%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV238^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 08:55:39 AM UTC 2026 % Result : Theorem 0.51s 0.72s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV238^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n019.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 18:21:49 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.51/0.72 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.51/0.72 % SZS status Theorem % 0.51/0.72 % SZS output start Proof % 0.51/0.72 ( % 0.51/0.72 (declare-sort $$unsorted 0) % 0.51/0.72 (define @t1 () (@var "Xx" $$unsorted)) % 0.51/0.72 (define @t2 () (@var "Xx0" $$unsorted)) % 0.51/0.72 (define @t3 () (@var "S" (-> $$unsorted Bool))) % 0.51/0.72 (define @t4 () (_ @t3 @t2)) % 0.51/0.72 (define @t5 () (@var "Xx1" $$unsorted)) % 0.51/0.72 (define @t6 () (@var "K" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.51/0.72 (define @t7 () (_ @t6 @t3)) % 0.51/0.72 (define @t8 () (_ @t7 @t5)) % 0.51/0.72 (define @t9 () (_ @t3 @t5)) % 0.51/0.72 (define @t10 () (@list @t5)) % 0.51/0.72 (define @t11 () (forall @t10 (=> @t9 @t8))) % 0.51/0.72 (define @t12 () (and @t11 @t4)) % 0.51/0.72 (define @t13 () (@list @t3)) % 0.51/0.72 (define @t14 () (exists @t13 @t12)) % 0.51/0.72 (define @t15 () (@list @t2)) % 0.51/0.72 (define @t16 () (lambda @t15 @t14)) % 0.51/0.72 (define @t17 () (_ @t6 @t16)) % 0.51/0.72 (define @t18 () (_ @t17 @t1)) % 0.51/0.72 (define @t19 () (@var "Xx2" $$unsorted)) % 0.51/0.72 (define @t20 () (_ @t7 @t19)) % 0.51/0.72 (define @t21 () (_ @t3 @t19)) % 0.51/0.72 (define @t22 () (@list @t19)) % 0.51/0.72 (define @t23 () (forall @t22 (=> @t21 @t20))) % 0.51/0.72 (define @t24 () (and @t23 @t9)) % 0.51/0.72 (define @t25 () (exists @t13 @t24)) % 0.51/0.72 (define @t26 () (lambda @t10 @t25)) % 0.51/0.72 (define @t27 () (_ @t6 @t26)) % 0.51/0.72 (define @t28 () (_ @t27 @t2)) % 0.51/0.72 (define @t29 () (=> @t28 (_ (_ @t6 @t27) @t2))) % 0.51/0.72 (define @t30 () (forall @t15 @t29)) % 0.51/0.72 (define @t31 () (and @t30 @t18)) % 0.51/0.72 (define @t32 () (= @t18 @t31)) % 0.51/0.72 (define @t33 () (@list @t1)) % 0.51/0.72 (define @t34 () (forall @t33 @t32)) % 0.51/0.72 (define @t35 () (=> @t18 (_ (_ @t6 @t17) @t1))) % 0.51/0.72 (define @t36 () (forall @t33 @t35)) % 0.51/0.72 (define @t37 () (_ @t3 @t1)) % 0.51/0.72 (define @t38 () (_ @t7 @t2)) % 0.51/0.72 (define @t39 () (forall @t15 (=> @t4 @t38))) % 0.51/0.72 (define @t40 () (and @t39 @t37)) % 0.51/0.72 (define @t41 () (exists @t13 @t40)) % 0.51/0.72 (define @t42 () (=> @t41 @t18)) % 0.51/0.72 (define @t43 () (forall @t33 @t42)) % 0.51/0.72 (define @t44 () (=> @t43 @t36)) % 0.51/0.72 (define @t45 () (@var "Xx" (-> $$unsorted Bool))) % 0.51/0.72 (define @t46 () (_ (_ @t6 @t45) @t2)) % 0.51/0.72 (define @t47 () (=> @t46 @t28)) % 0.51/0.72 (define @t48 () (forall @t15 @t47)) % 0.51/0.72 (define @t49 () (_ @t45 @t2)) % 0.51/0.72 (define @t50 () (=> @t49 @t14)) % 0.51/0.72 (define @t51 () (forall @t15 @t50)) % 0.51/0.72 (define @t52 () (=> @t51 @t48)) % 0.51/0.72 (define @t53 () (@list @t45)) % 0.51/0.72 (define @t54 () (forall @t53 @t52)) % 0.51/0.72 (define @t55 () (and @t54 @t44)) % 0.51/0.72 (define @t56 () (=> @t55 @t34)) % 0.51/0.72 (define @t57 () (@list @t6)) % 0.51/0.72 (define @t58 () (forall @t57 @t56)) % 0.51/0.72 (define @t59 () (not @t58)) % 0.51/0.72 (define @t60 () (_ @t3 @t2)) % 0.51/0.72 (define @t61 () (not @t60)) % 0.51/0.72 (define @t62 () (@var "BOUND_VARIABLE_7654" $$unsorted)) % 0.51/0.72 (define @t63 () (_ @t6 @t3 @t5)) % 0.51/0.72 (define @t64 () (_ @t3 @t5)) % 0.51/0.72 (define @t65 () (not @t64)) % 0.51/0.72 (define @t66 () (or @t65 @t63)) % 0.51/0.72 (define @t67 () (forall @t10 @t66)) % 0.51/0.72 (define @t68 () (not @t67)) % 0.51/0.72 (define @t69 () (or @t68 @t61)) % 0.51/0.72 (define @t70 () (forall @t13 @t69)) % 0.51/0.72 (define @t71 () (not @t70)) % 0.51/0.72 (define @t72 () (lambda @t15 @t71)) % 0.51/0.72 (define @t73 () (_ @t6 @t72 @t62)) % 0.51/0.72 (define @t74 () (_ @t6 @t3 @t19)) % 0.51/0.72 (define @t75 () (_ @t3 @t19)) % 0.51/0.72 (define @t76 () (not @t75)) % 0.51/0.72 (define @t77 () (or @t76 @t74)) % 0.51/0.72 (define @t78 () (forall @t22 @t77)) % 0.51/0.72 (define @t79 () (not @t78)) % 0.51/0.72 (define @t80 () (or @t79 @t65)) % 0.51/0.72 (define @t81 () (forall @t13 @t80)) % 0.51/0.72 (define @t82 () (not @t81)) % 0.51/0.72 (define @t83 () (lambda @t10 @t82)) % 0.51/0.72 (define @t84 () (_ @t6 @t83)) % 0.51/0.72 (define @t85 () (_ @t6 @t84 @t2)) % 0.51/0.72 (define @t86 () (_ @t6 @t83 @t2)) % 0.51/0.72 (define @t87 () (forall @t15 (or (not @t86) @t85))) % 0.51/0.72 (define @t88 () (= @t73 (and @t87 @t73))) % 0.51/0.72 (define @t89 () (_ @t6 @t72)) % 0.51/0.72 (define @t90 () (_ @t6 @t89 @t1)) % 0.51/0.72 (define @t91 () (_ @t6 @t72 @t1)) % 0.51/0.72 (define @t92 () (forall @t33 (or (not @t91) @t90))) % 0.51/0.72 (define @t93 () (not @t92)) % 0.51/0.72 (define @t94 () (@var "BOUND_VARIABLE_7639" $$unsorted)) % 0.51/0.72 (define @t95 () (@var "BOUND_VARIABLE_7641" (-> $$unsorted Bool))) % 0.51/0.72 (define @t96 () (or (_ @t6 @t72 @t94) (not (forall @t15 (or (not (_ @t95 @t2)) (_ @t6 @t95 @t2)))) (not (_ @t95 @t94)))) % 0.51/0.72 (define @t97 () (and @t96 @t93)) % 0.51/0.72 (define @t98 () (@var "BOUND_VARIABLE_7543" $$unsorted)) % 0.51/0.72 (define @t99 () (_ @t6 @t83 @t98)) % 0.51/0.72 (define @t100 () (not (_ @t6 @t45 @t98))) % 0.51/0.72 (define @t101 () (_ @t45 @t2)) % 0.51/0.72 (define @t102 () (not @t101)) % 0.51/0.72 (define @t103 () (forall @t15 (or @t102 @t71))) % 0.51/0.72 (define @t104 () (not @t103)) % 0.51/0.72 (define @t105 () (or @t104 @t100 @t99)) % 0.51/0.72 (define @t106 () (@list @t45 @t98)) % 0.51/0.72 (define @t107 () (forall @t106 @t105)) % 0.51/0.72 (define @t108 () (not @t107)) % 0.51/0.72 (define @t109 () (or @t108 @t97 @t88)) % 0.51/0.72 (define @t110 () (forall (@list @t6 @t94 @t95 @t62) @t109)) % 0.51/0.72 (define @t111 () (@quantifiers_skolemize @t110 0)) % 0.51/0.72 (define @t112 () (not (forall @t10 (or @t65 (_ @t111 @t3 @t5))))) % 0.51/0.72 (define @t113 () (not (forall @t13 (or @t112 @t61)))) % 0.51/0.72 (define @t114 () (lambda @t15 @t113)) % 0.51/0.72 (define @t115 () (@purify @t114)) % 0.51/0.72 (define @t116 () (_ @t115 @t2)) % 0.51/0.72 (define @t117 () (_ @t114 @t2)) % 0.51/0.72 (define @t118 () (= @t116 @t117)) % 0.51/0.72 (define @t119 () (forall @t15 @t118)) % 0.51/0.72 (define @t120 () (@const 0 $$unsorted)) % 0.51/0.72 (define @t121 () (not (_ @t3 @t120))) % 0.51/0.72 (define @t122 () (forall @t13 (or @t112 @t121))) % 0.51/0.72 (define @t123 () (not @t122)) % 0.51/0.72 (define @t124 () (_ @t115 @t120)) % 0.51/0.72 (define @t125 () (forall @t15 (= @t113 @t116))) % 0.51/0.72 (define @t126 () (= @t123 @t124)) % 0.51/0.72 (define @t127 () (@list @t120)) % 0.51/0.72 (define @t128 () (= @t124 @t123)) % 0.51/0.72 (define @t129 () (@list false)) % 0.51/0.72 (define @t130 () (forall (@list @t94 @t95 @t62) @t109)) % 0.51/0.72 (define @t131 () (forall (@list @t62) @t88)) % 0.51/0.72 (define @t132 () (@list @t94 @t95)) % 0.51/0.72 (define @t133 () (forall @t132 @t93)) % 0.51/0.72 (define @t134 () (forall @t132 @t96)) % 0.51/0.72 (define @t135 () (@var "BOUND_VARIABLE_7583" (-> $$unsorted Bool))) % 0.51/0.72 (define @t136 () (and @t134 @t133)) % 0.51/0.72 (define @t137 () (forall @t132 @t97)) % 0.51/0.72 (define @t138 () (or @t108 @t137 @t131)) % 0.51/0.72 (define @t139 () (forall @t33 (= @t91 (and @t87 @t91)))) % 0.51/0.72 (define @t140 () (not (_ @t135 @t1))) % 0.51/0.72 (define @t141 () (not (forall @t15 (or (not (_ @t135 @t2)) (_ @t6 @t135 @t2))))) % 0.51/0.72 (define @t142 () (or @t91 @t141 @t140)) % 0.51/0.72 (define @t143 () (@list @t1 @t135)) % 0.51/0.72 (define @t144 () (forall @t143 @t142)) % 0.51/0.72 (define @t145 () (and @t144 @t93)) % 0.51/0.72 (define @t146 () (or @t108 @t145 @t139)) % 0.51/0.72 (define @t147 () (=> @t144 @t92)) % 0.51/0.72 (define @t148 () (and @t107 @t147)) % 0.51/0.72 (define @t149 () (not @t4)) % 0.51/0.72 (define @t150 () (not @t9)) % 0.51/0.72 (define @t151 () (or @t150 @t8)) % 0.51/0.72 (define @t152 () (forall @t10 @t151)) % 0.51/0.72 (define @t153 () (lambda @t15 (not (forall @t13 (or (not @t152) @t149))))) % 0.51/0.72 (define @t154 () (_ @t89 @t1)) % 0.51/0.72 (define @t155 () (_ @t6 @t153)) % 0.51/0.72 (define @t156 () (and @t87 @t154)) % 0.51/0.72 (define @t157 () (= @t154 @t156)) % 0.51/0.72 (define @t158 () (or @t68 @t149)) % 0.51/0.72 (define @t159 () (and @t67 @t4)) % 0.51/0.72 (define @t160 () (forall @t13 (not @t159))) % 0.51/0.72 (define @t161 () (not @t160)) % 0.51/0.72 (define @t162 () (not @t21)) % 0.51/0.72 (define @t163 () (or @t162 @t20)) % 0.51/0.72 (define @t164 () (forall @t22 @t163)) % 0.51/0.72 (define @t165 () (lambda @t10 (not (forall @t13 (or (not @t164) @t150))))) % 0.51/0.72 (define @t166 () (_ @t6 @t165)) % 0.51/0.72 (define @t167 () (_ (_ @t6 @t84) @t2)) % 0.51/0.72 (define @t168 () (_ @t84 @t2)) % 0.51/0.72 (define @t169 () (not @t168)) % 0.51/0.72 (define @t170 () (or @t169 @t167)) % 0.51/0.72 (define @t171 () (or @t79 @t150)) % 0.51/0.72 (define @t172 () (and @t78 @t9)) % 0.51/0.72 (define @t173 () (forall @t13 (not @t172))) % 0.51/0.72 (define @t174 () (not @t173)) % 0.51/0.72 (define @t175 () (_ (_ @t6 @t89) @t1)) % 0.51/0.72 (define @t176 () (not @t154)) % 0.51/0.72 (define @t177 () (or @t176 @t175)) % 0.51/0.72 (define @t178 () (or @t141 @t140)) % 0.51/0.72 (define @t179 () (or @t178 @t91)) % 0.51/0.72 (define @t180 () (forall @t143 @t179)) % 0.51/0.72 (define @t181 () (@list @t135)) % 0.51/0.72 (define @t182 () (forall @t181 @t179)) % 0.51/0.72 (define @t183 () (forall @t181 @t178)) % 0.51/0.72 (define @t184 () (or @t183 @t91)) % 0.51/0.72 (define @t185 () (_ @t3 @t1)) % 0.51/0.72 (define @t186 () (_ @t6 @t3 @t2)) % 0.51/0.72 (define @t187 () (forall @t15 (or @t61 @t186))) % 0.51/0.72 (define @t188 () (not @t187)) % 0.51/0.72 (define @t189 () (forall @t13 (or @t188 (not @t185)))) % 0.51/0.72 (define @t190 () (or @t189 @t154)) % 0.51/0.72 (define @t191 () (not @t189)) % 0.51/0.72 (define @t192 () (not @t37)) % 0.51/0.72 (define @t193 () (or @t188 @t192)) % 0.51/0.72 (define @t194 () (and @t187 @t37)) % 0.51/0.72 (define @t195 () (forall @t13 (not @t194))) % 0.51/0.72 (define @t196 () (not @t195)) % 0.51/0.72 (define @t197 () (or @t149 @t38)) % 0.51/0.72 (define @t198 () (or @t100 @t99)) % 0.51/0.72 (define @t199 () (or @t104 @t198)) % 0.51/0.72 (define @t200 () (forall @t106 @t199)) % 0.51/0.72 (define @t201 () (@list @t98)) % 0.51/0.72 (define @t202 () (forall @t201 @t199)) % 0.51/0.72 (define @t203 () (forall @t201 @t198)) % 0.51/0.72 (define @t204 () (@list @t2)) % 0.51/0.72 (define @t205 () (or @t104 @t203)) % 0.51/0.72 (define @t206 () (_ @t6 @t45 @t2)) % 0.51/0.72 (define @t207 () (forall @t15 (or (not @t206) @t86))) % 0.51/0.72 (define @t208 () (not @t46)) % 0.51/0.72 (define @t209 () (or @t208 @t168)) % 0.51/0.72 (define @t210 () (not @t49)) % 0.51/0.72 (define @t211 () (or @t210 @t71)) % 0.51/0.72 (define @t212 () (@quantifiers_skolemize @t110 3)) % 0.51/0.72 (define @t213 () (_ @t111 @t115 @t212)) % 0.51/0.72 (define @t214 () (not (forall @t22 (or @t76 (_ @t111 @t3 @t19))))) % 0.51/0.72 (define @t215 () (not (forall @t13 (or @t214 @t65)))) % 0.51/0.72 (define @t216 () (lambda @t10 @t215)) % 0.51/0.72 (define @t217 () (forall @t15 (or (not (_ @t111 @t216 @t2)) (_ @t111 (_ @t111 @t216) @t2)))) % 0.51/0.72 (define @t218 () (and @t217 @t213)) % 0.51/0.72 (define @t219 () (= @t213 @t218)) % 0.51/0.72 (define @t220 () (forall @t33 (or (not (_ @t111 @t114 @t1)) (_ @t111 (_ @t111 @t114) @t1)))) % 0.51/0.72 (define @t221 () (not @t220)) % 0.51/0.72 (define @t222 () (@quantifiers_skolemize @t110 1)) % 0.51/0.72 (define @t223 () (@quantifiers_skolemize @t110 2)) % 0.51/0.72 (define @t224 () (_ @t223 @t222)) % 0.51/0.72 (define @t225 () (not @t224)) % 0.51/0.72 (define @t226 () (not (_ @t223 @t2))) % 0.51/0.72 (define @t227 () (forall @t15 (or @t226 (_ @t111 @t223 @t2)))) % 0.51/0.72 (define @t228 () (not @t227)) % 0.51/0.72 (define @t229 () (_ @t111 @t115 @t222)) % 0.51/0.72 (define @t230 () (or @t229 @t228 @t225)) % 0.51/0.72 (define @t231 () (and @t230 @t221)) % 0.51/0.72 (define @t232 () (forall @t106 (or (not (forall @t15 (or @t102 @t113))) (not (_ @t111 @t45 @t98)) (_ @t111 @t216 @t98)))) % 0.51/0.72 (define @t233 () (not @t232)) % 0.51/0.72 (define @t234 () (or @t233 @t231 @t219)) % 0.51/0.72 (define @t235 () (not @t234)) % 0.51/0.72 (define @t236 () (not @t110)) % 0.51/0.72 (define @t237 () (_ @t111 @t114 @t212)) % 0.51/0.72 (define @t238 () (and @t217 @t237)) % 0.51/0.72 (define @t239 () (= @t237 @t238)) % 0.51/0.72 (define @t240 () (_ @t111 @t114 @t222)) % 0.51/0.72 (define @t241 () (or @t240 @t228 @t225)) % 0.51/0.72 (define @t242 () (and @t241 @t221)) % 0.51/0.72 (define @t243 () (or @t233 @t242 @t239)) % 0.51/0.72 (define @t244 () (not @t243)) % 0.51/0.72 (define @t245 () (@list true)) % 0.51/0.72 (define @t246 () (@list @t234)) % 0.51/0.72 (define @t247 () (@purify @t216)) % 0.51/0.72 (define @t248 () (_ @t111 @t216 @t222)) % 0.51/0.72 (define @t249 () (_ @t111 @t223 @t222)) % 0.51/0.72 (define @t250 () (not @t249)) % 0.51/0.72 (define @t251 () (forall @t15 (or @t226 @t113))) % 0.51/0.72 (define @t252 () (not @t251)) % 0.51/0.72 (define @t253 () (or @t252 @t250 @t248)) % 0.51/0.72 (define @t254 () (_ @t111 @t247 @t222)) % 0.51/0.72 (define @t255 () (or @t252 @t250 @t254)) % 0.51/0.72 (define @t256 () (@quantifiers_skolemize @t251 0)) % 0.51/0.72 (define @t257 () (_ @t223 @t256)) % 0.51/0.72 (define @t258 () (forall @t13 (or @t112 (not (_ @t3 @t256))))) % 0.51/0.72 (define @t259 () (not @t258)) % 0.51/0.72 (define @t260 () (not @t257)) % 0.51/0.72 (define @t261 () (or @t260 @t259)) % 0.51/0.72 (define @t262 () (@list true true)) % 0.51/0.72 (define @t263 () (@list @t219 @t218)) % 0.51/0.72 (define @t264 () (not @t217)) % 0.51/0.72 (define @t265 () (not @t213)) % 0.51/0.72 (define @t266 () (@list true false)) % 0.51/0.72 (define @t267 () (@var "BOUND_VARIABLE_7922" $$unsorted)) % 0.51/0.72 (define @t268 () (@var "BOUND_VARIABLE_7919" $$unsorted)) % 0.51/0.72 (define @t269 () (@var "BOUND_VARIABLE_7921" (-> $$unsorted Bool))) % 0.51/0.72 (define @t270 () (@var "BOUND_VARIABLE_7920" $$unsorted)) % 0.51/0.72 (define @t271 () (lambda (@list @t268) (not (forall (@list @t269) (or (not (forall (@list @t270) (or (not (_ @t269 @t270)) (_ @t111 @t269 @t270)))) (not (_ @t269 @t268))))))) % 0.51/0.72 (define @t272 () (@list @t268 @t270 @t269 @t267)) % 0.51/0.72 (define @t273 () (not @t230)) % 0.51/0.72 (define @t274 () (@list @t230)) % 0.51/0.72 (define @t275 () (forall @t10 (or (not (_ @t223 @t5)) (_ @t111 @t223 @t5)))) % 0.51/0.72 (define @t276 () (not @t275)) % 0.51/0.72 (define @t277 () (or @t276 @t260)) % 0.51/0.72 (define @t278 () (not @t261)) % 0.51/0.72 (define @t279 () (or @t225 @t249)) % 0.51/0.72 (define @t280 () (@list false false)) % 0.51/0.72 (define @t281 () (not @t229)) % 0.51/0.72 (define @t282 () (not @t254)) % 0.51/0.72 (define @t283 () (= @t115 @t247)) % 0.51/0.72 (define @t284 () (not @t283)) % 0.51/0.72 (define @t285 () (and @t254 @t283 @t281)) % 0.51/0.72 (define @t286 () (_ @t247 @t120)) % 0.51/0.72 (define @t287 () (= @t124 @t286)) % 0.51/0.72 (define @t288 () (not @t287)) % 0.51/0.72 (define @t289 () (not @t128)) % 0.51/0.72 (define @t290 () (not @t124)) % 0.51/0.72 (define @t291 () (_ @t247 @t5)) % 0.51/0.72 (define @t292 () (_ @t216 @t5)) % 0.51/0.72 (define @t293 () (= @t291 @t292)) % 0.51/0.72 (define @t294 () (forall @t10 @t293)) % 0.51/0.72 (define @t295 () (forall @t13 (or @t214 @t121))) % 0.51/0.72 (define @t296 () (not @t295)) % 0.51/0.72 (define @t297 () (forall @t10 (= @t215 @t291))) % 0.51/0.72 (define @t298 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:premises (@p463 @p461 @p451 @p385) :args (@t254 (@list false false false) (@list @t249 @t251 @t255))) % 0.51/0.72 (step @p465 :rule cnf_or_neg :args (@t230 0)) % 0.51/0.72 (step @p466 :rule chain_m_resolution :premises (@p465 @p423) :args (@t281 @t245 @t274)) % 0.51/0.72 (step @p467 :rule refl :args (@t282)) % 0.51/0.72 (step @p468 :rule refl :args (@t284)) % 0.51/0.72 (step @p469 :rule bool-double-not-elim :args (@t229)) % 0.51/0.72 (step @p470 :rule nary_cong :premises (@p469 @p468 @p467) :args ((or (not @t281) @t284 @t282))) % 0.51/0.72 (assume-push @p569 @t254) % 0.51/0.72 (assume-push @p570 @t283) % 0.51/0.72 (assume-push @p571 @t281) % 0.51/0.72 (step @p474 :rule evaluate :args ((= false true))) % 0.51/0.72 (step @p475 :rule true_intro :premises (@p569)) % 0.51/0.72 (step @p476 :rule cong :premises (@p570 @p343) :args (@t229)) % 0.51/0.72 (step @p477 :rule false_intro :premises (@p466)) % 0.51/0.72 (step @p478 :rule symm :premises (@p477)) % 0.51/0.72 (step @p479 :rule trans :premises (@p478 @p476 @p475)) % 0.51/0.72 (step @p480 false :rule eq_resolve :premises (@p479 @p474)) % 0.51/0.72 (step-pop @p572 :rule scope :premises (@p480)) % 0.51/0.72 (step-pop @p573 :rule scope :premises (@p572)) % 0.51/0.72 (step-pop @p574 :rule scope :premises (@p573)) % 0.51/0.72 (step @p481 :rule process_scope :premises (@p574) :args (false)) % 0.51/0.72 (assume-push @p575 @t281) % 0.51/0.72 (assume-push @p576 @t283) % 0.51/0.72 (assume-push @p577 @t254) % 0.51/0.72 (step @p488 :rule and_intro :premises (@p577 @p576 @p466)) % 0.51/0.72 (step-pop @p578 :rule scope :premises (@p488)) % 0.51/0.72 (step-pop @p579 :rule scope :premises (@p578)) % 0.51/0.72 (step-pop @p580 :rule scope :premises (@p579)) % 0.51/0.72 (step @p489 :rule process_scope :premises (@p580) :args (@t285)) % 0.51/0.72 (step @p493 :rule implies_elim :premises (@p489)) % 0.51/0.72 (step @p494 :rule resolution :premises (@p493 @p481) :args (true @t285)) % 0.51/0.72 (step @p495 :rule not_and :premises (@p494)) % 0.51/0.72 (step @p496 :rule eq_resolve :premises (@p495 @p470)) % 0.51/0.72 (step @p497 :rule chain_m_resolution :premises (@p496 @p466 @p464) :args (@t284 @t266 (@list @t229 @t254))) % 0.51/0.72 ; WARNING: add trust step for TRUST % 0.51/0.72 ; trust TRUST THEORY_LEMMA % 0.51/0.72 (step @p498 :rule trust :premises () :args ((or @t283 @t288))) % 0.51/0.72 (step @p499 :rule chain_m_resolution :premises (@p498 @p497) :args (@t288 @t245 (@list @t283))) % 0.51/0.72 (step @p500 :rule cnf_equiv_neg2 :args (@t287)) % 0.51/0.72 (step @p501 :rule cnf_equiv_pos1 :args (@t128)) % 0.51/0.72 (step @p502 :rule reordering :premises (@p501) :args ((or @t290 @t123 @t289))) % 0.51/0.72 (step @p503 :rule eq-symm :args (@t291 @t215)) % 0.51/0.72 (step @p504 :rule beta-reduce :args ((= @t292 @t215))) % 0.51/0.72 (step @p505 :rule refl :args (@t291)) % 0.51/0.72 (step @p506 :rule cong :premises (@p505 @p504) :args (@t293)) % 0.51/0.72 (step @p507 :rule trans :premises (@p506 @p503)) % 0.51/0.72 (step @p508 :rule cong :premises (@p507) :args (@t294)) % 0.51/0.72 (step @p509 :rule quant-unused-vars :args ((= (forall @t10 true) true))) % 0.51/0.72 (step @p510 :rule eq-refl :args (@t292)) % 0.51/0.72 (step @p511 :rule cong :premises (@p510) :args ((forall @t10 (= @t292 @t292)))) % 0.51/0.72 (step @p512 :rule trans :premises (@p511 @p509)) % 0.51/0.72 (step @p513 :rule refl :args (@t292)) % 0.51/0.72 (step @p514 :rule refl :args (@t5)) % 0.51/0.72 (step @p515 :rule ho_cong :premises (@p368 @p514)) % 0.51/0.73 (step @p516 :rule cong :premises (@p515 @p513) :args (@t293)) % 0.51/0.73 (step @p517 :rule cong :premises (@p516) :args (@t294)) % 0.51/0.73 (step @p518 :rule trans :premises (@p517 @p512)) % 0.51/0.73 (step @p519 :rule true_elim :premises (@p518)) % 0.51/0.73 (step @p520 :rule eq_resolve :premises (@p519 @p508)) % 0.51/0.73 (step @p521 :rule eq-symm :args (@t296 @t286)) % 0.51/0.73 (step @p522 :rule refl :args (@t297)) % 0.51/0.73 (step @p523 :rule cong :premises (@p522 @p521) :args ((=> @t297 @t298))) % 0.51/0.73 (assume-push @p581 @t297) % 0.51/0.73 (step @p525 :rule instantiate :premises (@p520) :args (@t127)) % 0.51/0.73 (step-pop @p582 :rule scope :premises (@p525)) % 0.51/0.73 (step @p526 :rule process_scope :premises (@p582) :args (@t298)) % 0.51/0.73 (step @p528 :rule eq_resolve :premises (@p526 @p523)) % 0.51/0.73 (step @p529 :rule implies_elim :premises (@p528)) % 0.51/0.73 (step @p530 :rule chain_m_resolution :premises (@p529 @p520) :args (@t299 @t129 (@list @t297))) % 0.51/0.73 (step @p531 :rule bool-double-not-elim :args (@t295)) % 0.51/0.73 (step @p532 :rule refl :args (@t286)) % 0.51/0.73 (step @p533 :rule refl :args (@t300)) % 0.51/0.73 (step @p534 :rule nary_cong :premises (@p533 @p532 @p531) :args ((or @t300 @t286 (not @t296)))) % 0.51/0.73 (step @p535 :rule cnf_equiv_pos2 :args (@t299)) % 0.51/0.73 (step @p536 :rule eq_resolve :premises (@p535 @p534)) % 0.51/0.73 (step @p537 :rule reordering :premises (@p536) :args ((or @t286 @t295 @t300))) % 0.51/0.73 (step @p538 :rule alpha_equiv :args ((forall (@list @t301) (or (not (forall (@list @t302) (or (not (_ @t301 @t302)) (_ @t111 @t301 @t302)))) (not (_ @t301 @t120)))) @t303 (@list @t19 @t3))) % 0.51/0.73 (step @p539 :rule alpha_equiv :args (@t122 (@list @t5 @t3) @t303)) % 0.51/0.73 (step @p540 :rule trans :premises (@p539 @p538)) % 0.51/0.73 (step @p541 :rule equiv_elim2 :premises (@p540)) % 0.51/0.73 (step @p542 :rule chain_m_resolution :premises (@p541 @p537 @p530 @p502 @p31 @p500 @p499) :args (@t290 (@list false false true false true true) (@list @t295 @t299 @t122 @t128 @t286 @t287))) % 0.51/0.73 (step @p543 :rule bool-double-not-elim :args (@t122)) % 0.51/0.73 (step @p544 :rule refl :args (@t124)) % 0.51/0.73 (step @p545 :rule refl :args (@t289)) % 0.51/0.73 (step @p546 :rule nary_cong :premises (@p545 @p544 @p543) :args ((or @t289 @t124 (not @t123)))) % 0.51/0.73 (step @p547 :rule cnf_equiv_pos2 :args (@t128)) % 0.51/0.73 (step @p548 :rule eq_resolve :premises (@p547 @p546)) % 0.51/0.73 (step @p549 :rule reordering :premises (@p548) :args ((or @t124 @t122 @t289))) % 0.51/0.73 (step @p550 :rule chain_m_resolution :premises (@p549 @p542 @p31) :args (@t122 @t266 (@list @t124 @t128))) % 0.51/0.73 (step @p551 :rule cnf_equiv_neg1 :args (@t287)) % 0.51/0.73 (step @p552 :rule reordering :premises (@p551) :args ((or @t124 @t286 @t287))) % 0.51/0.73 (step @p553 :rule chain_m_resolution :premises (@p552 @p542 @p499) :args (@t286 @t262 (@list @t124 @t287))) % 0.51/0.73 (step @p554 :rule cnf_equiv_pos1 :args (@t299)) % 0.51/0.73 (step @p555 :rule reordering :premises (@p554) :args ((or (not @t286) @t296 @t300))) % 0.51/0.73 (step @p556 :rule chain_m_resolution :premises (@p555 @p553 @p530) :args (@t296 @t280 (@list @t286 @t299))) % 0.51/0.73 (step @p557 :rule equiv_elim1 :premises (@p540)) % 0.51/0.73 (step @p558 false :rule chain_m_resolution :premises (@p557 @p556 @p550) :args (false @t266 (@list @t295 @t122))) % 0.51/0.73 ) % 0.51/0.73 % SZS output end Proof % 0.51/0.73 % cvc5 exiting %------------------------------------------------------------------------------