%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC305+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 20:24:38 EDT 2023

% Result   : Theorem 35.05s 35.24s
% Output   : Proof 35.05s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem    : SWC305+1 : TPTP v8.1.2. Released v2.4.0.
% 0.02/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 16:50:40 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 35.05/35.24  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.8e3Ip2UEFl/cvc5---1.0.5_31774.p...
% 35.05/35.24  ------- get file name : TPTP file name is SWC305+1
% 35.05/35.24  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31774.smt2...
% 35.05/35.24  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 35.05/35.24  --- Run --no-e-matching --full-saturate-quant at 5...
% 35.05/35.24  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 35.05/35.24  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 35.05/35.24  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 35.05/35.24  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 35.05/35.24  % SZS status Theorem for SWC305+1
% 35.05/35.24  % SZS output start Proof for SWC305+1
% 35.05/35.24  (
% 35.05/35.24  (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)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.frontsegP X W)) (not (tptp.strictorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.frontsegP X Y) (tptp.segmentP Y W) (tptp.strictorderedP Y))) (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (forall ((X1 $$unsorted)) (=> (tptp.ssItem X1) (forall ((X2 $$unsorted)) (=> (tptp.ssList X2) (forall ((X3 $$unsorted)) (=> (tptp.ssList X3) (forall ((X4 $$unsorted)) (=> (tptp.ssList X4) (or (not (= (tptp.app (tptp.app (tptp.app (tptp.app X2 (tptp.cons Z tptp.nil)) X3) (tptp.cons X1 tptp.nil)) X4) U)) (not (tptp.lt X1 Z))))))))))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_8 (tptp.ssList tptp.nil))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_10 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))))) (let ((_let_11 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_11))) (let ((_let_13 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil))) (let ((_let_14 (tptp.app _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_15 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_13))) (let ((_let_16 (tptp.app _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (= _let_16 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_14)))) (let ((_let_18 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_19 (tptp.app _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_20 (tptp.app (tptp.app _let_16 _let_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_21 (= _let_20 (tptp.app _let_16 _let_19)))) (let ((_let_22 (= _let_14 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_11)))) (let ((_let_23 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_24 (= _let_19 _let_23))) (let ((_let_25 (= _let_20 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_23)))) (let ((_let_26 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_12))) (let ((_let_29 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_38 (not _let_37))) (let ((_let_39 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.strictorderedP _let_20))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.ssList _let_20))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42 _let_40 _let_38 _let_36 _let_34 _let_27 _let_32 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20)) (not (forall ((Y $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (or (not (tptp.ssList Y)) (not (tptp.neq _let_1 Y)) (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)) (not (tptp.segmentP Y _let_1)) (not (tptp.strictorderedP Y))))))))) (let ((_let_46 (forall ((BOUND_VARIABLE_5464 $$unsorted) (BOUND_VARIABLE_5441 $$unsorted) (BOUND_VARIABLE_5439 $$unsorted) (BOUND_VARIABLE_5437 $$unsorted) (BOUND_VARIABLE_5435 $$unsorted) (BOUND_VARIABLE_5433 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5435 (tptp.cons BOUND_VARIABLE_5433 tptp.nil)) BOUND_VARIABLE_5439) (tptp.cons BOUND_VARIABLE_5441 tptp.nil)) BOUND_VARIABLE_5437))) (or (not (tptp.ssList _let_1)) (not (tptp.strictorderedP _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5433)) (not (tptp.ssItem BOUND_VARIABLE_5441)) (not (tptp.lt BOUND_VARIABLE_5441 BOUND_VARIABLE_5433)) (not (tptp.ssList BOUND_VARIABLE_5435)) (not (tptp.ssList BOUND_VARIABLE_5439)) (not (tptp.ssList BOUND_VARIABLE_5437)) (not (tptp.ssList BOUND_VARIABLE_5464)) (not (tptp.frontsegP BOUND_VARIABLE_5464 _let_1)) (not (forall ((Y $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5435 (tptp.cons BOUND_VARIABLE_5433 tptp.nil)) BOUND_VARIABLE_5439) (tptp.cons BOUND_VARIABLE_5441 tptp.nil)) BOUND_VARIABLE_5437))) (or (not (tptp.ssList Y)) (not (tptp.neq _let_1 Y)) (not (tptp.frontsegP BOUND_VARIABLE_5464 Y)) (not (tptp.segmentP Y _let_1)) (not (tptp.strictorderedP Y))))))))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or))) (let ((_let_50 (not _let_46))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_48) :args (_let_50))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_46))) (REFL :args (_let_47)) :args _let_49)) _let_48 :args (_let_47 true _let_46)))) (let ((_let_52 (REFL :args (_let_45)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 6)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_49)) :args ((or _let_26 _let_45))) _let_51 :args (_let_26 true _let_45)))) (let ((_let_54 (tptp.ssList _let_13))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_34 _let_55 _let_27 _let_17))) (let ((_let_57 (forall ((U $$unsorted) (BOUND_VARIABLE_4856 $$unsorted) (BOUND_VARIABLE_4854 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4854)) (not (tptp.ssList BOUND_VARIABLE_4856)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4854) BOUND_VARIABLE_4856) (tptp.app U (tptp.app BOUND_VARIABLE_4854 BOUND_VARIABLE_4856))))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (_let_57))) (let ((_let_60 ((tptp.app (tptp.app U BOUND_VARIABLE_4854) BOUND_VARIABLE_4856)))) (let ((_let_61 (not _let_8))) (let ((_let_62 (or _let_61 _let_40 _let_54))) (let ((_let_63 (forall ((U $$unsorted) (BOUND_VARIABLE_3324 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3324)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3324 U)))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 2)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_49)) :args ((or _let_39 _let_45))) _let_51 :args (_let_39 true _let_45)))) (let ((_let_67 (ASSUME :args (_let_8)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_61 _let_40 _let_54 (not _let_62)))) _let_67 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_65)) _let_64 :args (_let_62 false _let_63)) :args (_let_54 false _let_8 false _let_39 false _let_62)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 5)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_49)) :args ((or _let_33 _let_45))) _let_51 :args (_let_33 true _let_45)))) (let ((_let_70 (tptp.ssList _let_18))) (let ((_let_71 (not _let_70))) (let ((_let_72 (tptp.ssList _let_16))) (let ((_let_73 (not _let_72))) (let ((_let_74 (or _let_73 _let_71 _let_32 _let_21))) (let ((_let_75 (tptp.ssList _let_15))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_76 _let_27 _let_72))) (let ((_let_78 (forall ((U $$unsorted) (BOUND_VARIABLE_3582 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3582)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3582)))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 (or _let_34 _let_55 _let_75))) (let ((_let_82 (or _let_61 _let_38 _let_70))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 3)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_49)) :args ((or _let_37 _let_45))) _let_51 :args (_let_37 true _let_45)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 7)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_49)) :args ((or _let_31 _let_45))) _let_51 :args (_let_31 true _let_45)))) (let ((_let_85 (or _let_27 _let_61 _let_40 _let_22))) (let ((_let_86 (forall ((U $$unsorted) (BOUND_VARIABLE_3624 $$unsorted) (BOUND_VARIABLE_3622 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3622)) (not (tptp.ssItem BOUND_VARIABLE_3624)) (= (tptp.cons BOUND_VARIABLE_3624 (tptp.app BOUND_VARIABLE_3622 U)) (tptp.app (tptp.cons BOUND_VARIABLE_3624 BOUND_VARIABLE_3622) U)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (or _let_32 _let_38 _let_24))) (let ((_let_89 (forall ((U $$unsorted) (BOUND_VARIABLE_4812 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4812)) (= (tptp.cons BOUND_VARIABLE_4812 U) (tptp.app (tptp.cons BOUND_VARIABLE_4812 tptp.nil) U)))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (not _let_25))) (let ((_let_92 (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_93 (or _let_40 _let_38 _let_92 _let_34 _let_27 _let_32 _let_91))) (let ((_let_94 (forall ((V $$unsorted) (BOUND_VARIABLE_3024 $$unsorted) (BOUND_VARIABLE_3022 $$unsorted) (BOUND_VARIABLE_3020 $$unsorted) (BOUND_VARIABLE_3018 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_3018)) (tptp.lt V BOUND_VARIABLE_3018) (not (tptp.ssList BOUND_VARIABLE_3024)) (not (tptp.ssList BOUND_VARIABLE_3020)) (not (tptp.ssList BOUND_VARIABLE_3022)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_3024 (tptp.cons V BOUND_VARIABLE_3020)) (tptp.cons BOUND_VARIABLE_3018 BOUND_VARIABLE_3022)) (tptp.app (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))) (let ((_let_95 (= _let_41 _let_94))) (let ((_let_96 (or _let_44 _let_95))) (let ((_let_97 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.strictorderedP U) (forall ((V $$unsorted) (BOUND_VARIABLE_3024 $$unsorted) (BOUND_VARIABLE_3022 $$unsorted) (BOUND_VARIABLE_3020 $$unsorted) (BOUND_VARIABLE_3018 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_3018)) (tptp.lt V BOUND_VARIABLE_3018) (not (tptp.ssList BOUND_VARIABLE_3024)) (not (tptp.ssList BOUND_VARIABLE_3020)) (not (tptp.ssList BOUND_VARIABLE_3022)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_3024 (tptp.cons V BOUND_VARIABLE_3020)) (tptp.cons BOUND_VARIABLE_3018 BOUND_VARIABLE_3022))))))))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (_let_94))) (let ((_let_100 (not _let_92))) (let ((_let_101 (or _let_38 _let_40 _let_36 _let_100))) (let ((_let_102 (forall ((U $$unsorted) (BOUND_VARIABLE_3768 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_3768)) (not (tptp.lt U BOUND_VARIABLE_3768)) (not (tptp.lt BOUND_VARIABLE_3768 U)))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (ASSUME :args (_let_91)))) (let ((_let_105 (APPLY_UF tptp.app))) (let ((_let_106 (ASSUME :args (_let_24)))) (let ((_let_107 (ASSUME :args (_let_12)))) (let ((_let_108 (ASSUME :args (_let_22)))) (let ((_let_109 (ASSUME :args (_let_17)))) (let ((_let_110 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_104 (MODUS_PONENS (AND_INTRO _let_107 _let_108 _let_109 _let_106 _let_110) (SCOPE (TRANS (SYMM (SYMM _let_110)) (CONG (TRANS (SYMM (SYMM _let_109)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (TRANS (SYMM (SYMM _let_108)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (SYMM _let_107) :args (APPLY_UF tptp.cons))) :args _let_105)) (SYMM (SYMM _let_106)) :args _let_105)) :args (_let_12 _let_22 _let_17 _let_24 _let_21)))) :args (_let_12 _let_17 _let_21 _let_22 _let_24 _let_91)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_25)))))) (FALSE_INTRO _let_104))) :args (_let_91 _let_25)) :args ((not (and _let_12 _let_17 _let_21 _let_22 _let_24 _let_91)) SB_LITERAL))) (CONG (REFL :args ((not _let_12))) (REFL :args ((not _let_17))) (REFL :args ((not _let_21))) (REFL 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$$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 $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_3 _let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) (forall ((U $$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))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$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)))))))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 35.05/35.25  )
% 35.05/35.25  % SZS output end Proof for SWC305+1
% 35.05/35.25  % cvc5---1.0.5 exiting
% 35.05/35.25  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------