TSTP Solution File: SWW628_2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW628_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : Fri Sep 1 00:21:45 EDT 2023
% Result : Theorem 49.55s 49.81s
% Output : Proof 49.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW628_2 : TPTP v8.1.2. Released v6.1.0.
% 0.14/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n004.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 : Sun Aug 27 21:44:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_ARI
% 49.55/49.81 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.WD2S2eF6WQ/cvc5---1.0.5_7156.p...
% 49.55/49.81 ------- get file name : TPTP file name is SWW628_2
% 49.55/49.81 ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7156.smt2...
% 49.55/49.81 --- Run --finite-model-find --decision=internal at 15...
% 49.55/49.81 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 49.55/49.81 --- Run --no-e-matching --full-saturate-quant at 15...
% 49.55/49.81 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15...
% 49.55/49.81 % SZS status Theorem for SWW628_2
% 49.55/49.81 % SZS output start Proof for SWW628_2
% 49.55/49.81 (
% 49.55/49.81 (let ((_let_1 (not (forall ((Q1 tptp.list_elt) (Q2 tptp.list_elt) (Q tptp.list_elt)) (=> (and (= Q (tptp.tb2t (tptp.nil tptp.elt))) (tptp.sorted1 Q1) (tptp.sorted1 Q2)) (forall ((Q3 tptp.list_elt) (Q21 tptp.list_elt) (Q11 tptp.list_elt)) (let ((_let_1 (tptp.t2tb Q21))) (let ((_let_2 (tptp.t2tb Q11))) (let ((_let_3 (tptp.length2 tptp.elt _let_2))) (=> (and (tptp.sorted1 Q11) (tptp.sorted1 Q21) (tptp.sorted1 Q3) (forall ((X tptp.elt1) (Y tptp.elt1)) (=> (tptp.mem tptp.elt (tptp.t2tb1 X) (tptp.t2tb Q3)) (=> (tptp.mem tptp.elt (tptp.t2tb1 Y) (tptp.t2tb Q11)) (tptp.le1 X Y)))) (forall ((X tptp.elt1) (Y tptp.elt1)) (=> (tptp.mem tptp.elt (tptp.t2tb1 X) (tptp.t2tb Q3)) (=> (tptp.mem tptp.elt (tptp.t2tb1 Y) (tptp.t2tb Q21)) (tptp.le1 X Y)))) (tptp.permut tptp.elt (tptp.infix_plpl tptp.elt (tptp.infix_plpl tptp.elt (tptp.t2tb Q3) _let_2) _let_1) (tptp.infix_plpl tptp.elt (tptp.t2tb Q1) (tptp.t2tb Q2)))) (=> (< 0 _let_3) (=> (not (= _let_3 0)) (=> (not (= (tptp.length2 tptp.elt _let_1) 0)) (=> (not (= Q11 (tptp.tb2t (tptp.nil tptp.elt)))) (forall ((X1 tptp.elt1)) (=> (exists ((X tptp.elt1) (X2 tptp.list_elt)) (and (= Q11 (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 X) (tptp.t2tb X2)))) (= X1 X))) (=> (not (= Q21 (tptp.tb2t (tptp.nil tptp.elt)))) (forall ((X2 tptp.elt1)) (=> (exists ((X tptp.elt1) (X3 tptp.list_elt)) (and (= Q21 (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 X) (tptp.t2tb X3)))) (= X2 X))) (=> (not (tptp.le1 X1 X2)) (=> (not (= Q21 (tptp.tb2t (tptp.nil tptp.elt)))) (forall ((Q22 tptp.list_elt) (O tptp.elt1)) (=> (exists ((X tptp.elt1) (X3 tptp.list_elt)) (and (= Q21 (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 X) (tptp.t2tb X3)))) (= O X) (= Q22 X3))) (forall ((Q4 tptp.list_elt)) (=> (= Q4 (tptp.tb2t (tptp.infix_plpl tptp.elt (tptp.t2tb Q3) (tptp.cons tptp.elt (tptp.t2tb1 O) (tptp.nil tptp.elt))))) (tptp.permut tptp.elt (tptp.infix_plpl tptp.elt (tptp.infix_plpl tptp.elt (tptp.t2tb Q4) (tptp.t2tb Q11)) (tptp.t2tb Q22)) (tptp.infix_plpl tptp.elt (tptp.t2tb Q1) (tptp.t2tb Q2)))))))))))))))))))))))))))) (let ((_let_2 (forall ((X tptp.elt1)) (tptp.sort1 tptp.elt (tptp.t2tb1 X))))) (let ((_let_3 (tptp.nil tptp.elt))) (let ((_let_4 (tptp.tb2t _let_3))) (let ((_let_5 (forall ((J tptp.uni)) (= (tptp.t2tb (tptp.tb2t J)) J)))) (let ((_let_6 (forall ((A tptp.ty) (X tptp.uni) (L1 tptp.uni) (L2 tptp.uni)) (tptp.permut A (tptp.infix_plpl A (tptp.cons A X L1) L2) (tptp.infix_plpl A L1 (tptp.cons A X L2)))))) (let ((_let_7 (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni) (L3 tptp.uni)) (=> (tptp.permut A L1 L2) (=> (tptp.permut A L2 L3) (tptp.permut A L1 L3)))))) (let ((_let_8 (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni)) (=> (tptp.permut A L1 L2) (tptp.permut A L2 L1))))) (let ((_let_9 (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni) (L3 tptp.uni)) (= (tptp.infix_plpl A L1 (tptp.infix_plpl A L2 L3)) (tptp.infix_plpl A (tptp.infix_plpl A L1 L2) L3))))) (let ((_let_10 (forall ((A tptp.ty) (L2 tptp.uni)) (and (= (tptp.infix_plpl A (tptp.nil A) L2) L2) (forall ((X tptp.uni) (X1 tptp.uni)) (= (tptp.infix_plpl A (tptp.cons A X X1) L2) (tptp.cons A X (tptp.infix_plpl A X1 L2)))))))) (let ((_let_11 (forall ((A tptp.ty) (U tptp.uni) (U1 tptp.uni)) (= (tptp.cons_proj_21 A (tptp.cons A U U1)) U1)))) (let ((_let_12 (forall ((A tptp.ty) (U tptp.uni) (U1 tptp.uni)) (=> (tptp.sort1 A U) (= (tptp.cons_proj_11 A (tptp.cons A U U1)) U))))) (let ((_let_13 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90))) (let ((_let_14 (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92))))) (let ((_let_15 (tptp.t2tb _let_14))) (let ((_let_16 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93))) (let ((_let_17 (tptp.infix_plpl tptp.elt _let_16 _let_15))) (let ((_let_18 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91))) (let ((_let_19 (tptp.infix_plpl tptp.elt (tptp.cons tptp.elt _let_18 _let_17) _let_13))) (let ((_let_20 (tptp.infix_plpl tptp.elt (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86)))) (let ((_let_21 (tptp.permut tptp.elt _let_20 _let_19))) (let ((_let_22 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_87))) (let ((_let_23 (tptp.infix_plpl tptp.elt _let_15 _let_22))) (let ((_let_24 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_88))) (let ((_let_25 (tptp.cons tptp.elt _let_24 _let_23))) (let ((_let_26 (tptp.infix_plpl tptp.elt _let_16 _let_25))) (let ((_let_27 (tptp.permut tptp.elt _let_20 _let_26))) (let ((_let_28 (tptp.permut tptp.elt _let_19 _let_26))) (let ((_let_29 (not _let_28))) (let ((_let_30 (not _let_21))) (let ((_let_31 (or _let_30 _let_29 _let_27))) (let ((_let_32 (tptp.permut tptp.elt _let_19 _let_20))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_21))) (let ((_let_35 (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni)) (or (not (tptp.permut A L1 L2)) (tptp.permut A L2 L1))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (_let_35))) (let ((_let_38 (tptp.cons tptp.elt _let_18 _let_13))) (let ((_let_39 (tptp.infix_plpl tptp.elt _let_17 _let_38))) (let ((_let_40 (tptp.permut tptp.elt _let_39 _let_20))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.permut tptp.elt _let_19 _let_39))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_41 _let_32))) (let ((_let_45 (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni) (L3 tptp.uni)) (or (not (tptp.permut A L1 L2)) (not (tptp.permut A L2 L3)) (tptp.permut A L1 L3))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (_let_45))) (let ((_let_48 (tptp.tb2t _let_38))) (let ((_let_49 (= _let_38 (tptp.t2tb _let_48)))) (let ((_let_50 (tptp.cons tptp.elt _let_24 _let_22))) (let ((_let_51 (tptp.tb2t _let_50))) (let ((_let_52 (= _let_51 _let_48))) (let ((_let_53 (tptp.t2tb _let_51))) (let ((_let_54 (tptp.permut tptp.elt (tptp.infix_plpl tptp.elt _let_17 _let_53) _let_20))) (let ((_let_55 (forall ((J tptp.uni)) (= J (tptp.t2tb (tptp.tb2t J)))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (_let_55))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_38 QUANTIFIERS_INST_CBQI_PROP)) :args _let_57)) _let_56 :args (_let_49 false _let_55)))) (let ((_let_59 (not _let_52))) (let ((_let_60 (tptp.cons tptp.elt _let_24 _let_3))) (let ((_let_61 (tptp.infix_plpl tptp.elt _let_16 _let_60))) (let ((_let_62 (tptp.t2tb (tptp.tb2t _let_61)))) (let ((_let_63 (tptp.infix_plpl tptp.elt (tptp.infix_plpl tptp.elt _let_62 _let_15) _let_22))) (let ((_let_64 (tptp.permut tptp.elt _let_63 _let_20))) (let ((_let_65 (tptp.length2 tptp.elt _let_15))) (let ((_let_66 (not _let_54))) (let ((_let_67 (or (not (tptp.sorted1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85)) (not (tptp.sorted1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86)) (not (tptp.sorted1 _let_14)) (not (tptp.sorted1 _let_51)) (not (tptp.sorted1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93)) (not (forall ((X tptp.elt1) (Y tptp.elt1)) (or (not (tptp.mem tptp.elt (tptp.t2tb1 X) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93))) (not (tptp.mem tptp.elt (tptp.t2tb1 Y) (tptp.t2tb (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92)))))) (tptp.le1 X Y)))) (not (forall ((X tptp.elt1) (Y tptp.elt1)) (or (not (tptp.mem tptp.elt (tptp.t2tb1 X) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93))) (not (tptp.mem tptp.elt (tptp.t2tb1 Y) (tptp.t2tb (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_88) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_87)))))) (tptp.le1 X Y)))) _let_66 (not (>= _let_65 1)) (= _let_65 0) (= (tptp.length2 tptp.elt _let_53) 0) (= _let_4 _let_14) (= _let_4 _let_51) _let_64 _let_59 (tptp.le1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91)))) (let ((_let_68 (forall ((Q1 tptp.list_elt) (Q2 tptp.list_elt) (BOUND_VARIABLE_2214 tptp.list_elt) (BOUND_VARIABLE_2212 tptp.elt1) (BOUND_VARIABLE_2210 tptp.elt1) (BOUND_VARIABLE_2208 tptp.list_elt) (BOUND_VARIABLE_2206 tptp.elt1) (BOUND_VARIABLE_2204 tptp.list_elt) (BOUND_VARIABLE_2202 tptp.list_elt)) (let ((_let_1 (tptp.t2tb BOUND_VARIABLE_2214))) (let ((_let_2 (tptp.t2tb1 BOUND_VARIABLE_2212))) (let ((_let_3 (tptp.tb2t (tptp.cons tptp.elt _let_2 _let_1)))) (let ((_let_4 (tptp.infix_plpl tptp.elt (tptp.t2tb Q1) (tptp.t2tb Q2)))) (let ((_let_5 (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 BOUND_VARIABLE_2210) (tptp.t2tb BOUND_VARIABLE_2204))))) (let ((_let_6 (tptp.t2tb _let_5))) (let ((_let_7 (tptp.nil tptp.elt))) (let ((_let_8 (tptp.t2tb BOUND_VARIABLE_2202))) (let ((_let_9 (tptp.tb2t _let_7))) (let ((_let_10 (tptp.t2tb _let_3))) (let ((_let_11 (tptp.length2 tptp.elt _let_6))) (or (not (tptp.sorted1 Q1)) (not (tptp.sorted1 Q2)) (not (tptp.sorted1 _let_5)) (not (tptp.sorted1 _let_3)) (not (tptp.sorted1 BOUND_VARIABLE_2202)) (not (forall ((X tptp.elt1) (Y tptp.elt1)) (or (not (tptp.mem tptp.elt (tptp.t2tb1 X) (tptp.t2tb BOUND_VARIABLE_2202))) (not (tptp.mem tptp.elt (tptp.t2tb1 Y) (tptp.t2tb (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 BOUND_VARIABLE_2210) (tptp.t2tb BOUND_VARIABLE_2204)))))) (tptp.le1 X Y)))) (not (forall ((X tptp.elt1) (Y tptp.elt1)) (or (not (tptp.mem tptp.elt (tptp.t2tb1 X) (tptp.t2tb BOUND_VARIABLE_2202))) (not (tptp.mem tptp.elt (tptp.t2tb1 Y) (tptp.t2tb (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 BOUND_VARIABLE_2212) (tptp.t2tb BOUND_VARIABLE_2214)))))) (tptp.le1 X Y)))) (not (tptp.permut tptp.elt (tptp.infix_plpl tptp.elt (tptp.infix_plpl tptp.elt _let_8 _let_6) _let_10) _let_4)) (not (>= _let_11 1)) (= _let_11 0) (= (tptp.length2 tptp.elt _let_10) 0) (= _let_9 _let_5) (= _let_9 _let_3) (tptp.permut tptp.elt (tptp.infix_plpl tptp.elt (tptp.infix_plpl tptp.elt (tptp.t2tb (tptp.tb2t (tptp.infix_plpl tptp.elt _let_8 (tptp.cons tptp.elt _let_2 _let_7)))) _let_6) _let_1) _let_4) (not (= _let_3 (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 BOUND_VARIABLE_2206) (tptp.t2tb BOUND_VARIABLE_2208))))) (tptp.le1 BOUND_VARIABLE_2210 BOUND_VARIABLE_2206)))))))))))))))) (let ((_let_69 (not _let_67))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (or))) (let ((_let_72 (not _let_68))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_70) :args (_let_72))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_68))) (REFL :args (_let_69)) :args _let_71)) _let_70 :args (_let_69 true _let_68)))) (let ((_let_74 (REFL :args (_let_67)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_67 14)) (CONG _let_74 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_52))) :args _let_71)) :args ((or _let_52 _let_67))) _let_73 :args (_let_52 true _let_67)))) (let ((_let_76 (and _let_54 _let_52 _let_49))) (let ((_let_77 (_let_54 _let_52 _let_49))) (let ((_let_78 (ASSUME :args (_let_54)))) (let ((_let_79 (APPLY_UF tptp.permut))) (let ((_let_80 (REFL :args (_let_20)))) (let ((_let_81 (APPLY_UF tptp.infix_plpl))) (let ((_let_82 (ASSUME :args (_let_52)))) (let ((_let_83 (CONG (SYMM _let_82) :args (APPLY_UF tptp.t2tb)))) (let ((_let_84 (ASSUME :args (_let_49)))) (let ((_let_85 (SYMM (SYMM _let_84)))) (let ((_let_86 (REFL :args (_let_17)))) (let ((_let_87 (REFL :args (tptp.elt)))) (let ((_let_88 (_let_6))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 (tptp.infix_plpl tptp.elt _let_60 _let_15))) (let ((_let_91 (tptp.infix_plpl tptp.elt _let_16 _let_90))) (let ((_let_92 (= (tptp.infix_plpl tptp.elt _let_16 (tptp.infix_plpl tptp.elt _let_90 _let_22)) (tptp.infix_plpl tptp.elt _let_91 _let_22)))) (let ((_let_93 (= (tptp.infix_plpl tptp.elt (tptp.cons tptp.elt _let_24 _let_15) _let_22) _let_25))) (let ((_let_94 (tptp.infix_plpl tptp.elt _let_3 _let_15))) (let ((_let_95 (= _let_90 (tptp.cons tptp.elt _let_24 _let_94)))) (let ((_let_96 (= _let_15 _let_94))) (let ((_let_97 (= _let_91 (tptp.infix_plpl tptp.elt _let_61 _let_15)))) (let ((_let_98 (tptp.permut tptp.elt _let_20 _let_63))) (let ((_let_99 (= _let_61 _let_62))) (let ((_let_100 (not _let_27))) (let ((_let_101 (_let_9))) (let ((_let_102 (ASSUME :args _let_101))) (let ((_let_103 ((tptp.infix_plpl A (tptp.infix_plpl A L1 L2) L3)))) (let ((_let_104 (forall ((BOUND_VARIABLE_1645 tptp.ty) (BOUND_VARIABLE_1647 tptp.uni) (X tptp.uni) (X1 tptp.uni)) (= (tptp.infix_plpl BOUND_VARIABLE_1645 (tptp.cons BOUND_VARIABLE_1645 X X1) BOUND_VARIABLE_1647) (tptp.cons BOUND_VARIABLE_1645 X (tptp.infix_plpl BOUND_VARIABLE_1645 X1 BOUND_VARIABLE_1647)))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (AND_ELIM _let_105 :args (1)))) (let ((_let_107 (_let_104))) (let ((_let_108 (ASSUME :args _let_107))) (let ((_let_109 (forall ((BOUND_VARIABLE_1636 tptp.ty) (BOUND_VARIABLE_1638 tptp.uni)) (= BOUND_VARIABLE_1638 (tptp.infix_plpl BOUND_VARIABLE_1636 (tptp.nil BOUND_VARIABLE_1636) BOUND_VARIABLE_1638))))) (let ((_let_110 (_let_109))) (let ((_let_111 (not _let_98))) (let ((_let_112 (or _let_111 _let_64))) (let ((_let_113 (not _let_92))) (let ((_let_114 (not _let_93))) (let ((_let_115 (not _let_95))) (let ((_let_116 (not _let_96))) (let ((_let_117 (not _let_97))) (let ((_let_118 (not _let_99))) (let ((_let_119 (and _let_99 _let_97 _let_111 _let_96 _let_95 _let_93 _let_92))) (let ((_let_120 (ASSUME :args (_let_111)))) (let ((_let_121 (REFL :args (_let_22)))) (let ((_let_122 (ASSUME :args (_let_99)))) (let ((_let_123 (ASSUME :args (_let_97)))) (let ((_let_124 (ASSUME :args (_let_92)))) (let ((_let_125 (ASSUME :args (_let_95)))) (let ((_let_126 (APPLY_UF tptp.cons))) (let ((_let_127 (ASSUME :args (_let_96)))) (let ((_let_128 (ASSUME :args (_let_93)))) (let ((_let_129 (tptp.cons tptp.elt _let_24 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(forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni)) (= (tptp.length2 A (tptp.infix_plpl A L1 L2)) (+ (tptp.length2 A L1) (tptp.length2 A L2)))) (forall ((A tptp.ty) (X tptp.uni) (L1 tptp.uni) (L2 tptp.uni)) (= (tptp.mem A X (tptp.infix_plpl A L1 L2)) (or (tptp.mem A X L1) (tptp.mem A X L2)))) (forall ((A tptp.ty) (X tptp.uni) (L tptp.uni)) (=> (tptp.mem A X L) (exists ((L1 tptp.uni) (L2 tptp.uni)) (let ((_let_1 (tptp.list A))) (and (tptp.sort1 _let_1 L1) (tptp.sort1 _let_1 L2) (= L (tptp.infix_plpl A L1 (tptp.cons A X L2)))))))) (forall ((A tptp.ty) (X tptp.uni)) (=> (tptp.sort1 A X) (and (= (tptp.num_occ1 A X (tptp.nil A)) 0) (forall ((X1 tptp.uni) (X2 tptp.uni)) (let ((_let_1 (tptp.num_occ1 A X X2))) (let ((_let_2 (tptp.num_occ1 A X (tptp.cons A X1 X2)))) (let ((_let_3 (= X X1))) (=> (tptp.sort1 A X1) (and (=> _let_3 (= _let_2 (+ 1 _let_1))) (=> (not _let_3) (= _let_2 (+ 0 _let_1)))))))))))) (forall ((A tptp.ty) (X tptp.uni) (L tptp.uni)) (= (tptp.mem A X L) (< 0 (tptp.num_occ1 A X L)))) (forall ((A tptp.ty) (X tptp.uni) (L1 tptp.uni) (L2 tptp.uni)) (= (tptp.num_occ1 A X (tptp.infix_plpl A L1 L2)) (+ (tptp.num_occ1 A X L1) (tptp.num_occ1 A X L2)))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.list A) (tptp.reverse A X))) (forall ((A tptp.ty)) (let ((_let_1 (tptp.nil A))) (and (= (tptp.reverse A _let_1) _let_1) (forall ((X tptp.uni) (X1 tptp.uni)) (= (tptp.reverse A (tptp.cons A X X1)) (tptp.infix_plpl A (tptp.reverse A X1) (tptp.cons A X (tptp.nil A)))))))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni) (X tptp.uni)) (= (tptp.infix_plpl A (tptp.reverse A (tptp.cons A X L1)) L2) (tptp.infix_plpl A (tptp.reverse A L1) (tptp.cons A X L2)))) (forall ((A tptp.ty) (L tptp.uni) (X tptp.uni)) (= (tptp.reverse A (tptp.cons A X L)) (tptp.infix_plpl A (tptp.reverse A L) (tptp.cons A X (tptp.nil A))))) (forall ((A tptp.ty) (L tptp.uni)) (= (tptp.reverse A (tptp.reverse A L)) L)) (forall ((A tptp.ty) (L tptp.uni) (X tptp.uni)) (= (tptp.mem A X L) (tptp.mem A X (tptp.reverse A L)))) (forall ((A tptp.ty) (L tptp.uni)) (= (tptp.length2 A (tptp.reverse A L)) (tptp.length2 A L))) (forall ((A tptp.ty) (X tptp.uni) (L tptp.uni)) (= (tptp.num_occ1 A X L) (tptp.num_occ1 A X (tptp.reverse A L)))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni)) (let ((_let_1 (tptp.permut A L1 L2))) (and (=> _let_1 (forall ((X tptp.uni)) (= (tptp.num_occ1 A X L1) (tptp.num_occ1 A X L2)))) (=> (forall ((X tptp.uni)) (=> (tptp.sort1 A X) (= (tptp.num_occ1 A X L1) (tptp.num_occ1 A X L2)))) _let_1)))) (forall ((A tptp.ty) (L tptp.uni)) (tptp.permut A L L)) _let_8 _let_7 (forall ((A tptp.ty) (X tptp.uni) (L1 tptp.uni) (L2 tptp.uni)) (=> (tptp.permut A L1 L2) (tptp.permut A (tptp.cons A X L1) (tptp.cons A X L2)))) (forall ((A tptp.ty) (X tptp.uni) (Y tptp.uni) (L tptp.uni)) (tptp.permut A (tptp.cons A X (tptp.cons A Y L)) (tptp.cons A Y (tptp.cons A X L)))) _let_6 (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni) (L3 tptp.uni)) (tptp.permut A (tptp.infix_plpl A (tptp.infix_plpl A L1 L2) L3) (tptp.infix_plpl A L1 (tptp.infix_plpl A L2 L3)))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni) (K1 tptp.uni) (K2 tptp.uni)) (=> (tptp.permut A L1 K1) (=> (tptp.permut A L2 K2) (tptp.permut A (tptp.infix_plpl A L1 L2) (tptp.infix_plpl A K1 K2))))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni)) (tptp.permut A (tptp.infix_plpl A L1 L2) (tptp.infix_plpl A L2 L1))) (forall ((A tptp.ty) (X tptp.uni) (L1 tptp.uni) (L2 tptp.uni)) (=> (tptp.permut A L1 L2) (=> (tptp.mem A X L1) (tptp.mem A X L2)))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni)) (=> (tptp.permut A L1 L2) (= (tptp.length2 A L1) (tptp.length2 A L2)))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.t A) (tptp.mk_t A X))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.list A) (tptp.elts A X))) (forall ((A tptp.ty) (U tptp.uni)) (= (tptp.elts A (tptp.mk_t A U)) U)) (forall ((A tptp.ty) (U tptp.uni)) (= U (tptp.mk_t A (tptp.elts A U)))) (forall ((A tptp.ty) (Q tptp.uni)) (= (tptp.length3 A Q) (tptp.length2 A (tptp.elts A Q)))) (forall ((X tptp.elt1)) (tptp.le1 X X)) (forall ((X tptp.elt1) (Y tptp.elt1) (Z tptp.elt1)) (=> (tptp.le1 X Y) (=> (tptp.le1 Y Z) (tptp.le1 X Z)))) (forall ((X tptp.elt1) (Y tptp.elt1)) (or (tptp.le1 X Y) (tptp.le1 Y X))) (forall ((X tptp.list_elt)) (tptp.sort1 (tptp.list tptp.elt) (tptp.t2tb X))) (forall ((I tptp.list_elt)) (= (tptp.tb2t (tptp.t2tb I)) I)) _let_5 (tptp.sorted1 _let_4) _let_2 (forall ((I tptp.elt1)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)) (forall ((J tptp.uni)) (=> (tptp.sort1 tptp.elt J) (= (tptp.t2tb1 (tptp.tb2t1 J)) J))) (forall ((X tptp.elt1)) (tptp.sorted1 (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 X) (tptp.nil tptp.elt))))) (forall ((X tptp.elt1) (Y tptp.elt1) (L tptp.list_elt)) (let ((_let_1 (tptp.cons tptp.elt (tptp.t2tb1 Y) (tptp.t2tb L)))) (=> (tptp.le1 X Y) (=> (tptp.sorted1 (tptp.tb2t _let_1)) (tptp.sorted1 (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 X) _let_1))))))) (forall ((Z tptp.list_elt)) (=> (tptp.sorted1 Z) (or (= Z (tptp.tb2t (tptp.nil tptp.elt))) (exists ((X tptp.elt1)) (= Z (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 X) (tptp.nil tptp.elt))))) (exists ((X tptp.elt1) (Y tptp.elt1) (L tptp.list_elt)) (let ((_let_1 (tptp.cons tptp.elt (tptp.t2tb1 Y) (tptp.t2tb L)))) (and (tptp.le1 X Y) (tptp.sorted1 (tptp.tb2t _let_1)) (= Z (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 X) _let_1))))))))) (forall ((X tptp.elt1) (L tptp.list_elt)) (= (and (forall ((Y tptp.elt1)) (=> (tptp.mem tptp.elt (tptp.t2tb1 Y) (tptp.t2tb L)) (tptp.le1 X Y))) (tptp.sorted1 L)) (tptp.sorted1 (tptp.tb2t (tptp.cons tptp.elt (tptp.t2tb1 X) (tptp.t2tb L)))))) (forall ((L1 tptp.list_elt) (L2 tptp.list_elt)) (= (and (tptp.sorted1 L1) (tptp.sorted1 L2) (forall ((X tptp.elt1) (Y tptp.elt1)) (=> (tptp.mem tptp.elt (tptp.t2tb1 X) (tptp.t2tb L1)) (=> (tptp.mem tptp.elt (tptp.t2tb1 Y) (tptp.t2tb L2)) (tptp.le1 X Y))))) (tptp.sorted1 (tptp.tb2t (tptp.infix_plpl tptp.elt (tptp.t2tb L1) (tptp.t2tb L2)))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 49.55/49.81 )
% 49.55/49.81 % SZS output end Proof for SWW628_2
% 49.55/49.81 % cvc5---1.0.5 exiting
% 49.55/49.82 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------