%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : COM131+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n010.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 18:37:16 EDT 2023

% Result   : Theorem 25.83s 26.21s
% Output   : Proof 25.83s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : COM131+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n010.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 12:56:48 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 25.83/26.21  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.FwV5IHAHVR/cvc5---1.0.5_30227.p...
% 25.83/26.21  ------- get file name : TPTP file name is COM131+1
% 25.83/26.21  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30227.smt2...
% 25.83/26.21  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.83/26.21  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.83/26.21  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.83/26.21  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.83/26.21  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.83/26.21  % SZS status Theorem for COM131+1
% 25.83/26.21  % SZS output start Proof for COM131+1
% 25.83/26.21  (
% 25.83/26.21  (let ((_let_1 (not (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Vy $$unsorted) (VS $$unsorted) (VT2 $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS tptp.veabs))) (=> (and (not (= Vx Vy)) (not (tptp.visFreeVar Vy Ve)) (tptp.vtcheck VC Ve VT) (tptp.vtcheck (tptp.vbind Vx VT VC) _let_1 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve _let_1) VT2))))))) (let ((_let_2 (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VT2 $$unsorted)) (=> (and (tptp.vtcheck VC Ve VT) (tptp.vtcheck (tptp.vbind Vx VT VC) tptp.veabs VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve tptp.veabs) VT2))))) (let ((_let_3 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Ve $$unsorted) (VT $$unsorted)) (=> (and (not (tptp.visFreeVar Vx Ve)) (tptp.vtcheck VC Ve VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT))))) (let ((_let_4 (forall ((Ve $$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_5 (forall ((VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VS $$unsorted) (VT $$unsorted)) (=> (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT) (tptp.vtcheck VC (tptp.vabs Vx VS Ve) (tptp.varrow VS VT)))))) (let ((_let_6 (= tptp.vnoExp tptp.vnoExp))) (let ((_let_7 (forall ((VVar0 $$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))))))))) (let ((_let_8 (forall ((Vy $$unsorted) (VTy $$unsorted) (Vx $$unsorted) (VTx $$unsorted) (VC $$unsorted) (Ve $$unsorted) (VT $$unsorted)) (=> (and (not (= Vx Vy)) (tptp.vtcheck (tptp.vbind Vx VTx (tptp.vbind Vy VTy VC)) Ve VT)) (tptp.vtcheck (tptp.vbind Vy VTy (tptp.vbind Vx VTx VC)) Ve VT))))) (let ((_let_9 (= tptp.vnoType tptp.vnoType))) (let ((_let_10 (= tptp.vempty tptp.vempty))) (let ((_let_11 (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (VExp2 $$unsorted)) (not (= (tptp.vabs VVar0 VTyp0 VExp0) (tptp.vapp VExp1 VExp2)))))) (let ((_let_12 (forall ((VVar0 $$unsorted) (VVar1 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vabs VVar1 VTyp0 VExp0)))))) (let ((_let_13 (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_14 (tptp.vapp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_110 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_111))) (let ((_let_15 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (_let_11))) (let ((_let_18 (ASSUME :args _let_17))) (let ((_let_19 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_20 (not (tptp.vtcheck _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_111 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_112)))) (let ((_let_21 (not (tptp.vtcheck _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_110 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_112 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))) (let ((_let_22 (not _let_16))) (let ((_let_23 (or _let_22 _let_21 _let_20))) (let ((_let_24 (forall ((Ve1 $$unsorted) (Ve2 $$unsorted) (VS $$unsorted)) (let ((_let_1 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (or (not (= (tptp.vapp Ve1 Ve2) (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (not (tptp.vtcheck _let_1 Ve1 (tptp.varrow VS SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (not (tptp.vtcheck _let_1 Ve2 VS))))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (not _let_24))) (let ((_let_27 (forall ((Vx $$unsorted) (Ve2 $$unsorted) (VT1 $$unsorted) (VT2 $$unsorted)) (or (not (= (tptp.vabs Vx VT1 Ve2) (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (not (= (tptp.varrow VT1 VT2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.vtcheck (tptp.vbind Vx VT1 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) Ve2 VT2)))))) (let ((_let_28 (not _let_27))) (let ((_let_29 (forall ((Vx $$unsorted)) (or (not (= (tptp.vvar Vx) (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (not (= (tptp.vlookup Vx (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.vsomeType SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.vtcheck _let_19 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_30 _let_28 _let_26))) (let ((_let_34 (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_35 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (tptp.vtcheck (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_38))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_42 (= _let_15 _let_41))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_40 _let_37))) (let ((_let_45 (= tptp.veabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_46 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_47 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_48 (and _let_47 _let_46 _let_45))) (let ((_let_49 (or _let_43 _let_48))) (let ((_let_50 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_51 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_52 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_15))) (let ((_let_53 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_54 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.veabs))) (let ((_let_55 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_54))) (let ((_let_56 (= _let_52 _let_55))) (let ((_let_57 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_55 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))) (let ((_let_58 (tptp.vtcheck (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_59 (or _let_51 _let_37 _let_58))) (let ((_let_60 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_61 (tptp.vtcheck _let_60 _let_54 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_62 (not _let_61))) (let ((_let_63 (or _let_62 _let_57))) (let ((_let_64 (tptp.vtcheck _let_60 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_65 (tptp.vtcheck (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_60) tptp.veabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_66 (not _let_65))) (let ((_let_67 (not _let_64))) (let ((_let_68 (or _let_67 _let_66 _let_61))) (let ((_let_69 (or))) (let ((_let_70 (REFL :args (_let_44)))) (let ((_let_71 (forall ((BOUND_VARIABLE_1818 $$unsorted) (BOUND_VARIABLE_1820 $$unsorted) (BOUND_VARIABLE_1822 $$unsorted) (BOUND_VARIABLE_1824 $$unsorted) (BOUND_VARIABLE_1826 $$unsorted) (BOUND_VARIABLE_1828 $$unsorted)) (or (not (= (tptp.vabs BOUND_VARIABLE_1818 BOUND_VARIABLE_1820 BOUND_VARIABLE_1822) (tptp.vabs BOUND_VARIABLE_1824 BOUND_VARIABLE_1826 BOUND_VARIABLE_1828))) (and (= BOUND_VARIABLE_1818 BOUND_VARIABLE_1824) (= BOUND_VARIABLE_1820 BOUND_VARIABLE_1826) (= BOUND_VARIABLE_1822 BOUND_VARIABLE_1828)))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (not _let_48))) (let ((_let_74 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_75 (not _let_74))) (let ((_let_76 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_77 (or _let_50 _let_76 _let_75 _let_32 _let_53))) (let ((_let_78 (not _let_50))) (let ((_let_79 (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Vy $$unsorted) (VS $$unsorted) (VT2 $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS tptp.veabs))) (or (= Vx Vy) (tptp.visFreeVar Vy Ve) (not (tptp.vtcheck VC Ve VT)) (not (tptp.vtcheck (tptp.vbind Vx VT VC) _let_1 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve _let_1) VT2)))))) (let ((_let_80 (not _let_77))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (not _let_79))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_81) :args (_let_82))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_79))) (REFL :args (_let_80)) :args _let_69)) _let_81 :args (_let_80 true _let_79)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_77 0)) _let_83 :args (_let_78 true _let_77)))) (let ((_let_85 (and _let_78 _let_47))) (let ((_let_86 (_let_78 _let_47))) (let ((_let_87 (ASSUME :args (_let_78)))) (let ((_let_88 (ASSUME :args (_let_47)))) (let ((_let_89 (SYMM _let_88))) (let ((_let_90 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_91 (not _let_53))) (let ((_let_92 (or _let_50 _let_76 _let_56))) (let ((_let_93 (forall ((Vy $$unsorted) (VT $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Ve1 $$unsorted)) (or (= Vy Vx) (tptp.visFreeVar Vy Ve) (= (tptp.vabs Vy VT (tptp.vsubst Vx Ve Ve1)) (tptp.vsubst Vx Ve (tptp.vabs Vy VT Ve1))))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_77 1)) _let_83 :args ((not _let_76) true _let_77)))) (let ((_let_96 (and _let_91 _let_56 _let_39 _let_46))) (let ((_let_97 (_let_91 _let_56 _let_39 _let_46))) (let ((_let_98 (ASSUME :args (_let_91)))) (let ((_let_99 (APPLY_UF tptp.vtcheck))) (let ((_let_100 (ASSUME :args (_let_39)))) (let ((_let_101 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))) (let ((_let_102 (ASSUME :args (_let_46)))) (let ((_let_103 (SYMM (SYMM _let_102)))) (let ((_let_104 (ASSUME :args (_let_56)))) (let ((_let_105 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_106 (forall ((Vy $$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_107 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (forall ((VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VS $$unsorted) (VT $$unsorted)) (or (not (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT)) (tptp.vtcheck VC (tptp.vabs Vx VS Ve) (tptp.varrow VS VT)))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (or _let_76 _let_75 _let_64))) (let ((_let_111 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Ve $$unsorted) (VT $$unsorted)) (or (tptp.visFreeVar Vx Ve) (not (tptp.vtcheck VC Ve VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (REFL :args (_let_77)))) (let ((_let_114 (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VT2 $$unsorted)) (or (not (tptp.vtcheck VC Ve VT)) (not (tptp.vtcheck (tptp.vbind Vx VT VC) tptp.veabs VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve tptp.veabs) VT2))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (and _let_47 _let_46 _let_45 _let_58))) (let ((_let_117 (ASSUME :args (_let_58)))) (let ((_let_118 (ASSUME :args (_let_45)))) (let ((_let_119 (APPLY_UF tptp.vbind))) (let ((_let_120 (_let_28))) (let ((_let_121 (tptp.vlookup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_19))) (let ((_let_122 (tptp.vsomeType SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_123 (tptp.vvar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_124 (= _let_15 _let_123))) (let ((_let_125 (not _let_124))) (let ((_let_126 (or _let_125 (not (= _let_122 _let_121))))) (let ((_let_127 (_let_12))) (let ((_let_128 (ASSUME :args _let_127))) (let ((_let_129 (_let_30))) (let ((_let_130 (_let_26))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_110 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_111 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_17)) (MACRO_RESOLUTION_TRUST 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Ve1 Ve2))) (=> (= RESULT (tptp.vsubst VVar0 VExp0 VExp1)) (= RESULT (tptp.vapp (tptp.vsubst Vx Ve Ve1) (tptp.vsubst Vx Ve Ve2)))))) (forall ((Ve $$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)))))))) _let_7 (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_6 true) (=> true _let_6)) (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_5 (forall ((VS $$unsorted) (VC $$unsorted) (Ve1 $$unsorted) (Ve2 $$unsorted) (VT $$unsorted)) (=> (and (tptp.vtcheck VC Ve1 (tptp.varrow VS VT)) (tptp.vtcheck VC Ve2 VS)) (tptp.vtcheck VC (tptp.vapp Ve1 Ve2) VT))) _let_4 (forall ((Vx $$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 $$unsorted)) (=> (and (not (tptp.visFreeVar Vx Ve)) (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT)) (tptp.vtcheck VC Ve VT))) _let_3 _let_2 (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Vy $$unsorted) (VS $$unsorted) (Ve1 $$unsorted) (VT2 $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS Ve1))) (=> (and (= Vx Vy) (tptp.vtcheck VC Ve VT) (tptp.vtcheck (tptp.vbind Vx VT VC) _let_1 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve _let_1) VT2)))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.83/26.22  )
% 25.83/26.22  % SZS output end Proof for COM131+1
% 25.83/26.22  % cvc5---1.0.5 exiting
% 25.83/26.22  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------