TSTP Solution File: COM134+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : COM134+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 25.96s 26.32s
% Output : Proof 25.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM134+1 : TPTP v8.1.2. Released v6.4.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 13:22:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 25.96/26.32 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.UK0fk2JCgR/cvc5---1.0.5_32060.p...
% 25.96/26.32 ------- get file name : TPTP file name is COM134+1
% 25.96/26.32 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32060.smt2...
% 25.96/26.32 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.96/26.32 --- Run --no-e-matching --full-saturate-quant at 5...
% 25.96/26.32 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.96/26.32 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.96/26.32 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.96/26.32 % SZS status Theorem for COM134+1
% 25.96/26.32 % SZS output start Proof for COM134+1
% 25.96/26.32 (
% 25.96/26.32 (let ((_let_1 (not (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VT2 $$unsorted)) (let ((_let_1 (tptp.vapp tptp.ve1 tptp.ve2))) (=> (and (tptp.vtcheck VC Ve VT) (tptp.vtcheck (tptp.vbind Vx VT VC) _let_1 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve _let_1) VT2))))))) (let ((_let_2 (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VT2 $$unsorted)) (=> (and (tptp.vtcheck VC Ve VT) (tptp.vtcheck (tptp.vbind Vx VT VC) tptp.ve2 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve tptp.ve2) VT2))))) (let ((_let_3 (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VT2 $$unsorted)) (=> (and (tptp.vtcheck VC Ve VT) (tptp.vtcheck (tptp.vbind Vx VT VC) tptp.ve1 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve tptp.ve1) VT2))))) (let ((_let_4 (forall ((Ve $$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 $$unsorted)) (=> (and (tptp.vtcheck VC Ve1 (tptp.varrow VS VT)) (tptp.vtcheck VC Ve2 VS)) (tptp.vtcheck VC (tptp.vapp Ve1 Ve2) VT))))) (let ((_let_6 (= tptp.vnoExp tptp.vnoExp))) (let ((_let_7 (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (RESULT $$unsorted) (Ve1 $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Ve2 $$unsorted)) (=> (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vapp Ve1 Ve2))) (=> (= RESULT (tptp.vsubst VVar0 VExp0 VExp1)) (= RESULT (tptp.vapp (tptp.vsubst Vx Ve Ve1) (tptp.vsubst Vx Ve Ve2)))))))) (let ((_let_8 (= tptp.vnoType tptp.vnoType))) (let ((_let_9 (= tptp.vempty tptp.vempty))) (let ((_let_10 (forall ((VVar0 $$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 $$unsorted)) (let ((_let_1 (= (tptp.vapp VExp0 VExp1) (tptp.vapp VExp2 VExp3)))) (let ((_let_2 (and (= VExp0 VExp2) (= VExp1 VExp3)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))))) (let ((_let_13 (tptp.vapp tptp.ve1 tptp.ve2))) (let ((_let_14 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_13))) (let ((_let_15 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_16 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.ve2))) (let ((_let_17 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.ve1))) (let ((_let_18 (tptp.vapp _let_17 _let_16))) (let ((_let_19 (= _let_14 _let_18))) (let ((_let_20 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_21 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_22 (tptp.vtcheck _let_21 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_15))) (let ((_let_27 (not _let_15))) (let ((_let_28 (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (VT2 $$unsorted)) (let ((_let_1 (tptp.vapp tptp.ve1 tptp.ve2))) (or (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_29 (not _let_26))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (or))) (let ((_let_32 (not _let_28))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_30) :args (_let_32))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_28))) (REFL :args (_let_29)) :args _let_31)) _let_30 :args (_let_29 true _let_28)))) (let ((_let_34 (forall ((Ve1 $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Ve2 $$unsorted)) (= (tptp.vapp (tptp.vsubst Vx Ve Ve1) (tptp.vsubst Vx Ve Ve2)) (tptp.vsubst Vx Ve (tptp.vapp Ve1 Ve2)))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_39 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_17 _let_38))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_37 _let_20))) (let ((_let_42 (forall ((VS $$unsorted) (VC $$unsorted) (Ve1 $$unsorted) (Ve2 $$unsorted) (VT $$unsorted)) (or (not (tptp.vtcheck VC Ve1 (tptp.varrow VS VT))) (not (tptp.vtcheck VC Ve2 VS)) (tptp.vtcheck VC (tptp.vapp Ve1 Ve2) VT))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.vtcheck _let_21 tptp.ve2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_25 _let_45 _let_36))) (let ((_let_47 (forall ((VT $$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.ve2 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve tptp.ve2) VT2))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (= tptp.ve2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_50 (tptp.vtcheck _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_51 (= tptp.ve1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_52 (and _let_51 _let_49))) (let ((_let_53 (tptp.vapp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_54 (= _let_13 _let_53))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_52))) (let ((_let_57 (forall ((BOUND_VARIABLE_1885 $$unsorted) (BOUND_VARIABLE_1887 $$unsorted) (BOUND_VARIABLE_1889 $$unsorted) (BOUND_VARIABLE_1891 $$unsorted)) (or (not (= (tptp.vapp BOUND_VARIABLE_1885 BOUND_VARIABLE_1887) (tptp.vapp BOUND_VARIABLE_1889 BOUND_VARIABLE_1891))) (and (= BOUND_VARIABLE_1885 BOUND_VARIABLE_1889) (= BOUND_VARIABLE_1887 BOUND_VARIABLE_1891)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (not _let_50))) (let ((_let_60 (tptp.vtcheck _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 _let_38))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_55 _let_61 _let_59))) (let ((_let_63 (forall ((Ve1 $$unsorted) (Ve2 $$unsorted) (VS $$unsorted)) (let ((_let_1 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (or (not (= (tptp.vapp Ve1 Ve2) (tptp.vapp tptp.ve1 tptp.ve2))) (not (tptp.vtcheck _let_1 Ve1 (tptp.varrow VS SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (not (tptp.vtcheck _let_1 Ve2 VS))))))) (let ((_let_64 (not _let_62))) (let ((_let_65 (not _let_63))) (let ((_let_66 (forall ((Vx $$unsorted) (Ve2 $$unsorted) (VT1 $$unsorted) (VT2 $$unsorted)) (or (not (= (tptp.vabs Vx VT1 Ve2) (tptp.vapp tptp.ve1 tptp.ve2))) (not (= (tptp.varrow VT1 VT2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.vtcheck (tptp.vbind Vx VT1 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) Ve2 VT2)))))) (let ((_let_67 (not _let_66))) (let ((_let_68 (forall ((Vx $$unsorted)) (or (not (= (tptp.vvar Vx) (tptp.vapp tptp.ve1 tptp.ve2))) (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_6))))))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_23 _let_69 _let_67 _let_65))) (let ((_let_71 (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_72 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (not (tptp.vtcheck (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_21) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))) (let ((_let_74 (tptp.varrow SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_75 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_76 (= _let_13 _let_75))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_74)) _let_73))) (let ((_let_79 (_let_10))) (let ((_let_80 (ASSUME :args _let_79))) (let ((_let_81 (_let_67))) (let ((_let_82 (tptp.vlookup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_21))) (let ((_let_83 (tptp.vsomeType SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_84 (tptp.vvar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_85 (= _let_13 _let_84))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_86 (not (= _let_83 _let_82))))) (let ((_let_88 (_let_11))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 (_let_69))) (let ((_let_91 (REFL :args (_let_26)))) (let ((_let_92 (_let_65))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_92)) :args _let_92) (REWRITE :args ((=> _let_65 (not (or (not (= _let_53 _let_13)) _let_61 _let_59))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_63))) (REFL :args (_let_64)) :args _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_23 _let_69 _let_67 _let_65 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 1)) (CONG _let_91 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_31)) :args ((or _let_22 _let_26))) _let_33 :args (_let_22 true _let_26)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_90)) :args _let_90) (REWRITE :args ((=> _let_69 (not (or (not (= _let_84 _let_13)) (not (= _let_82 _let_83))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) (REFL :args ((not _let_87))) :args _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_87 0)) (CONG (REFL :args (_let_87)) (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_85))) :args _let_31)) :args ((or _let_85 _let_87))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_89 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 tptp.ve1 tptp.ve2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_88))) _let_89 :args (_let_86 false _let_11)) :args (_let_87 true _let_85)) :args (_let_68 false _let_87)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_81)) :args _let_81) (REWRITE :args ((=> _let_67 (not (or (not (= _let_75 _let_13)) (not (= _let_74 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_73))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) (REFL :args ((not _let_78))) :args _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 0)) (CONG (REFL :args (_let_78)) (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_76))) :args _let_31)) :args ((or _let_76 _let_78))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 tptp.ve1 tptp.ve2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79))) _let_80 :args (_let_77 false _let_10)) :args (_let_78 true _let_76)) :args (_let_66 false _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.vtcheck VC Ve VT) false))))) :args (_let_71)))) _let_72 :args (_let_70 false _let_71)) :args (_let_65 false _let_22 false _let_68 false _let_66 false _let_70)) :args (_let_64 true _let_63)))) (let ((_let_94 (REFL :args (_let_62)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_55 _let_52 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 0)) (CONG _let_94 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_31)) :args ((or _let_54 _let_62))) _let_93 :args (_let_54 true _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.ve1 tptp.ve2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_57))) _let_58 :args (_let_56 false _let_57)) :args (_let_52 false _let_54 false _let_56)))) (let ((_let_96 (not _let_52))) (let ((_let_97 (and _let_50 _let_49))) (let ((_let_98 (_let_50 _let_49))) (let ((_let_99 (ASSUME :args (_let_50)))) (let ((_let_100 (APPLY_UF tptp.vtcheck))) (let ((_let_101 (ASSUME :args (_let_49)))) (let ((_let_102 (REFL :args (_let_21)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG _let_91 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_31)) :args ((or _let_24 _let_26))) _let_33 :args (_let_24 true _let_26)))) (let ((_let_104 (tptp.vtcheck _let_21 tptp.ve1 _let_38))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_25 _let_105 _let_39))) (let ((_let_107 (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.ve1 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve tptp.ve1) VT2))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (and _let_60 _let_51))) (let ((_let_110 (_let_60 _let_51))) (let ((_let_111 (ASSUME :args (_let_60)))) (let ((_let_112 (ASSUME :args (_let_51)))) (let ((_let_113 (ASSUME :args (_let_20)))) (let ((_let_114 (ASSUME :args (_let_19)))) (let ((_let_115 (ASSUME :args (_let_27)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_113 _let_114 _let_115) :args (_let_27 _let_19 _let_20)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_115)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (SYMM (SYMM _let_114)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args _let_100) (TRUE_INTRO _let_113))) :args (_let_20 _let_19 _let_27)) :args ((not (and _let_27 _let_19 _let_20)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_15))) (REFL :args ((not _let_19))) (REFL :args ((not _let_20))) :args _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_37 _let_20 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_25 _let_105 _let_39 (not _let_106)))) _let_103 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_109)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_111 _let_112) (SCOPE (TRUE_ELIM (TRANS (CONG _let_102 (SYMM (SYMM _let_112)) (REFL :args (_let_38)) :args _let_100) (TRUE_INTRO _let_111))) :args _let_110)) :args _let_110)) :args (true _let_109)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 1)) (CONG _let_94 (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_31)) :args ((or _let_60 _let_62))) _let_93 :args (_let_60 true _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_52 0)) :args ((or _let_51 _let_96))) _let_95 :args (_let_51 false _let_52)) :args (_let_104 false _let_60 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_38 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.vtcheck VC Ve VT) false)) (not (= (tptp.vtcheck (tptp.vbind Vx VT VC) tptp.ve1 VT2) false))))) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_39 false _let_24 false _let_104 false _let_106)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_25 _let_45 _let_36 (not _let_46)))) _let_103 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_97)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_99 _let_101) (SCOPE (TRUE_ELIM (TRANS (CONG _let_102 (SYMM (SYMM _let_101)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23)) :args _let_100) (TRUE_INTRO _let_99))) :args _let_98)) :args _let_98)) :args (true _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 2)) (CONG _let_94 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_50))) :args _let_31)) :args ((or _let_50 _let_62))) _let_93 :args (_let_50 true _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_52 1)) :args ((or _let_49 _let_96))) _let_95 :args (_let_49 false _let_52)) :args (_let_44 false _let_50 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.vtcheck VC Ve VT) false)) (not (= (tptp.vtcheck (tptp.vbind Vx VT VC) tptp.ve2 VT2) false))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_36 false _let_24 false _let_44 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_17 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_20 false _let_39 false _let_36 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.ve1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.ve2 QUANTIFIERS_INST_E_MATCHING ((tptp.vsubst Vx Ve (tptp.vapp Ve1 Ve2))))) :args (_let_34)))) _let_35 :args (_let_19 false _let_34)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 2)) _let_33 :args (_let_27 true _let_26)) :args (false false _let_20 false _let_19 true _let_15)) :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_12 (forall ((VVar0 $$unsorted) (VVar1 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vabs VVar1 VTyp0 VExp0)))) _let_11 _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 $$unsorted)) (let ((_let_1 (= Vx Vv))) (let ((_let_2 (tptp.visFreeVar VVar0 VExp0))) (=> (and (= VVar0 Vv) (= VExp0 (tptp.vvar Vx))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))) (forall ((VT $$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_9 true) (=> true _let_9)) (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_8 true) (=> true _let_8)) (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)))))) _let_7 (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_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))) (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))) (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Ve $$unsorted) (VT $$unsorted)) (=> (and (not (tptp.visFreeVar Vx Ve)) (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT)) (tptp.vtcheck VC Ve VT))) (forall ((Vx $$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_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.96/26.33 )
% 25.96/26.33 % SZS output end Proof for COM134+1
% 25.96/26.33 % cvc5---1.0.5 exiting
% 25.96/26.33 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------