TSTP Solution File: SWC045+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC045+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 20:22:49 EDT 2023
% Result : Theorem 43.63s 43.97s
% Output : Proof 43.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC045+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n022.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 17:08:39 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 43.63/43.97 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.plf6Od1Kp4/cvc5---1.0.5_15066.p...
% 43.63/43.97 ------- get file name : TPTP file name is SWC045+1
% 43.63/43.97 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15066.smt2...
% 43.63/43.97 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 43.63/43.97 --- Run --no-e-matching --full-saturate-quant at 5...
% 43.63/43.97 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 43.63/43.97 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 43.63/43.97 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 43.63/43.97 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 43.63/43.97 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 43.63/43.97 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 43.63/43.97 % SZS status Theorem for SWC045+1
% 43.63/43.97 % SZS output start Proof for SWC045+1
% 43.63/43.97 (
% 43.63/43.97 (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 (= tptp.nil V)) (not (= V X)) (not (= U W)) (= tptp.nil U) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.memberP W Y))) (and (tptp.ssItem Y) (or (and (not _let_1) (exists ((Z $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (and (tptp.ssList Z) (tptp.segmentP X (tptp.app (tptp.app _let_1 Z) _let_1)))))) (and (forall ((Z $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (=> (tptp.ssList Z) (not (tptp.segmentP X (tptp.app (tptp.app _let_1 Z) _let_1)))))) _let_1))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))) (let ((_let_3 (forall ((U $$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) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))))) (let ((_let_12 (tptp.ssList tptp.nil))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_14 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.cons _let_14 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_16 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.tl _let_16)))) (let ((_let_19 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14))) (let ((_let_20 (tptp.memberP (tptp.cons _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) _let_14))) (let ((_let_21 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_15))) (let ((_let_25 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (forall ((Y $$unsorted) (BOUND_VARIABLE_5245 $$unsorted)) (let ((_let_1 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y))) (let ((_let_2 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (and (or _let_1 (not (tptp.ssList BOUND_VARIABLE_5245)) (not (tptp.segmentP tptp.nil (tptp.app (tptp.app _let_2 BOUND_VARIABLE_5245) _let_2)))) (or (not (forall ((Z $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssList Z)) (not (tptp.segmentP tptp.nil (tptp.app (tptp.app _let_1 Z) _let_1))))))) (not _let_1))))))))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_23 _let_21 _let_28))) (let ((_let_30 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5245 $$unsorted)) (let ((_let_1 (tptp.memberP U Y))) (let ((_let_2 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (and (or _let_1 (not (tptp.ssList BOUND_VARIABLE_5245)) (not (tptp.segmentP tptp.nil (tptp.app (tptp.app _let_2 BOUND_VARIABLE_5245) _let_2)))) (or (not (forall ((Z $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssList Z)) (not (tptp.segmentP tptp.nil (tptp.app (tptp.app _let_1 Z) _let_1))))))) (not _let_1)))))))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (NOT_OR_ELIM _let_32 :args (1)))) (let ((_let_34 (or))) (let ((_let_35 (not _let_30))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args (_let_35))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_30))) (REFL :args (_let_31)) :args _let_34)) _let_33 :args (_let_31 true _let_30)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 1)) _let_36 :args ((not _let_21) true _let_29)))) (let ((_let_38 (REFL :args (_let_29)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_34)) :args ((or _let_22 _let_29))) _let_36 :args (_let_22 true _let_29)))) (let ((_let_40 (not _let_17))) (let ((_let_41 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42 _let_40))) (let ((_let_46 (forall ((V $$unsorted) (BOUND_VARIABLE_3453 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3453)) (not (= (tptp.cons BOUND_VARIABLE_3453 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (not _let_46))) (let ((_let_49 (or _let_23 _let_21 _let_48))) (let ((_let_50 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((V $$unsorted) (BOUND_VARIABLE_3453 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3453)) (not (= U (tptp.cons BOUND_VARIABLE_3453 V)))))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (_let_48))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_52)) :args _let_52) (REWRITE :args ((=> _let_48 (not (or _let_44 _let_42 (not (= _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_46))) (REFL :args (_let_47)) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_23 _let_21 _let_48 (not _let_49)))) _let_39 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_50)))) _let_51 :args (_let_49 false _let_50)) :args (_let_48 false _let_22 true _let_21 false _let_49)) :args (_let_47 true _let_46)))) (let ((_let_54 (REFL :args (_let_45)))) (let ((_let_55 (or _let_44 _let_42 _let_18))) (let ((_let_56 (forall ((U $$unsorted) (BOUND_VARIABLE_3542 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3542)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3542 U))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_34)) :args ((or _let_43 _let_45))) _let_53 :args (_let_43 true _let_45)))) (let ((_let_59 (not _let_19))) (let ((_let_60 (forall ((Z $$unsorted)) (let ((_let_1 (tptp.cons (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) tptp.nil))) (or (not (tptp.ssList Z)) (not (tptp.segmentP tptp.nil (tptp.app (tptp.app _let_1 Z) _let_1)))))))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_59))) (let ((_let_63 (tptp.cons _let_14 tptp.nil))) (let ((_let_64 (not _let_12))) (let ((_let_65 (and (or _let_19 _let_64 (not (tptp.segmentP tptp.nil (tptp.app (tptp.app _let_63 tptp.nil) _let_63)))) _let_62))) (let ((_let_66 (tptp.ssItem _let_14))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_65))) (let ((_let_69 (_let_27))) (let ((_let_70 (or _let_23 _let_21 _let_66))) (let ((_let_71 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_23 _let_21 _let_66 (not _let_70)))) _let_39 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_66 false _let_22 true _let_21 false _let_70)))) (let ((_let_74 (tptp.app _let_63 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_75 (tptp.app _let_74 _let_63))) (let ((_let_76 (tptp.segmentP tptp.nil _let_75))) (let ((_let_77 (not _let_76))) (let ((_let_78 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_77))) (let ((_let_81 (tptp.cons _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_82 (= _let_74 _let_81))) (let ((_let_83 (or _let_79 _let_67 _let_82))) (let ((_let_84 (tptp.ssList _let_81))) (let ((_let_85 (or _let_79 _let_67 _let_84))) (let ((_let_86 (tptp.ssList _let_74))) (let ((_let_87 (tptp.ssList _let_63))) (let ((_let_88 (= tptp.nil _let_63))) (let ((_let_89 (and _let_88 (= tptp.nil _let_74)))) (let ((_let_90 (= tptp.nil _let_75))) (let ((_let_91 (= _let_90 _let_89))) (let ((_let_92 (not _let_87))) (let ((_let_93 (not _let_86))) (let ((_let_94 (or _let_93 _let_92 _let_91))) (let ((_let_95 (tptp.ssList _let_75))) (let ((_let_96 (or _let_93 _let_92 _let_95))) (let ((_let_97 (= _let_76 _let_90))) (let ((_let_98 (not _let_95))) (let ((_let_99 (or _let_98 _let_97))) (let ((_let_100 (REFL :args (_let_80)))) (let ((_let_101 (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_102 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (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_104 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (_let_103))) (let ((_let_106 (and _let_82 _let_84))) (let ((_let_107 (ASSUME :args (_let_84)))) (let ((_let_108 (ASSUME :args (_let_82)))) (let ((_let_109 (or _let_64 _let_67 _let_87))) (let ((_let_110 (NOT_NOT_ELIM (NOT_OR_ELIM _let_32 :args (0))))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_109)) :args ((or _let_64 _let_67 _let_87 (not _let_109)))) _let_110 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (tptp.nil _let_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_105)) _let_104 :args (_let_109 false _let_103)) :args (_let_87 false _let_12 false _let_66 false _let_109)))) (let ((_let_112 (forall ((U $$unsorted) (BOUND_VARIABLE_4864 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4864)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4864)) (and (= tptp.nil BOUND_VARIABLE_4864) (= tptp.nil U))))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (forall ((U $$unsorted) (BOUND_VARIABLE_3564 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3564)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3564)))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (not _let_89))) (let ((_let_117 (tptp.memberP _let_63 _let_14))) (let ((_let_118 (tptp.memberP tptp.nil _let_14))) (let ((_let_119 (not _let_88))) (let ((_let_120 (or _let_67 _let_67 _let_64 _let_117))) (let ((_let_121 (forall ((U $$unsorted) (BOUND_VARIABLE_3920 $$unsorted) (BOUND_VARIABLE_3918 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_3918)) 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(MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_135 (_let_61))) (let ((_let_136 (or _let_67 _let_67 _let_44 _let_20))) (let ((_let_137 (ASSUME :args (_let_20)))) (let ((_let_138 (ASSUME :args (_let_18)))) (let ((_let_139 (ASSUME :args (_let_17)))) (let ((_let_140 (ASSUME :args (_let_15)))) (let ((_let_141 (ASSUME :args (_let_59)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_137 _let_138 _let_139 _let_140 _let_141) :args (_let_15 _let_17 _let_18 _let_59 _let_20)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_141)) (CONG (TRANS (SYMM (SYMM _let_140)) (CONG _let_130 (TRANS (CONG (SYMM (SYMM _let_139)) :args (APPLY_UF tptp.tl)) (SYMM _let_138)) :args (APPLY_UF tptp.cons))) _let_130 :args _let_129) (TRUE_INTRO _let_137))) :args (_let_20 _let_18 _let_17 _let_15 _let_59)) :args ((not (and _let_15 _let_17 _let_18 _let_59 _let_20)) SB_LITERAL))) (CONG (REFL :args ((not _let_15))) (REFL :args 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$$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 $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) _let_5 (forall ((U $$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_4 (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 $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) _let_2 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 43.76/43.98 )
% 43.76/43.98 % SZS output end Proof for SWC045+1
% 43.76/43.98 % cvc5---1.0.5 exiting
% 43.76/43.98 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------