%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV127^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n027.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 08:55:29 AM UTC 2026 % Result : Theorem 0.45s 0.68s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV127^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n027.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 18:14:51 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.45/0.68 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.68 % SZS status Theorem % 0.45/0.68 % SZS output start Proof % 0.45/0.68 ( % 0.45/0.68 (declare-sort tptp.a 0) % 0.45/0.68 (define @t1 () (@var "Xy" tptp.a)) % 0.45/0.68 (define @t2 () (@var "Xx" tptp.a)) % 0.45/0.68 (define @t3 () (@var "Xp" (-> tptp.a tptp.a Bool))) % 0.45/0.68 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.45/0.68 (define @t5 () (@var "P" (-> (-> tptp.a tptp.a Bool) Bool))) % 0.45/0.68 (define @t6 () (_ @t5 @t3)) % 0.45/0.68 (define @t7 () (@var "Xy0" tptp.a)) % 0.45/0.68 (define @t8 () (@var "Xx0" tptp.a)) % 0.45/0.68 (define @t9 () (_ (_ @t3 @t8) @t7)) % 0.45/0.68 (define @t10 () (@var "S" (-> tptp.a tptp.a Bool))) % 0.45/0.68 (define @t11 () (_ (_ @t10 @t8) @t7)) % 0.45/0.68 (define @t12 () (@var "R" (-> tptp.a tptp.a Bool))) % 0.45/0.68 (define @t13 () (_ (_ @t12 @t8) @t7)) % 0.45/0.68 (define @t14 () (or @t13 @t11)) % 0.45/0.68 (define @t15 () (@list @t8 @t7)) % 0.45/0.68 (define @t16 () (forall @t15 (=> @t14 @t9))) % 0.45/0.68 (define @t17 () (and @t16 @t6)) % 0.45/0.68 (define @t18 () (=> @t17 @t4)) % 0.45/0.68 (define @t19 () (@list @t3)) % 0.45/0.68 (define @t20 () (forall @t19 @t18)) % 0.45/0.68 (define @t21 () (@var "Xp0" (-> tptp.a tptp.a Bool))) % 0.45/0.68 (define @t22 () (_ (_ @t21 @t8) @t7)) % 0.45/0.68 (define @t23 () (_ @t5 @t21)) % 0.45/0.68 (define @t24 () (@var "Xy1" tptp.a)) % 0.45/0.68 (define @t25 () (@var "Xx1" tptp.a)) % 0.45/0.68 (define @t26 () (_ (_ @t21 @t25) @t24)) % 0.45/0.68 (define @t27 () (_ (_ @t10 @t25) @t24)) % 0.45/0.68 (define @t28 () (@list @t25 @t24)) % 0.45/0.68 (define @t29 () (forall @t28 (=> @t27 @t26))) % 0.45/0.68 (define @t30 () (and @t29 @t23)) % 0.45/0.68 (define @t31 () (=> @t30 @t22)) % 0.45/0.68 (define @t32 () (@list @t21)) % 0.45/0.68 (define @t33 () (forall @t32 @t31)) % 0.45/0.68 (define @t34 () (_ (_ @t12 @t25) @t24)) % 0.45/0.68 (define @t35 () (forall @t28 (=> @t34 @t26))) % 0.45/0.68 (define @t36 () (and @t35 @t23)) % 0.45/0.68 (define @t37 () (=> @t36 @t22)) % 0.45/0.68 (define @t38 () (forall @t32 @t37)) % 0.45/0.68 (define @t39 () (or @t38 @t33)) % 0.45/0.68 (define @t40 () (=> @t39 @t9)) % 0.45/0.68 (define @t41 () (forall @t15 @t40)) % 0.45/0.68 (define @t42 () (and @t41 @t6)) % 0.45/0.68 (define @t43 () (=> @t42 @t4)) % 0.45/0.68 (define @t44 () (forall @t19 @t43)) % 0.45/0.68 (define @t45 () (=> @t44 @t20)) % 0.45/0.68 (define @t46 () (@list @t5 @t12 @t10 @t2 @t1)) % 0.45/0.68 (define @t47 () (forall @t46 @t45)) % 0.45/0.68 (define @t48 () (not @t47)) % 0.45/0.68 (define @t49 () (@var "BOUND_VARIABLE_7562" (-> tptp.a tptp.a Bool))) % 0.45/0.68 (define @t50 () (_ @t49 @t2 @t1)) % 0.45/0.68 (define @t51 () (not (_ @t5 @t49))) % 0.45/0.68 (define @t52 () (_ @t10 @t8 @t7)) % 0.45/0.68 (define @t53 () (_ @t12 @t8 @t7)) % 0.45/0.68 (define @t54 () (and (not @t53) (not @t52))) % 0.45/0.68 (define @t55 () (not (forall @t15 (or @t54 (_ @t49 @t8 @t7))))) % 0.45/0.68 (define @t56 () (_ @t3 @t2 @t1)) % 0.45/0.68 (define @t57 () (_ @t5 @t3)) % 0.45/0.68 (define @t58 () (not @t57)) % 0.45/0.68 (define @t59 () (_ @t3 @t8 @t7)) % 0.45/0.68 (define @t60 () (_ @t21 @t8 @t7)) % 0.45/0.68 (define @t61 () (_ @t5 @t21)) % 0.45/0.68 (define @t62 () (not @t61)) % 0.45/0.68 (define @t63 () (_ @t21 @t25 @t24)) % 0.45/0.68 (define @t64 () (_ @t10 @t25 @t24)) % 0.45/0.68 (define @t65 () (forall @t28 (or (not @t64) @t63))) % 0.45/0.68 (define @t66 () (not @t65)) % 0.45/0.68 (define @t67 () (forall @t32 (or @t66 @t62 @t60))) % 0.45/0.68 (define @t68 () (_ @t12 @t25 @t24)) % 0.45/0.68 (define @t69 () (forall @t28 (or (not @t68) @t63))) % 0.45/0.68 (define @t70 () (not @t69)) % 0.45/0.68 (define @t71 () (forall @t32 (or @t70 @t62 @t60))) % 0.45/0.68 (define @t72 () (and (not @t71) (not @t67))) % 0.45/0.68 (define @t73 () (forall @t15 (or @t72 @t59))) % 0.45/0.68 (define @t74 () (not @t73)) % 0.45/0.68 (define @t75 () (forall @t19 (or @t74 @t58 @t56))) % 0.45/0.68 (define @t76 () (not @t75)) % 0.45/0.68 (define @t77 () (or @t76 @t55 @t51 @t50)) % 0.45/0.68 (define @t78 () (or @t55 @t51 @t50)) % 0.45/0.68 (define @t79 () (or @t76 @t78)) % 0.45/0.68 (define @t80 () (@list @t5 @t12 @t10 @t2 @t1 @t49)) % 0.45/0.68 (define @t81 () (forall @t80 @t79)) % 0.45/0.68 (define @t82 () (@list @t49)) % 0.45/0.68 (define @t83 () (forall @t82 @t79)) % 0.45/0.68 (define @t84 () (forall @t82 @t78)) % 0.45/0.68 (define @t85 () (or @t76 @t84)) % 0.45/0.68 (define @t86 () (forall @t15 (or @t54 @t59))) % 0.45/0.68 (define @t87 () (not @t86)) % 0.45/0.68 (define @t88 () (forall @t19 (or @t87 @t58 @t56))) % 0.45/0.68 (define @t89 () (not @t6)) % 0.45/0.68 (define @t90 () (or @t87 @t89 @t4)) % 0.45/0.68 (define @t91 () (and @t86 @t6)) % 0.45/0.68 (define @t92 () (not @t11)) % 0.45/0.68 (define @t93 () (not @t13)) % 0.45/0.68 (define @t94 () (and @t93 @t92)) % 0.45/0.68 (define @t95 () (or @t94 @t9)) % 0.45/0.68 (define @t96 () (or @t74 @t89 @t4)) % 0.45/0.68 (define @t97 () (and @t73 @t6)) % 0.45/0.68 (define @t98 () (or @t72 @t9)) % 0.45/0.68 (define @t99 () (or @t71 @t67)) % 0.45/0.68 (define @t100 () (not @t23)) % 0.45/0.68 (define @t101 () (or @t66 @t100 @t22)) % 0.45/0.68 (define @t102 () (and @t65 @t23)) % 0.45/0.68 (define @t103 () (not @t27)) % 0.45/0.68 (define @t104 () (or @t103 @t26)) % 0.45/0.68 (define @t105 () (or @t70 @t100 @t22)) % 0.45/0.68 (define @t106 () (and @t69 @t23)) % 0.45/0.68 (define @t107 () (not @t34)) % 0.45/0.68 (define @t108 () (or @t107 @t26)) % 0.45/0.68 (define @t109 () (forall @t80 @t77)) % 0.45/0.68 (define @t110 () (@quantifiers_skolemize @t109 4)) % 0.45/0.68 (define @t111 () (@quantifiers_skolemize @t109 3)) % 0.45/0.68 (define @t112 () (@quantifiers_skolemize @t109 0)) % 0.45/0.68 (define @t113 () (not (_ @t112 @t21))) % 0.45/0.68 (define @t114 () (@quantifiers_skolemize @t109 2)) % 0.45/0.68 (define @t115 () (not (_ @t114 @t25 @t24))) % 0.45/0.68 (define @t116 () (not (forall @t28 (or @t115 @t63)))) % 0.45/0.68 (define @t117 () (@quantifiers_skolemize @t109 1)) % 0.45/0.68 (define @t118 () (not (_ @t117 @t25 @t24))) % 0.45/0.68 (define @t119 () (not (forall @t28 (or @t118 @t63)))) % 0.45/0.68 (define @t120 () (and (not (forall @t32 (or @t119 @t113 @t60))) (not (forall @t32 (or @t116 @t113 @t60))))) % 0.45/0.68 (define @t121 () (forall @t19 (or (not (forall @t15 (or @t120 @t59))) (not (_ @t112 @t3)) (_ @t3 @t111 @t110)))) % 0.45/0.68 (define @t122 () (@quantifiers_skolemize @t109 5)) % 0.45/0.68 (define @t123 () (_ @t122 @t111 @t110)) % 0.45/0.68 (define @t124 () (_ @t112 @t122)) % 0.45/0.68 (define @t125 () (not @t124)) % 0.45/0.68 (define @t126 () (_ @t122 @t8 @t7)) % 0.45/0.68 (define @t127 () (forall @t15 (or (and (not (_ @t117 @t8 @t7)) (not (_ @t114 @t8 @t7))) @t126))) % 0.45/0.68 (define @t128 () (not @t127)) % 0.45/0.68 (define @t129 () (not @t121)) % 0.45/0.68 (define @t130 () (or @t129 @t128 @t125 @t123)) % 0.45/0.68 (define @t131 () (@list true)) % 0.45/0.68 (define @t132 () (@list @t130)) % 0.45/0.68 (define @t133 () (@list @t122)) % 0.45/0.68 (define @t134 () (forall @t15 (or @t120 @t126))) % 0.45/0.68 (define @t135 () (not @t134)) % 0.45/0.68 (define @t136 () (or @t135 @t125 @t123)) % 0.45/0.68 (define @t137 () (@list false true false)) % 0.45/0.68 (define @t138 () (@quantifiers_skolemize @t134 1)) % 0.45/0.68 (define @t139 () (@quantifiers_skolemize @t134 0)) % 0.45/0.68 (define @t140 () (_ @t122 @t139 @t138)) % 0.45/0.68 (define @t141 () (_ @t21 @t139 @t138)) % 0.45/0.68 (define @t142 () (forall @t32 (or @t116 @t113 @t141))) % 0.45/0.68 (define @t143 () (not @t142)) % 0.45/0.68 (define @t144 () (forall @t32 (or @t119 @t113 @t141))) % 0.45/0.68 (define @t145 () (not @t144)) % 0.45/0.68 (define @t146 () (and @t145 @t143)) % 0.45/0.68 (define @t147 () (or @t146 @t140)) % 0.45/0.68 (define @t148 () (@list @t147)) % 0.45/0.68 (define @t149 () (_ @t122 @t25 @t24)) % 0.45/0.68 (define @t150 () (forall @t28 (or @t118 @t149))) % 0.45/0.68 (define @t151 () (@quantifiers_skolemize @t150 1)) % 0.45/0.68 (define @t152 () (@quantifiers_skolemize @t150 0)) % 0.45/0.68 (define @t153 () (_ @t117 @t152 @t151)) % 0.45/0.68 (define @t154 () (_ @t122 @t152 @t151)) % 0.45/0.68 (define @t155 () (not @t153)) % 0.45/0.68 (define @t156 () (or @t155 @t154)) % 0.45/0.68 (define @t157 () (and @t155 (not (_ @t114 @t152 @t151)))) % 0.45/0.68 (define @t158 () (or @t157 @t154)) % 0.45/0.68 (define @t159 () (not @t156)) % 0.45/0.68 (define @t160 () (not @t150)) % 0.45/0.68 (define @t161 () (@list false)) % 0.45/0.68 (define @t162 () (or @t160 @t125 @t140)) % 0.45/0.68 (define @t163 () (not @t162)) % 0.45/0.68 (define @t164 () (forall @t28 (or @t115 @t149))) % 0.45/0.68 (define @t165 () (not @t164)) % 0.45/0.68 (define @t166 () (or @t165 @t125 @t140)) % 0.45/0.68 (define @t167 () (@quantifiers_skolemize @t164 1)) % 0.45/0.68 (define @t168 () (@quantifiers_skolemize @t164 0)) % 0.45/0.68 (define @t169 () (_ @t122 @t168 @t167)) % 0.45/0.68 (define @t170 () (_ @t114 @t168 @t167)) % 0.45/0.68 (define @t171 () (not @t170)) % 0.45/0.68 (define @t172 () (or @t171 @t169)) % 0.45/0.68 (define @t173 () (not @t172)) % 0.45/0.68 (define @t174 () (@list @t172)) % 0.45/0.68 (define @t175 () (and (not (_ @t117 @t168 @t167)) @t171)) % 0.45/0.68 (define @t176 () (not @t175)) % 0.45/0.68 (define @t177 () (or @t175 @t169)) % 0.45/0.68 (assume @p1 @t48) % 0.45/0.68 (assume @p2 true) % 0.45/0.68 (step @p3 :rule aci_norm :args ((= @t79 @t77))) % 0.45/0.68 (step @p4 :rule cong :premises (@p3) :args (@t81)) % 0.45/0.68 (step @p5 :rule quant-merge-prenex :args ((= (forall @t46 @t83) @t81))) % 0.45/0.68 (step @p6 :rule alpha_equiv :args (@t84 (@list @t49) (@list @t3))) % 0.45/0.68 (step @p7 :rule refl :args (@t76)) % 0.45/0.68 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t85)) % 0.45/0.68 (step @p9 :rule quant-miniscope-or :args ((= @t83 @t85))) % 0.45/0.68 (step @p10 :rule trans :premises (@p9 @p8)) % 0.45/0.68 (step @p11 :rule symm :premises (@p10)) % 0.45/0.68 (step @p12 :rule cong :premises (@p11) :args ((forall @t46 (or @t76 @t88)))) % 0.45/0.68 (step @p13 :rule trans :premises (@p12 @p5)) % 0.45/0.68 (step @p14 :rule trans :premises (@p13 @p4)) % 0.45/0.68 (step @p15 :rule bool-impl-elim :args (@t75 @t88)) % 0.45/0.68 (step @p16 :rule cong :premises (@p15) :args ((forall @t46 (=> @t75 @t88)))) % 0.45/0.68 (step @p17 :rule trans :premises (@p16 @p14)) % 0.45/0.68 (step @p18 :rule refl :args (@t56)) % 0.45/0.68 (step @p19 :rule refl :args (@t4)) % 0.45/0.68 (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t4 @t56))) % 0.45/0.68 (step @p21 :rule symm :premises (@p20)) % 0.45/0.68 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.45/0.68 (step @p23 :rule refl :args (@t57)) % 0.45/0.68 (step @p24 :rule refl :args (@t6)) % 0.45/0.68 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t6 @t57))) % 0.45/0.68 (step @p26 :rule symm :premises (@p25)) % 0.45/0.68 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.45/0.68 (step @p28 :rule cong :premises (@p27) :args (@t89)) % 0.45/0.68 (step @p29 :rule refl :args (@t87)) % 0.45/0.68 (step @p30 :rule nary_cong :premises (@p29 @p28 @p22) :args (@t90)) % 0.45/0.68 (step @p31 :rule cong :premises (@p30) :args ((forall @t19 @t90))) % 0.45/0.68 (step @p32 :rule aci_norm :args ((= (or (or @t87 @t89) @t4) @t90))) % 0.45/0.68 (step @p33 :rule bool-and-de-morgan :args (@t86 @t6 true)) % 0.45/0.68 (step @p34 :rule nary_cong :premises (@p33 @p19) :args ((or (not @t91) @t4))) % 0.45/0.68 (step @p35 :rule trans :premises (@p34 @p32)) % 0.45/0.68 (step @p36 :rule bool-impl-elim :args (@t91 @t4)) % 0.45/0.68 (step @p37 :rule trans :premises (@p36 @p35)) % 0.45/0.68 (step @p38 :rule cong :premises (@p37) :args ((forall @t19 (=> @t91 @t4)))) % 0.45/0.68 (step @p39 :rule trans :premises (@p38 @p31)) % 0.45/0.68 (step @p40 :rule refl :args (@t4)) % 0.45/0.68 (step @p41 :rule refl :args (@t6)) % 0.45/0.68 (step @p42 :rule refl :args (@t59)) % 0.45/0.68 (step @p43 :rule refl :args (@t9)) % 0.45/0.68 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t9 @t59))) % 0.45/0.68 (step @p45 :rule symm :premises (@p44)) % 0.45/0.68 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.45/0.68 (step @p47 :rule refl :args (@t52)) % 0.45/0.68 (step @p48 :rule refl :args (@t11)) % 0.45/0.68 (step @p49 :rule cong :premises (@p48 @p47) :args ((= @t11 @t52))) % 0.45/0.68 (step @p50 :rule symm :premises (@p49)) % 0.45/0.68 (step @p51 :rule eq_resolve :premises (@p48 @p50)) % 0.45/0.68 (step @p52 :rule cong :premises (@p51) :args (@t92)) % 0.45/0.68 (step @p53 :rule refl :args (@t53)) % 0.45/0.68 (step @p54 :rule refl :args (@t13)) % 0.45/0.68 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t13 @t53))) % 0.45/0.68 (step @p56 :rule symm :premises (@p55)) % 0.45/0.68 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 0.45/0.68 (step @p58 :rule cong :premises (@p57) :args (@t93)) % 0.45/0.68 (step @p59 :rule nary_cong :premises (@p58 @p52) :args (@t94)) % 0.45/0.68 (step @p60 :rule nary_cong :premises (@p59 @p46) :args (@t95)) % 0.45/0.68 (step @p61 :rule cong :premises (@p60) :args ((forall @t15 @t95))) % 0.45/0.68 (step @p62 :rule bool-or-de-morgan :args (@t13 @t11 false)) % 0.45/0.68 (step @p63 :rule nary_cong :premises (@p62 @p43) :args ((or (not @t14) @t9))) % 0.45/0.68 (step @p64 :rule bool-impl-elim :args (@t14 @t9)) % 0.45/0.68 (step @p65 :rule trans :premises (@p64 @p63)) % 0.45/0.68 (step @p66 :rule cong :premises (@p65) :args (@t16)) % 0.45/0.68 (step @p67 :rule trans :premises (@p66 @p61)) % 0.45/0.68 (step @p68 :rule nary_cong :premises (@p67 @p41) :args (@t17)) % 0.45/0.68 (step @p69 :rule cong :premises (@p68 @p40) :args (@t18)) % 0.45/0.68 (step @p70 :rule cong :premises (@p69) :args (@t20)) % 0.45/0.68 (step @p71 :rule trans :premises (@p70 @p39)) % 0.45/0.68 (step @p72 :rule refl :args (@t74)) % 0.45/0.68 (step @p73 :rule nary_cong :premises (@p72 @p28 @p22) :args (@t96)) % 0.45/0.68 (step @p74 :rule cong :premises (@p73) :args ((forall @t19 @t96))) % 0.45/0.68 (step @p75 :rule aci_norm :args ((= (or (or @t74 @t89) @t4) @t96))) % 0.45/0.68 (step @p76 :rule bool-and-de-morgan :args (@t73 @t6 true)) % 0.45/0.68 (step @p77 :rule nary_cong :premises (@p76 @p19) :args ((or (not @t97) @t4))) % 0.45/0.68 (step @p78 :rule trans :premises (@p77 @p75)) % 0.45/0.68 (step @p79 :rule bool-impl-elim :args (@t97 @t4)) % 0.45/0.68 (step @p80 :rule trans :premises (@p79 @p78)) % 0.45/0.68 (step @p81 :rule cong :premises (@p80) :args ((forall @t19 (=> @t97 @t4)))) % 0.45/0.68 (step @p82 :rule trans :premises (@p81 @p74)) % 0.45/0.68 (step @p83 :rule refl :args (@t72)) % 0.45/0.68 (step @p84 :rule nary_cong :premises (@p83 @p46) :args (@t98)) % 0.45/0.68 (step @p85 :rule cong :premises (@p84) :args ((forall @t15 @t98))) % 0.45/0.68 (step @p86 :rule bool-or-de-morgan :args (@t71 @t67 false)) % 0.45/0.68 (step @p87 :rule nary_cong :premises (@p86 @p43) :args ((or (not @t99) @t9))) % 0.45/0.68 (step @p88 :rule bool-impl-elim :args (@t99 @t9)) % 0.45/0.68 (step @p89 :rule trans :premises (@p88 @p87)) % 0.45/0.68 (step @p90 :rule cong :premises (@p89) :args ((forall @t15 (=> @t99 @t9)))) % 0.45/0.68 (step @p91 :rule trans :premises (@p90 @p85)) % 0.45/0.68 (step @p92 :rule refl :args (@t9)) % 0.45/0.68 (step @p93 :rule refl :args (@t60)) % 0.45/0.68 (step @p94 :rule refl :args (@t22)) % 0.45/0.68 (step @p95 :rule cong 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