TSTP Solution File: SWC396+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC396+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 20:25:19 EDT 2023
% Result : Theorem 20.58s 20.89s
% Output : Proof 20.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC396+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n025.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 18:42:09 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 20.58/20.89 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.TlX1phvOii/cvc5---1.0.5_19729.p...
% 20.58/20.89 ------- get file name : TPTP file name is SWC396+1
% 20.58/20.89 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19729.smt2...
% 20.58/20.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 20.58/20.89 --- Run --no-e-matching --full-saturate-quant at 5...
% 20.58/20.89 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.58/20.89 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 20.58/20.89 % SZS status Theorem for SWC396+1
% 20.58/20.89 % SZS output start Proof for SWC396+1
% 20.58/20.89 (
% 20.58/20.89 (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)) (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (or (not (tptp.memberP U Y)) (tptp.memberP V Y)))) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (tptp.neq X tptp.nil) (or (not (tptp.neq W tptp.nil)) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (not (= X Z)) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (exists ((X2 $$unsorted)) (and (tptp.ssList X2) (= (tptp.tl W) X1) (= (tptp.app X1 X2) Z) (exists ((X3 $$unsorted)) (and (tptp.ssItem X3) (= (tptp.cons X3 tptp.nil) X2) (= (tptp.hd W) X3) (tptp.neq tptp.nil W))) (tptp.neq tptp.nil W))))))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))))) (let ((_let_4 (forall ((U $$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))))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_9 (tptp.ssList tptp.nil))) (let ((_let_10 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_12 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_14 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (tptp.cons _let_14 _let_13))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_15))) (let ((_let_17 (tptp.memberP _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (not _let_12))) (let ((_let_20 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.cons _let_14 tptp.nil))) (let ((_let_23 (tptp.app _let_13 _let_22))) (let ((_let_24 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_23))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.ssList _let_23))) (let ((_let_27 (tptp.ssList _let_13))) (let ((_let_28 (tptp.ssList _let_22))) (let ((_let_29 (tptp.ssItem _let_14))) (let ((_let_30 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_31 (and _let_30 _let_29 _let_28 _let_27 _let_26 _let_25))) (let ((_let_32 (not (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil)))) (let ((_let_33 (or _let_32 _let_31))) (let ((_let_34 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_35 (and _let_34 _let_33))) (let ((_let_36 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_37 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (not _let_37))) (let ((_let_39 (and _let_38 _let_36))) (let ((_let_40 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_41 _let_39 _let_35 _let_21 _let_19 _let_18))) (let ((_let_45 (forall ((U $$unsorted) (BOUND_VARIABLE_5433 $$unsorted) (BOUND_VARIABLE_5431 $$unsorted)) (let ((_let_1 (tptp.hd U))) (let ((_let_2 (tptp.cons _let_1 tptp.nil))) (let ((_let_3 (tptp.tl U))) (let ((_let_4 (tptp.app _let_3 _let_2))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5431)) (and (not (= tptp.nil U)) (= tptp.nil BOUND_VARIABLE_5431)) (and (tptp.neq BOUND_VARIABLE_5431 tptp.nil) (or (not (tptp.neq U tptp.nil)) (and (tptp.neq tptp.nil U) (tptp.ssItem _let_1) (tptp.ssList _let_2) (tptp.ssList _let_3) (tptp.ssList _let_4) (not (= _let_4 BOUND_VARIABLE_5431))))) (not (tptp.ssItem BOUND_VARIABLE_5433)) (not (tptp.memberP U BOUND_VARIABLE_5433)) (tptp.memberP BOUND_VARIABLE_5431 BOUND_VARIABLE_5433))))))))) (let ((_let_46 (not _let_44))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (or))) (let ((_let_49 (not _let_45))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_47) :args (_let_49)) (REWRITE :args ((=> _let_49 (not (or _let_43 _let_41 _let_39 (and _let_34 (or _let_32 (and _let_30 _let_29 _let_28 _let_27 _let_26 (not (= _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) _let_21 _let_19 _let_18))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_45))) (REFL :args (_let_46)) :args _let_48)) _let_47 :args (_let_46 true _let_45)))) (let ((_let_51 (REFL :args (_let_44)))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 5)) (CONG _let_51 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_12))) :args _let_48)) :args ((or _let_12 _let_44))) _let_50 :args (_let_12 true _let_44)))) (let ((_let_53 (or _let_43 _let_37 _let_16))) (let ((_let_54 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (tptp.memberP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_21 _let_57))) (let ((_let_59 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.memberP tptp.nil U)))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 4)) (CONG _let_51 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_48)) :args ((or _let_20 _let_44))) _let_50 :args (_let_20 true _let_44)))) (let ((_let_62 (REFL :args (_let_19)))) (let ((_let_63 (ASSUME :args (_let_12)))) (let ((_let_64 (TRUE_INTRO _let_63))) (let ((_let_65 (APPLY_UF tptp.memberP))) (let ((_let_66 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_67 (ASSUME :args (_let_37)))) (let ((_let_68 (ASSUME :args (_let_57)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_63 _let_67 _let_68) :args (_let_37 _let_12 _let_57)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_68)) (CONG (SYMM (SYMM _let_67)) _let_66 :args _let_65) _let_64)) :args (_let_12 _let_37 _let_57)) :args ((not (and _let_37 _let_12 _let_57)) SB_LITERAL))) (CONG (REFL :args (_let_38)) _let_62 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_21 _let_57 (not _let_58)))) _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_57 false _let_20 false _let_58)) _let_52 :args (_let_38 true _let_56 false _let_12)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_44 0)) (CONG _let_51 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_48)) :args ((or _let_42 _let_44))) _let_50 :args (_let_42 true _let_44)))) (let ((_let_71 (tptp.memberP _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_72 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_14))) (let ((_let_73 (or _let_72 _let_71))) (let ((_let_74 (= _let_17 _let_73))) (let ((_let_75 (not _let_17))) (let ((_let_76 (not _let_27))) (let ((_let_77 (not _let_29))) (let ((_let_78 (or _let_21 _let_77 _let_76 _let_74))) (let ((_let_79 (forall ((U $$unsorted) (BOUND_VARIABLE_3938 $$unsorted) (BOUND_VARIABLE_3936 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_3936)) (not (tptp.ssList BOUND_VARIABLE_3938)) (= (tptp.memberP (tptp.cons BOUND_VARIABLE_3936 BOUND_VARIABLE_3938) U) (or (= U BOUND_VARIABLE_3936) (tptp.memberP BOUND_VARIABLE_3938 U))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_79))) (let ((_let_82 (or _let_43 _let_37 _let_27))) (let ((_let_83 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssList (tptp.tl U)))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_43 _let_37 _let_27 (not _let_82)))) _let_70 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args _let_85) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_27 false _let_42 true _let_37 false _let_82)))) (let ((_let_87 (or _let_43 _let_37 _let_29))) (let ((_let_88 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_43 _let_37 _let_29 (not _let_87)))) _let_70 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args _let_85) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_29 false _let_42 true _let_37 false _let_87)))) (let ((_let_91 (not _let_73))) (let ((_let_92 (tptp.memberP _let_22 _let_14))) (let ((_let_93 (tptp.memberP _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_94 (not _let_72))) (let ((_let_95 (not _let_9))) (let ((_let_96 (or _let_77 _let_77 _let_95 _let_92))) (let ((_let_97 (ASSUME :args (_let_9)))) (let ((_let_98 (or _let_71 _let_93))) (let ((_let_99 (not _let_93))) (let ((_let_100 (tptp.memberP _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_101 (= _let_100 _let_98))) (let ((_let_102 (not _let_98))) (let ((_let_103 (not _let_28))) (let ((_let_104 (or _let_21 _let_76 _let_103 _let_101))) (let ((_let_105 (forall ((U $$unsorted) (BOUND_VARIABLE_3889 $$unsorted) (BOUND_VARIABLE_3887 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList BOUND_VARIABLE_3887)) (not (tptp.ssList BOUND_VARIABLE_3889)) (= (tptp.memberP (tptp.app BOUND_VARIABLE_3887 BOUND_VARIABLE_3889) U) (or (tptp.memberP BOUND_VARIABLE_3887 U) (tptp.memberP BOUND_VARIABLE_3889 U))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (or _let_95 _let_77 _let_28))) (let ((_let_108 (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_109 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_95 _let_28 _let_77 (not _let_107)))) _let_97 _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (tptp.nil _let_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_108))) _let_109 :args (_let_107 false _let_108)) :args (_let_28 false _let_9 false _let_29 false _let_107)))) (let ((_let_111 (not _let_100))) (let ((_let_112 (or _let_76 _let_103 _let_26))) (let ((_let_113 (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_114 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (= _let_38 _let_30))) (let ((_let_116 (or _let_95 _let_43 _let_115))) (let ((_let_117 (forall ((U $$unsorted) (BOUND_VARIABLE_3301 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3301)) (= (tptp.neq U BOUND_VARIABLE_3301) (not (= U BOUND_VARIABLE_3301))))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT 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:args (_let_24 _let_130))) :args (true _let_131)) (CONG (REFL :args (_let_25)) (MACRO_SR_PRED_INTRO :args ((= (not _let_130) _let_18))) (REFL :args (_let_111)) :args _let_48)) :args ((or _let_18 _let_25 _let_111))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_44 6)) _let_50 :args (_let_130 true _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_129) (CONG (REFL :args _let_129) (REFL :args (_let_128)) (REFL :args (_let_77)) (REFL :args (_let_103)) (REFL :args (_let_76)) (REFL :args (_let_127)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_48)) :args ((or _let_24 _let_31 _let_128 _let_77 _let_103 _let_76 _let_127))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 1)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_35)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_44 3)) _let_50 :args ((not _let_35) true _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_123)) (CONG (REFL :args (_let_126)) 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(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)))))))))) (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_2 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (forall ((U $$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))))))))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 20.58/20.90 )
% 20.58/20.90 % SZS output end Proof for SWC396+1
% 20.58/20.90 % cvc5---1.0.5 exiting
% 20.58/20.90 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------