TSTP Solution File: SWC314+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC314+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 20:24:42 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC314+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 16:48:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.65 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.DruEkVusjR/cvc5---1.0.5_7879.p...
% 0.20/0.65 ------- get file name : TPTP file name is SWC314+1
% 0.20/0.65 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7879.smt2...
% 0.20/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.65 % SZS status Theorem for SWC314+1
% 0.20/0.65 % SZS output start Proof for SWC314+1
% 0.20/0.65 (
% 0.20/0.65 (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)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (exists ((Y $$unsorted)) (and (tptp.ssList Y) (not (= W Y)) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (= (tptp.tl X) Z) (= (tptp.app Z X1) Y) (exists ((X2 $$unsorted)) (and (tptp.ssItem X2) (= (tptp.cons X2 tptp.nil) X1) (= (tptp.hd X) X2) (tptp.neq tptp.nil X))) (tptp.neq tptp.nil X))))))) (tptp.neq X tptp.nil)) (and (forall ((X3 $$unsorted)) (=> (tptp.ssItem X3) (forall ((X4 $$unsorted)) (let ((_let_1 (tptp.cons X3 tptp.nil))) (or (not (tptp.ssList X4)) (not (= (tptp.app _let_1 X4) V)) (= (tptp.app X4 _let_1) U)))))) (or (not (= tptp.nil V)) (= tptp.nil U)))))))))))))) (let ((_let_2 (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))))))))) (let ((_let_3 (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))))))))) (let ((_let_4 (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_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_6 (forall ((U $$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) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_10 (tptp.ssList tptp.nil))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_13 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil))) (let ((_let_14 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_15 (tptp.cons _let_14 tptp.nil))) (let ((_let_16 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_17 (tptp.app _let_16 _let_15))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.ssList _let_17))) (let ((_let_21 (tptp.ssList _let_16))) (let ((_let_22 (tptp.ssList _let_15))) (let ((_let_23 (tptp.ssItem _let_14))) (let ((_let_24 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_25 (and _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_13))) (let ((_let_26 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_27 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_28 (not _let_27))) (let ((_let_29 (and _let_28 _let_26))) (let ((_let_30 (not _let_26))) (let ((_let_31 (or _let_30 _let_27))) (let ((_let_32 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_33 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_32))) (let ((_let_34 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_33))) (let ((_let_35 (tptp.app _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_36 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_35))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_39 _let_37 _let_34))) (let ((_let_43 (and _let_42 _let_31))) (let ((_let_44 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_45 _let_43 _let_29 _let_25))) (let ((_let_47 (forall ((U $$unsorted) (BOUND_VARIABLE_5461 $$unsorted) (BOUND_VARIABLE_5459 $$unsorted) (BOUND_VARIABLE_5457 $$unsorted)) (let ((_let_1 (tptp.hd BOUND_VARIABLE_5457))) (let ((_let_2 (tptp.cons _let_1 tptp.nil))) (let ((_let_3 (tptp.tl BOUND_VARIABLE_5457))) (let ((_let_4 (tptp.app _let_3 _let_2))) (let ((_let_5 (= tptp.nil BOUND_VARIABLE_5457))) (let ((_let_6 (= tptp.nil U))) (let ((_let_7 (tptp.cons BOUND_VARIABLE_5461 tptp.nil))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5457)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5461)) (not (tptp.ssList BOUND_VARIABLE_5459)) (not (= BOUND_VARIABLE_5457 (tptp.app _let_7 BOUND_VARIABLE_5459))) (= U (tptp.app BOUND_VARIABLE_5459 _let_7))) (or (not _let_5) _let_6)) (and (not _let_6) _let_5) (and (tptp.neq tptp.nil BOUND_VARIABLE_5457) (tptp.ssItem _let_1) (tptp.ssList _let_2) (tptp.ssList _let_3) (tptp.ssList _let_4) (not (= U _let_4)) (tptp.neq BOUND_VARIABLE_5457 tptp.nil))))))))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (or))) (let ((_let_51 (not _let_47))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_49) :args (_let_51))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_47))) (REFL :args (_let_48)) :args _let_50)) _let_49 :args (_let_48 true _let_47)))) (let ((_let_53 (= _let_30 _let_13))) (let ((_let_54 (not _let_10))) (let ((_let_55 (or _let_45 _let_54 _let_53))) (let ((_let_56 (forall ((U $$unsorted) (BOUND_VARIABLE_3311 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3311)) (= (tptp.neq U BOUND_VARIABLE_3311) (not (= U BOUND_VARIABLE_3311))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (_let_56))) (let ((_let_59 ((tptp.neq U BOUND_VARIABLE_3311)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_50)) :args ((or _let_44 _let_46))) _let_52 :args (_let_44 true _let_46)))) (let ((_let_61 (ASSUME :args (_let_10)))) (let ((_let_62 (= tptp.nil _let_35))) (let ((_let_63 (= tptp.nil _let_32))) (let ((_let_64 (and (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_63))) (let ((_let_65 (= _let_62 _let_64))) (let ((_let_66 (not _let_62))) (let ((_let_67 (tptp.ssList _let_32))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_39 _let_65))) (let ((_let_70 (forall ((U $$unsorted) (BOUND_VARIABLE_4892 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4892)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4892)) (and (= tptp.nil BOUND_VARIABLE_4892) (= tptp.nil U))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (or _let_54 _let_41 _let_67))) (let ((_let_73 (forall ((U $$unsorted) (BOUND_VARIABLE_3334 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3334)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3334 U)))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))))) (let ((_let_76 (REFL :args (_let_30)))) (let ((_let_77 (_let_29))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_43)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 2)) _let_52 :args ((not _let_43) true _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_77) (CONG (REFL :args _let_77) (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) _let_76 :args _let_50)) :args ((or _let_30 _let_27 _let_29))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 3)) _let_52 :args ((not _let_29) true _let_46)) (CNF_OR_NEG :args (_let_31 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG (REFL :args (_let_31)) _let_75 :args _let_50)) :args ((or _let_26 _let_31))) :args (_let_31 true _let_29 true _let_27 false _let_26)) :args ((not _let_42) true _let_43 false _let_31)))) (let ((_let_79 (REFL :args (_let_42)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_50)) :args ((or _let_40 _let_42))) _let_78 :args (_let_40 true _let_42)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_54 _let_41 _let_67 (not _let_72)))) _let_61 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3334 U)))) :args (_let_73))) _let_74 :args (_let_72 false _let_73)) :args (_let_67 false _let_10 false _let_40 false _let_72)))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 1)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_50)) :args ((or _let_38 _let_42))) _let_78 :args (_let_38 true _let_42)))) (let ((_let_83 (not _let_64))) (let ((_let_84 (not _let_63))) (let ((_let_85 (or _let_54 _let_41 _let_84))) (let ((_let_86 (forall ((U $$unsorted) (BOUND_VARIABLE_3359 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3359)) (not (= U (tptp.cons BOUND_VARIABLE_3359 U))))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_54 _let_41 _let_84 (not _let_85)))) _let_61 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3359 U)))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_84 false _let_10 false _let_40 false _let_85)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 2)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_50)) :args ((or _let_36 _let_42))) _let_78 :args (_let_36 true _let_42)))) (let ((_let_90 (REFL :args (_let_37)))) (let ((_let_91 (and _let_36 _let_66))) (let ((_let_92 (ASSUME :args (_let_66)))) (let ((_let_93 (=))) (let ((_let_94 (ASSUME :args (_let_36)))) (let ((_let_95 (SYMM (SYMM _let_94)))) (let ((_let_96 (REFL :args (tptp.nil)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_91)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_92 _let_94) (SCOPE (FALSE_ELIM (TRANS (CONG _let_96 _let_95 :args _let_93) (FALSE_INTRO _let_92))) :args (_let_66 _let_36))) :args (_let_36 _let_66))) :args (true _let_91)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_62))) _let_76 :args _let_50)) :args ((or _let_37 _let_30 _let_62))) _let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_65)) :args ((or _let_64 _let_66 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_64 1)) :args ((or _let_63 _let_83))) _let_88 :args (_let_83 true _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_39 _let_68 _let_65 (not _let_69)))) _let_82 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (_let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.app U BOUND_VARIABLE_4892)))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_65 false _let_38 false _let_67 false _let_69)) :args (_let_66 true _let_64 false _let_65)) :args (_let_30 false _let_36 true _let_62)))) (let ((_let_98 (not _let_53))) (let ((_let_99 (tptp.tl _let_32))) (let ((_let_100 (= (tptp.tl _let_35) (tptp.app _let_99 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_101 (tptp.hd _let_32))) (let ((_let_102 (= _let_101 (tptp.hd _let_35)))) (let ((_let_103 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_104 (= tptp.nil _let_99))) (let ((_let_105 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_101))) (let ((_let_106 (or _let_68 _let_63 _let_39 _let_100))) (let ((_let_107 (forall ((U $$unsorted) (BOUND_VARIABLE_4955 $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (tptp.ssList BOUND_VARIABLE_4955)) (= (tptp.tl (tptp.app U BOUND_VARIABLE_4955)) (tptp.app (tptp.tl U) BOUND_VARIABLE_4955)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_39 _let_63 _let_68 _let_100 (not _let_106)))) _let_82 _let_88 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.tl (tptp.app U BOUND_VARIABLE_4955))))) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_100 false _let_38 true _let_63 false _let_67 false _let_106)))) (let ((_let_110 (or _let_68 _let_63 _let_39 _let_102))) (let ((_let_111 (forall ((U $$unsorted) (BOUND_VARIABLE_4927 $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (tptp.ssList BOUND_VARIABLE_4927)) (= (tptp.hd U) (tptp.hd (tptp.app U BOUND_VARIABLE_4927))))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or 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U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$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)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> 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(tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$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)))))))) (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 $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) _let_3 _let_2 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.65 )
% 0.20/0.65 % SZS output end Proof for SWC314+1
% 0.20/0.65 % cvc5---1.0.5 exiting
% 0.20/0.66 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------