%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU146+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.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 : Wed Jun 3 08:50:42 AM UTC 2026 % Result : Theorem 0.46s 0.64s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU146+2 : TPTP v9.2.1. Released v3.3.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n005.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:32:03 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.46/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.46/0.64 % SZS status Theorem % 0.46/0.64 % SZS output start Proof % 0.46/0.64 ( % 0.46/0.64 (declare-sort $$unsorted 0) % 0.46/0.64 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.46/0.64 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.64 (declare-const tptp.empty_set $$unsorted) % 0.46/0.64 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.46/0.64 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.64 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.64 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.46/0.64 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.64 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.46/0.64 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.46/0.64 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.46/0.64 (define @t1 () (@var "A" $$unsorted)) % 0.46/0.64 (define @t2 () (@var "B" $$unsorted)) % 0.46/0.64 (define @t3 () (not (tptp.in @t2 @t1))) % 0.46/0.64 (define @t4 () (tptp.in @t1 @t2)) % 0.46/0.64 (define @t5 () (@list @t1 @t2)) % 0.46/0.64 (define @t6 () (tptp.proper_subset @t2 @t1)) % 0.46/0.64 (define @t7 () (tptp.proper_subset @t1 @t2)) % 0.46/0.64 (define @t8 () (tptp.unordered_pair @t1 @t2)) % 0.46/0.64 (define @t9 () (tptp.set_union2 @t2 @t1)) % 0.46/0.64 (define @t10 () (tptp.set_union2 @t1 @t2)) % 0.46/0.64 (define @t11 () (tptp.set_intersection2 @t1 @t2)) % 0.46/0.64 (define @t12 () (tptp.subset @t1 @t2)) % 0.46/0.64 (define @t13 () (= @t1 @t2)) % 0.46/0.64 (define @t14 () (forall @t5 (= @t13 (and @t12 (tptp.subset @t2 @t1))))) % 0.46/0.64 (define @t15 () (@var "C" $$unsorted)) % 0.46/0.64 (define @t16 () (tptp.in @t15 @t2)) % 0.46/0.64 (define @t17 () (@list @t15)) % 0.46/0.64 (define @t18 () (tptp.singleton @t1)) % 0.46/0.64 (define @t19 () (= @t1 tptp.empty_set)) % 0.46/0.64 (define @t20 () (@list @t1)) % 0.46/0.64 (define @t21 () (@var "D" $$unsorted)) % 0.46/0.64 (define @t22 () (tptp.in @t21 @t15)) % 0.46/0.64 (define @t23 () (@list @t21)) % 0.46/0.64 (define @t24 () (@list @t1 @t2 @t15)) % 0.46/0.64 (define @t25 () (tptp.in @t21 @t2)) % 0.46/0.64 (define @t26 () (tptp.in @t21 @t1)) % 0.46/0.64 (define @t27 () (tptp.in @t15 @t1)) % 0.46/0.64 (define @t28 () (forall @t17 (=> @t27 @t16))) % 0.46/0.64 (define @t29 () (= @t12 @t28)) % 0.46/0.64 (define @t30 () (forall @t5 @t29)) % 0.46/0.64 (define @t31 () (tptp.set_difference @t1 @t2)) % 0.46/0.64 (define @t32 () (tptp.disjoint @t1 @t2)) % 0.46/0.64 (define @t33 () (not @t13)) % 0.46/0.64 (define @t34 () (tptp.empty @t1)) % 0.46/0.64 (define @t35 () (not @t34)) % 0.46/0.64 (define @t36 () (tptp.subset @t18 @t2)) % 0.46/0.64 (define @t37 () (forall @t5 (= @t36 @t4))) % 0.46/0.64 (define @t38 () (= @t31 tptp.empty_set)) % 0.46/0.64 (define @t39 () (forall @t5 (= @t38 @t12))) % 0.46/0.64 (define @t40 () (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t15)))) % 0.46/0.64 (define @t41 () (or @t27 @t40)) % 0.46/0.64 (define @t42 () (forall @t24 (=> @t12 @t41))) % 0.46/0.64 (define @t43 () (tptp.singleton @t2)) % 0.46/0.64 (define @t44 () (forall @t5 (= (tptp.subset @t1 @t43) (or @t19 (= @t1 @t43))))) % 0.46/0.64 (define @t45 () (not @t44)) % 0.46/0.64 (define @t46 () (tptp.set_intersection2 @t2 @t15)) % 0.46/0.64 (define @t47 () (tptp.subset @t1 @t15)) % 0.46/0.64 (define @t48 () (=> @t12 (= @t11 @t1))) % 0.46/0.64 (define @t49 () (forall @t5 @t48)) % 0.46/0.64 (define @t50 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.46/0.64 (define @t51 () (and @t27 @t16)) % 0.46/0.64 (define @t52 () (not @t32)) % 0.46/0.64 (define @t53 () (tptp.in @t15 @t11)) % 0.46/0.64 (define @t54 () (forall @t5 (not (and @t12 @t6)))) % 0.46/0.64 (define @t55 () (tptp.empty @t2)) % 0.46/0.64 (define @t56 () (not @t12)) % 0.46/0.64 (define @t57 () (or @t56 @t27 @t40)) % 0.46/0.64 (define @t58 () (@quantifiers_skolemize @t44 1)) % 0.46/0.64 (define @t59 () (tptp.singleton @t58)) % 0.46/0.64 (define @t60 () (@quantifiers_skolemize @t44 0)) % 0.46/0.64 (define @t61 () (@list @t60 @t59)) % 0.46/0.64 (define @t62 () (= @t1 @t11)) % 0.46/0.64 (define @t63 () (forall @t17 (or (not (tptp.in @t15 @t60)) (tptp.in @t15 @t59)))) % 0.46/0.64 (define @t64 () (tptp.subset @t60 @t59)) % 0.46/0.64 (define @t65 () (= @t64 @t63)) % 0.46/0.64 (define @t66 () (not @t65)) % 0.46/0.64 (define @t67 () (not @t64)) % 0.46/0.64 (define @t68 () (= @t60 @t59)) % 0.46/0.64 (define @t69 () (= tptp.empty_set @t60)) % 0.46/0.64 (define @t70 () (or @t69 @t68)) % 0.46/0.64 (define @t71 () (= @t64 @t70)) % 0.46/0.64 (define @t72 () (not @t71)) % 0.46/0.64 (define @t73 () (or (= @t60 tptp.empty_set) @t68)) % 0.46/0.64 (define @t74 () (= @t64 @t73)) % 0.46/0.64 (define @t75 () (not @t74)) % 0.46/0.64 (define @t76 () (@list true)) % 0.46/0.64 (define @t77 () (@quantifiers_skolemize @t63 0)) % 0.46/0.64 (define @t78 () (tptp.in @t77 @t59)) % 0.46/0.64 (define @t79 () (tptp.in @t77 @t60)) % 0.46/0.64 (define @t80 () (not @t79)) % 0.46/0.64 (define @t81 () (or @t80 @t78)) % 0.46/0.64 (define @t82 () (not @t81)) % 0.46/0.64 (define @t83 () (not @t63)) % 0.46/0.64 (define @t84 () (tptp.subset tptp.empty_set @t59)) % 0.46/0.64 (define @t85 () (not @t84)) % 0.46/0.64 (define @t86 () (not @t69)) % 0.46/0.64 (define @t87 () (= true false)) % 0.46/0.64 (define @t88 () (and @t67 @t69 @t84)) % 0.46/0.64 (define @t89 () (not @t70)) % 0.46/0.64 (define @t90 () (not @t68)) % 0.46/0.64 (define @t91 () (not @t78)) % 0.46/0.64 (define @t92 () (and @t91 @t68 @t79)) % 0.46/0.64 (define @t93 () (@list false false)) % 0.46/0.64 (define @t94 () (tptp.set_intersection2 @t60 @t59)) % 0.46/0.64 (define @t95 () (= @t60 @t94)) % 0.46/0.64 (define @t96 () (or @t67 @t95)) % 0.46/0.64 (define @t97 () (tptp.subset @t94 @t60)) % 0.46/0.64 (define @t98 () (tptp.subset @t60 @t60)) % 0.46/0.64 (define @t99 () (and @t95 @t97)) % 0.46/0.64 (define @t100 () (tptp.in @t58 @t60)) % 0.46/0.64 (define @t101 () (tptp.subset @t59 @t60)) % 0.46/0.64 (define @t102 () (forall @t5 (= @t4 @t36))) % 0.46/0.64 (define @t103 () (= @t100 @t101)) % 0.46/0.64 (define @t104 () (= @t101 @t100)) % 0.46/0.64 (define @t105 () (@list false)) % 0.46/0.64 (define @t106 () (@list true false)) % 0.46/0.64 (define @t107 () (@list @t70)) % 0.46/0.64 (define @t108 () (and @t64 @t90)) % 0.46/0.64 (define @t109 () (tptp.proper_subset @t60 @t59)) % 0.46/0.64 (define @t110 () (= @t109 @t108)) % 0.46/0.64 (define @t111 () (not @t109)) % 0.46/0.64 (define @t112 () (not @t101)) % 0.46/0.64 (define @t113 () (or @t112 @t111)) % 0.46/0.64 (define @t114 () (not @t100)) % 0.46/0.64 (define @t115 () (tptp.set_difference @t60 @t59)) % 0.46/0.64 (define @t116 () (tptp.subset @t60 @t115)) % 0.46/0.64 (define @t117 () (tptp.subset @t115 @t60)) % 0.46/0.64 (define @t118 () (and @t117 @t116)) % 0.46/0.64 (define @t119 () (= @t115 @t60)) % 0.46/0.64 (define @t120 () (= @t119 @t118)) % 0.46/0.64 (define @t121 () (= @t60 @t115)) % 0.46/0.64 (define @t122 () (= @t121 @t118)) % 0.46/0.64 (define @t123 () (= tptp.empty_set @t115)) % 0.46/0.64 (define @t124 () (= @t64 @t123)) % 0.46/0.64 (define @t125 () (not @t121)) % 0.46/0.64 (define @t126 () (not @t123)) % 0.46/0.64 (define @t127 () (and @t86 @t123)) % 0.46/0.64 (define @t128 () (not @t118)) % 0.46/0.64 (define @t129 () (not @t116)) % 0.46/0.64 (define @t130 () (not @t98)) % 0.46/0.64 (define @t131 () (or @t130 @t100 @t116)) % 0.46/0.64 (define @t132 () (not @t131)) % 0.46/0.64 (define @t133 () (forall @t24 @t57)) % 0.46/0.64 (assume @p1 (forall @t5 (=> @t4 @t3))) % 0.46/0.64 (assume @p2 (forall @t5 (=> @t7 (not @t6)))) % 0.46/0.64 (assume @p3 (forall @t5 (= @t8 (tptp.unordered_pair @t2 @t1)))) % 0.46/0.64 (assume @p4 (forall @t5 (= @t10 @t9))) % 0.46/0.64 (assume @p5 (forall @t5 (= @t11 (tptp.set_intersection2 @t2 @t1)))) % 0.46/0.64 (assume @p6 @t14) % 0.46/0.64 (assume @p7 (forall @t5 (= (= @t2 @t18) (forall @t17 (= @t16 (= @t15 @t1)))))) % 0.46/0.64 (assume @p8 (forall @t20 (= @t19 (forall (@list @t2) @t3)))) % 0.46/0.64 (assume @p9 (forall @t24 (= (= @t15 @t8) (forall @t23 (= @t22 (or (= @t21 @t1) (= @t21 @t2))))))) % 0.46/0.64 (assume @p10 (forall @t24 (= (= @t15 @t10) (forall @t23 (= @t22 (or @t26 @t25)))))) % 0.46/0.64 (assume @p11 @t30) % 0.46/0.64 (assume @p12 (forall @t24 (= (= @t15 @t11) (forall @t23 (= @t22 (and @t26 @t25)))))) % 0.46/0.64 (assume @p13 (forall @t24 (= (= @t15 @t31) (forall @t23 (= @t22 (and @t26 (not @t25))))))) % 0.46/0.64 (assume @p14 (forall @t5 (= @t32 (= @t11 tptp.empty_set)))) % 0.46/0.64 (assume @p15 (forall @t5 (= @t7 (and @t12 @t33)))) % 0.46/0.64 (assume @p16 true) % 0.46/0.64 (assume @p17 (tptp.empty tptp.empty_set)) % 0.46/0.64 (assume @p18 (forall @t5 (=> @t35 (not (tptp.empty @t10))))) % 0.46/0.64 (assume @p19 (forall @t5 (=> @t35 (not (tptp.empty @t9))))) % 0.46/0.64 (assume @p20 (forall @t5 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.46/0.64 (assume @p21 (forall @t5 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.46/0.64 (assume @p22 (forall @t5 (not (tptp.proper_subset @t1 @t1)))) % 0.46/0.64 (assume @p23 (forall @t20 (not (= @t18 tptp.empty_set)))) % 0.46/0.64 (assume @p24 @t37) % 0.46/0.64 (assume @p25 @t39) % 0.46/0.64 (assume @p26 @t42) % 0.46/0.64 (assume @p27 @t45) % 0.46/0.64 (assume @p28 (exists @t20 @t34)) % 0.46/0.64 (assume @p29 (exists @t20 @t35)) % 0.46/0.64 (assume @p30 (forall @t5 (tptp.subset @t1 @t1))) % 0.46/0.64 (assume @p31 (forall @t5 (=> @t32 (tptp.disjoint @t2 @t1)))) % 0.46/0.64 (assume @p32 (forall @t5 (=> @t12 (= @t10 @t2)))) % 0.46/0.64 (assume @p33 (forall @t5 (tptp.subset @t11 @t1))) % 0.46/0.64 (assume @p34 (forall @t24 (=> (and @t12 @t47) (tptp.subset @t1 @t46)))) % 0.46/0.64 (assume @p35 (forall @t20 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.46/0.64 (assume @p36 (forall @t24 (=> (and @t12 (tptp.subset @t2 @t15)) @t47))) % 0.46/0.64 (assume @p37 (forall @t24 (=> @t12 (tptp.subset (tptp.set_intersection2 @t1 @t15) @t46)))) % 0.46/0.64 (assume @p38 @t49) % 0.46/0.64 (assume @p39 (forall @t20 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.46/0.64 (assume @p40 (forall @t5 (=> (forall @t17 (= @t27 @t16)) @t13))) % 0.46/0.64 (assume @p41 (forall @t20 (tptp.subset tptp.empty_set @t1))) % 0.46/0.64 (assume @p42 (forall @t24 (=> @t12 (tptp.subset (tptp.set_difference @t1 @t15) (tptp.set_difference @t2 @t15))))) % 0.46/0.64 (assume @p43 (forall @t5 (tptp.subset @t31 @t1))) % 0.46/0.64 (assume @p44 (forall @t5 (= @t50 @t10))) % 0.46/0.64 (assume @p45 (forall @t20 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.46/0.64 (assume @p46 (forall @t5 (and (not (and @t52 (forall @t17 (not @t51)))) (not (and (exists @t17 @t51) @t32))))) % 0.46/0.64 (assume @p47 (forall @t20 (=> (tptp.subset @t1 tptp.empty_set) @t19))) % 0.46/0.64 (assume @p48 (forall @t5 (= (tptp.set_difference @t10 @t2) @t31))) % 0.46/0.64 (assume @p49 (forall @t5 (=> @t12 (= @t2 @t50)))) % 0.46/0.64 (assume @p50 (forall @t5 (= (tptp.set_difference @t1 @t31) @t11))) % 0.46/0.64 (assume @p51 (forall @t20 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.46/0.64 (assume @p52 (forall @t5 (and (not (and @t52 (forall @t17 (not @t53)))) (not (and (exists @t17 @t53) @t32))))) % 0.46/0.64 (assume @p53 @t54) % 0.46/0.64 (assume @p54 (forall @t24 (=> (and @t12 (tptp.disjoint @t2 @t15)) (tptp.disjoint @t1 @t15)))) % 0.46/0.64 (assume @p55 (forall @t20 (= (tptp.unordered_pair @t1 @t1) @t18))) % 0.46/0.64 (assume @p56 (forall @t20 (=> @t34 @t19))) % 0.46/0.64 (assume @p57 (forall @t5 (not (and @t4 @t55)))) % 0.46/0.64 (assume @p58 (forall @t5 (tptp.subset @t1 @t10))) % 0.46/0.64 (assume @p59 (forall @t5 (= @t32 (= @t31 @t1)))) % 0.46/0.64 (assume @p60 (forall @t5 (not (and @t34 @t33 @t55)))) % 0.46/0.64 (assume @p61 (forall @t24 (=> (and @t12 (tptp.subset @t15 @t2)) (tptp.subset (tptp.set_union2 @t1 @t15) @t2)))) % 0.46/0.64 (step @p62 :rule aci_norm :args ((= (or @t56 @t41) @t57))) % 0.46/0.64 (step @p63 :rule bool-impl-elim :args (@t12 @t41)) % 0.46/0.64 (step @p64 :rule trans :premises (@p63 @p62)) % 0.46/0.64 (step @p65 :rule cong :premises (@p64) :args (@t42)) % 0.46/0.64 (step @p66 :rule eq_resolve :premises (@p26 @p65)) % 0.46/0.64 (step @p67 :rule instantiate :premises (@p33) :args (@t61)) % 0.46/0.64 (step @p68 :rule bool-impl-elim :args (@t12 @t62)) % 0.46/0.64 (step @p69 :rule cong :premises (@p68) :args ((forall @t5 (=> @t12 @t62)))) % 0.46/0.64 (step @p70 :rule eq-symm :args (@t11 @t1)) % 0.46/0.64 (step @p71 :rule refl :args (@t12)) % 0.46/0.64 (step @p72 :rule cong :premises (@p71 @p70) :args (@t48)) % 0.46/0.64 (step @p73 :rule cong :premises (@p72) :args (@t49)) % 0.46/0.64 (step @p74 :rule trans :premises (@p73 @p69)) % 0.46/0.64 (step @p75 :rule eq_resolve :premises (@p38 @p74)) % 0.46/0.64 (step @p76 :rule instantiate :premises (@p75) :args (@t61)) % 0.46/0.64 (step @p77 :rule bool-impl-elim :args (@t27 @t16)) % 0.46/0.64 (step @p78 :rule cong :premises (@p77) :args (@t28)) % 0.46/0.64 (step @p79 :rule cong :premises (@p71 @p78) :args (@t29)) % 0.46/0.64 (step @p80 :rule cong :premises (@p79) :args (@t30)) % 0.46/0.64 (step @p81 :rule eq_resolve :premises (@p11 @p80)) % 0.46/0.64 (step @p82 :rule instantiate :premises (@p81) :args (@t61)) % 0.46/0.64 (step @p83 :rule cnf_equiv_pos1 :args (@t65)) % 0.46/0.64 (step @p84 :rule reordering :premises (@p83) :args ((or @t67 @t63 @t66))) % 0.46/0.64 (step @p85 :rule refl :args (@t72)) % 0.46/0.64 (step @p86 :rule bool-double-not-elim :args (@t44)) % 0.46/0.64 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or (not @t45) @t72))) % 0.46/0.64 (step @p88 :rule refl :args (@t68)) % 0.46/0.64 (step @p89 :rule eq-symm :args (@t60 tptp.empty_set)) % 0.46/0.64 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t73)) % 0.46/0.64 (step @p91 :rule refl :args (@t64)) % 0.46/0.64 (step @p92 :rule cong :premises (@p91 @p90) :args (@t74)) % 0.46/0.64 (step @p93 :rule cong :premises (@p92) :args (@t75)) % 0.46/0.64 (step @p94 :rule refl :args (@t45)) % 0.46/0.64 (step @p95 :rule cong :premises (@p94 @p93) :args ((=> @t45 @t75))) % 0.46/0.64 (assume-push @p328 @t45) % 0.46/0.64 (step @p97 :rule skolemize :premises (@p27)) % 0.46/0.64 (step-pop @p329 :rule scope :premises (@p97)) % 0.46/0.64 (step @p98 :rule process_scope :premises (@p329) :args (@t75)) % 0.46/0.64 (step @p100 :rule eq_resolve :premises (@p98 @p95)) % 0.46/0.64 (step @p101 :rule implies_elim :premises (@p100)) % 0.46/0.64 (step @p102 :rule eq_resolve :premises (@p101 @p87)) % 0.46/0.64 (step @p103 :rule chain_m_resolution :premises (@p102 @p27) :args (@t72 @t76 (@list @t44))) % 0.46/0.64 (step @p104 :rule cnf_equiv_neg1 :args (@t71)) % 0.46/0.64 (step @p105 :rule reordering :premises (@p104) :args ((or @t64 @t70 @t71))) % 0.46/0.64 (step @p106 :rule refl :args (@t82)) % 0.46/0.64 (step @p107 :rule bool-double-not-elim :args (@t63)) % 0.46/0.64 (step @p108 :rule nary_cong :premises (@p107 @p106) :args ((or (not @t83) @t82))) % 0.46/0.64 (assume-push @p330 @t83) % 0.46/0.64 (step @p110 :rule skolemize :premises (@p330)) % 0.46/0.64 (step-pop @p331 :rule scope :premises (@p110)) % 0.46/0.64 (step @p111 :rule process_scope :premises (@p331) :args (@t82)) % 0.46/0.64 (step @p113 :rule implies_elim 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0.46/0.64 % SZS output end Proof % 0.46/0.64 % cvc5 exiting %------------------------------------------------------------------------------