%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM860_1 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n012.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 08:40:52 AM UTC 2026 % Result : Theorem 142.01s 142.39s % Output : Proof 105.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM860_1 : TPTP v9.2.1. Released v4.1.0. % 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.06/0.25 % Computer : n012.cluster.edu % 0.06/0.25 % Model : x86_64 x86_64 % 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.25 % Memory : 8042.1875MB % 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.25 % CPULimit : 300 % 0.06/0.25 % WCLimit : 300 % 0.06/0.25 % DateTime : Tue Jun 2 12:30:18 EDT 2026 % 0.06/0.25 % CPUTime : % 0.06/0.32 %----Proving TF0_ARI % 142.01/142.39 --- Run --finite-model-find --decision=internal at 45... % 142.01/142.39 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 142.01/142.39 --- Run --no-e-matching --full-saturate-quant at 45... % 142.01/142.39 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 45... % 142.01/142.39 % SZS status Theorem % 142.01/142.39 % SZS output start Proof % 142.01/142.39 ( % 142.01/142.39 (declare-const tptp.minsol_model_ub (-> Int Int Int Bool)) % 142.01/142.39 (declare-const tptp.minsol_model_max (-> Int Int Int Bool)) % 142.01/142.39 (declare-const tptp.model_ub (-> Int Int Int Bool)) % 142.01/142.39 (declare-const tptp.model_max (-> Int Int Int Bool)) % 142.01/142.39 (declare-const tptp.ub (-> Int Int Int Bool)) % 142.01/142.39 (declare-const tptp.max (-> Int Int Int)) % 142.01/142.39 (declare-const tptp.summation (-> Int Int)) % 142.01/142.39 (define @t1 () (@var "Y" Int)) % 142.01/142.39 (define @t2 () (tptp.summation @t1)) % 142.01/142.39 (define @t3 () (@var "X" Int)) % 142.01/142.39 (define @t4 () (tptp.summation @t3)) % 142.01/142.39 (define @t5 () (<= @t3 @t1)) % 142.01/142.39 (define @t6 () (= @t5 (<= @t4 @t2))) % 142.01/142.39 (define @t7 () (@list @t3 @t1)) % 142.01/142.39 (define @t8 () (forall @t7 @t6)) % 142.01/142.39 (define @t9 () (not (<= @t1 @t3))) % 142.01/142.39 (define @t10 () (tptp.max @t3 @t1)) % 142.01/142.39 (define @t11 () (= @t10 @t3)) % 142.01/142.39 (define @t12 () (or @t11 @t9)) % 142.01/142.39 (define @t13 () (forall @t7 @t12)) % 142.01/142.39 (define @t14 () (not @t5)) % 142.01/142.39 (define @t15 () (= @t10 @t1)) % 142.01/142.39 (define @t16 () (or @t15 @t14)) % 142.01/142.39 (define @t17 () (forall @t7 @t16)) % 142.01/142.39 (define @t18 () (@var "Z" Int)) % 142.01/142.39 (define @t19 () (and (<= @t3 @t18) (<= @t1 @t18))) % 142.01/142.39 (define @t20 () (tptp.ub @t3 @t1 @t18)) % 142.01/142.39 (define @t21 () (= @t20 @t19)) % 142.01/142.39 (define @t22 () (@list @t3 @t1 @t18)) % 142.01/142.39 (define @t23 () (forall @t22 @t21)) % 142.01/142.39 (define @t24 () (@var "N" Int)) % 142.01/142.39 (define @t25 () (tptp.summation @t10)) % 142.01/142.39 (define @t26 () (tptp.model_max @t3 @t1 @t24)) % 142.01/142.39 (define @t27 () (= @t26 (<= @t25 @t24))) % 142.01/142.39 (define @t28 () (@list @t3 @t1 @t24)) % 142.01/142.39 (define @t29 () (forall @t28 @t27)) % 142.01/142.39 (define @t30 () (tptp.summation @t18)) % 142.01/142.39 (define @t31 () (and @t20 (<= @t30 @t24))) % 142.01/142.39 (define @t32 () (@list @t18)) % 142.01/142.39 (define @t33 () (exists @t32 @t31)) % 142.01/142.39 (define @t34 () (tptp.model_ub @t3 @t1 @t24)) % 142.01/142.39 (define @t35 () (= @t34 @t33)) % 142.01/142.39 (define @t36 () (forall @t28 @t35)) % 142.01/142.39 (define @t37 () (<= @t24 @t18)) % 142.01/142.39 (define @t38 () (tptp.model_max @t3 @t1 @t18)) % 142.01/142.39 (define @t39 () (=> @t38 @t37)) % 142.01/142.39 (define @t40 () (forall @t32 @t39)) % 142.01/142.39 (define @t41 () (and @t26 @t40)) % 142.01/142.39 (define @t42 () (tptp.minsol_model_max @t3 @t1 @t24)) % 142.01/142.39 (define @t43 () (= @t42 @t41)) % 142.01/142.39 (define @t44 () (forall @t28 @t43)) % 142.01/142.39 (define @t45 () (tptp.model_ub @t3 @t1 @t18)) % 142.01/142.39 (define @t46 () (=> @t45 @t37)) % 142.01/142.39 (define @t47 () (forall @t32 @t46)) % 142.01/142.39 (define @t48 () (and @t34 @t47)) % 142.01/142.39 (define @t49 () (tptp.minsol_model_ub @t3 @t1 @t24)) % 142.01/142.39 (define @t50 () (= @t49 @t48)) % 142.01/142.39 (define @t51 () (forall @t28 @t50)) % 142.01/142.39 (define @t52 () (forall @t22 (= (tptp.minsol_model_ub @t3 @t1 @t18) (tptp.minsol_model_max @t3 @t1 @t18)))) % 142.01/142.39 (define @t53 () (* -1 @t18)) % 142.01/142.39 (define @t54 () (+ @t1 @t53)) % 142.01/142.39 (define @t55 () (+ @t18 1)) % 142.01/142.39 (define @t56 () (>= @t1 @t55)) % 142.01/142.39 (define @t57 () (+ @t3 @t53)) % 142.01/142.39 (define @t58 () (>= @t3 @t55)) % 142.01/142.39 (define @t59 () (* -1 @t30)) % 142.01/142.39 (define @t60 () (@quantifiers_skolemize @t52 2)) % 142.01/142.39 (define @t61 () (+ @t60 @t59)) % 142.01/142.39 (define @t62 () (>= @t61 1)) % 142.01/142.39 (define @t63 () (@quantifiers_skolemize @t52 1)) % 142.01/142.39 (define @t64 () (@quantifiers_skolemize @t52 0)) % 142.01/142.39 (define @t65 () (not (tptp.ub @t64 @t63 @t18))) % 142.01/142.39 (define @t66 () (forall @t32 (or @t65 (not @t62)))) % 142.01/142.39 (define @t67 () (@quantifiers_skolemize @t66 0)) % 142.01/142.39 (define @t68 () (+ @t24 @t59)) % 142.01/142.39 (define @t69 () (>= @t68 0)) % 142.01/142.39 (define @t70 () (and @t20 @t69)) % 142.01/142.39 (define @t71 () (forall @t32 (not @t70))) % 142.01/142.39 (define @t72 () (not @t71)) % 142.01/142.39 (define @t73 () (* -1 @t60)) % 142.01/142.39 (define @t74 () (>= (+ @t18 @t73) 0)) % 142.01/142.39 (define @t75 () (forall @t32 (or (not (tptp.model_ub @t64 @t63 @t18)) @t74))) % 142.01/142.39 (define @t76 () (@quantifiers_skolemize @t75 0)) % 142.01/142.39 (define @t77 () (@list @t64 @t63 @t60)) % 142.01/142.39 (define @t78 () (tptp.max @t64 @t63)) % 142.01/142.39 (define @t79 () (* -1 @t78)) % 142.01/142.39 (define @t80 () (+ @t64 @t79)) % 142.01/142.39 (define @t81 () (* 1 (- @t80 0))) % 142.01/142.39 (define @t82 () (* 1 (- @t64 @t78))) % 142.01/142.39 (define @t83 () (>= @t80 0)) % 142.01/142.39 (define @t84 () (>= @t64 @t78)) % 142.01/142.39 (define @t85 () (+ @t78 1)) % 142.01/142.39 (define @t86 () (>= @t80 1)) % 142.01/142.39 (define @t87 () (>= @t64 @t85)) % 142.01/142.39 (define @t88 () (<= @t64 @t78)) % 142.01/142.39 (define @t89 () (not @t84)) % 142.01/142.39 (define @t90 () (not @t88)) % 142.01/142.39 (define @t91 () (not true)) % 142.01/142.39 (define @t92 () (>= 0 0)) % 142.01/142.39 (define @t93 () (+ @t79 @t78)) % 142.01/142.39 (define @t94 () (= @t93 0)) % 142.01/142.39 (define @t95 () (+ (* -1 @t64) @t64)) % 142.01/142.39 (define @t96 () (>= @t95 @t93)) % 142.01/142.39 (define @t97 () (< -1 0)) % 142.01/142.39 (define @t98 () (= @t64 @t78)) % 142.01/142.39 (define @t99 () (<= 0 -1)) % 142.01/142.39 (define @t100 () (+ -1 0)) % 142.01/142.39 (define @t101 () (* -1 1)) % 142.01/142.39 (define @t102 () (+ @t101 0)) % 142.01/142.39 (define @t103 () (+ 0 0)) % 142.01/142.39 (define @t104 () (* 0 @t64)) % 142.01/142.39 (define @t105 () (= @t104 0)) % 142.01/142.39 (define @t106 () (* 0 @t78)) % 142.01/142.39 (define @t107 () (= @t106 0)) % 142.01/142.39 (define @t108 () (+ @t106 @t104)) % 142.01/142.39 (define @t109 () (* -1 @t80)) % 142.01/142.39 (define @t110 () (+ @t109 @t80)) % 142.01/142.39 (define @t111 () (= @t81 @t82)) % 142.01/142.39 (define @t112 () (= @t80 0)) % 142.01/142.39 (define @t113 () (= @t112 @t98)) % 142.01/142.39 (define @t114 () (not @t86)) % 142.01/142.39 (define @t115 () (+ @t3 (* -1 @t1))) % 142.01/142.39 (define @t116 () (@list @t64 @t63)) % 142.01/142.39 (define @t117 () (* -1 @t63)) % 142.01/142.39 (define @t118 () (+ @t64 @t117)) % 142.01/142.39 (define @t119 () (>= @t118 0)) % 142.01/142.39 (define @t120 () (not @t119)) % 142.01/142.39 (define @t121 () (or @t98 @t120)) % 142.01/142.39 (define @t122 () (>= @t118 1)) % 142.01/142.39 (define @t123 () (< @t118 0)) % 142.01/142.39 (define @t124 () (+ 0 @t101)) % 142.01/142.39 (define @t125 () (* 0 @t63)) % 142.01/142.39 (define @t126 () (= @t125 0)) % 142.01/142.39 (define @t127 () (+ @t125 @t104)) % 142.01/142.39 (define @t128 () (* -1 @t118)) % 142.01/142.39 (define @t129 () (+ @t118 @t128)) % 142.01/142.39 (define @t130 () (>= @t129 @t124)) % 142.01/142.39 (define @t131 () (not @t122)) % 142.01/142.39 (define @t132 () (not @t83)) % 142.01/142.39 (define @t133 () (= @t63 @t78)) % 142.01/142.39 (define @t134 () (not @t133)) % 142.01/142.39 (define @t135 () (* -1 0)) % 142.01/142.39 (define @t136 () (+ @t135 0 -1)) % 142.01/142.39 (define @t137 () (+ @t106 @t117 @t63 @t104)) % 142.01/142.39 (define @t138 () (+ @t63 @t79)) % 142.01/142.39 (define @t139 () (+ @t109 @t138 @t118)) % 142.01/142.39 (define @t140 () (* 1 (- @t63 @t78))) % 142.01/142.39 (define @t141 () (* 1 (- @t138 0))) % 142.01/142.39 (define @t142 () (= @t141 @t140)) % 142.01/142.39 (define @t143 () (= @t138 0)) % 142.01/142.39 (define @t144 () (= @t143 @t133)) % 142.01/142.39 (define @t145 () (>= @t115 1)) % 142.01/142.39 (define @t146 () (+ @t1 1)) % 142.01/142.39 (define @t147 () (>= @t3 @t146)) % 142.01/142.39 (define @t148 () (or @t133 @t122)) % 142.01/142.39 (define @t149 () (>= @t138 1)) % 142.01/142.39 (define @t150 () (not @t149)) % 142.01/142.39 (define @t151 () (and @t114 @t150)) % 142.01/142.39 (define @t152 () (not @t114)) % 142.01/142.39 (define @t153 () (+ @t106 @t125)) % 142.01/142.39 (define @t154 () (* -1 @t138)) % 142.01/142.39 (define @t155 () (+ @t154 @t138)) % 142.01/142.39 (define @t156 () (and @t149 @t133)) % 142.01/142.39 (define @t157 () (>= @t138 0)) % 142.01/142.39 (define @t158 () (>= @t63 @t78)) % 142.01/142.39 (define @t159 () (>= @t63 @t85)) % 142.01/142.39 (define @t160 () (<= @t63 @t78)) % 142.01/142.39 (define @t161 () (not @t158)) % 142.01/142.39 (define @t162 () (not @t160)) % 142.01/142.39 (define @t163 () (+ @t117 @t63)) % 142.01/142.39 (define @t164 () (>= @t163 @t93)) % 142.01/142.39 (define @t165 () (not @t157)) % 142.01/142.39 (define @t166 () (< @t80 1)) % 142.01/142.39 (define @t167 () (+ 1 @t101 @t135)) % 142.01/142.39 (define @t168 () (+ @t106 @t63 @t117 @t104)) % 142.01/142.39 (define @t169 () (+ @t80 @t128 @t154)) % 142.01/142.39 (define @t170 () (>= @t169 @t167)) % 142.01/142.39 (define @t171 () (and @t157 @t122 @t114)) % 142.01/142.39 (define @t172 () (@list true)) % 142.01/142.39 (define @t173 () (tptp.ub @t64 @t63 @t78)) % 142.01/142.39 (define @t174 () (= @t173 @t151)) % 142.01/142.39 (define @t175 () (@list false false)) % 142.01/142.39 (define @t176 () (+ @t24 (* -1 @t25))) % 142.01/142.39 (define @t177 () (>= @t176 0)) % 142.01/142.39 (define @t178 () (+ @t18 (* -1 @t24))) % 142.01/142.39 (define @t179 () (>= @t178 0)) % 142.01/142.39 (define @t180 () (tptp.minsol_model_max @t64 @t63 @t60)) % 142.01/142.39 (define @t181 () (tptp.minsol_model_ub @t64 @t63 @t60)) % 142.01/142.39 (define @t182 () (= @t181 @t180)) % 142.01/142.39 (define @t183 () (tptp.model_ub @t64 @t63 @t60)) % 142.01/142.39 (define @t184 () (and @t183 @t75)) % 142.01/142.39 (define @t185 () (= @t181 @t184)) % 142.01/142.39 (define @t186 () (not @t185)) % 142.01/142.39 (define @t187 () (not @t181)) % 142.01/142.39 (define @t188 () (forall @t32 (or (not (tptp.model_max @t64 @t63 @t18)) @t74))) % 142.01/142.39 (define @t189 () (tptp.model_max @t64 @t63 @t60)) % 142.01/142.39 (define @t190 () (and @t189 @t188)) % 142.01/142.39 (define @t191 () (= @t180 @t190)) % 142.01/142.39 (define @t192 () (not @t191)) % 142.01/142.39 (define @t193 () (not @t190)) % 142.01/142.39 (define @t194 () (not @t184)) % 142.01/142.39 (define @t195 () (forall @t32 (or @t65 (not (>= @t61 0))))) % 142.01/142.39 (define @t196 () (not @t195)) % 142.01/142.39 (define @t197 () (= @t183 @t196)) % 142.01/142.39 (define @t198 () (not @t197)) % 142.01/142.39 (define @t199 () (+ -1 @t60)) % 142.01/142.39 (define @t200 () (tptp.model_ub @t64 @t63 @t199)) % 142.01/142.39 (define @t201 () (not @t200)) % 142.01/142.39 (define @t202 () (+ @t73 @t60 -1)) % 142.01/142.39 (define @t203 () (+ @t199 @t73)) % 142.01/142.39 (define @t204 () (>= @t203 0)) % 142.01/142.39 (define @t205 () (or @t201 @t204)) % 142.01/142.39 (define @t206 () (@list @t199)) % 142.01/142.39 (define @t207 () (@quantifiers_skolemize @t195 0)) % 142.01/142.39 (define @t208 () (tptp.summation @t207)) % 142.01/142.39 (define @t209 () (* -1 @t208)) % 142.01/142.39 (define @t210 () (+ @t60 @t209)) % 142.01/142.39 (define @t211 () (>= @t210 0)) % 142.01/142.39 (define @t212 () (not @t211)) % 142.01/142.39 (define @t213 () (tptp.ub @t64 @t63 @t207)) % 142.01/142.39 (define @t214 () (not @t213)) % 142.01/142.39 (define @t215 () (or @t214 @t212)) % 142.01/142.39 (define @t216 () (not @t215)) % 142.01/142.39 (define @t217 () (not @t196)) % 142.01/142.39 (define @t218 () (+ -1 @t60 @t59)) % 142.01/142.39 (define @t219 () (+ @t60 @t59 -1)) % 142.01/142.39 (define @t220 () (+ @t199 @t59)) % 142.01/142.39 (define @t221 () (>= @t220 0)) % 142.01/142.39 (define @t222 () (not @t221)) % 142.01/142.39 (define @t223 () (or @t65 @t222)) % 142.01/142.39 (define @t224 () (forall @t32 @t223)) % 142.01/142.39 (define @t225 () (not @t224)) % 142.01/142.39 (define @t226 () (= @t200 @t225)) % 142.01/142.39 (define @t227 () (forall @t28 (= @t34 (not (forall @t32 (or (not @t20) (not @t69))))))) % 142.01/142.39 (define @t228 () (@list @t64 @t63 @t199)) % 142.01/142.39 (define @t229 () (not @t66)) % 142.01/142.39 (define @t230 () (= @t200 @t229)) % 142.01/142.39 (define @t231 () (@list false)) % 142.01/142.39 (define @t232 () (not @t230)) % 142.01/142.39 (define @t233 () (not @t229)) % 142.01/142.39 (define @t234 () (@list @t78)) % 142.01/142.39 (define @t235 () (tptp.summation @t78)) % 142.01/142.39 (define @t236 () (* -1 @t235)) % 142.01/142.39 (define @t237 () (+ @t60 @t236)) % 142.01/142.39 (define @t238 () (>= @t237 1)) % 142.01/142.39 (define @t239 () (not @t238)) % 142.01/142.39 (define @t240 () (not @t173)) % 142.01/142.39 (define @t241 () (or @t240 @t239)) % 142.01/142.39 (define @t242 () (* -1 @t207)) % 142.01/142.39 (define @t243 () (+ @t63 @t242)) % 142.01/142.39 (define @t244 () (>= @t243 1)) % 142.01/142.39 (define @t245 () (not @t244)) % 142.01/142.39 (define @t246 () (+ @t64 @t242)) % 142.01/142.39 (define @t247 () (>= @t246 1)) % 142.01/142.39 (define @t248 () (not @t247)) % 142.01/142.39 (define @t249 () (and @t248 @t245)) % 142.01/142.39 (define @t250 () (= @t213 @t249)) % 142.01/142.39 (define @t251 () (not @t249)) % 142.01/142.39 (define @t252 () (+ @t207 @t79)) % 142.01/142.39 (define @t253 () (>= @t252 0)) % 142.01/142.39 (define @t254 () (not @t253)) % 142.01/142.39 (define @t255 () (not @t254)) % 142.01/142.39 (define @t256 () (+ @t135 1 -1)) % 142.01/142.39 (define @t257 () (= (+ @t242 0 @t207 0) 0)) % 142.01/142.39 (define @t258 () (+ @t242 @t106 @t207 @t125)) % 142.01/142.39 (define @t259 () (+ @t154 @t243 @t252)) % 142.01/142.39 (define @t260 () (>= @t259 @t256)) % 142.01/142.39 (define @t261 () (and @t254 @t245 @t133)) % 142.01/142.39 (define @t262 () (not @t98)) % 142.01/142.39 (define @t263 () (+ 0 1)) % 142.01/142.39 (define @t264 () (>= @t246 @t263)) % 142.01/142.39 (define @t265 () (<= @t246 0)) % 142.01/142.39 (define @t266 () (+ 0 0 0)) % 142.01/142.39 (define @t267 () (+ 0 0 @t135)) % 142.01/142.39 (define @t268 () (+ @t242 @t106 @t207 @t104)) % 142.01/142.39 (define @t269 () (+ @t246 @t252 @t109)) % 142.01/142.39 (define @t270 () (>= @t269 @t267)) % 142.01/142.39 (define @t271 () (and @t98 @t254 @t248)) % 142.01/142.39 (define @t272 () (+ @t4 (* -1 @t2))) % 142.01/142.39 (define @t273 () (+ @t2 1)) % 142.01/142.39 (define @t274 () (>= @t272 1)) % 142.01/142.39 (define @t275 () (>= @t4 @t273)) % 142.01/142.39 (define @t276 () (+ @t235 @t209)) % 142.01/142.39 (define @t277 () (>= @t276 1)) % 142.01/142.39 (define @t278 () (not @t277)) % 142.01/142.39 (define @t279 () (+ @t242 @t78)) % 142.01/142.39 (define @t280 () (+ @t252 1)) % 142.01/142.39 (define @t281 () (+ @t78 @t242)) % 142.01/142.39 (define @t282 () (>= @t281 1)) % 142.01/142.39 (define @t283 () (not @t282)) % 142.01/142.39 (define @t284 () (= @t283 @t278)) % 142.01/142.39 (define @t285 () (forall @t7 (= (not @t145) (not @t274)))) % 142.01/142.39 (define @t286 () (= @t278 @t253)) % 142.01/142.39 (define @t287 () (@list @t285)) % 142.01/142.39 (define @t288 () (>= @t237 0)) % 142.01/142.39 (define @t289 () (not @t288)) % 142.01/142.39 (define @t290 () (+ 1 0 -1)) % 142.01/142.39 (define @t291 () (+ 1 @t135 -1)) % 142.01/142.39 (define @t292 () (= (+ 0 @t236 @t235 0) 0)) % 142.01/142.39 (define @t293 () (* 0 @t60)) % 142.01/142.39 (define @t294 () (= @t293 0)) % 142.01/142.39 (define @t295 () (* 0 @t208)) % 142.01/142.39 (define @t296 () (+ @t295 @t236 @t235 @t293)) % 142.01/142.39 (define @t297 () (+ @t276 (* -1 @t210) @t237)) % 142.01/142.39 (define @t298 () (>= @t297 @t291)) % 142.01/142.39 (define @t299 () (= @t189 @t288)) % 142.01/142.39 (define @t300 () (not @t299)) % 142.01/142.39 (define @t301 () (@quantifiers_skolemize @t188 0)) % 142.01/142.39 (define @t302 () (* -1 @t301)) % 142.01/142.39 (define @t303 () (+ @t60 @t302)) % 142.01/142.39 (define @t304 () (>= @t303 1)) % 142.01/142.39 (define @t305 () (not @t304)) % 142.01/142.39 (define @t306 () (tptp.model_max @t64 @t63 @t301)) % 142.01/142.39 (define @t307 () (not @t306)) % 142.01/142.39 (define @t308 () (or @t307 @t305)) % 142.01/142.39 (define @t309 () (not @t308)) % 142.01/142.39 (define @t310 () (not @t188)) % 142.01/142.39 (define @t311 () (+ @t73 @t301)) % 142.01/142.39 (define @t312 () (+ @t303 1)) % 142.01/142.39 (define @t313 () (+ @t301 @t73)) % 142.01/142.39 (define @t314 () (>= @t313 0)) % 142.01/142.39 (define @t315 () (or @t307 @t314)) % 142.01/142.39 (define @t316 () (not @t315)) % 142.01/142.39 (define @t317 () (+ @t301 @t236)) % 142.01/142.39 (define @t318 () (>= @t317 0)) % 142.01/142.39 (define @t319 () (= @t306 @t318)) % 142.01/142.39 (define @t320 () (not @t318)) % 142.01/142.39 (define @t321 () (not @t239)) % 142.01/142.39 (define @t322 () (+ 1 @t135 @t101)) % 142.01/142.39 (define @t323 () (* 0 @t235)) % 142.01/142.39 (define @t324 () (+ @t301 @t302 @t323 @t293)) % 142.01/142.39 (define @t325 () (+ @t237 (* -1 @t317) (* -1 @t303))) % 142.01/142.39 (define @t326 () (>= @t325 @t322)) % 142.01/142.39 (define @t327 () (@list true true)) % 142.01/142.39 (define @t328 () (@list @t190)) % 142.01/142.39 (define @t329 () (or @t240 @t289)) % 142.01/142.39 (define @t330 () (not @t329)) % 142.01/142.39 (define @t331 () (@list true false)) % 142.01/142.39 (define @t332 () (not @t75)) % 142.01/142.39 (define @t333 () (* -1 @t76)) % 142.01/142.39 (define @t334 () (+ @t60 @t333)) % 142.01/142.39 (define @t335 () (>= @t334 1)) % 142.01/142.39 (define @t336 () (not @t335)) % 142.01/142.39 (define @t337 () (tptp.model_ub @t64 @t63 @t76)) % 142.01/142.39 (define @t338 () (not @t337)) % 142.01/142.39 (define @t339 () (or @t338 @t336)) % 142.01/142.39 (define @t340 () (not @t339)) % 142.01/142.39 (define @t341 () (+ @t73 @t76)) % 142.01/142.39 (define @t342 () (+ @t334 1)) % 142.01/142.39 (define @t343 () (+ @t76 @t73)) % 142.01/142.39 (define @t344 () (>= @t343 0)) % 142.01/142.39 (define @t345 () (or @t338 @t344)) % 142.01/142.39 (define @t346 () (not @t345)) % 142.01/142.39 (define @t347 () (@list @t339)) % 142.01/142.39 (define @t348 () (forall @t32 (or @t65 (not (>= (+ @t76 @t59) 0))))) % 142.01/142.39 (define @t349 () (not @t348)) % 142.01/142.39 (define @t350 () (= @t337 @t349)) % 142.01/142.39 (define @t351 () (@quantifiers_skolemize @t348 0)) % 142.01/142.39 (define @t352 () (tptp.summation @t351)) % 142.01/142.39 (define @t353 () (* -1 @t352)) % 142.01/142.39 (define @t354 () (+ @t76 @t353)) % 142.01/142.39 (define @t355 () (>= @t354 0)) % 142.01/142.39 (define @t356 () (not @t355)) % 142.01/142.39 (define @t357 () (tptp.ub @t64 @t63 @t351)) % 142.01/142.39 (define @t358 () (not @t357)) % 142.01/142.39 (define @t359 () (or @t358 @t356)) % 142.01/142.39 (define @t360 () (not @t359)) % 142.01/142.39 (define @t361 () (@list @t359)) % 142.01/142.39 (define @t362 () (+ @t60 @t353)) % 142.01/142.39 (define @t363 () (>= @t362 1)) % 142.01/142.39 (define @t364 () (not @t363)) % 142.01/142.39 (define @t365 () (* 0 @t352)) % 142.01/142.39 (define @t366 () (+ @t365 @t76 @t333 @t293)) % 142.01/142.39 (define @t367 () (+ @t362 (* -1 @t354) (* -1 @t334))) % 142.01/142.39 (define @t368 () (>= @t367 @t322)) % 142.01/142.39 (define @t369 () (or @t358 @t364)) % 142.01/142.39 (define @t370 () (not @t369)) % 142.01/142.39 (define @t371 () (tptp.summation @t67)) % 142.01/142.39 (define @t372 () (* -1 @t371)) % 142.01/142.39 (define @t373 () (+ @t60 @t372)) % 142.01/142.39 (define @t374 () (>= @t373 1)) % 142.01/142.39 (define @t375 () (not @t374)) % 142.01/142.39 (define @t376 () (tptp.ub @t64 @t63 @t67)) % 142.01/142.39 (define @t377 () (not @t376)) % 142.01/142.39 (define @t378 () (or @t377 @t375)) % 142.01/142.39 (define @t379 () (not @t378)) % 142.01/142.39 (define @t380 () (@list @t378)) % 142.01/142.39 (define @t381 () (* -1 @t67)) % 142.01/142.39 (define @t382 () (+ @t63 @t381)) % 142.01/142.39 (define @t383 () (>= @t382 1)) % 142.01/142.39 (define @t384 () (not @t383)) % 142.01/142.39 (define @t385 () (+ @t64 @t381)) % 142.01/142.39 (define @t386 () (>= @t385 1)) % 142.01/142.39 (define @t387 () (not @t386)) % 142.01/142.39 (define @t388 () (and @t387 @t384)) % 142.01/142.39 (define @t389 () (= @t376 @t388)) % 142.01/142.39 (define @t390 () (not @t388)) % 142.01/142.39 (define @t391 () (@list @t388)) % 142.01/142.39 (define @t392 () (+ @t235 @t372)) % 142.01/142.39 (define @t393 () (>= @t392 1)) % 142.01/142.39 (define @t394 () (not @t393)) % 142.01/142.39 (define @t395 () (+ @t67 @t79)) % 142.01/142.39 (define @t396 () (>= @t395 0)) % 142.01/142.39 (define @t397 () (+ @t381 @t78)) % 142.01/142.39 (define @t398 () (+ @t395 1)) % 142.01/142.39 (define @t399 () (+ @t78 @t381)) % 142.01/142.39 (define @t400 () (>= @t399 1)) % 142.01/142.39 (define @t401 () (not @t400)) % 142.01/142.39 (define @t402 () (= @t401 @t394)) % 142.01/142.39 (define @t403 () (= @t396 @t394)) % 142.01/142.39 (define @t404 () (tptp.model_max @t64 @t63 @t199)) % 142.01/142.39 (define @t405 () (+ -1 @t60 @t236)) % 142.01/142.39 (define @t406 () (+ @t236 @t60 -1)) % 142.01/142.39 (define @t407 () (+ @t199 @t236)) % 142.01/142.39 (define @t408 () (>= @t407 0)) % 142.01/142.39 (define @t409 () (= @t404 @t408)) % 142.01/142.39 (define @t410 () (forall @t28 (= @t26 @t177))) % 142.01/142.39 (define @t411 () (= @t238 @t404)) % 142.01/142.39 (define @t412 () (not @t404)) % 142.01/142.39 (define @t413 () (or @t412 @t204)) % 142.01/142.39 (define @t414 () (+ @t101 0 1)) % 142.01/142.39 (define @t415 () (* 0 @t371)) % 142.01/142.39 (define @t416 () (+ @t415 @t236 @t235 @t293)) % 142.01/142.39 (define @t417 () (+ (* -1 @t373) @t237 @t392)) % 142.01/142.39 (define @t418 () (>= @t417 @t414)) % 142.01/142.39 (define @t419 () (and @t394 @t239 @t374)) % 142.01/142.39 (define @t420 () (not @t396)) % 142.01/142.39 (define @t421 () (not @t420)) % 142.01/142.39 (define @t422 () (+ 0 @t135 0)) % 142.01/142.39 (define @t423 () (= (+ @t381 @t67 0 0) 0)) % 142.01/142.39 (define @t424 () (+ @t381 @t67 @t106 @t125)) % 142.01/142.39 (define @t425 () (+ @t395 @t154 @t382)) % 142.01/142.39 (define @t426 () (>= @t425 @t422)) % 142.01/142.39 (define @t427 () (>= @t385 @t263)) % 142.01/142.39 (define @t428 () (<= @t385 0)) % 142.01/142.39 (define @t429 () (+ @t381 @t67 @t106 @t104)) % 142.01/142.39 (define @t430 () (+ @t385 @t395 @t109)) % 142.01/142.39 (define @t431 () (>= @t430 @t267)) % 142.01/142.39 (define @t432 () (and @t98 @t420 @t387)) % 142.01/142.39 (assume @p1 @t8) % 142.01/142.39 (assume @p2 @t13) % 142.01/142.39 (assume @p3 @t17) % 142.01/142.39 (assume @p4 @t23) % 142.01/142.39 (assume @p5 @t29) % 142.01/142.39 (assume @p6 @t36) % 142.01/142.39 (assume @p7 @t44) % 142.01/142.39 (assume @p8 @t51) % 142.01/142.39 (assume @p9 (not @t52)) % 142.01/142.39 (assume @p10 true) % 142.01/142.39 (step @p11 :rule arith_poly_norm :args ((= (* -1 (- @t1 @t55)) (* -1 (- @t54 1))))) % 142.01/142.39 (step @p12 :rule arith_poly_norm_rel :premises (@p11) :args ((= @t56 (>= @t54 1)))) % 142.01/142.39 (step @p13 :rule cong :premises (@p12) :args ((not @t56))) % 142.01/142.39 (step @p14 :rule arith-leq-norm :args (@t1 @t18)) % 142.01/142.39 (step @p15 :rule trans :premises (@p14 @p13)) % 142.01/142.39 (step @p16 :rule arith_poly_norm :args ((= (* -1 (- @t3 @t55)) (* -1 (- @t57 1))))) % 142.01/142.39 (step @p17 :rule arith_poly_norm_rel :premises (@p16) :args ((= @t58 (>= @t57 1)))) % 142.01/142.39 (step @p18 :rule cong :premises (@p17) :args ((not @t58))) % 142.01/142.39 (step @p19 :rule arith-leq-norm :args (@t3 @t18)) % 142.01/142.39 (step @p20 :rule trans :premises (@p19 @p18)) % 142.01/142.39 (step @p21 :rule nary_cong :premises (@p20 @p15) :args (@t19)) % 142.01/142.39 (step @p22 :rule refl :args (@t20)) % 142.01/142.39 (step @p23 :rule cong :premises (@p22 @p21) :args (@t21)) % 142.01/142.39 (step @p24 :rule cong :premises (@p23) :args (@t23)) % 142.01/142.39 (step @p25 :rule eq_resolve :premises (@p4 @p24)) % 142.01/142.39 (step @p26 :rule instantiate :premises (@p25) :args ((@list @t64 @t63 @t67))) % 142.01/142.39 (step @p27 :rule bool-and-de-morgan :args (@t20 @t69 true)) % 142.01/142.39 (step @p28 :rule cong :premises (@p27) :args (@t71)) % 142.01/142.39 (step @p29 :rule cong :premises (@p28) :args (@t72)) % 142.01/142.39 (step @p30 :rule exists-elim :args ((= (exists @t32 @t70) @t72))) % 142.01/142.39 (step @p31 :rule trans :premises (@p30 @p29)) % 142.01/142.39 (step @p32 :rule arith_poly_norm :args ((= (* 1 (- @t24 @t30)) (* 1 (- @t68 0))))) % 142.01/142.39 (step @p33 :rule arith_poly_norm_rel :premises (@p32) :args ((= (>= @t24 @t30) @t69))) % 142.01/142.39 (step @p34 :rule arith-elim-leq :args (@t30 @t24)) % 142.01/142.39 (step @p35 :rule trans :premises (@p34 @p33)) % 142.01/142.39 (step @p36 :rule nary_cong :premises (@p22 @p35) :args (@t31)) % 142.01/142.39 (step @p37 :rule cong :premises (@p36) :args (@t33)) % 142.01/142.39 (step @p38 :rule trans :premises (@p37 @p31)) % 142.01/142.39 (step @p39 :rule refl :args (@t34)) % 142.01/142.39 (step @p40 :rule cong :premises (@p39 @p38) :args (@t35)) % 142.01/142.39 (step @p41 :rule cong :premises (@p40) :args (@t36)) % 142.01/142.39 (step @p42 :rule eq_resolve :premises (@p6 @p41)) % 142.01/142.39 (step @p43 :rule instantiate :premises (@p42) :args ((@list @t64 @t63 @t76))) % 142.01/142.39 (step @p44 :rule instantiate :premises (@p42) :args (@t77)) % 142.01/142.39 (step @p45 :rule instantiate :premises (@p25) :args ((@list @t64 @t63 @t78))) % 142.01/142.39 (step @p46 :rule arith_poly_norm :args ((= @t82 @t81))) % 142.01/142.39 (step @p47 :rule arith_poly_norm_rel :premises (@p46) :args ((= @t84 @t83))) % 142.01/142.39 (step @p48 :rule arith_poly_norm :args ((= (* -1 (- @t64 @t85)) (* -1 (- @t80 1))))) % 142.01/142.39 (step @p49 :rule arith_poly_norm_rel :premises (@p48) :args ((= @t87 @t86))) % 142.01/142.39 (step @p50 :rule cong :premises (@p49) :args ((not @t87))) % 142.01/142.39 (step @p51 :rule arith-leq-norm :args (@t64 @t78)) % 142.01/142.39 (step @p52 :rule trans :premises (@p51 @p50)) % 142.01/142.39 (step @p53 :rule nary_cong :premises (@p52 @p47) :args ((or @t88 @t84))) % 142.01/142.39 (step @p54 :rule symm :premises (@p53)) % 142.01/142.39 (step @p55 :rule bool-double-not-elim :args (@t84)) % 142.01/142.39 (step @p56 :rule trans :premises (@p55 @p47)) % 142.01/142.39 (step @p57 :rule bool-double-not-elim :args (@t88)) % 142.01/142.39 (step @p58 :rule trans :premises (@p57 @p52)) % 142.01/142.39 (step @p59 :rule nary_cong :premises (@p58 @p56) :args ((or (not @t90) (not @t89)))) % 142.01/142.39 (step @p60 :rule trans :premises (@p59 @p54)) % 142.01/142.39 (assume-push @p1217 @t90) % 142.01/142.39 (assume-push @p1218 @t89) % 142.01/142.39 (step @p63 :rule evaluate :args (@t91)) % 142.01/142.39 (step @p64 :rule evaluate :args (@t92)) % 142.01/142.39 (step @p65 :rule arith_poly_norm :args (@t94)) % 142.01/142.39 (step @p66 :rule arith_poly_norm :args ((= @t95 0))) % 142.01/142.39 (step @p67 :rule cong :premises (@p66 @p65) :args (@t96)) % 142.01/142.39 (step @p68 :rule trans :premises (@p67 @p64)) % 142.01/142.39 (step @p69 :rule cong :premises (@p68) :args ((not @t96))) % 142.01/142.39 (step @p70 :rule trans :premises (@p69 @p63)) % 142.01/142.39 (step @p71 :rule arith-elim-lt :args (@t95 @t93)) % 142.01/142.39 (step @p72 :rule trans :premises (@p71 @p70)) % 142.01/142.39 (step @p73 :rule cong :premises (@p47) :args (@t89)) % 142.01/142.39 (step @p74 :rule arith-elim-lt :args (@t64 @t78)) % 142.01/142.39 (step @p75 :rule trans :premises (@p74 @p73)) % 142.01/142.39 (step @p76 :rule symm :premises (@p75)) % 142.01/142.39 (step @p77 :rule trans :premises (@p73 @p76)) % 142.01/142.39 (step @p78 :rule eq_resolve :premises (@p1218 @p77)) % 142.01/142.39 (step @p79 :rule arith_mult_neg :args (-1 (> @t64 @t78))) % 142.01/142.39 (step @p80 :rule bool-double-not-elim :args (@t86)) % 142.01/142.39 (step @p81 :rule cong :premises (@p52) :args (@t90)) % 142.01/142.39 (step @p82 :rule trans :premises (@p81 @p80)) % 142.01/142.39 (step @p83 :rule arith-elim-leq :args (@t64 @t78)) % 142.01/142.39 (step @p84 :rule symm :premises (@p83)) % 142.01/142.39 (step @p85 :rule cong :premises (@p84) :args ((not (>= @t78 @t64)))) % 142.01/142.39 (step @p86 :rule arith-elim-gt :args (@t64 @t78)) % 142.01/142.39 (step @p87 :rule trans :premises (@p86 @p85)) % 142.01/142.39 (step @p88 :rule trans :premises (@p87 @p82)) % 142.01/142.39 (step @p89 :rule symm :premises (@p88)) % 142.01/142.39 (step @p90 :rule trans :premises (@p82 @p89)) % 142.01/142.39 (step @p91 :rule eq_resolve :premises (@p1217 @p90)) % 142.01/142.39 (step @p92 :rule evaluate :args (@t97)) % 142.01/142.39 (step @p93 :rule true_elim :premises (@p92)) % 142.01/142.39 (step @p94 :rule and_intro :premises (@p93 @p91)) % 142.01/142.39 (step @p95 :rule modus_ponens :premises (@p94 @p79)) % 142.01/142.39 (step @p96 :rule arith_sum_ub :premises (@p95 @p78)) % 142.01/142.39 (step @p97 false :rule eq_resolve :premises (@p96 @p72)) % 142.01/142.39 (step-pop @p1219 :rule scope :premises (@p97)) % 142.01/142.39 (step-pop @p1220 :rule scope :premises (@p1219)) % 142.01/142.39 (step @p98 :rule process_scope :premises (@p1220) :args (false)) % 142.01/142.39 (step @p101 :rule not_and :premises (@p98)) % 142.01/142.39 (step @p102 :rule eq_resolve :premises (@p101 @p60)) % 142.01/142.39 (step @p103 :rule eq_resolve :premises (@p102 @p53)) % 142.01/142.39 (assume-push @p1221 @t98) % 142.01/142.39 (assume-push @p1222 @t98) % 142.01/142.39 (step @p106 :rule arith-elim-lt :args (@t80 1)) % 142.01/142.39 (step @p107 :rule symm :premises (@p106)) % 142.01/142.39 (assume-push @p1223 @t86) % 142.01/142.39 (step @p109 :rule evaluate :args (@t99)) % 142.01/142.39 (step @p110 :rule evaluate :args (@t100)) % 142.01/142.39 (step @p111 :rule refl :args (0)) % 142.01/142.39 (step @p112 :rule evaluate :args (@t101)) % 142.01/142.39 (step @p113 :rule nary_cong :premises (@p112 @p111) :args (@t102)) 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(@t92)) % 142.01/142.39 (step @p612 :rule evaluate :args (@t266)) % 142.01/142.39 (step @p201 :rule evaluate :args (@t135)) % 142.01/142.39 (step @p613 :rule nary_cong :premises (@p111 @p111 @p201) :args (@t267)) % 142.01/142.39 (step @p614 :rule trans :premises (@p613 @p612)) % 142.01/142.39 (step @p1119 :rule arith_poly_norm :args (@t423)) % 142.01/142.39 (step @p116 :rule arith_poly_norm :args (@t105)) % 142.01/142.39 (step @p117 :rule arith_poly_norm :args (@t107)) % 142.01/142.39 (step @p1120 :rule refl :args (@t67)) % 142.01/142.39 (step @p1121 :rule refl :args (@t381)) % 142.01/142.39 (step @p1175 :rule nary_cong :premises (@p1121 @p1120 @p117 @p116) :args (@t429)) % 142.01/142.39 (step @p1176 :rule trans :premises (@p1175 @p1119)) % 142.01/142.39 (step @p1177 :rule arith_poly_norm :args ((= @t430 @t429))) % 142.01/142.39 (step @p1178 :rule trans :premises (@p1177 @p1176)) % 142.01/142.39 (step @p1179 :rule cong :premises (@p1178 @p614) :args (@t431)) % 142.01/142.39 (step @p1180 :rule trans :premises (@p1179 @p64)) % 142.01/142.39 (step @p1181 :rule cong :premises (@p1180) :args ((not @t431))) % 142.01/142.39 (step @p1182 :rule trans :premises (@p1181 @p63)) % 142.01/142.39 (step @p1183 :rule arith-elim-lt :args (@t430 @t267)) % 142.01/142.39 (step @p1184 :rule trans :premises (@p1183 @p1182)) % 142.01/142.39 (step @p625 :rule arith_mult_neg :args (-1 @t112)) % 142.01/142.39 (step @p124 :rule arith_poly_norm :args (@t111)) % 142.01/142.39 (step @p125 :rule arith_poly_norm_rel :premises (@p124) :args (@t113)) % 142.01/142.39 (step @p126 :rule symm :premises (@p125)) % 142.01/142.39 (step @p1185 :rule eq_resolve :premises (@p1361 @p126)) % 142.01/142.39 (step @p92 :rule evaluate :args (@t97)) % 142.01/142.39 (step @p93 :rule true_elim :premises (@p92)) % 142.01/142.39 (step @p1186 :rule and_intro :premises (@p93 @p1185)) % 142.01/142.39 (step @p1187 :rule modus_ponens :premises (@p1186 @p625)) % 142.01/142.39 (step @p1139 :rule arith-elim-lt :args (@t395 0)) % 142.01/142.39 (step @p1140 :rule symm :premises (@p1139)) % 142.01/142.39 (step @p1188 :rule eq_resolve :premises (@p1362 @p1140)) % 142.01/142.39 (step @p1189 :rule arith_sum_ub :premises (@p1364 @p1188 @p1187)) % 142.01/142.39 (step @p1190 false :rule eq_resolve :premises (@p1189 @p1184)) % 142.01/142.39 (step-pop @p1365 :rule scope :premises (@p1190)) % 142.01/142.39 (step @p1191 :rule process_scope :premises (@p1365) :args (false)) % 142.01/142.39 (step @p1193 :rule eq_resolve :premises (@p1191 @p1173)) % 142.01/142.39 (step @p1194 :rule eq_resolve :premises (@p1193 @p1163)) % 142.01/142.39 (step @p1195 :rule arith-elim-lt :args (@t385 1)) % 105.79/142.40 (step @p1196 :rule symm :premises (@p1195)) % 105.79/142.40 (step @p1197 :rule eq_resolve :premises (@p1363 @p1196)) % 105.79/142.40 (step @p1198 :rule int_tight_ub :premises (@p1197)) % 105.79/142.40 (step @p1199 false :rule contra :premises (@p1198 @p1194)) % 105.79/142.40 (step-pop @p1366 :rule scope :premises (@p1199)) % 105.79/142.40 (step-pop @p1367 :rule scope :premises (@p1366)) % 105.79/142.40 (step-pop @p1368 :rule scope :premises (@p1367)) % 105.79/142.40 (step @p1200 :rule process_scope :premises (@p1368) :args (false)) % 105.79/142.40 (assume-push @p1369 @t98) % 105.79/142.40 (assume-push @p1370 @t387) % 105.79/142.40 (assume-push @p1371 @t420) % 105.79/142.40 (step @p1207 :rule and_intro :premises (@p1369 @p1371 @p1370)) % 105.79/142.40 (step-pop @p1372 :rule scope :premises (@p1207)) % 105.79/142.40 (step-pop @p1373 :rule scope :premises (@p1372)) % 105.79/142.40 (step-pop @p1374 :rule scope :premises (@p1373)) % 105.79/142.40 (step @p1208 :rule process_scope :premises (@p1374) :args (@t432)) % 105.79/142.40 (step @p1212 :rule implies_elim :premises (@p1208)) % 105.79/142.40 (step @p1213 :rule resolution :premises (@p1212 @p1200) :args (true @t432)) % 105.79/142.40 (step @p1214 :rule not_and :premises (@p1213)) % 105.79/142.40 (step @p1215 :rule eq_resolve :premises (@p1214 @p1155)) % 105.79/142.40 (step @p1216 false :rule chain_m_resolution :premises (@p1215 @p1153 @p1108 @p984) :args (false (@list false true true) (@list @t98 @t396 @t386))) % 105.79/142.40 ) % 105.79/142.40 % SZS output end Proof % 105.79/142.40 % cvc5 exiting %------------------------------------------------------------------------------