%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP023+1 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:24:46 AM UTC 2026 % Result : Theorem 0.45s 0.65s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP023+1 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n002.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 04:05:18 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.65 % SZS status Theorem % 0.45/0.65 % SZS output start Proof % 0.45/0.65 ( % 0.45/0.65 (declare-sort $$unsorted 0) % 0.45/0.65 (declare-const tptp.c_2Epred__set_2ESUBSET_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ereal__topology_2Ecball_2E1 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ereal__topology_2Ecball_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Ereal__topology_2Eball_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.combin_s_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.combin_k_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.tyop_2Erealax_2Ereal $$unsorted) % 0.45/0.65 (declare-const tptp.combin_i_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.p (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.tyop_2Emin_2Ebool $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Emin_2E_3D_3D_3E_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Epair_2E_2C_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_7E_2E1 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ebool_2EF_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.s (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ereal__topology_2Eball_2E1 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_3F_2E1 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ebool_2ET_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_2F_5C_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ereal__topology_2Ebounded__def_2E1 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.tyop_2Emin_2Efun (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Emin_2E_3D_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ereal__topology_2Ebounded__def_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Epair_2E_2C_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_21_2E1 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.app_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_2F_5C_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_7E_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Emin_2E_3D_3D_3E_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_5C_2F_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Emin_2E_3D_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_5C_2F_2E2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_21_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Epred__set_2ESUBSET_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.c_2Ebool_2E_3F_2E0 $$unsorted) % 0.45/0.65 (declare-const tptp.tyop_2Epair_2Eprod (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (define @t1 () (@var "V1g_2E0" $$unsorted)) % 0.45/0.65 (define @t2 () (@var "A_27b" $$unsorted)) % 0.45/0.65 (define @t3 () (@var "A_27a" $$unsorted)) % 0.45/0.65 (define @t4 () (tptp.tyop_2Emin_2Efun @t3 @t2)) % 0.45/0.65 (define @t5 () (tptp.s @t4 @t1)) % 0.45/0.65 (define @t6 () (@var "V0f_2E0" $$unsorted)) % 0.45/0.65 (define @t7 () (tptp.s @t4 @t6)) % 0.45/0.65 (define @t8 () (@var "V2x_2E0" $$unsorted)) % 0.45/0.65 (define @t9 () (tptp.s @t3 @t8)) % 0.45/0.65 (define @t10 () (tptp.s @t2 (tptp.app_2E2 @t5 @t9))) % 0.45/0.65 (define @t11 () (@list @t8)) % 0.45/0.65 (define @t12 () (@var "V1_2E0" $$unsorted)) % 0.45/0.65 (define @t13 () (tptp.s tptp.tyop_2Emin_2Ebool @t12)) % 0.45/0.65 (define @t14 () (@var "V0_2E0" $$unsorted)) % 0.45/0.65 (define @t15 () (tptp.s tptp.tyop_2Emin_2Ebool @t14)) % 0.45/0.65 (define @t16 () (tptp.p @t13)) % 0.45/0.65 (define @t17 () (tptp.p @t15)) % 0.45/0.65 (define @t18 () (@list @t14 @t12)) % 0.45/0.65 (define @t19 () (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2ET_2E0)) % 0.45/0.65 (define @t20 () (tptp.p @t19)) % 0.45/0.65 (define @t21 () (tptp.s tptp.tyop_2Emin_2Ebool tptp.c_2Ebool_2EF_2E0)) % 0.45/0.65 (define @t22 () (tptp.p @t21)) % 0.45/0.65 (define @t23 () (not @t22)) % 0.45/0.65 (define @t24 () (@var "V0t_2E0" $$unsorted)) % 0.45/0.65 (define @t25 () (tptp.s tptp.tyop_2Emin_2Ebool @t24)) % 0.45/0.65 (define @t26 () (= @t25 @t21)) % 0.45/0.65 (define @t27 () (= @t25 @t19)) % 0.45/0.65 (define @t28 () (@list @t24)) % 0.45/0.65 (define @t29 () (@var "V0x_2E0" $$unsorted)) % 0.45/0.65 (define @t30 () (tptp.s @t3 @t29)) % 0.45/0.65 (define @t31 () (@var "V1y_2E0" $$unsorted)) % 0.45/0.65 (define @t32 () (tptp.tyop_2Emin_2Efun @t2 @t3)) % 0.45/0.65 (define @t33 () (@var "A_27c" $$unsorted)) % 0.45/0.65 (define @t34 () (tptp.tyop_2Emin_2Efun @t2 @t33)) % 0.45/0.65 (define @t35 () (tptp.tyop_2Emin_2Efun @t3 @t34)) % 0.45/0.65 (define @t36 () (tptp.s @t35 @t6)) % 0.45/0.65 (define @t37 () (tptp.tyop_2Emin_2Efun @t3 @t33)) % 0.45/0.65 (define @t38 () (tptp.tyop_2Emin_2Efun @t4 @t37)) % 0.45/0.65 (define @t39 () (tptp.s @t3 @t12)) % 0.45/0.65 (define @t40 () (tptp.s @t3 @t14)) % 0.45/0.65 (define @t41 () (@var "V1x_2E0" $$unsorted)) % 0.45/0.65 (define @t42 () (tptp.s @t3 @t41)) % 0.45/0.65 (define @t43 () (tptp.tyop_2Emin_2Efun @t3 tptp.tyop_2Emin_2Ebool)) % 0.45/0.65 (define @t44 () (tptp.s @t43 @t6)) % 0.45/0.65 (define @t45 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t44 @t42)))) % 0.45/0.65 (define @t46 () (@list @t41)) % 0.45/0.65 (define @t47 () (@list @t3 @t6)) % 0.45/0.65 (define @t48 () (@var "X1_2E0" $$unsorted)) % 0.45/0.65 (define @t49 () (tptp.s tptp.tyop_2Emin_2Ebool @t48)) % 0.45/0.65 (define @t50 () (@var "X0_2E0" $$unsorted)) % 0.45/0.65 (define @t51 () (tptp.s tptp.tyop_2Emin_2Ebool @t50)) % 0.45/0.65 (define @t52 () (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool tptp.tyop_2Emin_2Ebool)) % 0.45/0.65 (define @t53 () (tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool @t52)) % 0.45/0.65 (define @t54 () (tptp.p @t49)) % 0.45/0.65 (define @t55 () (tptp.p @t51)) % 0.45/0.65 (define @t56 () (@list @t50 @t48)) % 0.45/0.65 (define @t57 () (@list @t50)) % 0.45/0.65 (define @t58 () (tptp.s @t3 @t48)) % 0.45/0.65 (define @t59 () (tptp.s @t3 @t50)) % 0.45/0.65 (define @t60 () (tptp.s @t43 @t50)) % 0.45/0.65 (define @t61 () (tptp.tyop_2Emin_2Efun @t43 tptp.tyop_2Emin_2Ebool)) % 0.45/0.65 (define @t62 () (@list @t3 @t50)) % 0.45/0.65 (define @t63 () (tptp.tyop_2Emin_2Efun tptp.tyop_2Erealax_2Ereal tptp.tyop_2Emin_2Ebool)) % 0.45/0.65 (define @t64 () (tptp.s @t63 @t50)) % 0.45/0.65 (define @t65 () (tptp.tyop_2Emin_2Efun @t63 tptp.tyop_2Emin_2Ebool)) % 0.45/0.65 (define @t66 () (tptp.s tptp.tyop_2Erealax_2Ereal @t48)) % 0.45/0.65 (define @t67 () (tptp.s tptp.tyop_2Erealax_2Ereal @t50)) % 0.45/0.65 (define @t68 () (tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal tptp.tyop_2Erealax_2Ereal)) % 0.45/0.65 (define @t69 () (tptp.tyop_2Emin_2Efun tptp.tyop_2Erealax_2Ereal @t68)) % 0.45/0.65 (define @t70 () (tptp.s @t68 @t50)) % 0.45/0.65 (define @t71 () (tptp.tyop_2Emin_2Efun @t68 @t63)) % 0.45/0.65 (define @t72 () (tptp.s @t63 @t48)) % 0.45/0.65 (define @t73 () (@var "V1t2_2E0" $$unsorted)) % 0.45/0.65 (define @t74 () (tptp.s tptp.tyop_2Emin_2Ebool @t73)) % 0.45/0.65 (define @t75 () (@var "V0t1_2E0" $$unsorted)) % 0.45/0.65 (define @t76 () (tptp.s tptp.tyop_2Emin_2Ebool @t75)) % 0.45/0.65 (define @t77 () (tptp.p @t76)) % 0.45/0.65 (define @t78 () (tptp.p @t74)) % 0.45/0.65 (define @t79 () (tptp.p @t25)) % 0.45/0.65 (define @t80 () (not @t79)) % 0.45/0.65 (define @t81 () (=> @t79 @t22)) % 0.45/0.65 (define @t82 () (forall @t28 (= (not @t80) @t79))) % 0.45/0.65 (define @t83 () (tptp.s @t3 @t31)) % 0.45/0.65 (define @t84 () (@var "V0P_2E0" $$unsorted)) % 0.45/0.65 (define @t85 () (tptp.s @t43 @t84)) % 0.45/0.65 (define @t86 () (@var "V2C_2E0" $$unsorted)) % 0.45/0.65 (define @t87 () (@var "V1B_2E0" $$unsorted)) % 0.45/0.65 (define @t88 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t87))) % 0.45/0.65 (define @t89 () (@var "V0A_2E0" $$unsorted)) % 0.45/0.65 (define @t90 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t89))) % 0.45/0.65 (define @t91 () (or @t90 @t88 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t86)))) % 0.45/0.65 (define @t92 () (or @t90 @t88)) % 0.45/0.65 (define @t93 () (@list @t89 @t87)) % 0.45/0.65 (define @t94 () (not @t88)) % 0.45/0.65 (define @t95 () (not @t90)) % 0.45/0.65 (define @t96 () (@var "V1e_2E0" $$unsorted)) % 0.45/0.65 (define @t97 () (tptp.s @t68 (tptp.c_2Epair_2E_2C_2E2 (tptp.s tptp.tyop_2Erealax_2Ereal @t29) (tptp.s tptp.tyop_2Erealax_2Ereal @t96)))) % 0.45/0.65 (define @t98 () (tptp.s @t63 (tptp.c_2Ereal__topology_2Ecball_2E1 @t97))) % 0.45/0.65 (define @t99 () (tptp.s @t63 (tptp.c_2Ereal__topology_2Eball_2E1 @t97))) % 0.45/0.65 (define @t100 () (@list @t29 @t96)) % 0.45/0.65 (define @t101 () (@var "V0s_2E0" $$unsorted)) % 0.45/0.65 (define @t102 () (tptp.s @t63 @t101)) % 0.45/0.65 (define @t103 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ereal__topology_2Ebounded__def_2E1 @t102)))) % 0.45/0.65 (define @t104 () (@var "V1t_2E0" $$unsorted)) % 0.45/0.65 (define @t105 () (tptp.s @t63 @t104)) % 0.45/0.65 (define @t106 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Epred__set_2ESUBSET_2E2 @t102 @t105)))) % 0.45/0.65 (define @t107 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ereal__topology_2Ebounded__def_2E1 @t105)))) % 0.45/0.65 (define @t108 () (and @t107 @t106)) % 0.45/0.65 (define @t109 () (@list @t101 @t104)) % 0.45/0.65 (define @t110 () (forall @t109 (=> @t108 @t103))) % 0.45/0.65 (define @t111 () (=> @t95 @t22)) % 0.45/0.65 (define @t112 () (@list @t89)) % 0.45/0.65 (define @t113 () (@var "V0B_2E0" $$unsorted)) % 0.45/0.65 (define @t114 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t113))) % 0.45/0.65 (define @t115 () (=> (not @t114) @t22)) % 0.45/0.65 (define @t116 () (@var "V1A_2E0" $$unsorted)) % 0.45/0.65 (define @t117 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t116))) % 0.45/0.65 (define @t118 () (@list @t113 @t116)) % 0.45/0.65 (define @t119 () (@var "V2p_2E0" $$unsorted)) % 0.45/0.65 (define @t120 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t119))) % 0.45/0.65 (define @t121 () (not @t120)) % 0.45/0.65 (define @t122 () (@var "V1q_2E0" $$unsorted)) % 0.45/0.65 (define @t123 () (tptp.s tptp.tyop_2Emin_2Ebool @t122)) % 0.45/0.65 (define @t124 () (tptp.p @t123)) % 0.45/0.65 (define @t125 () (not @t124)) % 0.45/0.65 (define @t126 () (@var "V0r_2E0" $$unsorted)) % 0.45/0.65 (define @t127 () (tptp.s tptp.tyop_2Emin_2Ebool @t126)) % 0.45/0.65 (define @t128 () (tptp.p @t127)) % 0.45/0.65 (define @t129 () (not @t128)) % 0.45/0.65 (define @t130 () (@list @t126 @t122 @t119)) % 0.45/0.65 (define @t131 () (or @t120 @t129)) % 0.45/0.65 (define @t132 () (@var "V1p_2E0" $$unsorted)) % 0.45/0.65 (define @t133 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t132))) % 0.45/0.65 (define @t134 () (@var "V0q_2E0" $$unsorted)) % 0.45/0.65 (define @t135 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool @t134))) % 0.45/0.65 (define @t136 () (not @t135)) % 0.45/0.65 (define @t137 () (forall @t100 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ereal__topology_2Ebounded__def_2E1 @t99))))) % 0.45/0.65 (define @t138 () (not @t106)) % 0.45/0.65 (define @t139 () (not @t107)) % 0.45/0.65 (define @t140 () (or @t139 @t138 @t103)) % 0.45/0.65 (define @t141 () (@quantifiers_skolemize @t137 1)) % 0.45/0.65 (define @t142 () (@quantifiers_skolemize @t137 0)) % 0.45/0.65 (define @t143 () (@list @t142 @t141)) % 0.45/0.65 (define @t144 () (tptp.s @t68 (tptp.c_2Epair_2E_2C_2E2 (tptp.s tptp.tyop_2Erealax_2Ereal @t142) (tptp.s tptp.tyop_2Erealax_2Ereal @t141)))) % 0.45/0.65 (define @t145 () (tptp.c_2Ereal__topology_2Eball_2E1 @t144)) % 0.45/0.65 (define @t146 () (tptp.s @t63 @t145)) % 0.45/0.65 (define @t147 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ereal__topology_2Ebounded__def_2E1 @t146)))) % 0.45/0.65 (define @t148 () (tptp.c_2Ereal__topology_2Ecball_2E1 @t144)) % 0.45/0.65 (define @t149 () (tptp.s @t63 @t148)) % 0.45/0.65 (define @t150 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Epred__set_2ESUBSET_2E2 @t146 @t149)))) % 0.45/0.65 (define @t151 () (not @t150)) % 0.45/0.65 (define @t152 () (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ereal__topology_2Ebounded__def_2E1 @t149)))) % 0.45/0.65 (define @t153 () (not @t152)) % 0.45/0.65 (define @t154 () (or @t153 @t151 @t147)) % 0.45/0.65 (define @t155 () (not @t154)) % 0.45/0.65 (define @t156 () (forall @t109 @t140)) % 0.45/0.65 (assume @p1 (forall (@list @t3 @t2 @t6 @t1) (=> (forall @t11 (= (tptp.s @t2 (tptp.app_2E2 @t7 @t9)) @t10)) (= @t7 @t5)))) % 0.45/0.65 (assume @p2 (forall @t18 (=> (= @t17 @t16) (= @t15 @t13)))) % 0.45/0.65 (assume @p3 @t20) % 0.45/0.65 (assume @p4 @t23) % 0.45/0.65 (assume @p5 (forall @t28 (or @t27 @t26))) % 0.45/0.65 (assume @p6 (forall (@list @t3 @t29) (= (tptp.s @t3 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t3 @t3) tptp.combin_i_2E0) @t30)) @t30))) % 0.45/0.65 (assume @p7 (forall (@list @t3 @t2 @t29 @t31) (= (tptp.s @t3 (tptp.app_2E2 (tptp.s @t32 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t3 @t32) tptp.combin_k_2E0) @t30)) (tptp.s @t2 @t31))) @t30))) % 0.45/0.65 (assume @p8 (forall (@list @t3 @t2 @t33 @t6 @t1 @t8) (= (tptp.s @t33 (tptp.app_2E2 (tptp.s @t37 (tptp.app_2E2 (tptp.s @t38 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t35 @t38) tptp.combin_s_2E0) @t36)) @t5)) @t9)) (tptp.s @t33 (tptp.app_2E2 (tptp.s @t34 (tptp.app_2E2 @t36 @t9)) @t10))))) % 0.45/0.65 (assume @p9 (forall @t18 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_2F_5C_2E2 @t15 @t13))) (and @t17 @t16)))) % 0.45/0.65 (assume @p10 (forall @t18 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_5C_2F_2E2 @t15 @t13))) (or @t17 @t16)))) % 0.45/0.65 (assume @p11 (forall (@list @t14) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_7E_2E1 @t15))) (not @t17)))) % 0.45/0.65 (assume @p12 (forall @t18 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_3D_3E_2E2 @t15 @t13))) (=> @t17 @t16)))) % 0.45/0.65 (assume @p13 (forall (@list @t3 @t14 @t12) (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Emin_2E_3D_2E2 @t40 @t39))) (= @t40 @t39)))) % 0.45/0.65 (assume @p14 (forall @t47 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 @t44))) (forall @t46 @t45)))) % 0.45/0.65 (assume @p15 (forall @t47 (= (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 @t44))) (exists @t46 @t45)))) % 0.45/0.65 (assume @p16 (forall @t56 (= (and @t55 @t54) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 (tptp.app_2E2 (tptp.s @t53 tptp.c_2Ebool_2E_2F_5C_2E0) @t51)) @t49)))))) % 0.45/0.65 (assume @p17 (forall @t56 (= (or @t55 @t54) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 (tptp.app_2E2 (tptp.s @t53 tptp.c_2Ebool_2E_5C_2F_2E0) @t51)) @t49)))))) % 0.45/0.65 (assume @p18 (forall @t57 (= (not @t55) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 tptp.c_2Ebool_2E_7E_2E0) @t51)))))) % 0.45/0.65 (assume @p19 (forall @t56 (= (=> @t55 @t54) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t52 (tptp.app_2E2 (tptp.s @t53 tptp.c_2Emin_2E_3D_3D_3E_2E0) @t51)) @t49)))))) % 0.45/0.65 (assume @p20 (forall (@list @t3 @t50 @t48) (= (= @t59 @t58) (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t43 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t3 @t43) tptp.c_2Emin_2E_3D_2E0) @t59)) @t58)))))) % 0.45/0.65 (assume @p21 (forall @t62 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_21_2E1 @t60)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t61 tptp.c_2Ebool_2E_21_2E0) @t60))))) % 0.45/0.65 (assume @p22 (forall @t62 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ebool_2E_3F_2E1 @t60)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t61 tptp.c_2Ebool_2E_3F_2E0) @t60))))) % 0.45/0.65 (assume @p23 (forall @t57 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ereal__topology_2Ebounded__def_2E1 @t64)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t65 tptp.c_2Ereal__topology_2Ebounded__def_2E0) @t64))))) % 0.45/0.65 (assume @p24 (forall @t56 (= (tptp.s @t68 (tptp.c_2Epair_2E_2C_2E2 @t67 @t66)) (tptp.s @t68 (tptp.app_2E2 (tptp.s @t69 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun tptp.tyop_2Erealax_2Ereal @t69) tptp.c_2Epair_2E_2C_2E0) @t67)) @t66))))) % 0.45/0.65 (assume @p25 (forall @t57 (= (tptp.s @t63 (tptp.c_2Ereal__topology_2Eball_2E1 @t70)) (tptp.s @t63 (tptp.app_2E2 (tptp.s @t71 tptp.c_2Ereal__topology_2Eball_2E0) @t70))))) % 0.45/0.65 (assume @p26 (forall @t57 (= (tptp.s @t63 (tptp.c_2Ereal__topology_2Ecball_2E1 @t70)) (tptp.s @t63 (tptp.app_2E2 (tptp.s @t71 tptp.c_2Ereal__topology_2Ecball_2E0) @t70))))) % 0.45/0.65 (assume @p27 (forall @t56 (= (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Epred__set_2ESUBSET_2E2 @t64 @t72)) (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 (tptp.s @t65 (tptp.app_2E2 (tptp.s (tptp.tyop_2Emin_2Efun @t63 @t65) tptp.c_2Epred__set_2ESUBSET_2E0) @t64)) @t72))))) % 0.45/0.65 (assume @p28 (forall (@list @t75 @t73) (=> (=> @t77 @t78) (=> (=> @t78 @t77) (= @t76 @t74))))) % 0.45/0.65 (assume @p29 (forall @t28 (=> @t81 @t80))) % 0.45/0.65 (assume @p30 (forall @t28 (=> @t80 @t81))) % 0.45/0.65 (assume @p31 (forall @t28 (and (= (=> @t20 @t79) @t79) (= (=> @t79 @t20) @t20) (= (=> @t22 @t79) @t20) (= (=> @t79 @t79) @t20) (= @t81 @t80)))) % 0.45/0.65 (assume @p32 (and @t82 (= (not @t20) @t22) (= @t23 @t20))) % 0.45/0.65 (assume @p33 (forall (@list @t3 @t29 @t31) (= (= @t30 @t83) (= @t83 @t30)))) % 0.45/0.65 (assume @p34 (forall @t28 (and (= (= @t19 @t25) @t79) (= @t27 @t79) (= (= @t21 @t25) @t80) (= @t26 @t80)))) % 0.45/0.65 (assume @p35 (forall (@list @t3 @t84) (= (not (forall @t46 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t85 @t42))))) (exists @t11 (not (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.app_2E2 @t85 @t9)))))))) % 0.45/0.65 (assume @p36 (forall (@list @t89 @t87 @t86) (= @t91 @t91))) % 0.45/0.65 (assume @p37 (forall @t93 (= @t92 (or @t88 @t90)))) % 0.45/0.65 (assume @p38 (forall @t93 (and (= (not (and @t90 @t88)) (or @t95 @t94)) (= (not @t92) (and @t95 @t94))))) % 0.45/0.65 (assume @p39 (forall @t100 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Epred__set_2ESUBSET_2E2 @t99 @t98))))) % 0.45/0.65 (assume @p40 @t110) % 0.45/0.65 (assume @p41 (forall @t100 (tptp.p (tptp.s tptp.tyop_2Emin_2Ebool (tptp.c_2Ereal__topology_2Ebounded__def_2E1 @t98))))) % 0.45/0.65 (assume @p42 @t82) % 0.45/0.65 (assume @p43 (forall @t112 (=> @t90 @t111))) % 0.45/0.65 (assume @p44 (forall @t118 (= (=> (not (or @t117 @t114)) @t22) (=> (=> @t117 @t22) @t115)))) % 0.45/0.65 (assume @p45 (forall @t118 (= (=> (not (or (not @t117) @t114)) @t22) (=> @t117 @t115)))) % 0.45/0.65 (assume @p46 (forall @t112 (=> @t111 (=> (=> @t90 @t22) @t22)))) % 0.45/0.65 (assume @p47 (forall @t130 (= (= @t120 (= @t123 @t127)) (and (or @t120 @t124 @t128) (or @t120 @t129 @t125) (or @t124 @t129 @t121) (or @t128 @t125 @t121))))) % 0.45/0.65 (assume @p48 (forall @t130 (= (= @t120 (and @t124 @t128)) (and (or @t120 @t125 @t129) (or @t124 @t121) (or @t128 @t121))))) % 0.45/0.65 (assume @p49 (forall @t130 (= (= @t120 (or @t124 @t128)) (and (or @t120 @t125) @t131 (or @t124 @t128 @t121))))) % 0.45/0.65 (assume @p50 (forall @t130 (= (= @t120 (=> @t124 @t128)) (and (or @t120 @t124) @t131 (or @t125 @t128 @t121))))) % 0.45/0.65 (assume @p51 (forall (@list @t134 @t132) (= (= @t133 @t136) (and (or @t133 @t135) (or @t136 (not @t133)))))) % 0.45/0.65 (assume @p52 (not @t137)) % 0.45/0.65 (assume @p53 true) % 0.45/0.65 (step @p54 :rule aci_norm :args ((= (or (or @t139 @t138) @t103) @t140))) % 0.45/0.65 (step @p55 :rule refl :args (@t103)) % 0.45/0.65 (step @p56 :rule bool-and-de-morgan :args (@t107 @t106 true)) % 0.45/0.65 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or (not @t108) @t103))) % 0.45/0.65 (step @p58 :rule trans :premises (@p57 @p54)) % 0.45/0.65 (step @p59 :rule bool-impl-elim :args (@t108 @t103)) % 0.45/0.65 (step @p60 :rule trans :premises (@p59 @p58)) % 0.45/0.65 (step @p61 :rule cong :premises (@p60) :args (@t110)) % 0.45/0.65 (step @p62 :rule eq_resolve :premises (@p40 @p61)) % 0.45/0.65 (step @p63 :rule instantiate :premises (@p41) :args (@t143)) % 0.45/0.65 (step @p64 :rule instantiate :premises (@p39) :args (@t143)) % 0.45/0.65 (step @p65 :rule skolemize :premises (@p52)) % 0.45/0.65 (step @p66 :rule cnf_or_pos :args (@t154)) % 0.45/0.65 (step @p67 :rule reordering :premises (@p66) :args ((or @t147 @t151 @t153 @t155))) % 0.45/0.65 (step @p68 :rule chain_m_resolution :premises (@p67 @p65 @p64 @p63) :args (@t155 (@list true false false) (@list @t147 @t150 @t152))) % 0.45/0.65 (assume-push @p75 @t156) % 0.45/0.65 (step @p70 :rule instantiate :premises (@p62) :args ((@list @t145 @t148))) % 0.45/0.65 (step-pop @p76 :rule scope :premises (@p70)) % 0.45/0.65 (step @p71 :rule process_scope :premises (@p76) :args (@t154)) % 0.45/0.65 (step @p73 :rule implies_elim :premises (@p71)) % 0.45/0.65 (step @p74 false :rule chain_m_resolution :premises (@p73 @p68 @p62) :args (false (@list true false) (@list @t154 @t156))) % 0.45/0.65 ) % 0.45/0.65 % SZS output end Proof % 0.45/0.65 % cvc5 exiting %------------------------------------------------------------------------------