TSTP Solution File: SWC376+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC376+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 20:25:10 EDT 2023
% Result : Theorem 20.72s 20.91s
% Output : Proof 20.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWC376+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n006.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon Aug 28 16:57:36 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 20.72/20.91 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.xhkf0mwilg/cvc5---1.0.5_24979.p...
% 20.72/20.91 ------- get file name : TPTP file name is SWC376+1
% 20.72/20.91 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24979.smt2...
% 20.72/20.91 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 20.72/20.91 --- Run --no-e-matching --full-saturate-quant at 5...
% 20.72/20.91 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.72/20.91 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 20.72/20.91 % SZS status Theorem for SWC376+1
% 20.72/20.91 % SZS output start Proof for SWC376+1
% 20.72/20.91 (
% 20.72/20.91 (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 $$unsorted)) (let ((_let_1 (tptp.memberP U Y))) (let ((_let_2 (tptp.memberP V Y))) (=> (tptp.ssItem Y) (or (and (not _let_2) (not _let_1)) (and _let_2 _let_1)))))) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (tptp.neq X tptp.nil) (or (not (tptp.neq W tptp.nil)) (exists ((Z $$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 $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_12 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_12))) (let ((_let_14 (tptp.memberP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (or _let_13 _let_14))) (let ((_let_16 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (tptp.memberP _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (or _let_13 _let_17))) (let ((_let_19 (tptp.cons _let_12 _let_16))) (let ((_let_20 (tptp.memberP _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (= _let_20 _let_18))) (let ((_let_22 (tptp.ssList _let_16))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.ssItem _let_12))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23 _let_21))) (let ((_let_29 (forall ((U $$unsorted) (BOUND_VARIABLE_3941 $$unsorted) (BOUND_VARIABLE_3939 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_3939)) (not (tptp.ssList BOUND_VARIABLE_3941)) (= (tptp.memberP (tptp.cons BOUND_VARIABLE_3939 BOUND_VARIABLE_3941) U) (or (= U BOUND_VARIABLE_3939) (tptp.memberP BOUND_VARIABLE_3941 U))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (_let_29))) (let ((_let_32 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_22))) (let ((_let_36 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssList (tptp.tl U)))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_39 (tptp.neq tptp.nil tptp.nil))) (let ((_let_40 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_41 (tptp.cons _let_12 tptp.nil))) (let ((_let_42 (tptp.app _let_16 _let_41))) (let ((_let_43 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_42))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.ssList _let_42))) (let ((_let_46 (tptp.ssList _let_41))) (let ((_let_47 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_48 (and _let_47 _let_24 _let_46 _let_22 _let_45 _let_44))) (let ((_let_49 (not _let_40))) (let ((_let_50 (or _let_49 _let_48))) (let ((_let_51 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_52 (and _let_51 _let_50))) (let ((_let_53 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_54 (not _let_53))) (let ((_let_55 (= _let_51 _let_54))) (let ((_let_56 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_57 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_58 (not _let_57))) (let ((_let_59 (not _let_56))) (let ((_let_60 (and _let_59 _let_58))) (let ((_let_61 (not _let_32))) (let ((_let_62 (not _let_39))) (let ((_let_63 (not _let_9))) (let ((_let_64 (or _let_63 _let_63 _let_62))) (let ((_let_65 (forall ((U $$unsorted) (BOUND_VARIABLE_3304 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3304)) (= (tptp.neq U BOUND_VARIABLE_3304) (not (= U BOUND_VARIABLE_3304))))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (_let_65))) (let ((_let_68 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (tptp.nil tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_67))))) (let ((_let_69 (ASSUME :args (_let_9)))) (let ((_let_70 (REORDERING (FACTORING (CNF_OR_POS :args (_let_64))) :args ((or _let_63 _let_62 (not _let_64)))))) (let ((_let_71 (or))) (let ((_let_72 (REFL :args (_let_61)))) (let ((_let_73 (and _let_32 _let_62))) (let ((_let_74 (ASSUME :args (_let_62)))) (let ((_let_75 (ASSUME :args (_let_32)))) (let ((_let_76 (SYMM _let_75))) (let ((_let_77 (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_73)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_74 _let_75) (SCOPE (FALSE_ELIM (TRANS (CONG _let_76 (REFL :args (tptp.nil)) :args (APPLY_UF tptp.neq)) (FALSE_INTRO _let_74))) :args (_let_62 _let_32))) :args (_let_32 _let_62))) :args (true _let_73)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_39))) (REFL :args (_let_49)) :args _let_71)) :args ((or _let_61 _let_49 _let_39))))) (let ((_let_78 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 0)) (CONG (REFL :args (_let_50)) (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_40))) :args _let_71)) :args ((or _let_40 _let_50))))) (let ((_let_79 (and _let_56 _let_57))) (let ((_let_80 (and _let_61 _let_53))) (let ((_let_81 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_82 (not _let_81))) (let ((_let_83 (or _let_34 _let_82 _let_80 _let_52 _let_27 _let_60 _let_79))) (let ((_let_84 (forall ((U $$unsorted) (BOUND_VARIABLE_5439 $$unsorted) (BOUND_VARIABLE_5437 $$unsorted)) (let ((_let_1 (tptp.memberP U BOUND_VARIABLE_5439))) (let ((_let_2 (tptp.memberP BOUND_VARIABLE_5437 BOUND_VARIABLE_5439))) (let ((_let_3 (tptp.hd U))) (let ((_let_4 (tptp.cons _let_3 tptp.nil))) (let ((_let_5 (tptp.tl U))) (let ((_let_6 (tptp.app _let_5 _let_4))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5437)) (and (not (= tptp.nil U)) (= tptp.nil BOUND_VARIABLE_5437)) (and (tptp.neq BOUND_VARIABLE_5437 tptp.nil) (or (not (tptp.neq U tptp.nil)) (and (tptp.neq tptp.nil U) (tptp.ssItem _let_3) (tptp.ssList _let_4) (tptp.ssList _let_5) (tptp.ssList _let_6) (not (= _let_6 BOUND_VARIABLE_5437))))) (not (tptp.ssItem BOUND_VARIABLE_5439)) (and (not _let_2) (not _let_1)) (and _let_2 _let_1))))))))))) (let ((_let_85 (not _let_83))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (not _let_84))) (let ((_let_88 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_86) :args (_let_87)) (REWRITE :args ((=> _let_87 (not (or _let_34 _let_82 _let_80 (and _let_51 (or _let_49 (and _let_47 _let_24 _let_46 _let_22 _let_45 (not (= _let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) _let_27 _let_60 _let_79))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_84))) (REFL :args (_let_85)) :args _let_71)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST _let_88 _let_86 :args (_let_85 true _let_84)))) (let ((_let_90 (CNF_OR_NEG :args (_let_83 3)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST _let_90 _let_89 :args ((not _let_52) true _let_83)))) (let ((_let_92 (CNF_AND_NEG :args (_let_52)))) (let ((_let_93 (or _let_82 _let_63 _let_55))) (let ((_let_94 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_67))))) (let ((_let_95 (REFL :args (_let_83)))) (let ((_let_96 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_83 1)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_81))) :args _let_71)) :args ((or _let_81 _let_83))))) (let ((_let_97 (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_63 _let_82 _let_55 (not _let_93)))))) (let ((_let_98 (MACRO_RESOLUTION_TRUST _let_97 _let_69 (MACRO_RESOLUTION_TRUST _let_96 _let_89 :args (_let_81 true _let_83)) (MACRO_RESOLUTION_TRUST _let_94 _let_66 :args (_let_93 false _let_65)) :args (_let_55 false _let_9 false _let_81 false _let_93)))) (let ((_let_99 (not _let_55))) (let ((_let_100 (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_55)) (CONG (REFL :args (_let_99)) (REFL :args (_let_51)) (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_71)) :args ((or _let_53 _let_51 _let_99))))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_83 6)) _let_89 :args ((not _let_79) true _let_83)))) (let ((_let_102 (REORDERING (CNF_AND_NEG :args (_let_79)) :args ((or _let_59 _let_58 _let_79))))) (let ((_let_103 (and _let_32 _let_53 _let_56))) (let ((_let_104 (ASSUME :args (_let_56)))) (let ((_let_105 (TRUE_INTRO _let_104))) (let ((_let_106 (APPLY_UF tptp.memberP))) (let ((_let_107 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_108 (ASSUME :args (_let_53)))) (let ((_let_109 (CONG (TRANS _let_76 (SYMM (SYMM _let_108))) _let_107 :args _let_106))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_83 5)) _let_89 :args ((not _let_60) true _let_83)))) (let ((_let_111 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))))) (let ((_let_112 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_56))))) (let ((_let_113 (_let_60))) (let ((_let_114 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_113) (CONG (REFL :args _let_113) _let_112 _let_111 :args _let_71)) :args ((or _let_56 _let_57 _let_60))))) (let ((_let_115 (_let_58))) (let ((_let_116 (REFL :args (_let_54)))) (let ((_let_117 (and _let_32 _let_53 _let_59))) (let ((_let_118 (ASSUME :args (_let_59)))) (let ((_let_119 (FALSE_INTRO _let_118))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_117)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_118 _let_108 _let_75) (SCOPE (FALSE_ELIM (TRANS _let_109 _let_119)) :args (_let_59 _let_53 _let_32))) :args (_let_32 _let_53 _let_59))) :args (true _let_117)) (CONG _let_72 _let_116 _let_112 (REFL :args _let_115) :args _let_71)) :args ((or _let_61 _let_56 _let_58 _let_54))) _let_114 _let_110 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_103)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_104 _let_108 _let_75) (SCOPE (TRUE_ELIM (TRANS _let_109 _let_105)) :args (_let_56 _let_53 _let_32))) :args (_let_32 _let_53 _let_56))) :args (true _let_103)) :args ((or _let_61 _let_59 _let_57 _let_54))) _let_102 _let_101 _let_100 _let_97 _let_96 _let_94 _let_92 _let_90 _let_88 _let_86 _let_78 _let_77 _let_70 _let_69 _let_68 _let_66 :args ((or _let_61 _let_59) true _let_57 true _let_79 false _let_53 false _let_55 false _let_81 false _let_93 true _let_51 true _let_52 true _let_83 true _let_84 false _let_50 true _let_40 true _let_39 false _let_9 false _let_64 false _let_65)) _let_100 _let_98 _let_92 _let_91 _let_78 _let_77 (MACRO_RESOLUTION_TRUST _let_70 _let_69 (MACRO_RESOLUTION_TRUST _let_68 _let_66 :args (_let_64 false _let_65)) :args (_let_62 false _let_9 false _let_64)) :args (_let_61 false _let_57 true _let_60 true _let_56 false _let_53 false _let_55 true _let_51 true _let_52 false _let_50 true _let_40 true _let_39)))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_83 0)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_71)) :args ((or _let_33 _let_83))) _let_89 :args (_let_33 true _let_83)))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_32 _let_22 (not _let_35)))) _let_121 _let_120 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args _let_38) :args (_let_36))) _let_37 :args (_let_35 false _let_36)) :args (_let_22 false _let_33 true _let_32 false _let_35)))) (let ((_let_123 (or _let_34 _let_32 _let_24))) (let ((_let_124 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_34 _let_32 _let_24 (not _let_123)))) _let_121 _let_120 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_125 :args _let_38) :args (_let_124))) _let_125 :args (_let_123 false _let_124)) :args (_let_24 false _let_33 true _let_32 false _let_123)))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_83 4)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_71)) :args ((or _let_26 _let_83))) _let_89 :args (_let_26 true _let_83)))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_25 _let_23 _let_21 (not _let_28)))) _let_127 _let_126 _let_122 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_16 _let_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_31)) _let_30 :args (_let_28 false _let_29)) :args (_let_21 false _let_26 false _let_24 false _let_22 false _let_28)))) (let ((_let_129 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_19))) (let ((_let_130 (or _let_34 _let_32 _let_129))) (let ((_let_131 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let 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((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))) (forall ((U $$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))))))))))))) _let_11 _let_10 _let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (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 $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) _let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) _let_6 (forall ((U $$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)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))) (forall ((U $$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)))))) _let_5 _let_4 _let_3 (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)))))))))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 20.72/20.91 )
% 20.72/20.91 % SZS output end Proof for SWC376+1
% 20.72/20.91 % cvc5---1.0.5 exiting
% 20.72/20.92 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------