%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP023^2 : TPTP v9.2.1. Bugfixed v7.5.0. % 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 08:24:47 AM UTC 2026 % Result : Theorem 9.84s 10.12s % Output : Proof 9.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP023^2 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n027.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 04:05:36 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 9.84/10.12 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 9.84/10.12 % SZS status Theorem % 9.84/10.12 % SZS output start Proof % 9.84/10.12 ( % 9.84/10.12 (declare-sort tptp.del 0) % 9.84/10.12 (declare-sort $$unsorted 0) % 9.84/10.12 (declare-sort tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal 0) % 9.84/10.12 (declare-sort tptp.tp__ty_2Erealax_2Ereal 0) % 9.84/10.12 (declare-const tptp.c_2Emin_2E_3D (-> tptp.del $$unsorted)) % 9.84/10.12 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 9.84/10.12 (declare-const tptp.c_2Ereal__topology_2Ebounded__def $$unsorted) % 9.84/10.12 (declare-const tptp.c_2Ebool_2E_5C_2F $$unsorted) % 9.84/10.12 (declare-const tptp.c_2Epred__set_2ESUBSET (-> tptp.del $$unsorted)) % 9.84/10.12 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 9.84/10.12 (declare-const tptp.c_2Ebool_2EF $$unsorted) % 9.84/10.12 (declare-const tptp.ty_2Epair_2Eprod (-> tptp.del tptp.del tptp.del)) % 9.84/10.12 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 9.84/10.12 (declare-const tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (-> $$unsorted tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)) % 9.84/10.12 (declare-const tptp.inj__o (-> Bool $$unsorted)) % 9.84/10.12 (declare-const tptp.c_2Ereal__topology_2Eball $$unsorted) % 9.84/10.12 (declare-const tptp.p (-> $$unsorted Bool)) % 9.84/10.12 (declare-const tptp.bool tptp.del) % 9.84/10.12 (declare-const tptp.inj__ty_2Erealax_2Ereal (-> tptp.tp__ty_2Erealax_2Ereal $$unsorted)) % 9.84/10.12 (declare-const tptp.mem (-> $$unsorted tptp.del Bool)) % 9.84/10.12 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 9.84/10.12 (declare-const tptp.arr (-> tptp.del tptp.del tptp.del)) % 9.84/10.12 (declare-const tptp.c_2Ebool_2E_21 (-> tptp.del $$unsorted)) % 9.84/10.12 (declare-const tptp.c_2Ebool_2ET $$unsorted) % 9.84/10.12 (declare-const tptp.c_2Ereal__topology_2Ecball $$unsorted) % 9.84/10.12 (declare-const tptp.lam (-> tptp.del (-> $$unsorted $$unsorted) $$unsorted)) % 9.84/10.12 (declare-const tptp.c_2Epair_2E_2C (-> tptp.del tptp.del $$unsorted)) % 9.84/10.12 (declare-const tptp.ty_2Erealax_2Ereal tptp.del) % 9.84/10.12 (declare-const tptp.c_2Ebool_2E_3F (-> tptp.del $$unsorted)) % 9.84/10.12 (declare-const tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (-> tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal $$unsorted)) % 9.84/10.12 (declare-const tptp.surj__ty_2Erealax_2Ereal (-> $$unsorted tptp.tp__ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t1 () (@var "X" Bool)) % 9.84/10.12 (define @t2 () (_ tptp.inj__o @t1)) % 9.84/10.12 (define @t3 () (@list @t1)) % 9.84/10.12 (define @t4 () (@var "X" $$unsorted)) % 9.84/10.12 (define @t5 () (_ tptp.mem @t4)) % 9.84/10.12 (define @t6 () (@list @t4)) % 9.84/10.12 (define @t7 () (@var "B" tptp.del)) % 9.84/10.12 (define @t8 () (@var "F" $$unsorted)) % 9.84/10.12 (define @t9 () (_ (_ tptp.ap @t8) @t4)) % 9.84/10.12 (define @t10 () (_ (_ tptp.mem @t9) @t7)) % 9.84/10.12 (define @t11 () (@var "A" tptp.del)) % 9.84/10.12 (define @t12 () (_ @t5 @t11)) % 9.84/10.12 (define @t13 () (forall @t6 (=> @t12 @t10))) % 9.84/10.12 (define @t14 () (_ tptp.arr @t11)) % 9.84/10.12 (define @t15 () (_ @t14 @t7)) % 9.84/10.12 (define @t16 () (_ tptp.mem @t8)) % 9.84/10.12 (define @t17 () (_ @t16 @t15)) % 9.84/10.12 (define @t18 () (=> @t17 @t13)) % 9.84/10.12 (define @t19 () (@list @t11 @t7 @t8)) % 9.84/10.12 (define @t20 () (forall @t19 @t18)) % 9.84/10.12 (define @t21 () (@var "F" (-> $$unsorted $$unsorted))) % 9.84/10.12 (define @t22 () (_ (_ tptp.lam @t11) @t21)) % 9.84/10.12 (define @t23 () (_ @t21 @t4)) % 9.84/10.12 (define @t24 () (@var "G" $$unsorted)) % 9.84/10.12 (define @t25 () (@var "A_27a" tptp.del)) % 9.84/10.12 (define @t26 () (_ tptp.arr @t25)) % 9.84/10.12 (define @t27 () (_ @t26 tptp.bool)) % 9.84/10.12 (define @t28 () (_ tptp.arr @t27)) % 9.84/10.12 (define @t29 () (_ @t28 tptp.bool)) % 9.84/10.12 (define @t30 () (@list @t25)) % 9.84/10.12 (define @t31 () (@var "Q" $$unsorted)) % 9.84/10.12 (define @t32 () (_ tptp.p (_ (_ tptp.ap @t31) @t4))) % 9.84/10.12 (define @t33 () (_ tptp.mem @t31)) % 9.84/10.12 (define @t34 () (_ @t33 (_ @t14 tptp.bool))) % 9.84/10.12 (define @t35 () (@list @t11 @t31)) % 9.84/10.12 (define @t36 () (@var "X" tptp.tp__ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t37 () (_ tptp.inj__ty_2Erealax_2Ereal @t36)) % 9.84/10.12 (define @t38 () (@list @t36)) % 9.84/10.12 (define @t39 () (_ (_ tptp.mem @t37) tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t40 () (forall @t38 @t39)) % 9.84/10.12 (define @t41 () (@var "X" tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t42 () (_ tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t41)) % 9.84/10.12 (define @t43 () (@list @t41)) % 9.84/10.12 (define @t44 () (_ (_ tptp.ty_2Epair_2Eprod tptp.ty_2Erealax_2Ereal) tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t45 () (_ (_ tptp.arr tptp.ty_2Erealax_2Ereal) tptp.bool)) % 9.84/10.12 (define @t46 () (_ (_ tptp.arr @t44) @t45)) % 9.84/10.12 (define @t47 () (_ tptp.mem tptp.c_2Ereal__topology_2Eball)) % 9.84/10.12 (define @t48 () (_ @t47 @t46)) % 9.84/10.12 (define @t49 () (@var "A_27b" tptp.del)) % 9.84/10.12 (define @t50 () (_ (_ tptp.ty_2Epair_2Eprod @t25) @t49)) % 9.84/10.12 (define @t51 () (_ tptp.arr @t49)) % 9.84/10.12 (define @t52 () (_ @t51 @t50)) % 9.84/10.12 (define @t53 () (_ @t26 @t52)) % 9.84/10.12 (define @t54 () (_ (_ tptp.c_2Epair_2E_2C @t25) @t49)) % 9.84/10.12 (define @t55 () (_ (_ tptp.mem @t54) @t53)) % 9.84/10.12 (define @t56 () (forall (@list @t25 @t49) @t55)) % 9.84/10.12 (define @t57 () (_ tptp.mem tptp.c_2Ereal__topology_2Ecball)) % 9.84/10.12 (define @t58 () (_ @t57 @t46)) % 9.84/10.12 (define @t59 () (_ tptp.arr tptp.bool)) % 9.84/10.12 (define @t60 () (_ @t59 tptp.bool)) % 9.84/10.12 (define @t61 () (_ @t59 @t60)) % 9.84/10.12 (define @t62 () (@var "R" $$unsorted)) % 9.84/10.12 (define @t63 () (_ tptp.p @t62)) % 9.84/10.12 (define @t64 () (_ tptp.p @t31)) % 9.84/10.12 (define @t65 () (_ (_ tptp.mem @t62) tptp.bool)) % 9.84/10.12 (define @t66 () (@list @t62)) % 9.84/10.12 (define @t67 () (_ @t33 tptp.bool)) % 9.84/10.12 (define @t68 () (@list @t31)) % 9.84/10.12 (define @t69 () (@var "Y" $$unsorted)) % 9.84/10.12 (define @t70 () (@var "V1t2" $$unsorted)) % 9.84/10.12 (define @t71 () (_ tptp.p @t70)) % 9.84/10.12 (define @t72 () (@var "V0t1" $$unsorted)) % 9.84/10.12 (define @t73 () (_ tptp.p @t72)) % 9.84/10.12 (define @t74 () (@var "V0t" $$unsorted)) % 9.84/10.12 (define @t75 () (_ tptp.p @t74)) % 9.84/10.12 (define @t76 () (not @t75)) % 9.84/10.12 (define @t77 () (=> @t75 false)) % 9.84/10.12 (define @t78 () (_ (_ tptp.mem @t74) tptp.bool)) % 9.84/10.12 (define @t79 () (@list @t74)) % 9.84/10.12 (define @t80 () (forall @t79 (=> @t78 (= (not @t76) @t75)))) % 9.84/10.12 (define @t81 () (@var "V0x" $$unsorted)) % 9.84/10.12 (define @t82 () (@var "V1y" $$unsorted)) % 9.84/10.12 (define @t83 () (@var "V2x" $$unsorted)) % 9.84/10.12 (define @t84 () (@var "V0P" $$unsorted)) % 9.84/10.12 (define @t85 () (_ tptp.ap @t84)) % 9.84/10.12 (define @t86 () (@var "V1x" $$unsorted)) % 9.84/10.12 (define @t87 () (@var "V2C" $$unsorted)) % 9.84/10.12 (define @t88 () (@var "V1B" $$unsorted)) % 9.84/10.12 (define @t89 () (_ tptp.p @t88)) % 9.84/10.12 (define @t90 () (@var "V0A" $$unsorted)) % 9.84/10.12 (define @t91 () (_ tptp.p @t90)) % 9.84/10.12 (define @t92 () (or @t91 @t89 (_ tptp.p @t87))) % 9.84/10.12 (define @t93 () (_ (_ tptp.mem @t88) tptp.bool)) % 9.84/10.12 (define @t94 () (@list @t88)) % 9.84/10.12 (define @t95 () (_ (_ tptp.mem @t90) tptp.bool)) % 9.84/10.12 (define @t96 () (@list @t90)) % 9.84/10.12 (define @t97 () (or @t91 @t89)) % 9.84/10.12 (define @t98 () (not @t89)) % 9.84/10.12 (define @t99 () (not @t91)) % 9.84/10.12 (define @t100 () (not @t97)) % 9.84/10.12 (define @t101 () (@var "V1e" tptp.tp__ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t102 () (_ tptp.inj__ty_2Erealax_2Ereal @t101)) % 9.84/10.12 (define @t103 () (@var "V0x" tptp.tp__ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t104 () (_ tptp.inj__ty_2Erealax_2Ereal @t103)) % 9.84/10.12 (define @t105 () (_ (_ tptp.c_2Epair_2E_2C tptp.ty_2Erealax_2Ereal) tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t106 () (_ (_ tptp.ap @t105) @t104)) % 9.84/10.12 (define @t107 () (_ (_ tptp.ap @t106) @t102)) % 9.84/10.12 (define @t108 () (_ tptp.ap tptp.c_2Ereal__topology_2Ecball)) % 9.84/10.12 (define @t109 () (_ @t108 @t107)) % 9.84/10.12 (define @t110 () (_ tptp.ap tptp.c_2Ereal__topology_2Eball)) % 9.84/10.12 (define @t111 () (_ @t110 @t107)) % 9.84/10.12 (define @t112 () (_ tptp.c_2Epred__set_2ESUBSET tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t113 () (_ tptp.ap @t112)) % 9.84/10.12 (define @t114 () (_ @t113 @t111)) % 9.84/10.12 (define @t115 () (_ (_ tptp.ap @t114) @t109)) % 9.84/10.12 (define @t116 () (_ tptp.p @t115)) % 9.84/10.12 (define @t117 () (@list @t103 @t101)) % 9.84/10.12 (define @t118 () (forall @t117 @t116)) % 9.84/10.12 (define @t119 () (@var "V0s" $$unsorted)) % 9.84/10.12 (define @t120 () (_ tptp.ap tptp.c_2Ereal__topology_2Ebounded__def)) % 9.84/10.12 (define @t121 () (_ @t120 @t119)) % 9.84/10.12 (define @t122 () (_ tptp.p @t121)) % 9.84/10.12 (define @t123 () (@var "V1t" $$unsorted)) % 9.84/10.12 (define @t124 () (_ @t113 @t119)) % 9.84/10.12 (define @t125 () (_ (_ tptp.ap @t124) @t123)) % 9.84/10.12 (define @t126 () (_ tptp.p @t125)) % 9.84/10.12 (define @t127 () (_ @t120 @t123)) % 9.84/10.12 (define @t128 () (_ tptp.p @t127)) % 9.84/10.12 (define @t129 () (and @t128 @t126)) % 9.84/10.12 (define @t130 () (=> @t129 @t122)) % 9.84/10.12 (define @t131 () (_ tptp.mem @t123)) % 9.84/10.12 (define @t132 () (_ @t131 @t45)) % 9.84/10.12 (define @t133 () (@list @t123)) % 9.84/10.12 (define @t134 () (forall @t133 (=> @t132 @t130))) % 9.84/10.12 (define @t135 () (_ tptp.mem @t119)) % 9.84/10.12 (define @t136 () (_ @t135 @t45)) % 9.84/10.12 (define @t137 () (=> @t136 @t134)) % 9.84/10.12 (define @t138 () (@list @t119)) % 9.84/10.12 (define @t139 () (forall @t138 @t137)) % 9.84/10.12 (define @t140 () (_ @t120 @t109)) % 9.84/10.12 (define @t141 () (_ tptp.p @t140)) % 9.84/10.12 (define @t142 () (forall @t117 @t141)) % 9.84/10.12 (define @t143 () (=> @t99 false)) % 9.84/10.12 (define @t144 () (=> @t98 false)) % 9.84/10.12 (define @t145 () (=> @t91 false)) % 9.84/10.12 (define @t146 () (@var "V0p" $$unsorted)) % 9.84/10.12 (define @t147 () (_ tptp.p @t146)) % 9.84/10.12 (define @t148 () (not @t147)) % 9.84/10.12 (define @t149 () (@var "V1q" $$unsorted)) % 9.84/10.12 (define @t150 () (_ tptp.p @t149)) % 9.84/10.12 (define @t151 () (not @t150)) % 9.84/10.12 (define @t152 () (@var "V2r" $$unsorted)) % 9.84/10.12 (define @t153 () (_ tptp.p @t152)) % 9.84/10.12 (define @t154 () (not @t153)) % 9.84/10.12 (define @t155 () (_ (_ tptp.mem @t152) tptp.bool)) % 9.84/10.12 (define @t156 () (@list @t152)) % 9.84/10.12 (define @t157 () (_ (_ tptp.mem @t149) tptp.bool)) % 9.84/10.12 (define @t158 () (@list @t149)) % 9.84/10.12 (define @t159 () (_ (_ tptp.mem @t146) tptp.bool)) % 9.84/10.12 (define @t160 () (@list @t146)) % 9.84/10.12 (define @t161 () (or @t147 @t154)) % 9.84/10.12 (define @t162 () (or @t147 @t150)) % 9.84/10.12 (define @t163 () (_ @t120 @t111)) % 9.84/10.12 (define @t164 () (_ tptp.p @t163)) % 9.84/10.12 (define @t165 () (forall @t117 @t164)) % 9.84/10.12 (define @t166 () (not @t165)) % 9.84/10.12 (define @t167 () (@var "BOUND_VARIABLE_8063" $$unsorted)) % 9.84/10.12 (define @t168 () (tptp.mem (tptp.ap @t8 @t167) @t7)) % 9.84/10.12 (define @t169 () (not (tptp.mem @t167 @t11))) % 9.84/10.12 (define @t170 () (tptp.arr @t11 @t7)) % 9.84/10.12 (define @t171 () (tptp.mem @t8 @t170)) % 9.84/10.12 (define @t172 () (not @t171)) % 9.84/10.12 (define @t173 () (or @t172 @t169 @t168)) % 9.84/10.12 (define @t174 () (or @t169 @t168)) % 9.84/10.12 (define @t175 () (or @t172 @t174)) % 9.84/10.12 (define @t176 () (@list @t11 @t7 @t8 @t167)) % 9.84/10.12 (define @t177 () (forall @t176 @t175)) % 9.84/10.12 (define @t178 () (@list @t167)) % 9.84/10.12 (define @t179 () (forall @t178 @t175)) % 9.84/10.12 (define @t180 () (forall @t178 @t174)) % 9.84/10.12 (define @t181 () (or @t172 @t180)) % 9.84/10.12 (define @t182 () (tptp.ap @t8 @t4)) % 9.84/10.12 (define @t183 () (tptp.mem @t182 @t7)) % 9.84/10.12 (define @t184 () (tptp.mem @t4 @t11)) % 9.84/10.12 (define @t185 () (forall @t6 (or (not @t184) @t183))) % 9.84/10.12 (define @t186 () (not @t17)) % 9.84/10.12 (define @t187 () (or @t186 @t185)) % 9.84/10.12 (define @t188 () (not @t12)) % 9.84/10.12 (define @t189 () (or @t188 @t10)) % 9.84/10.12 (define @t190 () (tptp.inj__ty_2Erealax_2Ereal @t101)) % 9.84/10.12 (define @t191 () (tptp.inj__ty_2Erealax_2Ereal @t103)) % 9.84/10.12 (define @t192 () (tptp.c_2Epair_2E_2C tptp.ty_2Erealax_2Ereal tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t193 () (tptp.ap @t192 @t191)) % 9.84/10.12 (define @t194 () (tptp.ap @t193 @t190)) % 9.84/10.12 (define @t195 () (tptp.ap tptp.c_2Ereal__topology_2Eball @t194)) % 9.84/10.12 (define @t196 () (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t195)) % 9.84/10.12 (define @t197 () (tptp.p @t196)) % 9.84/10.12 (define @t198 () (forall @t117 @t197)) % 9.84/10.12 (define @t199 () (@quantifiers_skolemize @t198 1)) % 9.84/10.12 (define @t200 () (tptp.inj__ty_2Erealax_2Ereal @t199)) % 9.84/10.12 (define @t201 () (@quantifiers_skolemize @t198 0)) % 9.84/10.12 (define @t202 () (tptp.inj__ty_2Erealax_2Ereal @t201)) % 9.84/10.12 (define @t203 () (tptp.ap @t192 @t202)) % 9.84/10.12 (define @t204 () (tptp.ty_2Epair_2Eprod tptp.ty_2Erealax_2Ereal tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t205 () (tptp.arr tptp.ty_2Erealax_2Ereal @t204)) % 9.84/10.12 (define @t206 () (tptp.ty_2Epair_2Eprod @t25 @t49)) % 9.84/10.12 (define @t207 () (tptp.arr @t49 @t206)) % 9.84/10.12 (define @t208 () (tptp.arr @t25 @t207)) % 9.84/10.12 (define @t209 () (tptp.c_2Epair_2E_2C @t25 @t49)) % 9.84/10.12 (define @t210 () (tptp.mem @t209 @t208)) % 9.84/10.12 (define @t211 () (tptp.inj__ty_2Erealax_2Ereal @t36)) % 9.84/10.12 (define @t212 () (tptp.mem @t211 tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t213 () (tptp.mem @t203 @t205)) % 9.84/10.12 (define @t214 () (tptp.mem @t202 tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t215 () (not @t214)) % 9.84/10.12 (define @t216 () (tptp.mem @t192 (tptp.arr tptp.ty_2Erealax_2Ereal @t205))) % 9.84/10.12 (define @t217 () (not @t216)) % 9.84/10.12 (define @t218 () (or @t217 @t215 @t213)) % 9.84/10.12 (define @t219 () (@list false false false)) % 9.84/10.12 (define @t220 () (tptp.ap @t203 @t200)) % 9.84/10.12 (define @t221 () (tptp.mem @t220 @t204)) % 9.84/10.12 (define @t222 () (tptp.mem @t200 tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t223 () (not @t222)) % 9.84/10.12 (define @t224 () (not @t213)) % 9.84/10.12 (define @t225 () (or @t224 @t223 @t221)) % 9.84/10.12 (define @t226 () (@var "BOUND_VARIABLE_8712" $$unsorted)) % 9.84/10.12 (define @t227 () (tptp.c_2Epred__set_2ESUBSET tptp.ty_2Erealax_2Ereal)) % 9.84/10.12 (define @t228 () (tptp.ap @t227 @t119)) % 9.84/10.12 (define @t229 () (not (tptp.p (tptp.ap @t228 @t226)))) % 9.84/10.12 (define @t230 () (not (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t226)))) % 9.84/10.12 (define @t231 () (tptp.arr tptp.ty_2Erealax_2Ereal tptp.bool)) % 9.84/10.12 (define @t232 () (not (tptp.mem @t226 @t231))) % 9.84/10.12 (define @t233 () (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t119)) % 9.84/10.12 (define @t234 () (tptp.p @t233)) % 9.84/10.12 (define @t235 () (tptp.mem @t119 @t231)) % 9.84/10.12 (define @t236 () (not @t235)) % 9.84/10.12 (define @t237 () (or @t232 @t230 @t229)) % 9.84/10.12 (define @t238 () (or @t236 @t234 @t237)) % 9.84/10.12 (define @t239 () (forall (@list @t119 @t226) @t238)) % 9.84/10.12 (define @t240 () (@list @t226)) % 9.84/10.12 (define @t241 () (forall @t240 @t238)) % 9.84/10.12 (define @t242 () (forall @t240 @t237)) % 9.84/10.12 (define @t243 () (or @t236 @t234 @t242)) % 9.84/10.12 (define @t244 () (tptp.ap @t228 @t123)) % 9.84/10.12 (define @t245 () (tptp.p @t244)) % 9.84/10.12 (define @t246 () (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t123)) % 9.84/10.12 (define @t247 () (tptp.p @t246)) % 9.84/10.12 (define @t248 () (tptp.mem @t123 @t231)) % 9.84/10.12 (define @t249 () (forall @t133 (or (not @t248) (not @t247) (not @t245)))) % 9.84/10.12 (define @t250 () (not @t136)) % 9.84/10.12 (define @t251 () (or @t250 @t122 @t249)) % 9.84/10.12 (define @t252 () (or @t122 @t249)) % 9.84/10.12 (define @t253 () (_ tptp.ap @t227)) % 9.84/10.12 (define @t254 () (not @t126)) % 9.84/10.12 (define @t255 () (not @t128)) % 9.84/10.12 (define @t256 () (not @t132)) % 9.84/10.12 (define @t257 () (or @t256 @t255 @t254)) % 9.84/10.12 (define @t258 () (forall @t133 @t257)) % 9.84/10.12 (define @t259 () (or @t122 @t258)) % 9.84/10.12 (define @t260 () (or @t122 @t257)) % 9.84/10.12 (define @t261 () (or @t256 @t255 @t254 @t122)) % 9.84/10.12 (define @t262 () (or @t255 @t254 @t122)) % 9.84/10.12 (define @t263 () (tptp.ap tptp.c_2Ereal__topology_2Ecball @t220)) % 9.84/10.12 (define @t264 () (tptp.ap tptp.c_2Ereal__topology_2Eball @t220)) % 9.84/10.12 (define @t265 () (tptp.arr @t204 @t231)) % 9.84/10.12 (define @t266 () (tptp.mem tptp.c_2Ereal__topology_2Eball @t265)) % 9.84/10.12 (define @t267 () (tptp.mem @t264 @t231)) % 9.84/10.12 (define @t268 () (not @t221)) % 9.84/10.12 (define @t269 () (not @t266)) % 9.84/10.12 (define @t270 () (or @t269 @t268 @t267)) % 9.84/10.12 (define @t271 () (tptp.ap tptp.c_2Ereal__topology_2Ecball @t194)) % 9.84/10.12 (define @t272 () (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t271)) % 9.84/10.12 (define @t273 () (tptp.p @t272)) % 9.84/10.12 (define @t274 () (@list @t201 @t199)) % 9.84/10.12 (define @t275 () (tptp.ap @t227 @t195)) % 9.84/10.12 (define @t276 () (tptp.ap @t275 @t271)) % 9.84/10.12 (define @t277 () (tptp.p @t276)) % 9.84/10.12 (define @t278 () (tptp.p (tptp.ap (tptp.ap @t227 @t264) @t263))) % 9.84/10.12 (define @t279 () (not @t278)) % 9.84/10.12 (define @t280 () (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t263))) % 9.84/10.12 (define @t281 () (not @t280)) % 9.84/10.12 (define @t282 () (tptp.mem @t263 @t231)) % 9.84/10.12 (define @t283 () (not @t282)) % 9.84/10.12 (define @t284 () (tptp.p (tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t264))) % 9.84/10.12 (define @t285 () (not @t267)) % 9.84/10.12 (define @t286 () (or @t285 @t284 @t283 @t281 @t279)) % 9.84/10.12 (define @t287 () (tptp.mem tptp.c_2Ereal__topology_2Ecball @t265)) % 9.84/10.12 (define @t288 () (not @t287)) % 9.84/10.12 (define @t289 () (or @t288 @t268 @t282)) % 9.84/10.12 (define @t290 () (not @t289)) % 9.84/10.12 (define @t291 () (forall @t176 @t173)) % 9.84/10.12 (assume @p1 (forall @t3 (= (_ tptp.p @t2) @t1))) % 9.84/10.12 (assume @p2 (forall @t3 (_ (_ tptp.mem @t2) tptp.bool))) % 9.84/10.12 (assume @p3 (forall @t6 (=> (_ @t5 tptp.bool) (= @t4 (_ tptp.inj__o (_ tptp.p @t4)))))) % 9.84/10.12 (assume @p4 @t20) % 9.84/10.12 (assume @p5 (forall (@list @t11 @t7 @t21) (=> (forall @t6 (=> @t12 (_ (_ tptp.mem @t23) @t7))) (_ (_ tptp.mem @t22) @t15)))) % 9.84/10.12 (assume @p6 (forall @t19 (=> @t17 (forall (@list @t24) (=> (_ (_ tptp.mem @t24) @t15) (=> (forall @t6 (=> @t12 (= @t9 (_ (_ tptp.ap @t24) @t4)))) (= @t8 @t24))))))) % 9.84/10.12 (assume @p7 (forall (@list @t11 @t21 @t4) (=> @t12 (= (_ (_ tptp.ap @t22) @t4) @t23)))) % 9.84/10.12 (assume @p8 (_ (_ tptp.mem tptp.c_2Ebool_2ET) tptp.bool)) % 9.84/10.12 (assume @p9 (_ tptp.p tptp.c_2Ebool_2ET)) % 9.84/10.12 (assume @p10 (forall @t30 (_ (_ tptp.mem (_ tptp.c_2Ebool_2E_3F @t25)) @t29))) % 9.84/10.12 (assume @p11 (forall @t35 (=> @t34 (= (_ tptp.p (_ (_ tptp.ap (_ tptp.c_2Ebool_2E_3F @t11)) @t31)) (exists @t6 (and @t12 @t32)))))) % 9.84/10.12 (assume @p12 (forall @t38 (= (_ tptp.surj__ty_2Erealax_2Ereal @t37) @t36))) % 9.84/10.12 (assume @p13 @t40) % 9.84/10.12 (assume @p14 (forall @t6 (=> (_ @t5 tptp.ty_2Erealax_2Ereal) (= @t4 (_ tptp.inj__ty_2Erealax_2Ereal (_ tptp.surj__ty_2Erealax_2Ereal @t4)))))) % 9.84/10.12 (assume @p15 (forall @t43 (= (_ tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t42) @t41))) % 9.84/10.12 (assume @p16 (forall @t43 (_ (_ tptp.mem @t42) @t44))) % 9.84/10.12 (assume @p17 (forall @t6 (=> (_ @t5 @t44) (= @t4 (_ tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (_ tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t4)))))) % 9.84/10.12 (assume @p18 @t48) % 9.84/10.12 (assume @p19 (forall @t30 (_ (_ tptp.mem (_ tptp.c_2Epred__set_2ESUBSET @t25)) (_ @t28 @t29)))) % 9.84/10.12 (assume @p20 @t56) % 9.84/10.12 (assume @p21 @t58) % 9.84/10.12 (assume @p22 (_ (_ tptp.mem tptp.c_2Ereal__topology_2Ebounded__def) (_ (_ tptp.arr @t45) tptp.bool))) % 9.84/10.12 (assume @p23 (_ (_ tptp.mem tptp.c_2Ebool_2EF) tptp.bool)) % 9.84/10.12 (assume @p24 (not (_ tptp.p tptp.c_2Ebool_2EF))) % 9.84/10.12 (assume @p25 (_ (_ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) @t61)) % 9.84/10.12 (assume @p26 (forall @t68 (=> @t67 (forall @t66 (=> @t65 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) @t31)) @t62)) (=> @t64 @t63))))))) % 9.84/10.12 (assume @p27 (_ (_ tptp.mem tptp.c_2Ebool_2E_5C_2F) @t61)) % 9.84/10.12 (assume @p28 (forall @t68 (=> @t67 (forall @t66 (=> @t65 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Ebool_2E_5C_2F) @t31)) @t62)) (or @t64 @t63))))))) % 9.84/10.12 (assume @p29 (_ (_ tptp.mem tptp.c_2Ebool_2E_2F_5C) @t61)) % 9.84/10.12 (assume @p30 (forall @t68 (=> @t67 (forall @t66 (=> @t65 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Ebool_2E_2F_5C) @t31)) @t62)) (and @t64 @t63))))))) % 9.84/10.12 (assume @p31 (_ (_ tptp.mem tptp.c_2Ebool_2E_7E) @t60)) % 9.84/10.12 (assume @p32 (forall @t68 (=> @t67 (= (_ tptp.p (_ (_ tptp.ap tptp.c_2Ebool_2E_7E) @t31)) (not @t64))))) % 9.84/10.12 (assume @p33 (forall @t30 (_ (_ tptp.mem (_ tptp.c_2Emin_2E_3D @t25)) (_ @t26 @t27)))) % 9.84/10.12 (assume @p34 (forall (@list @t11 @t4) (=> @t12 (forall (@list @t69) (=> (_ (_ tptp.mem @t69) @t11) (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap (_ tptp.c_2Emin_2E_3D @t11)) @t4)) @t69)) (= @t4 @t69))))))) % 9.84/10.12 (assume @p35 (forall @t30 (_ (_ tptp.mem (_ tptp.c_2Ebool_2E_21 @t25)) @t29))) % 9.84/10.12 (assume @p36 (forall @t35 (=> @t34 (= (_ tptp.p (_ (_ tptp.ap (_ tptp.c_2Ebool_2E_21 @t11)) @t31)) (forall @t6 (=> @t12 @t32)))))) % 9.84/10.12 (assume @p37 true) % 9.84/10.12 (assume @p38 (forall (@list @t72) (=> (_ (_ tptp.mem @t72) tptp.bool) (forall (@list @t70) (=> (_ (_ tptp.mem @t70) tptp.bool) (=> (=> @t73 @t71) (=> (=> @t71 @t73) (= @t73 @t71)))))))) % 9.84/10.12 (assume @p39 (forall @t79 (=> @t78 (=> @t77 @t76)))) % 9.84/10.12 (assume @p40 (forall @t79 (=> @t78 (=> @t76 @t77)))) % 9.84/10.12 (assume @p41 (forall @t79 (=> @t78 (and (= (=> true @t75) @t75) (= (=> @t75 true) true) (= (=> false @t75) true) (= (=> @t75 @t75) true) (= @t77 @t76))))) % 9.84/10.12 (assume @p42 (and @t80 (= (not true) false) (= (not false) true))) % 9.84/10.12 (assume @p43 (forall (@list @t25 @t81) (=> (_ (_ tptp.mem @t81) @t25) (forall (@list @t82) (=> (_ (_ tptp.mem @t82) @t25) (= (= @t81 @t82) (= @t82 @t81))))))) % 9.84/10.12 (assume @p44 (forall @t79 (=> @t78 (and (= (= true @t75) @t75) (= (= @t75 true) @t75) (= (= false @t75) @t76) (= (= @t75 false) @t76))))) % 9.84/10.12 (assume @p45 (forall (@list @t25 @t84) (=> (_ (_ tptp.mem @t84) @t27) (= (not (forall (@list @t86) (=> (_ (_ tptp.mem @t86) @t25) (_ tptp.p (_ @t85 @t86))))) (exists (@list @t83) (and (_ (_ tptp.mem @t83) @t25) (not (_ tptp.p (_ @t85 @t83))))))))) % 9.84/10.12 (assume @p46 (forall @t96 (=> @t95 (forall @t94 (=> @t93 (forall (@list @t87) (=> (_ (_ tptp.mem @t87) tptp.bool) (= @t92 @t92)))))))) % 9.84/10.12 (assume @p47 (forall @t96 (=> @t95 (forall @t94 (=> @t93 (= @t97 (or @t89 @t91))))))) % 9.84/10.12 (assume @p48 (forall @t96 (=> @t95 (forall @t94 (=> @t93 (and (= (not (and @t91 @t89)) (or @t99 @t98)) (= @t100 (and @t99 @t98)))))))) % 9.84/10.12 (assume @p49 @t118) % 9.84/10.12 (assume @p50 @t139) % 9.84/10.12 (assume @p51 @t142) % 9.84/10.12 (assume @p52 @t80) % 9.84/10.12 (assume @p53 (forall @t96 (=> @t95 (=> @t91 @t143)))) % 9.84/10.12 (assume @p54 (forall @t96 (=> @t95 (forall @t94 (=> @t93 (= (=> @t100 false) (=> @t145 @t144))))))) % 9.84/10.12 (assume @p55 (forall @t96 (=> @t95 (forall @t94 (=> @t93 (= (=> (not (or @t99 @t89)) false) (=> @t91 @t144))))))) % 9.84/10.12 (assume @p56 (forall @t96 (=> @t95 (=> @t143 (=> @t145 false))))) % 9.84/10.12 (assume @p57 (forall @t160 (=> @t159 (forall @t158 (=> @t157 (forall @t156 (=> @t155 (= (= @t147 (= @t150 @t153)) (and (or @t147 @t150 @t153) (or @t147 @t154 @t151) (or @t150 @t154 @t148) (or @t153 @t151 @t148)))))))))) % 9.84/10.12 (assume @p58 (forall @t160 (=> @t159 (forall @t158 (=> @t157 (forall @t156 (=> @t155 (= (= @t147 (and @t150 @t153)) (and (or @t147 @t151 @t154) (or @t150 @t148) (or @t153 @t148)))))))))) % 9.84/10.12 (assume @p59 (forall @t160 (=> @t159 (forall @t158 (=> @t157 (forall @t156 (=> @t155 (= (= @t147 (or @t150 @t153)) (and (or @t147 @t151) @t161 (or @t150 @t153 @t148)))))))))) % 9.84/10.12 (assume @p60 (forall @t160 (=> @t159 (forall @t158 (=> @t157 (forall @t156 (=> @t155 (= (= @t147 (=> @t150 @t153)) (and @t162 @t161 (or @t151 @t153 @t148)))))))))) % 9.84/10.12 (assume @p61 (forall @t160 (=> @t159 (forall @t158 (=> @t157 (= (= @t147 @t151) (and @t162 (or @t151 @t148)))))))) % 9.84/10.12 (assume @p62 @t166) % 9.84/10.12 (step @p63 :rule aci_norm :args ((= @t175 @t173))) % 9.84/10.12 (step @p64 :rule cong :premises (@p63) :args (@t177)) % 9.84/10.12 (step @p65 :rule quant-merge-prenex :args ((= (forall @t19 @t179) @t177))) % 9.84/10.12 (step @p66 :rule alpha_equiv :args (@t180 (@list @t167) (@list @t4))) % 9.84/10.12 (step @p67 :rule refl :args (@t172)) % 9.84/10.12 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t181)) % 9.84/10.12 (step @p69 :rule quant-miniscope-or :args ((= @t179 @t181))) % 9.84/10.12 (step @p70 :rule trans :premises (@p69 @p68)) % 9.84/10.12 (step @p71 :rule symm :premises (@p70)) % 9.84/10.12 (step @p72 :rule cong :premises (@p71) :args ((forall @t19 (or @t172 @t185)))) % 9.84/10.12 (step @p73 :rule trans :premises (@p72 @p65)) % 9.84/10.12 (step @p74 :rule trans :premises (@p73 @p64)) % 9.84/10.12 (step @p75 :rule refl :args (@t185)) % 9.84/10.12 (step @p76 :rule refl :args ((tptp.mem @t8 @t15))) % 9.84/10.12 (step @p77 :rule refl :args (@t170)) % 9.84/10.12 (step @p78 :rule refl :args (@t8)) % 9.84/10.12 (step @p79 :rule cong :premises (@p78 @p77) :args (@t171)) % 9.84/10.12 (step @p80 :rule trans :premises (@p79 @p76)) % 9.84/10.12 (step @p81 :rule refl :args (@t16)) % 9.84/10.12 (step @p82 :rule ho_cong :premises (@p81 @p77)) % 9.84/10.12 (step @p83 :rule cong :premises (@p82 @p80) :args ((= (_ @t16 @t170) @t171))) % 9.84/10.12 (step @p84 :rule symm :premises (@p83)) % 9.84/10.12 (step @p85 :rule refl :args (@t17)) % 9.84/10.12 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 9.84/10.12 (step @p87 :rule refl :args (@t15)) % 9.84/10.12 (step @p88 :rule cong :premises (@p87 @p77) :args ((= @t15 @t170))) % 9.84/10.12 (step @p89 :rule symm :premises (@p88)) % 9.84/10.12 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 9.84/10.12 (step @p91 :rule ho_cong :premises (@p81 @p90)) % 9.84/10.12 (step @p92 :rule trans :premises (@p91 @p86)) % 9.84/10.12 (step @p93 :rule cong :premises (@p92) :args (@t186)) % 9.84/10.12 (step @p94 :rule nary_cong :premises (@p93 @p75) :args (@t187)) % 9.84/10.12 (step @p95 :rule cong :premises (@p94) :args ((forall @t19 @t187))) % 9.84/10.12 (step @p96 :rule trans :premises (@p95 @p74)) % 9.84/10.12 (step @p97 :rule bool-impl-elim :args (@t17 @t185)) % 9.84/10.12 (step @p98 :rule cong :premises (@p97) :args ((forall @t19 (=> @t17 @t185)))) % 9.84/10.12 (step @p99 :rule trans :premises (@p98 @p96)) % 9.84/10.12 (step @p100 :rule refl :args ((tptp.mem @t9 @t7))) % 9.84/10.12 (step @p101 :rule refl :args (@t7)) % 9.84/10.12 (step @p102 :rule refl :args (@t182)) % 9.84/10.12 (step @p103 :rule cong :premises (@p102 @p101) :args (@t183)) % 9.84/10.12 (step @p104 :rule trans :premises (@p103 @p100)) % 9.84/10.12 (step @p105 :rule refl :args (tptp.mem)) % 9.84/10.12 (step @p106 :rule ho_cong :premises (@p105 @p102)) % 9.84/10.12 (step @p107 :rule ho_cong :premises (@p106 @p101)) % 9.84/10.12 (step @p108 :rule cong :premises (@p107 @p104) :args ((= (_ (_ tptp.mem @t182) @t7) @t183))) % 9.84/10.12 (step @p109 :rule symm :premises (@p108)) % 9.84/10.12 (step @p110 :rule refl :args (@t10)) % 9.84/10.12 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 9.84/10.12 (step @p112 :rule refl :args (@t9)) % 9.84/10.12 (step @p113 :rule cong :premises (@p112 @p102) :args ((= @t9 @t182))) % 9.84/10.12 (step @p114 :rule symm :premises (@p113)) % 9.84/10.12 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 9.84/10.12 (step @p116 :rule ho_cong :premises (@p105 @p115)) % 9.84/10.12 (step @p117 :rule ho_cong :premises (@p116 @p101)) % 9.84/10.12 (step @p118 :rule trans :premises (@p117 @p111)) % 9.84/10.12 (step @p119 :rule refl :args (@t184)) % 9.84/10.12 (step @p120 :rule refl :args (@t12)) % 9.84/10.12 (step @p121 :rule cong :premises (@p120 @p119) :args ((= @t12 @t184))) % 9.84/10.13 (step 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@p355) :args ((or @t256 @t130))) % 9.84/10.13 (step @p358 :rule trans :premises (@p357 @p349)) % 9.84/10.13 (step @p359 :rule bool-impl-elim :args (@t132 @t130)) % 9.84/10.13 (step @p360 :rule trans :premises (@p359 @p358)) % 9.84/10.13 (step @p361 :rule cong :premises (@p360) :args (@t134)) % 9.84/10.13 (step @p362 :rule trans :premises (@p361 @p348)) % 9.84/10.13 (step @p363 :rule refl :args (@t136)) % 9.84/10.13 (step @p364 :rule cong :premises (@p363 @p362) :args (@t137)) % 9.84/10.13 (step @p365 :rule cong :premises (@p364) :args (@t139)) % 9.84/10.13 (step @p366 :rule trans :premises (@p365 @p269)) % 9.84/10.13 (step @p367 :rule eq_resolve :premises (@p50 @p366)) % 9.84/10.13 (step @p368 :rule instantiate :premises (@p367) :args ((@list @t264 @t263))) % 9.84/10.13 (step @p369 :rule instantiate :premises (@p134) :args ((@list @t204 @t231 tptp.c_2Ereal__topology_2Eball @t220))) % 9.84/10.13 (step @p370 :rule refl :args ((tptp.mem tptp.c_2Ereal__topology_2Eball @t46))) % 9.84/10.13 (step @p371 :rule refl :args ((tptp.arr @t44 @t45))) % 9.84/10.13 (step @p372 :rule refl :args (@t204)) % 9.84/10.13 (step @p373 :rule cong :premises (@p372 @p245) :args (@t265)) % 9.84/10.13 (step @p374 :rule trans :premises (@p373 @p371)) % 9.84/10.13 (step @p375 :rule refl :args (tptp.c_2Ereal__topology_2Eball)) % 9.84/10.13 (step @p376 :rule cong :premises (@p375 @p374) :args (@t266)) % 9.84/10.13 (step @p377 :rule trans :premises (@p376 @p370)) % 9.84/10.13 (step @p378 :rule refl :args (@t47)) % 9.84/10.13 (step @p379 :rule ho_cong :premises (@p378 @p374)) % 9.84/10.13 (step @p380 :rule cong :premises (@p379 @p377) :args ((= (_ @t47 @t265) @t266))) % 9.84/10.13 (step @p381 :rule symm :premises (@p380)) % 9.84/10.13 (step @p382 :rule refl :args (@t48)) % 9.84/10.13 (step @p383 :rule eq_resolve :premises (@p382 @p381)) % 9.84/10.13 (step @p384 :rule refl :args (tptp.arr)) % 9.84/10.13 (step @p385 :rule ho_cong :premises (@p384 @p372)) % 9.84/10.13 (step @p386 :rule ho_cong :premises (@p385 @p245)) % 9.84/10.13 (step @p387 :rule cong :premises (@p386 @p374) :args ((= (_ (_ tptp.arr @t204) @t231) @t265))) % 9.84/10.13 (step @p388 :rule symm :premises (@p387)) % 9.84/10.13 (step @p389 :rule refl :args (@t46)) % 9.84/10.13 (step @p390 :rule eq_resolve :premises (@p389 @p388)) % 9.84/10.13 (step @p391 :rule refl :args (@t44)) % 9.84/10.13 (step @p392 :rule cong :premises (@p391 @p372) :args ((= @t44 @t204))) % 9.84/10.13 (step @p393 :rule symm :premises (@p392)) % 9.84/10.13 (step @p394 :rule eq_resolve :premises (@p391 @p393)) % 9.84/10.13 (step @p395 :rule refl :args (tptp.arr)) % 9.84/10.13 (step @p396 :rule ho_cong :premises (@p395 @p394)) % 9.84/10.13 (step @p397 :rule ho_cong :premises (@p396 @p258)) % 9.84/10.13 (step @p398 :rule trans :premises (@p397 @p390)) % 9.84/10.13 (step @p399 :rule refl :args (@t47)) % 9.84/10.13 (step @p400 :rule ho_cong :premises (@p399 @p398)) % 9.84/10.13 (step @p401 :rule trans :premises (@p400 @p383)) % 9.84/10.13 (step @p402 :rule eq_resolve :premises (@p18 @p401)) % 9.84/10.13 (step @p403 :rule cnf_or_pos :args (@t270)) % 9.84/10.13 (step @p404 :rule reordering :premises (@p403) :args ((or @t269 @t267 @t268 (not @t270)))) % 9.84/10.13 (step @p405 :rule chain_m_resolution :premises (@p404 @p402 @p213 @p369) :args (@t267 @t219 (@list @t266 @t221 @t270))) % 9.84/10.13 (step @p406 :rule refl :args ((tptp.p @t140))) % 9.84/10.13 (step @p407 :rule refl :args ((tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t109))) % 9.84/10.13 (step @p408 :rule refl :args ((tptp.ap tptp.c_2Ereal__topology_2Ecball @t107))) % 9.84/10.13 (step @p409 :rule refl :args ((tptp.ap @t106 @t102))) % 9.84/10.13 (step @p410 :rule refl :args (@t190)) % 9.84/10.13 (step @p411 :rule refl :args ((tptp.ap @t105 @t104))) % 9.84/10.13 (step @p412 :rule refl :args (@t191)) % 9.84/10.13 (step @p413 :rule refl :args (@t192)) % 9.84/10.13 (step @p414 :rule cong :premises (@p413 @p412) :args (@t193)) % 9.84/10.13 (step @p415 :rule trans :premises (@p414 @p411)) % 9.84/10.13 (step @p416 :rule cong :premises (@p415 @p410) :args (@t194)) % 9.84/10.13 (step @p417 :rule trans :premises (@p416 @p409)) % 9.84/10.13 (step @p418 :rule refl :args (tptp.c_2Ereal__topology_2Ecball)) % 9.84/10.13 (step @p419 :rule cong :premises (@p418 @p417) :args (@t271)) % 9.84/10.13 (step @p420 :rule trans :premises (@p419 @p408)) % 9.84/10.13 (step @p421 :rule refl :args (tptp.c_2Ereal__topology_2Ebounded__def)) % 9.84/10.13 (step @p422 :rule cong :premises (@p421 @p420) :args (@t272)) % 9.84/10.13 (step @p423 :rule trans :premises (@p422 @p407)) % 9.84/10.13 (step @p424 :rule cong :premises (@p423) :args (@t273)) % 9.84/10.13 (step @p425 :rule trans :premises (@p424 @p406)) % 9.84/10.13 (step @p426 :rule ho_cong :premises (@p232 @p423)) % 9.84/10.13 (step @p427 :rule cong :premises (@p426 @p425) :args ((= (_ tptp.p @t272) @t273))) % 9.84/10.13 (step @p428 :rule symm :premises (@p427)) % 9.84/10.13 (step @p429 :rule refl :args (@t141)) % 9.84/10.13 (step @p430 :rule eq_resolve :premises (@p429 @p428)) % 9.84/10.13 (step @p431 :rule refl :args (@t120)) % 9.84/10.13 (step @p432 :rule ho_cong :premises (@p431 @p420)) % 9.84/10.13 (step @p433 :rule cong :premises (@p432 @p423) :args ((= (_ @t120 @t271) @t272))) % 9.84/10.13 (step @p434 :rule symm :premises (@p433)) % 9.84/10.13 (step @p435 :rule refl :args (@t140)) % 9.84/10.13 (step @p436 :rule eq_resolve :premises (@p435 @p434)) % 9.84/10.13 (step @p437 :rule refl :args (@t108)) % 9.84/10.13 (step @p438 :rule ho_cong :premises (@p437 @p417)) % 9.84/10.13 (step @p439 :rule cong :premises (@p438 @p420) :args ((= (_ @t108 @t194) @t271))) % 9.84/10.13 (step @p440 :rule symm :premises (@p439)) % 9.84/10.13 (step @p441 :rule refl :args (@t109)) % 9.84/10.13 (step @p442 :rule eq_resolve :premises (@p441 @p440)) % 9.84/10.13 (step @p443 :rule ho_cong :premises (@p286 @p415)) % 9.84/10.13 (step @p444 :rule ho_cong :premises (@p443 @p410)) % 9.84/10.13 (step @p445 :rule cong :premises (@p444 @p417) :args ((= (_ (_ tptp.ap @t193) @t190) @t194))) % 9.84/10.13 (step @p446 :rule symm :premises (@p445)) % 9.84/10.13 (step @p447 :rule refl :args (@t107)) % 9.84/10.13 (step @p448 :rule eq_resolve :premises (@p447 @p446)) % 9.84/10.13 (step @p449 :rule refl :args (@t102)) % 9.84/10.13 (step @p450 :rule cong :premises (@p449 @p410) :args ((= @t102 @t190))) % 9.84/10.13 (step @p451 :rule symm :premises (@p450)) % 9.84/10.13 (step @p452 :rule eq_resolve :premises (@p449 @p451)) % 9.84/10.13 (step @p453 :rule ho_cong :premises (@p286 @p413)) % 9.84/10.13 (step @p454 :rule ho_cong :premises (@p453 @p412)) % 9.84/10.13 (step @p455 :rule cong :premises (@p454 @p415) :args ((= (_ (_ tptp.ap @t192) @t191) @t193))) % 9.84/10.13 (step @p456 :rule symm :premises (@p455)) % 9.84/10.13 (step @p457 :rule refl :args (@t106)) % 9.84/10.13 (step @p458 :rule eq_resolve :premises (@p457 @p456)) % 9.84/10.13 (step @p459 :rule refl :args (@t104)) % 9.84/10.13 (step @p460 :rule cong :premises (@p459 @p412) :args ((= @t104 @t191))) % 9.84/10.13 (step @p461 :rule symm :premises (@p460)) % 9.84/10.13 (step @p462 :rule eq_resolve :premises (@p459 @p461)) % 9.84/10.13 (step @p463 :rule refl :args (@t105)) % 9.84/10.13 (step @p464 :rule cong :premises (@p463 @p413) :args ((= @t105 @t192))) % 9.84/10.13 (step @p465 :rule symm :premises (@p464)) % 9.84/10.13 (step @p466 :rule eq_resolve :premises (@p463 @p465)) % 9.84/10.13 (step @p467 :rule ho_cong :premises (@p286 @p466)) % 9.84/10.13 (step @p468 :rule ho_cong :premises (@p467 @p462)) % 9.84/10.13 (step @p469 :rule trans :premises (@p468 @p458)) % 9.84/10.13 (step @p470 :rule ho_cong :premises (@p286 @p469)) % 9.84/10.13 (step @p471 :rule ho_cong :premises (@p470 @p452)) % 9.84/10.13 (step @p472 :rule trans :premises (@p471 @p448)) % 9.84/10.13 (step @p473 :rule ho_cong :premises (@p437 @p472)) % 9.84/10.13 (step @p474 :rule trans :premises (@p473 @p442)) % 9.84/10.13 (step @p475 :rule ho_cong :premises (@p431 @p474)) % 9.84/10.13 (step @p476 :rule trans :premises (@p475 @p436)) % 9.84/10.13 (step @p477 :rule ho_cong :premises (@p232 @p476)) % 9.84/10.13 (step @p478 :rule trans :premises (@p477 @p430)) % 9.84/10.13 (step @p479 :rule cong :premises (@p478) :args (@t142)) % 9.84/10.13 (step @p480 :rule eq_resolve :premises (@p51 @p479)) % 9.84/10.13 (step @p481 :rule instantiate :premises (@p480) :args (@t274)) % 9.84/10.13 (step @p482 :rule refl :args ((tptp.p @t115))) % 9.84/10.13 (step @p483 :rule refl :args ((tptp.ap @t114 @t109))) % 9.84/10.13 (step @p484 :rule refl :args ((tptp.ap @t112 @t111))) % 9.84/10.13 (step @p485 :rule refl :args ((tptp.ap tptp.c_2Ereal__topology_2Eball @t107))) % 9.84/10.13 (step @p486 :rule cong :premises (@p375 @p417) :args (@t195)) % 9.84/10.13 (step @p487 :rule trans :premises (@p486 @p485)) % 9.84/10.13 (step @p488 :rule cong :premises (@p274 @p487) :args (@t275)) % 9.84/10.13 (step @p489 :rule trans :premises (@p488 @p484)) % 9.84/10.13 (step @p490 :rule cong :premises (@p489 @p420) :args (@t276)) % 9.84/10.13 (step @p491 :rule trans :premises (@p490 @p483)) % 9.84/10.13 (step @p492 :rule cong :premises (@p491) :args (@t277)) % 9.84/10.13 (step @p493 :rule trans :premises (@p492 @p482)) % 9.84/10.13 (step @p494 :rule ho_cong :premises (@p232 @p491)) % 9.84/10.13 (step @p495 :rule cong :premises (@p494 @p493) :args ((= (_ tptp.p @t276) @t277))) % 9.84/10.13 (step @p496 :rule symm :premises (@p495)) % 9.84/10.13 (step @p497 :rule refl :args (@t116)) % 9.84/10.13 (step @p498 :rule eq_resolve :premises (@p497 @p496)) % 9.84/10.13 (step @p499 :rule ho_cong :premises (@p286 @p489)) % 9.84/10.13 (step @p500 :rule ho_cong :premises (@p499 @p420)) % 9.84/10.13 (step @p501 :rule cong :premises (@p500 @p491) :args ((= (_ (_ tptp.ap @t275) @t271) @t276))) % 9.84/10.13 (step @p502 :rule symm :premises (@p501)) % 9.84/10.13 (step @p503 :rule refl :args (@t115)) % 9.84/10.13 (step @p504 :rule eq_resolve :premises (@p503 @p502)) % 9.84/10.13 (step @p505 :rule ho_cong :premises (@p293 @p487)) % 9.84/10.13 (step @p506 :rule cong :premises (@p505 @p489) :args ((= (_ @t253 @t195) @t275))) % 9.84/10.13 (step @p507 :rule symm :premises (@p506)) % 9.84/10.13 (step @p508 :rule refl :args (@t114)) % 9.84/10.13 (step @p509 :rule eq_resolve :premises (@p508 @p507)) % 9.84/10.13 (step @p510 :rule refl :args (@t110)) % 9.84/10.13 (step @p511 :rule ho_cong :premises (@p510 @p417)) % 9.84/10.13 (step @p512 :rule cong :premises (@p511 @p487) :args ((= (_ @t110 @t194) @t195))) % 9.84/10.13 (step @p513 :rule symm :premises (@p512)) % 9.84/10.13 (step @p514 :rule refl :args (@t111)) % 9.84/10.13 (step @p515 :rule eq_resolve :premises (@p514 @p513)) % 9.84/10.13 (step @p516 :rule ho_cong :premises (@p510 @p472)) % 9.97/10.13 (step @p517 :rule trans :premises (@p516 @p515)) % 9.97/10.13 (step @p518 :rule ho_cong :premises (@p303 @p517)) % 9.97/10.13 (step @p519 :rule trans :premises (@p518 @p509)) % 9.97/10.13 (step @p520 :rule ho_cong :premises (@p286 @p519)) % 9.97/10.13 (step @p521 :rule ho_cong :premises (@p520 @p474)) % 9.97/10.13 (step @p522 :rule trans :premises (@p521 @p504)) % 9.97/10.13 (step @p523 :rule ho_cong :premises (@p232 @p522)) % 9.97/10.13 (step @p524 :rule trans :premises (@p523 @p498)) % 9.97/10.13 (step @p525 :rule cong :premises (@p524) :args (@t118)) % 9.97/10.13 (step @p526 :rule eq_resolve :premises (@p49 @p525)) % 9.97/10.13 (step @p527 :rule instantiate :premises (@p526) :args (@t274)) % 9.97/10.13 (step @p528 :rule refl :args ((tptp.p @t163))) % 9.97/10.13 (step @p529 :rule refl :args ((tptp.ap tptp.c_2Ereal__topology_2Ebounded__def @t111))) % 9.97/10.13 (step @p530 :rule cong :premises (@p421 @p487) :args (@t196)) % 9.97/10.13 (step @p531 :rule trans :premises (@p530 @p529)) % 9.97/10.13 (step @p532 :rule cong :premises (@p531) :args (@t197)) % 9.97/10.13 (step @p533 :rule trans :premises (@p532 @p528)) % 9.97/10.13 (step @p534 :rule ho_cong :premises (@p232 @p531)) % 9.97/10.13 (step @p535 :rule cong :premises (@p534 @p533) :args ((= (_ tptp.p @t196) @t197))) % 9.97/10.13 (step @p536 :rule symm :premises (@p535)) % 9.97/10.13 (step @p537 :rule refl :args (@t164)) % 9.97/10.13 (step @p538 :rule eq_resolve :premises (@p537 @p536)) % 9.97/10.13 (step @p539 :rule ho_cong :premises (@p431 @p487)) % 9.97/10.13 (step @p540 :rule cong :premises (@p539 @p531) :args ((= (_ @t120 @t195) @t196))) % 9.97/10.13 (step @p541 :rule symm :premises (@p540)) % 9.97/10.13 (step @p542 :rule refl :args (@t163)) % 9.97/10.13 (step @p543 :rule eq_resolve :premises (@p542 @p541)) % 9.97/10.13 (step @p544 :rule ho_cong :premises (@p431 @p517)) % 9.97/10.13 (step @p545 :rule trans :premises (@p544 @p543)) % 9.97/10.13 (step @p546 :rule ho_cong :premises (@p232 @p545)) % 9.97/10.13 (step @p547 :rule trans :premises (@p546 @p538)) % 9.97/10.13 (step @p548 :rule cong :premises (@p547) :args (@t165)) % 9.97/10.13 (step @p549 :rule cong :premises (@p548) :args (@t166)) % 9.97/10.13 (step @p550 :rule eq_resolve :premises (@p62 @p549)) % 9.97/10.13 (step @p551 :rule skolemize :premises (@p550)) % 9.97/10.13 (step @p552 :rule cnf_or_pos :args (@t286)) % 9.97/10.13 (step @p553 :rule reordering :premises (@p552) :args ((or @t284 @t279 @t281 @t285 @t283 (not @t286)))) % 9.97/10.13 (step @p554 :rule chain_m_resolution :premises (@p553 @p551 @p527 @p481 @p405 @p368) :args (@t283 (@list true false false false false) (@list @t284 @t278 @t280 @t267 @t286))) % 9.97/10.13 (step @p555 :rule refl :args ((tptp.mem tptp.c_2Ereal__topology_2Ecball @t46))) % 9.97/10.13 (step @p556 :rule cong :premises (@p418 @p374) :args (@t287)) % 9.97/10.13 (step @p557 :rule trans :premises (@p556 @p555)) % 9.97/10.13 (step @p558 :rule refl :args (@t57)) % 9.97/10.13 (step @p559 :rule ho_cong :premises (@p558 @p374)) % 9.97/10.13 (step @p560 :rule cong :premises (@p559 @p557) :args ((= (_ @t57 @t265) @t287))) % 9.97/10.13 (step @p561 :rule symm :premises (@p560)) % 9.97/10.13 (step @p562 :rule refl :args (@t58)) % 9.97/10.13 (step @p563 :rule eq_resolve :premises (@p562 @p561)) % 9.97/10.13 (step @p564 :rule refl :args (@t57)) % 9.97/10.13 (step @p565 :rule ho_cong :premises (@p564 @p398)) % 9.97/10.13 (step @p566 :rule trans :premises (@p565 @p563)) % 9.97/10.13 (step @p567 :rule eq_resolve :premises (@p21 @p566)) % 9.97/10.13 (step @p568 :rule cnf_or_pos :args (@t289)) % 9.97/10.13 (step @p569 :rule reordering :premises (@p568) :args ((or @t288 @t282 @t268 @t290))) % 9.97/10.13 (step @p570 :rule chain_m_resolution :premises (@p569 @p567 @p554 @p213) :args (@t290 (@list false true false) (@list @t287 @t282 @t221))) % 9.97/10.13 (assume-push @p577 @t291) % 9.97/10.13 (step @p572 :rule instantiate :premises (@p134) :args ((@list @t204 @t231 tptp.c_2Ereal__topology_2Ecball @t220))) % 9.97/10.13 (step-pop @p578 :rule scope :premises (@p572)) % 9.97/10.13 (step @p573 :rule process_scope :premises (@p578) :args (@t289)) % 9.97/10.13 (step @p575 :rule implies_elim :premises (@p573)) % 9.97/10.13 (step @p576 false :rule chain_m_resolution :premises (@p575 @p570 @p134) :args (false (@list true false) (@list @t289 @t291))) % 9.97/10.13 ) % 9.97/10.13 % SZS output end Proof % 9.97/10.13 % cvc5 exiting %------------------------------------------------------------------------------