TSTP Solution File: SWC383+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC383+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 20:25:13 EDT 2023
% Result : Theorem 31.24s 31.45s
% Output : Proof 31.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWC383+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon Aug 28 18:14:10 EDT 2023
% 0.23/0.37 % CPUTime :
% 0.23/0.52 %----Proving TF0_NAR, FOF, or CNF
% 31.24/31.45 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.iitnW6OtKb/cvc5---1.0.5_24303.p...
% 31.24/31.45 ------- get file name : TPTP file name is SWC383+1
% 31.24/31.45 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24303.smt2...
% 31.24/31.45 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.24/31.45 --- Run --no-e-matching --full-saturate-quant at 5...
% 31.24/31.45 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.24/31.45 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.24/31.45 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.24/31.45 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.24/31.45 % SZS status Theorem for SWC383+1
% 31.24/31.45 % SZS output start Proof for SWC383+1
% 31.24/31.45 (
% 31.24/31.45 (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (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 Y Z)))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))) (and (tptp.singletonP U) (tptp.segmentP V U)))))))))))))) (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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_7 (tptp.ssList tptp.nil))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))) (let ((_let_12 (forall ((U $$unsorted) (BOUND_VARIABLE_3306 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3306)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3306 U)))))) (let ((_let_13 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_14 (tptp.ssList _let_13))) (let ((_let_15 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16 _let_14))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (not _let_19))) (let ((_let_22 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_13))) (let ((_let_23 (tptp.segmentP (tptp.app _let_22 tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_24 (not _let_7))) (let ((_let_25 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.segmentP _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_30 (not _let_29))) (let ((_let_31 (not _let_14))) (let ((_let_32 (or _let_31 _let_30 _let_28 _let_26 _let_24 _let_23))) (let ((_let_33 (forall ((U $$unsorted) (BOUND_VARIABLE_4457 $$unsorted) (BOUND_VARIABLE_4455 $$unsorted) (BOUND_VARIABLE_4453 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4453)) (not (tptp.segmentP U BOUND_VARIABLE_4453)) (not (tptp.ssList BOUND_VARIABLE_4457)) (not (tptp.ssList BOUND_VARIABLE_4455)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4457 U) BOUND_VARIABLE_4455) BOUND_VARIABLE_4453))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_22))) (let ((_let_37 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_38 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_39 (not _let_23))) (let ((_let_40 (not _let_36))) (let ((_let_41 (or _let_26 _let_18 _let_40))) (let ((_let_42 (forall ((W $$unsorted) (BOUND_VARIABLE_2148 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2148)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2148)))))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (not _let_42))) (let ((_let_45 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_46 (= _let_45 _let_44))) (let ((_let_47 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_16 _let_46))) (let ((_let_50 (forall ((U $$unsorted) (BOUND_VARIABLE_2174 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2174)) (= (tptp.memberP U BOUND_VARIABLE_2174) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2148 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2148)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2174 BOUND_VARIABLE_2148)))))))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (not _let_45))) (let ((_let_53 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_54 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_53))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_16 _let_55 _let_52 (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (= Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Z)) (not (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Z)))))))) (let ((_let_57 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 (not (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_60 (and _let_56 _let_59))) (let ((_let_61 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_62 (= _let_61 _let_58))) (let ((_let_63 (or _let_48 _let_24 _let_62))) (let ((_let_64 (forall ((U $$unsorted) (BOUND_VARIABLE_3283 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3283)) (= (tptp.neq U BOUND_VARIABLE_3283) (not (= U BOUND_VARIABLE_3283))))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (tptp.singletonP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_67 (and _let_66 _let_38))) (let ((_let_68 (not _let_61))) (let ((_let_69 (or _let_30 _let_48 _let_68 _let_67 _let_60))) (let ((_let_70 (forall ((U $$unsorted) (BOUND_VARIABLE_5421 $$unsorted) (BOUND_VARIABLE_5419 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5419)) (not (tptp.neq BOUND_VARIABLE_5419 tptp.nil)) (and (tptp.singletonP U) (tptp.segmentP BOUND_VARIABLE_5419 U)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5421)) (not (= U (tptp.cons BOUND_VARIABLE_5421 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5419 BOUND_VARIABLE_5421)) (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (= Z BOUND_VARIABLE_5421) (not (tptp.memberP BOUND_VARIABLE_5419 Z)) (not (tptp.leq BOUND_VARIABLE_5421 Z)))))) (or (not (= tptp.nil BOUND_VARIABLE_5419)) (not (= tptp.nil U)))))))) (let ((_let_71 (not _let_69))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (or))) (let ((_let_74 (not _let_70))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_72) :args (_let_74))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_70))) (REFL :args (_let_71)) :args _let_73)) _let_72 :args (_let_71 true _let_70)))) (let ((_let_76 (REFL :args (_let_69)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 1)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_73)) :args ((or _let_47 _let_69))) _let_75 :args (_let_47 true _let_69)))) (let ((_let_78 (ASSUME :args (_let_7)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_60)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_69 4)) _let_75 :args ((not _let_60) true _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 0)) (CONG (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_73)) :args ((or _let_57 _let_59))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_62)) :args ((or _let_68 _let_58 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 2)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_61))) :args _let_73)) :args ((or _let_61 _let_69))) _let_75 :args (_let_61 true _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_24 _let_48 _let_62 (not _let_63)))) _let_78 _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args (_let_64)))) _let_65 :args (_let_63 false _let_64)) :args (_let_62 false _let_7 false _let_47 false _let_63)) :args (_let_58 false _let_61 false _let_62)) :args (_let_59 true _let_57)) :args ((not _let_56) true _let_60 false _let_59)))) (let ((_let_80 (REFL :args (_let_56)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_73)) :args ((or _let_15 _let_56))) _let_79 :args (_let_15 true _let_56)))) (let ((_let_82 (_let_44))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_82)) :args _let_82)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_42))) (REFL :args (_let_43)) :args _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_46)) :args ((or _let_52 _let_44 (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 2)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_45))) :args _let_73)) :args ((or _let_45 _let_56))) _let_79 :args (_let_45 true _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_16 _let_46 (not _let_49)))) _let_77 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.memberP U BOUND_VARIABLE_2174)))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_46 false _let_47 false _let_15 false _let_49)) :args (_let_44 false _let_45 false _let_46)) :args (_let_43 true _let_42)))) (let ((_let_84 (REFL :args (_let_41)))) (let ((_let_85 (or _let_48 _let_37))) (let ((_let_86 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (not _let_38))) (let ((_let_89 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= (tptp.cons V tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_90 (not _let_89))) (let ((_let_91 (= _let_66 _let_90))) (let ((_let_92 (or _let_30 _let_91))) (let ((_let_93 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.singletonP U) (not (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= U (tptp.cons V tptp.nil))))))))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 0)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_73)) :args ((or _let_29 _let_69))) _let_75 :args (_let_29 true _let_69)))) (let ((_let_96 (or _let_16 _let_55))) (let ((_let_97 (not _let_96))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 1)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_73)) :args ((or _let_54 _let_56))) _let_79 :args (_let_54 true _let_56)))) (let ((_let_99 (_let_89))) (let ((_let_100 (not _let_91))) (let ((_let_101 (and _let_88 _let_37 _let_36))) (let ((_let_102 (_let_88 _let_37 _let_36))) (let ((_let_103 (ASSUME :args (_let_88)))) (let ((_let_104 (APPLY_UF tptp.segmentP))) (let ((_let_105 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_106 (ASSUME :args (_let_37)))) (let ((_let_107 (APPLY_UF tptp.app))) (let ((_let_108 (ASSUME :args (_let_36)))) (let ((_let_109 (tptp.app tptp.nil 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SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_120 (or _let_18 _let_16 _let_111))) (let ((_let_121 (forall ((U $$unsorted) (BOUND_VARIABLE_4794 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4794)) (= (tptp.cons BOUND_VARIABLE_4794 U) (tptp.app (tptp.cons BOUND_VARIABLE_4794 tptp.nil) U)))))) (let ((_let_122 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (or _let_30 _let_112))) (let ((_let_124 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (and _let_54 _let_112 _let_111 _let_110))) (let ((_let_127 (ASSUME :args (_let_110)))) (let ((_let_128 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_129 (ASSUME :args (_let_112)))) (let ((_let_130 (ASSUME :args (_let_54)))) (let ((_let_131 (ASSUME :args (_let_111)))) (SCOPE (SCOPE 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(tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_5 _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))) (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))) (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_3 (forall ((U $$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))))))) _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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.24/31.45 )
% 31.24/31.45 % SZS output end Proof for SWC383+1
% 31.24/31.45 % cvc5---1.0.5 exiting
% 31.24/31.45 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------