TSTP Solution File: COM126+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : COM126+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 62.26s 62.56s
% Output : Proof 62.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : COM126+1 : TPTP v8.1.2. Released v6.4.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 12:49:37 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 62.26/62.56 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.yRDlbdXXNY/cvc5---1.0.5_10269.p...
% 62.26/62.56 ------- get file name : TPTP file name is COM126+1
% 62.26/62.56 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10269.smt2...
% 62.26/62.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 62.26/62.56 --- Run --no-e-matching --full-saturate-quant at 5...
% 62.26/62.56 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 62.26/62.56 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 62.26/62.56 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 62.26/62.56 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 62.26/62.56 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 62.26/62.56 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 62.26/62.56 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 62.26/62.56 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 62.26/62.56 --- Run --relevant-triggers --full-saturate-quant at 5...
% 62.26/62.56 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 62.26/62.56 % SZS status Theorem for COM126+1
% 62.26/62.56 % SZS output start Proof for COM126+1
% 62.26/62.56 (
% 62.26/62.56 (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 VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vx VS 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 VC tptp.ve2app VT)) (tptp.vtcheck (tptp.vbind Vx VS 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 VC tptp.ve1app VT)) (tptp.vtcheck (tptp.vbind Vx VS 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 $$unsorted)) (let ((_let_1 (= (tptp.vapp VExp0 VExp1) (tptp.vapp VExp2 VExp3)))) (let ((_let_2 (and (= VExp0 VExp2) (= VExp1 VExp3)))) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))))) (let ((_let_13 (io_tptp.varrow_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_120 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_14 (io_tptp.vtcheck_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_118 _let_13))) (let ((_let_15 (= i_tptp.ve1app_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_118))) (let ((_let_16 (io_tptp.vtcheck_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 i_tptp.ve1app_23 _let_13))) (let ((_let_17 (io_tptp.vtcheck_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_119 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_120))) (let ((_let_18 (not _let_17))) (let ((_let_19 (not _let_14))) (let ((_let_20 (io_tptp.vapp_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_118 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_119))) (let ((_let_21 (io_tptp.vapp_4 i_tptp.ve1app_23 i_tptp.ve2app_24))) (let ((_let_22 (= _let_21 _let_20))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_19 _let_18))) (let ((_let_25 (forall ((b_Ve1 it_4_$$unsorted) (b_Ve2 it_4_$$unsorted) (b_VS it_7_$$unsorted)) (or (not (= (io_tptp.vapp_4 b_Ve1 b_Ve2) (io_tptp.vapp_4 i_tptp.ve1app_23 i_tptp.ve2app_24))) (not (io_tptp.vtcheck_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 b_Ve1 (io_tptp.varrow_22 b_VS SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (not (io_tptp.vtcheck_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 b_Ve2 b_VS)))))) (let ((_let_26 (not _let_24))) (let ((_let_27 (not _let_25))) (let ((_let_28 (forall ((Vx $$unsorted) (b_Ve2 it_4_$$unsorted) (b_VT1 it_7_$$unsorted) (b_VT2 it_7_$$unsorted)) (or (not (= (io_tptp.vabs_3 Vx b_VT1 b_Ve2) (io_tptp.vapp_4 i_tptp.ve1app_23 i_tptp.ve2app_24))) (not (= (io_tptp.varrow_22 b_VT1 b_VT2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36)) (not (io_tptp.vtcheck_14 (io_tptp.vbind_7 Vx b_VT1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35) b_Ve2 b_VT2)))))) (let ((_let_29 (not _let_28))) (let ((_let_30 (forall ((Vx $$unsorted)) (or (not (= (io_tptp.vvar_2 Vx) (io_tptp.vapp_4 i_tptp.ve1app_23 i_tptp.ve2app_24))) (not (= (io_tptp.vsomeType_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36) (io_tptp.vlookup_13 Vx SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))))))) (let ((_let_31 (not _let_30))) (let ((_let_32 (io_tptp.vtcheck_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31 _let_29 _let_27))) (let ((_let_35 (forall ((b_Ve it_4_$$unsorted) (b_VT it_7_$$unsorted) (b_VC it_67_$$unsorted)) (or (not (io_tptp.vtcheck_14 b_VC b_Ve b_VT)) (not (forall ((Vx $$unsorted)) (or (not (= b_Ve (io_tptp.vvar_2 Vx))) (not (= (io_tptp.vlookup_13 Vx b_VC) (io_tptp.vsomeType_8 b_VT)))))) (not (forall ((Vx $$unsorted) (b_Ve2 it_4_$$unsorted) (b_VT1 it_7_$$unsorted) (b_VT2 it_7_$$unsorted)) (or (not (= b_Ve (io_tptp.vabs_3 Vx b_VT1 b_Ve2))) (not (= b_VT (io_tptp.varrow_22 b_VT1 b_VT2))) (not (io_tptp.vtcheck_14 (io_tptp.vbind_7 Vx b_VT1 b_VC) b_Ve2 b_VT2))))) (not (forall ((b_Ve1 it_4_$$unsorted) (b_Ve2 it_4_$$unsorted) (b_VS it_7_$$unsorted)) (or (not (= b_Ve (io_tptp.vapp_4 b_Ve1 b_Ve2))) (not (io_tptp.vtcheck_14 b_VC b_Ve1 (io_tptp.varrow_22 b_VS b_VT))) (not (io_tptp.vtcheck_14 b_VC b_Ve2 b_VS))))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (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 $$unsorted)) (or (not (= Ve (tptp.vapp Ve1 Ve2))) (not (tptp.vtcheck VC Ve1 (tptp.varrow VS VT))) (not (tptp.vtcheck VC Ve2 VS))))))) _let_35))))))) (let ((_let_37 (not (io_tptp.vtcheck_14 (io_tptp.vbind_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_116 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_115 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117)))) (let ((_let_38 (io_tptp.varrow_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_116 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117))) (let ((_let_39 (io_tptp.vabs_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_116 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_115))) (let ((_let_40 (= _let_21 _let_39))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 _let_38)) _let_37))) (let ((_let_43 (forall ((VVar0 $$unsorted) (b_VTyp0 it_7_$$unsorted) (b_VExp0 it_4_$$unsorted) (b_VExp1 it_4_$$unsorted) (b_VExp2 it_4_$$unsorted)) (not (= (io_tptp.vabs_3 VVar0 b_VTyp0 b_VExp0) (io_tptp.vapp_4 b_VExp1 b_VExp2)))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_10)) (PREPROCESS :args ((= _let_10 _let_43)))))) (let ((_let_45 (or))) (let ((_let_46 (_let_29))) (let ((_let_47 (not (= (io_tptp.vsomeType_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36) (io_tptp.vlookup_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_113 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))))) (let ((_let_48 (io_tptp.vvar_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_113))) (let ((_let_49 (= _let_21 _let_48))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_47))) (let ((_let_52 (forall ((VVar0 $$unsorted) (b_VExp0 it_4_$$unsorted) (b_VExp1 it_4_$$unsorted)) (not (= (io_tptp.vvar_2 VVar0) (io_tptp.vapp_4 b_VExp0 b_VExp1)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_11)) (PREPROCESS :args ((= _let_11 _let_52)))))) (let ((_let_54 (_let_31))) (let ((_let_55 (io_tptp.vbind_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))) (let ((_let_56 (io_tptp.vtcheck_14 _let_55 _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_57 (io_tptp.visFreeVar_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 _let_21))) (let ((_let_58 (or _let_57 _let_33 _let_56))) (let ((_let_59 (forall ((Vx $$unsorted) (b_VS it_7_$$unsorted) (b_VC it_67_$$unsorted) (b_VT it_7_$$unsorted)) (let ((_let_1 (io_tptp.vapp_4 i_tptp.ve1app_23 i_tptp.ve2app_24))) (or (io_tptp.visFreeVar_6 Vx _let_1) (not (io_tptp.vtcheck_14 b_VC _let_1 b_VT)) (io_tptp.vtcheck_14 (io_tptp.vbind_7 Vx b_VS b_VC) _let_1 b_VT)))))) (let ((_let_60 (not _let_58))) (let ((_let_61 (not _let_59))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Vx $$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 VC _let_1 VT)) (tptp.vtcheck (tptp.vbind Vx VS VC) _let_1 VT))))) _let_61))))))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_62) :args (_let_61))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_59))) (REFL :args (_let_60)) :args _let_45)) _let_62 :args (_let_60 true _let_59)))) (let ((_let_64 (_let_27))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_64)) :args _let_64) (REWRITE :args ((=> _let_27 (not (or (not (= _let_20 _let_21)) _let_19 _let_18))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_25))) (REFL :args (_let_26)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_31 _let_29 _let_27 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 1)) (CONG (REFL :args (_let_58)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_45)) :args ((or _let_32 _let_58))) _let_63 :args (_let_32 true _let_58)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_54)) :args _let_54) (REWRITE :args ((=> _let_31 (not (or (not (= _let_48 _let_21)) _let_47))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) (REFL :args ((not _let_51))) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG (REFL :args (_let_51)) (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_45)) :args ((or _let_49 _let_51))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_113 i_tptp.ve1app_23 i_tptp.ve2app_24 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_52)))) _let_53 :args (_let_50 false _let_52)) :args (_let_51 true _let_49)) :args (_let_30 false _let_51)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_46)) :args _let_46) (REWRITE :args ((=> _let_29 (not (or (not (= _let_39 _let_21)) (not (= _let_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36)) _let_37))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) (REFL :args ((not _let_42))) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG (REFL :args (_let_42)) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_45)) :args ((or _let_40 _let_42))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_114 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_116 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_115 i_tptp.ve1app_23 i_tptp.ve2app_24 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_43)))) _let_44 :args (_let_41 false _let_43)) :args (_let_42 true _let_40)) :args (_let_28 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (io_tptp.vtcheck_14 b_VC b_Ve b_VT) false))))) :args (_let_35)))) _let_36 :args (_let_34 false _let_35)) :args (_let_27 false _let_32 false _let_30 false _let_28 false _let_34)) :args (_let_26 true _let_25)))) (let ((_let_66 (REFL :args (_let_24)))) (let ((_let_67 (= i_tptp.ve2app_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_119))) (let ((_let_68 (and _let_15 _let_67))) (let ((_let_69 (or _let_23 _let_68))) (let ((_let_70 (forall ((b_BOUND_VARIABLE_1868 it_4_$$unsorted) (b_BOUND_VARIABLE_1870 it_4_$$unsorted) (b_BOUND_VARIABLE_1872 it_4_$$unsorted) (b_BOUND_VARIABLE_1874 it_4_$$unsorted)) (or (not (= (io_tptp.vapp_4 b_BOUND_VARIABLE_1868 b_BOUND_VARIABLE_1870) (io_tptp.vapp_4 b_BOUND_VARIABLE_1872 b_BOUND_VARIABLE_1874))) (and (= b_BOUND_VARIABLE_1868 b_BOUND_VARIABLE_1872) (= b_BOUND_VARIABLE_1870 b_BOUND_VARIABLE_1874)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((BOUND_VARIABLE_1868 $$unsorted) (BOUND_VARIABLE_1870 $$unsorted) (BOUND_VARIABLE_1872 $$unsorted) (BOUND_VARIABLE_1874 $$unsorted)) (or (not (= (tptp.vapp BOUND_VARIABLE_1868 BOUND_VARIABLE_1870) (tptp.vapp BOUND_VARIABLE_1872 BOUND_VARIABLE_1874))) (and (= BOUND_VARIABLE_1868 BOUND_VARIABLE_1872) (= BOUND_VARIABLE_1870 BOUND_VARIABLE_1874)))) _let_70))))))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_23 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_45)) :args ((or _let_22 _let_24))) _let_65 :args (_let_22 true _let_24)) 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(tptp.vlookup VVar0 VCtx0) RESULT) (or (exists ((Vx $$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_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))) _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 62.26/62.56 )
% 62.26/62.56 % SZS output end Proof for COM126+1
% 62.26/62.56 % cvc5---1.0.5 exiting
% 62.26/62.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------