%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN082+2 : TPTP v9.2.1. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n009.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 08:42:55 AM UTC 2026 % Result : Theorem 0.38s 0.62s % Output : Proof 0.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN082+2 : TPTP v9.2.1. Released v7.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n009.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 12:41:59 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.48 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.62 % SZS status Theorem % 0.38/0.62 % SZS output start Proof % 0.38/0.62 ( % 0.38/0.62 (declare-sort $$unsorted 0) % 0.38/0.62 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.r1 (-> $$unsorted Bool)) % 0.38/0.62 (define @t1 () (@var "Y24" $$unsorted)) % 0.38/0.62 (define @t2 () (@var "X19" $$unsorted)) % 0.38/0.62 (define @t3 () (= @t2 @t1)) % 0.38/0.62 (define @t4 () (tptp.r1 @t2)) % 0.38/0.62 (define @t5 () (and @t4 @t3)) % 0.38/0.62 (define @t6 () (not @t3)) % 0.38/0.62 (define @t7 () (not @t4)) % 0.38/0.62 (define @t8 () (and @t7 @t6)) % 0.38/0.62 (define @t9 () (or @t8 @t5)) % 0.38/0.62 (define @t10 () (@list @t2)) % 0.38/0.62 (define @t11 () (forall @t10 @t9)) % 0.38/0.62 (define @t12 () (@list @t1)) % 0.38/0.62 (define @t13 () (exists @t12 @t11)) % 0.38/0.62 (define @t14 () (@var "Y21" $$unsorted)) % 0.38/0.62 (define @t15 () (@var "X12" $$unsorted)) % 0.38/0.62 (define @t16 () (= @t15 @t14)) % 0.38/0.62 (define @t17 () (@var "X11" $$unsorted)) % 0.38/0.62 (define @t18 () (tptp.r2 @t17 @t15)) % 0.38/0.62 (define @t19 () (@var "Y22" $$unsorted)) % 0.38/0.62 (define @t20 () (@var "X15" $$unsorted)) % 0.38/0.62 (define @t21 () (= @t20 @t19)) % 0.38/0.62 (define @t22 () (@var "X14" $$unsorted)) % 0.38/0.62 (define @t23 () (@var "X13" $$unsorted)) % 0.38/0.62 (define @t24 () (tptp.r3 @t23 @t22 @t20)) % 0.38/0.62 (define @t25 () (and @t24 @t21)) % 0.38/0.62 (define @t26 () (not @t21)) % 0.38/0.62 (define @t27 () (not @t24)) % 0.38/0.62 (define @t28 () (and @t27 @t26)) % 0.38/0.62 (define @t29 () (or @t28 @t25)) % 0.38/0.62 (define @t30 () (@list @t20)) % 0.38/0.62 (define @t31 () (forall @t30 @t29)) % 0.38/0.62 (define @t32 () (@list @t19)) % 0.38/0.62 (define @t33 () (exists @t32 @t31)) % 0.38/0.62 (define @t34 () (forall (@list @t23 @t22) @t33)) % 0.38/0.62 (define @t35 () (@var "Y23" $$unsorted)) % 0.38/0.62 (define @t36 () (@var "X18" $$unsorted)) % 0.38/0.62 (define @t37 () (= @t36 @t35)) % 0.38/0.62 (define @t38 () (@var "X17" $$unsorted)) % 0.38/0.62 (define @t39 () (@var "X16" $$unsorted)) % 0.38/0.62 (define @t40 () (tptp.r4 @t39 @t38 @t36)) % 0.38/0.62 (define @t41 () (and @t40 @t37)) % 0.38/0.62 (define @t42 () (not @t37)) % 0.38/0.62 (define @t43 () (not @t40)) % 0.38/0.62 (define @t44 () (and @t43 @t42)) % 0.38/0.62 (define @t45 () (or @t44 @t41)) % 0.38/0.62 (define @t46 () (@list @t36)) % 0.38/0.62 (define @t47 () (forall @t46 @t45)) % 0.38/0.62 (define @t48 () (@list @t35)) % 0.38/0.62 (define @t49 () (exists @t48 @t47)) % 0.38/0.62 (define @t50 () (forall (@list @t39 @t38) @t49)) % 0.38/0.62 (define @t51 () (@var "Y7" $$unsorted)) % 0.38/0.62 (define @t52 () (@var "X8" $$unsorted)) % 0.38/0.62 (define @t53 () (@var "X1" $$unsorted)) % 0.38/0.62 (define @t54 () (@var "Y4" $$unsorted)) % 0.38/0.62 (define @t55 () (@var "Y5" $$unsorted)) % 0.38/0.62 (define @t56 () (@var "Y15" $$unsorted)) % 0.38/0.62 (define @t57 () (@list @t55)) % 0.38/0.62 (define @t58 () (@list @t54)) % 0.38/0.62 (define @t59 () (@var "Y6" $$unsorted)) % 0.38/0.62 (define @t60 () (@var "X9" $$unsorted)) % 0.38/0.62 (define @t61 () (@var "X2" $$unsorted)) % 0.38/0.62 (define @t62 () (tptp.r4 @t61 @t60 @t59)) % 0.38/0.62 (define @t63 () (@var "Y2" $$unsorted)) % 0.38/0.62 (define @t64 () (tptp.r3 @t59 @t61 @t63)) % 0.38/0.62 (define @t65 () (and @t64 @t62)) % 0.38/0.62 (define @t66 () (@list @t59)) % 0.38/0.62 (define @t67 () (exists @t66 @t65)) % 0.38/0.62 (define @t68 () (@var "Y3" $$unsorted)) % 0.38/0.62 (define @t69 () (= @t68 @t63)) % 0.38/0.62 (define @t70 () (@var "Y14" $$unsorted)) % 0.38/0.62 (define @t71 () (tptp.r4 @t61 @t70 @t68)) % 0.38/0.62 (define @t72 () (tptp.r2 @t60 @t70)) % 0.38/0.62 (define @t73 () (and @t72 @t71)) % 0.38/0.62 (define @t74 () (@list @t70)) % 0.38/0.62 (define @t75 () (exists @t74 @t73)) % 0.38/0.62 (define @t76 () (and @t75 @t69)) % 0.38/0.62 (define @t77 () (@list @t68)) % 0.38/0.62 (define @t78 () (exists @t77 @t76)) % 0.38/0.62 (define @t79 () (and @t78 @t67)) % 0.38/0.62 (define @t80 () (@list @t63)) % 0.38/0.62 (define @t81 () (exists @t80 @t79)) % 0.38/0.62 (define @t82 () (forall (@list @t61 @t60) @t81)) % 0.38/0.62 (define @t83 () (@var "X10" $$unsorted)) % 0.38/0.62 (define @t84 () (@var "X3" $$unsorted)) % 0.38/0.62 (define @t85 () (@var "Y12" $$unsorted)) % 0.38/0.62 (define @t86 () (@var "Y13" $$unsorted)) % 0.38/0.62 (define @t87 () (@var "X4" $$unsorted)) % 0.38/0.62 (define @t88 () (@var "Y9" $$unsorted)) % 0.38/0.62 (define @t89 () (= @t88 @t87)) % 0.38/0.62 (define @t90 () (@var "Y16" $$unsorted)) % 0.38/0.62 (define @t91 () (tptp.r3 @t87 @t90 @t88)) % 0.38/0.62 (define @t92 () (tptp.r1 @t90)) % 0.38/0.62 (define @t93 () (and @t92 @t91)) % 0.38/0.62 (define @t94 () (@list @t90)) % 0.38/0.62 (define @t95 () (exists @t94 @t93)) % 0.38/0.62 (define @t96 () (and @t95 @t89)) % 0.38/0.62 (define @t97 () (@list @t88)) % 0.38/0.62 (define @t98 () (exists @t97 @t96)) % 0.38/0.62 (define @t99 () (forall (@list @t87) @t98)) % 0.38/0.62 (define @t100 () (@var "Y18" $$unsorted)) % 0.38/0.62 (define @t101 () (@var "Y8" $$unsorted)) % 0.38/0.62 (define @t102 () (= @t101 @t100)) % 0.38/0.62 (define @t103 () (tptp.r1 @t100)) % 0.38/0.62 (define @t104 () (and @t103 @t102)) % 0.38/0.62 (define @t105 () (@list @t100)) % 0.38/0.62 (define @t106 () (exists @t105 @t104)) % 0.38/0.62 (define @t107 () (@var "Y17" $$unsorted)) % 0.38/0.62 (define @t108 () (@var "X5" $$unsorted)) % 0.38/0.62 (define @t109 () (tptp.r4 @t108 @t107 @t101)) % 0.38/0.62 (define @t110 () (tptp.r1 @t107)) % 0.38/0.62 (define @t111 () (and @t110 @t109)) % 0.38/0.62 (define @t112 () (@list @t107)) % 0.38/0.62 (define @t113 () (exists @t112 @t111)) % 0.38/0.62 (define @t114 () (and @t113 @t106)) % 0.38/0.62 (define @t115 () (@list @t101)) % 0.38/0.62 (define @t116 () (exists @t115 @t114)) % 0.38/0.62 (define @t117 () (forall (@list @t108) @t116)) % 0.38/0.62 (define @t118 () (@var "Y11" $$unsorted)) % 0.38/0.62 (define @t119 () (@var "X6" $$unsorted)) % 0.38/0.62 (define @t120 () (@var "Y1" $$unsorted)) % 0.38/0.62 (define @t121 () (@var "Y19" $$unsorted)) % 0.38/0.62 (define @t122 () (@var "Y10" $$unsorted)) % 0.38/0.62 (define @t123 () (@var "X7" $$unsorted)) % 0.38/0.62 (define @t124 () (@var "Y20" $$unsorted)) % 0.38/0.62 (define @t125 () (tptp.r1 @t55)) % 0.38/0.62 (define @t126 () (and @t125 (= @t63 @t55))) % 0.38/0.62 (define @t127 () (exists @t57 @t126)) % 0.38/0.62 (define @t128 () (tptp.r2 @t54 @t68)) % 0.38/0.62 (define @t129 () (tptp.r1 @t54)) % 0.38/0.62 (define @t130 () (and @t129 @t128)) % 0.38/0.62 (define @t131 () (exists @t58 @t130)) % 0.38/0.62 (define @t132 () (tptp.r4 @t120 @t68 @t63)) % 0.38/0.62 (define @t133 () (and @t132 @t131)) % 0.38/0.62 (define @t134 () (exists @t77 @t133)) % 0.38/0.62 (define @t135 () (and @t134 @t127)) % 0.38/0.62 (define @t136 () (@list @t120 @t63)) % 0.38/0.62 (define @t137 () (exists @t136 @t135)) % 0.38/0.62 (define @t138 () (not @t137)) % 0.38/0.62 (define @t139 () (@var "BOUND_VARIABLE_7637" $$unsorted)) % 0.38/0.62 (define @t140 () (tptp.r1 @t139)) % 0.38/0.62 (define @t141 () (not @t140)) % 0.38/0.62 (define @t142 () (@list @t139)) % 0.38/0.62 (define @t143 () (forall @t142 (or @t141 (and @t140 (= @t1 @t139))))) % 0.38/0.62 (define @t144 () (tptp.r1 @t1)) % 0.38/0.62 (define @t145 () (and @t143 @t144)) % 0.38/0.62 (define @t146 () (forall @t12 (not @t145))) % 0.38/0.62 (define @t147 () (not @t146)) % 0.38/0.62 (define @t148 () (= @t1 @t1)) % 0.38/0.62 (define @t149 () (and @t144 @t148)) % 0.38/0.62 (define @t150 () (not @t148)) % 0.38/0.62 (define @t151 () (or @t150 @t149)) % 0.38/0.62 (define @t152 () (@var "BOUND_VARIABLE_7646" $$unsorted)) % 0.38/0.62 (define @t153 () (= @t1 @t152)) % 0.38/0.62 (define @t154 () (and (tptp.r1 @t152) @t153)) % 0.38/0.62 (define @t155 () (not @t153)) % 0.38/0.62 (define @t156 () (@list @t152)) % 0.38/0.62 (define @t157 () (or @t155 @t155 @t154)) % 0.38/0.62 (define @t158 () (or @t155 @t154)) % 0.38/0.62 (define @t159 () (forall @t156 @t158)) % 0.38/0.62 (define @t160 () (= @t1 @t2)) % 0.38/0.62 (define @t161 () (and @t4 @t160)) % 0.38/0.62 (define @t162 () (not @t160)) % 0.38/0.62 (define @t163 () (or @t162 @t161)) % 0.38/0.62 (define @t164 () (forall @t10 @t163)) % 0.38/0.62 (define @t165 () (@list @t2)) % 0.38/0.62 (define @t166 () (or @t7 @t161)) % 0.38/0.62 (define @t167 () (forall @t10 @t166)) % 0.38/0.62 (define @t168 () (and @t167 @t164)) % 0.38/0.62 (define @t169 () (forall @t12 (or (not @t143) (not @t144)))) % 0.38/0.62 (define @t170 () (@quantifiers_skolemize @t169 0)) % 0.38/0.62 (define @t171 () (tptp.r1 @t170)) % 0.38/0.62 (define @t172 () (not @t171)) % 0.38/0.62 (define @t173 () (forall @t142 (or @t141 (and @t140 (= @t139 @t170))))) % 0.38/0.62 (define @t174 () (not @t173)) % 0.38/0.62 (define @t175 () (or @t174 @t172)) % 0.38/0.62 (define @t176 () (not @t175)) % 0.38/0.62 (define @t177 () (not @t169)) % 0.38/0.62 (define @t178 () (and @t140 (= @t170 @t139))) % 0.38/0.62 (define @t179 () (or @t141 @t178)) % 0.38/0.62 (define @t180 () (forall @t142 @t179)) % 0.38/0.62 (define @t181 () (not @t180)) % 0.38/0.62 (define @t182 () (or @t181 @t172)) % 0.38/0.62 (define @t183 () (not @t182)) % 0.38/0.62 (define @t184 () (@list true)) % 0.38/0.62 (define @t185 () (@list @t175)) % 0.38/0.62 (define @t186 () (@var "BOUND_VARIABLE_7732" $$unsorted)) % 0.38/0.62 (define @t187 () (= @t19 @t186)) % 0.38/0.62 (define @t188 () (tptp.r3 @t23 @t22 @t186)) % 0.38/0.62 (define @t189 () (@list @t186)) % 0.38/0.62 (define @t190 () (forall @t189 (or (not @t188) (and @t188 @t187)))) % 0.38/0.62 (define @t191 () (tptp.r3 @t23 @t22 @t19)) % 0.38/0.62 (define @t192 () (and @t190 @t191)) % 0.38/0.62 (define @t193 () (forall @t32 (not @t192))) % 0.38/0.62 (define @t194 () (not @t193)) % 0.38/0.62 (define @t195 () (= @t19 @t19)) % 0.38/0.62 (define @t196 () (and @t191 @t195)) % 0.38/0.62 (define @t197 () (not @t195)) % 0.38/0.62 (define @t198 () (or @t197 @t196)) % 0.38/0.62 (define @t199 () (@var "BOUND_VARIABLE_7741" $$unsorted)) % 0.38/0.62 (define @t200 () (= @t19 @t199)) % 0.38/0.62 (define @t201 () (and (tptp.r3 @t23 @t22 @t199) @t200)) % 0.38/0.62 (define @t202 () (not @t200)) % 0.38/0.62 (define @t203 () (@list @t199)) % 0.38/0.62 (define @t204 () (or @t202 @t202 @t201)) % 0.38/0.62 (define @t205 () (or @t202 @t201)) % 0.38/0.62 (define @t206 () (forall @t203 @t205)) % 0.38/0.62 (define @t207 () (= @t19 @t20)) % 0.38/0.62 (define @t208 () (and @t24 @t207)) % 0.38/0.62 (define @t209 () (not @t207)) % 0.38/0.62 (define @t210 () (or @t209 @t208)) % 0.38/0.62 (define @t211 () (forall @t30 @t210)) % 0.38/0.62 (define @t212 () (@list @t20)) % 0.38/0.62 (define @t213 () (or @t27 @t208)) % 0.38/0.62 (define @t214 () (forall @t30 @t213)) % 0.38/0.62 (define @t215 () (and @t214 @t211)) % 0.38/0.62 (define @t216 () (@list @t170 @t170)) % 0.38/0.62 (define @t217 () (tptp.r3 @t170 @t170 @t186)) % 0.38/0.62 (define @t218 () (not @t217)) % 0.38/0.62 (define @t219 () (forall @t32 (or (not (forall @t189 (or @t218 (and @t217 @t187)))) (not (tptp.r3 @t170 @t170 @t19))))) % 0.38/0.62 (define @t220 () (@quantifiers_skolemize @t219 0)) % 0.38/0.62 (define @t221 () (not (tptp.r3 @t170 @t170 @t220))) % 0.38/0.62 (define @t222 () (forall @t189 (or @t218 (and @t217 (= @t186 @t220))))) % 0.38/0.62 (define @t223 () (not @t222)) % 0.38/0.62 (define @t224 () (or @t223 @t221)) % 0.38/0.62 (define @t225 () (not @t224)) % 0.38/0.62 (define @t226 () (not @t219)) % 0.38/0.62 (define @t227 () (and @t217 (= @t220 @t186))) % 0.38/0.62 (define @t228 () (or @t218 @t227)) % 0.38/0.62 (define @t229 () (forall @t189 @t228)) % 0.38/0.62 (define @t230 () (not @t229)) % 0.38/0.62 (define @t231 () (or @t230 @t221)) % 0.38/0.62 (define @t232 () (not @t231)) % 0.38/0.62 (define @t233 () (@list @t170)) % 0.38/0.62 (define @t234 () (@var "BOUND_VARIABLE_8016" $$unsorted)) % 0.38/0.62 (define @t235 () (not (tptp.r3 @t87 @t234 @t87))) % 0.38/0.62 (define @t236 () (not (tptp.r1 @t234))) % 0.38/0.62 (define @t237 () (not (= @t87 @t87))) % 0.38/0.62 (define @t238 () (or @t237 @t236 @t235)) % 0.38/0.62 (define @t239 () (@list @t234)) % 0.38/0.62 (define @t240 () (not (tptp.r3 @t87 @t234 @t88))) % 0.38/0.62 (define @t241 () (= @t87 @t88)) % 0.38/0.62 (define @t242 () (not @t241)) % 0.38/0.62 (define @t243 () (or @t242 @t242 @t236 @t240)) % 0.38/0.62 (define @t244 () (or @t242 @t236 @t240)) % 0.38/0.62 (define @t245 () (forall @t97 @t244)) % 0.38/0.62 (define @t246 () (forall @t239 @t245)) % 0.38/0.62 (define @t247 () (forall (@list @t234 @t88) @t244)) % 0.38/0.62 (define @t248 () (@list @t88 @t234)) % 0.38/0.62 (define @t249 () (or @t236 @t240)) % 0.38/0.62 (define @t250 () (or @t249 @t242)) % 0.38/0.62 (define @t251 () (forall @t248 @t250)) % 0.38/0.62 (define @t252 () (forall @t239 @t250)) % 0.38/0.62 (define @t253 () (forall @t239 @t249)) % 0.38/0.62 (define @t254 () (or @t253 @t242)) % 0.38/0.62 (define @t255 () (forall @t94 (or (not @t92) (not @t91)))) % 0.38/0.62 (define @t256 () (not @t255)) % 0.38/0.62 (define @t257 () (and @t256 @t241)) % 0.38/0.62 (define @t258 () (forall @t97 (not @t257))) % 0.38/0.62 (define @t259 () (not @t258)) % 0.38/0.62 (define @t260 () (forall @t94 (not @t93))) % 0.38/0.62 (define @t261 () (not @t260)) % 0.38/0.62 (define @t262 () (@quantifiers_skolemize (forall @t239 (or @t236 (not (tptp.r3 @t170 @t234 @t170)))) 0)) % 0.38/0.62 (define @t263 () (tptp.r3 @t170 @t262 @t170)) % 0.38/0.62 (define @t264 () (not @t263)) % 0.38/0.62 (define @t265 () (tptp.r1 @t262)) % 0.38/0.62 (define @t266 () (not @t265)) % 0.38/0.62 (define @t267 () (or @t266 @t264)) % 0.38/0.62 (define @t268 () (@list @t267)) % 0.38/0.62 (define @t269 () (and @t265 (= @t262 @t170))) % 0.38/0.62 (define @t270 () (or @t266 @t269)) % 0.38/0.62 (define @t271 () (= @t170 @t262)) % 0.38/0.62 (define @t272 () (and @t265 @t271)) % 0.38/0.62 (define @t273 () (or @t266 @t272)) % 0.38/0.62 (define @t274 () (@list false)) % 0.38/0.62 (define @t275 () (@list @t173)) % 0.38/0.62 (define @t276 () (@list false false)) % 0.38/0.62 (define @t277 () (tptp.r3 @t170 @t170 @t170)) % 0.38/0.62 (define @t278 () (= @t170 @t220)) % 0.38/0.62 (define @t279 () (and @t277 @t278)) % 0.38/0.62 (define @t280 () (not @t277)) % 0.38/0.62 (define @t281 () (or @t280 @t279)) % 0.38/0.62 (define @t282 () (@var "BOUND_VARIABLE_7957" $$unsorted)) % 0.38/0.62 (define @t283 () (@var "BOUND_VARIABLE_7950" $$unsorted)) % 0.38/0.62 (define @t284 () (@list @t63 @t283 @t282)) % 0.38/0.62 (define @t285 () (forall @t284 (or (not (tptp.r2 @t170 @t283)) (not (tptp.r4 @t170 @t283 @t63)) (not (tptp.r3 @t282 @t170 @t63)) (not (tptp.r4 @t170 @t170 @t282))))) % 0.38/0.62 (define @t286 () (@quantifiers_skolemize @t285 0)) % 0.38/0.62 (define @t287 () (tptp.r3 @t170 @t170 @t286)) % 0.38/0.62 (define @t288 () (and @t287 (= @t286 @t220))) % 0.38/0.62 (define @t289 () (not @t287)) % 0.38/0.62 (define @t290 () (or @t289 @t288)) % 0.38/0.62 (define @t291 () (= @t220 @t286)) % 0.38/0.62 (define @t292 () (and @t287 @t291)) % 0.38/0.62 (define @t293 () (or @t289 @t292)) % 0.38/0.62 (define @t294 () (not (tptp.r4 @t61 @t60 @t282))) % 0.38/0.62 (define @t295 () (not (tptp.r3 @t282 @t61 @t63))) % 0.38/0.62 (define @t296 () (not (tptp.r4 @t61 @t283 @t63))) % 0.38/0.62 (define @t297 () (not (tptp.r2 @t60 @t283))) % 0.38/0.62 (define @t298 () (or @t295 @t294)) % 0.38/0.62 (define @t299 () (or @t297 @t296)) % 0.38/0.62 (define @t300 () (or @t299 @t298)) % 0.38/0.62 (define @t301 () (forall @t284 @t300)) % 0.38/0.62 (define @t302 () (forall (@list @t283 @t282) @t300)) % 0.38/0.62 (define @t303 () (forall (@list @t282) @t298)) % 0.38/0.62 (define @t304 () (forall (@list @t283) @t299)) % 0.38/0.62 (define @t305 () (@var "BOUND_VARIABLE_7912" $$unsorted)) % 0.38/0.62 (define @t306 () (@list @t305)) % 0.38/0.62 (define @t307 () (or @t304 @t303)) % 0.38/0.62 (define @t308 () (forall @t66 (or (not @t64) (not @t62)))) % 0.38/0.62 (define @t309 () (not (tptp.r4 @t61 @t305 @t63))) % 0.38/0.62 (define @t310 () (not (tptp.r2 @t60 @t305))) % 0.38/0.62 (define @t311 () (or @t310 @t309)) % 0.38/0.62 (define @t312 () (@list @t305)) % 0.38/0.62 (define @t313 () (forall @t312 @t311)) % 0.38/0.62 (define @t314 () (not @t308)) % 0.38/0.62 (define @t315 () (not @t313)) % 0.38/0.62 (define @t316 () (and @t315 @t314)) % 0.38/0.62 (define @t317 () (forall @t80 (not @t316))) % 0.38/0.62 (define @t318 () (not @t317)) % 0.38/0.62 (define @t319 () (forall @t66 (not @t65))) % 0.38/0.62 (define @t320 () (not @t319)) % 0.38/0.62 (define @t321 () (not (= @t63 @t63))) % 0.38/0.62 (define @t322 () (or @t321 @t310 @t309)) % 0.38/0.62 (define @t323 () (not (tptp.r4 @t61 @t305 @t68))) % 0.38/0.62 (define @t324 () (= @t63 @t68)) % 0.38/0.62 (define @t325 () (not @t324)) % 0.38/0.62 (define @t326 () (or @t325 @t325 @t310 @t323)) % 0.38/0.62 (define @t327 () (or @t325 @t310 @t323)) % 0.38/0.62 (define @t328 () (forall @t77 @t327)) % 0.38/0.62 (define @t329 () (forall @t312 @t328)) % 0.38/0.62 (define @t330 () (forall (@list @t305 @t68) @t327)) % 0.38/0.62 (define @t331 () (@list @t68 @t305)) % 0.38/0.62 (define @t332 () (or @t310 @t323)) % 0.38/0.62 (define @t333 () (or @t332 @t325)) % 0.38/0.62 (define @t334 () (forall @t331 @t333)) % 0.38/0.62 (define @t335 () (forall @t312 @t333)) % 0.38/0.62 (define @t336 () (forall @t312 @t332)) % 0.38/0.62 (define @t337 () (or @t336 @t325)) % 0.38/0.62 (define @t338 () (forall @t74 (or (not @t72) (not @t71)))) % 0.38/0.62 (define @t339 () (not @t338)) % 0.38/0.62 (define @t340 () (and @t339 @t324)) % 0.38/0.62 (define @t341 () (forall @t77 (not @t340))) % 0.38/0.62 (define @t342 () (not @t341)) % 0.38/0.62 (define @t343 () (forall @t74 (not @t73))) % 0.38/0.62 (define @t344 () (not @t343)) % 0.38/0.62 (define @t345 () (@quantifiers_skolemize @t285 2)) % 0.38/0.62 (define @t346 () (tptp.r3 @t345 @t170 @t286)) % 0.38/0.62 (define @t347 () (tptp.r4 @t170 @t170 @t345)) % 0.38/0.62 (define @t348 () (not @t347)) % 0.38/0.62 (define @t349 () (not @t346)) % 0.38/0.62 (define @t350 () (@quantifiers_skolemize @t285 1)) % 0.38/0.62 (define @t351 () (tptp.r4 @t170 @t350 @t286)) % 0.38/0.62 (define @t352 () (not @t351)) % 0.38/0.62 (define @t353 () (tptp.r2 @t170 @t350)) % 0.38/0.62 (define @t354 () (not @t353)) % 0.38/0.62 (define @t355 () (or @t354 @t352 @t349 @t348)) % 0.38/0.62 (define @t356 () (@list @t355)) % 0.38/0.62 (define @t357 () (@var "BOUND_VARIABLE_7780" $$unsorted)) % 0.38/0.62 (define @t358 () (= @t35 @t357)) % 0.38/0.62 (define @t359 () (tptp.r4 @t39 @t38 @t357)) % 0.38/0.62 (define @t360 () (@list @t357)) % 0.38/0.62 (define @t361 () (forall @t360 (or (not @t359) (and @t359 @t358)))) % 0.38/0.62 (define @t362 () (tptp.r4 @t39 @t38 @t35)) % 0.38/0.62 (define @t363 () (and @t361 @t362)) % 0.38/0.62 (define @t364 () (forall @t48 (not @t363))) % 0.38/0.62 (define @t365 () (not @t364)) % 0.38/0.62 (define @t366 () (= @t35 @t35)) % 0.38/0.62 (define @t367 () (and @t362 @t366)) % 0.38/0.62 (define @t368 () (not @t366)) % 0.38/0.62 (define @t369 () (or @t368 @t367)) % 0.38/0.62 (define @t370 () (@var "BOUND_VARIABLE_7789" $$unsorted)) % 0.38/0.62 (define @t371 () (= @t35 @t370)) % 0.38/0.62 (define @t372 () (and (tptp.r4 @t39 @t38 @t370) @t371)) % 0.38/0.62 (define @t373 () (not @t371)) % 0.38/0.62 (define @t374 () (@list @t370)) % 0.38/0.62 (define @t375 () (or @t373 @t373 @t372)) % 0.38/0.62 (define @t376 () (or @t373 @t372)) % 0.38/0.62 (define @t377 () (forall @t374 @t376)) % 0.38/0.62 (define @t378 () (= @t35 @t36)) % 0.38/0.62 (define @t379 () (and @t40 @t378)) % 0.38/0.62 (define @t380 () (not @t378)) % 0.38/0.62 (define @t381 () (or @t380 @t379)) % 0.38/0.62 (define @t382 () (forall @t46 @t381)) % 0.38/0.62 (define @t383 () (@list @t36)) % 0.38/0.62 (define @t384 () (or @t43 @t379)) % 0.38/0.62 (define @t385 () (forall @t46 @t384)) % 0.38/0.62 (define @t386 () (and @t385 @t382)) % 0.38/0.62 (define @t387 () (tptp.r4 @t170 @t170 @t357)) % 0.38/0.62 (define @t388 () (not @t387)) % 0.38/0.62 (define @t389 () (forall @t48 (or (not (forall @t360 (or @t388 (and @t387 @t358)))) (not (tptp.r4 @t170 @t170 @t35))))) % 0.38/0.62 (define @t390 () (@quantifiers_skolemize @t389 0)) % 0.38/0.62 (define @t391 () (not (tptp.r4 @t170 @t170 @t390))) % 0.38/0.62 (define @t392 () (forall @t360 (or @t388 (and @t387 (= @t357 @t390))))) % 0.38/0.62 (define @t393 () (not @t392)) % 0.38/0.62 (define @t394 () (or @t393 @t391)) % 0.38/0.62 (define @t395 () (not @t394)) % 0.38/0.62 (define @t396 () (not @t389)) % 0.38/0.62 (define @t397 () (and @t387 (= @t390 @t357))) % 0.38/0.62 (define @t398 () (or @t388 @t397)) % 0.38/0.62 (define @t399 () (forall @t360 @t398)) % 0.38/0.62 (define @t400 () (not @t399)) % 0.38/0.62 (define @t401 () (or @t400 @t391)) % 0.38/0.62 (define @t402 () (not @t401)) % 0.38/0.62 (define @t403 () (and @t347 (= @t345 @t390))) % 0.38/0.62 (define @t404 () (or @t348 @t403)) % 0.38/0.62 (define @t405 () (= @t390 @t345)) % 0.38/0.62 (define @t406 () (and @t347 @t405)) % 0.38/0.62 (define @t407 () (or @t348 @t406)) % 0.38/0.62 (define @t408 () (@var "BOUND_VARIABLE_8070" $$unsorted)) % 0.38/0.62 (define @t409 () (not (tptp.r4 @t108 @t408 @t101))) % 0.38/0.62 (define @t410 () (not (tptp.r1 @t408))) % 0.38/0.62 (define @t411 () (tptp.r1 @t101)) % 0.38/0.62 (define @t412 () (not @t411)) % 0.38/0.62 (define @t413 () (or @t410 @t409)) % 0.38/0.62 (define @t414 () (or @t413 @t412)) % 0.38/0.62 (define @t415 () (@list @t101 @t408)) % 0.38/0.62 (define @t416 () (forall @t415 @t414)) % 0.38/0.62 (define @t417 () (@list @t408)) % 0.38/0.62 (define @t418 () (forall @t417 @t414)) % 0.38/0.62 (define @t419 () (forall @t417 @t413)) % 0.38/0.62 (define @t420 () (or @t419 @t412)) % 0.38/0.62 (define @t421 () (forall @t112 (or (not @t110) (not @t109)))) % 0.38/0.62 (define @t422 () (not @t421)) % 0.38/0.62 (define @t423 () (and @t422 @t411)) % 0.38/0.62 (define @t424 () (forall @t115 (not @t423))) % 0.38/0.62 (define @t425 () (not @t424)) % 0.38/0.62 (define @t426 () (not (= @t101 @t101))) % 0.38/0.62 (define @t427 () (or @t412 @t426)) % 0.38/0.62 (define @t428 () (not @t102)) % 0.38/0.62 (define @t429 () (not @t103)) % 0.38/0.62 (define @t430 () (or @t428 @t429 @t428)) % 0.38/0.62 (define @t431 () (or @t429 @t428)) % 0.38/0.62 (define @t432 () (forall @t105 (not @t104))) % 0.38/0.62 (define @t433 () (not @t432)) % 0.38/0.62 (define @t434 () (forall @t112 (not @t111))) % 0.38/0.62 (define @t435 () (not @t434)) % 0.38/0.62 (define @t436 () (forall @t415 (or @t412 @t410 (not (tptp.r4 @t170 @t408 @t101))))) % 0.38/0.62 (define @t437 () (@quantifiers_skolemize @t436 0)) % 0.38/0.62 (define @t438 () (@quantifiers_skolemize @t436 1)) % 0.38/0.62 (define @t439 () (tptp.r4 @t170 @t438 @t437)) % 0.38/0.62 (define @t440 () (not @t439)) % 0.38/0.62 (define @t441 () (tptp.r1 @t438)) % 0.38/0.62 (define @t442 () (not @t441)) % 0.38/0.62 (define @t443 () (tptp.r1 @t437)) % 0.38/0.62 (define @t444 () (not @t443)) % 0.38/0.62 (define @t445 () (or @t444 @t442 @t440)) % 0.38/0.62 (define @t446 () (@list @t445)) % 0.38/0.62 (define @t447 () (and @t443 (= @t437 @t170))) % 0.38/0.62 (define @t448 () (or @t444 @t447)) % 0.38/0.62 (define @t449 () (= @t170 @t437)) % 0.38/0.62 (define @t450 () (and @t443 @t449)) % 0.38/0.62 (define @t451 () (or @t444 @t450)) % 0.38/0.62 (define @t452 () (and @t441 (= @t438 @t170))) % 0.38/0.62 (define @t453 () (or @t442 @t452)) % 0.38/0.62 (define @t454 () (= @t170 @t438)) % 0.38/0.62 (define @t455 () (and @t441 @t454)) % 0.38/0.62 (define @t456 () (or @t442 @t455)) % 0.38/0.62 (define @t457 () (tptp.r4 @t170 @t170 @t170)) % 0.38/0.62 (define @t458 () (= @t170 @t390)) % 0.38/0.62 (define @t459 () (and @t457 @t458)) % 0.38/0.62 (define @t460 () (not @t457)) % 0.38/0.62 (define @t461 () (or @t460 @t459)) % 0.38/0.62 (define @t462 () (tptp.r1 @t286)) % 0.38/0.62 (define @t463 () (@var "BOUND_VARIABLE_8181" $$unsorted)) % 0.38/0.62 (define @t464 () (@var "BOUND_VARIABLE_8183" $$unsorted)) % 0.38/0.62 (define @t465 () (not (tptp.r2 @t464 @t463))) % 0.38/0.62 (define @t466 () (not (tptp.r1 @t464))) % 0.38/0.62 (define @t467 () (not (tptp.r4 @t120 @t463 @t63))) % 0.38/0.62 (define @t468 () (tptp.r1 @t63)) % 0.38/0.62 (define @t469 () (not @t468)) % 0.38/0.62 (define @t470 () (or @t469 @t467 @t466 @t465)) % 0.38/0.62 (define @t471 () (@list @t120 @t63 @t463 @t464)) % 0.38/0.62 (define @t472 () (or @t467 @t466 @t465)) % 0.38/0.62 (define @t473 () (or @t472 @t469)) % 0.38/0.62 (define @t474 () (forall @t471 @t473)) % 0.38/0.62 (define @t475 () (@list @t463 @t464)) % 0.38/0.62 (define @t476 () (forall @t475 @t473)) % 0.38/0.62 (define @t477 () (forall @t475 @t472)) % 0.38/0.62 (define @t478 () (@var "BOUND_VARIABLE_8146" $$unsorted)) % 0.38/0.62 (define @t479 () (or @t477 @t469)) % 0.38/0.62 (define @t480 () (not (tptp.r2 @t478 @t68))) % 0.38/0.62 (define @t481 () (not (tptp.r1 @t478))) % 0.38/0.62 (define @t482 () (not @t132)) % 0.38/0.62 (define @t483 () (or @t482 @t481 @t480)) % 0.38/0.62 (define @t484 () (@list @t68 @t478)) % 0.38/0.62 (define @t485 () (forall @t484 @t483)) % 0.38/0.62 (define @t486 () (not @t485)) % 0.38/0.62 (define @t487 () (and @t486 @t468)) % 0.38/0.62 (define @t488 () (forall @t136 (not @t487))) % 0.38/0.62 (define @t489 () (not @t488)) % 0.38/0.62 (define @t490 () (or @t469 @t321)) % 0.38/0.62 (define @t491 () (= @t55 @t63)) % 0.38/0.62 (define @t492 () (not @t491)) % 0.38/0.62 (define @t493 () (not @t125)) % 0.38/0.62 (define @t494 () (or @t492 @t493 @t492)) % 0.38/0.62 (define @t495 () (or @t493 @t492)) % 0.38/0.62 (define @t496 () (and @t125 @t491)) % 0.38/0.62 (define @t497 () (forall @t57 (not @t496))) % 0.38/0.62 (define @t498 () (not @t497)) % 0.38/0.62 (define @t499 () (or @t481 @t480)) % 0.38/0.62 (define @t500 () (or @t482 @t499)) % 0.38/0.62 (define @t501 () (forall @t484 @t500)) % 0.38/0.62 (define @t502 () (@list @t478)) % 0.38/0.62 (define @t503 () (forall @t502 @t500)) % 0.38/0.62 (define @t504 () (forall @t502 @t499)) % 0.38/0.62 (define @t505 () (or @t482 @t504)) % 0.38/0.62 (define @t506 () (forall @t58 (or (not @t129) (not @t128)))) % 0.38/0.62 (define @t507 () (not @t506)) % 0.38/0.62 (define @t508 () (and @t132 @t507)) % 0.38/0.62 (define @t509 () (forall @t77 (not @t508))) % 0.38/0.62 (define @t510 () (not @t509)) % 0.38/0.62 (define @t511 () (forall @t58 (not @t130))) % 0.38/0.62 (define @t512 () (not @t511)) % 0.38/0.62 (define @t513 () (not @t462)) % 0.38/0.62 (define @t514 () (or @t513 @t352 @t172 @t354)) % 0.38/0.62 (assume @p1 @t13) % 0.38/0.62 (assume @p2 (forall (@list @t17) (exists (@list @t14) (forall (@list @t15) (or (and (not @t18) (not @t16)) (and @t18 @t16)))))) % 0.38/0.62 (assume @p3 @t34) % 0.38/0.62 (assume @p4 @t50) % 0.38/0.62 (assume @p5 (forall (@list @t53 @t52) (exists @t58 (and (exists @t57 (and (exists (@list @t56) (and (tptp.r2 @t52 @t56) (tptp.r3 @t53 @t56 @t55))) (= @t55 @t54))) (exists (@list @t51) (and (tptp.r2 @t51 @t54) (tptp.r3 @t53 @t52 @t51))))))) % 0.38/0.62 (assume @p6 @t82) % 0.38/0.62 (assume @p7 (forall (@list @t84 @t83) (or (forall (@list @t85) (or (forall (@list @t86) (or (not (tptp.r2 @t84 @t86)) (not (= @t86 @t85)))) (not (tptp.r2 @t83 @t85)))) (= @t84 @t83)))) % 0.38/0.62 (assume @p8 @t99) % 0.38/0.62 (assume @p9 @t117) % 0.38/0.62 (assume @p10 (forall (@list @t119) (or (exists (@list @t121) (and (tptp.r1 @t121) (= @t119 @t121))) (exists (@list @t120 @t118) (and (tptp.r2 @t120 @t118) (= @t119 @t118)))))) % 0.38/0.62 (assume @p11 (forall (@list @t123 @t122) (or (forall (@list @t124) (or (not (tptp.r1 @t124)) (not (= @t124 @t122)))) (not (tptp.r2 @t123 @t122))))) % 0.38/0.62 (assume @p12 @t138) % 0.38/0.62 (assume @p13 true) % 0.38/0.62 (step @p14 :rule evaluate :args ((= false true))) % 0.38/0.62 (step @p15 :rule bool-and-de-morgan :args (@t143 @t144 true)) % 0.38/0.62 (step @p16 :rule cong :premises (@p15) :args (@t146)) % 0.38/0.62 (step @p17 :rule cong :premises (@p16) :args (@t147)) % 0.38/0.62 (step @p18 :rule exists-elim :args ((= (exists @t12 @t145) @t147))) % 0.38/0.62 (step @p19 :rule trans :premises (@p18 @p17)) % 0.38/0.62 (step @p20 :rule aci_norm :args ((= (or false @t144) @t144))) % 0.38/0.62 (step @p21 :rule aci_norm :args ((= (and @t144 true) @t144))) % 0.38/0.62 (step @p22 :rule eq-refl :args (@t1)) % 0.38/0.62 (step @p23 :rule refl :args (@t144)) % 0.38/0.62 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t149)) % 0.38/0.62 (step @p25 :rule trans :premises (@p24 @p21)) % 0.38/0.62 (step @p26 :rule evaluate :args ((not true))) % 0.38/0.62 (step @p27 :rule cong :premises (@p22) :args (@t150)) % 0.38/0.62 (step @p28 :rule trans :premises (@p27 @p26)) % 0.38/0.62 (step @p29 :rule nary_cong :premises (@p28 @p25) :args (@t151)) % 0.38/0.62 (step @p30 :rule trans :premises (@p29 @p20)) % 0.38/0.62 (step @p31 :rule quant-var-elim-eq :args ((= (forall @t156 (or (not (= @t152 @t1)) @t155 @t154)) @t151))) % 0.38/0.62 (step @p32 :rule refl :args (@t154)) % 0.38/0.62 (step @p33 :rule refl :args (@t155)) % 0.38/0.62 (step @p34 :rule eq-symm :args (@t1 @t152)) % 0.38/0.62 (step @p35 :rule cong :premises (@p34) :args (@t155)) % 0.38/0.62 (step @p36 :rule nary_cong :premises (@p35 @p33 @p32) :args 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@p731)) % 0.49/0.62 (step @p734 :rule reordering :premises (@p733) :args ((or @t351 @t355))) % 0.49/0.62 (step @p735 :rule chain_m_resolution :premises (@p734 @p392) :args (@t351 @t184 @t356)) % 0.49/0.62 (step @p736 :rule bool-double-not-elim :args (@t353)) % 0.49/0.62 (step @p737 :rule nary_cong :premises (@p394 @p736) :args ((or @t355 (not @t354)))) % 0.49/0.62 (step @p738 :rule cnf_or_neg :args (@t355 0)) % 0.49/0.62 (step @p739 :rule eq_resolve :premises (@p738 @p737)) % 0.49/0.62 (step @p740 :rule reordering :premises (@p739) :args ((or @t353 @t355))) % 0.49/0.62 (step @p741 :rule chain_m_resolution :premises (@p740 @p392) :args (@t353 @t184 @t356)) % 0.49/0.62 (step @p742 :rule cnf_or_pos :args (@t514)) % 0.49/0.62 (step @p743 :rule reordering :premises (@p742) :args ((or @t172 @t354 @t352 @t513 (not @t514)))) % 0.49/0.62 (step @p744 :rule chain_m_resolution :premises (@p743 @p94 @p741 @p735 @p729) :args (@t513 (@list false false false false) (@list @t171 @t353 @t351 @t514))) % 0.49/0.62 (step @p745 :rule false_intro :premises (@p744)) % 0.49/0.62 (step @p746 :rule symm :premises (@p745)) % 0.49/0.62 (step @p747 :rule trans :premises (@p746 @p648 @p95)) % 0.49/0.62 (step @p748 false :rule eq_resolve :premises (@p747 @p14)) % 0.49/0.62 ) % 0.49/0.62 % SZS output end Proof % 0.49/0.62 % cvc5 exiting %------------------------------------------------------------------------------