%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWW672_2 : TPTP v9.2.1. Released v6.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n014.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 09:05:27 AM UTC 2026 % Result : Theorem 0.72s 0.91s % Output : Proof 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWW672_2 : TPTP v9.2.1. Released v6.1.0. % 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 : n014.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 22:23:43 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_ARI % 0.72/0.91 --- Run --finite-model-find --decision=internal at 45... % 0.72/0.91 % SZS status Theorem % 0.72/0.91 % SZS output start Proof % 0.72/0.91 ( % 0.72/0.91 (declare-sort tptp.set_vertex 0) % 0.72/0.91 (declare-sort tptp.vertex1 0) % 0.72/0.91 (declare-sort tptp.tuple02 0) % 0.72/0.91 (declare-sort tptp.bool1 0) % 0.72/0.91 (declare-sort tptp.ty 0) % 0.72/0.91 (declare-sort tptp.uni 0) % 0.72/0.91 (declare-const tptp.closure1 (-> tptp.set_vertex tptp.set_vertex tptp.set_vertex tptp.vertex1 Bool)) % 0.72/0.91 (declare-const tptp.empty (-> tptp.ty tptp.uni)) % 0.72/0.91 (declare-const tptp.t2tb1 (-> tptp.vertex1 tptp.uni)) % 0.72/0.91 (declare-const tptp.set (-> tptp.ty tptp.ty)) % 0.72/0.91 (declare-const tptp.infix_eqeq (-> tptp.ty tptp.uni tptp.uni Bool)) % 0.72/0.91 (declare-const tptp.false1 tptp.bool1) % 0.72/0.91 (declare-const tptp.mk_ref (-> tptp.ty tptp.uni tptp.uni)) % 0.72/0.91 (declare-const tptp.true1 tptp.bool1) % 0.72/0.91 (declare-const tptp.subset (-> tptp.ty tptp.uni tptp.uni Bool)) % 0.72/0.91 (declare-const tptp.ref (-> tptp.ty tptp.ty)) % 0.72/0.91 (declare-const tptp.mem (-> tptp.ty tptp.uni tptp.uni Bool)) % 0.72/0.91 (declare-const tptp.sort1 (-> tptp.ty tptp.uni Bool)) % 0.72/0.91 (declare-const tptp.inv1 (-> tptp.vertex1 tptp.vertex1 tptp.set_vertex tptp.set_vertex tptp.set_vertex Int Bool)) % 0.72/0.91 (declare-const tptp.is_empty (-> tptp.ty tptp.uni Bool)) % 0.72/0.91 (declare-const tptp.tb2t1 (-> tptp.uni tptp.vertex1)) % 0.72/0.91 (declare-const tptp.add (-> tptp.ty tptp.uni tptp.uni tptp.uni)) % 0.72/0.91 (declare-const tptp.cardinal1 (-> tptp.ty tptp.uni Int)) % 0.72/0.91 (declare-const tptp.tuple03 tptp.tuple02) % 0.72/0.91 (declare-const tptp.contents (-> tptp.ty tptp.uni tptp.uni)) % 0.72/0.91 (declare-const tptp.witness1 (-> tptp.ty tptp.uni)) % 0.72/0.91 (declare-const tptp.union (-> tptp.ty tptp.uni tptp.uni tptp.uni)) % 0.72/0.91 (declare-const tptp.match_bool1 (-> tptp.ty tptp.bool1 tptp.uni tptp.uni tptp.uni)) % 0.72/0.91 (declare-const tptp.inter (-> tptp.ty tptp.uni tptp.uni tptp.uni)) % 0.72/0.91 (declare-const tptp.diff (-> tptp.ty tptp.uni tptp.uni tptp.uni)) % 0.72/0.91 (declare-const tptp.remove (-> tptp.ty tptp.uni tptp.uni tptp.uni)) % 0.72/0.91 (declare-const tptp.tb2t (-> tptp.uni tptp.set_vertex)) % 0.72/0.91 (declare-const tptp.choose (-> tptp.ty tptp.uni tptp.uni)) % 0.72/0.91 (declare-const tptp.t2tb (-> tptp.set_vertex tptp.uni)) % 0.72/0.91 (declare-const tptp.vertex tptp.ty) % 0.72/0.91 (declare-const tptp.succ1 (-> tptp.vertex1 tptp.set_vertex)) % 0.72/0.91 (declare-const tptp.path1 (-> tptp.vertex1 tptp.vertex1 Int Bool)) % 0.72/0.91 (declare-const tptp.shortest_path1 (-> tptp.vertex1 tptp.vertex1 Int Bool)) % 0.72/0.91 (define @t1 () (@var "A" tptp.ty)) % 0.72/0.91 (define @t2 () (@list @t1)) % 0.72/0.91 (define @t3 () (@var "X2" tptp.uni)) % 0.72/0.91 (define @t4 () (@var "X1" tptp.uni)) % 0.72/0.91 (define @t5 () (@var "X" tptp.bool1)) % 0.72/0.91 (define @t6 () (@var "Z" tptp.uni)) % 0.72/0.91 (define @t7 () (@var "Z1" tptp.uni)) % 0.72/0.91 (define @t8 () (@list @t1 @t6 @t7)) % 0.72/0.91 (define @t9 () (@var "U" tptp.bool1)) % 0.72/0.91 (define @t10 () (@var "U" tptp.tuple02)) % 0.72/0.91 (define @t11 () (@var "Z" Int)) % 0.72/0.91 (define @t12 () (@var "Y" Int)) % 0.72/0.91 (define @t13 () (@var "X" Int)) % 0.72/0.91 (define @t14 () (@var "S2" tptp.uni)) % 0.72/0.91 (define @t15 () (@var "S1" tptp.uni)) % 0.72/0.91 (define @t16 () (tptp.infix_eqeq @t1 @t15 @t14)) % 0.72/0.91 (define @t17 () (@var "X" tptp.uni)) % 0.72/0.91 (define @t18 () (tptp.mem @t1 @t17 @t14)) % 0.72/0.91 (define @t19 () (tptp.mem @t1 @t17 @t15)) % 0.72/0.91 (define @t20 () (= @t19 @t18)) % 0.72/0.91 (define @t21 () (tptp.sort1 @t1 @t17)) % 0.72/0.91 (define @t22 () (@list @t17)) % 0.72/0.91 (define @t23 () (@list @t1 @t15 @t14)) % 0.72/0.91 (define @t24 () (tptp.set @t1)) % 0.72/0.91 (define @t25 () (tptp.subset @t1 @t15 @t14)) % 0.72/0.91 (define @t26 () (=> @t19 @t18)) % 0.72/0.91 (define @t27 () (@var "S" tptp.uni)) % 0.72/0.91 (define @t28 () (@list @t1 @t27)) % 0.72/0.91 (define @t29 () (@var "S3" tptp.uni)) % 0.72/0.91 (define @t30 () (tptp.empty @t1)) % 0.72/0.91 (define @t31 () (tptp.is_empty @t1 @t27)) % 0.72/0.91 (define @t32 () (tptp.mem @t1 @t17 @t27)) % 0.72/0.91 (define @t33 () (not @t32)) % 0.72/0.91 (define @t34 () (forall @t22 (=> @t21 @t33))) % 0.72/0.91 (define @t35 () (=> @t34 @t31)) % 0.72/0.91 (define @t36 () (forall @t22 @t33)) % 0.72/0.91 (define @t37 () (=> @t31 @t36)) % 0.72/0.91 (define @t38 () (and @t37 @t35)) % 0.72/0.91 (define @t39 () (forall @t28 @t38)) % 0.72/0.91 (define @t40 () (@list @t1 @t17)) % 0.72/0.91 (define @t41 () (@list @t1 @t17 @t4)) % 0.72/0.91 (define @t42 () (@var "Y" tptp.uni)) % 0.72/0.91 (define @t43 () (= @t17 @t42)) % 0.72/0.91 (define @t44 () (tptp.sort1 @t1 @t42)) % 0.72/0.91 (define @t45 () (tptp.remove @t1 @t17 @t27)) % 0.72/0.91 (define @t46 () (@list @t1 @t17 @t27)) % 0.72/0.91 (define @t47 () (tptp.add @t1 @t17 @t27)) % 0.72/0.91 (define @t48 () (@list @t1 @t15 @t14 @t17)) % 0.72/0.91 (define @t49 () (tptp.diff @t1 @t15 @t14)) % 0.72/0.91 (define @t50 () (tptp.choose @t1 @t27)) % 0.72/0.91 (define @t51 () (not @t31)) % 0.72/0.91 (define @t52 () (tptp.cardinal1 @t1 @t27)) % 0.72/0.91 (define @t53 () (@var "V" tptp.vertex1)) % 0.72/0.91 (define @t54 () (@list @t53)) % 0.72/0.91 (define @t55 () (@var "X" tptp.set_vertex)) % 0.72/0.91 (define @t56 () (tptp.set tptp.vertex)) % 0.72/0.91 (define @t57 () (@var "I" tptp.set_vertex)) % 0.72/0.91 (define @t58 () (@var "J" tptp.uni)) % 0.72/0.91 (define @t59 () (@list @t58)) % 0.72/0.91 (define @t60 () (@var "X" tptp.vertex1)) % 0.72/0.91 (define @t61 () (tptp.t2tb1 @t60)) % 0.72/0.91 (define @t62 () (@list @t60)) % 0.72/0.91 (define @t63 () (@var "I" tptp.vertex1)) % 0.72/0.91 (define @t64 () (@var "N" Int)) % 0.72/0.91 (define @t65 () (+ @t64 1)) % 0.72/0.91 (define @t66 () (@var "V3" tptp.vertex1)) % 0.72/0.91 (define @t67 () (@var "V1" tptp.vertex1)) % 0.72/0.91 (define @t68 () (tptp.path1 @t67 @t66 @t65)) % 0.72/0.91 (define @t69 () (@var "V2" tptp.vertex1)) % 0.72/0.91 (define @t70 () (tptp.mem tptp.vertex (tptp.t2tb1 @t66) (tptp.t2tb (tptp.succ1 @t69)))) % 0.72/0.91 (define @t71 () (tptp.path1 @t67 @t69 @t64)) % 0.72/0.91 (define @t72 () (@list @t67 @t69 @t66 @t64)) % 0.72/0.91 (define @t73 () (@var "Z2" Int)) % 0.72/0.91 (define @t74 () (@var "Z1" tptp.vertex1)) % 0.72/0.91 (define @t75 () (@var "Z" tptp.vertex1)) % 0.72/0.91 (define @t76 () (<= 0 @t64)) % 0.72/0.91 (define @t77 () (@list @t67 @t69 @t64)) % 0.72/0.91 (define @t78 () (@var "S" tptp.set_vertex)) % 0.72/0.91 (define @t79 () (tptp.t2tb @t78)) % 0.72/0.91 (define @t80 () (@var "Y" tptp.vertex1)) % 0.72/0.91 (define @t81 () (tptp.t2tb1 @t80)) % 0.72/0.91 (define @t82 () (tptp.mem tptp.vertex @t81 (tptp.t2tb (tptp.succ1 @t60)))) % 0.72/0.91 (define @t83 () (@list @t80)) % 0.72/0.91 (define @t84 () (@var "M" Int)) % 0.72/0.91 (define @t85 () (@list @t84)) % 0.72/0.91 (define @t86 () (tptp.ref @t1)) % 0.72/0.91 (define @t87 () (@var "U" tptp.uni)) % 0.72/0.91 (define @t88 () (@list @t1 @t87)) % 0.72/0.91 (define @t89 () (@var "Next" tptp.set_vertex)) % 0.72/0.91 (define @t90 () (tptp.t2tb @t89)) % 0.72/0.91 (define @t91 () (@var "T" tptp.vertex1)) % 0.72/0.91 (define @t92 () (tptp.t2tb1 @t91)) % 0.72/0.91 (define @t93 () (@var "Current" tptp.set_vertex)) % 0.72/0.91 (define @t94 () (tptp.t2tb @t93)) % 0.72/0.91 (define @t95 () (@var "Visited" tptp.set_vertex)) % 0.72/0.91 (define @t96 () (tptp.t2tb @t95)) % 0.72/0.91 (define @t97 () (tptp.mem tptp.vertex @t61 @t96)) % 0.72/0.91 (define @t98 () (not @t97)) % 0.72/0.91 (define @t99 () (tptp.mem tptp.vertex @t61 @t90)) % 0.72/0.91 (define @t100 () (@var "D" Int)) % 0.72/0.91 (define @t101 () (+ @t100 1)) % 0.72/0.91 (define @t102 () (@var "S" tptp.vertex1)) % 0.72/0.91 (define @t103 () (tptp.shortest_path1 @t102 @t60 @t101)) % 0.72/0.91 (define @t104 () (tptp.path1 @t102 @t60 @t84)) % 0.72/0.91 (define @t105 () (tptp.mem tptp.vertex @t61 @t94)) % 0.72/0.91 (define @t106 () (tptp.inv1 @t102 @t91 @t95 @t93 @t89 @t100)) % 0.72/0.91 (define @t107 () (tptp.mem tptp.vertex @t81 @t96)) % 0.72/0.91 (define @t108 () (forall @t83 (=> @t82 @t107))) % 0.72/0.91 (define @t109 () (not @t99)) % 0.72/0.91 (define @t110 () (=> @t109 @t108)) % 0.72/0.91 (define @t111 () (not @t105)) % 0.72/0.91 (define @t112 () (=> @t111 @t110)) % 0.72/0.91 (define @t113 () (=> @t97 @t112)) % 0.72/0.91 (define @t114 () (tptp.closure1 @t95 @t93 @t89 @t60)) % 0.72/0.91 (define @t115 () (= @t114 @t113)) % 0.72/0.91 (define @t116 () (@list @t95 @t93 @t89 @t60)) % 0.72/0.91 (define @t117 () (forall @t116 @t115)) % 0.72/0.91 (define @t118 () (@var "Next2" tptp.set_vertex)) % 0.72/0.91 (define @t119 () (@var "Current2" tptp.set_vertex)) % 0.72/0.91 (define @t120 () (@var "Visited1" tptp.set_vertex)) % 0.72/0.91 (define @t121 () (forall @t62 (tptp.closure1 @t120 @t119 @t118 @t60))) % 0.72/0.91 (define @t122 () (@var "D1" Int)) % 0.72/0.91 (define @t123 () (= @t122 @t101)) % 0.72/0.91 (define @t124 () (=> @t123 @t121)) % 0.72/0.91 (define @t125 () (@list @t122)) % 0.72/0.91 (define @t126 () (forall @t125 @t124)) % 0.72/0.91 (define @t127 () (tptp.tb2t (tptp.empty tptp.vertex))) % 0.72/0.91 (define @t128 () (= @t118 @t127)) % 0.72/0.91 (define @t129 () (=> @t128 @t126)) % 0.72/0.91 (define @t130 () (@list @t118)) % 0.72/0.91 (define @t131 () (forall @t130 @t129)) % 0.72/0.91 (define @t132 () (@var "Next1" tptp.set_vertex)) % 0.72/0.91 (define @t133 () (= @t119 @t132)) % 0.72/0.91 (define @t134 () (=> @t133 @t131)) % 0.72/0.91 (define @t135 () (@list @t119)) % 0.72/0.91 (define @t136 () (forall @t135 @t134)) % 0.72/0.91 (define @t137 () (@var "Result" tptp.bool1)) % 0.72/0.91 (define @t138 () (= @t137 tptp.true1)) % 0.72/0.91 (define @t139 () (=> @t138 @t136)) % 0.72/0.91 (define @t140 () (@var "Current1" tptp.set_vertex)) % 0.72/0.91 (define @t141 () (tptp.is_empty tptp.vertex (tptp.t2tb @t140))) % 0.72/0.91 (define @t142 () (= @t138 @t141)) % 0.72/0.91 (define @t143 () (=> @t142 @t139)) % 0.72/0.91 (define @t144 () (@list @t137)) % 0.72/0.91 (define @t145 () (forall @t144 @t143)) % 0.72/0.91 (define @t146 () (forall @t62 (tptp.closure1 @t120 @t140 @t132 @t60))) % 0.72/0.91 (define @t147 () (tptp.t2tb (tptp.succ1 @t53))) % 0.72/0.91 (define @t148 () (tptp.subset tptp.vertex @t147 (tptp.t2tb @t120))) % 0.72/0.91 (define @t149 () (tptp.inv1 @t102 @t91 @t120 @t140 @t132 @t100)) % 0.72/0.91 (define @t150 () (and @t149 @t148 @t146)) % 0.72/0.91 (define @t151 () (=> @t150 @t145)) % 0.72/0.91 (define @t152 () (@list @t132 @t120)) % 0.72/0.91 (define @t153 () (forall @t152 @t151)) % 0.72/0.91 (define @t154 () (tptp.closure1 @t95 @t140 @t89 @t60)) % 0.72/0.91 (define @t155 () (not (= @t60 @t53))) % 0.72/0.91 (define @t156 () (=> @t155 @t154)) % 0.72/0.91 (define @t157 () (forall @t62 @t156)) % 0.72/0.91 (define @t158 () (tptp.shortest_path1 @t102 @t53 @t100)) % 0.72/0.91 (define @t159 () (tptp.inv1 @t102 @t91 @t95 @t140 @t89 @t100)) % 0.72/0.91 (define @t160 () (and @t159 @t158 @t157)) % 0.72/0.91 (define @t161 () (=> @t160 @t153)) % 0.72/0.91 (define @t162 () (= @t53 @t91)) % 0.72/0.91 (define @t163 () (not @t162)) % 0.72/0.91 (define @t164 () (=> @t163 @t161)) % 0.72/0.91 (define @t165 () (tptp.t2tb1 @t53)) % 0.72/0.91 (define @t166 () (tptp.tb2t (tptp.remove tptp.vertex @t165 @t94))) % 0.72/0.91 (define @t167 () (= @t140 @t166)) % 0.72/0.91 (define @t168 () (tptp.mem tptp.vertex @t165 @t94)) % 0.72/0.91 (define @t169 () (and @t168 @t167)) % 0.72/0.91 (define @t170 () (=> @t169 @t164)) % 0.72/0.91 (define @t171 () (@list @t140 @t53)) % 0.72/0.91 (define @t172 () (forall @t171 @t170)) % 0.72/0.91 (define @t173 () (tptp.is_empty tptp.vertex @t94)) % 0.72/0.91 (define @t174 () (not @t173)) % 0.72/0.91 (define @t175 () (=> @t174 @t172)) % 0.72/0.91 (define @t176 () (@var "O" tptp.bool1)) % 0.72/0.91 (define @t177 () (= @t176 tptp.true1)) % 0.72/0.91 (define @t178 () (not @t177)) % 0.72/0.91 (define @t179 () (=> @t178 @t175)) % 0.72/0.91 (define @t180 () (=> (= @t177 @t173) @t179)) % 0.72/0.91 (define @t181 () (@list @t176)) % 0.72/0.91 (define @t182 () (forall @t181 @t180)) % 0.72/0.91 (define @t183 () (forall @t62 @t114)) % 0.72/0.91 (define @t184 () (tptp.is_empty tptp.vertex @t90)) % 0.72/0.91 (define @t185 () (=> @t173 @t184)) % 0.72/0.91 (define @t186 () (and @t106 @t185 @t183 (<= 0 @t100))) % 0.72/0.91 (define @t187 () (=> @t186 @t182)) % 0.72/0.91 (define @t188 () (@list @t102 @t91 @t100 @t89 @t93 @t95)) % 0.72/0.91 (define @t189 () (forall @t188 @t187)) % 0.72/0.91 (define @t190 () (not @t189)) % 0.72/0.91 (define @t191 () (@var "BOUND_VARIABLE_8781" tptp.bool1)) % 0.72/0.91 (define @t192 () (= tptp.true1 @t191)) % 0.72/0.91 (define @t193 () (= @t174 @t192)) % 0.72/0.91 (define @t194 () (@var "BOUND_VARIABLE_8749" tptp.vertex1)) % 0.72/0.91 (define @t195 () (@var "BOUND_VARIABLE_8745" tptp.set_vertex)) % 0.72/0.91 (define @t196 () (@var "BOUND_VARIABLE_8747" tptp.set_vertex)) % 0.72/0.91 (define @t197 () (tptp.closure1 @t196 @t195 @t127 @t194)) % 0.72/0.91 (define @t198 () (@var "BOUND_VARIABLE_8743" tptp.vertex1)) % 0.72/0.91 (define @t199 () (tptp.t2tb1 @t198)) % 0.72/0.91 (define @t200 () (tptp.tb2t (tptp.remove tptp.vertex @t199 @t94))) % 0.72/0.91 (define @t201 () (not (forall @t62 (tptp.closure1 @t196 @t200 @t195 @t60)))) % 0.72/0.91 (define @t202 () (not (tptp.subset tptp.vertex (tptp.t2tb (tptp.succ1 @t198)) (tptp.t2tb @t196)))) % 0.72/0.91 (define @t203 () (not (tptp.inv1 @t102 @t91 @t196 @t200 @t195 @t100))) % 0.72/0.91 (define @t204 () (not (tptp.is_empty tptp.vertex (tptp.t2tb @t200)))) % 0.72/0.91 (define @t205 () (tptp.closure1 @t95 @t200 @t89 @t60)) % 0.72/0.91 (define @t206 () (or (= @t198 @t60) @t205)) % 0.72/0.91 (define @t207 () (forall @t62 @t206)) % 0.72/0.91 (define @t208 () (not @t207)) % 0.72/0.91 (define @t209 () (not (tptp.shortest_path1 @t102 @t198 @t100))) % 0.72/0.91 (define @t210 () (not (tptp.inv1 @t102 @t91 @t95 @t200 @t89 @t100))) % 0.72/0.91 (define @t211 () (not (tptp.mem tptp.vertex @t199 @t94))) % 0.72/0.91 (define @t212 () (>= @t100 0)) % 0.72/0.91 (define @t213 () (not @t212)) % 0.72/0.91 (define @t214 () (not @t183)) % 0.72/0.91 (define @t215 () (and @t173 (not @t184))) % 0.72/0.91 (define @t216 () (not @t106)) % 0.72/0.91 (define @t217 () (= @t198 @t91)) % 0.72/0.91 (define @t218 () (or @t216 @t215 @t214 @t213 @t173 @t211 @t217 @t210 @t209 @t208 @t204 @t203 @t202 @t201 @t197 @t193 @t192)) % 0.72/0.91 (define @t219 () (or @t193 @t192)) % 0.72/0.91 (define @t220 () (or @t211 @t217 @t210 @t209 @t208 @t204 @t203 @t202 @t201 @t197)) % 0.72/0.91 (define @t221 () (or @t216 @t215 @t214 @t213 @t173 @t220 @t219)) % 0.72/0.91 (define @t222 () (@list @t102 @t91 @t100 @t89 @t93 @t95 @t198 @t195 @t196 @t194 @t191)) % 0.72/0.91 (define @t223 () (forall @t222 @t221)) % 0.72/0.91 (define @t224 () (forall (@list @t198 @t195 @t196 @t194 @t191) @t221)) % 0.72/0.91 (define @t225 () (forall (@list @t191) @t219)) % 0.72/0.91 (define @t226 () (forall (@list @t198 @t195 @t196 @t194) @t220)) % 0.72/0.91 (define @t227 () (@var "BOUND_VARIABLE_8679" tptp.vertex1)) % 0.72/0.91 (define @t228 () (@var "BOUND_VARIABLE_8677" tptp.set_vertex)) % 0.72/0.91 (define @t229 () (@var "BOUND_VARIABLE_8675" tptp.set_vertex)) % 0.72/0.91 (define @t230 () (or @t216 @t215 @t214 @t213 @t173 @t226 @t225)) % 0.72/0.91 (define @t231 () (= tptp.true1 @t176)) % 0.72/0.91 (define @t232 () (= @t174 @t231)) % 0.72/0.91 (define @t233 () (or @t232 @t231)) % 0.72/0.91 (define @t234 () (forall @t181 @t233)) % 0.72/0.91 (define @t235 () (tptp.closure1 @t228 @t229 @t127 @t227)) % 0.72/0.91 (define @t236 () (not (forall @t62 (tptp.closure1 @t228 @t166 @t229 @t60)))) % 0.72/0.91 (define @t237 () (not (tptp.subset tptp.vertex @t147 (tptp.t2tb @t228)))) % 0.72/0.91 (define @t238 () (not (tptp.inv1 @t102 @t91 @t228 @t166 @t229 @t100))) % 0.72/0.91 (define @t239 () (not (tptp.is_empty tptp.vertex (tptp.t2tb @t166)))) % 0.72/0.91 (define @t240 () (= @t53 @t60)) % 0.72/0.91 (define @t241 () (not (forall @t62 (or @t240 (tptp.closure1 @t95 @t166 @t89 @t60))))) % 0.72/0.91 (define @t242 () (not @t158)) % 0.72/0.91 (define @t243 () (not (tptp.inv1 @t102 @t91 @t95 @t166 @t89 @t100))) % 0.72/0.91 (define @t244 () (not @t168)) % 0.72/0.91 (define @t245 () (or @t244 @t162 @t243 @t242 @t241 @t239 @t238 @t237 @t236 @t235)) % 0.72/0.91 (define @t246 () (@list @t53 @t229 @t228 @t227)) % 0.72/0.91 (define @t247 () (forall @t246 @t245)) % 0.72/0.91 (define @t248 () (or @t216 @t215 @t214 @t213 @t173 @t247 @t234)) % 0.72/0.91 (define @t249 () (or @t173 @t247 @t234)) % 0.72/0.91 (define @t250 () (not @t185)) % 0.72/0.91 (define @t251 () (or @t216 @t250 @t214 @t213)) % 0.72/0.91 (define @t252 () (and @t106 @t185 @t183 @t212)) % 0.72/0.91 (define @t253 () (or @t173 @t247 @t233)) % 0.72/0.91 (define @t254 () (or @t232 @t231 @t173 @t247)) % 0.72/0.91 (define @t255 () (or @t231 @t173 @t247)) % 0.72/0.91 (define @t256 () (=> @t174 @t247)) % 0.72/0.91 (define @t257 () (not @t231)) % 0.72/0.91 (define @t258 () (=> @t257 @t256)) % 0.72/0.91 (define @t259 () (= @t173 @t231)) % 0.72/0.91 (define @t260 () (not (= @t166 @t166))) % 0.72/0.91 (define @t261 () (or @t244 @t260 @t162 @t243 @t242 @t241 @t239 @t238 @t237 @t236 @t235)) % 0.72/0.91 (define @t262 () (not (forall @t62 (tptp.closure1 @t228 @t140 @t229 @t60)))) % 0.72/0.91 (define @t263 () (not (tptp.inv1 @t102 @t91 @t228 @t140 @t229 @t100))) % 0.72/0.91 (define @t264 () (not @t141)) % 0.72/0.91 (define @t265 () (forall @t62 (or @t240 @t154))) % 0.72/0.91 (define @t266 () (not @t265)) % 0.72/0.91 (define @t267 () (not @t159)) % 0.72/0.91 (define @t268 () (not @t167)) % 0.72/0.91 (define @t269 () (or @t268 @t244 @t268 @t162 @t267 @t242 @t266 @t264 @t263 @t237 @t262 @t235)) % 0.72/0.91 (define @t270 () (@list @t140)) % 0.72/0.91 (define @t271 () (or @t244 @t268 @t162 @t267 @t242 @t266 @t264 @t263 @t237 @t262 @t235)) % 0.72/0.91 (define @t272 () (forall @t270 @t271)) % 0.72/0.91 (define @t273 () (forall @t246 @t272)) % 0.72/0.91 (define @t274 () (forall (@list @t53 @t229 @t228 @t227 @t140) @t271)) % 0.72/0.91 (define @t275 () (@list @t140 @t53 @t229 @t228 @t227)) % 0.72/0.91 (define @t276 () (or @t263 @t237 @t262 @t235)) % 0.72/0.91 (define @t277 () (or @t244 @t268 @t162 @t267 @t242 @t266 @t264 @t276)) % 0.72/0.91 (define @t278 () (forall @t275 @t277)) % 0.72/0.91 (define @t279 () (@list @t229 @t228 @t227)) % 0.72/0.91 (define @t280 () (forall @t279 @t277)) % 0.72/0.91 (define @t281 () (forall @t279 @t276)) % 0.72/0.91 (define @t282 () (@var "BOUND_VARIABLE_8651" tptp.vertex1)) % 0.72/0.91 (define @t283 () (or @t244 @t268 @t162 @t267 @t242 @t266 @t264 @t281)) % 0.72/0.91 (define @t284 () (tptp.closure1 @t120 @t132 @t127 @t282)) % 0.72/0.91 (define @t285 () (not @t146)) % 0.72/0.91 (define @t286 () (not @t148)) % 0.72/0.91 (define @t287 () (not @t149)) % 0.72/0.91 (define @t288 () (or @t287 @t286 @t285 @t284)) % 0.72/0.91 (define @t289 () (forall (@list @t132 @t120 @t282) @t288)) % 0.72/0.91 (define @t290 () (or @t244 @t268 @t162 @t267 @t242 @t266 @t264 @t289)) % 0.72/0.91 (define @t291 () (or @t162 @t267 @t242 @t266 @t264 @t289)) % 0.72/0.91 (define @t292 () (or @t267 @t242 @t266 @t264 @t289)) % 0.72/0.91 (define @t293 () (or @t264 @t289)) % 0.72/0.91 (define @t294 () (or @t267 @t242 @t266)) % 0.72/0.91 (define @t295 () (and @t159 @t158 @t265)) % 0.72/0.91 (define @t296 () (=> @t295 @t293)) % 0.72/0.91 (define @t297 () (=> @t163 @t296)) % 0.72/0.91 (define @t298 () (@list @t282)) % 0.72/0.91 (define @t299 () (forall @t298 @t288)) % 0.72/0.91 (define @t300 () (forall @t298 @t284)) % 0.72/0.91 (define @t301 () (@var "BOUND_VARIABLE_8601" tptp.vertex1)) % 0.72/0.91 (define @t302 () (@list @t301)) % 0.72/0.91 (define @t303 () (or @t287 @t286 @t285 @t300)) % 0.72/0.91 (define @t304 () (tptp.closure1 @t120 @t132 @t127 @t301)) % 0.72/0.91 (define @t305 () (@list @t301)) % 0.72/0.91 (define @t306 () (forall @t305 @t304)) % 0.72/0.91 (define @t307 () (or @t287 @t286 @t285 @t306)) % 0.72/0.91 (define @t308 () (forall @t152 @t307)) % 0.72/0.91 (define @t309 () (or @t264 @t308)) % 0.72/0.91 (define @t310 () (or @t264 @t307)) % 0.72/0.91 (define @t311 () (or @t287 @t286 @t285 @t306 @t264)) % 0.72/0.91 (define @t312 () (or @t306 @t264)) % 0.72/0.91 (define @t313 () (or @t287 @t286 @t285)) % 0.72/0.91 (define @t314 () (= tptp.true1 tptp.true1)) % 0.72/0.91 (define @t315 () (not @t314)) % 0.72/0.91 (define @t316 () (or (= @t314 @t264) @t315)) % 0.72/0.91 (define @t317 () (= tptp.true1 @t137)) % 0.72/0.91 (define @t318 () (not @t317)) % 0.72/0.91 (define @t319 () (= @t317 @t264)) % 0.72/0.91 (define @t320 () (or @t318 @t319 @t318)) % 0.72/0.91 (define @t321 () (or @t319 @t318)) % 0.72/0.91 (define @t322 () (forall @t144 @t321)) % 0.72/0.91 (define @t323 () (or @t306 @t322)) % 0.72/0.91 (define @t324 () (or @t306 @t321)) % 0.72/0.91 (define @t325 () (or @t319 @t318 @t306)) % 0.72/0.91 (define @t326 () (= @t264 @t317)) % 0.72/0.91 (define @t327 () (or @t326 @t318 @t306)) % 0.72/0.91 (define @t328 () (=> @t317 @t306)) % 0.72/0.91 (define @t329 () (= @t141 @t317)) % 0.72/0.91 (define @t330 () (not (= @t132 @t132))) % 0.72/0.91 (define @t331 () (or @t330 @t304)) % 0.72/0.91 (define @t332 () (tptp.closure1 @t120 @t119 @t127 @t301)) % 0.72/0.91 (define @t333 () (= @t132 @t119)) % 0.72/0.91 (define @t334 () (not @t333)) % 0.72/0.91 (define @t335 () (or @t334 @t334 @t332)) % 0.72/0.91 (define @t336 () (or @t334 @t332)) % 0.72/0.91 (define @t337 () (forall @t135 @t336)) % 0.72/0.91 (define @t338 () (forall @t305 @t337)) % 0.72/0.91 (define @t339 () (forall (@list @t301 @t119) @t336)) % 0.72/0.91 (define @t340 () (forall (@list @t119 @t301) @t336)) % 0.72/0.91 (define @t341 () (forall @t305 @t336)) % 0.72/0.91 (define @t342 () (forall @t305 @t332)) % 0.72/0.91 (define @t343 () (@var "BOUND_VARIABLE_8582" tptp.vertex1)) % 0.72/0.91 (define @t344 () (@list @t343)) % 0.72/0.91 (define @t345 () (or @t334 @t342)) % 0.72/0.91 (define @t346 () (tptp.closure1 @t120 @t119 @t127 @t343)) % 0.72/0.91 (define @t347 () (@list @t343)) % 0.72/0.91 (define @t348 () (forall @t347 @t346)) % 0.72/0.91 (define @t349 () (not (= @t127 @t127))) % 0.72/0.91 (define @t350 () (or @t349 @t346)) % 0.72/0.91 (define @t351 () (tptp.closure1 @t120 @t119 @t118 @t343)) % 0.72/0.91 (define @t352 () (not @t128)) % 0.72/0.91 (define @t353 () (or @t352 @t352 @t351)) % 0.72/0.91 (define @t354 () (or @t352 @t351)) % 0.72/0.91 (define @t355 () (forall @t130 @t354)) % 0.72/0.91 (define @t356 () (forall @t347 @t355)) % 0.72/0.91 (define @t357 () (forall (@list @t343 @t118) @t354)) % 0.72/0.91 (define @t358 () (forall (@list @t118 @t343) @t354)) % 0.72/0.91 (define @t359 () (forall @t347 @t354)) % 0.72/0.91 (define @t360 () (forall @t347 @t351)) % 0.72/0.91 (define @t361 () (or @t352 @t360)) % 0.72/0.91 (define @t362 () (+ 1 @t100)) % 0.72/0.91 (define @t363 () (+ -1 @t362)) % 0.72/0.91 (define @t364 () (= @t100 @t363)) % 0.72/0.91 (define @t365 () (not @t364)) % 0.72/0.91 (define @t366 () (+ -1 @t122)) % 0.72/0.91 (define @t367 () (= @t100 @t366)) % 0.72/0.91 (define @t368 () (not @t367)) % 0.72/0.91 (define @t369 () (= @t122 @t362)) % 0.72/0.91 (define @t370 () (* 1 (- @t122 @t362))) % 0.72/0.91 (define @t371 () (* -1 (- @t100 @t366))) % 0.72/0.91 (define @t372 () (or @t368 @t368)) % 0.72/0.91 (define @t373 () (forall @t125 @t368)) % 0.72/0.91 (define @t374 () (or @t121 @t373)) % 0.72/0.91 (define @t375 () (or @t121 @t368)) % 0.72/0.91 (define @t376 () (or @t368 @t121)) % 0.72/0.91 (define @t377 () (not @t240)) % 0.72/0.91 (define @t378 () (forall @t222 (or @t216 @t215 @t214 @t213 @t173 @t211 (= @t91 @t198) @t210 @t209 (not (forall @t62 (or (= @t60 @t198) @t205))) @t204 @t203 @t202 @t201 @t197 @t193 @t192))) % 0.72/0.91 (define @t379 () (@quantifiers_skolemize @t378 7)) % 0.72/0.91 (define @t380 () (@quantifiers_skolemize @t378 4)) % 0.72/0.91 (define @t381 () (tptp.t2tb @t380)) % 0.72/0.91 (define @t382 () (@quantifiers_skolemize @t378 6)) % 0.72/0.91 (define @t383 () (tptp.t2tb1 @t382)) % 0.72/0.91 (define @t384 () (tptp.tb2t (tptp.remove tptp.vertex @t383 @t381))) % 0.72/0.91 (define @t385 () (@quantifiers_skolemize @t378 8)) % 0.72/0.91 (define @t386 () (forall @t62 (tptp.closure1 @t385 @t384 @t379 @t60))) % 0.72/0.91 (define @t387 () (= tptp.true1 (@quantifiers_skolemize @t378 10))) % 0.72/0.91 (define @t388 () (tptp.is_empty tptp.vertex @t381)) % 0.72/0.91 (define @t389 () (@quantifiers_skolemize @t378 9)) % 0.72/0.91 (define @t390 () (tptp.closure1 @t385 @t379 @t127 @t389)) % 0.72/0.91 (define @t391 () (not @t386)) % 0.72/0.91 (define @t392 () (tptp.t2tb @t385)) % 0.72/0.91 (define @t393 () (@quantifiers_skolemize @t378 2)) % 0.72/0.91 (define @t394 () (@quantifiers_skolemize @t378 1)) % 0.72/0.91 (define @t395 () (@quantifiers_skolemize @t378 0)) % 0.72/0.91 (define @t396 () (tptp.t2tb @t384)) % 0.72/0.91 (define @t397 () (tptp.is_empty tptp.vertex @t396)) % 0.72/0.91 (define @t398 () (not @t397)) % 0.72/0.91 (define @t399 () (@quantifiers_skolemize @t378 3)) % 0.72/0.91 (define @t400 () (@quantifiers_skolemize @t378 5)) % 0.72/0.91 (define @t401 () (or (not (tptp.inv1 @t395 @t394 @t400 @t380 @t399 @t393)) (and @t388 (not (tptp.is_empty tptp.vertex (tptp.t2tb @t399)))) (not (forall @t62 (tptp.closure1 @t400 @t380 @t399 @t60))) (not (>= @t393 0)) @t388 (not (tptp.mem tptp.vertex @t383 @t381)) (= @t394 @t382) (not (tptp.inv1 @t395 @t394 @t400 @t384 @t399 @t393)) (not (tptp.shortest_path1 @t395 @t382 @t393)) (not (forall @t62 (or (= @t60 @t382) (tptp.closure1 @t400 @t384 @t399 @t60)))) @t398 (not (tptp.inv1 @t395 @t394 @t385 @t384 @t379 @t393)) (not (tptp.subset tptp.vertex (tptp.t2tb (tptp.succ1 @t382)) @t392)) @t391 @t390 (= (not @t388) @t387) @t387)) % 0.72/0.91 (define @t402 () (@list true)) % 0.72/0.91 (define @t403 () (@list @t401)) % 0.72/0.91 (define @t404 () (@var "BOUND_VARIABLE_8170" tptp.uni)) % 0.72/0.91 (define @t405 () (@var "BOUND_VARIABLE_8168" tptp.ty)) % 0.72/0.91 (define @t406 () (forall (@list @t405 @t404) (or (not (forall @t22 (or (not (tptp.sort1 @t405 @t17)) (not (tptp.mem @t405 @t17 @t404))))) (tptp.is_empty @t405 @t404)))) % 0.72/0.91 (define @t407 () (@var "BOUND_VARIABLE_8158" tptp.uni)) % 0.72/0.91 (define @t408 () (@var "BOUND_VARIABLE_8184" tptp.uni)) % 0.72/0.91 (define @t409 () (@var "BOUND_VARIABLE_8156" tptp.ty)) % 0.72/0.91 (define @t410 () (not (tptp.mem @t409 @t408 @t407))) % 0.72/0.91 (define @t411 () (not (tptp.is_empty @t409 @t407))) % 0.72/0.91 (define @t412 () (or @t411 @t410)) % 0.72/0.91 (define @t413 () (@list @t408)) % 0.72/0.91 (define @t414 () (forall @t413 @t412)) % 0.72/0.91 (define @t415 () (@list @t409 @t407)) % 0.72/0.91 (define @t416 () (forall @t413 @t410)) % 0.72/0.91 (define @t417 () (or @t411 @t416)) % 0.72/0.91 (define @t418 () (forall @t415 (or @t411 (forall @t22 (not (tptp.mem @t409 @t17 @t407)))))) % 0.72/0.91 (define @t419 () (forall @t22 (or (not @t21) @t33))) % 0.72/0.91 (define @t420 () (or (not @t419) @t31)) % 0.72/0.91 (define @t421 () (forall @t28 @t420)) % 0.72/0.91 (define @t422 () (@list @t1 @t27)) % 0.72/0.91 (define @t423 () (or @t51 @t36)) % 0.72/0.91 (define @t424 () (forall @t28 @t423)) % 0.72/0.91 (define @t425 () (and @t424 @t421)) % 0.72/0.91 (define @t426 () (and @t37 (=> @t419 @t31))) % 0.72/0.91 (define @t427 () (tptp.t2tb1 @t389)) % 0.72/0.91 (define @t428 () (tptp.mem tptp.vertex @t427 @t396)) % 0.72/0.91 (define @t429 () (not @t428)) % 0.72/0.91 (define @t430 () (or @t398 @t429)) % 0.72/0.91 (define @t431 () (forall @t83 (or (not @t82) @t107))) % 0.72/0.91 (define @t432 () (or @t105 @t99 @t431)) % 0.72/0.91 (define @t433 () (=> @t109 @t431)) % 0.72/0.91 (define @t434 () (=> @t111 @t433)) % 0.72/0.91 (define @t435 () (= @t114 (=> @t97 @t434))) % 0.72/0.91 (define @t436 () (forall @t83 (or (not (tptp.mem tptp.vertex @t81 (tptp.t2tb (tptp.succ1 @t389)))) (tptp.mem tptp.vertex @t81 @t392)))) % 0.72/0.91 (define @t437 () (tptp.mem tptp.vertex @t427 (tptp.t2tb @t379))) % 0.72/0.91 (define @t438 () (tptp.mem tptp.vertex @t427 @t392)) % 0.72/0.91 (define @t439 () (not @t438)) % 0.72/0.91 (define @t440 () (or @t439 @t437 (tptp.mem tptp.vertex @t427 (tptp.t2tb @t127)) @t436)) % 0.72/0.91 (define @t441 () (= @t390 @t440)) % 0.72/0.91 (define @t442 () (not @t440)) % 0.72/0.91 (define @t443 () (@list @t440)) % 0.72/0.91 (define @t444 () (or @t439 @t428 @t437 @t436)) % 0.72/0.91 (define @t445 () (not @t444)) % 0.72/0.91 (define @t446 () (tptp.closure1 @t385 @t384 @t379 @t389)) % 0.72/0.91 (define @t447 () (= @t446 @t444)) % 0.72/0.91 (assume @p1 (forall @t2 (tptp.sort1 @t1 (tptp.witness1 @t1)))) % 0.72/0.91 (assume @p2 (forall (@list @t1 @t5 @t4 @t3) (tptp.sort1 @t1 (tptp.match_bool1 @t1 @t5 @t4 @t3)))) % 0.72/0.91 (assume @p3 (forall @t8 (=> (tptp.sort1 @t1 @t6) (= (tptp.match_bool1 @t1 tptp.true1 @t6 @t7) @t6)))) % 0.72/0.91 (assume @p4 (forall @t8 (=> (tptp.sort1 @t1 @t7) (= (tptp.match_bool1 @t1 tptp.false1 @t6 @t7) @t7)))) % 0.72/0.91 (assume @p5 (not (= tptp.true1 tptp.false1))) % 0.72/0.91 (assume @p6 (forall (@list @t9) (or (= @t9 tptp.true1) (= @t9 tptp.false1)))) % 0.72/0.91 (assume @p7 (forall (@list @t10) (= @t10 tptp.tuple03))) % 0.72/0.91 (assume @p8 (forall (@list @t13 @t12 @t11) (=> (<= @t13 @t12) (=> (<= 0 @t11) (<= (* @t13 @t11) (* @t12 @t11)))))) % 0.72/0.91 (assume @p9 (forall @t23 (and (=> @t16 (forall @t22 @t20)) (=> (forall @t22 (=> @t21 @t20)) @t16)))) % 0.72/0.91 (assume @p10 (forall @t23 (=> (tptp.sort1 @t24 @t15) (=> (tptp.sort1 @t24 @t14) (=> @t16 (= @t15 @t14)))))) % 0.72/0.91 (assume @p11 (forall @t23 (and (=> @t25 (forall @t22 @t26)) (=> (forall @t22 (=> @t21 @t26)) @t25)))) % 0.72/0.91 (assume @p12 (forall @t28 (tptp.subset @t1 @t27 @t27))) % 0.72/0.91 (assume @p13 (forall (@list @t1 @t15 @t14 @t29) (=> @t25 (=> (tptp.subset @t1 @t14 @t29) (tptp.subset @t1 @t15 @t29))))) % 0.72/0.91 (assume @p14 (forall @t2 (tptp.sort1 @t24 @t30))) % 0.72/0.91 (assume @p15 @t39) % 0.72/0.91 (assume @p16 (forall @t2 (tptp.is_empty @t1 @t30))) % 0.72/0.91 (assume @p17 (forall @t40 (= (tptp.mem @t1 @t17 @t30) false))) % 0.72/0.91 (assume @p18 (forall @t41 (tptp.sort1 @t24 (tptp.add @t1 @t17 @t4)))) % 0.72/0.91 (assume @p19 (forall (@list @t1 @t17 @t42) (=> @t21 (=> @t44 (forall (@list @t27) (= (tptp.mem @t1 @t17 (tptp.add @t1 @t42 @t27)) (or @t43 @t32))))))) % 0.72/0.91 (assume @p20 (forall @t41 (tptp.sort1 @t24 (tptp.remove @t1 @t17 @t4)))) % 0.72/0.91 (assume @p21 (forall (@list @t1 @t17 @t42 @t27) (=> @t21 (=> @t44 (= (tptp.mem @t1 @t17 (tptp.remove @t1 @t42 @t27)) (and (not @t43) @t32)))))) % 0.72/0.91 (assume @p22 (forall @t46 (=> (tptp.sort1 @t24 @t27) (=> @t32 (= (tptp.add @t1 @t17 @t45) @t27))))) % 0.72/0.91 (assume @p23 (forall @t46 (= (tptp.remove @t1 @t17 @t47) @t45))) % 0.72/0.91 (assume @p24 (forall @t46 (tptp.subset @t1 @t45 @t27))) % 0.72/0.91 (assume @p25 (forall @t41 (tptp.sort1 @t24 (tptp.union @t1 @t17 @t4)))) % 0.72/0.91 (assume @p26 (forall @t48 (= (tptp.mem @t1 @t17 (tptp.union @t1 @t15 @t14)) (or @t19 @t18)))) % 0.72/0.91 (assume @p27 (forall @t41 (tptp.sort1 @t24 (tptp.inter @t1 @t17 @t4)))) % 0.72/0.91 (assume @p28 (forall @t48 (= (tptp.mem @t1 @t17 (tptp.inter @t1 @t15 @t14)) (and @t19 @t18)))) % 0.72/0.91 (assume @p29 (forall @t41 (tptp.sort1 @t24 (tptp.diff @t1 @t17 @t4)))) % 0.72/0.91 (assume @p30 (forall @t48 (= (tptp.mem @t1 @t17 @t49) (and @t19 (not @t18))))) % 0.72/0.91 (assume @p31 (forall @t23 (tptp.subset @t1 @t49 @t15))) % 0.72/0.91 (assume @p32 (forall @t40 (tptp.sort1 @t1 (tptp.choose @t1 @t17)))) % 0.72/0.91 (assume @p33 (forall @t28 (=> @t51 (tptp.mem @t1 @t50 @t27)))) % 0.72/0.91 (assume @p34 (forall @t28 (<= 0 @t52))) % 0.72/0.91 (assume @p35 (forall @t28 (= (= @t52 0) @t31))) % 0.72/0.91 (assume @p36 (forall @t46 (=> @t33 (= (tptp.cardinal1 @t1 @t47) (+ 1 @t52))))) % 0.72/0.91 (assume @p37 (forall @t46 (=> @t32 (= @t52 (+ 1 (tptp.cardinal1 @t1 @t45)))))) % 0.72/0.91 (assume @p38 (forall @t23 (=> @t25 (<= (tptp.cardinal1 @t1 @t15) (tptp.cardinal1 @t1 @t14))))) % 0.72/0.91 (assume @p39 (forall @t28 (=> (= @t52 1) (forall @t22 (=> @t21 (=> @t32 (= @t17 @t50))))))) % 0.72/0.91 (assume @p40 (forall @t54 (tptp.path1 @t53 @t53 0))) % 0.72/0.91 (assume @p41 (forall (@list @t55) (tptp.sort1 @t56 (tptp.t2tb @t55)))) % 0.72/0.91 (assume @p42 (forall (@list @t57) (= (tptp.tb2t (tptp.t2tb @t57)) @t57))) % 0.72/0.91 (assume @p43 (forall @t59 (=> (tptp.sort1 @t56 @t58) (= (tptp.t2tb (tptp.tb2t @t58)) @t58)))) % 0.72/0.91 (assume @p44 (forall @t62 (tptp.sort1 tptp.vertex @t61))) % 0.72/0.91 (assume @p45 (forall (@list @t63) (= (tptp.tb2t1 (tptp.t2tb1 @t63)) @t63))) % 0.72/0.91 (assume @p46 (forall @t59 (=> (tptp.sort1 tptp.vertex @t58) (= (tptp.t2tb1 (tptp.tb2t1 @t58)) @t58)))) % 0.72/0.91 (assume @p47 (forall @t72 (=> @t71 (=> @t70 @t68)))) % 0.72/0.91 (assume @p48 (forall (@list @t75 @t74 @t73) (=> (tptp.path1 @t75 @t74 @t73) (or (exists @t54 (and (= @t75 @t53) (= @t74 @t53) (= @t73 0))) (exists @t72 (and @t71 @t70 (= @t75 @t67) (= @t74 @t66) (= @t73 @t65))))))) % 0.72/0.91 (assume @p49 (forall @t77 (=> @t71 @t76))) % 0.72/0.91 (assume @p50 (forall (@list @t67 @t66 @t64) (=> @t76 (=> @t68 (exists (@list @t69) (and @t71 @t70)))))) % 0.72/0.91 (assume @p51 (forall (@list @t78) (=> (forall @t62 (=> (tptp.mem tptp.vertex @t61 @t79) (forall @t83 (=> @t82 (tptp.mem tptp.vertex @t81 @t79))))) (forall @t77 (=> @t71 (=> (tptp.mem tptp.vertex (tptp.t2tb1 @t67) @t79) (tptp.mem tptp.vertex (tptp.t2tb1 @t69) @t79))))))) % 0.72/0.91 (assume @p52 (forall @t77 (= (tptp.shortest_path1 @t67 @t69 @t64) (and @t71 (forall @t85 (=> (< @t84 @t64) (not (tptp.path1 @t67 @t69 @t84)))))))) % 0.72/0.91 (assume @p53 (forall @t40 (tptp.sort1 @t86 (tptp.mk_ref @t1 @t17)))) % 0.72/0.91 (assume @p54 (forall @t40 (tptp.sort1 @t1 (tptp.contents @t1 @t17)))) % 0.72/0.91 (assume @p55 (forall @t88 (=> (tptp.sort1 @t1 @t87) (= (tptp.contents @t1 (tptp.mk_ref @t1 @t87)) @t87)))) % 0.72/0.91 (assume @p56 (forall @t88 (=> (tptp.sort1 @t86 @t87) (= @t87 (tptp.mk_ref @t1 (tptp.contents @t1 @t87)))))) % 0.72/0.91 (assume @p57 (forall (@list @t102 @t91 @t95 @t93 @t89 @t100) (= @t106 (and (tptp.subset tptp.vertex @t94 @t96) (forall @t62 (=> @t105 (tptp.shortest_path1 @t102 @t60 @t100))) (tptp.subset tptp.vertex @t90 @t96) (forall @t62 (=> @t99 @t103)) (forall (@list @t60 @t84) (=> @t104 (=> (<= @t84 @t100) @t97))) (forall @t62 (=> @t97 (exists @t85 (and @t104 (<= @t84 @t101))))) (forall @t62 (=> @t103 (or @t99 @t98))) (=> (tptp.mem tptp.vertex @t92 @t96) (or (tptp.mem tptp.vertex @t92 @t94) (tptp.mem tptp.vertex @t92 @t90))))))) % 0.72/0.91 (assume @p58 @t117) % 0.72/0.91 (assume @p59 @t190) % 0.72/0.91 (assume @p60 true) % 0.72/0.91 (step @p61 :rule refl :args (@t192)) % 0.72/0.91 (step @p62 :rule refl :args (@t193)) % 0.72/0.91 (step @p63 :rule refl :args (@t197)) % 0.72/0.91 (step @p64 :rule refl :args (@t201)) % 0.72/0.91 (step @p65 :rule refl :args (@t202)) % 0.72/0.91 (step @p66 :rule refl :args (@t203)) % 0.72/0.91 (step @p67 :rule refl :args (@t204)) % 0.72/0.91 (step @p68 :rule refl :args (@t205)) % 0.72/0.91 (step @p69 :rule eq-symm :args (@t198 @t60)) % 0.72/0.91 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t206)) % 0.72/0.91 (step @p71 :rule cong :premises (@p70) :args (@t207)) % 0.72/0.91 (step @p72 :rule cong :premises (@p71) :args (@t208)) % 0.72/0.91 (step @p73 :rule refl :args (@t209)) % 0.72/0.91 (step @p74 :rule refl :args (@t210)) % 0.72/0.91 (step @p75 :rule eq-symm :args (@t198 @t91)) % 0.72/0.91 (step @p76 :rule refl :args (@t211)) % 0.72/0.91 (step @p77 :rule refl :args (@t173)) % 0.72/0.91 (step @p78 :rule refl :args (@t213)) % 0.72/0.91 (step @p79 :rule refl :args (@t214)) % 0.72/0.91 (step @p80 :rule refl :args (@t215)) % 0.72/0.91 (step @p81 :rule refl :args (@t216)) % 0.72/0.91 (step @p82 :rule nary_cong :premises (@p81 @p80 @p79 @p78 @p77 @p76 @p75 @p74 @p73 @p72 @p67 @p66 @p65 @p64 @p63 @p62 @p61) :args (@t218)) % 0.72/0.91 (step @p83 :rule aci_norm :args ((= @t221 @t218))) % 0.72/0.91 (step @p84 :rule trans :premises (@p83 @p82)) % 0.72/0.91 (step @p85 :rule cong :premises (@p84) :args (@t223)) % 0.72/0.91 (step @p86 :rule quant-merge-prenex :args ((= (forall @t188 @t224) @t223))) % 0.72/0.91 (step @p87 :rule alpha_equiv :args (@t225 (@list @t191) (@list @t176))) % 0.72/0.91 (step @p88 :rule alpha_equiv :args (@t226 (@list @t198 @t195 @t196 @t194) (@list @t53 @t229 @t228 @t227))) % 0.72/0.91 (step @p89 :rule refl :args (@t173)) % 0.72/0.91 (step @p90 :rule refl :args (@t213)) % 0.72/0.91 (step @p91 :rule refl :args (@t214)) % 0.72/0.91 (step @p92 :rule refl :args (@t215)) % 0.72/0.91 (step @p93 :rule refl :args (@t216)) % 0.72/0.91 (step @p94 :rule nary_cong :premises (@p93 @p92 @p91 @p90 @p89 @p88 @p87) :args (@t230)) % 0.72/0.91 (step @p95 :rule quant-miniscope-or :args ((= @t224 @t230))) % 0.72/0.91 (step @p96 :rule trans :premises (@p95 @p94)) % 0.72/0.91 (step @p97 :rule symm :premises (@p96)) % 0.72/0.91 (step @p98 :rule cong :premises (@p97) :args ((forall @t188 @t248))) % 0.72/0.91 (step @p99 :rule trans :premises (@p98 @p86)) % 0.72/0.91 (step @p100 :rule trans :premises (@p99 @p85)) % 0.72/0.91 (step @p101 :rule aci_norm :args ((= (or (or @t216 @t215 @t214 @t213) @t249) @t248))) % 0.72/0.91 (step @p102 :rule refl :args (@t249)) % 0.72/0.91 (step @p103 :rule bool-implies-de-morgan :args (@t173 @t184)) % 0.72/0.91 (step @p104 :rule nary_cong :premises (@p93 @p103 @p91 @p90) :args (@t251)) % 0.72/0.91 (step @p105 :rule aci_norm :args ((= (or @t216 (or @t250 (or @t214 @t213))) @t251))) % 0.72/0.91 (step @p106 :rule bool-and-de-morgan :args (@t183 @t212 true)) % 0.72/0.91 (step @p107 :rule refl :args (@t250)) % 0.72/0.91 (step @p108 :rule nary_cong :premises (@p107 @p106) :args ((or @t250 (not (and @t183 @t212))))) % 0.72/0.91 (step @p109 :rule bool-and-de-morgan :args (@t185 @t183 (and @t212))) % 0.72/0.91 (step @p110 :rule trans :premises (@p109 @p108)) % 0.72/0.91 (step @p111 :rule nary_cong :premises (@p93 @p110) :args ((or @t216 (not (and @t185 @t183 @t212))))) % 0.72/0.91 (step @p112 :rule bool-and-de-morgan :args (@t106 @t185 (and @t183 @t212))) % 0.72/0.91 (step @p113 :rule trans :premises (@p112 @p111)) % 0.72/0.91 (step @p114 :rule trans :premises (@p113 @p105)) % 0.72/0.91 (step @p115 :rule trans :premises (@p114 @p104)) % 0.72/0.91 (step @p116 :rule nary_cong :premises (@p115 @p102) :args ((or (not @t252) @t249))) % 0.72/0.91 (step @p117 :rule trans :premises (@p116 @p101)) % 0.72/0.91 (step @p118 :rule bool-impl-elim :args (@t252 @t249)) % 0.72/0.91 (step @p119 :rule trans :premises (@p118 @p117)) % 0.72/0.91 (step @p120 :rule cong :premises (@p119) :args ((forall @t188 (=> @t252 @t249)))) % 0.72/0.91 (step @p121 :rule trans :premises (@p120 @p100)) % 0.72/0.91 (step @p122 :rule quant-miniscope-or :args ((= (forall @t181 @t253) @t249))) % 0.72/0.91 (step @p123 :rule aci_norm :args ((= @t254 @t253))) % 0.72/0.91 (step @p124 :rule cong :premises (@p123) :args ((forall @t181 @t254))) % 0.72/0.91 (step @p125 :rule trans :premises (@p124 @p122)) % 0.72/0.91 (step @p126 :rule aci_norm :args ((= (or @t232 @t255) @t254))) % 0.72/0.91 (step @p127 :rule aci_norm :args ((= (or @t231 (or @t173 @t247)) @t255))) % 0.72/0.91 (step @p128 :rule refl :args (@t247)) % 0.72/0.91 (step @p129 :rule bool-double-not-elim :args (@t173)) % 0.72/0.91 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((or (not @t174) @t247))) % 0.72/0.91 (step @p131 :rule bool-impl-elim :args (@t174 @t247)) % 0.72/0.91 (step @p132 :rule trans :premises (@p131 @p130)) % 0.72/0.91 (step @p133 :rule refl :args (@t231)) % 0.72/0.91 (step @p134 :rule nary_cong :premises (@p133 @p132) :args ((or @t231 @t256))) % 0.72/0.91 (step @p135 :rule trans :premises (@p134 @p127)) % 0.72/0.91 (step @p136 :rule refl :args (@t256)) % 0.72/0.91 (step @p137 :rule bool-double-not-elim :args (@t231)) % 0.72/0.91 (step @p138 :rule nary_cong :premises (@p137 @p136) :args ((or (not @t257) @t256))) % 0.72/0.91 (step @p139 :rule bool-impl-elim :args (@t257 @t256)) % 0.72/0.91 (step @p140 :rule trans :premises (@p139 @p138)) % 0.72/0.91 (step @p141 :rule trans :premises (@p140 @p135)) % 0.72/0.91 (step @p142 :rule bool-not-eq-elim1 :args (@t173 @t231)) % 0.72/0.91 (step @p143 :rule nary_cong :premises (@p142 @p141) :args ((or (not @t259) @t258))) % 0.72/0.91 (step @p144 :rule trans 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0.72/0.91 (step @p436 :rule cong :premises (@p435 @p433) :args (@t156)) % 0.72/0.91 (step @p437 :rule cong :premises (@p436) :args (@t157)) % 0.72/0.91 (step @p438 :rule trans :premises (@p437 @p432)) % 0.72/0.91 (step @p439 :rule refl :args (@t158)) % 0.72/0.91 (step @p440 :rule refl :args (@t159)) % 0.72/0.91 (step @p441 :rule nary_cong :premises (@p440 @p439 @p438) :args (@t160)) % 0.72/0.91 (step @p442 :rule cong :premises (@p441 @p426) :args (@t161)) % 0.72/0.91 (step @p443 :rule refl :args (@t163)) % 0.72/0.91 (step @p444 :rule cong :premises (@p443 @p442) :args (@t164)) % 0.72/0.91 (step @p445 :rule refl :args (@t169)) % 0.72/0.91 (step @p446 :rule cong :premises (@p445 @p444) :args (@t170)) % 0.72/0.91 (step @p447 :rule cong :premises (@p446) :args (@t172)) % 0.72/0.91 (step @p448 :rule trans :premises (@p447 @p224)) % 0.72/0.91 (step @p449 :rule refl :args (@t174)) % 0.72/0.91 (step @p450 :rule cong :premises (@p449 @p448) :args (@t175)) % 0.72/0.91 (step @p451 :rule eq-symm 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@p500)) % 0.72/0.91 (step @p509 :rule eq_resolve :premises (@p15 @p508)) % 0.72/0.91 (step @p510 :rule and_elim :premises (@p509) :args (0)) % 0.72/0.91 (step @p511 :rule instantiate :premises (@p510) :args ((@list tptp.vertex @t396 @t427))) % 0.72/0.91 (step @p512 :rule bool-double-not-elim :args (@t397)) % 0.72/0.91 (step @p513 :rule nary_cong :premises (@p472 @p512) :args ((or @t401 (not @t398)))) % 0.72/0.91 (step @p514 :rule cnf_or_neg :args (@t401 10)) % 0.72/0.91 (step @p515 :rule eq_resolve :premises (@p514 @p513)) % 0.72/0.91 (step @p516 :rule reordering :premises (@p515) :args ((or @t397 @t401))) % 0.72/0.91 (step @p517 :rule chain_m_resolution :premises (@p516 @p470) :args (@t397 @t402 @t403)) % 0.72/0.91 (step @p518 :rule cnf_or_pos :args (@t430)) % 0.72/0.91 (step @p519 :rule reordering :premises (@p518) :args ((or @t398 @t429 (not @t430)))) % 0.72/0.91 (step @p520 :rule chain_m_resolution :premises (@p519 @p517 @p511) :args (@t429 (@list false false) (@list @t397 @t430))) % 0.72/0.91 (step @p521 :rule aci_norm :args ((= (or @t98 @t432) (or @t98 @t105 @t99 @t431)))) % 0.72/0.91 (step @p522 :rule aci_norm :args ((= (or @t105 (or @t99 @t431)) @t432))) % 0.72/0.91 (step @p523 :rule refl :args (@t431)) % 0.72/0.91 (step @p524 :rule bool-double-not-elim :args (@t99)) % 0.72/0.91 (step @p525 :rule nary_cong :premises (@p524 @p523) :args ((or (not @t109) @t431))) % 0.72/0.91 (step @p526 :rule bool-impl-elim :args (@t109 @t431)) % 0.72/0.91 (step @p527 :rule trans :premises (@p526 @p525)) % 0.72/0.91 (step @p528 :rule refl :args (@t105)) % 0.72/0.91 (step @p529 :rule nary_cong :premises (@p528 @p527) :args ((or @t105 @t433))) % 0.72/0.91 (step @p530 :rule trans :premises (@p529 @p522)) % 0.72/0.91 (step @p531 :rule refl :args (@t433)) % 0.72/0.91 (step @p532 :rule bool-double-not-elim :args (@t105)) % 0.72/0.91 (step @p533 :rule nary_cong :premises (@p532 @p531) :args ((or (not @t111) @t433))) % 0.72/0.91 (step @p534 :rule bool-impl-elim :args (@t111 @t433)) % 0.72/0.91 (step @p535 :rule trans :premises (@p534 @p533)) % 0.72/0.91 (step @p536 :rule trans :premises (@p535 @p530)) % 0.72/0.91 (step @p537 :rule refl :args (@t98)) % 0.72/0.91 (step @p538 :rule nary_cong :premises (@p537 @p536) :args ((or @t98 @t434))) % 0.72/0.91 (step @p539 :rule trans :premises (@p538 @p521)) % 0.72/0.91 (step @p540 :rule bool-impl-elim :args (@t97 @t434)) % 0.72/0.91 (step @p541 :rule trans :premises (@p540 @p539)) % 0.72/0.91 (step @p542 :rule refl :args (@t114)) % 0.72/0.91 (step @p543 :rule cong :premises (@p542 @p541) :args (@t435)) % 0.72/0.91 (step @p544 :rule cong :premises (@p543) :args ((forall @t116 @t435))) % 0.72/0.91 (step @p545 :rule bool-impl-elim :args (@t82 @t107)) % 0.72/0.91 (step @p546 :rule cong :premises (@p545) :args (@t108)) % 0.72/0.91 (step @p547 :rule refl :args (@t109)) % 0.72/0.91 (step @p548 :rule cong :premises (@p547 @p546) :args (@t110)) % 0.72/0.91 (step @p549 :rule refl :args (@t111)) % 0.72/0.91 (step @p550 :rule cong :premises (@p549 @p548) :args (@t112)) % 0.72/0.91 (step @p551 :rule refl :args (@t97)) % 0.72/0.91 (step @p552 :rule cong :premises (@p551 @p550) :args (@t113)) % 0.72/0.91 (step @p553 :rule refl :args (@t114)) % 0.72/0.91 (step @p554 :rule cong :premises (@p553 @p552) :args (@t115)) % 0.72/0.91 (step @p555 :rule cong :premises (@p554) :args (@t117)) % 0.72/0.91 (step @p556 :rule trans :premises (@p555 @p544)) % 0.72/0.91 (step @p557 :rule eq_resolve :premises (@p58 @p556)) % 0.72/0.91 (step @p558 :rule instantiate :premises (@p557) :args ((@list @t385 @t379 @t127 @t389))) % 0.72/0.91 (step @p559 :rule cnf_or_neg :args (@t401 14)) % 0.72/0.91 (step @p560 :rule chain_m_resolution :premises (@p559 @p470) :args ((not @t390) @t402 @t403)) % 0.72/0.91 (step @p561 :rule cnf_equiv_pos2 :args (@t441)) % 0.72/0.91 (step @p562 :rule reordering :premises (@p561) :args ((or @t390 @t442 (not @t441)))) % 0.72/0.91 (step @p563 :rule chain_m_resolution :premises (@p562 @p560 @p558) :args (@t442 (@list true false) (@list @t390 @t441))) % 0.72/0.91 (step @p564 :rule cnf_or_neg :args (@t440 3)) % 0.72/0.91 (step @p565 :rule chain_m_resolution :premises (@p564 @p563) :args ((not @t436) @t402 @t443)) % 0.72/0.91 (step @p566 :rule cnf_or_neg :args (@t440 1)) % 0.72/0.91 (step @p567 :rule chain_m_resolution :premises (@p566 @p563) :args ((not @t437) @t402 @t443)) % 0.72/0.91 (step @p568 :rule bool-double-not-elim :args (@t438)) % 0.72/0.91 (step @p569 :rule refl :args (@t440)) % 0.72/0.91 (step @p570 :rule nary_cong :premises (@p569 @p568) :args ((or @t440 (not @t439)))) % 0.72/0.91 (step @p571 :rule cnf_or_neg :args (@t440 0)) % 0.72/0.91 (step @p572 :rule eq_resolve :premises (@p571 @p570)) % 0.72/0.91 (step @p573 :rule reordering :premises (@p572) :args ((or @t438 @t440))) % 0.72/0.91 (step @p574 :rule chain_m_resolution :premises (@p573 @p563) :args (@t438 @t402 @t443)) % 0.72/0.91 (step @p575 :rule cnf_or_pos :args (@t444)) % 0.72/0.91 (step @p576 :rule reordering :premises (@p575) :args ((or @t439 @t437 @t436 @t428 @t445))) % 0.72/0.91 (step @p577 :rule chain_m_resolution :premises (@p576 @p574 @p567 @p565 @p520) :args (@t445 (@list false true true true) (@list @t438 @t437 @t436 @t428))) % 0.72/0.91 (step @p578 :rule instantiate :premises (@p557) :args ((@list @t385 @t384 @t379 @t389))) % 0.72/0.91 (step @p579 :rule cnf_equiv_pos1 :args (@t447)) % 0.72/0.91 (step @p580 :rule reordering :premises (@p579) :args ((or (not @t446) @t444 (not @t447)))) % 0.72/0.91 (step @p581 false :rule chain_m_resolution :premises (@p580 @p578 @p577 @p478) :args (false (@list false true false) (@list @t447 @t444 @t446))) % 0.72/0.91 ) % 0.72/0.91 % SZS output end Proof % 0.72/0.91 % cvc5 exiting %------------------------------------------------------------------------------