%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV254^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n013.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 08:55:41 AM UTC 2026 % Result : Theorem 0.63s 0.85s % Output : Proof 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV254^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n013.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 18:22:30 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.63/0.85 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.63/0.85 % SZS status Theorem % 0.63/0.85 % SZS output start Proof % 0.63/0.85 ( % 0.63/0.85 (declare-sort $$unsorted 0) % 0.63/0.85 (define @t1 () (@var "Xx" $$unsorted)) % 0.63/0.85 (define @t2 () (@var "S" (-> $$unsorted Bool))) % 0.63/0.85 (define @t3 () (_ @t2 @t1)) % 0.63/0.85 (define @t4 () (@var "Xx0" $$unsorted)) % 0.63/0.85 (define @t5 () (@var "K" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.63/0.85 (define @t6 () (_ @t5 @t2)) % 0.63/0.85 (define @t7 () (_ @t6 @t4)) % 0.63/0.85 (define @t8 () (_ @t2 @t4)) % 0.63/0.85 (define @t9 () (@list @t4)) % 0.63/0.85 (define @t10 () (forall @t9 (=> @t8 @t7))) % 0.63/0.85 (define @t11 () (and @t10 @t3)) % 0.63/0.85 (define @t12 () (@list @t2)) % 0.63/0.85 (define @t13 () (exists @t12 @t11)) % 0.63/0.85 (define @t14 () (@var "Xx1" $$unsorted)) % 0.63/0.85 (define @t15 () (_ @t6 @t14)) % 0.63/0.85 (define @t16 () (_ @t2 @t14)) % 0.63/0.85 (define @t17 () (@list @t14)) % 0.63/0.85 (define @t18 () (forall @t17 (=> @t16 @t15))) % 0.63/0.85 (define @t19 () (and @t18 @t8)) % 0.63/0.85 (define @t20 () (exists @t12 @t19)) % 0.63/0.85 (define @t21 () (lambda @t9 @t20)) % 0.63/0.85 (define @t22 () (_ @t5 @t21)) % 0.63/0.85 (define @t23 () (_ @t22 @t1)) % 0.63/0.86 (define @t24 () (@list @t1)) % 0.63/0.86 (define @t25 () (forall @t24 (= @t23 @t13))) % 0.63/0.86 (define @t26 () (=> @t23 (_ (_ @t5 @t22) @t1))) % 0.63/0.86 (define @t27 () (forall @t24 @t26)) % 0.63/0.86 (define @t28 () (=> @t13 @t23)) % 0.63/0.86 (define @t29 () (forall @t24 @t28)) % 0.63/0.86 (define @t30 () (=> @t29 @t27)) % 0.63/0.86 (define @t31 () (@var "Xx2" $$unsorted)) % 0.63/0.86 (define @t32 () (_ @t6 @t31)) % 0.63/0.86 (define @t33 () (_ @t2 @t31)) % 0.63/0.86 (define @t34 () (@list @t31)) % 0.63/0.86 (define @t35 () (forall @t34 (=> @t33 @t32))) % 0.63/0.86 (define @t36 () (and @t35 @t16)) % 0.63/0.86 (define @t37 () (exists @t12 @t36)) % 0.63/0.86 (define @t38 () (lambda @t17 @t37)) % 0.63/0.86 (define @t39 () (@var "Xx" (-> $$unsorted Bool))) % 0.63/0.86 (define @t40 () (_ (_ @t5 @t39) @t4)) % 0.63/0.86 (define @t41 () (=> @t40 (_ (_ @t5 @t38) @t4))) % 0.63/0.86 (define @t42 () (forall @t9 @t41)) % 0.63/0.86 (define @t43 () (_ @t39 @t4)) % 0.63/0.86 (define @t44 () (=> @t43 @t20)) % 0.63/0.86 (define @t45 () (forall @t9 @t44)) % 0.63/0.86 (define @t46 () (=> @t45 @t42)) % 0.63/0.86 (define @t47 () (@list @t39)) % 0.63/0.86 (define @t48 () (forall @t47 @t46)) % 0.63/0.86 (define @t49 () (and @t48 @t30)) % 0.63/0.86 (define @t50 () (=> @t49 @t25)) % 0.63/0.86 (define @t51 () (@list @t5)) % 0.63/0.86 (define @t52 () (forall @t51 @t50)) % 0.63/0.86 (define @t53 () (not @t52)) % 0.63/0.86 (define @t54 () (@const 0 $$unsorted)) % 0.63/0.86 (define @t55 () (_ @t2 @t14)) % 0.63/0.86 (define @t56 () (not @t55)) % 0.63/0.86 (define @t57 () (@var "BOUND_VARIABLE_7637" $$unsorted)) % 0.63/0.86 (define @t58 () (_ @t2 @t4)) % 0.63/0.86 (define @t59 () (not @t58)) % 0.63/0.86 (define @t60 () (_ @t5 @t2 @t14)) % 0.63/0.86 (define @t61 () (or @t56 @t60)) % 0.63/0.86 (define @t62 () (forall @t17 @t61)) % 0.63/0.86 (define @t63 () (not @t62)) % 0.63/0.86 (define @t64 () (or @t63 @t59)) % 0.63/0.86 (define @t65 () (forall @t12 @t64)) % 0.63/0.86 (define @t66 () (not @t65)) % 0.63/0.86 (define @t67 () (lambda @t9 @t66)) % 0.63/0.86 (define @t68 () (_ @t5 @t2 @t4)) % 0.63/0.86 (define @t69 () (forall @t9 (or @t59 @t68))) % 0.63/0.86 (define @t70 () (not @t69)) % 0.63/0.86 (define @t71 () (= (not (forall @t12 (or @t70 (not (_ @t2 @t57))))) (_ @t5 @t67 @t57))) % 0.63/0.86 (define @t72 () (_ @t5 @t67)) % 0.63/0.86 (define @t73 () (_ @t5 @t72 @t1)) % 0.63/0.86 (define @t74 () (_ @t5 @t67 @t1)) % 0.63/0.86 (define @t75 () (forall @t24 (or (not @t74) @t73))) % 0.63/0.86 (define @t76 () (not @t75)) % 0.63/0.86 (define @t77 () (@var "BOUND_VARIABLE_7622" $$unsorted)) % 0.63/0.86 (define @t78 () (@var "BOUND_VARIABLE_7624" (-> $$unsorted Bool))) % 0.63/0.86 (define @t79 () (or (_ @t5 @t67 @t77) (not (forall @t9 (or (not (_ @t78 @t4)) (_ @t5 @t78 @t4)))) (not (_ @t78 @t77)))) % 0.63/0.86 (define @t80 () (and @t79 @t76)) % 0.63/0.86 (define @t81 () (@var "BOUND_VARIABLE_7538" $$unsorted)) % 0.63/0.86 (define @t82 () (_ @t5 @t2 @t31)) % 0.63/0.86 (define @t83 () (_ @t2 @t31)) % 0.63/0.86 (define @t84 () (not @t83)) % 0.63/0.86 (define @t85 () (or @t84 @t82)) % 0.63/0.86 (define @t86 () (forall @t34 @t85)) % 0.63/0.86 (define @t87 () (not @t86)) % 0.63/0.86 (define @t88 () (or @t87 @t56)) % 0.63/0.86 (define @t89 () (forall @t12 @t88)) % 0.63/0.86 (define @t90 () (not @t89)) % 0.63/0.86 (define @t91 () (lambda @t17 @t90)) % 0.63/0.86 (define @t92 () (_ @t5 @t91 @t81)) % 0.63/0.86 (define @t93 () (not (_ @t5 @t39 @t81))) % 0.63/0.86 (define @t94 () (_ @t39 @t4)) % 0.63/0.86 (define @t95 () (not @t94)) % 0.63/0.86 (define @t96 () (forall @t9 (or @t95 @t66))) % 0.63/0.86 (define @t97 () (not @t96)) % 0.63/0.86 (define @t98 () (or @t97 @t93 @t92)) % 0.63/0.86 (define @t99 () (@list @t39 @t81)) % 0.63/0.86 (define @t100 () (forall @t99 @t98)) % 0.63/0.86 (define @t101 () (not @t100)) % 0.63/0.86 (define @t102 () (or @t101 @t80 @t71)) % 0.63/0.86 (define @t103 () (forall (@list @t5 @t77 @t78 @t57) @t102)) % 0.63/0.86 (define @t104 () (@quantifiers_skolemize @t103 0)) % 0.63/0.86 (define @t105 () (not (forall @t34 (or @t84 (_ @t104 @t2 @t31))))) % 0.63/0.86 (define @t106 () (not (forall @t12 (or @t105 @t56)))) % 0.63/0.86 (define @t107 () (lambda @t17 @t106)) % 0.63/0.86 (define @t108 () (@purify @t107)) % 0.63/0.86 (define @t109 () (_ @t108 @t54)) % 0.63/0.86 (define @t110 () (not (forall @t17 (or @t56 (_ @t104 @t2 @t14))))) % 0.63/0.86 (define @t111 () (not (forall @t12 (or @t110 @t59)))) % 0.63/0.86 (define @t112 () (lambda @t9 @t111)) % 0.63/0.86 (define @t113 () (@purify @t112)) % 0.63/0.86 (define @t114 () (_ @t113 @t54)) % 0.63/0.86 (define @t115 () (= @t114 @t109)) % 0.63/0.86 (define @t116 () (_ @t113 @t4)) % 0.63/0.86 (define @t117 () (_ @t112 @t4)) % 0.63/0.86 (define @t118 () (= @t116 @t117)) % 0.63/0.86 (define @t119 () (forall @t9 @t118)) % 0.63/0.86 (define @t120 () (not (_ @t2 @t54))) % 0.63/0.86 (define @t121 () (forall @t12 (or @t110 @t120))) % 0.63/0.86 (define @t122 () (not @t121)) % 0.63/0.86 (define @t123 () (forall @t9 (= @t111 @t116))) % 0.63/0.86 (define @t124 () (= @t122 @t114)) % 0.63/0.86 (define @t125 () (@list @t54)) % 0.63/0.86 (define @t126 () (= @t114 @t122)) % 0.63/0.86 (define @t127 () (@list false)) % 0.63/0.86 (define @t128 () (not @t126)) % 0.63/0.86 (define @t129 () (not @t114)) % 0.63/0.86 (define @t130 () (_ @t108 @t14)) % 0.63/0.86 (define @t131 () (_ @t107 @t14)) % 0.63/0.86 (define @t132 () (= @t130 @t131)) % 0.63/0.86 (define @t133 () (forall @t17 @t132)) % 0.63/0.86 (define @t134 () (forall @t12 (or @t105 @t120))) % 0.63/0.86 (define @t135 () (not @t134)) % 0.63/0.86 (define @t136 () (forall @t17 (= @t106 @t130))) % 0.63/0.86 (define @t137 () (= @t135 @t109)) % 0.63/0.86 (define @t138 () (= @t109 @t135)) % 0.63/0.86 (define @t139 () (not @t138)) % 0.63/0.86 (define @t140 () (@var "BOUND_VARIABLE_11810" (-> $$unsorted Bool))) % 0.63/0.86 (define @t141 () (@var "BOUND_VARIABLE_11809" $$unsorted)) % 0.63/0.86 (define @t142 () (@list @t141 @t140)) % 0.63/0.86 (define @t143 () (= @t113 @t108)) % 0.63/0.86 (define @t144 () (forall (@list @t77 @t78 @t57) @t102)) % 0.63/0.86 (define @t145 () (forall (@list @t57) @t71)) % 0.63/0.86 (define @t146 () (@list @t77 @t78)) % 0.63/0.86 (define @t147 () (forall @t146 @t76)) % 0.63/0.86 (define @t148 () (forall @t146 @t79)) % 0.63/0.86 (define @t149 () (@var "BOUND_VARIABLE_7578" (-> $$unsorted Bool))) % 0.63/0.86 (define @t150 () (and @t148 @t147)) % 0.63/0.86 (define @t151 () (forall @t146 @t80)) % 0.63/0.86 (define @t152 () (or @t101 @t151 @t145)) % 0.63/0.86 (define @t153 () (_ @t2 @t1)) % 0.63/0.86 (define @t154 () (forall @t12 (or @t70 (not @t153)))) % 0.63/0.86 (define @t155 () (not @t154)) % 0.63/0.86 (define @t156 () (forall @t24 (= @t155 @t74))) % 0.63/0.86 (define @t157 () (not (_ @t149 @t1))) % 0.63/0.86 (define @t158 () (not (forall @t9 (or (not (_ @t149 @t4)) (_ @t5 @t149 @t4))))) % 0.63/0.86 (define @t159 () (or @t74 @t158 @t157)) % 0.63/0.86 (define @t160 () (@list @t1 @t149)) % 0.63/0.86 (define @t161 () (forall @t160 @t159)) % 0.63/0.86 (define @t162 () (and @t161 @t76)) % 0.63/0.86 (define @t163 () (or @t101 @t162 @t156)) % 0.63/0.86 (define @t164 () (=> @t161 @t75)) % 0.63/0.86 (define @t165 () (and @t100 @t164)) % 0.63/0.86 (define @t166 () (not @t8)) % 0.63/0.86 (define @t167 () (not @t16)) % 0.63/0.86 (define @t168 () (or @t167 @t15)) % 0.63/0.86 (define @t169 () (forall @t17 @t168)) % 0.63/0.86 (define @t170 () (lambda @t9 (not (forall @t12 (or (not @t169) @t166))))) % 0.63/0.86 (define @t171 () (_ @t72 @t1)) % 0.63/0.86 (define @t172 () (_ @t5 @t170)) % 0.63/0.86 (define @t173 () (= @t155 @t171)) % 0.63/0.86 (define @t174 () (or @t63 @t166)) % 0.63/0.86 (define @t175 () (and @t62 @t8)) % 0.63/0.86 (define @t176 () (forall @t12 (not @t175))) % 0.63/0.86 (define @t177 () (not @t176)) % 0.63/0.86 (define @t178 () (not @t3)) % 0.63/0.86 (define @t179 () (or @t70 @t178)) % 0.63/0.86 (define @t180 () (and @t69 @t3)) % 0.63/0.86 (define @t181 () (forall @t12 (not @t180))) % 0.63/0.86 (define @t182 () (not @t181)) % 0.63/0.86 (define @t183 () (or @t166 @t7)) % 0.63/0.86 (define @t184 () (_ (_ @t5 @t72) @t1)) % 0.63/0.86 (define @t185 () (not @t171)) % 0.63/0.86 (define @t186 () (or @t185 @t184)) % 0.63/0.86 (define @t187 () (or @t158 @t157)) % 0.63/0.86 (define @t188 () (or @t187 @t74)) % 0.63/0.86 (define @t189 () (forall @t160 @t188)) % 0.63/0.86 (define @t190 () (@list @t149)) % 0.63/0.86 (define @t191 () (forall @t190 @t188)) % 0.63/0.86 (define @t192 () (forall @t190 @t187)) % 0.63/0.86 (define @t193 () (or @t192 @t74)) % 0.63/0.86 (define @t194 () (or @t154 @t171)) % 0.63/0.86 (define @t195 () (or @t93 @t92)) % 0.63/0.86 (define @t196 () (or @t97 @t195)) % 0.63/0.86 (define @t197 () (forall @t99 @t196)) % 0.63/0.86 (define @t198 () (@list @t81)) % 0.63/0.86 (define @t199 () (forall @t198 @t196)) % 0.63/0.86 (define @t200 () (forall @t198 @t195)) % 0.63/0.86 (define @t201 () (@list @t4)) % 0.63/0.86 (define @t202 () (or @t97 @t200)) % 0.63/0.86 (define @t203 () (_ @t5 @t91 @t4)) % 0.63/0.86 (define @t204 () (_ @t5 @t39 @t4)) % 0.63/0.86 (define @t205 () (forall @t9 (or (not @t204) @t203))) % 0.63/0.86 (define @t206 () (not @t33)) % 0.63/0.86 (define @t207 () (or @t206 @t32)) % 0.63/0.86 (define @t208 () (forall @t34 @t207)) % 0.63/0.86 (define @t209 () (lambda @t17 (not (forall @t12 (or (not @t208) @t167))))) % 0.63/0.86 (define @t210 () (_ (_ @t5 @t91) @t4)) % 0.63/0.86 (define @t211 () (not @t40)) % 0.63/0.86 (define @t212 () (or @t211 @t210)) % 0.63/0.86 (define @t213 () (or @t87 @t167)) % 0.63/0.86 (define @t214 () (and @t86 @t16)) % 0.63/0.86 (define @t215 () (forall @t12 (not @t214))) % 0.63/0.86 (define @t216 () (not @t215)) % 0.63/0.86 (define @t217 () (not @t43)) % 0.63/0.86 (define @t218 () (or @t217 @t66)) % 0.63/0.86 (define @t219 () (@quantifiers_skolemize @t103 3)) % 0.63/0.86 (define @t220 () (_ @t104 @t113 @t219)) % 0.63/0.86 (define @t221 () (forall @t12 (or (not (forall @t9 (or @t59 (_ @t104 @t2 @t4)))) (not (_ @t2 @t219))))) % 0.63/0.86 (define @t222 () (not @t221)) % 0.63/0.86 (define @t223 () (= @t222 @t220)) % 0.63/0.86 (define @t224 () (_ @t104 @t112)) % 0.63/0.86 (define @t225 () (forall @t24 (or (not (_ @t104 @t112 @t1)) (_ @t104 @t224 @t1)))) % 0.63/0.86 (define @t226 () (not @t225)) % 0.63/0.86 (define @t227 () (@quantifiers_skolemize @t103 1)) % 0.63/0.86 (define @t228 () (@quantifiers_skolemize @t103 2)) % 0.63/0.86 (define @t229 () (_ @t228 @t227)) % 0.63/0.86 (define @t230 () (not @t229)) % 0.63/0.86 (define @t231 () (not (_ @t228 @t4))) % 0.63/0.86 (define @t232 () (forall @t9 (or @t231 (_ @t104 @t228 @t4)))) % 0.63/0.86 (define @t233 () (not @t232)) % 0.63/0.86 (define @t234 () (_ @t104 @t113 @t227)) % 0.63/0.86 (define @t235 () (or @t234 @t233 @t230)) % 0.63/0.86 (define @t236 () (and @t235 @t226)) % 0.63/0.86 (define @t237 () (forall @t99 (or (not (forall @t9 (or @t95 @t111))) (not (_ @t104 @t39 @t81)) (_ @t104 @t107 @t81)))) % 0.63/0.86 (define @t238 () (not @t237)) % 0.63/0.86 (define @t239 () (or @t238 @t236 @t223)) % 0.63/0.86 (define @t240 () (not @t239)) % 0.63/0.86 (define @t241 () (not @t103)) % 0.63/0.86 (define @t242 () (_ @t104 @t112 @t219)) % 0.63/0.86 (define @t243 () (= @t222 @t242)) % 0.63/0.86 (define @t244 () (_ @t104 @t112 @t227)) % 0.63/0.86 (define @t245 () (or @t244 @t233 @t230)) % 0.63/0.86 (define @t246 () (and @t245 @t226)) % 0.63/0.86 (define @t247 () (or @t238 @t246 @t243)) % 0.63/0.86 (define @t248 () (not @t247)) % 0.63/0.86 (define @t249 () (@list true)) % 0.63/0.86 (define @t250 () (@list @t239)) % 0.63/0.86 (define @t251 () (not @t220)) % 0.63/0.86 (define @t252 () (not @t222)) % 0.63/0.86 (define @t253 () (@quantifiers_skolemize @t221 0)) % 0.63/0.86 (define @t254 () (_ @t253 @t219)) % 0.63/0.86 (define @t255 () (not @t254)) % 0.63/0.86 (define @t256 () (not (_ @t253 @t4))) % 0.63/0.86 (define @t257 () (forall @t9 (or @t256 (_ @t104 @t253 @t4)))) % 0.63/0.86 (define @t258 () (not @t257)) % 0.63/0.86 (define @t259 () (or @t258 @t255)) % 0.63/0.86 (define @t260 () (not @t259)) % 0.63/0.86 (define @t261 () (_ @t104 @t253 @t219)) % 0.63/0.86 (define @t262 () (or @t255 @t261)) % 0.63/0.86 (define @t263 () (@list @t14)) % 0.63/0.86 (define @t264 () (forall @t9 (or @t256 @t111))) % 0.63/0.86 (define @t265 () (@quantifiers_skolemize @t264 0)) % 0.63/0.86 (define @t266 () (_ @t253 @t265)) % 0.63/0.86 (define @t267 () (forall @t12 (or @t110 (not (_ @t2 @t265))))) % 0.63/0.86 (define @t268 () (not @t267)) % 0.63/0.86 (define @t269 () (not @t266)) % 0.63/0.86 (define @t270 () (or @t269 @t268)) % 0.63/0.86 (define @t271 () (forall @t17 (or (not (_ @t253 @t14)) (_ @t104 @t253 @t14)))) % 0.63/0.86 (define @t272 () (not @t271)) % 0.63/0.86 (define @t273 () (or @t272 @t269)) % 0.63/0.86 (define @t274 () (@list true false false)) % 0.63/0.86 (define @t275 () (not @t270)) % 0.63/0.86 (define @t276 () (not @t264)) % 0.63/0.86 (define @t277 () (_ @t104 @t107 @t219)) % 0.63/0.86 (define @t278 () (not @t261)) % 0.63/0.86 (define @t279 () (or @t276 @t278 @t277)) % 0.63/0.86 (define @t280 () (_ @t104 @t108 @t219)) % 0.63/0.86 (define @t281 () (or @t276 @t278 @t280)) % 0.63/0.86 (define @t282 () (@list @t237)) % 0.63/0.86 (define @t283 () (not @t280)) % 0.63/0.86 (define @t284 () (not @t143)) % 0.63/0.86 (define @t285 () (and @t251 @t143)) % 0.63/0.86 (define @t286 () (_ @t104 @t113)) % 0.63/0.86 (define @t287 () (_ @t286 @t219)) % 0.63/0.86 (define @t288 () (not @t287)) % 0.63/0.86 (define @t289 () (_ @t104 @t286 @t4)) % 0.63/0.86 (define @t290 () (_ @t104 @t113 @t4)) % 0.63/0.86 (define @t291 () (forall @t9 (or (not @t290) @t289))) % 0.63/0.86 (define @t292 () (not @t291)) % 0.63/0.86 (define @t293 () (or @t292 @t288)) % 0.63/0.86 (define @t294 () (_ @t286 @t219)) % 0.63/0.86 (define @t295 () (not @t294)) % 0.63/0.86 (define @t296 () (_ @t286 @t4)) % 0.63/0.86 (define @t297 () (not @t296)) % 0.63/0.86 (define @t298 () (or @t297 @t289)) % 0.63/0.86 (define @t299 () (_ @t286 @t4)) % 0.63/0.86 (define @t300 () (not @t299)) % 0.63/0.86 (define @t301 () (or @t300 @t289)) % 0.63/0.86 (define @t302 () (forall @t9 @t301)) % 0.63/0.86 (define @t303 () (not @t302)) % 0.63/0.86 (define @t304 () (or @t303 @t295)) % 0.63/0.86 (define @t305 () (or @t292 @t251)) % 0.63/0.86 (define @t306 () (@list false false)) % 0.63/0.86 (define @t307 () (@quantifiers_skolemize @t291 0)) % 0.63/0.86 (define @t308 () (or (not (_ @t104 @t113 @t307)) (_ @t104 @t286 @t307))) % 0.63/0.86 (define @t309 () (not @t308)) % 0.63/0.86 (define @t310 () (_ @t104 @t224 @t307)) % 0.63/0.86 (define @t311 () (_ @t104 @t112 @t307)) % 0.63/0.86 (define @t312 () (not @t311)) % 0.63/0.86 (define @t313 () (or @t312 @t310)) % 0.63/0.86 (define @t314 () (not @t235)) % 0.63/0.86 (define @t315 () (not @t234)) % 0.63/0.86 (define @t316 () (@list @t235)) % 0.63/0.86 (define @t317 () (_ @t104 @t107 @t227)) % 0.63/0.86 (define @t318 () (_ @t104 @t228 @t227)) % 0.63/0.86 (define @t319 () (not @t318)) % 0.63/0.86 (define @t320 () (forall @t9 (or @t231 @t111))) % 0.63/0.86 (define @t321 () (not @t320)) % 0.63/0.86 (define @t322 () (or @t321 @t319 @t317)) % 0.63/0.86 (define @t323 () (_ @t104 @t108 @t227)) % 0.63/0.86 (define @t324 () (or @t321 @t319 @t323)) % 0.63/0.86 (define @t325 () (forall @t17 (or (not (_ @t228 @t14)) (_ @t104 @t228 @t14)))) % 0.63/0.86 (define @t326 () (@list @t232)) % 0.63/0.86 (define @t327 () (@quantifiers_skolemize @t320 0)) % 0.63/0.86 (define @t328 () (_ @t228 @t327)) % 0.63/0.86 (define @t329 () (forall @t12 (or @t110 (not (_ @t2 @t327))))) % 0.63/0.86 (define @t330 () (not @t329)) % 0.63/0.86 (define @t331 () (not @t328)) % 0.63/0.86 (define @t332 () (or @t331 @t330)) % 0.63/0.86 (define @t333 () (not @t325)) % 0.63/0.86 (define @t334 () (or @t333 @t331)) % 0.63/0.86 (define @t335 () (not @t332)) % 0.63/0.86 (define @t336 () (or @t230 @t318)) % 0.63/0.86 (define @t337 () (not @t323)) % 0.63/0.86 (define @t338 () (and @t315 @t143)) % 0.63/0.86 (assume @p1 @t53) % 0.63/0.86 (assume @p2 true) % 0.63/0.86 (step @p3 :rule cnf_equiv_neg2 :args (@t115)) % 0.63/0.86 (step @p4 :rule eq-symm :args (@t116 @t111)) % 0.63/0.86 (step @p5 :rule beta-reduce :args ((= @t117 @t111))) % 0.63/0.86 (step @p6 :rule refl :args (@t116)) % 0.63/0.86 (step @p7 :rule cong :premises (@p6 @p5) :args (@t118)) % 0.63/0.86 (step @p8 :rule trans :premises (@p7 @p4)) % 0.63/0.86 (step @p9 :rule cong :premises (@p8) :args (@t119)) % 0.63/0.86 (step @p10 :rule quant-unused-vars :args ((= (forall @t9 true) true))) % 0.63/0.86 (step @p11 :rule eq-refl :args (@t117)) % 0.63/0.86 (step @p12 :rule cong :premises (@p11) :args ((forall @t9 (= @t117 @t117)))) % 0.63/0.86 (step @p13 :rule trans :premises (@p12 @p10)) % 0.63/0.86 (step @p14 :rule refl :args (@t117)) % 0.63/0.86 (step @p15 :rule refl :args (@t4)) % 0.63/0.86 (step @p16 :rule skolem_intro :args (@t113)) % 0.63/0.86 (step @p17 :rule ho_cong :premises (@p16 @p15)) % 0.63/0.86 (step @p18 :rule cong :premises (@p17 @p14) :args (@t118)) % 0.63/0.86 (step @p19 :rule cong :premises (@p18) :args (@t119)) % 0.63/0.86 (step @p20 :rule trans :premises (@p19 @p13)) % 0.63/0.86 (step @p21 :rule true_elim :premises (@p20)) % 0.63/0.86 (step @p22 :rule eq_resolve :premises (@p21 @p9)) % 0.63/0.86 (step @p23 :rule eq-symm :args (@t122 @t114)) % 0.63/0.86 (step @p24 :rule refl :args (@t123)) % 0.63/0.86 (step @p25 :rule cong :premises (@p24 @p23) :args ((=> @t123 @t124))) % 0.63/0.86 (assume-push @p694 @t123) % 0.63/0.86 (step @p27 :rule instantiate :premises (@p22) :args (@t125)) % 0.63/0.86 (step-pop @p695 :rule scope :premises (@p27)) % 0.63/0.86 (step @p28 :rule process_scope :premises (@p695) :args (@t124)) % 0.63/0.86 (step @p30 :rule eq_resolve :premises (@p28 @p25)) % 0.63/0.86 (step @p31 :rule implies_elim :premises (@p30)) % 0.63/0.86 (step @p32 :rule chain_m_resolution :premises (@p31 @p22) :args (@t126 @t127 (@list @t123))) % 0.63/0.86 (step @p33 :rule cnf_equiv_pos1 :args (@t126)) % 0.63/0.86 (step @p34 :rule reordering :premises (@p33) :args ((or @t129 @t122 @t128))) % 0.63/0.86 (step @p35 :rule eq-symm :args (@t130 @t106)) % 0.63/0.86 (step @p36 :rule beta-reduce :args ((= @t131 @t106))) % 0.63/0.86 (step @p37 :rule refl :args (@t130)) % 0.63/0.86 (step @p38 :rule cong :premises (@p37 @p36) :args (@t132)) % 0.63/0.86 (step @p39 :rule trans :premises (@p38 @p35)) % 0.63/0.86 (step @p40 :rule cong :premises (@p39) :args (@t133)) % 0.63/0.86 (step @p41 :rule quant-unused-vars :args ((= (forall @t17 true) true))) % 0.63/0.86 (step @p42 :rule eq-refl :args (@t131)) % 0.63/0.86 (step @p43 :rule cong :premises (@p42) :args ((forall @t17 (= @t131 @t131)))) % 0.63/0.86 (step @p44 :rule trans :premises (@p43 @p41)) % 0.63/0.86 (step @p45 :rule refl :args (@t131)) % 0.63/0.86 (step @p46 :rule refl :args (@t14)) % 0.63/0.86 (step @p47 :rule skolem_intro :args (@t108)) % 0.63/0.86 (step @p48 :rule ho_cong :premises (@p47 @p46)) % 0.63/0.86 (step @p49 :rule cong :premises (@p48 @p45) :args (@t132)) % 0.63/0.86 (step @p50 :rule cong :premises (@p49) :args (@t133)) % 0.63/0.86 (step @p51 :rule trans :premises (@p50 @p44)) % 0.63/0.86 (step @p52 :rule true_elim :premises (@p51)) % 0.63/0.86 (step @p53 :rule eq_resolve :premises (@p52 @p40)) % 0.63/0.86 (step @p54 :rule eq-symm :args (@t135 @t109)) % 0.63/0.86 (step @p55 :rule refl :args (@t136)) % 0.63/0.86 (step @p56 :rule cong :premises (@p55 @p54) :args ((=> @t136 @t137))) % 0.63/0.86 (assume-push @p696 @t136) % 0.63/0.86 (step @p58 :rule instantiate :premises (@p53) :args (@t125)) % 0.63/0.86 (step-pop @p697 :rule scope :premises (@p58)) % 0.63/0.86 (step @p59 :rule process_scope :premises (@p697) :args (@t137)) % 0.63/0.86 (step @p61 :rule eq_resolve :premises (@p59 @p56)) % 0.63/0.86 (step @p62 :rule implies_elim :premises (@p61)) % 0.63/0.86 (step @p63 :rule chain_m_resolution :premises (@p62 @p53) :args (@t138 @t127 (@list @t136))) % 0.63/0.86 (step @p64 :rule bool-double-not-elim :args (@t134)) % 0.63/0.86 (step @p65 :rule refl :args (@t109)) % 0.63/0.86 (step @p66 :rule refl :args (@t139)) % 0.63/0.86 (step @p67 :rule nary_cong :premises (@p66 @p65 @p64) :args ((or @t139 @t109 (not @t135)))) % 0.63/0.86 (step @p68 :rule cnf_equiv_pos2 :args (@t138)) % 0.63/0.86 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.63/0.86 (step @p70 :rule reordering :premises (@p69) :args ((or @t109 @t134 @t139))) % 0.63/0.86 (step @p71 :rule alpha_equiv :args ((forall (@list @t140) (or (not (forall (@list @t141) (or (not (_ @t140 @t141)) (_ @t104 @t140 @t141)))) (not (_ @t140 @t54)))) @t142 (@list @t31 @t2))) % 0.63/0.86 (step @p72 :rule alpha_equiv :args (@t121 (@list @t14 @t2) @t142)) % 0.63/0.86 (step @p73 :rule trans :premises (@p72 @p71)) % 0.63/0.86 (step @p74 :rule equiv_elim2 :premises (@p73)) % 0.63/0.86 (step @p75 :rule chain_m_resolution :premises (@p74 @p70 @p63 @p34 @p32 @p3) :args ((or @t115 @t129) (@list false false true false true) (@list @t134 @t138 @t121 @t126 @t109))) % 0.63/0.86 (step @p76 :rule cnf_equiv_neg1 :args (@t115)) % 0.63/0.86 (step @p77 :rule reordering :premises (@p76) :args ((or @t114 @t109 @t115))) % 0.63/0.86 (step @p78 :rule bool-double-not-elim :args (@t121)) % 0.63/0.86 (step @p79 :rule refl :args (@t114)) % 0.63/0.86 (step @p80 :rule refl :args (@t128)) % 0.63/0.86 (step @p81 :rule nary_cong :premises (@p80 @p79 @p78) :args ((or @t128 @t114 (not @t122)))) % 0.63/0.86 (step @p82 :rule cnf_equiv_pos2 :args (@t126)) % 0.63/0.86 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.63/0.86 (step @p84 :rule reordering :premises (@p83) :args ((or @t114 @t121 @t128))) % 0.63/0.86 (step @p85 :rule cnf_equiv_pos1 :args (@t138)) % 0.63/0.86 (step @p86 :rule reordering :premises (@p85) :args ((or (not @t109) @t135 @t139))) % 0.63/0.86 (step @p87 :rule equiv_elim1 :premises (@p73)) % 0.63/0.86 (step @p88 :rule chain_m_resolution :premises (@p87 @p86 @p63 @p84 @p32 @p77 @p75) :args (@t115 (@list true false false false false true) (@list @t134 @t138 @t121 @t126 @t109 @t114))) % 0.63/0.86 ; WARNING: add trust step for TRUST % 0.63/0.86 ; trust TRUST THEORY_LEMMA % 0.63/0.86 (step @p89 :rule trust :premises () :args ((or @t143 (not @t115)))) % 0.63/0.86 (step @p90 :rule chain_m_resolution :premises (@p89 @p88) :args (@t143 @t127 (@list @t115))) % 0.63/0.86 (step @p91 :rule quant-merge-prenex :args ((= (forall @t51 @t144) @t103))) % 0.63/0.86 (step @p92 :rule alpha_equiv :args (@t145 (@list @t57) (@list @t1))) % 0.63/0.86 (step @p93 :rule quant-unused-vars :args ((= @t147 @t76))) % 0.63/0.86 (step @p94 :rule alpha_equiv :args (@t148 (@list @t77 @t78) (@list @t1 @t149))) % 0.63/0.86 (step @p95 :rule nary_cong :premises (@p94 @p93) :args (@t150)) % 0.63/0.86 (step @p96 :rule quant-miniscope-and :args ((= @t151 @t150))) % 0.63/0.86 (step @p97 :rule trans :premises (@p96 @p95)) % 0.63/0.86 (step @p98 :rule refl :args (@t101)) % 0.63/0.86 (step @p99 :rule nary_cong :premises (@p98 @p97 @p92) :args (@t152)) % 0.63/0.86 (step @p100 :rule quant-miniscope-or :args ((= @t144 @t152))) % 0.63/0.86 (step @p101 :rule trans :premises (@p100 @p99)) % 0.63/0.86 (step @p102 :rule symm :premises (@p101)) % 0.63/0.86 (step @p103 :rule cong :premises (@p102) :args ((forall @t51 @t163))) % 0.63/0.86 (step @p104 :rule trans :premises (@p103 @p91)) % 0.63/0.86 (step @p105 :rule aci_norm :args ((= (or (or @t101 @t162) @t156) @t163))) % 0.63/0.86 (step @p106 :rule refl :args (@t156)) % 0.63/0.86 (step @p107 :rule bool-implies-de-morgan :args (@t161 @t75)) % 0.63/0.86 (step @p108 :rule nary_cong :premises (@p98 @p107) :args ((or @t101 (not @t164)))) % 0.63/0.86 (step @p109 :rule bool-and-de-morgan :args (@t100 @t164 true)) % 0.63/0.86 (step @p110 :rule trans :premises (@p109 @p108)) % 0.63/0.86 (step @p111 :rule nary_cong :premises (@p110 @p106) :args ((or (not @t165) @t156))) % 0.63/0.86 (step @p112 :rule trans :premises (@p111 @p105)) % 0.63/0.86 (step @p113 :rule bool-impl-elim :args (@t165 @t156)) % 0.63/0.86 (step @p114 :rule trans :premises (@p113 @p112)) % 0.63/0.86 (step @p115 :rule cong :premises (@p114) :args ((forall @t51 (=> @t165 @t156)))) % 0.63/0.86 (step @p116 :rule trans :premises (@p115 @p104)) % 0.63/0.86 (step @p117 :rule refl :args ((_ @t5 @t170 @t1))) % 0.63/0.86 (step @p118 :rule refl :args (@t1)) % 0.63/0.86 (step @p119 :rule refl :args (@t58)) % 0.63/0.86 (step @p120 :rule cong :premises (@p119) :args (@t59)) % 0.63/0.86 (step @p121 :rule refl :args (@t60)) % 0.63/0.86 (step @p122 :rule refl :args (@t55)) % 0.63/0.86 (step @p123 :rule cong :premises (@p122) :args (@t56)) % 0.63/0.86 (step @p124 :rule nary_cong :premises (@p123 @p121) :args (@t61)) % 0.63/0.86 (step @p125 :rule cong :premises (@p124) :args (@t62)) % 0.63/0.86 (step @p126 :rule cong :premises (@p125) :args (@t63)) % 0.63/0.86 (step @p127 :rule nary_cong :premises (@p126 @p120) :args (@t64)) % 0.63/0.86 (step @p128 :rule cong :premises (@p127) :args (@t65)) % 0.63/0.86 (step @p129 :rule cong :premises (@p128) :args (@t66)) % 0.63/0.86 (step @p130 :rule cong :premises (@p129) :args (@t67)) % 0.63/0.86 (step @p131 :rule cong :premises (@p130 @p118) :args (@t74)) % 0.63/0.86 (step @p132 :rule trans :premises (@p131 @p117)) % 0.63/0.86 (step @p133 :rule refl :args (@t5)) % 0.63/0.86 (step @p134 :rule ho_cong :premises (@p133 @p130)) % 0.63/0.86 (step @p135 :rule ho_cong :premises (@p134 @p118)) % 0.63/0.86 (step @p136 :rule cong :premises (@p135 @p132) :args ((= @t171 @t74))) % 0.63/0.86 (step @p137 :rule symm :premises (@p136)) % 0.63/0.86 (step @p138 :rule refl :args ((_ @t172 @t1))) % 0.63/0.86 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.63/0.86 (step @p140 :rule refl :args (@t155)) % 0.63/0.86 (step @p141 :rule cong :premises (@p140 @p139) :args (@t173)) % 0.63/0.86 (step @p142 :rule cong :premises (@p141) :args ((forall @t24 @t173))) % 0.63/0.86 (step @p143 :rule refl :args (@t1)) % 0.63/0.86 (step @p144 :rule refl :args (@t8)) % 0.63/0.86 (step @p145 :rule cong :premises (@p144 @p119) :args ((= @t8 @t58))) % 0.63/0.86 (step @p146 :rule symm :premises (@p145)) % 0.63/0.86 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 0.63/0.86 (step @p148 :rule cong :premises (@p147) :args (@t166)) % 0.63/0.86 (step @p149 :rule refl :args (@t63)) % 0.63/0.86 (step @p150 :rule nary_cong :premises (@p149 @p148) :args (@t174)) % 0.63/0.86 (step @p151 :rule cong :premises (@p150) :args ((forall @t12 @t174))) % 0.63/0.86 (step @p152 :rule bool-and-de-morgan :args (@t62 @t8 true)) % 0.63/0.86 (step @p153 :rule cong :premises (@p152) :args (@t176)) % 0.63/0.86 (step @p154 :rule trans :premises (@p153 @p151)) % 0.63/0.86 (step @p155 :rule cong :premises (@p154) :args (@t177)) % 0.63/0.86 (step @p156 :rule exists-elim :args ((= (exists @t12 @t175) @t177))) % 0.63/0.86 (step @p157 :rule trans :premises (@p156 @p155)) % 0.63/0.86 (step @p158 :rule refl :args (@t8)) % 0.63/0.86 (step @p159 :rule refl :args (@t15)) % 0.63/0.86 (step @p160 :rule cong :premises (@p159 @p121) :args ((= @t15 @t60))) % 0.63/0.86 (step @p161 :rule symm :premises (@p160)) % 0.63/0.86 (step @p162 :rule eq_resolve :premises (@p159 @p161)) % 0.63/0.86 (step @p163 :rule refl :args (@t16)) % 0.63/0.86 (step @p164 :rule cong :premises (@p163 @p122) :args ((= @t16 @t55))) % 0.63/0.86 (step @p165 :rule symm :premises (@p164)) % 0.63/0.86 (step @p166 :rule eq_resolve :premises (@p163 @p165)) % 0.63/0.86 (step @p167 :rule cong :premises (@p166) :args (@t167)) % 0.63/0.86 (step @p168 :rule nary_cong :premises (@p167 @p162) :args (@t168)) % 0.63/0.86 (step @p169 :rule cong :premises (@p168) :args (@t169)) % 0.63/0.86 (step @p170 :rule bool-impl-elim :args (@t16 @t15)) % 0.63/0.86 (step @p171 :rule cong :premises (@p170) :args (@t18)) % 0.63/0.86 (step @p172 :rule trans :premises (@p171 @p169)) % 0.63/0.86 (step @p173 :rule nary_cong :premises (@p172 @p158) :args (@t19)) % 0.63/0.86 (step @p174 :rule cong :premises (@p173) :args (@t20)) % 0.63/0.86 (step @p175 :rule trans :premises (@p174 @p157)) % 0.63/0.86 (step @p176 :rule cong :premises (@p175) :args (@t21)) % 0.63/0.86 (step @p177 :rule refl :args (@t5)) % 0.63/0.86 (step @p178 :rule ho_cong :premises (@p177 @p176)) % 0.63/0.86 (step @p179 :rule ho_cong :premises (@p178 @p143)) % 0.63/0.86 (step @p180 :rule refl :args (@t153)) % 0.63/0.86 (step @p181 :rule refl :args (@t3)) % 0.63/0.86 (step @p182 :rule cong :premises (@p181 @p180) :args ((= @t3 @t153))) % 0.63/0.86 (step @p183 :rule symm :premises (@p182)) % 0.63/0.86 (step @p184 :rule eq_resolve :premises (@p181 @p183)) % 0.63/0.86 (step @p185 :rule cong :premises (@p184) :args (@t178)) % 0.63/0.86 (step @p186 :rule refl :args (@t70)) % 0.63/0.86 (step @p187 :rule nary_cong :premises (@p186 @p185) :args (@t179)) % 0.63/0.86 (step @p188 :rule cong :premises (@p187) :args ((forall @t12 @t179))) % 0.63/0.86 (step @p189 :rule bool-and-de-morgan :args (@t69 @t3 true)) % 0.63/0.86 (step @p190 :rule cong :premises (@p189) :args (@t181)) % 0.63/0.86 (step @p191 :rule trans :premises (@p190 @p188)) % 0.63/0.86 (step @p192 :rule cong :premises (@p191) :args (@t182)) % 0.63/0.86 (step @p193 :rule exists-elim :args ((= (exists @t12 @t180) @t182))) % 0.63/0.86 (step @p194 :rule trans :premises (@p193 @p192)) % 0.63/0.86 (step @p195 :rule refl :args (@t3)) % 0.63/0.86 (step @p196 :rule refl :args (@t68)) % 0.63/0.86 (step @p197 :rule refl :args (@t7)) % 0.63/0.86 (step @p198 :rule cong :premises (@p197 @p196) :args ((= @t7 @t68))) % 0.63/0.86 (step @p199 :rule symm :premises (@p198)) % 0.63/0.86 (step @p200 :rule eq_resolve :premises (@p197 @p199)) % 0.63/0.86 (step @p201 :rule nary_cong :premises (@p148 @p200) :args (@t183)) % 0.63/0.86 (step @p202 :rule cong :premises (@p201) :args ((forall @t9 @t183))) % 0.63/0.86 (step @p203 :rule bool-impl-elim :args (@t8 @t7)) % 0.63/0.86 (step @p204 :rule cong :premises (@p203) :args (@t10)) % 0.63/0.86 (step @p205 :rule trans :premises (@p204 @p202)) % 0.63/0.86 (step @p206 :rule nary_cong :premises (@p205 @p195) :args (@t11)) % 0.63/0.86 (step @p207 :rule cong :premises (@p206) :args (@t13)) % 0.63/0.86 (step @p208 :rule trans :premises (@p207 @p194)) % 0.63/0.86 (step @p209 :rule cong :premises (@p208 @p179) :args ((= @t13 @t23))) % 0.63/0.86 (step @p210 :rule eq-symm :args (@t23 @t13)) % 0.63/0.86 (step @p211 :rule trans :premises (@p210 @p209)) % 0.63/0.86 (step @p212 :rule cong :premises (@p211) :args (@t25)) % 0.63/0.86 (step @p213 :rule trans :premises (@p212 @p142)) % 0.63/0.86 (step @p214 :rule refl :args ((_ @t5 @t172 @t1))) % 0.63/0.86 (step @p215 :rule cong :premises (@p134 @p118) :args (@t73)) % 0.63/0.86 (step @p216 :rule trans :premises (@p215 @p214)) % 0.63/0.86 (step @p217 :rule ho_cong :premises (@p133 @p134)) % 0.63/0.86 (step @p218 :rule ho_cong :premises (@p217 @p118)) % 0.63/0.86 (step @p219 :rule cong :premises (@p218 @p216) :args ((= @t184 @t73))) % 0.63/0.86 (step @p220 :rule symm :premises (@p219)) % 0.63/0.86 (step @p221 :rule refl :args ((_ (_ @t5 @t172) @t1))) % 0.63/0.86 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 0.63/0.86 (step @p223 :rule cong :premises (@p139) :args (@t185)) % 0.63/0.86 (step @p224 :rule nary_cong :premises (@p223 @p222) :args (@t186)) % 0.63/0.86 (step @p225 :rule cong :premises (@p224) :args ((forall @t24 @t186))) % 0.63/0.86 (step @p226 :rule bool-impl-elim :args (@t171 @t184)) % 0.63/0.86 (step @p227 :rule cong :premises (@p226) :args ((forall @t24 (=> @t171 @t184)))) % 0.63/0.86 (step @p228 :rule trans :premises (@p227 @p225)) % 0.63/0.86 (step @p229 :rule ho_cong :premises (@p177 @p178)) % 0.63/0.86 (step @p230 :rule ho_cong :premises (@p229 @p143)) % 0.63/0.86 (step @p231 :rule cong :premises (@p179 @p230) :args (@t26)) % 0.63/0.86 (step @p232 :rule cong :premises (@p231) :args (@t27)) % 0.63/0.86 (step @p233 :rule trans :premises (@p232 @p228)) % 0.63/0.86 (step @p234 :rule aci_norm :args ((= @t188 @t159))) % 0.63/0.86 (step @p235 :rule cong :premises (@p234) :args (@t189)) % 0.63/0.86 (step @p236 :rule quant-merge-prenex :args ((= (forall @t24 @t191) @t189))) % 0.63/0.86 (step @p237 :rule refl :args (@t74)) % 0.63/0.86 (step @p238 :rule alpha_equiv :args (@t192 (@list @t149) (@list @t2))) % 0.63/0.86 (step @p239 :rule nary_cong :premises (@p238 @p237) :args (@t193)) % 0.63/0.86 (step @p240 :rule quant-miniscope-or :args ((= @t191 @t193))) % 0.63/0.86 (step @p241 :rule trans :premises (@p240 @p239)) % 0.63/0.86 (step @p242 :rule symm :premises (@p241)) % 0.63/0.86 (step @p243 :rule cong :premises (@p242) :args ((forall @t24 (or @t154 @t74)))) % 0.63/0.86 (step @p244 :rule trans :premises (@p243 @p236)) % 0.63/0.86 (step @p245 :rule trans :premises (@p244 @p235)) % 0.63/0.86 (step @p246 :rule refl :args (@t154)) % 0.63/0.86 (step @p247 :rule nary_cong :premises (@p246 @p139) :args (@t194)) % 0.63/0.86 (step @p248 :rule cong :premises (@p247) :args ((forall @t24 @t194))) % 0.63/0.86 (step @p249 :rule trans :premises (@p248 @p245)) % 0.63/0.86 (step @p250 :rule refl :args (@t171)) % 0.63/0.86 (step @p251 :rule bool-double-not-elim :args (@t154)) % 0.63/0.86 (step @p252 :rule nary_cong :premises (@p251 @p250) :args ((or (not @t155) @t171))) % 0.63/0.86 (step @p253 :rule bool-impl-elim :args (@t155 @t171)) % 0.63/0.86 (step @p254 :rule trans :premises (@p253 @p252)) % 0.63/0.86 (step @p255 :rule cong :premises (@p254) :args ((forall @t24 (=> @t155 @t171)))) % 0.63/0.86 (step @p256 :rule trans :premises (@p255 @p249)) % 0.63/0.86 (step @p257 :rule cong :premises (@p208 @p179) :args (@t28)) % 0.63/0.86 (step @p258 :rule cong :premises (@p257) :args (@t29)) % 0.63/0.86 (step @p259 :rule trans :premises (@p258 @p256)) % 0.63/0.86 (step @p260 :rule cong :premises (@p259 @p233) :args (@t30)) % 0.63/0.86 (step @p261 :rule aci_norm :args ((= @t196 @t98))) % 0.63/0.86 (step @p262 :rule cong :premises (@p261) :args (@t197)) % 0.63/0.86 (step @p263 :rule quant-merge-prenex :args ((= (forall @t47 @t199) @t197))) % 0.63/0.86 (step @p264 :rule alpha_equiv :args (@t200 (@list @t81) @t201)) % 0.63/0.86 (step @p265 :rule refl :args (@t97)) % 0.63/0.86 (step @p266 :rule nary_cong :premises (@p265 @p264) :args (@t202)) % 0.63/0.86 (step @p267 :rule quant-miniscope-or :args ((= @t199 @t202))) % 0.63/0.86 (step @p268 :rule trans :premises (@p267 @p266)) % 0.63/0.86 (step @p269 :rule symm :premises (@p268)) % 0.63/0.86 (step @p270 :rule cong :premises (@p269) :args ((forall @t47 (or @t97 @t205)))) % 0.63/0.86 (step @p271 :rule trans :premises (@p270 @p263)) % 0.63/0.86 (step @p272 :rule trans :premises (@p271 @p262)) % 0.63/0.86 (step @p273 :rule bool-impl-elim :args (@t96 @t205)) % 0.63/0.86 (step @p274 :rule cong :premises (@p273) :args ((forall @t47 (=> @t96 @t205)))) % 0.63/0.86 (step @p275 :rule trans :premises (@p274 @p272)) % 0.63/0.86 (step @p276 :rule refl :args ((_ @t5 @t209 @t4))) % 0.63/0.86 (step @p277 :rule refl :args (@t4)) % 0.63/0.86 (step @p278 :rule refl :args (@t82)) % 0.63/0.86 (step @p279 :rule refl :args (@t83)) % 0.63/0.86 (step @p280 :rule cong :premises (@p279) :args (@t84)) % 0.63/0.86 (step @p281 :rule nary_cong :premises (@p280 @p278) :args (@t85)) % 0.63/0.86 (step @p282 :rule cong :premises (@p281) :args (@t86)) % 0.63/0.86 (step @p283 :rule cong :premises (@p282) :args (@t87)) % 0.63/0.86 (step @p284 :rule nary_cong :premises (@p283 @p123) :args (@t88)) % 0.63/0.86 (step @p285 :rule cong :premises (@p284) :args (@t89)) % 0.63/0.86 (step @p286 :rule cong :premises (@p285) :args (@t90)) % 0.63/0.86 (step @p287 :rule cong :premises (@p286) :args (@t91)) % 0.63/0.86 (step @p288 :rule cong :premises (@p287 @p277) :args (@t203)) % 0.63/0.86 (step @p289 :rule trans :premises (@p288 @p276)) % 0.63/0.86 (step @p290 :rule ho_cong :premises (@p133 @p287)) % 0.63/0.86 (step @p291 :rule ho_cong :premises (@p290 @p277)) % 0.63/0.86 (step @p292 :rule cong :premises (@p291 @p289) :args ((= @t210 @t203))) % 0.63/0.86 (step @p293 :rule symm :premises (@p292)) % 0.63/0.86 (step @p294 :rule refl :args ((_ (_ @t5 @t209) @t4))) % 0.63/0.86 (step @p295 :rule eq_resolve :premises (@p294 @p293)) % 0.63/0.86 (step @p296 :rule refl :args (@t204)) % 0.63/0.86 (step @p297 :rule refl :args (@t40)) % 0.63/0.86 (step @p298 :rule cong :premises (@p297 @p296) :args ((= @t40 @t204))) % 0.63/0.86 (step @p299 :rule symm :premises (@p298)) % 0.63/0.86 (step @p300 :rule eq_resolve :premises (@p297 @p299)) % 0.63/0.86 (step @p301 :rule cong :premises (@p300) :args (@t211)) % 0.63/0.86 (step @p302 :rule nary_cong :premises (@p301 @p295) :args (@t212)) % 0.63/0.86 (step @p303 :rule cong :premises (@p302) :args ((forall @t9 @t212))) % 0.63/0.86 (step @p304 :rule bool-impl-elim :args (@t40 @t210)) % 0.63/0.86 (step @p305 :rule cong :premises (@p304) :args ((forall @t9 (=> @t40 @t210)))) % 0.63/0.86 (step @p306 :rule trans :premises (@p305 @p303)) % 0.63/0.86 (step @p307 :rule refl :args (@t87)) % 0.63/0.86 (step @p308 :rule nary_cong :premises (@p307 @p167) :args (@t213)) % 0.63/0.86 (step @p309 :rule cong :premises (@p308) :args ((forall @t12 @t213))) % 0.63/0.86 (step @p310 :rule bool-and-de-morgan :args (@t86 @t16 true)) % 0.63/0.86 (step @p311 :rule cong :premises (@p310) :args (@t215)) % 0.63/0.86 (step @p312 :rule trans :premises (@p311 @p309)) % 0.63/0.86 (step @p313 :rule cong :premises (@p312) :args (@t216)) % 0.63/0.86 (step @p314 :rule exists-elim :args ((= (exists @t12 @t214) @t216))) % 0.63/0.86 (step @p315 :rule trans :premises (@p314 @p313)) % 0.63/0.86 (step @p316 :rule refl :args (@t16)) % 0.63/0.86 (step @p317 :rule refl :args (@t32)) % 0.63/0.86 (step @p318 :rule cong :premises (@p317 @p278) :args ((= @t32 @t82))) % 0.63/0.86 (step @p319 :rule symm :premises (@p318)) % 0.63/0.86 (step @p320 :rule eq_resolve :premises (@p317 @p319)) % 0.63/0.86 (step @p321 :rule refl :args (@t33)) % 0.63/0.86 (step @p322 :rule cong :premises (@p321 @p279) :args ((= @t33 @t83))) % 0.63/0.86 (step @p323 :rule symm :premises (@p322)) % 0.63/0.86 (step @p324 :rule eq_resolve :premises (@p321 @p323)) % 0.63/0.86 (step @p325 :rule cong :premises (@p324) :args (@t206)) % 0.63/0.86 (step @p326 :rule nary_cong :premises (@p325 @p320) :args (@t207)) % 0.63/0.86 (step @p327 :rule cong :premises (@p326) :args (@t208)) % 0.63/0.86 (step @p328 :rule bool-impl-elim :args (@t33 @t32)) % 0.63/0.86 (step @p329 :rule cong :premises (@p328) :args (@t35)) % 0.63/0.86 (step @p330 :rule trans :premises (@p329 @p327)) % 0.63/0.86 (step @p331 :rule nary_cong :premises (@p330 @p316) :args (@t36)) % 0.63/0.86 (step @p332 :rule cong :premises (@p331) :args (@t37)) % 0.63/0.86 (step @p333 :rule trans :premises (@p332 @p315)) % 0.63/0.86 (step @p334 :rule cong :premises (@p333) :args (@t38)) % 0.63/0.86 (step @p335 :rule ho_cong :premises (@p177 @p334)) % 0.63/0.86 (step @p336 :rule ho_cong :premises (@p335 @p15)) % 0.63/0.86 (step @p337 :rule refl :args (@t40)) % 0.63/0.86 (step @p338 :rule cong :premises (@p337 @p336) :args (@t41)) % 0.63/0.86 (step @p339 :rule cong :premises (@p338) :args (@t42)) % 0.63/0.86 (step @p340 :rule trans :premises (@p339 @p306)) % 0.63/0.86 (step @p341 :rule refl :args (@t66)) % 0.63/0.86 (step @p342 :rule refl :args (@t94)) % 0.63/0.86 (step @p343 :rule refl :args (@t43)) % 0.63/0.86 (step @p344 :rule cong :premises (@p343 @p342) :args ((= @t43 @t94))) % 0.63/0.86 (step @p345 :rule symm :premises (@p344)) % 0.63/0.86 (step @p346 :rule eq_resolve :premises (@p343 @p345)) % 0.63/0.86 (step @p347 :rule cong :premises (@p346) :args (@t217)) % 0.63/0.86 (step @p348 :rule nary_cong :premises (@p347 @p341) :args (@t218)) % 0.63/0.86 (step @p349 :rule cong :premises (@p348) :args ((forall @t9 @t218))) % 0.63/0.86 (step @p350 :rule bool-impl-elim :args (@t43 @t66)) % 0.63/0.86 (step @p351 :rule cong :premises (@p350) :args ((forall @t9 (=> @t43 @t66)))) % 0.63/0.86 (step @p352 :rule trans :premises (@p351 @p349)) % 0.63/0.86 (step @p353 :rule refl :args (@t43)) % 0.63/0.86 (step @p354 :rule cong :premises (@p353 @p175) :args (@t44)) % 0.63/0.86 (step @p355 :rule cong :premises (@p354) :args (@t45)) % 0.63/0.86 (step @p356 :rule trans :premises (@p355 @p352)) % 0.63/0.86 (step @p357 :rule cong :premises (@p356 @p340) :args (@t46)) % 0.63/0.86 (step @p358 :rule cong :premises (@p357) :args (@t48)) % 0.63/0.86 (step @p359 :rule trans :premises (@p358 @p275)) % 0.63/0.86 (step @p360 :rule nary_cong :premises (@p359 @p260) :args (@t49)) % 0.63/0.86 (step @p361 :rule cong :premises (@p360 @p213) :args (@t50)) % 0.63/0.86 (step @p362 :rule cong :premises (@p361) :args (@t52)) % 0.63/0.86 (step @p363 :rule trans :premises (@p362 @p116)) % 0.63/0.86 (step @p364 :rule cong :premises (@p363) :args (@t53)) % 0.63/0.86 (step @p365 :rule eq_resolve :premises (@p1 @p364)) % 0.63/0.86 (step @p366 :rule refl :args (@t240)) % 0.63/0.86 (step @p367 :rule bool-double-not-elim :args (@t103)) % 0.63/0.86 (step @p368 :rule nary_cong :premises (@p367 @p366) :args ((or (not @t241) @t240))) % 0.63/0.86 (step @p369 :rule refl :args (@t219)) % 0.63/0.86 (step @p370 :rule eq-refl :args (@t112)) % 0.63/0.86 (step @p371 :rule refl :args (@t112)) % 0.63/0.86 (step @p372 :rule cong :premises (@p371 @p16) :args ((= @t112 @t113))) % 0.63/0.86 (step @p373 :rule trans :premises (@p372 @p370)) % 0.63/0.86 (step @p374 :rule true_elim :premises (@p373)) % 0.63/0.86 (step @p375 :rule cong :premises (@p374 @p369) :args (@t242)) % 0.63/0.86 (step @p376 :rule refl :args (@t222)) % 0.63/0.86 (step @p377 :rule cong :premises (@p376 @p375) :args (@t243)) % 0.63/0.86 (step @p378 :rule refl :args (@t226)) % 0.63/0.86 (step @p379 :rule refl :args (@t230)) % 0.63/0.86 (step @p380 :rule refl :args (@t233)) % 0.63/0.86 (step @p381 :rule refl :args (@t227)) % 0.63/0.86 (step @p382 :rule cong :premises (@p374 @p381) :args (@t244)) % 0.63/0.86 (step @p383 :rule nary_cong :premises (@p382 @p380 @p379) :args (@t245)) % 0.63/0.86 (step @p384 :rule nary_cong :premises (@p383 @p378) :args (@t246)) % 0.63/0.86 (step @p385 :rule refl :args (@t238)) % 0.63/0.86 (step @p386 :rule nary_cong :premises (@p385 @p384 @p377) :args (@t247)) % 0.63/0.86 (step @p387 :rule cong :premises (@p386) :args (@t248)) % 0.63/0.86 (step @p388 :rule refl :args (@t241)) % 0.63/0.86 (step @p389 :rule cong :premises (@p388 @p387) :args ((=> @t241 @t248))) % 0.63/0.86 (assume-push @p698 @t241) % 0.63/0.86 (step @p391 :rule skolemize :premises (@p365)) % 0.63/0.86 (step-pop @p699 :rule scope :premises (@p391)) % 0.63/0.86 (step @p392 :rule process_scope :premises (@p699) :args (@t248)) % 0.63/0.86 (step @p394 :rule eq_resolve :premises (@p392 @p389)) % 0.63/0.86 (step @p395 :rule implies_elim :premises (@p394)) % 0.63/0.86 (step @p396 :rule eq_resolve :premises (@p395 @p368)) % 0.63/0.86 (step @p397 :rule chain_m_resolution :premises (@p396 @p365) :args (@t240 @t249 (@list @t103))) % 0.63/0.86 (step @p398 :rule cnf_or_neg :args (@t239 1)) % 0.63/0.86 (step @p399 :rule chain_m_resolution :premises (@p398 @p397) :args ((not @t236) @t249 @t250)) % 0.63/0.86 (step @p400 :rule cnf_or_neg :args (@t239 2)) % 0.63/0.86 (step @p401 :rule chain_m_resolution :premises (@p400 @p397) :args ((not @t223) @t249 @t250)) % 0.63/0.86 (step @p402 :rule refl :args (@t251)) % 0.63/0.86 (step @p403 :rule bool-double-not-elim :args (@t221)) % 0.63/0.86 (step @p404 :rule refl :args (@t223)) % 0.63/0.86 (step @p405 :rule nary_cong :premises (@p404 @p403 @p402) :args ((or @t223 @t252 @t251))) % 0.63/0.86 (step @p406 :rule cnf_equiv_neg2 :args (@t223)) % 0.63/0.86 (step @p407 :rule eq_resolve :premises (@p406 @p405)) % 0.63/0.86 (step @p408 :rule reordering :premises (@p407) :args ((or @t221 @t223 @t251))) % 0.63/0.86 (step @p409 :rule refl :args (@t260)) % 0.63/0.86 (step @p410 :rule nary_cong :premises (@p403 @p409) :args ((or @t252 @t260))) % 0.63/0.86 (assume-push @p700 @t222) % 0.63/0.86 (step @p412 :rule skolemize :premises (@p700)) % 0.63/0.86 (step-pop @p701 :rule scope :premises (@p412)) % 0.63/0.86 (step @p413 :rule process_scope :premises (@p701) :args (@t260)) % 0.63/0.86 (step @p415 :rule implies_elim :premises (@p413)) % 0.63/0.86 (step @p416 :rule eq_resolve :premises (@p415 @p410)) % 0.63/0.86 (step @p417 :rule bool-double-not-elim :args (@t257)) % 0.63/0.86 (step @p418 :rule refl :args (@t259)) % 0.63/0.86 (step @p419 :rule nary_cong :premises (@p418 @p417) :args ((or @t259 (not @t258)))) % 0.63/0.86 (step @p420 :rule cnf_or_neg :args (@t259 0)) % 0.63/0.86 (step @p421 :rule eq_resolve :premises (@p420 @p419)) % 0.63/0.86 (step @p422 :rule reordering :premises (@p421) :args ((or @t257 @t259))) % 0.63/0.86 (step @p423 :rule bool-double-not-elim :args (@t254)) % 0.63/0.86 (step @p424 :rule nary_cong :premises (@p418 @p423) :args ((or @t259 (not @t255)))) % 0.63/0.86 (step @p425 :rule cnf_or_neg :args (@t259 1)) % 0.63/0.86 (step @p426 :rule eq_resolve :premises (@p425 @p424)) % 0.63/0.86 (step @p427 :rule reordering :premises (@p426) :args ((or @t254 @t259))) % 0.63/0.86 (assume-push @p702 @t257) % 0.63/0.86 (step @p429 :rule instantiate :premises (@p702) :args ((@list @t219))) % 0.63/0.86 (step-pop @p703 :rule scope :premises (@p429)) % 0.63/0.86 (step @p430 :rule process_scope :premises (@p703) :args (@t262)) % 0.63/0.86 (step @p432 :rule implies_elim :premises (@p430)) % 0.63/0.86 (step @p433 :rule alpha_equiv :args (@t257 @t201 @t263)) % 0.63/0.86 (step @p434 :rule equiv_elim1 :premises (@p433)) % 0.63/0.86 (step @p435 :rule cnf_or_pos :args (@t262)) % 0.63/0.86 (step @p436 :rule reordering :premises (@p435) :args ((or @t255 @t261 (not @t262)))) % 0.63/0.86 (step @p437 :rule bool-double-not-elim :args (@t266)) % 0.63/0.86 (step @p438 :rule refl :args (@t270)) % 0.63/0.86 (step @p439 :rule nary_cong :premises (@p438 @p437) :args ((or @t270 (not @t269)))) % 0.63/0.86 (step @p440 :rule cnf_or_neg :args (@t270 0)) % 0.63/0.86 (step @p441 :rule eq_resolve :premises (@p440 @p439)) % 0.63/0.86 (step @p442 :rule reordering :premises (@p441) :args ((or @t266 @t270))) % 0.63/0.86 (step @p443 :rule bool-double-not-elim :args (@t267)) % 0.63/0.86 (step @p444 :rule nary_cong :premises (@p438 @p443) :args ((or @t270 (not @t268)))) % 0.63/0.86 (step @p445 :rule cnf_or_neg :args (@t270 1)) % 0.63/0.86 (step @p446 :rule eq_resolve :premises (@p445 @p444)) % 0.63/0.86 (step @p447 :rule reordering :premises (@p446) :args ((or @t267 @t270))) % 0.63/0.86 (step @p448 :rule cnf_or_pos :args (@t273)) % 0.63/0.86 (step @p449 :rule reordering :premises (@p448) :args ((or @t269 @t272 (not @t273)))) % 0.63/0.86 (assume-push @p704 @t267) % 0.63/0.86 (step @p451 :rule instantiate :premises (@p704) :args ((@list @t253))) % 0.63/0.86 (step-pop @p705 :rule scope :premises (@p451)) % 0.63/0.86 (step @p452 :rule process_scope :premises (@p705) :args (@t273)) % 0.63/0.86 (step @p454 :rule implies_elim :premises (@p452)) % 0.63/0.86 (step @p455 :rule chain_m_resolution :premises (@p454 @p449 @p447 @p442) :args ((or @t270 @t272) @t274 (@list @t273 @t267 @t266))) % 0.63/0.86 (step @p456 :rule refl :args (@t275)) % 0.63/0.86 (step @p457 :rule bool-double-not-elim :args (@t264)) % 0.63/0.86 (step @p458 :rule nary_cong :premises (@p457 @p456) :args ((or (not @t276) @t275))) % 0.63/0.86 (assume-push @p706 @t276) % 0.63/0.86 (step @p460 :rule skolemize :premises (@p706)) % 0.63/0.86 (step-pop @p707 :rule scope :premises (@p460)) % 0.63/0.86 (step @p461 :rule process_scope :premises (@p707) :args (@t275)) % 0.63/0.86 (step @p463 :rule implies_elim :premises (@p461)) % 0.63/0.86 (step @p464 :rule eq_resolve :premises (@p463 @p458)) % 0.63/0.86 (step @p465 :rule bool-double-not-elim :args (@t237)) % 0.63/0.86 (step @p466 :rule refl :args (@t239)) % 0.63/0.86 (step @p467 :rule nary_cong :premises (@p466 @p465) :args ((or @t239 (not @t238)))) % 0.63/0.86 (step @p468 :rule cnf_or_neg :args (@t239 0)) % 0.63/0.86 (step @p469 :rule eq_resolve :premises (@p468 @p467)) % 0.63/0.86 (step @p470 :rule reordering :premises (@p469) :args ((or @t237 @t239))) % 0.63/0.86 (step @p471 :rule chain_m_resolution :premises (@p470 @p397) :args (@t237 @t249 @t250)) % 0.63/0.86 (step @p472 :rule eq-refl :args (@t107)) % 0.63/0.86 (step @p473 :rule refl :args (@t107)) % 0.63/0.86 (step @p474 :rule cong :premises (@p473 @p47) :args ((= @t107 @t108))) % 0.63/0.86 (step @p475 :rule trans :premises (@p474 @p472)) % 0.63/0.86 (step @p476 :rule true_elim :premises (@p475)) % 0.63/0.86 (step @p477 :rule cong :premises (@p476 @p369) :args (@t277)) % 0.63/0.86 (step @p478 :rule refl :args (@t278)) % 0.63/0.86 (step @p479 :rule refl :args (@t276)) % 0.63/0.86 (step @p480 :rule nary_cong :premises (@p479 @p478 @p477) :args (@t279)) % 0.63/0.86 (step @p481 :rule refl :args (@t237)) % 0.63/0.86 (step @p482 :rule cong :premises (@p481 @p480) :args ((=> @t237 @t279))) % 0.63/0.86 (assume-push @p708 @t237) % 0.63/0.86 (step @p484 :rule instantiate :premises (@p471) :args ((@list @t253 @t219))) % 0.63/0.86 (step-pop @p709 :rule scope :premises (@p484)) % 0.63/0.86 (step @p485 :rule process_scope :premises (@p709) :args (@t279)) % 0.63/0.86 (step @p487 :rule eq_resolve :premises (@p485 @p482)) % 0.63/0.86 (step @p488 :rule implies_elim :premises (@p487)) % 0.63/0.86 (step @p489 :rule chain_m_resolution :premises (@p488 @p471) :args (@t281 @t127 @t282)) % 0.63/0.86 (step @p490 :rule cnf_or_pos :args (@t281)) % 0.63/0.86 (step @p491 :rule reordering :premises (@p490) :args ((or @t278 @t276 @t280 (not @t281)))) % 0.63/0.86 (step @p492 :rule refl :args (@t283)) % 0.63/0.86 (step @p493 :rule refl :args (@t284)) % 0.63/0.86 (step @p494 :rule bool-double-not-elim :args (@t220)) % 0.63/0.86 (step @p495 :rule nary_cong :premises (@p494 @p493 @p492) :args ((or (not @t251) @t284 @t283))) % 0.63/0.86 (assume-push @p710 @t251) % 0.63/0.86 (assume-push @p711 @t143) % 0.63/0.86 (assume-push @p712 @t251) % 0.63/0.86 (assume-push @p713 @t143) % 0.63/0.86 (step @p500 :rule false_intro :premises (@p710)) % 0.63/0.86 (step @p501 :rule symm :premises (@p90)) % 0.63/0.86 (step @p502 :rule cong :premises (@p501 @p369) :args (@t280)) % 0.63/0.86 (step @p503 :rule trans :premises (@p502 @p500)) % 0.63/0.86 (step @p504 :rule false_elim :premises (@p503)) % 0.63/0.86 (step-pop @p714 :rule scope :premises (@p504)) % 0.63/0.86 (step-pop @p715 :rule scope :premises (@p714)) % 0.63/0.86 (step @p505 :rule process_scope :premises (@p715) :args (@t283)) % 0.63/0.86 (step @p508 :rule and_intro :premises (@p710 @p90)) % 0.63/0.86 (step @p509 :rule modus_ponens :premises (@p508 @p505)) % 0.63/0.86 (step-pop @p716 :rule scope :premises (@p509)) % 0.63/0.86 (step-pop @p717 :rule scope :premises (@p716)) % 0.63/0.86 (step @p510 :rule process_scope :premises (@p717) :args (@t283)) % 0.63/0.86 (step @p513 :rule implies_elim :premises (@p510)) % 0.63/0.86 (step @p514 :rule cnf_and_neg :args (@t285)) % 0.63/0.86 (step @p515 :rule resolution :premises (@p514 @p513) :args (true @t285)) % 0.63/0.86 (step @p516 :rule eq_resolve :premises (@p515 @p495)) % 0.63/0.86 (step @p517 :rule reordering :premises (@p516) :args ((or @t220 @t283 @t284))) % 0.63/0.86 (step @p518 :rule chain_m_resolution :premises (@p517 @p90 @p491 @p489 @p464 @p455 @p436 @p434 @p432 @p427 @p422 @p416 @p408 @p401) :args (@t221 (@list false false false false false false false false false false true true true) (@list @t143 @t280 @t281 @t264 @t270 @t261 @t271 @t262 @t254 @t257 @t259 @t220 @t223))) % 0.63/0.86 (step @p519 :rule refl :args (@t220)) % 0.63/0.86 (step @p520 :rule refl :args (@t287)) % 0.63/0.86 (step @p521 :rule cong :premises (@p520 @p519) :args ((= @t287 @t220))) % 0.63/0.86 (step @p522 :rule symm :premises (@p521)) % 0.63/0.86 (step @p523 :rule eq_resolve :premises (@p520 @p522)) % 0.63/0.86 (step @p524 :rule cong :premises (@p523) :args (@t288)) % 0.63/0.86 (step @p525 :rule refl :args (@t292)) % 0.63/0.86 (step @p526 :rule nary_cong :premises (@p525 @p524) :args (@t293)) % 0.63/0.86 (step @p527 :rule refl :args (@t221)) % 0.63/0.86 (step @p528 :rule cong :premises (@p527 @p526) :args ((=> @t221 @t293))) % 0.63/0.86 (step @p529 :rule refl :args (@t294)) % 0.63/0.86 (step @p530 :rule cong :premises (@p529) :args (@t295)) % 0.63/0.86 (step @p531 :rule refl :args (@t289)) % 0.63/0.86 (step @p532 :rule refl :args (@t290)) % 0.63/0.86 (step @p533 :rule refl :args (@t296)) % 0.63/0.86 (step @p534 :rule cong :premises (@p533 @p532) :args ((= @t296 @t290))) % 0.63/0.86 (step @p535 :rule symm :premises (@p534)) % 0.63/0.86 (step @p536 :rule eq_resolve :premises (@p533 @p535)) % 0.63/0.86 (step @p537 :rule cong :premises (@p536) :args (@t297)) % 0.63/0.86 (step @p538 :rule nary_cong :premises (@p537 @p531) :args (@t298)) % 0.63/0.86 (step @p539 :rule cong :premises (@p538) :args ((forall @t9 @t298))) % 0.63/0.86 (step @p540 :rule refl :args (@t289)) % 0.63/0.86 (step @p541 :rule refl :args (@t299)) % 0.63/0.86 (step @p542 :rule cong :premises (@p541) :args (@t300)) % 0.63/0.86 (step @p543 :rule nary_cong :premises (@p542 @p540) :args (@t301)) % 0.63/0.86 (step @p544 :rule cong :premises (@p543) :args (@t302)) % 0.63/0.86 (step @p545 :rule trans :premises (@p544 @p539)) % 0.63/0.86 (step @p546 :rule cong :premises (@p545) :args (@t303)) % 0.63/0.86 (step @p547 :rule nary_cong :premises (@p546 @p530) :args (@t304)) % 0.63/0.86 (step @p548 :rule cong :premises (@p527 @p547) :args ((=> @t221 @t304))) % 0.63/0.86 (assume-push @p718 @t221) % 0.63/0.86 (step @p550 :rule instantiate :premises (@p718) :args ((@list @t286))) % 0.63/0.86 (step-pop @p719 :rule scope :premises (@p550)) % 0.63/0.86 (step @p551 :rule process_scope :premises (@p719) :args (@t304)) % 0.63/0.86 (step @p553 :rule eq_resolve :premises (@p551 @p548)) % 0.63/0.86 (step @p554 :rule eq_resolve :premises (@p553 @p528)) % 0.63/0.86 (step @p555 :rule implies_elim :premises (@p554)) % 0.63/0.86 (step @p556 :rule chain_m_resolution :premises (@p555 @p518) :args (@t305 @t127 (@list @t221))) % 0.63/0.86 (step @p557 :rule cnf_equiv_neg1 :args (@t223)) % 0.63/0.86 (step @p558 :rule reordering :premises (@p557) :args ((or @t222 @t220 @t223))) % 0.63/0.86 (step @p559 :rule chain_m_resolution :premises (@p558 @p518 @p401) :args (@t220 (@list false true) (@list @t221 @t223))) % 0.63/0.86 (step @p560 :rule cnf_or_pos :args (@t305)) % 0.63/0.86 (step @p561 :rule reordering :premises (@p560) :args ((or @t251 @t292 (not @t305)))) % 0.63/0.86 (step @p562 :rule chain_m_resolution :premises (@p561 @p559 @p556) :args (@t292 @t306 (@list @t220 @t305))) % 0.63/0.86 (step @p563 :rule refl :args (@t309)) % 0.63/0.86 (step @p564 :rule bool-double-not-elim :args (@t291)) % 0.63/0.86 (step @p565 :rule nary_cong :premises (@p564 @p563) :args ((or (not @t292) @t309))) % 0.63/0.86 (assume-push @p720 @t292) % 0.63/0.86 (step @p567 :rule skolemize :premises (@p720)) % 0.63/0.86 (step-pop @p721 :rule scope :premises (@p567)) % 0.63/0.86 (step @p568 :rule process_scope :premises (@p721) :args (@t309)) % 0.63/0.86 (step @p570 :rule implies_elim :premises (@p568)) % 0.63/0.86 (step @p571 :rule eq_resolve :premises (@p570 @p565)) % 0.63/0.86 (step @p572 :rule chain_m_resolution :premises (@p571 @p562) :args (@t309 @t249 (@list @t291))) % 0.63/0.86 (step @p573 :rule refl :args (@t307)) % 0.63/0.86 (step @p574 :rule refl :args (@t104)) % 0.63/0.86 (step @p575 :rule ho_cong :premises (@p574 @p374)) % 0.63/0.86 (step @p576 :rule cong :premises (@p575 @p573) :args (@t310)) % 0.63/0.86 (step @p577 :rule cong :premises (@p374 @p573) :args (@t311)) % 0.63/0.86 (step @p578 :rule cong :premises (@p577) :args (@t312)) % 0.63/0.86 (step @p579 :rule nary_cong :premises (@p578 @p576) :args (@t313)) % 0.63/0.86 (step @p580 :rule refl :args (@t225)) % 0.63/0.86 (step @p581 :rule cong :premises (@p580 @p579) :args ((=> @t225 @t313))) % 0.63/0.86 (assume-push @p722 @t225) % 0.63/0.86 (step @p583 :rule instantiate :premises (@p722) :args ((@list @t307))) % 0.63/0.86 (step-pop @p723 :rule scope :premises (@p583)) % 0.63/0.86 (step @p584 :rule process_scope :premises (@p723) :args (@t313)) % 0.63/0.86 (step @p586 :rule eq_resolve :premises (@p584 @p581)) % 0.63/0.86 (step @p587 :rule implies_elim :premises (@p586)) % 0.63/0.86 (step @p588 :rule chain_m_resolution :premises (@p587 @p572) :args (@t226 @t249 (@list @t308))) % 0.63/0.86 (step @p589 :rule bool-double-not-elim :args (@t225)) % 0.63/0.86 (step @p590 :rule refl :args (@t314)) % 0.63/0.86 (step @p591 :rule refl :args (@t236)) % 0.63/0.86 (step @p592 :rule nary_cong :premises (@p591 @p590 @p589) :args ((or @t236 @t314 (not @t226)))) % 0.63/0.86 (step @p593 :rule cnf_and_neg :args (@t236)) % 0.63/0.86 (step @p594 :rule eq_resolve :premises (@p593 @p592)) % 0.63/0.86 (step @p595 :rule reordering :premises (@p594) :args ((or @t225 @t236 @t314))) % 0.63/0.86 (step @p596 :rule chain_m_resolution :premises (@p595 @p588 @p399) :args (@t314 (@list true true) (@list @t225 @t236))) % 0.63/0.86 (step @p597 :rule cnf_or_neg :args (@t235 0)) % 0.63/0.86 (step @p598 :rule chain_m_resolution :premises (@p597 @p596) :args (@t315 @t249 @t316)) % 0.63/0.86 (step @p599 :rule cong :premises (@p476 @p381) :args (@t317)) % 0.63/0.86 (step @p600 :rule refl :args (@t319)) % 0.63/0.86 (step @p601 :rule refl :args (@t321)) % 0.63/0.86 (step @p602 :rule nary_cong :premises (@p601 @p600 @p599) :args (@t322)) % 0.63/0.86 (step @p603 :rule cong :premises (@p481 @p602) :args ((=> @t237 @t322))) % 0.63/0.86 (assume-push @p724 @t237) % 0.63/0.86 (step @p605 :rule instantiate :premises (@p471) :args ((@list @t228 @t227))) % 0.63/0.86 (step-pop @p725 :rule scope :premises (@p605)) % 0.63/0.86 (step @p606 :rule process_scope :premises (@p725) :args (@t322)) % 0.63/0.86 (step @p608 :rule eq_resolve :premises (@p606 @p603)) % 0.63/0.86 (step @p609 :rule implies_elim :premises (@p608)) % 0.63/0.86 (step @p610 :rule chain_m_resolution :premises (@p609 @p471) :args (@t324 @t127 @t282)) % 0.63/0.86 (step @p611 :rule bool-double-not-elim :args (@t232)) % 0.63/0.86 (step @p612 :rule refl :args (@t235)) % 0.63/0.86 (step @p613 :rule nary_cong :premises (@p612 @p611) :args ((or @t235 (not @t233)))) % 0.63/0.86 (step @p614 :rule cnf_or_neg :args (@t235 1)) % 0.63/0.86 (step @p615 :rule eq_resolve :premises (@p614 @p613)) % 0.63/0.86 (step @p616 :rule reordering :premises (@p615) :args ((or @t232 @t235))) % 0.63/0.86 (step @p617 :rule chain_m_resolution :premises (@p616 @p596) :args (@t232 @t249 @t316)) % 0.63/0.86 (step @p618 :rule alpha_equiv :args (@t232 @t201 @t263)) % 0.63/0.86 (step @p619 :rule equiv_elim1 :premises (@p618)) % 0.63/0.86 (step @p620 :rule chain_m_resolution :premises (@p619 @p617) :args (@t325 @t127 @t326)) % 0.63/0.86 (step @p621 :rule bool-double-not-elim :args (@t328)) % 0.63/0.86 (step @p622 :rule refl :args (@t332)) % 0.63/0.86 (step @p623 :rule nary_cong :premises (@p622 @p621) :args ((or @t332 (not @t331)))) % 0.63/0.86 (step @p624 :rule cnf_or_neg :args (@t332 0)) % 0.63/0.86 (step @p625 :rule eq_resolve :premises (@p624 @p623)) % 0.63/0.86 (step @p626 :rule reordering :premises (@p625) :args ((or @t328 @t332))) % 0.63/0.86 (step @p627 :rule bool-double-not-elim :args (@t329)) % 0.63/0.86 (step @p628 :rule nary_cong :premises (@p622 @p627) :args ((or @t332 (not @t330)))) % 0.63/0.86 (step @p629 :rule cnf_or_neg :args (@t332 1)) % 0.63/0.86 (step @p630 :rule eq_resolve :premises (@p629 @p628)) % 0.63/0.86 (step @p631 :rule reordering :premises (@p630) :args ((or @t329 @t332))) % 0.63/0.86 (step @p632 :rule cnf_or_pos :args (@t334)) % 0.63/0.86 (step @p633 :rule reordering :premises (@p632) :args ((or @t331 @t333 (not @t334)))) % 0.63/0.86 (assume-push @p726 @t329) % 0.63/0.86 (step @p635 :rule instantiate :premises (@p726) :args ((@list @t228))) % 0.63/0.86 (step-pop @p727 :rule scope :premises (@p635)) % 0.63/0.86 (step @p636 :rule process_scope :premises (@p727) :args (@t334)) % 0.63/0.86 (step @p638 :rule implies_elim :premises (@p636)) % 0.63/0.86 (step @p639 :rule chain_m_resolution :premises (@p638 @p633 @p631 @p626) :args ((or @t332 @t333) @t274 (@list @t334 @t329 @t328))) % 0.63/0.86 (step @p640 :rule chain_m_resolution :premises (@p639 @p620) :args (@t332 @t127 (@list @t325))) % 0.63/0.86 (step @p641 :rule refl :args (@t335)) % 0.63/0.86 (step @p642 :rule bool-double-not-elim :args (@t320)) % 0.63/0.86 (step @p643 :rule nary_cong :premises (@p642 @p641) :args ((or (not @t321) @t335))) % 0.63/0.86 (assume-push @p728 @t321) % 0.63/0.86 (step @p645 :rule skolemize :premises (@p728)) % 0.63/0.86 (step-pop @p729 :rule scope :premises (@p645)) % 0.63/0.86 (step @p646 :rule process_scope :premises (@p729) :args (@t335)) % 0.63/0.86 (step @p648 :rule implies_elim :premises (@p646)) % 0.63/0.86 (step @p649 :rule eq_resolve :premises (@p648 @p643)) % 0.63/0.86 (step @p650 :rule chain_m_resolution :premises (@p649 @p640) :args (@t320 @t127 (@list @t332))) % 0.63/0.86 (assume-push @p730 @t232) % 0.63/0.86 (step @p652 :rule instantiate :premises (@p730) :args ((@list @t227))) % 0.63/0.86 (step-pop @p731 :rule scope :premises (@p652)) % 0.63/0.86 (step @p653 :rule process_scope :premises (@p731) :args (@t336)) % 0.63/0.86 (step @p655 :rule implies_elim :premises (@p653)) % 0.63/0.86 (step @p656 :rule chain_m_resolution :premises (@p655 @p617) :args (@t336 @t127 @t326)) % 0.63/0.86 (step @p657 :rule bool-double-not-elim :args (@t229)) % 0.63/0.86 (step @p658 :rule nary_cong :premises (@p612 @p657) :args ((or @t235 (not @t230)))) % 0.63/0.86 (step @p659 :rule cnf_or_neg :args (@t235 2)) % 0.63/0.86 (step @p660 :rule eq_resolve :premises (@p659 @p658)) % 0.63/0.86 (step @p661 :rule reordering :premises (@p660) :args ((or @t229 @t235))) % 0.63/0.86 (step @p662 :rule chain_m_resolution :premises (@p661 @p596) :args (@t229 @t249 @t316)) % 0.63/0.86 (step @p663 :rule cnf_or_pos :args (@t336)) % 0.63/0.86 (step @p664 :rule reordering :premises (@p663) :args ((or @t230 @t318 (not @t336)))) % 0.63/0.86 (step @p665 :rule chain_m_resolution :premises (@p664 @p662 @p656) :args (@t318 @t306 (@list @t229 @t336))) % 0.63/0.86 (step @p666 :rule cnf_or_pos :args (@t324)) % 0.63/0.86 (step @p667 :rule reordering :premises (@p666) :args ((or @t319 @t321 @t323 (not @t324)))) % 0.63/0.86 (step @p668 :rule chain_m_resolution :premises (@p667 @p665 @p650 @p610) :args (@t323 (@list false false false) (@list @t318 @t320 @t324))) % 0.63/0.86 (step @p669 :rule refl :args (@t337)) % 0.63/0.86 (step @p670 :rule bool-double-not-elim :args (@t234)) % 0.63/0.86 (step @p671 :rule nary_cong :premises (@p670 @p493 @p669) :args ((or (not @t315) @t284 @t337))) % 0.63/0.86 (assume-push @p732 @t315) % 0.63/0.86 (assume-push @p733 @t143) % 0.63/0.86 (assume-push @p734 @t315) % 0.63/0.86 (assume-push @p735 @t143) % 0.63/0.86 (step @p676 :rule false_intro :premises (@p732)) % 0.63/0.86 (step @p501 :rule symm :premises (@p90)) % 0.63/0.86 (step @p677 :rule cong :premises (@p501 @p381) :args (@t323)) % 0.63/0.86 (step @p678 :rule trans :premises (@p677 @p676)) % 0.63/0.86 (step @p679 :rule false_elim :premises (@p678)) % 0.63/0.86 (step-pop @p736 :rule scope :premises (@p679)) % 0.63/0.86 (step-pop @p737 :rule scope :premises (@p736)) % 0.63/0.86 (step @p680 :rule process_scope :premises (@p737) :args (@t337)) % 0.63/0.86 (step @p683 :rule and_intro :premises (@p732 @p90)) % 0.63/0.86 (step @p684 :rule modus_ponens :premises (@p683 @p680)) % 0.63/0.86 (step-pop @p738 :rule scope :premises (@p684)) % 0.63/0.86 (step-pop @p739 :rule scope :premises (@p738)) % 0.63/0.86 (step @p685 :rule process_scope :premises (@p739) :args (@t337)) % 0.63/0.86 (step @p688 :rule implies_elim :premises (@p685)) % 0.63/0.86 (step @p689 :rule cnf_and_neg :args (@t338)) % 0.63/0.86 (step @p690 :rule resolution :premises (@p689 @p688) :args (true @t338)) % 0.63/0.86 (step @p691 :rule eq_resolve :premises (@p690 @p671)) % 0.63/0.86 (step @p692 :rule reordering :premises (@p691) :args ((or @t234 @t337 @t284))) % 0.63/0.86 (step @p693 false :rule chain_m_resolution :premises (@p692 @p668 @p598 @p90) :args (false (@list false true false) (@list @t323 @t234 @t143))) % 0.63/0.86 ) % 0.63/0.86 % SZS output end Proof % 0.63/0.86 % cvc5 exiting %------------------------------------------------------------------------------