%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC152+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n022.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 : Thu Aug 31 20:23:38 EDT 2023

% Result   : Theorem 44.38s 44.61s
% Output   : Proof 44.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SWC152+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n022.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   : Mon Aug 28 15:46:24 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 44.38/44.61  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.X8mjZVqCu6/cvc5---1.0.5_18465.p...
% 44.38/44.61  ------- get file name : TPTP file name is SWC152+1
% 44.38/44.61  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18465.smt2...
% 44.38/44.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 44.38/44.61  --- Run --no-e-matching --full-saturate-quant at 5...
% 44.38/44.61  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 44.38/44.61  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 44.38/44.61  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 44.38/44.61  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 44.38/44.61  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 44.38/44.61  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 44.38/44.61  % SZS status Theorem for SWC152+1
% 44.38/44.61  % SZS output start Proof for SWC152+1
% 44.38/44.61  (
% 44.38/44.61  (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (forall ((X2 $$unsorted)) (=> (tptp.ssList X2) (forall ((X3 $$unsorted)) (or (not (tptp.ssList X3)) (not (= (tptp.app (tptp.app (tptp.app (tptp.app X1 (tptp.cons Y tptp.nil)) X2) (tptp.cons Z tptp.nil)) X3) U)) (not (tptp.leq Z Y)) (and (forall ((X4 $$unsorted)) (or (not (tptp.ssItem X4)) (not (tptp.memberP X2 X4)) (and (tptp.leq Y X4) (tptp.leq X4 Z)))) (tptp.leq Y Z)))))))))))) (and (forall ((X5 $$unsorted)) (or (not (tptp.ssItem X5)) (not (= (tptp.cons X5 tptp.nil) W)) (not (tptp.memberP X X5)) (exists ((X6 $$unsorted)) (and (tptp.ssItem X6) (not (= X5 X6)) (tptp.memberP X X6) (tptp.leq X5 X6))))) (or (not (= tptp.nil X)) (not (= tptp.nil W))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_11 (tptp.ssList tptp.nil))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))))) (let ((_let_14 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_14))) (let ((_let_16 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_16))) (let ((_let_18 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.nil))) (let ((_let_19 (tptp.app _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_18))) (let ((_let_21 (tptp.app _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (= _let_21 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_19)))) (let ((_let_23 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_24 (tptp.app _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_25 (tptp.app _let_21 _let_23))) (let ((_let_26 (tptp.app _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_27 (= _let_26 (tptp.app _let_21 _let_24)))) (let ((_let_28 (= _let_19 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_14)))) (let ((_let_29 (= _let_24 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16)))) (let ((_let_30 (= _let_26 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_31 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_15))) (let ((_let_34 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (_let_34))) (let ((_let_37 ((not (= (tptp.ssList U) false))))) (let ((_let_38 (= tptp.nil _let_26))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or (not (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) _let_39))) (let ((_let_41 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_42 (= _let_26 _let_41))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_43 (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((X6 $$unsorted)) (or (not (tptp.ssItem X6)) (= X6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 X6)) (not (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 X6)))))))) (let ((_let_47 (and _let_46 _let_40))) (let ((_let_48 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.ssList _let_26))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 _let_57 _let_55 _let_53 _let_51 _let_32 (and (or (not (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (and (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_49 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) _let_47))) (let ((_let_61 (forall ((BOUND_VARIABLE_5633 $$unsorted) (BOUND_VARIABLE_5631 $$unsorted) (BOUND_VARIABLE_5668 $$unsorted) (BOUND_VARIABLE_5629 $$unsorted) (BOUND_VARIABLE_5666 $$unsorted) (BOUND_VARIABLE_5627 $$unsorted) (BOUND_VARIABLE_5625 $$unsorted) (BOUND_VARIABLE_5623 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5625 (tptp.cons BOUND_VARIABLE_5623 tptp.nil)) BOUND_VARIABLE_5631) (tptp.cons BOUND_VARIABLE_5633 tptp.nil)) BOUND_VARIABLE_5629))) (or (not (tptp.ssList _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5623)) (not (tptp.ssItem BOUND_VARIABLE_5633)) (not (tptp.leq BOUND_VARIABLE_5633 BOUND_VARIABLE_5623)) (not (tptp.ssList BOUND_VARIABLE_5625)) (not (tptp.ssList BOUND_VARIABLE_5631)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5627)) (not (tptp.memberP BOUND_VARIABLE_5631 BOUND_VARIABLE_5627)) (and (tptp.leq BOUND_VARIABLE_5623 BOUND_VARIABLE_5627) (tptp.leq BOUND_VARIABLE_5627 BOUND_VARIABLE_5633))) (tptp.leq BOUND_VARIABLE_5623 BOUND_VARIABLE_5633)) (not (tptp.ssList BOUND_VARIABLE_5629)) (not (tptp.ssList BOUND_VARIABLE_5666)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5668)) (not (= _let_1 (tptp.cons BOUND_VARIABLE_5668 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5666 BOUND_VARIABLE_5668)) (not (forall ((X6 $$unsorted)) (or (not (tptp.ssItem X6)) (= X6 BOUND_VARIABLE_5668) (not (tptp.memberP BOUND_VARIABLE_5666 X6)) (not (tptp.leq BOUND_VARIABLE_5668 X6)))))) (or (not (= tptp.nil BOUND_VARIABLE_5666)) (not (= tptp.nil _let_1))))))))) (let ((_let_62 (not _let_60))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (or))) (let ((_let_65 (not _let_61))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_63) :args (_let_65))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_61))) (REFL :args (_let_62)) :args _let_64)) _let_63 :args (_let_62 true _let_61)))) (let ((_let_67 (REFL :args (_let_60)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 5)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_64)) :args ((or _let_31 _let_60))) _let_66 :args (_let_31 true _let_60)))) (let ((_let_69 (or _let_49 _let_17))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 7)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_64)) :args ((or _let_48 _let_60))) _let_66 :args (_let_48 true _let_60)))) (let ((_let_71 (tptp.ssList _let_18))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_51 _let_72 _let_32 _let_22))) (let ((_let_74 (forall ((U $$unsorted) (BOUND_VARIABLE_4882 $$unsorted) (BOUND_VARIABLE_4880 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4880)) (not (tptp.ssList BOUND_VARIABLE_4882)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4880) BOUND_VARIABLE_4882) (tptp.app U (tptp.app BOUND_VARIABLE_4880 BOUND_VARIABLE_4882))))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (_let_74))) (let ((_let_77 ((tptp.app (tptp.app U BOUND_VARIABLE_4880) BOUND_VARIABLE_4882)))) (let ((_let_78 (not _let_11))) (let ((_let_79 (or _let_78 _let_57 _let_71))) (let ((_let_80 (forall ((U $$unsorted) (BOUND_VARIABLE_3350 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3350)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3350 U)))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 ((tptp.cons BOUND_VARIABLE_3350 U)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 1)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_64)) :args ((or _let_56 _let_60))) _let_66 :args (_let_56 true _let_60)))) (let ((_let_85 (ASSUME :args (_let_11)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_78 _let_57 _let_71 (not _let_79)))) _let_85 _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_82)) _let_81 :args (_let_79 false _let_80)) :args (_let_71 false _let_11 false _let_56 false _let_79)))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 4)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_64)) :args ((or _let_50 _let_60))) _let_66 :args (_let_50 true _let_60)))) (let ((_let_88 (tptp.ssList _let_23))) (let ((_let_89 (not _let_88))) (let ((_let_90 (tptp.ssList _let_21))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_91 _let_89 _let_49 _let_27))) (let ((_let_93 (or _let_78 _let_55 _let_88))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 2)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_64)) :args ((or _let_54 _let_60))) _let_66 :args (_let_54 true _let_60)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_78 _let_55 _let_88 (not _let_93)))) _let_85 _let_94 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_82)) _let_81 :args (_let_93 false _let_80)) :args (_let_88 false _let_11 false _let_54 false _let_93)))) (let ((_let_96 (tptp.ssList _let_20))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_97 _let_32 _let_90))) (let ((_let_99 (forall ((U $$unsorted) (BOUND_VARIABLE_3608 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3608)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3608)))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (_let_99))) (let ((_let_102 ((tptp.app U BOUND_VARIABLE_3608)))) (let ((_let_103 (or _let_51 _let_72 _let_96))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_32 _let_97 _let_90 (not _let_98)))) _let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_51 _let_72 _let_96 (not _let_103)))) _let_87 _let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_101)) _let_100 :args (_let_103 false _let_99)) :args (_let_96 false _let_50 false _let_71 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (_let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_101)) _let_100 :args (_let_98 false _let_99)) :args (_let_90 false _let_31 false _let_96 false _let_98)))) (let ((_let_105 (or _let_32 _let_78 _let_57 _let_28))) (let ((_let_106 (forall ((U $$unsorted) (BOUND_VARIABLE_3650 $$unsorted) (BOUND_VARIABLE_3648 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3648)) (not (tptp.ssItem BOUND_VARIABLE_3650)) (= (tptp.cons BOUND_VARIABLE_3650 (tptp.app BOUND_VARIABLE_3648 U)) (tptp.app (tptp.cons BOUND_VARIABLE_3650 BOUND_VARIABLE_3648) U)))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (_let_106))) (let ((_let_109 (or _let_49 _let_78 _let_55 _let_29))) (let ((_let_110 (not _let_30))) (let ((_let_111 (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_112 (or _let_57 _let_55 _let_111 _let_51 _let_32 _let_49 _let_110))) (let ((_let_113 (forall ((V $$unsorted) (BOUND_VARIABLE_3050 $$unsorted) (BOUND_VARIABLE_3048 $$unsorted) (BOUND_VARIABLE_3046 $$unsorted) (BOUND_VARIABLE_3044 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_3044)) (tptp.lt V BOUND_VARIABLE_3044) (not (tptp.ssList BOUND_VARIABLE_3050)) (not (tptp.ssList BOUND_VARIABLE_3046)) (not (tptp.ssList 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false _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_51 _let_32 _let_72 _let_22 (not _let_73)))) _let_87 _let_68 _let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_18 QUANTIFIERS_INST_E_MATCHING _let_77)) :args _let_76)) _let_75 :args (_let_73 false _let_74)) :args (_let_22 false _let_50 false _let_31 false _let_71 false _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_49 _let_17 (not _let_69)))) _let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_69 false _let_34)) :args (_let_17 false _let_48 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_15 (not _let_33)))) _let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_36)) _let_35 :args (_let_33 false _let_34)) :args (_let_15 false _let_31 false _let_33)) :args (false true _let_30 false _let_29 false _let_28 false _let_27 false _let_22 false _let_17 false _let_15)) :args ((forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))) (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) _let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_12 _let_11 _let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) _let_9 _let_8 _let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) (not (tptp.singletonP tptp.nil)) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))) (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) _let_6 (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))) (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) _let_5 _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) _let_3 _let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 44.38/44.62  )
% 44.38/44.62  % SZS output end Proof for SWC152+1
% 44.38/44.62  % cvc5---1.0.5 exiting
% 44.38/44.62  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------