_121 (ASSUME :args (_let_43)))) (let ((_let_122 (SYMM (SYMM _let_121)))) (let ((_let_123 (and _let_61 _let_43))) (let ((_let_124 (_let_61 _let_43))) (let ((_let_125 (ASSUME :args (_let_61)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_13 _let_18 _let_16 (not _let_19)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_123)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_125 _let_121) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_14)) _let_122 _let_120 :args _let_102) (TRUE_INTRO _let_125))) :args _let_124)) :args _let_124)) :args (true _let_123)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 2)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_61))) :args _let_35)) :args ((or _let_61 _let_65))) _let_95 :args (_let_61 true _let_65)) _let_117 :args (_let_17 false _let_61 false _let_43)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_118)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_119 _let_121) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (_let_15)) _let_122 _let_120 :args _let_102) (FALSE_INTRO _let_119))) :args (_let_46 _let_43))) :args (_let_43 _let_46))) :args (true _let_118)) (CONG (REFL :args ((not _let_43))) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_42))) (REFL :args (_let_44)) :args _let_35)) _let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_47 _let_45 _let_46 (not _let_48)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_113)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_115 _let_116) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (SYMM _let_116) :args (=)) (FALSE_INTRO _let_115))) :args _let_114)) :args _let_114)) :args (true _let_113)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_23))) (REFL :args ((not _let_105))) (REFL :args (_let_106)) :args _let_35)) _let_39 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_107 0)) :args ((or _let_105 _let_112))) _let_111 :args (_let_105 false _let_107)) :args (_let_106 true _let_23 false _let_105)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_54 _let_53 (not _let_55)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_99)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_101 _let_104 _let_103) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (_let_27)) (SYMM _let_104) (SYMM _let_103) :args _let_102) (FALSE_INTRO _let_101))) :args _let_100)) :args _let_100)) :args (true _let_99)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_98) _let_28))) (REFL :args (_let_64)) (REFL :args (_let_63)) (REFL :args (_let_60)) :args _let_35)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 3)) _let_37 :args (_let_98 true _let_31)) _let_97 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 1)) (CONG _let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_58))) :args _let_35)) :args ((or _let_58 _let_65))) _let_95 :args (_let_58 true _let_65)) :args (_let_60 true _let_28 false _let_59 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (_let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.vtcheck VC (tptp.vabs Vx VS Ve) (tptp.varrow VS VT)) true))))) :args (_let_56))) _let_57 :args (_let_55 false _let_56)) :args (_let_54 true _let_53 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.vtcheck (tptp.vbind Vy VTy (tptp.vbind Vx VTx VC)) Ve VT) true))))) :args (_let_49)))) _let_50 :args (_let_48 false _let_49)) :args (_let_46 true _let_47 true _let_45 false _let_48)) :args (_let_44 false _let_43 true _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.vtcheck (tptp.vbind Vx VS VC) tptp.veabs VT) true))))) :args (_let_40))) _let_41 :args (_let_19 false _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_21 _let_22 (not _let_24)))) _let_39 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 1)) _let_37 :args ((not _let_21) true _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.veabs QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.visFreeVar BOUND_VARIABLE_2050 (tptp.vabs BOUND_VARIABLE_2048 BOUND_VARIABLE_2046 BOUND_VARIABLE_2052)) true))))) :args _let_26))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args (_let_24 false _let_25)) :args (_let_22 true _let_23 true _let_21 false _let_24)) :args (false false _let_17 true _let_16 false _let_19 true _let_13)) :args ((forall ((VVar0 $$unsorted) (VVar1 $$unsorted)) (let ((_let_1 (= (tptp.vvar VVar0) (tptp.vvar VVar1)))) (let ((_let_2 (= VVar0 VVar1))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))) _let_12 (forall ((VExp0 $$unsorted) (VExp1 $$unsorted) (VExp2 $$unsorted) (VExp3 $$unsorted)) (let ((_let_1 (= (tptp.vapp VExp0 VExp1) (tptp.vapp VExp2 VExp3)))) (let ((_let_2 (and (= VExp0 VExp2) (= VExp1 VExp3)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))) _let_11 (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vapp VExp0 VExp1)))) _let_10 (forall ((Vx $$unsorted) (VS $$unsorted) (Ve $$unsorted) (VExp0 $$unsorted)) (=> (= VExp0 (tptp.vabs Vx VS Ve)) (tptp.visValue VExp0))) (forall ((Vx $$unsorted) (VExp0 $$unsorted)) (=> (= VExp0 (tptp.vvar Vx)) (not (tptp.visValue VExp0)))) (forall ((Ve1 $$unsorted) (Ve2 $$unsorted) (VExp0 $$unsorted)) (=> (= VExp0 (tptp.vapp Ve1 Ve2)) (not (tptp.visValue VExp0)))) (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (Vx $$unsorted) (Vv $$unsorted)) (let ((_let_1 (= Vx Vv))) (let ((_let_2 (tptp.visFreeVar VVar0 VExp0))) (=> (and (= VVar0 Vv) (= VExp0 (tptp.vvar Vx))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))) _let_9 (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (Ve1 $$unsorted) (Vv $$unsorted) (Ve2 $$unsorted)) (let ((_let_1 (or (tptp.visFreeVar Vv Ve1) (tptp.visFreeVar Vv Ve2)))) (let ((_let_2 (tptp.visFreeVar VVar0 VExp0))) (=> (and (= VVar0 Vv) (= VExp0 (tptp.vapp Ve1 Ve2))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))) (and (=> _let_8 true) (=> true _let_8)) (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VCtx0 $$unsorted) (VVar1 $$unsorted) (VTyp1 $$unsorted) (VCtx1 $$unsorted)) (let ((_let_1 (= (tptp.vbind VVar0 VTyp0 VCtx0) (tptp.vbind VVar1 VTyp1 VCtx1)))) (let ((_let_2 (and (= VVar0 VVar1) (= VTyp0 VTyp1) (= VCtx0 VCtx1)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))) (and (=> _let_7 true) (=> true _let_7)) (forall ((VTyp0 $$unsorted) (VTyp1 $$unsorted)) (let ((_let_1 (= (tptp.vsomeType VTyp0) (tptp.vsomeType VTyp1)))) (let ((_let_2 (= VTyp0 VTyp1))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))) (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VCtx0 $$unsorted)) (not (= tptp.vempty (tptp.vbind VVar0 VTyp0 VCtx0)))) (forall ((VTyp0 $$unsorted)) (not (= tptp.vnoType (tptp.vsomeType VTyp0)))) (forall ((VOptTyp0 $$unsorted)) (=> (= VOptTyp0 tptp.vnoType) (not (tptp.visSomeType VOptTyp0)))) (forall ((Ve $$unsorted) (VOptTyp0 $$unsorted)) (=> (= VOptTyp0 (tptp.vsomeType Ve)) (tptp.visSomeType VOptTyp0))) (forall ((VOptTyp0 $$unsorted) (RESULT $$unsorted) (Ve $$unsorted)) (=> (= VOptTyp0 (tptp.vsomeType Ve)) (=> (= RESULT (tptp.vgetSomeType VOptTyp0)) (= RESULT Ve)))) (forall ((Vx $$unsorted) (VVar0 $$unsorted) (VCtx0 $$unsorted) (RESULT $$unsorted)) (=> (and (= VVar0 Vx) (= VCtx0 tptp.vempty)) (=> (= RESULT (tptp.vlookup VVar0 VCtx0)) (= RESULT tptp.vnoType)))) (forall ((VC $$unsorted) (Vx $$unsorted) (Vy $$unsorted) (VVar0 $$unsorted) (VCtx0 $$unsorted) (RESULT $$unsorted) (VTy $$unsorted)) (=> (and (= VVar0 Vx) (= VCtx0 (tptp.vbind Vy VTy VC))) (=> (= Vx Vy) (=> (= RESULT (tptp.vlookup VVar0 VCtx0)) (= RESULT (tptp.vsomeType VTy)))))) (forall ((VTy $$unsorted) (Vy $$unsorted) (VVar0 $$unsorted) (VCtx0 $$unsorted) (RESULT $$unsorted) (Vx $$unsorted) (VC $$unsorted)) (=> (and (= VVar0 Vx) (= VCtx0 (tptp.vbind Vy VTy VC))) (=> (not (= Vx Vy)) (=> (= RESULT (tptp.vlookup VVar0 VCtx0)) (= RESULT (tptp.vlookup Vx VC)))))) (forall ((VVar0 $$unsorted) (VCtx0 $$unsorted) (RESULT $$unsorted)) (=> (= (tptp.vlookup VVar0 VCtx0) RESULT) (or (exists ((Vx $$unsorted)) (and (= VVar0 Vx) (= VCtx0 tptp.vempty) (= RESULT tptp.vnoType))) (exists ((VC $$unsorted) (Vx $$unsorted) (Vy $$unsorted) (VTy $$unsorted)) (and (= VVar0 Vx) (= VCtx0 (tptp.vbind Vy VTy VC)) (= Vx Vy) (= RESULT (tptp.vsomeType VTy)))) (exists ((VTy $$unsorted) (Vy $$unsorted) (Vx $$unsorted) (VC $$unsorted)) (and (= VVar0 Vx) (= VCtx0 (tptp.vbind Vy VTy VC)) (not (= Vx Vy)) (= RESULT (tptp.vlookup Vx VC))))))) (forall ((Vy $$unsorted) (VTy $$unsorted) (Vx $$unsorted) (VTx $$unsorted) (VC $$unsorted) (Ve $$unsorted) (VT $$unsorted)) (=> (and (= Vx Vy) (tptp.vtcheck (tptp.vbind Vx VTx (tptp.vbind Vy VTy VC)) Ve VT)) (tptp.vtcheck (tptp.vbind Vx VTx VC) Ve VT))) _let_6 (forall ((Vv $$unsorted) (Ve $$unsorted)) (=> (= (tptp.vgensym Ve) Vv) (not (tptp.visFreeVar Vv Ve)))) (forall ((Vx $$unsorted) (Vy $$unsorted) (VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (RESULT $$unsorted) (Ve $$unsorted)) (=> (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vvar Vy))) (=> (= Vx Vy) (=> (= RESULT (tptp.vsubst VVar0 VExp0 VExp1)) (= RESULT Ve))))) (forall ((Ve $$unsorted) (Vx $$unsorted) (VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (RESULT $$unsorted) (Vy $$unsorted)) (let ((_let_1 (tptp.vvar Vy))) (=> (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 _let_1)) (=> (not (= Vx Vy)) (=> (= RESULT (tptp.vsubst VVar0 VExp0 VExp1)) (= RESULT _let_1)))))) (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (RESULT $$unsorted) (Ve1 $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Ve2 $$unsorted)) (=> (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vapp Ve1 Ve2))) (=> (= RESULT (tptp.vsubst VVar0 VExp0 VExp1)) (= RESULT (tptp.vapp (tptp.vsubst Vx Ve Ve1) (tptp.vsubst Vx Ve Ve2)))))) (forall ((Ve $$unsorted) (Vx $$unsorted) (VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (RESULT $$unsorted) (Vy $$unsorted) (VT $$unsorted) (Ve1 $$unsorted)) (let ((_let_1 (tptp.vabs Vy VT Ve1))) (=> (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 _let_1)) (=> (= Vx Vy) (=> (= RESULT (tptp.vsubst VVar0 VExp0 VExp1)) (= RESULT _let_1)))))) (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (RESULT $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VT $$unsorted) (Vy $$unsorted) (Vfresh $$unsorted) (Ve1 $$unsorted)) (=> (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vabs Vy VT Ve1))) (=> (and (not (= Vx Vy)) (tptp.visFreeVar Vy Ve) (= Vfresh (tptp.vgensym (tptp.vapp (tptp.vapp Ve Ve1) (tptp.vvar Vx))))) (=> (= RESULT (tptp.vsubst VVar0 VExp0 VExp1)) (= RESULT (tptp.vsubst Vx Ve (tptp.vabs Vfresh VT (tptp.vsubst Vy (tptp.vvar Vfresh) Ve1)))))))) (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (RESULT $$unsorted) (Vy $$unsorted) (VT $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Ve1 $$unsorted)) (=> (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vabs Vy VT Ve1))) (=> (and (not (= Vx Vy)) (not (tptp.visFreeVar Vy Ve))) (=> (= RESULT (tptp.vsubst VVar0 VExp0 VExp1)) (= RESULT (tptp.vabs Vy VT (tptp.vsubst Vx Ve Ve1))))))) (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (RESULT $$unsorted)) (=> (= (tptp.vsubst VVar0 VExp0 VExp1) RESULT) (or (exists ((Vx $$unsorted) (Vy $$unsorted) (Ve $$unsorted)) (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vvar Vy)) (= Vx Vy) (= RESULT Ve))) (exists ((Ve $$unsorted) (Vx $$unsorted) (Vy $$unsorted)) (let ((_let_1 (tptp.vvar Vy))) (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 _let_1) (not (= Vx Vy)) (= RESULT _let_1)))) (exists ((Ve1 $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Ve2 $$unsorted)) (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vapp Ve1 Ve2)) (= RESULT (tptp.vapp (tptp.vsubst Vx Ve Ve1) (tptp.vsubst Vx Ve Ve2))))) (exists ((Ve $$unsorted) (Vx $$unsorted) (Vy $$unsorted) (VT $$unsorted) (Ve1 $$unsorted)) (let ((_let_1 (tptp.vabs Vy VT Ve1))) (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 _let_1) (= Vx Vy) (= RESULT _let_1)))) (exists ((Vx $$unsorted) (Ve $$unsorted) (VT $$unsorted) (Vy $$unsorted) (Vfresh $$unsorted) (Ve1 $$unsorted)) (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vabs Vy VT Ve1)) (not (= Vx Vy)) (tptp.visFreeVar Vy Ve) (= Vfresh (tptp.vgensym (tptp.vapp (tptp.vapp Ve Ve1) (tptp.vvar Vx)))) (= RESULT (tptp.vsubst Vx Ve (tptp.vabs Vfresh VT (tptp.vsubst Vy (tptp.vvar Vfresh) Ve1)))))) (exists ((Vy $$unsorted) (VT $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Ve1 $$unsorted)) (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vabs Vy VT Ve1)) (not (= Vx Vy)) (not (tptp.visFreeVar Vy Ve)) (= RESULT (tptp.vabs Vy VT (tptp.vsubst Vx Ve Ve1)))))))) (and (=> _let_5 true) (=> true _let_5)) (forall ((VExp0 $$unsorted) (VExp1 $$unsorted)) (let ((_let_1 (= (tptp.vsomeExp VExp0) (tptp.vsomeExp VExp1)))) (let ((_let_2 (= VExp0 VExp1))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))) (forall ((VExp0 $$unsorted)) (not (= tptp.vnoExp (tptp.vsomeExp VExp0)))) (forall ((VOptExp0 $$unsorted)) (=> (= VOptExp0 tptp.vnoExp) (not (tptp.visSomeExp VOptExp0)))) (forall ((Ve $$unsorted) (VOptExp0 $$unsorted)) (=> (= VOptExp0 (tptp.vsomeExp Ve)) (tptp.visSomeExp VOptExp0))) (forall ((VOptExp0 $$unsorted) (RESULT $$unsorted) (Ve $$unsorted)) (=> (= VOptExp0 (tptp.vsomeExp Ve)) (=> (= RESULT (tptp.vgetSomeExp VOptExp0)) (= RESULT Ve)))) (forall ((Vx $$unsorted) (VExp0 $$unsorted) (RESULT $$unsorted)) (=> (= VExp0 (tptp.vvar Vx)) (=> (= RESULT (tptp.vreduce VExp0)) (= RESULT tptp.vnoExp)))) (forall ((Vx $$unsorted) (VS $$unsorted) (Ve $$unsorted) (VExp0 $$unsorted) (RESULT $$unsorted)) (=> (= VExp0 (tptp.vabs Vx VS Ve)) (=> (= RESULT (tptp.vreduce VExp0)) (= RESULT tptp.vnoExp)))) (forall ((Ve2 $$unsorted) (VExp0 $$unsorted) (RESULT $$unsorted) (Vx $$unsorted) (VS $$unsorted) (Ve1 $$unsorted) (Ve2red $$unsorted)) (let ((_let_1 (tptp.vabs Vx VS Ve1))) (=> (= VExp0 (tptp.vapp _let_1 Ve2)) (=> (and (= Ve2red (tptp.vreduce Ve2)) (tptp.visSomeExp Ve2red)) (=> (= RESULT (tptp.vreduce VExp0)) (= RESULT (tptp.vsomeExp (tptp.vapp _let_1 (tptp.vgetSomeExp Ve2red))))))))) (forall ((VS $$unsorted) (Ve2red $$unsorted) (VExp0 $$unsorted) (RESULT $$unsorted) (Vx $$unsorted) (Ve2 $$unsorted) (Ve1 $$unsorted)) (=> (= VExp0 (tptp.vapp (tptp.vabs Vx VS Ve1) Ve2)) (=> (and (= Ve2red (tptp.vreduce Ve2)) (not (tptp.visSomeExp Ve2red)) (tptp.visValue Ve2)) (=> (= RESULT (tptp.vreduce VExp0)) (= RESULT (tptp.vsomeExp (tptp.vsubst Vx Ve2 Ve1))))))) (forall ((Vx $$unsorted) (VS $$unsorted) (Ve1 $$unsorted) (Ve2red $$unsorted) (Ve2 $$unsorted) (VExp0 $$unsorted) (RESULT $$unsorted)) (=> (= VExp0 (tptp.vapp (tptp.vabs Vx VS Ve1) Ve2)) (=> (and (= Ve2red (tptp.vreduce Ve2)) (not (tptp.visSomeExp Ve2red)) (not (tptp.visValue Ve2))) (=> (= RESULT (tptp.vreduce VExp0)) (= RESULT tptp.vnoExp))))) (forall ((Ve1 $$unsorted) (VExp0 $$unsorted) (RESULT $$unsorted) (Ve1red $$unsorted) (Ve2 $$unsorted)) (=> (and (= VExp0 (tptp.vapp Ve1 Ve2)) (forall ((VVx0 $$unsorted) (VVS0 $$unsorted) (VVe10 $$unsorted)) (not (= Ve1 (tptp.vabs VVx0 VVS0 VVe10))))) (=> (and (= Ve1red (tptp.vreduce Ve1)) (tptp.visSomeExp Ve1red)) (=> (= RESULT (tptp.vreduce VExp0)) (= RESULT (tptp.vsomeExp (tptp.vapp (tptp.vgetSomeExp Ve1red) Ve2))))))) (forall ((Ve2 $$unsorted) (Ve1 $$unsorted) (Ve1red $$unsorted) (VExp0 $$unsorted) (RESULT $$unsorted)) (=> (and (= VExp0 (tptp.vapp Ve1 Ve2)) (forall ((VVx0 $$unsorted) (VVS0 $$unsorted) (VVe10 $$unsorted)) (not (= Ve1 (tptp.vabs VVx0 VVS0 VVe10))))) (=> (and (= Ve1red (tptp.vreduce Ve1)) (not (tptp.visSomeExp Ve1red))) (=> (= RESULT (tptp.vreduce VExp0)) (= RESULT tptp.vnoExp))))) (forall ((VExp0 $$unsorted) (RESULT $$unsorted)) (=> (= (tptp.vreduce VExp0) RESULT) (or (exists ((Vx $$unsorted)) (and (= VExp0 (tptp.vvar Vx)) (= RESULT tptp.vnoExp))) (exists ((Vx $$unsorted) (VS $$unsorted) (Ve $$unsorted)) (and (= VExp0 (tptp.vabs Vx VS Ve)) (= RESULT tptp.vnoExp))) (exists ((Ve2 $$unsorted) (Vx $$unsorted) (VS $$unsorted) (Ve1 $$unsorted) (Ve2red $$unsorted)) (let ((_let_1 (tptp.vabs Vx VS Ve1))) (and (= VExp0 (tptp.vapp _let_1 Ve2)) (= Ve2red (tptp.vreduce Ve2)) (tptp.visSomeExp Ve2red) (= RESULT (tptp.vsomeExp (tptp.vapp _let_1 (tptp.vgetSomeExp Ve2red))))))) (exists ((VS $$unsorted) (Ve2red $$unsorted) (Vx $$unsorted) (Ve2 $$unsorted) (Ve1 $$unsorted)) (and (= VExp0 (tptp.vapp (tptp.vabs Vx VS Ve1) Ve2)) (= Ve2red (tptp.vreduce Ve2)) (not (tptp.visSomeExp Ve2red)) (tptp.visValue Ve2) (= RESULT (tptp.vsomeExp (tptp.vsubst Vx Ve2 Ve1))))) (exists ((Vx $$unsorted) (VS $$unsorted) (Ve1 $$unsorted) (Ve2red $$unsorted) (Ve2 $$unsorted)) (and (= VExp0 (tptp.vapp (tptp.vabs Vx VS Ve1) Ve2)) (= Ve2red (tptp.vreduce Ve2)) (not (tptp.visSomeExp Ve2red)) (not (tptp.visValue Ve2)) (= RESULT tptp.vnoExp))) (exists ((Ve1 $$unsorted) (Ve1red $$unsorted) (Ve2 $$unsorted)) (and (= VExp0 (tptp.vapp Ve1 Ve2)) (forall ((VVx0 $$unsorted) (VVS0 $$unsorted) (VVe10 $$unsorted)) (not (= Ve1 (tptp.vabs VVx0 VVS0 VVe10)))) (= Ve1red (tptp.vreduce Ve1)) (tptp.visSomeExp Ve1red) (= RESULT (tptp.vsomeExp (tptp.vapp (tptp.vgetSomeExp Ve1red) Ve2))))) (exists ((Ve2 $$unsorted) (Ve1 $$unsorted) (Ve1red $$unsorted)) (and (= VExp0 (tptp.vapp Ve1 Ve2)) (forall ((VVx0 $$unsorted) (VVS0 $$unsorted) (VVe10 $$unsorted)) (not (= Ve1 (tptp.vabs VVx0 VVS0 VVe10)))) (= Ve1red (tptp.vreduce Ve1)) (not (tptp.visSomeExp Ve1red)) (= RESULT tptp.vnoExp)))))) (forall ((VTyp0 $$unsorted) (VTyp1 $$unsorted) (VTyp2 $$unsorted) (VTyp3 $$unsorted)) (let ((_let_1 (= (tptp.varrow VTyp0 VTyp1) (tptp.varrow VTyp2 VTyp3)))) (let ((_let_2 (and (= VTyp0 VTyp2) (= VTyp1 VTyp3)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))) (forall ((VC $$unsorted) (Vx $$unsorted) (VT $$unsorted)) (=> (= (tptp.vlookup Vx VC) (tptp.vsomeType VT)) (tptp.vtcheck VC (tptp.vvar Vx) VT))) _let_4 (forall ((VS $$unsorted) (VC $$unsorted) (Ve1 $$unsorted) (Ve2 $$unsorted) (VT $$unsorted)) (=> (and (tptp.vtcheck VC Ve1 (tptp.varrow VS VT)) (tptp.vtcheck VC Ve2 VS)) (tptp.vtcheck VC (tptp.vapp Ve1 Ve2) VT))) _let_3 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Ve $$unsorted) (VT $$unsorted)) (=> (and (= (tptp.vlookup Vx VC) tptp.vnoType) (tptp.vtcheck VC Ve VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT))) (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Ve $$unsorted) (VT $$unsorted)) (=> (and (not (tptp.visFreeVar Vx Ve)) (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT)) (tptp.vtcheck VC Ve VT))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.95/1.18  )
% 0.95/1.18  % SZS output end Proof for COM123+1
% 0.95/1.18  % cvc5---1.0.5 exiting
% 0.95/1.19  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------