TSTP Solution File: COM148+1 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : COM148+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.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 18:37:20 EDT 2023

% Result   : Theorem 25.68s 26.07s
% Output   : Proof 25.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : COM148+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n026.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Aug 29 13:18:05 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 25.68/26.07  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.3JOZ2pxf5r/cvc5---1.0.5_1266.p...
% 25.68/26.07  ------- get file name : TPTP file name is COM148+1
% 25.68/26.07  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1266.smt2...
% 25.68/26.07  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.68/26.07  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.68/26.07  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.68/26.07  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.68/26.07  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.68/26.07  % SZS status Theorem for COM148+1
% 25.68/26.07  % SZS output start Proof for COM148+1
% 25.68/26.07  (
% 25.68/26.07  (let ((_let_1 (not (forall ((VT $$unsorted)) (let ((_let_1 (tptp.vapp tptp.ve1 tptp.ve2))) (=> (and (tptp.vtcheck tptp.vempty _let_1 VT) (not (tptp.visValue _let_1))) (exists ((Veout $$unsorted)) (= (tptp.vreduce (tptp.vapp tptp.ve1 tptp.ve2)) (tptp.vsomeExp Veout))))))))) (let ((_let_2 (forall ((VT $$unsorted)) (=> (and (tptp.vtcheck tptp.vempty tptp.ve2 VT) (not (tptp.visValue tptp.ve2))) (exists ((Veout $$unsorted)) (= (tptp.vreduce tptp.ve2) (tptp.vsomeExp Veout))))))) (let ((_let_3 (forall ((VT $$unsorted)) (=> (and (tptp.vtcheck tptp.vempty tptp.ve1 VT) (not (tptp.visValue tptp.ve1))) (exists ((Veout $$unsorted)) (= (tptp.vreduce tptp.ve1) (tptp.vsomeExp Veout))))))) (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 $$unsorted)) (and (= Ve (tptp.vapp Ve1 Ve2)) (tptp.vtcheck VC Ve1 (tptp.varrow VS VT)) (tptp.vtcheck VC Ve2 VS)))))))) (let ((_let_5 (forall ((VExp0 $$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)))))))) (let ((_let_6 (forall ((VS $$unsorted) (Ve2red $$unsorted) (VExp0 $$unsorted) (RESULT $$unsorted) (Vx $$unsorted) (Ve2 $$unsorted) (Ve1 $$unsorted)) (=> (= VExp0 (tptp.vapp (tptp.vabs Vx VS Ve1) Ve2)) (=> (and (= Ve2red (tptp.vreduce Ve2)) (not (tptp.visSomeExp Ve2red)) (tptp.visValue Ve2)) (=> (= RESULT (tptp.vreduce VExp0)) (= RESULT (tptp.vsomeExp (tptp.vsubst Vx Ve2 Ve1))))))))) (let ((_let_7 (forall ((Ve2 $$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))))))))))) (let ((_let_8 (forall ((Ve $$unsorted) (VOptExp0 $$unsorted)) (=> (= VOptExp0 (tptp.vsomeExp Ve)) (tptp.visSomeExp VOptExp0))))) (let ((_let_9 (= tptp.vnoExp tptp.vnoExp))) (let ((_let_10 (= tptp.vnoType tptp.vnoType))) (let ((_let_11 (= tptp.vempty tptp.vempty))) (let ((_let_12 (forall ((Ve1 $$unsorted) (Ve2 $$unsorted) (VExp0 $$unsorted)) (=> (= VExp0 (tptp.vapp Ve1 Ve2)) (not (tptp.visValue VExp0)))))) (let ((_let_13 (forall ((Vx $$unsorted) (VExp0 $$unsorted)) (=> (= VExp0 (tptp.vvar Vx)) (not (tptp.visValue VExp0)))))) (let ((_let_14 (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (VExp2 $$unsorted)) (not (= (tptp.vabs VVar0 VTyp0 VExp0) (tptp.vapp VExp1 VExp2)))))) (let ((_let_15 (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vapp VExp0 VExp1)))))) (let ((_let_16 (forall ((VExp0 $$unsorted) (VExp1 $$unsorted) (VExp2 $$unsorted) (VExp3 $$unsorted)) (let ((_let_1 (= (tptp.vapp VExp0 VExp1) (tptp.vapp VExp2 VExp3)))) (let ((_let_2 (and (= VExp0 VExp2) (= VExp1 VExp3)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))))) (let ((_let_17 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (tptp.vtcheck tptp.vempty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_17))) (let ((_let_19 (= tptp.ve1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_20 (tptp.vtcheck tptp.vempty tptp.ve1 _let_17))) (let ((_let_21 (tptp.vtcheck tptp.vempty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_22 (not _let_21))) (let ((_let_23 (not _let_18))) (let ((_let_24 (tptp.vapp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_25 (tptp.vapp tptp.ve1 tptp.ve2))) (let ((_let_26 (= _let_25 _let_24))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_23 _let_22))) (let ((_let_29 (forall ((Ve1 $$unsorted) (Ve2 $$unsorted) (VS $$unsorted)) (or (not (= (tptp.vapp Ve1 Ve2) (tptp.vapp tptp.ve1 tptp.ve2))) (not (tptp.vtcheck tptp.vempty Ve1 (tptp.varrow VS SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (not (tptp.vtcheck tptp.vempty Ve2 VS)))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (not _let_29))) (let ((_let_32 (forall ((Vx $$unsorted) (Ve2 $$unsorted) (VT1 $$unsorted) (VT2 $$unsorted)) (or (not (= (tptp.vabs Vx VT1 Ve2) (tptp.vapp tptp.ve1 tptp.ve2))) (not (= (tptp.varrow VT1 VT2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.vtcheck (tptp.vbind Vx VT1 tptp.vempty) Ve2 VT2)))))) (let ((_let_33 (not _let_32))) (let ((_let_34 (forall ((Vx $$unsorted)) (or (not (= (tptp.vvar Vx) (tptp.vapp tptp.ve1 tptp.ve2))) (not (= (tptp.vlookup Vx tptp.vempty) (tptp.vsomeType SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.vtcheck tptp.vempty _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_33 _let_31))) (let ((_let_39 (forall ((Ve $$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_40 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (not (tptp.vtcheck (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.vempty) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_42 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_43 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_44 (= _let_25 _let_43))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_42)) _let_41))) (let ((_let_47 (_let_14))) (let ((_let_48 (ASSUME :args _let_47))) (let ((_let_49 (or))) (let ((_let_50 (_let_33))) (let ((_let_51 (tptp.vlookup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.vempty))) (let ((_let_52 (tptp.vsomeType SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_53 (tptp.vvar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_54 (= _let_25 _let_53))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 (not (= _let_52 _let_51))))) (let ((_let_57 (_let_15))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 (_let_35))) (let ((_let_60 (forall ((VT $$unsorted)) (not (tptp.vtcheck tptp.vempty (tptp.vapp tptp.ve1 tptp.ve2) VT))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (not _let_60))) (let ((_let_63 (_let_62))) (let ((_let_64 (_let_31))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_64)) :args _let_64) (REWRITE :args ((=> _let_31 (not (or (not (= _let_24 _let_25)) _let_23 _let_22))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_29))) (REFL :args (_let_30)) :args _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_35 _let_33 _let_31 (not _let_38)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_63)) :args _let_63) (REWRITE :args ((=> _let_62 (not _let_37)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_60))) (REFL :args (_let_36)) :args _let_49)) (NOT_OR_ELIM _let_61 :args (2)) :args (_let_36 true _let_60)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_59)) :args _let_59) (REWRITE :args ((=> _let_35 (not (or (not (= _let_53 _let_25)) (not (= _let_51 _let_52))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) (REFL :args ((not _let_56))) :args _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG (REFL :args (_let_56)) (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_49)) :args ((or _let_54 _let_56))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.ve1 tptp.ve2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_57))) _let_58 :args (_let_55 false _let_15)) :args (_let_56 true _let_54)) :args (_let_34 false _let_56)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_50)) :args _let_50) (REWRITE :args ((=> _let_33 (not (or (not (= _let_43 _let_25)) (not (= _let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) _let_41))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) (REFL :args ((not _let_46))) :args _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_49)) :args ((or _let_44 _let_46))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.ve1 tptp.ve2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_47))) _let_48 :args (_let_45 false _let_14)) :args (_let_46 true _let_44)) :args (_let_32 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (_let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.vempty QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.vtcheck VC Ve VT) false))))) :args (_let_39)))) _let_40 :args (_let_38 false _let_39)) :args (_let_31 false _let_36 false _let_34 false _let_32 false _let_38)) :args (_let_30 true _let_29)))) (let ((_let_66 (REFL :args (_let_28)))) (let ((_let_67 (= tptp.ve2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_68 (and _let_19 _let_67))) (let ((_let_69 (or _let_27 _let_68))) (let ((_let_70 (forall ((BOUND_VARIABLE_1871 $$unsorted) (BOUND_VARIABLE_1873 $$unsorted) (BOUND_VARIABLE_1875 $$unsorted) (BOUND_VARIABLE_1877 $$unsorted)) (or (not (= (tptp.vapp BOUND_VARIABLE_1871 BOUND_VARIABLE_1873) (tptp.vapp BOUND_VARIABLE_1875 BOUND_VARIABLE_1877))) (and (= BOUND_VARIABLE_1871 BOUND_VARIABLE_1875) (= BOUND_VARIABLE_1873 BOUND_VARIABLE_1877)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_70))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_49)) :args ((or _let_26 _let_28))) _let_65 :args (_let_26 true _let_28)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_27 _let_68 (not _let_69)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.ve1 tptp.ve2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_CBQI_PROP)) :args _let_72)) _let_71 :args (_let_69 false _let_70)) :args (_let_68 false _let_26 false _let_69)))) (let ((_let_75 (not _let_68))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 0)) :args ((or _let_19 _let_75))) _let_74 :args (_let_19 false _let_68)))) (let ((_let_77 (forall ((VT $$unsorted)) (not (tptp.vtcheck tptp.vempty tptp.ve1 VT))))) (let ((_let_78 (not _let_20))) (let ((_let_79 (forall ((Veout $$unsorted)) (not (= (tptp.vreduce tptp.ve1) (tptp.vsomeExp Veout)))))) (let ((_let_80 (tptp.visValue tptp.ve1))) (let ((_let_81 (tptp.vsomeExp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64))) (let ((_let_82 (tptp.vreduce tptp.ve1))) (let ((_let_83 (= _let_82 _let_81))) (let ((_let_84 (forall ((Ve2 $$unsorted) (Ve1 $$unsorted)) (or (not (= (tptp.vapp Ve1 Ve2) (tptp.vapp tptp.ve1 tptp.ve2))) (not (forall ((VVx0 $$unsorted) (VVS0 $$unsorted) (VVe10 $$unsorted)) (not (= Ve1 (tptp.vabs VVx0 VVS0 VVe10))))) (tptp.visSomeExp (tptp.vreduce Ve1)))))) (let ((_let_85 (not _let_84))) (let ((_let_86 (tptp.vreduce _let_25))) (let ((_let_87 (= tptp.vnoExp _let_86))) (let ((_let_88 (and _let_87 _let_85))) (let ((_let_89 (not _let_83))) (let ((_let_90 (forall ((Ve1 $$unsorted) (Ve2 $$unsorted)) (let ((_let_1 (tptp.vreduce Ve1))) (let ((_let_2 (tptp.vapp tptp.ve1 tptp.ve2))) (or (not (= (tptp.vapp Ve1 Ve2) _let_2)) (not (forall ((VVx0 $$unsorted) (VVS0 $$unsorted) (VVe10 $$unsorted)) (not (= Ve1 (tptp.vabs VVx0 VVS0 VVe10))))) (not (tptp.visSomeExp _let_1)) (not (= (tptp.vreduce _let_2) (tptp.vsomeExp (tptp.vapp (tptp.vgetSomeExp _let_1) Ve2)))))))))) (let ((_let_91 (not _let_90))) (let ((_let_92 (forall ((Vx $$unsorted) (VS $$unsorted) (Ve1 $$unsorted) (Ve2 $$unsorted)) (or (not (= (tptp.vapp (tptp.vabs Vx VS Ve1) Ve2) (tptp.vapp tptp.ve1 tptp.ve2))) 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:args ((= (not _let_23) _let_18))) :args _let_49)) :args ((or _let_18 _let_28))) _let_65 :args (_let_18 true _let_28)) :args (false true _let_20 false _let_19 false _let_18)) :args ((forall ((VVar0 $$unsorted) (VVar1 $$unsorted)) (let ((_let_1 (= (tptp.vvar VVar0) (tptp.vvar VVar1)))) (let ((_let_2 (= VVar0 VVar1))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))) (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted) (VVar1 $$unsorted) (VTyp1 $$unsorted) (VExp1 $$unsorted)) (let ((_let_1 (= (tptp.vabs VVar0 VTyp0 VExp0) (tptp.vabs VVar1 VTyp1 VExp1)))) (let ((_let_2 (and (= VVar0 VVar1) (= VTyp0 VTyp1) (= VExp0 VExp1)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))) _let_16 (forall ((VVar0 $$unsorted) (VVar1 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vabs VVar1 VTyp0 VExp0)))) _let_15 _let_14 (forall ((Vx $$unsorted) (VS $$unsorted) (Ve $$unsorted) (VExp0 $$unsorted)) (=> (= VExp0 (tptp.vabs Vx VS Ve)) (tptp.visValue VExp0))) _let_13 _let_12 (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (Vx $$unsorted) (Vv $$unsorted)) (let ((_let_1 (= Vx Vv))) (let ((_let_2 (tptp.visFreeVar VVar0 VExp0))) (=> (and (= VVar0 Vv) (= VExp0 (tptp.vvar Vx))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))) (forall ((VT $$unsorted) (VVar0 $$unsorted) (VExp0 $$unsorted) (Vx $$unsorted) (Vv $$unsorted) (Ve $$unsorted)) (let ((_let_1 (and (not (= Vx Vv)) (tptp.visFreeVar Vv Ve)))) (let ((_let_2 (tptp.visFreeVar VVar0 VExp0))) (=> (and (= VVar0 Vv) (= VExp0 (tptp.vabs Vx VT Ve))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))) (forall ((VVar0 $$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_11 true) (=> true _let_11)) (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_10 true) (=> true _let_10)) (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 $$unsorted)) (=> (and (= Vx Vy) (tptp.vtcheck (tptp.vbind Vx VTx (tptp.vbind Vy VTy VC)) Ve VT)) (tptp.vtcheck (tptp.vbind Vx VTx VC) Ve VT))) (forall ((Vy $$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))) (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_9 true) (=> true _let_9)) (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)))) _let_8 (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 $$unsorted)) (=> (= VExp0 (tptp.vabs Vx VS Ve)) (=> (= RESULT (tptp.vreduce VExp0)) (= RESULT tptp.vnoExp)))) _let_7 _let_6 (forall ((Vx $$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))))) _let_5 (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 $$unsorted)) (=> (= (tptp.vlookup Vx VC) (tptp.vsomeType VT)) (tptp.vtcheck VC (tptp.vvar Vx) VT))) (forall ((VC $$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)))) (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 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.68/26.07  )
% 25.68/26.07  % SZS output end Proof for COM148+1
% 25.68/26.07  % cvc5---1.0.5 exiting
% 25.68/26.07  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------