%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC368+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 20:25:06 EDT 2023

% Result   : Theorem 39.43s 39.64s
% Output   : Proof 39.43s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWC368+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Aug 28 14:32:08 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 39.43/39.64  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.MWjI6zsO49/cvc5---1.0.5_27305.p...
% 39.43/39.64  ------- get file name : TPTP file name is SWC368+1
% 39.43/39.64  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27305.smt2...
% 39.43/39.64  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 39.43/39.64  --- Run --no-e-matching --full-saturate-quant at 5...
% 39.43/39.64  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 39.43/39.64  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 39.43/39.64  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 39.43/39.64  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 39.43/39.64  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 39.43/39.64  % SZS status Theorem for SWC368+1
% 39.43/39.64  % SZS output start Proof for SWC368+1
% 39.43/39.64  (
% 39.43/39.64  (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)) (tptp.segmentP V U) (and (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (or (not (= (tptp.cons Y tptp.nil) W)) (not (tptp.memberP X Y)) (exists ((Z $$unsorted)) (and (tptp.ssItem Z) (not (= Y Z)) (tptp.memberP X Z) (tptp.leq Z Y)))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (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 $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_9 (tptp.ssList tptp.nil))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))) (let ((_let_13 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14))) (let ((_let_16 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_17 (not _let_16))) (let ((_let_18 (not _let_15))) (let ((_let_19 (not _let_13))) (let ((_let_20 (or _let_19 _let_18 _let_17 (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (= Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Z)) (not (tptp.leq Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))))) (let ((_let_21 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (not _let_21))) (let ((_let_23 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22))) (let ((_let_26 (and _let_20 _let_25))) (let ((_let_27 (= tptp.nil (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_28 (= _let_21 _let_27))) (let ((_let_29 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_30 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_29))) (let ((_let_31 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_32 (or))) (let ((_let_33 (REFL :args (_let_25)))) (let ((_let_34 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_32)) :args ((or _let_21 _let_25))))) (let ((_let_35 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_36 _let_28))) (let ((_let_38 (forall ((U $$unsorted) (BOUND_VARIABLE_4860 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4860)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4860)) (and (= tptp.nil BOUND_VARIABLE_4860) (= tptp.nil U))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_41 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_36 _let_42 _let_40 _let_26))) (let ((_let_44 (forall ((U $$unsorted) (BOUND_VARIABLE_5417 $$unsorted) (BOUND_VARIABLE_5415 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5415)) (tptp.segmentP BOUND_VARIABLE_5415 U) (and (or (not (tptp.ssItem BOUND_VARIABLE_5417)) (not (= U (tptp.cons BOUND_VARIABLE_5417 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5415 BOUND_VARIABLE_5417)) (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (= Z BOUND_VARIABLE_5417) (not (tptp.memberP BOUND_VARIABLE_5415 Z)) (not (tptp.leq Z BOUND_VARIABLE_5417)))))) (or (not (= tptp.nil BOUND_VARIABLE_5415)) (not (= tptp.nil U)))))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (not _let_44))) (let ((_let_48 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_46) :args (_let_47))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_44))) (REFL :args (_let_45)) :args _let_32)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST _let_48 _let_46 :args (_let_45 true _let_44)))) (let ((_let_50 (REFL :args (_let_43)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 0)) (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_32)) :args ((or _let_35 _let_43))) _let_49 :args (_let_35 true _let_43)))) (let ((_let_52 (or _let_36 _let_30))) (let ((_let_53 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_36 _let_30 (not _let_52)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_53))) _let_54 :args (_let_52 false _let_53)) :args (_let_30 false _let_35 false _let_52)))) (let ((_let_56 (not _let_31))) (let ((_let_57 (not _let_9))) (let ((_let_58 (or _let_57 _let_36 _let_56))) (let ((_let_59 (forall ((W $$unsorted) (BOUND_VARIABLE_2309 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2309)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2309))))))) (let ((_let_60 (not _let_59))) (let ((_let_61 (= _let_40 _let_60))) (let ((_let_62 (or _let_42 _let_36 _let_61))) (let ((_let_63 (forall ((U $$unsorted) (BOUND_VARIABLE_2334 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2334)) (= (tptp.segmentP U BOUND_VARIABLE_2334) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2309 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2309)) (not (= U (tptp.app (tptp.app W BOUND_VARIABLE_2334) BOUND_VARIABLE_2309))))))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 1)) (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_32)) :args ((or _let_41 _let_43))))) (let ((_let_66 (MACRO_RESOLUTION_TRUST _let_65 _let_49 :args (_let_41 true _let_43)))) (let ((_let_67 (not _let_40))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 2)) _let_49 :args (_let_67 true _let_43)))) (let ((_let_69 (not _let_61))) (let ((_let_70 (_let_59))) (let ((_let_71 (ASSUME :args (_let_9)))) (let ((_let_72 (not _let_27))) (let ((_let_73 (not _let_30))) (let ((_let_74 (and _let_23 _let_30 _let_56))) (let ((_let_75 (ASSUME :args (_let_56)))) (let ((_let_76 (=))) (let ((_let_77 (APPLY_UF tptp.app))) (let ((_let_78 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_79 (ASSUME :args (_let_30)))) (let ((_let_80 (SYMM (SYMM _let_79)))) (let ((_let_81 (ASSUME :args (_let_23)))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 3)) _let_49 :args ((not _let_26) true _let_43)))) (let ((_let_83 (CNF_AND_NEG :args (_let_26)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST _let_83 _let_82 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_74)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_75 _let_81 _let_79) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM (SYMM _let_81)) (CONG _let_80 _let_78 :args _let_77) :args _let_76) (FALSE_INTRO _let_75))) :args (_let_56 _let_23 _let_30))) :args (_let_23 _let_30 _let_56))) :args (true _let_74)) (CONG (REFL :args (_let_24)) (REFL :args (_let_73)) (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_31))) (REFL :args (_let_72)) :args _let_32)) :args ((or _let_24 _let_73 _let_72 _let_31))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_36 _let_56 (not _let_58)))) _let_71 _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_70) :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_PROP)) :args _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_61)) (CONG (REFL :args (_let_69)) (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_32)) :args ((or _let_40 _let_59 _let_69))) _let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_36 _let_42 _let_61 (not _let_62)))) _let_51 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_61 false _let_35 false _let_41 false _let_62)) :args (_let_59 true _let_40 false _let_61)) :args (_let_58 false _let_59)) :args (_let_56 false _let_9 false _let_35 false _let_58)) _let_55 (REORDERING (CNF_EQUIV_POS1 :args (_let_28)) :args ((or _let_22 _let_27 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_37))) :args ((or _let_36 _let_28 (not _let_37)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.ssList U) false)) (not (= (tptp.ssList BOUND_VARIABLE_4860) false))))) :args (_let_38)))) _let_39 :args (_let_37 false _let_38)) :args (_let_28 false _let_35 false _let_37)) _let_34 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_33 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_32)) :args ((or _let_23 _let_25))) :args (_let_25 true _let_31 false _let_30 false _let_27 false _let_28 false _let_21 false _let_23)) :args ((not _let_20) true _let_26 false _let_25)))) (let ((_let_85 (REFL :args (_let_20)))) (let ((_let_86 (forall ((U $$unsorted) (BOUND_VARIABLE_2170 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2170)) (= (tptp.memberP U BOUND_VARIABLE_2170) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2144 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2144)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2170 BOUND_VARIABLE_2144)))))))))))) (let ((_let_87 (forall ((W $$unsorted) (BOUND_VARIABLE_2144 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2144)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2144)))))))) (let ((_let_88 (not _let_87))) (let ((_let_89 (= _let_16 _let_88))) (let ((_let_90 (or _let_42 _let_19 _let_89))) (let ((_let_91 (forall ((U $$unsorted) (BOUND_VARIABLE_3327 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3327)) (not (= U (tptp.cons BOUND_VARIABLE_3327 U))))))) (let ((_let_92 (= tptp.nil _let_14))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_57 _let_19 _let_93))) (let ((_let_95 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_96 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_95))) (let ((_let_97 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_96))) (let ((_let_98 (not _let_97))) (let ((_let_99 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_100 (not _let_99))) (let ((_let_101 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_102 (not _let_101))) (let ((_let_103 (or _let_102 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(tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$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)))))) _let_6 _let_5 (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_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) _let_3 _let_2 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 39.43/39.65  )
% 39.43/39.65  % SZS output end Proof for SWC368+1
% 39.43/39.65  % cvc5---1.0.5 exiting
% 39.43/39.65  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------