TSTP Solution File: COM137+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : COM137+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 18:37:17 EDT 2023
% Result : Theorem 25.68s 25.90s
% Output : Proof 25.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM137+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n019.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 13:01:13 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.23/0.50 %----Proving TF0_NAR, FOF, or CNF
% 25.68/25.90 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.gJQOLTnqIR/cvc5---1.0.5_7505.p...
% 25.68/25.90 ------- get file name : TPTP file name is COM137+1
% 25.68/25.90 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7505.smt2...
% 25.68/25.90 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.68/25.90 --- Run --no-e-matching --full-saturate-quant at 5...
% 25.68/25.90 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.68/25.90 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.68/25.90 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.68/25.90 % SZS status Theorem for COM137+1
% 25.68/25.90 % SZS output start Proof for COM137+1
% 25.68/25.90 (
% 25.68/25.90 (let ((_let_1 (not (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vapp tptp.ve1app tptp.ve2app))) (=> (and (not (tptp.visFreeVar Vx _let_1)) (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT)) (tptp.vtcheck VC _let_1 VT))))))) (let ((_let_2 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (VT $$unsorted)) (=> (and (not (tptp.visFreeVar Vx tptp.ve2app)) (tptp.vtcheck (tptp.vbind Vx VS VC) tptp.ve2app VT)) (tptp.vtcheck VC tptp.ve2app VT))))) (let ((_let_3 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (VT $$unsorted)) (=> (and (not (tptp.visFreeVar Vx tptp.ve1app)) (tptp.vtcheck (tptp.vbind Vx VS VC) tptp.ve1app VT)) (tptp.vtcheck VC tptp.ve1app 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 $$unsorted)) (and (= Ve (tptp.vapp Ve1 Ve2)) (tptp.vtcheck VC Ve1 (tptp.varrow VS VT)) (tptp.vtcheck VC Ve2 VS)))))))) (let ((_let_5 (forall ((VS $$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 ((_let_6 (= tptp.vnoExp tptp.vnoExp))) (let ((_let_7 (= tptp.vnoType tptp.vnoType))) (let ((_let_8 (= tptp.vempty tptp.vempty))) (let ((_let_9 (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (Ve1 $$unsorted) (Vv $$unsorted) (Ve2 $$unsorted)) (let ((_let_1 (or (tptp.visFreeVar Vv Ve1) (tptp.visFreeVar Vv Ve2)))) (let ((_let_2 (tptp.visFreeVar VVar0 VExp0))) (=> (and (= VVar0 Vv) (= VExp0 (tptp.vapp Ve1 Ve2))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))))) (let ((_let_10 (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (VExp2 $$unsorted)) (not (= (tptp.vabs VVar0 VTyp0 VExp0) (tptp.vapp VExp1 VExp2)))))) (let ((_let_11 (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vapp VExp0 VExp1)))))) (let ((_let_12 (forall ((VExp0 $$unsorted) (VExp1 $$unsorted) (VExp2 $$unsorted) (VExp3 $$unsorted)) (let ((_let_1 (= (tptp.vapp VExp0 VExp1) (tptp.vapp VExp2 VExp3)))) (let ((_let_2 (and (= VExp0 VExp2) (= VExp1 VExp3)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))))) (let ((_let_13 (forall ((VS $$unsorted) (VC $$unsorted) (Ve1 $$unsorted) (Ve2 $$unsorted) (VT $$unsorted)) (or (not (tptp.vtcheck VC Ve1 (tptp.varrow VS VT))) (not (tptp.vtcheck VC Ve2 VS)) (tptp.vtcheck VC (tptp.vapp Ve1 Ve2) VT))))) (let ((_let_14 (tptp.vapp tptp.ve1app tptp.ve2app))) (let ((_let_15 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.ve2app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.ve1app _let_18))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_17 _let_15))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (tptp.vtcheck _let_24 tptp.ve2app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.ve2app))) (let ((_let_28 (or _let_27 _let_26 _let_16))) (let ((_let_29 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (VT $$unsorted)) (or (tptp.visFreeVar Vx tptp.ve2app) (not (tptp.vtcheck (tptp.vbind Vx VS VC) tptp.ve2app VT)) (tptp.vtcheck VC tptp.ve2app VT))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (= tptp.ve2app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_32 (tptp.vtcheck _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_33 (= tptp.ve1app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_34 (and _let_33 _let_31))) (let ((_let_35 (tptp.vapp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_36 (= _let_14 _let_35))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_34))) (let ((_let_39 (forall ((BOUND_VARIABLE_1854 $$unsorted) (BOUND_VARIABLE_1856 $$unsorted) (BOUND_VARIABLE_1858 $$unsorted) (BOUND_VARIABLE_1860 $$unsorted)) (or (not (= (tptp.vapp BOUND_VARIABLE_1854 BOUND_VARIABLE_1856) (tptp.vapp BOUND_VARIABLE_1858 BOUND_VARIABLE_1860))) (and (= BOUND_VARIABLE_1854 BOUND_VARIABLE_1858) (= BOUND_VARIABLE_1856 BOUND_VARIABLE_1860)))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (not _let_32))) (let ((_let_42 (tptp.vtcheck _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_18))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_37 _let_43 _let_41))) (let ((_let_45 (forall ((Ve1 $$unsorted) (Ve2 $$unsorted) (VS $$unsorted)) (let ((_let_1 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (or (not (= (tptp.vapp Ve1 Ve2) (tptp.vapp tptp.ve1app tptp.ve2app))) (not (tptp.vtcheck _let_1 Ve1 (tptp.varrow VS SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (not (tptp.vtcheck _let_1 Ve2 VS))))))) (let ((_let_46 (not _let_44))) (let ((_let_47 (not _let_45))) (let ((_let_48 (forall ((Vx $$unsorted) (Ve2 $$unsorted) (VT1 $$unsorted) (VT2 $$unsorted)) (or (not (= (tptp.vabs Vx VT1 Ve2) (tptp.vapp tptp.ve1app tptp.ve2app))) (not (= (tptp.varrow VT1 VT2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.vtcheck (tptp.vbind Vx VT1 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) Ve2 VT2)))))) (let ((_let_49 (not _let_48))) (let ((_let_50 (forall ((Vx $$unsorted)) (or (not (= (tptp.vvar Vx) (tptp.vapp tptp.ve1app tptp.ve2app))) (not (= (tptp.vlookup Vx (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.vsomeType SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.vtcheck _let_24 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_51 _let_49 _let_47))) (let ((_let_55 (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 $$unsorted)) (or (not (= Ve (tptp.vapp Ve1 Ve2))) (not (tptp.vtcheck VC Ve1 (tptp.varrow VS VT))) (not (tptp.vtcheck VC Ve2 VS))))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (not (tptp.vtcheck (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_24) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)))) (let ((_let_58 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_59 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_60 (= _let_14 _let_59))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_58)) _let_57))) (let ((_let_63 (_let_10))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 (or))) (let ((_let_66 (_let_49))) (let ((_let_67 (tptp.vlookup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_24))) (let ((_let_68 (tptp.vsomeType SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_69 (tptp.vvar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_70 (= _let_14 _let_69))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_71 (not (= _let_68 _let_67))))) (let ((_let_73 (_let_11))) (let ((_let_74 (ASSUME :args _let_73))) (let ((_let_75 (_let_51))) (let ((_let_76 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_77 (or _let_76 _let_53 _let_15))) (let ((_let_78 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vapp tptp.ve1app tptp.ve2app))) (or (tptp.visFreeVar Vx _let_1) (not (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT)) (tptp.vtcheck VC _let_1 VT)))))) (let ((_let_79 (not _let_77))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (not _let_78))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_80) :args (_let_81))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_78))) (REFL :args (_let_79)) :args _let_65)) _let_80 :args (_let_79 true _let_78)))) (let ((_let_83 (_let_47))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_83)) :args _let_83) (REWRITE :args ((=> _let_47 (not (or (not (= _let_35 _let_14)) _let_43 _let_41))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_45))) (REFL :args (_let_46)) :args _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_51 _let_49 _let_47 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 1)) (CONG (REFL :args (_let_77)) (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_65)) :args ((or _let_52 _let_77))) _let_82 :args (_let_52 true _let_77)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_75)) :args _let_75) (REWRITE :args ((=> _let_51 (not (or (not (= _let_69 _let_14)) (not (= _let_67 _let_68))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) (REFL :args ((not _let_72))) :args _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG (REFL :args (_let_72)) (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_65)) :args ((or _let_70 _let_72))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_74 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.ve1app tptp.ve2app QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_73))) _let_74 :args (_let_71 false _let_11)) :args (_let_72 true _let_70)) :args (_let_50 false _let_72)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66) (REWRITE :args ((=> _let_49 (not (or (not (= _let_59 _let_14)) (not (= _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_57))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) (REFL :args ((not _let_62))) :args _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 0)) (CONG (REFL :args (_let_62)) (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_65)) :args ((or _let_60 _let_62))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 tptp.ve1app tptp.ve2app QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_63))) _let_64 :args (_let_61 false _let_10)) :args (_let_62 true _let_60)) :args (_let_48 false _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.vtcheck VC Ve VT) false))))) :args (_let_55)))) _let_56 :args (_let_54 false _let_55)) :args (_let_47 false _let_52 false _let_50 false _let_48 false _let_54)) :args (_let_46 true _let_45)))) (let ((_let_85 (REFL :args (_let_44)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_34 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 0)) (CONG _let_85 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_65)) :args ((or _let_36 _let_44))) _let_84 :args (_let_36 true _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.ve1app tptp.ve2app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_34 false _let_36 false _let_38)))) (let ((_let_87 (not _let_34))) (let ((_let_88 (and _let_32 _let_31))) (let ((_let_89 (_let_32 _let_31))) (let ((_let_90 (ASSUME :args (_let_32)))) (let ((_let_91 (APPLY_UF tptp.vtcheck))) (let ((_let_92 (ASSUME :args (_let_31)))) (let ((_let_93 (REFL :args (_let_24)))) (let ((_let_94 (not _let_27))) (let ((_let_95 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.ve1app))) (let ((_let_96 (not _let_95))) (let ((_let_97 (and _let_96 _let_94))) (let ((_let_98 (or _let_97 _let_76))) (let ((_let_99 (forall ((BOUND_VARIABLE_2161 $$unsorted) (BOUND_VARIABLE_2163 $$unsorted) (BOUND_VARIABLE_2165 $$unsorted)) (or (and (not (tptp.visFreeVar BOUND_VARIABLE_2163 BOUND_VARIABLE_2161)) (not (tptp.visFreeVar BOUND_VARIABLE_2163 BOUND_VARIABLE_2165))) (tptp.visFreeVar BOUND_VARIABLE_2163 (tptp.vapp BOUND_VARIABLE_2161 BOUND_VARIABLE_2165)))))) (let ((_let_100 (_let_99))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_76 _let_97 (not _let_98)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_77 0)) _let_82 :args ((not _let_76) true _let_77)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_100) :args (tptp.ve1app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.ve2app QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.visFreeVar BOUND_VARIABLE_2163 (tptp.vapp BOUND_VARIABLE_2161 BOUND_VARIABLE_2165)) true))))) :args _let_100)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args (_let_98 false _let_99)) :args (_let_97 true _let_76 false _let_98)))) (let ((_let_102 (not _let_97))) (let ((_let_103 (tptp.vtcheck _let_24 tptp.ve1app _let_18))) (let ((_let_104 (not _let_103))) (let ((_let_105 (or _let_95 _let_104 _let_19))) (let ((_let_106 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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 $$unsorted)) (=> (= (tptp.vlookup Vx VC) (tptp.vsomeType VT)) (tptp.vtcheck VC (tptp.vvar Vx) VT))) (forall ((VC $$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_5 _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))) _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.68/25.91 )
% 25.68/25.91 % SZS output end Proof for COM137+1
% 25.68/25.91 % cvc5---1.0.5 exiting
% 25.68/25.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------