TSTP Solution File: COM132+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : COM132+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 18:37:16 EDT 2023
% Result : Theorem 42.00s 42.25s
% Output : Proof 42.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : COM132+1 : TPTP v8.1.2. Released v6.4.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n002.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 13:46:35 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 42.00/42.25 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.eZ1alwGaHI/cvc5---1.0.5_7024.p...
% 42.00/42.25 ------- get file name : TPTP file name is COM132+1
% 42.00/42.25 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7024.smt2...
% 42.00/42.25 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 42.00/42.25 --- Run --no-e-matching --full-saturate-quant at 5...
% 42.00/42.25 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 42.00/42.25 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 42.00/42.25 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 42.00/42.25 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 42.00/42.25 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 42.00/42.25 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 42.00/42.25 % SZS status Theorem for COM132+1
% 42.00/42.25 % SZS output start Proof for COM132+1
% 42.00/42.25 (
% 42.00/42.25 (let ((_let_1 (not (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Vy $$unsorted) (VS $$unsorted) (VT2 $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS tptp.veabs))) (=> (and (not (= Vx Vy)) (tptp.visFreeVar Vy Ve) (tptp.vtcheck VC Ve VT) (tptp.vtcheck (tptp.vbind Vx VT VC) _let_1 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve _let_1) VT2))))))) (let ((_let_2 (forall ((Ve $$unsorted) (Vx $$unsorted) (Vfresh $$unsorted) (Ve1 $$unsorted)) (=> (= Vfresh (tptp.vgensym (tptp.vapp (tptp.vapp Ve Ve1) (tptp.vvar Vx)))) (not (tptp.visFreeVar Vfresh Ve1)))))) (let ((_let_3 (forall ((Ve $$unsorted) (Ve1 $$unsorted) (Vx $$unsorted) (Vfresh $$unsorted)) (=> (= Vfresh (tptp.vgensym (tptp.vapp (tptp.vapp Ve Ve1) (tptp.vvar Vx)))) (not (= Vx Vfresh)))))) (let ((_let_4 (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Vy $$unsorted) (VS $$unsorted) (Ve1 $$unsorted) (VT2 $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS Ve1))) (=> (and (not (= Vx Vy)) (not (tptp.visFreeVar Vy Ve)) (tptp.vtcheck VC Ve VT) (tptp.vtcheck (tptp.vbind Vx VT VC) _let_1 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve _let_1) VT2)))))) (let ((_let_5 (forall ((Ve $$unsorted) (VC $$unsorted) (Ve1 $$unsorted) (VT $$unsorted)) (=> (and (tptp.vtcheck VC Ve VT) (tptp.valphaEquivalent Ve Ve1)) (tptp.vtcheck VC Ve1 VT))))) (let ((_let_6 (forall ((VS $$unsorted) (Vx $$unsorted) (Vy $$unsorted) (Ve $$unsorted)) (=> (not (tptp.visFreeVar Vy Ve)) (tptp.valphaEquivalent (tptp.vabs Vx VS Ve) (tptp.vabs Vy VS (tptp.vsubst Vx (tptp.vvar Vy) Ve))))))) (let ((_let_7 (= tptp.vnoExp tptp.vnoExp))) (let ((_let_8 (forall ((VVar0 $$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 $$unsorted)) (and (= VVar0 Vx) (= VExp0 Ve) (= VExp1 (tptp.vabs Vy VT Ve1)) (not (= Vx Vy)) (not (tptp.visFreeVar Vy Ve)) (= RESULT (tptp.vabs Vy VT (tptp.vsubst Vx Ve Ve1)))))))))) (let ((_let_9 (forall ((Vv $$unsorted) (Ve $$unsorted)) (=> (= (tptp.vgensym Ve) Vv) (not (tptp.visFreeVar Vv Ve)))))) (let ((_let_10 (= tptp.vnoType tptp.vnoType))) (let ((_let_11 (= tptp.vempty tptp.vempty))) (let ((_let_12 (forall ((VVar0 $$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_13 (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted) (VExp2 $$unsorted)) (not (= (tptp.vabs VVar0 VTyp0 VExp0) (tptp.vapp VExp1 VExp2)))))) (let ((_let_14 (forall ((VVar0 $$unsorted) (VVar1 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted)) (not (= (tptp.vvar VVar0) (tptp.vabs VVar1 VTyp0 VExp0)))))) (let ((_let_15 (forall ((VVar0 $$unsorted) (VTyp0 $$unsorted) (VExp0 $$unsorted) (VVar1 $$unsorted) (VTyp1 $$unsorted) (VExp1 $$unsorted)) (let ((_let_1 (= (tptp.vabs VVar0 VTyp0 VExp0) (tptp.vabs VVar1 VTyp1 VExp1)))) (let ((_let_2 (and (= VVar0 VVar1) (= VTyp0 VTyp1) (= VExp0 VExp1)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))))) (let ((_let_16 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_265))) (let ((_let_18 (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_265 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_265 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_266 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_267))) (let ((_let_20 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_21 (tptp.vbind SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_22 (tptp.vtcheck _let_21 _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_23 (not _let_22))) (let ((_let_24 (not _let_16))) (let ((_let_25 (or _let_17 _let_18 _let_24 _let_23 _let_20))) (let ((_let_26 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (let ((_let_27 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_26))) (let ((_let_28 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_29 (tptp.vtcheck _let_21 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_30 (not _let_29))) (let ((_let_31 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_32 (or _let_31 (not (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_24 _let_30 _let_28))) (let ((_let_33 (forall ((VT $$unsorted) (VC $$unsorted) (Vx $$unsorted) (Ve $$unsorted) (Vy $$unsorted) (VS $$unsorted) (VT2 $$unsorted)) (let ((_let_1 (tptp.vabs Vy VS tptp.veabs))) (or (= Vx Vy) (not (tptp.visFreeVar Vy Ve)) (not (tptp.vtcheck VC Ve VT)) (not (tptp.vtcheck (tptp.vbind Vx VT VC) _let_1 VT2)) (tptp.vtcheck VC (tptp.vsubst Vx Ve _let_1) VT2)))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (or))) (let ((_let_37 (not _let_33))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_35) :args (_let_37))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_33))) (REFL :args (_let_34)) :args _let_36)) _let_35 :args (_let_34 true _let_33)))) (let ((_let_39 (REFL :args (_let_32)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 2)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_16))) :args _let_36)) :args ((or _let_16 _let_32))) _let_38 :args (_let_16 true _let_32)))) (let ((_let_41 (not (= _let_27 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_265 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_266 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_267)))))) (let ((_let_42 (= _let_26 _let_19))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_17 _let_18 _let_41))) (let ((_let_45 (forall ((Vy $$unsorted) (VT $$unsorted) (Ve1 $$unsorted)) (let ((_let_1 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (or (not (= (tptp.vabs Vy VT Ve1) _let_1)) (= Vy SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.visFreeVar Vy SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (not (= (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_1) (tptp.vabs Vy VT (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Ve1))))))))) (let ((_let_46 (not _let_44))) (let ((_let_47 (not _let_45))) (let ((_let_48 (forall ((VT $$unsorted) (Vy $$unsorted) (Ve1 $$unsorted)) (let ((_let_1 (tptp.vgensym (tptp.vapp (tptp.vapp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Ve1) (tptp.vvar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_2 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (or (not (= (tptp.vabs Vy VT Ve1) _let_2)) (= Vy SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (not (tptp.visFreeVar Vy SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (= (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_2) (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.vabs _let_1 VT (tptp.vsubst Vy (tptp.vvar _let_1) Ve1))))))))))) (let ((_let_49 (not _let_48))) (let ((_let_50 (forall ((VT $$unsorted) (Ve1 $$unsorted)) (let ((_let_1 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 VT Ve1))) (let ((_let_2 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (or (not (= _let_2 _let_1)) (not (= (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_2) _let_1)))))))) (let ((_let_51 (not _let_50))) (let ((_let_52 (forall ((Ve1 $$unsorted) (Ve2 $$unsorted)) (let ((_let_1 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (or (not (= (tptp.vapp Ve1 Ve2) _let_1)) (not (= (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_1) (tptp.vapp (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Ve1) (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Ve2))))))))) (let ((_let_53 (not _let_52))) (let ((_let_54 (forall ((Vy $$unsorted)) (let ((_let_1 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.veabs))) (let ((_let_2 (tptp.vvar Vy))) (or (not (= _let_2 _let_1)) (= Vy SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (not (= _let_2 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_1))))))))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.vvar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_57 (= _let_26 _let_56))) (let ((_let_58 (and _let_57 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_27)))) (let ((_let_59 (or _let_58 _let_55 _let_53 _let_51 _let_49 _let_47))) (let ((_let_60 (forall ((VVar0 $$unsorted) (VExp0 $$unsorted) (VExp1 $$unsorted)) (or (and (= VExp1 (tptp.vvar VVar0)) (= VExp0 (tptp.vsubst VVar0 VExp0 VExp1))) (not (forall ((Vy $$unsorted)) (let ((_let_1 (tptp.vvar Vy))) (or (not (= VExp1 _let_1)) (= VVar0 Vy) (not (= (tptp.vsubst VVar0 VExp0 VExp1) _let_1)))))) (not (forall ((Ve1 $$unsorted) (Ve2 $$unsorted)) (or (not (= VExp1 (tptp.vapp Ve1 Ve2))) (not (= (tptp.vsubst VVar0 VExp0 VExp1) (tptp.vapp (tptp.vsubst VVar0 VExp0 Ve1) (tptp.vsubst VVar0 VExp0 Ve2))))))) (not (forall ((VT $$unsorted) (Ve1 $$unsorted)) (let ((_let_1 (tptp.vabs VVar0 VT Ve1))) (or (not (= VExp1 _let_1)) (not (= (tptp.vsubst VVar0 VExp0 VExp1) _let_1)))))) (not (forall ((VT $$unsorted) (Vy $$unsorted) (Ve1 $$unsorted)) (let ((_let_1 (tptp.vgensym (tptp.vapp (tptp.vapp VExp0 Ve1) (tptp.vvar VVar0))))) (or (not (= VExp1 (tptp.vabs Vy VT Ve1))) (= VVar0 Vy) (not (tptp.visFreeVar Vy VExp0)) (not (= (tptp.vsubst VVar0 VExp0 VExp1) (tptp.vsubst VVar0 VExp0 (tptp.vabs _let_1 VT (tptp.vsubst Vy (tptp.vvar _let_1) Ve1))))))))) (not (forall ((Vy $$unsorted) (VT $$unsorted) (Ve1 $$unsorted)) (or (not (= VExp1 (tptp.vabs Vy VT Ve1))) (= VVar0 Vy) (tptp.visFreeVar Vy VExp0) (not (= (tptp.vsubst VVar0 VExp0 VExp1) (tptp.vabs Vy VT (tptp.vsubst VVar0 VExp0 Ve1))))))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (tptp.vapp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_63 (tptp.vapp _let_62 _let_56))) (let ((_let_64 (tptp.vgensym _let_63))) (let ((_let_65 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 (tptp.vvar _let_64) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_66 (tptp.vabs _let_64 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 _let_65))) (let ((_let_67 (tptp.vsubst SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_66))) (let ((_let_68 (= _let_27 _let_67))) (let ((_let_69 (not _let_68))) (let ((_let_70 (not (tptp.visFreeVar SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_71 (tptp.vabs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_72 (= _let_26 _let_71))) (let ((_let_73 (not _let_72))) (let ((_let_74 (or _let_73 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) _let_70 _let_69))) (let ((_let_75 (tptp.vtcheck _let_21 _let_71 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_76 (tptp.vtcheck SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_67 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_77 (tptp.valphaEquivalent _let_71 _let_66))) (let ((_let_78 (tptp.vtcheck _let_21 _let_66 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_79 (not _let_77))) (let ((_let_80 (not _let_75))) (let ((_let_81 (or _let_80 _let_79 _let_78))) (let ((_let_82 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_64))) (let ((_let_83 (tptp.visFreeVar _let_64 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_84 (not _let_78))) (let ((_let_85 (or _let_82 _let_83 _let_24 _let_84 _let_76))) (let ((_let_86 (REFL :args (_let_74)))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 3)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_36)) :args ((or _let_29 _let_32))) _let_38 :args (_let_29 true _let_32)))) (let ((_let_88 (and _let_29 _let_72))) (let ((_let_89 (_let_29 _let_72))) (let 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(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 (= 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$$unsorted) (VTy $$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))) _let_9 (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 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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 ((Ve $$unsorted)) (tptp.valphaEquivalent Ve Ve)) (forall ((Ve2 $$unsorted) (Ve1 $$unsorted)) (=> (tptp.valphaEquivalent Ve1 Ve2) (tptp.valphaEquivalent Ve2 Ve1))) (forall ((Ve2 $$unsorted) (Ve1 $$unsorted) (Ve3 $$unsorted)) (=> (and (tptp.valphaEquivalent Ve1 Ve2) (tptp.valphaEquivalent Ve2 Ve3)) (tptp.valphaEquivalent Ve1 Ve3))) _let_6 _let_5 (forall ((Ve $$unsorted) (Vx $$unsorted) (Ve1 $$unsorted)) (=> (and (not (tptp.visFreeVar Vx Ve)) (tptp.valphaEquivalent Ve Ve1)) (not (tptp.visFreeVar Vx Ve1)))) (forall ((Vx $$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_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 42.00/42.25 )
% 42.00/42.25 % SZS output end Proof for COM132+1
% 42.00/42.25 % cvc5---1.0.5 exiting
% 42.00/42.25 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------