TSTP Solution File: COM125+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : COM125+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 18:37:14 EDT 2023
% Result : Theorem 0.21s 0.62s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM125+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 12:53:49 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.zM7jS8frzc/cvc5---1.0.5_16172.p...
% 0.21/0.62 ------- get file name : TPTP file name is COM125+1
% 0.21/0.62 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16172.smt2...
% 0.21/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.62 % SZS status Theorem for COM125+1
% 0.21/0.62 % SZS output start Proof for COM125+1
% 0.21/0.62 (
% 0.21/0.62 (let ((_let_1 (not (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Vy $$unsorted) (VS1 $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS1 tptp.veabs))) (=> (and (not (tptp.visFreeVar Vx _let_1)) (tptp.vtcheck VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT))))))) (let ((_let_2 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Vy $$unsorted) (VS1 $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS1 tptp.veabs))) (=> (and (= Vx Vy) (not (tptp.visFreeVar Vx _let_1)) (tptp.vtcheck VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT)))))) (let ((_let_3 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Vy $$unsorted) (VS1 $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS1 tptp.veabs))) (=> (and (not (= Vx Vy)) (not (tptp.visFreeVar Vx _let_1)) (tptp.vtcheck VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT)))))) (let ((_let_4 (= tptp.vnoExp tptp.vnoExp))) (let ((_let_5 (= tptp.vnoType tptp.vnoType))) (let ((_let_6 (= tptp.vempty tptp.vempty))) (let ((_let_7 (forall ((VT $$unsorted) (VVar0 $$unsorted) (VExp0 $$unsorted) (Vx $$unsorted) (Vv $$unsorted) (Ve $$unsorted)) (let ((_let_1 (and (not (= Vx Vv)) (tptp.visFreeVar Vv Ve)))) (let ((_let_2 (tptp.visFreeVar VVar0 VExp0))) (=> (and (= VVar0 Vv) (= VExp0 (tptp.vabs Vx VT Ve))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))))) (let ((_let_8 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.veabs))) (let ((_let_9 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8))) (let ((_let_10 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (tptp.vtcheck _let_10 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_12 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_9 _let_13 _let_11))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.veabs))) (let ((_let_17 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_16))) (let ((_let_18 (not _let_9))) (let ((_let_19 (tptp.vtcheck _let_10 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_20 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_16))) (let ((_let_23 (or _let_15 _let_22 _let_21 _let_19))) (let ((_let_24 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Vy $$unsorted) (VS1 $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS1 tptp.veabs))) (or (= Vx Vy) (tptp.visFreeVar Vx _let_1) (not (tptp.vtcheck VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT)))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (or _let_22 _let_21 _let_19))) (let ((_let_27 (not _let_19))) (let ((_let_28 (forall ((Vx $$unsorted) (VS $$unsorted) (VC $$unsorted) (Vy $$unsorted) (VS1 $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS1 tptp.veabs))) (or (tptp.visFreeVar Vx _let_1) (not (tptp.vtcheck VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT)))))) (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 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 2)) _let_33 :args (_let_27 true _let_26)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 1)) (CONG (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_31)) :args ((or _let_20 _let_26))) _let_33 :args (_let_20 true _let_26)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_21 _let_19 _let_15 (not _let_23)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 0)) _let_33 :args ((not _let_22) true _let_26)) _let_35 _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :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_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.vtcheck (tptp.vbind Vx VS VC) (tptp.vabs Vy VS1 tptp.veabs) VT) true))))) :args (_let_24))) _let_25 :args (_let_23 false _let_24)) :args (_let_15 true _let_22 false _let_20 true _let_19 false _let_23)))) (let ((_let_37 (forall ((BOUND_VARIABLE_2118 $$unsorted) (BOUND_VARIABLE_2122 $$unsorted) (BOUND_VARIABLE_2124 $$unsorted)) (not (tptp.visFreeVar BOUND_VARIABLE_2122 (tptp.vabs BOUND_VARIABLE_2122 BOUND_VARIABLE_2118 BOUND_VARIABLE_2124)))))) (let ((_let_38 (not _let_17))) (let ((_let_39 (_let_37))) (let ((_let_40 (not _let_15))) (let ((_let_41 (REFL :args (_let_40)))) (let ((_let_42 (and _let_15 _let_38))) (let ((_let_43 (ASSUME :args (_let_38)))) (let ((_let_44 (ASSUME :args (_let_15)))) (let ((_let_45 (SYMM (SYMM _let_44)))) (let ((_let_46 (CONG _let_45 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (REFL :args (tptp.veabs)) :args (APPLY_UF tptp.vabs)))) (let ((_let_47 (forall ((VS $$unsorted) (VC $$unsorted) (Vy $$unsorted) (VS1 $$unsorted) (VT $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS1 tptp.veabs))) (or (tptp.visFreeVar Vy _let_1) (not (tptp.vtcheck VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vy VS VC) _let_1 VT)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (not _let_11))) (let ((_let_50 (and _let_27 _let_15))) (let ((_let_51 (_let_27 _let_15))) (let ((_let_52 (ASSUME :args (_let_27)))) (let ((_let_53 (APPLY_UF tptp.vtcheck))) (let ((_let_54 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_55 (and _let_20 _let_15))) (let ((_let_56 (_let_20 _let_15))) (let ((_let_57 (ASSUME :args (_let_20)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_9 _let_13 _let_11 (not _let_14)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_55)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_57 _let_44) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_46 _let_54 :args _let_53) (TRUE_INTRO _let_57))) :args _let_56)) :args _let_56)) :args (true _let_55)) _let_35 _let_36 :args (_let_12 false _let_20 false _let_15)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_50)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_52 _let_44) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (_let_10)) _let_46 _let_54 :args _let_53) (FALSE_INTRO _let_52))) :args _let_51)) :args _let_51)) :args (true _let_50)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_19))) _let_41 (REFL :args (_let_49)) :args _let_31)) _let_34 _let_36 :args (_let_49 true _let_19 false _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.vtcheck (tptp.vbind Vy VS VC) (tptp.vabs Vy VS1 tptp.veabs) VT) true))))) :args (_let_47))) _let_48 :args (_let_14 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_42)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_43 _let_44) (SCOPE (FALSE_ELIM (TRANS (CONG _let_45 _let_46 :args (APPLY_UF tptp.visFreeVar)) (FALSE_INTRO _let_43))) :args (_let_38 _let_15))) :args (_let_15 _let_38))) :args (true _let_42)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_17))) (REFL :args (_let_18)) :args _let_31)) :args ((or _let_17 _let_40 _let_18))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_39) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.veabs QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.vabs BOUND_VARIABLE_2122 BOUND_VARIABLE_2118 BOUND_VARIABLE_2124)))) :args _let_39)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_38 false _let_37)) _let_36 :args (_let_18 true _let_17 false _let_15)) :args (false false _let_12 true _let_11 false _let_14 true _let_9)) :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))))) (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))))) (forall ((VVar0 $$unsorted) (VVar1 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vabs VVar1 VTyp0 VExp0)))) (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vapp VExp0 VExp1)))) (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (VExp2 $$unsorted)) (not (= (tptp.vabs VVar0 VTyp0 VExp0) (tptp.vapp VExp1 VExp2)))) (forall ((Vx $$unsorted) (VS $$unsorted) (Ve $$unsorted) (VExp0 $$unsorted)) (=> (= VExp0 (tptp.vabs Vx VS Ve)) (tptp.visValue VExp0))) (forall ((Vx $$unsorted) (VExp0 $$unsorted)) (=> (= VExp0 (tptp.vvar Vx)) (not (tptp.visValue VExp0)))) (forall ((Ve1 $$unsorted) (Ve2 $$unsorted) (VExp0 $$unsorted)) (=> (= VExp0 (tptp.vapp Ve1 Ve2)) (not (tptp.visValue VExp0)))) (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (Vx $$unsorted) (Vv $$unsorted)) (let ((_let_1 (= Vx Vv))) (let ((_let_2 (tptp.visFreeVar VVar0 VExp0))) (=> (and (= VVar0 Vv) (= VExp0 (tptp.vvar Vx))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))) _let_7 (forall ((VVar0 $$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_6 true) (=> true _let_6)) (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_5 true) (=> true _let_5)) (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_4 true) (=> true _let_4)) (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 $$unsorted)) (=> (tptp.vtcheck (tptp.vbind Vx VS VC) Ve VT) (tptp.vtcheck VC (tptp.vabs Vx VS Ve) (tptp.varrow VS VT)))) (forall ((VS $$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))) (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 $$unsorted)) (and (= Ve (tptp.vapp Ve1 Ve2)) (tptp.vtcheck VC Ve1 (tptp.varrow VS VT)) (tptp.vtcheck VC Ve2 VS)))))) (forall ((Vx $$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) (VT $$unsorted)) (=> (and (not (tptp.visFreeVar Vx tptp.veabs)) (tptp.vtcheck VC tptp.veabs VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) tptp.veabs VT))) _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.63 )
% 0.21/0.63 % SZS output end Proof for COM125+1
% 0.21/0.63 % cvc5---1.0.5 exiting
% 0.21/0.63 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------