TSTP Solution File: SWC410+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC410+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 20:25:25 EDT 2023
% Result : Theorem 20.57s 20.86s
% Output : Proof 20.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SWC410+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n009.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 15:12:05 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 20.57/20.86 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Z1rCVBPy4V/cvc5---1.0.5_20895.p...
% 20.57/20.86 ------- get file name : TPTP file name is SWC410+1
% 20.57/20.86 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20895.smt2...
% 20.57/20.86 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 20.57/20.86 --- Run --no-e-matching --full-saturate-quant at 5...
% 20.57/20.86 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.57/20.86 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 20.57/20.86 % SZS status Theorem for SWC410+1
% 20.57/20.86 % SZS output start Proof for SWC410+1
% 20.57/20.86 (
% 20.57/20.86 (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 $$unsorted)) (=> (tptp.ssItem Y) (or (not (tptp.memberP V Y)) (tptp.memberP U Y)))) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (tptp.neq X tptp.nil) (or (not (tptp.neq W tptp.nil)) (exists ((Z $$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.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_14 (tptp.ssItem _let_13))) (let ((_let_15 (tptp.memberP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_13))) (let ((_let_17 (or _let_16 _let_15))) (let ((_let_18 (tptp.cons _let_13 tptp.nil))) (let ((_let_19 (tptp.memberP _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (= _let_19 _let_17))) (let ((_let_21 (not _let_9))) (let ((_let_22 (not _let_14))) (let ((_let_23 (not _let_12))) (let ((_let_24 (or _let_23 _let_22 _let_21 _let_20))) (let ((_let_25 (ASSUME :args (_let_9)))) (let ((_let_26 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_27 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_30 (tptp.app _let_29 _let_18))) (let ((_let_31 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_30))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.ssList _let_30))) (let ((_let_34 (tptp.ssList _let_29))) (let ((_let_35 (tptp.ssList _let_18))) (let ((_let_36 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (and _let_36 _let_14 _let_35 _let_34 _let_33 _let_32))) (let ((_let_38 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_42 (and _let_41 _let_40))) (let ((_let_43 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_44 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_45 (not _let_44))) (let ((_let_46 (and _let_45 _let_43))) (let ((_let_47 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48 _let_46 _let_42 _let_23 _let_28 _let_26))) (let ((_let_52 (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 BOUND_VARIABLE_5431 BOUND_VARIABLE_5433)) (tptp.memberP U BOUND_VARIABLE_5433))))))))) (let ((_let_53 (not _let_51))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (or))) (let ((_let_56 (not _let_52))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_54) :args (_let_56)) (REWRITE :args ((=> _let_56 (not (or _let_50 _let_48 _let_46 (and _let_41 (or _let_39 (and _let_36 _let_14 _let_35 _let_34 _let_33 (not (= _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) _let_23 _let_28 _let_26))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_52))) (REFL :args (_let_53)) :args _let_55)) _let_54 :args (_let_53 true _let_52)))) (let ((_let_58 (REFL :args (_let_51)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 4)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_12))) :args _let_55)) :args ((or _let_12 _let_51))) _let_57 :args (_let_12 true _let_51)))) (let ((_let_60 (or _let_50 _let_44 _let_14))) (let ((_let_61 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_64 (tptp.neq tptp.nil tptp.nil))) (let ((_let_65 (not _let_43))) (let ((_let_66 (= _let_41 _let_65))) (let ((_let_67 (not _let_64))) (let ((_let_68 (or _let_21 _let_21 _let_67))) (let ((_let_69 (forall ((U $$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_70 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_69))) (let ((_let_72 (REFL :args (_let_45)))) (let ((_let_73 (and _let_44 _let_67))) (let ((_let_74 (ASSUME :args (_let_67)))) (let ((_let_75 (ASSUME :args (_let_44)))) (let ((_let_76 (SYMM (SYMM _let_75)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 3)) _let_57 :args ((not _let_42) true _let_51)))) (let ((_let_78 (CNF_AND_NEG :args (_let_42)))) (let ((_let_79 (or _let_48 _let_21 _let_66))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_21 _let_48 _let_66 (not _let_79)))) _let_25 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 1)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_55)) :args ((or _let_47 _let_51))) _let_57 :args (_let_47 true _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_71))) _let_70 :args (_let_79 false _let_69)) :args (_let_66 false _let_9 false _let_47 false _let_79)))) (let ((_let_81 (not _let_66))) (let ((_let_82 (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_66)) (CONG (REFL :args (_let_81)) (REFL :args (_let_41)) (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_43))) :args _let_55)) :args ((or _let_43 _let_41 _let_81))))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 5)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_55)) :args ((or _let_27 _let_51))) _let_57 :args (_let_27 true _let_51)))) (let ((_let_84 (not _let_26))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 6)) _let_57 :args (_let_84 true _let_51)))) (let ((_let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_84) _let_26))))) (let ((_let_87 (REFL :args (_let_65)))) (let ((_let_88 (ASSUME :args (_let_84)))) (let ((_let_89 (FALSE_INTRO _let_88))) (let ((_let_90 (APPLY_UF tptp.memberP))) (let ((_let_91 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_92 (ASSUME :args (_let_43)))) (let ((_let_93 (ASSUME :args (_let_27)))) (let ((_let_94 (TRUE_INTRO _let_93))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_88 _let_75 _let_92 _let_93) :args (_let_44 _let_43 _let_27 _let_84)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_94) (CONG (TRANS (SYMM _let_92) _let_76) _let_91 :args _let_90) _let_89)) :args (_let_84 _let_44 _let_43 _let_27)) :args ((not (and _let_44 _let_43 _let_27 _let_84)) SB_LITERAL))) (CONG _let_72 _let_87 (REFL :args (_let_28)) _let_86 :args _let_55)) :args ((or _let_45 _let_28 _let_26 _let_65))) _let_85 _let_83 _let_82 _let_80 _let_78 _let_77 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_55)) :args ((or _let_38 _let_40))) (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 (SYMM _let_76) (REFL :args (tptp.nil)) :args (APPLY_UF tptp.neq)) (FALSE_INTRO _let_74))) :args (_let_67 _let_44))) :args (_let_44 _let_67))) :args (true _let_73)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_64))) (REFL :args (_let_39)) :args _let_55)) :args ((or _let_45 _let_39 _let_64))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_68))) :args ((or _let_21 _let_67 (not _let_68)))) _let_25 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.nil tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_71))) _let_70 :args (_let_68 false _let_69)) :args (_let_67 false _let_9 false _let_68)) :args (_let_45 true _let_26 false _let_27 false _let_43 false _let_66 true _let_41 true _let_42 false _let_40 true _let_38 true _let_64)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_55)) :args ((or _let_49 _let_51))) _let_57 :args (_let_49 true _let_51)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_50 _let_44 _let_14 (not _let_60)))) _let_96 _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args _let_63) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_14 false _let_49 true _let_44 false _let_60)))) (let ((_let_98 (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_99 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (_let_98))) (let ((_let_101 (not _let_20))) (let ((_let_102 (not _let_17))) (let ((_let_103 (tptp.memberP _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_104 (or _let_16 _let_103))) (let ((_let_105 (not _let_16))) (let ((_let_106 (tptp.cons _let_13 _let_29))) (let ((_let_107 (tptp.memberP _let_106 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_108 (= _let_107 _let_104))) (let ((_let_109 (not _let_104))) (let ((_let_110 (not _let_34))) (let ((_let_111 (or _let_23 _let_22 _let_110 _let_108))) (let ((_let_112 (or _let_50 _let_44 _let_34))) (let ((_let_113 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssList (tptp.tl U)))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_50 _let_44 _let_34 (not _let_112)))) _let_96 _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args _let_63) :args (_let_113))) _let_114 :args (_let_112 false _let_113)) :args (_let_34 false _let_49 true _let_44 false _let_112)))) (let ((_let_116 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_106))) (let ((_let_117 (not _let_107))) (let ((_let_118 (or _let_50 _let_44 _let_116))) (let ((_let_119 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (and _let_84 _let_116))) (let ((_let_122 (_let_84 _let_116))) (let ((_let_123 (ASSUME :args (_let_116)))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_108)) :args ((or _let_107 _let_109 (not _let_108)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_121)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_88 _let_123) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_123) _let_91 :args _let_90) _let_89)) :args _let_122)) :args _let_122)) :args (true _let_121)) (CONG _let_86 (REFL :args ((not _let_116))) (REFL :args (_let_117)) :args _let_55)) _let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_50 _let_44 _let_116 (not _let_118)))) _let_96 _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_119))) _let_120 :args (_let_118 false _let_119)) :args (_let_116 false _let_49 true _let_44 false _let_118)) :args (_let_117 true _let_26 false _let_116)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_23 _let_22 _let_110 _let_108 (not _let_111)))) _let_59 _let_97 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_29 _let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_100)) _let_99 :args (_let_111 false _let_98)) :args (_let_108 false _let_12 false _let_14 false _let_34 false _let_111)) :args (_let_109 true _let_107 false _let_108)))) (let ((_let_125 (not _let_15))) (let ((_let_126 (or _let_23 _let_125))) (let ((_let_127 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.memberP tptp.nil U)))))) (let ((_let_128 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_129 (or _let_103 _let_19))) (let ((_let_130 (tptp.memberP _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_131 (= _let_130 _let_129))) (let ((_let_132 (not _let_35))) (let ((_let_133 (or _let_23 _let_110 _let_132 _let_131))) (let ((_let_134 (forall ((U $$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_135 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_136 (or _let_21 _let_22 _let_35))) (let ((_let_137 (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_138 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_139 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_136)) :args ((or _let_21 _let_35 _let_22 (not _let_136)))) _let_25 _let_97 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_138 :args (tptp.nil _let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_137))) _let_138 :args (_let_136 false _let_137)) :args (_let_35 false _let_9 false _let_14 false _let_136)))) (let ((_let_140 (or _let_110 _let_132 _let_33))) (let ((_let_141 (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_142 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_143 (= _let_45 _let_36))) (let ((_let_144 (or _let_21 _let_50 _let_143))) (let ((_let_145 (not _let_143))) (let ((_let_146 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))))) (let ((_let_147 (_let_46))) (let ((_let_148 (not _let_33))) (let ((_let_149 (not _let_36))) (let ((_let_150 (_let_37))) (let ((_let_151 (and _let_27 _let_31))) (let ((_let_152 (_let_27 _let_31))) (let ((_let_153 (ASSUME :args (_let_31)))) (let ((_let_154 (not _let_103))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_21 _let_23 _let_22 _let_20 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_20)) :args ((or (not _let_19) _let_17 _let_101))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_129)) :args ((or _let_103 _let_19 (not _let_129)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_104 1)) :args ((or _let_154 _let_104))) _let_124 :args (_let_154 true _let_104)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_131)) :args ((or _let_129 (not _let_130) (not _let_131)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_151)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_93 _let_153) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_153) _let_91 :args _let_90) _let_94)) :args _let_152)) :args _let_152)) :args (true _let_151)) _let_83 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_150) (CONG (REFL :args _let_150) (REFL :args (_let_149)) (REFL :args (_let_22)) (REFL :args (_let_132)) (REFL :args (_let_110)) (REFL :args (_let_148)) (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_55)) :args ((or _let_31 _let_37 _let_149 _let_22 _let_132 _let_110 _let_148))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 1)) (MACRO_RESOLUTION_TRUST _let_78 _let_77 (MACRO_RESOLUTION_TRUST _let_82 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_147) (CONG (REFL :args _let_147) _let_146 _let_87 :args _let_55)) :args ((or _let_44 _let_46 _let_65))) _let_95 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 2)) _let_57 :args ((not _let_46) true _let_51)) :args (_let_65 true _let_44 true _let_46)) _let_80 :args (_let_41 true _let_43 false _let_66)) :args ((not _let_40) true _let_42 false _let_41)) :args ((not _let_37) true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args (_let_143)) (CONG (REFL :args (_let_145)) _let_146 (REFL :args (_let_36)) :args _let_55)) :args ((or _let_44 _let_36 _let_145))) _let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_144)) :args ((or _let_21 _let_50 _let_143 (not _let_144)))) _let_25 _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_71))) _let_70 :args (_let_144 false _let_69)) :args (_let_143 false _let_9 false _let_49 false _let_144)) :args (_let_36 true _let_44 false _let_143)) _let_97 _let_139 _let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_140)) :args ((or _let_33 _let_132 _let_110 (not _let_140)))) _let_139 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_142 :args (_let_29 _let_18 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_141))) _let_142 :args (_let_140 false _let_141)) :args (_let_33 false _let_35 false _let_34 false _let_140)) :args (_let_31 true _let_37 false _let_36 false _let_14 false _let_35 false _let_34 false _let_33)) :args (_let_130 false _let_27 false _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_133)) :args ((or _let_23 _let_132 _let_110 _let_131 (not _let_133)))) _let_59 _let_139 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_135 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_18 _let_29 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_134))) _let_135 :args (_let_133 false _let_134)) :args (_let_131 false _let_12 false _let_35 false _let_34 false _let_133)) :args (_let_129 false _let_130 false _let_131)) :args (_let_19 true _let_103 false _let_129)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_15 _let_16 _let_102))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_23 _let_125 (not _let_126)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_128 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_127))) _let_128 :args (_let_126 false _let_127)) :args (_let_125 false _let_12 false _let_126)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_104 0)) :args ((or _let_105 _let_104))) _let_124 :args (_let_105 true _let_104)) :args (_let_102 true _let_15 true _let_16)) :args (_let_101 false _let_19 true _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil _let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_100)) _let_99 :args (_let_24 false _let_98)) _let_97 _let_59 _let_25 :args (false true _let_20 false _let_24 false _let_14 false _let_12 false _let_9)) :args ((forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))) (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) (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))))))))))))))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 20.57/20.87 )
% 20.57/20.87 % SZS output end Proof for SWC410+1
% 20.57/20.87 % cvc5---1.0.5 exiting
% 20.73/20.87 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------