%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO515^1 : TPTP v9.2.1. Bugfixed v9.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:13:02 AM UTC 2026 % Result : Theorem 0.39s 0.61s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO515^1 : TPTP v9.2.1. Bugfixed v9.2.1. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n001.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 00:19:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.39/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.61 % SZS status Theorem % 0.39/0.61 % SZS output start Proof % 0.39/0.61 ( % 0.39/0.61 (define tptp.t () (let ((_let_1 (@var "X" Bool))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@list _let_1))) (let ((_let_4 (@var "P" (-> (-> Bool Bool) Bool)))) (lambda (@list _let_4 _let_1) (and (not (_ _let_4 (lambda _let_3 false))) (or (_ _let_4 (lambda _let_3 true)) (= (_ _let_4 (lambda _let_3 _let_2)) _let_2))))))))) % 0.39/0.61 (define @t1 () (@var "P" (-> (-> Bool Bool) Bool))) % 0.39/0.61 (define @t2 () (@var "Y" (-> Bool Bool))) % 0.39/0.61 (define @t3 () (_ @t1 @t2)) % 0.39/0.61 (define @t4 () (@list @t2)) % 0.39/0.61 (define @t5 () (exists @t4 @t3)) % 0.39/0.61 (define @t6 () (=> @t5 (_ @t1 (_ tptp.t @t1)))) % 0.39/0.61 (define @t7 () (@list @t1)) % 0.39/0.61 (define @t8 () (forall @t7 @t6)) % 0.39/0.61 (define @t9 () (not @t8)) % 0.39/0.61 (define @t10 () (@var "X" Bool)) % 0.39/0.61 (define @t11 () (not @t10)) % 0.39/0.61 (define @t12 () (@list @t10)) % 0.39/0.61 (define @t13 () (lambda @t12 @t11)) % 0.39/0.61 (define @t14 () (_ @t1 @t13)) % 0.39/0.61 (define @t15 () (lambda @t12 true)) % 0.39/0.61 (define @t16 () (or (_ @t1 @t15) (= @t14 @t11))) % 0.39/0.61 (define @t17 () (lambda @t12 false)) % 0.39/0.61 (define @t18 () (not (_ @t1 @t17))) % 0.39/0.61 (define @t19 () (and @t18 @t16)) % 0.39/0.61 (define @t20 () (@list @t1 @t10)) % 0.39/0.61 (define @t21 () (lambda @t20 @t19)) % 0.39/0.61 (define @t22 () (@var "BOUND_VARIABLE_7573" Bool)) % 0.39/0.61 (define @t23 () (= @t22 true)) % 0.39/0.61 (define @t24 () (@list @t22)) % 0.39/0.61 (define @t25 () (lambda @t24 (ite @t23 false true))) % 0.39/0.61 (define @t26 () (_ @t1 @t25)) % 0.39/0.61 (define @t27 () (= @t11 @t26)) % 0.39/0.61 (define @t28 () (@var "BOUND_VARIABLE_7594" Bool)) % 0.39/0.61 (define @t29 () (lambda (@list @t28) true)) % 0.39/0.61 (define @t30 () (_ @t1 @t29)) % 0.39/0.61 (define @t31 () (or @t30 @t27)) % 0.39/0.61 (define @t32 () (@var "BOUND_VARIABLE_7613" Bool)) % 0.39/0.61 (define @t33 () (lambda (@list @t32) false)) % 0.39/0.61 (define @t34 () (_ @t1 @t33)) % 0.39/0.61 (define @t35 () (not @t34)) % 0.39/0.61 (define @t36 () (and @t35 @t31)) % 0.39/0.61 (define @t37 () (lambda @t12 @t36)) % 0.39/0.61 (define @t38 () (_ @t1 @t37)) % 0.39/0.61 (define @t39 () (@var "BOUND_VARIABLE_7493" (-> Bool Bool))) % 0.39/0.61 (define @t40 () (not (_ @t1 @t39))) % 0.39/0.61 (define @t41 () (or @t40 @t38)) % 0.39/0.61 (define @t42 () (forall (@list @t1 @t39) @t41)) % 0.39/0.61 (define @t43 () (@list @t39)) % 0.39/0.61 (define @t44 () (forall @t43 @t41)) % 0.39/0.61 (define @t45 () (forall @t43 @t40)) % 0.39/0.61 (define @t46 () (or @t45 @t38)) % 0.39/0.61 (define @t47 () (_ @t1 @t2)) % 0.39/0.61 (define @t48 () (forall @t4 (not @t47))) % 0.39/0.61 (define @t49 () (_ @t1 @t25)) % 0.39/0.61 (define @t50 () (_ @t1 @t29)) % 0.39/0.61 (define @t51 () (_ @t1 @t33)) % 0.39/0.61 (define @t52 () (lambda @t12 (and (not @t51) (or @t50 (= @t11 @t49))))) % 0.39/0.61 (define @t53 () (_ @t1 @t25)) % 0.39/0.61 (define @t54 () (= @t11 @t53)) % 0.39/0.61 (define @t55 () (_ @t1 @t29)) % 0.39/0.61 (define @t56 () (or @t55 @t54)) % 0.39/0.61 (define @t57 () (_ @t1 @t33)) % 0.39/0.61 (define @t58 () (not @t57)) % 0.39/0.61 (define @t59 () (and @t58 @t56)) % 0.39/0.61 (define @t60 () (lambda @t12 @t59)) % 0.39/0.61 (define @t61 () (_ @t1 @t60)) % 0.39/0.61 (define @t62 () (or @t48 @t61)) % 0.39/0.61 (define @t63 () (not @t48)) % 0.39/0.61 (define @t64 () (_ (lambda @t20 @t59) @t1)) % 0.39/0.61 (define @t65 () (not @t3)) % 0.39/0.61 (define @t66 () (forall @t4 @t65)) % 0.39/0.61 (define @t67 () (not @t66)) % 0.39/0.61 (define @t68 () (=> @t5 (_ @t1 @t64))) % 0.39/0.61 (define @t69 () (forall @t7 @t68)) % 0.39/0.61 (define @t70 () (not @t23)) % 0.39/0.61 (define @t71 () (@list @t10)) % 0.39/0.61 (define @t72 () (@quantifiers_skolemize @t42 0)) % 0.39/0.61 (define @t73 () (_ @t72 @t25)) % 0.39/0.61 (define @t74 () (@purify @t73)) % 0.39/0.61 (define @t75 () (= @t11 @t74)) % 0.39/0.61 (define @t76 () (_ @t72 @t29)) % 0.39/0.61 (define @t77 () (@purify @t76)) % 0.39/0.61 (define @t78 () (or @t77 @t75)) % 0.39/0.61 (define @t79 () (_ @t72 @t33)) % 0.39/0.61 (define @t80 () (@purify @t79)) % 0.39/0.61 (define @t81 () (not @t80)) % 0.39/0.61 (define @t82 () (@purify @t81)) % 0.39/0.61 (define @t83 () (and @t82 @t78)) % 0.39/0.61 (define @t84 () (lambda @t12 @t83)) % 0.39/0.61 (define @t85 () (@purify @t84)) % 0.39/0.61 (define @t86 () (_ @t72 @t85)) % 0.39/0.61 (define @t87 () (@quantifiers_skolemize @t42 1)) % 0.39/0.61 (define @t88 () (_ @t72 @t87)) % 0.39/0.61 (define @t89 () (not @t88)) % 0.39/0.61 (define @t90 () (or @t89 @t86)) % 0.39/0.61 (define @t91 () (not @t90)) % 0.39/0.61 (define @t92 () (not @t42)) % 0.39/0.61 (define @t93 () (not @t79)) % 0.39/0.61 (define @t94 () (lambda @t12 (and @t93 (or @t76 (= @t11 @t73))))) % 0.39/0.61 (define @t95 () (_ @t72 @t94)) % 0.39/0.61 (define @t96 () (or @t89 @t95)) % 0.39/0.61 (define @t97 () (not @t96)) % 0.39/0.61 (define @t98 () (@list true)) % 0.39/0.61 (define @t99 () (not @t86)) % 0.39/0.61 (define @t100 () (@list @t90)) % 0.39/0.61 (define @t101 () (@purify @t33)) % 0.39/0.61 (define @t102 () (_ @t72 @t101)) % 0.39/0.61 (define @t103 () (@purify @t29)) % 0.39/0.61 (define @t104 () (_ @t72 @t103)) % 0.39/0.61 (define @t105 () (not @t77)) % 0.39/0.61 (define @t106 () (@const 0 Bool)) % 0.39/0.61 (define @t107 () (@purify @t106)) % 0.39/0.61 (define @t108 () (not @t107)) % 0.39/0.61 (define @t109 () (= @t74 @t108)) % 0.39/0.61 (define @t110 () (or @t77 @t109)) % 0.39/0.61 (define @t111 () (and @t82 @t110)) % 0.39/0.61 (define @t112 () (not @t82)) % 0.39/0.61 (define @t113 () (_ @t103 @t106)) % 0.39/0.61 (define @t114 () (not @t106)) % 0.39/0.61 (define @t115 () (and @t93 (or @t76 (= @t73 @t114)))) % 0.39/0.61 (define @t116 () (or @t76 (= @t114 @t73))) % 0.39/0.61 (define @t117 () (and @t93 @t116)) % 0.39/0.61 (define @t118 () (_ @t94 @t106)) % 0.39/0.61 (define @t119 () (_ @t85 @t106)) % 0.39/0.61 (define @t120 () (= @t119 @t113)) % 0.39/0.61 (define @t121 () (not @t120)) % 0.39/0.61 (define @t122 () (= @t85 @t103)) % 0.39/0.61 (define @t123 () (or @t122 @t121)) % 0.39/0.61 (define @t124 () (not @t122)) % 0.39/0.61 (define @t125 () (not @t104)) % 0.39/0.61 (define @t126 () (not @t99)) % 0.39/0.61 (define @t127 () (= true false)) % 0.39/0.61 (define @t128 () (and @t99 @t122 @t104)) % 0.39/0.61 (define @t129 () (= @t87 @t103)) % 0.39/0.61 (define @t130 () (not @t129)) % 0.39/0.61 (define @t131 () (= false true)) % 0.39/0.61 (define @t132 () (and @t88 @t129 @t125)) % 0.39/0.61 (define @t133 () (@const 1 Bool)) % 0.39/0.61 (define @t134 () (@purify @t133)) % 0.39/0.61 (define @t135 () (_ @t87 @t134)) % 0.39/0.61 (define @t136 () (_ @t103 @t133)) % 0.39/0.61 (define @t137 () (_ @t87 @t133)) % 0.39/0.61 (define @t138 () (= @t137 @t136)) % 0.39/0.61 (define @t139 () (not @t138)) % 0.39/0.61 (define @t140 () (or @t129 @t139)) % 0.39/0.61 (define @t141 () (= @t87 @t101)) % 0.39/0.61 (define @t142 () (not @t141)) % 0.39/0.61 (define @t143 () (not @t102)) % 0.39/0.61 (define @t144 () (and @t88 @t141 @t143)) % 0.39/0.61 (define @t145 () (@const 2 Bool)) % 0.39/0.61 (define @t146 () (@purify @t145)) % 0.39/0.61 (define @t147 () (_ @t87 @t146)) % 0.39/0.61 (define @t148 () (_ @t33 @t145)) % 0.39/0.61 (define @t149 () (_ @t101 @t146)) % 0.39/0.61 (define @t150 () (_ @t101 @t145)) % 0.39/0.61 (define @t151 () (_ @t87 @t145)) % 0.39/0.61 (define @t152 () (= @t151 @t150)) % 0.39/0.61 (define @t153 () (not @t152)) % 0.39/0.61 (define @t154 () (or @t141 @t153)) % 0.39/0.61 (define @t155 () (@purify @t25)) % 0.39/0.61 (define @t156 () (_ @t72 @t155)) % 0.39/0.61 (define @t157 () (not @t74)) % 0.39/0.61 (define @t158 () (@const 3 Bool)) % 0.39/0.61 (define @t159 () (@purify @t158)) % 0.39/0.61 (define @t160 () (not @t159)) % 0.39/0.61 (define @t161 () (= @t74 @t160)) % 0.39/0.61 (define @t162 () (not @t160)) % 0.39/0.61 (define @t163 () (or @t77 @t161)) % 0.39/0.61 (define @t164 () (and @t82 @t163)) % 0.39/0.61 (define @t165 () (not @t164)) % 0.39/0.61 (define @t166 () (= @t160 @t164)) % 0.39/0.61 (define @t167 () (not @t163)) % 0.39/0.61 (define @t168 () (not @t158)) % 0.39/0.61 (define @t169 () (= @t158 true)) % 0.39/0.61 (define @t170 () (not @t169)) % 0.39/0.61 (define @t171 () (_ @t25 @t158)) % 0.39/0.61 (define @t172 () (_ @t155 @t158)) % 0.39/0.61 (define @t173 () (and @t93 (or @t76 (= @t73 @t168)))) % 0.39/0.61 (define @t174 () (or @t76 (= @t168 @t73))) % 0.39/0.61 (define @t175 () (and @t93 @t174)) % 0.39/0.61 (define @t176 () (_ @t94 @t158)) % 0.39/0.61 (define @t177 () (_ @t85 @t158)) % 0.39/0.61 (define @t178 () (= @t177 @t172)) % 0.39/0.61 (define @t179 () (not @t178)) % 0.39/0.61 (define @t180 () (= @t85 @t155)) % 0.39/0.61 (define @t181 () (or @t180 @t179)) % 0.39/0.61 (define @t182 () (not @t180)) % 0.39/0.61 (define @t183 () (not @t156)) % 0.39/0.61 (define @t184 () (and @t99 @t180 @t156)) % 0.39/0.61 (define @t185 () (= @t87 @t155)) % 0.39/0.61 (define @t186 () (not @t185)) % 0.39/0.61 (define @t187 () (and @t88 @t185 @t183)) % 0.39/0.61 (define @t188 () (@const 4 Bool)) % 0.39/0.61 (define @t189 () (@purify @t188)) % 0.39/0.61 (define @t190 () (_ @t87 @t189)) % 0.39/0.61 (define @t191 () (not @t189)) % 0.39/0.61 (define @t192 () (not @t188)) % 0.39/0.61 (define @t193 () (= @t188 true)) % 0.39/0.61 (define @t194 () (not @t193)) % 0.39/0.61 (define @t195 () (_ @t25 @t188)) % 0.39/0.61 (define @t196 () (_ @t155 @t188)) % 0.39/0.61 (define @t197 () (_ @t87 @t188)) % 0.39/0.61 (define @t198 () (= @t197 @t196)) % 0.39/0.61 (define @t199 () (not @t198)) % 0.39/0.61 (define @t200 () (or @t185 @t199)) % 0.39/0.61 (define @t201 () (@const 5 Bool)) % 0.39/0.61 (define @t202 () (@purify @t201)) % 0.39/0.61 (define @t203 () (not @t202)) % 0.39/0.61 (define @t204 () (= @t74 @t203)) % 0.39/0.61 (define @t205 () (or @t77 @t204)) % 0.39/0.61 (define @t206 () (and @t82 @t205)) % 0.39/0.61 (define @t207 () (not @t205)) % 0.39/0.61 (define @t208 () (= @t87 @t85)) % 0.39/0.61 (define @t209 () (not @t208)) % 0.39/0.61 (define @t210 () (and @t88 @t208 @t99)) % 0.39/0.61 (define @t211 () (_ @t87 @t202)) % 0.39/0.61 (define @t212 () (not @t201)) % 0.39/0.61 (define @t213 () (and @t93 (or @t76 (= @t73 @t212)))) % 0.39/0.61 (define @t214 () (or @t76 (= @t212 @t73))) % 0.39/0.61 (define @t215 () (and @t93 @t214)) % 0.39/0.61 (define @t216 () (_ @t94 @t201)) % 0.39/0.61 (define @t217 () (_ @t85 @t201)) % 0.39/0.61 (define @t218 () (_ @t87 @t201)) % 0.39/0.61 (define @t219 () (= @t218 @t217)) % 0.39/0.61 (define @t220 () (not @t219)) % 0.39/0.61 (define @t221 () (or @t208 @t220)) % 0.39/0.61 (define @t222 () (= @t206 @t211)) % 0.39/0.61 (define @t223 () (= @t191 @t190)) % 0.39/0.61 (define @t224 () (not @t190)) % 0.39/0.61 (define @t225 () (not @t211)) % 0.39/0.61 (define @t226 () (not @t225)) % 0.39/0.61 (define @t227 () (and @t202 @t225 @t189)) % 0.39/0.61 (define @t228 () (@list false)) % 0.39/0.61 (define @t229 () (@list @t190)) % 0.39/0.61 (define @t230 () (not @t191)) % 0.39/0.61 (define @t231 () (not @t147)) % 0.39/0.61 (define @t232 () (not @t146)) % 0.39/0.61 (define @t233 () (and @t191 @t147 @t232)) % 0.39/0.61 (define @t234 () (and @t225 @t202 @t146 @t147)) % 0.39/0.61 (define @t235 () (not @t204)) % 0.39/0.61 (define @t236 () (not @t203)) % 0.39/0.61 (define @t237 () (not @t134)) % 0.39/0.61 (define @t238 () (not @t135)) % 0.39/0.61 (define @t239 () (not @t238)) % 0.39/0.61 (define @t240 () (and @t238 @t134 @t146 @t147)) % 0.39/0.61 (define @t241 () (and @t189 @t134 @t238)) % 0.39/0.61 (define @t242 () (@list false false true)) % 0.39/0.61 (define @t243 () (and @t211 @t203 @t237 @t238)) % 0.39/0.61 (define @t244 () (@list @t82)) % 0.39/0.61 (define @t245 () (@const 6 Bool)) % 0.39/0.61 (define @t246 () (@purify @t245)) % 0.39/0.61 (define @t247 () (not @t246)) % 0.39/0.61 (define @t248 () (= @t74 @t247)) % 0.39/0.61 (define @t249 () (or @t77 @t248)) % 0.39/0.61 (define @t250 () (and @t82 @t249)) % 0.39/0.61 (define @t251 () (not @t250)) % 0.39/0.61 (define @t252 () (_ @t33 @t245)) % 0.39/0.61 (define @t253 () (_ @t101 @t246)) % 0.39/0.61 (define @t254 () (_ @t101 @t245)) % 0.39/0.61 (define @t255 () (not @t245)) % 0.39/0.61 (define @t256 () (and @t93 (or @t76 (= @t73 @t255)))) % 0.39/0.61 (define @t257 () (or @t76 (= @t255 @t73))) % 0.39/0.61 (define @t258 () (and @t93 @t257)) % 0.39/0.61 (define @t259 () (_ @t94 @t245)) % 0.39/0.61 (define @t260 () (_ @t85 @t245)) % 0.39/0.61 (define @t261 () (= @t260 @t254)) % 0.39/0.61 (define @t262 () (not @t261)) % 0.39/0.61 (define @t263 () (= @t85 @t101)) % 0.39/0.61 (define @t264 () (or @t263 @t262)) % 0.39/0.61 (define @t265 () (not @t263)) % 0.39/0.61 (define @t266 () (and @t99 @t263 @t102)) % 0.39/0.61 (assume @p1 @t9) % 0.39/0.61 (assume @p2 true) % 0.39/0.61 (step @p3 (= tptp.t @t21) :rule refl :args (@t21)) % 0.39/0.61 (step @p4 :rule quant-merge-prenex :args ((= (forall @t7 @t44) @t42))) % 0.39/0.61 (step @p5 :rule refl :args (@t38)) % 0.39/0.61 (step @p6 :rule alpha_equiv :args (@t45 (@list @t39) (@list @t2))) % 0.39/0.61 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t46)) % 0.39/0.61 (step @p8 :rule quant-miniscope-or :args ((= @t44 @t46))) % 0.39/0.61 (step @p9 :rule trans :premises (@p8 @p7)) % 0.39/0.61 (step @p10 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:args ((or @t88 @t90))) % 0.39/0.61 (step @p290 :rule chain_m_resolution :premises (@p289 @p162) :args (@t88 @t98 @t100)) % 0.39/0.61 (step @p291 :rule refl :args (@t130)) % 0.39/0.61 (step @p292 :rule bool-double-not-elim :args (@t104)) % 0.39/0.61 (step @p293 :rule nary_cong :premises (@p150 @p292 @p291) :args ((or @t89 (not @t125) @t130))) % 0.39/0.61 (assume-push @p1005 @t88) % 0.39/0.61 (assume-push @p1006 @t129) % 0.39/0.61 (assume-push @p1007 @t125) % 0.39/0.61 (step @p297 :rule evaluate :args (@t131)) % 0.39/0.61 (step @p298 :rule true_intro :premises (@p290)) % 0.39/0.61 (step @p299 :rule symm :premises (@p1006)) % 0.39/0.61 (step @p300 :rule cong :premises (@p299) :args (@t104)) % 0.39/0.61 (step @p301 :rule false_intro :premises (@p1007)) % 0.39/0.61 (step @p302 :rule symm :premises (@p301)) % 0.39/0.61 (step @p303 :rule trans :premises (@p302 @p300 @p298)) % 0.39/0.61 (step @p304 false :rule eq_resolve :premises (@p303 @p297)) % 0.39/0.61 (step-pop @p1008 :rule scope :premises (@p304)) % 0.39/0.61 (step-pop @p1009 :rule scope :premises (@p1008)) % 0.39/0.61 (step-pop @p1010 :rule scope :premises (@p1009)) % 0.39/0.61 (step @p305 :rule process_scope :premises (@p1010) :args (false)) % 0.39/0.61 (assume-push @p1011 @t88) % 0.39/0.61 (assume-push @p1012 @t125) % 0.39/0.61 (assume-push @p1013 @t129) % 0.39/0.61 (step @p312 :rule and_intro :premises (@p290 @p1013 @p1012)) % 0.39/0.61 (step-pop @p1014 :rule scope :premises (@p312)) % 0.39/0.61 (step-pop @p1015 :rule scope :premises (@p1014)) % 0.39/0.61 (step-pop @p1016 :rule scope :premises (@p1015)) % 0.39/0.61 (step @p313 :rule process_scope :premises (@p1016) :args (@t132)) % 0.39/0.61 (step @p317 :rule implies_elim :premises (@p313)) % 0.39/0.61 (step @p318 :rule resolution :premises (@p317 @p305) :args (true @t132)) % 0.39/0.61 (step @p319 :rule not_and :premises (@p318)) % 0.39/0.61 (step @p320 :rule eq_resolve :premises (@p319 @p293)) % 0.39/0.61 (step @p321 :rule bool-eq-true :args (@t135)) % 0.39/0.61 (step @p322 :rule beta-reduce :args ((= (_ @t29 @t133) true))) % 0.39/0.61 (step @p323 :rule skolem_intro :args (@t134)) % 0.39/0.61 (step @p324 :rule ho_cong :premises (@p190 @p323)) % 0.39/0.61 (step @p325 :rule bool-eq-true :args ((_ @t103 @t134))) % 0.39/0.61 (step @p326 :rule trans :premises (@p325 @p324 @p322)) % 0.39/0.61 (step @p327 :rule true_elim :premises (@p326)) % 0.39/0.61 (step @p328 :rule eq-refl :args (@t133)) % 0.39/0.61 (step @p329 :rule refl :args (@t133)) % 0.39/0.61 (step @p330 :rule cong :premises (@p329 @p323) :args ((= @t133 @t134))) % 0.39/0.61 (step @p331 :rule trans :premises (@p330 @p328)) % 0.39/0.61 (step @p332 :rule true_elim :premises (@p331)) % 0.39/0.61 (step @p333 :rule cong :premises (@p332) :args (@t136)) % 0.39/0.61 (step @p334 :rule trans :premises (@p333 @p327)) % 0.39/0.61 (step @p335 :rule cong :premises (@p332) :args (@t137)) % 0.39/0.61 (step @p336 :rule cong :premises (@p335 @p334) :args (@t138)) % 0.39/0.61 (step @p337 :rule trans :premises (@p336 @p321)) % 0.39/0.61 (step @p338 :rule cong :premises (@p337) :args (@t139)) % 0.39/0.61 (step @p339 :rule refl :args (@t129)) % 0.39/0.61 (step @p340 :rule nary_cong :premises (@p339 @p338) :args (@t140)) % 0.39/0.61 ; trust TRUST THEORY_LEMMA % 0.39/0.61 (step @p341 :rule trust :premises () :args (@t140)) % 0.39/0.61 (step @p342 :rule eq_resolve :premises (@p341 @p340)) % 0.39/0.61 (step @p343 :rule refl :args (@t142)) % 0.39/0.61 (step @p344 :rule bool-double-not-elim :args (@t102)) % 0.39/0.61 (step @p345 :rule nary_cong :premises (@p150 @p344 @p343) :args ((or @t89 (not @t143) @t142))) % 0.39/0.61 (assume-push @p1017 @t88) % 0.39/0.61 (assume-push @p1018 @t141) % 0.39/0.61 (assume-push @p1019 @t143) % 0.39/0.61 (step @p297 :rule evaluate :args (@t131)) % 0.39/0.61 (step @p298 :rule true_intro :premises (@p290)) % 0.39/0.61 (step @p349 :rule symm :premises (@p1018)) % 0.39/0.61 (step @p350 :rule cong :premises (@p349) :args (@t102)) % 0.39/0.61 (step @p351 :rule false_intro :premises (@p1019)) % 0.39/0.61 (step @p352 :rule symm :premises (@p351)) % 0.39/0.61 (step @p353 :rule trans :premises (@p352 @p350 @p298)) % 0.39/0.61 (step @p354 false :rule eq_resolve :premises (@p353 @p297)) % 0.39/0.61 (step-pop @p1020 :rule scope :premises (@p354)) % 0.39/0.61 (step-pop @p1021 :rule scope :premises (@p1020)) % 0.39/0.61 (step-pop @p1022 :rule scope :premises (@p1021)) % 0.39/0.61 (step @p355 :rule process_scope :premises (@p1022) :args (false)) % 0.39/0.61 (assume-push @p1023 @t88) % 0.39/0.61 (assume-push @p1024 @t143) % 0.39/0.61 (assume-push @p1025 @t141) % 0.39/0.61 (step @p362 :rule and_intro :premises (@p290 @p1025 @p1024)) % 0.39/0.61 (step-pop @p1026 :rule scope :premises (@p362)) % 0.39/0.61 (step-pop @p1027 :rule scope :premises (@p1026)) % 0.39/0.61 (step-pop @p1028 :rule scope :premises (@p1027)) % 0.39/0.61 (step @p363 :rule process_scope :premises (@p1028) :args (@t144)) % 0.39/0.61 (step @p367 :rule implies_elim :premises (@p363)) % 0.39/0.61 (step @p368 :rule resolution :premises (@p367 @p355) :args (true @t144)) % 0.39/0.61 (step @p369 :rule not_and :premises (@p368)) % 0.39/0.61 (step @p370 :rule eq_resolve :premises (@p369 @p345)) % 0.39/0.61 (step @p371 :rule bool-double-not-elim :args (@t147)) % 0.39/0.61 (step @p372 :rule bool-eq-false :args (@t147)) % 0.39/0.61 (step @p373 :rule evaluate :args ((not false))) % 0.39/0.61 (step @p374 :rule beta-reduce :args ((= @t148 false))) % 0.39/0.61 (step @p375 :rule cong :premises (@p374) :args ((not @t148))) % 0.39/0.61 (step @p376 :rule trans :premises (@p375 @p373)) % 0.39/0.61 (step @p377 :rule skolem_intro :args (@t146)) % 0.39/0.61 (step @p378 :rule ho_cong :premises (@p173 @p377)) % 0.39/0.61 (step @p379 :rule cong :premises (@p378) :args ((not @t149))) % 0.39/0.61 (step @p380 :rule bool-eq-false :args (@t149)) % 0.39/0.61 (step @p381 :rule trans :premises (@p380 @p379 @p376)) % 0.39/0.61 (step @p382 :rule true_elim :premises (@p381)) % 0.39/0.61 (step @p383 :rule eq-refl :args (@t145)) % 0.39/0.61 (step @p384 :rule refl :args (@t145)) % 0.39/0.61 (step @p385 :rule cong :premises (@p384 @p377) :args ((= @t145 @t146))) % 0.39/0.61 (step @p386 :rule trans :premises (@p385 @p383)) % 0.39/0.61 (step @p387 :rule true_elim :premises (@p386)) % 0.39/0.61 (step @p388 :rule cong :premises (@p387) :args (@t150)) % 0.39/0.61 (step @p389 :rule trans :premises (@p388 @p382)) % 0.39/0.61 (step @p390 :rule cong :premises (@p387) :args (@t151)) % 0.39/0.61 (step @p391 :rule cong :premises (@p390 @p389) :args (@t152)) % 0.39/0.61 (step @p392 :rule trans :premises (@p391 @p372)) % 0.39/0.61 (step @p393 :rule cong :premises (@p392) :args (@t153)) % 0.39/0.61 (step @p394 :rule trans :premises (@p393 @p371)) % 0.39/0.61 (step @p395 :rule refl :args (@t141)) % 0.39/0.61 (step @p396 :rule nary_cong :premises (@p395 @p394) :args (@t154)) % 0.39/0.61 ; trust TRUST THEORY_LEMMA % 0.39/0.61 (step @p397 :rule trust :premises () :args (@t154)) % 0.39/0.61 (step @p398 :rule eq_resolve :premises (@p397 @p396)) % 0.39/0.61 (step @p399 :rule eq-symm :args (@t156 @t74)) % 0.39/0.61 (step @p400 :rule refl :args (@t74)) % 0.39/0.61 (step @p401 :rule eq-refl :args (@t25)) % 0.39/0.61 (step @p402 :rule trans :premises (@p99 @p90)) % 0.39/0.61 (step @p403 :rule cong :premises (@p91) :args (@t70)) % 0.39/0.61 (step @p404 :rule aci_norm :args ((= (and @t70 true) @t70))) % 0.39/0.61 (step @p405 :rule ite-then-false :args (@t23 true)) % 0.39/0.61 (step @p406 :rule trans :premises (@p405 @p404)) % 0.39/0.61 (step @p407 :rule trans :premises (@p406 @p403)) % 0.39/0.61 (step @p408 :rule cong :premises (@p407) :args (@t25)) % 0.39/0.61 (step @p409 :rule trans :premises (@p408 @p402)) % 0.39/0.61 (step @p410 :rule refl :args (@t25)) % 0.39/0.61 (step @p411 :rule cong :premises (@p410 @p409) :args ((= @t25 @t25))) % 0.39/0.61 (step @p412 :rule trans :premises (@p411 @p401)) % 0.39/0.61 (step @p413 :rule skolem_intro :args (@t155)) % 0.39/0.61 (step @p414 :rule cong :premises (@p410 @p413) :args ((= @t25 @t155))) % 0.39/0.61 (step @p415 :rule trans :premises (@p414 @p412)) % 0.39/0.61 (step @p416 :rule true_elim :premises (@p415)) % 0.39/0.61 (step @p417 :rule cong :premises (@p416) :args (@t73)) % 0.39/0.61 (step @p418 :rule cong :premises (@p417 @p400) :args ((= @t73 @t74))) % 0.39/0.61 (step @p419 :rule trans :premises (@p418 @p399)) % 0.39/0.61 (step @p420 :rule eq-symm :args (@t74 @t73)) % 0.39/0.61 (step @p421 :rule trans :premises (@p420 @p419)) % 0.39/0.61 (step @p422 :rule eq_resolve :premises (@p133 @p421)) % 0.39/0.61 (step @p423 :rule equiv_elim1 :premises (@p422)) % 0.39/0.61 (step @p424 :rule reordering :premises (@p423) :args ((or @t156 @t157))) % 0.39/0.61 (step @p425 :rule bool-double-not-elim :args (@t159)) % 0.39/0.61 (step @p426 :rule refl :args (@t157)) % 0.39/0.61 (step @p427 :rule refl :args (@t161)) % 0.39/0.61 (step @p428 :rule nary_cong :premises (@p427 @p426 @p425) :args ((or @t161 @t157 @t162))) % 0.39/0.61 (step @p429 :rule cnf_equiv_neg2 :args (@t161)) % 0.39/0.61 (step @p430 :rule eq_resolve :premises (@p429 @p428)) % 0.39/0.61 (step @p431 :rule reordering :premises (@p430) :args ((or @t157 @t159 @t161))) % 0.39/0.61 (step @p432 :rule refl :args (@t165)) % 0.39/0.61 (step @p433 :rule refl :args (@t166)) % 0.39/0.61 (step @p434 :rule nary_cong :premises (@p433 @p425 @p432) :args ((or @t166 @t162 @t165))) % 0.39/0.61 (step @p435 :rule cnf_equiv_neg2 :args (@t166)) % 0.39/0.61 (step @p436 :rule eq_resolve :premises (@p435 @p434)) % 0.39/0.61 (step @p437 :rule reordering :premises (@p436) :args ((or @t159 @t166 @t165))) % 0.39/0.61 (step @p438 :rule cnf_or_neg :args (@t163 1)) % 0.39/0.61 (step @p439 :rule cnf_and_neg :args (@t164)) % 0.39/0.61 (step @p440 :rule reordering :premises (@p439) :args ((or @t112 @t164 @t167))) % 0.39/0.61 (step @p441 :rule chain_m_resolution :premises (@p440 @p438 @p437 @p431) :args ((or @t157 @t112 @t159 @t166) (@list false true false) (@list @t163 @t164 @t161))) % 0.39/0.61 (step @p442 :rule cnf_equiv_pos1 :args (@t161)) % 0.39/0.61 (step @p443 :rule reordering :premises (@p442) :args ((or @t157 @t160 (not @t161)))) % 0.39/0.61 (step @p444 :rule cnf_equiv_neg1 :args (@t166)) % 0.39/0.61 (step @p445 :rule reordering :premises (@p444) :args ((or @t160 @t164 @t166))) % 0.39/0.61 (step @p446 :rule cnf_or_pos :args (@t163)) % 0.39/0.61 (step @p447 :rule reordering :premises (@p446) :args ((or @t77 @t161 @t167))) % 0.39/0.61 (step @p448 :rule cnf_and_pos :args (@t164 1)) % 0.39/0.61 (step @p449 :rule reordering :premises (@p448) :args ((or @t163 @t165))) % 0.39/0.61 (step @p450 :rule chain_m_resolution :premises (@p449 @p447 @p445 @p443 @p441 @p282) :args ((or @t157 @t112 @t166) (@list true false true false true) (@list @t163 @t164 @t161 @t159 @t77))) % 0.39/0.61 (step @p451 :rule eq-symm :args (@t164 @t160)) % 0.39/0.61 (step @p452 :rule eq-refl :args (@t168)) % 0.39/0.61 (step @p453 :rule bool-eq-true :args (@t158)) % 0.39/0.61 (step @p454 :rule cong :premises (@p453) :args (@t170)) % 0.39/0.61 (step @p455 :rule aci_norm :args ((= (and @t170 true) @t170))) % 0.39/0.61 (step @p456 :rule ite-then-false :args (@t169 true)) % 0.39/0.61 (step @p457 :rule trans :premises (@p456 @p455)) % 0.39/0.61 (step @p458 :rule trans :premises (@p457 @p454)) % 0.39/0.61 (step @p459 :rule beta-reduce :args ((= @t171 (ite @t169 false true)))) % 0.39/0.61 (step @p460 :rule trans :premises (@p459 @p458)) % 0.39/0.61 (step @p461 :rule refl :args (@t168)) % 0.39/0.61 (step @p462 :rule cong :premises (@p461 @p460) :args ((= @t168 @t171))) % 0.39/0.61 (step @p463 :rule trans :premises (@p462 @p452)) % 0.39/0.61 (step @p464 :rule eq-symm :args (@t171 @t168)) % 0.39/0.61 (step @p465 :rule trans :premises (@p464 @p463)) % 0.39/0.61 (step @p466 :rule skolem_intro :args (@t159)) % 0.39/0.61 (step @p467 :rule cong :premises (@p466) :args (@t160)) % 0.39/0.61 (step @p468 :rule ho_cong :premises (@p413 @p466)) % 0.39/0.61 (step @p469 :rule cong :premises (@p468 @p467) :args ((= (_ @t155 @t159) @t160))) % 0.39/0.61 (step @p470 :rule trans :premises (@p469 @p465)) % 0.39/0.61 (step @p471 :rule true_elim :premises (@p470)) % 0.39/0.61 (step @p472 :rule eq-refl :args (@t158)) % 0.39/0.61 (step @p473 :rule refl :args (@t158)) % 0.39/0.61 (step @p474 :rule cong :premises (@p473 @p466) :args ((= @t158 @t159))) % 0.39/0.61 (step @p475 :rule trans :premises (@p474 @p472)) % 0.39/0.61 (step @p476 :rule true_elim :premises (@p475)) % 0.39/0.61 (step @p477 :rule cong :premises (@p476) :args (@t172)) % 0.39/0.61 (step @p478 :rule trans :premises (@p477 @p471)) % 0.39/0.61 (step @p479 :rule eq-refl :args (@t173)) % 0.39/0.61 (step @p480 :rule eq-symm :args (@t168 @t73)) % 0.39/0.61 (step @p481 :rule nary_cong :premises (@p222 @p480) :args (@t174)) % 0.39/0.61 (step @p482 :rule nary_cong :premises (@p224 @p481) :args (@t175)) % 0.39/0.61 (step @p483 :rule beta-reduce :args ((= @t176 @t175))) % 0.39/0.61 (step @p484 :rule trans :premises (@p483 @p482)) % 0.39/0.61 (step @p485 :rule refl :args (@t173)) % 0.39/0.61 (step @p486 :rule cong :premises (@p485 @p484) :args ((= @t173 @t176))) % 0.39/0.61 (step @p487 :rule trans :premises (@p486 @p479)) % 0.39/0.61 (step @p488 :rule eq-symm :args (@t176 @t173)) % 0.39/0.61 (step @p489 :rule trans :premises (@p488 @p487)) % 0.39/0.61 (step @p490 :rule cong :premises (@p133 @p467) :args (@t161)) % 0.39/0.61 (step @p491 :rule nary_cong :premises (@p135 @p490) :args (@t163)) % 0.39/0.61 (step @p492 :rule nary_cong :premises (@p140 @p491) :args (@t164)) % 0.39/0.61 (step @p493 :rule ho_cong :premises (@p144 @p466)) % 0.39/0.61 (step @p494 :rule cong :premises (@p493 @p492) :args ((= (_ @t85 @t159) @t164))) % 0.39/0.61 (step @p495 :rule trans :premises (@p494 @p489)) % 0.39/0.61 (step @p496 :rule true_elim :premises (@p495)) % 0.39/0.61 (step @p497 :rule cong :premises (@p476) :args (@t177)) % 0.39/0.61 (step @p498 :rule trans :premises (@p497 @p496)) % 0.39/0.61 (step @p499 :rule cong :premises (@p498 @p478) :args (@t178)) % 0.39/0.61 (step @p500 :rule trans :premises (@p499 @p451)) % 0.39/0.61 (step @p501 :rule cong :premises (@p500) :args (@t179)) % 0.39/0.61 (step @p502 :rule refl :args (@t180)) % 0.39/0.61 (step @p503 :rule nary_cong :premises (@p502 @p501) :args (@t181)) % 0.39/0.61 ; trust TRUST THEORY_LEMMA % 0.39/0.61 (step @p504 :rule trust :premises () :args (@t181)) % 0.39/0.61 (step @p505 :rule eq_resolve :premises (@p504 @p503)) % 0.39/0.61 (step @p506 :rule refl :args (@t182)) % 0.39/0.61 (step @p507 :rule refl :args (@t183)) % 0.39/0.61 (step @p508 :rule nary_cong :premises (@p507 @p251 @p506) :args ((or @t183 @t126 @t182))) % 0.39/0.61 (assume-push @p1029 @t99) % 0.39/0.61 (assume-push @p1030 @t180) % 0.39/0.61 (assume-push @p1031 @t156) % 0.39/0.61 (step @p257 :rule evaluate :args (@t127)) % 0.39/0.61 (step @p258 :rule false_intro :premises (@p164)) % 0.39/0.61 (step @p512 :rule symm :premises (@p1030)) % 0.39/0.61 (step @p513 :rule cong :premises (@p512) :args (@t156)) % 0.39/0.61 (step @p514 :rule true_intro :premises (@p1031)) % 0.39/0.61 (step @p515 :rule symm :premises (@p514)) % 0.39/0.61 (step @p516 :rule trans :premises (@p515 @p513 @p258)) % 0.39/0.61 (step @p517 false :rule eq_resolve :premises (@p516 @p257)) % 0.39/0.61 (step-pop @p1032 :rule scope :premises (@p517)) % 0.39/0.61 (step-pop @p1033 :rule scope :premises (@p1032)) % 0.39/0.61 (step-pop @p1034 :rule scope :premises (@p1033)) % 0.39/0.61 (step @p518 :rule process_scope :premises (@p1034) :args (false)) % 0.39/0.61 (assume-push @p1035 @t156) % 0.39/0.61 (assume-push @p1036 @t99) % 0.39/0.61 (assume-push @p1037 @t180) % 0.39/0.61 (step @p525 :rule and_intro :premises (@p164 @p1037 @p1035)) % 0.39/0.61 (step-pop @p1038 :rule scope :premises (@p525)) % 0.39/0.61 (step-pop @p1039 :rule scope :premises (@p1038)) % 0.39/0.61 (step-pop @p1040 :rule scope :premises (@p1039)) % 0.39/0.61 (step @p526 :rule process_scope :premises (@p1040) :args (@t184)) % 0.39/0.61 (step @p530 :rule implies_elim :premises (@p526)) % 0.39/0.61 (step @p531 :rule resolution :premises (@p530 @p518) :args (true @t184)) % 0.39/0.61 (step @p532 :rule not_and :premises (@p531)) % 0.39/0.61 (step @p533 :rule eq_resolve :premises (@p532 @p508)) % 0.39/0.61 (step @p534 :rule reordering :premises (@p533) :args ((or @t86 @t183 @t182))) % 0.39/0.61 (step @p535 :rule chain_m_resolution :premises (@p534 @p164 @p505 @p450 @p424) :args ((or @t157 @t112) (@list true false false false) (@list @t86 @t180 @t166 @t156))) % 0.39/0.61 (step @p536 :rule equiv_elim2 :premises (@p422)) % 0.39/0.61 (step @p537 :rule refl :args (@t186)) % 0.39/0.61 (step @p538 :rule bool-double-not-elim :args (@t156)) % 0.39/0.61 (step @p539 :rule nary_cong :premises (@p150 @p538 @p537) :args ((or @t89 (not @t183) @t186))) % 0.39/0.61 (assume-push @p1041 @t88) % 0.39/0.61 (assume-push @p1042 @t185) % 0.39/0.61 (assume-push @p1043 @t183) % 0.39/0.61 (step @p297 :rule evaluate :args (@t131)) % 0.39/0.61 (step @p298 :rule true_intro :premises (@p290)) % 0.39/0.61 (step @p543 :rule symm :premises (@p1042)) % 0.39/0.61 (step @p544 :rule cong :premises (@p543) :args (@t156)) % 0.39/0.61 (step @p545 :rule false_intro :premises (@p1043)) % 0.39/0.61 (step @p546 :rule symm :premises (@p545)) % 0.39/0.61 (step @p547 :rule trans :premises (@p546 @p544 @p298)) % 0.39/0.61 (step @p548 false :rule eq_resolve :premises (@p547 @p297)) % 0.39/0.61 (step-pop @p1044 :rule scope :premises (@p548)) % 0.39/0.61 (step-pop @p1045 :rule scope :premises (@p1044)) % 0.39/0.61 (step-pop @p1046 :rule scope :premises (@p1045)) % 0.39/0.61 (step @p549 :rule process_scope :premises (@p1046) :args (false)) % 0.39/0.61 (assume-push @p1047 @t88) % 0.39/0.61 (assume-push @p1048 @t183) % 0.39/0.61 (assume-push @p1049 @t185) % 0.39/0.61 (step @p556 :rule and_intro :premises (@p290 @p1049 @p1048)) % 0.39/0.61 (step-pop @p1050 :rule scope :premises (@p556)) % 0.39/0.61 (step-pop @p1051 :rule scope :premises (@p1050)) % 0.39/0.61 (step-pop @p1052 :rule scope :premises (@p1051)) % 0.39/0.61 (step @p557 :rule process_scope :premises (@p1052) :args (@t187)) % 0.39/0.61 (step @p561 :rule implies_elim :premises (@p557)) % 0.39/0.61 (step @p562 :rule resolution :premises (@p561 @p549) :args (true @t187)) % 0.39/0.61 (step @p563 :rule not_and :premises (@p562)) % 0.39/0.61 (step @p564 :rule eq_resolve :premises (@p563 @p539)) % 0.39/0.61 (step @p565 :rule eq-symm :args (@t190 @t191)) % 0.39/0.61 (step @p566 :rule eq-refl :args (@t192)) % 0.39/0.61 (step @p567 :rule bool-eq-true :args (@t188)) % 0.39/0.61 (step @p568 :rule cong :premises (@p567) :args (@t194)) % 0.39/0.61 (step @p569 :rule aci_norm :args ((= (and @t194 true) @t194))) % 0.39/0.61 (step @p570 :rule ite-then-false :args (@t193 true)) % 0.39/0.61 (step @p571 :rule trans :premises (@p570 @p569)) % 0.39/0.61 (step @p572 :rule trans :premises (@p571 @p568)) % 0.39/0.61 (step @p573 :rule beta-reduce :args ((= @t195 (ite @t193 false true)))) % 0.39/0.61 (step @p574 :rule trans :premises (@p573 @p572)) % 0.39/0.61 (step @p575 :rule refl :args (@t192)) % 0.39/0.61 (step @p576 :rule cong :premises (@p575 @p574) :args ((= @t192 @t195))) % 0.39/0.61 (step @p577 :rule trans :premises (@p576 @p566)) % 0.39/0.61 (step @p578 :rule eq-symm :args (@t195 @t192)) % 0.39/0.61 (step @p579 :rule trans :premises (@p578 @p577)) % 0.39/0.61 (step @p580 :rule skolem_intro :args (@t189)) % 0.39/0.61 (step @p581 :rule cong :premises (@p580) :args (@t191)) % 0.39/0.61 (step @p582 :rule ho_cong :premises (@p413 @p580)) % 0.39/0.61 (step @p583 :rule cong :premises (@p582 @p581) :args ((= (_ @t155 @t189) @t191))) % 0.39/0.61 (step @p584 :rule trans :premises (@p583 @p579)) % 0.39/0.61 (step @p585 :rule true_elim :premises (@p584)) % 0.39/0.61 (step @p586 :rule eq-refl :args (@t188)) % 0.39/0.61 (step @p587 :rule refl :args (@t188)) % 0.39/0.61 (step @p588 :rule cong :premises (@p587 @p580) :args ((= @t188 @t189))) % 0.39/0.61 (step @p589 :rule trans :premises (@p588 @p586)) % 0.39/0.61 (step @p590 :rule true_elim :premises (@p589)) % 0.39/0.61 (step @p591 :rule cong :premises (@p590) :args (@t196)) % 0.39/0.61 (step @p592 :rule trans :premises (@p591 @p585)) % 0.39/0.61 (step @p593 :rule cong :premises (@p590) :args (@t197)) % 0.39/0.61 (step @p594 :rule cong :premises (@p593 @p592) :args (@t198)) % 0.39/0.61 (step @p595 :rule trans :premises (@p594 @p565)) % 0.39/0.61 (step @p596 :rule cong :premises (@p595) :args (@t199)) % 0.39/0.61 (step @p597 :rule refl :args (@t185)) % 0.39/0.61 (step @p598 :rule nary_cong :premises (@p597 @p596) :args (@t200)) % 0.39/0.61 ; trust TRUST THEORY_LEMMA % 0.39/0.61 (step @p599 :rule trust :premises () :args (@t200)) % 0.39/0.61 (step @p600 :rule eq_resolve :premises (@p599 @p598)) % 0.39/0.61 (step @p601 :rule cnf_equiv_neg1 :args (@t204)) % 0.39/0.61 (step @p602 :rule reordering :premises (@p601) :args ((or @t74 @t203 @t204))) % 0.39/0.61 (step @p603 :rule cnf_or_neg :args (@t205 1)) % 0.39/0.61 (step @p604 :rule cnf_and_neg :args (@t206)) % 0.39/0.61 (step @p605 :rule reordering :premises (@p604) :args ((or @t112 @t206 @t207))) % 0.39/0.61 (step @p606 :rule refl :args (@t209)) % 0.39/0.61 (step @p607 :rule nary_cong :premises (@p150 @p251 @p606) :args ((or @t89 @t126 @t209))) % 0.39/0.61 (assume-push @p1053 @t88) % 0.39/0.61 (assume-push @p1054 @t208) % 0.39/0.61 (assume-push @p1055 @t99) % 0.39/0.61 (step @p297 :rule evaluate :args (@t131)) % 0.39/0.61 (step @p298 :rule true_intro :premises (@p290)) % 0.39/0.61 (step @p611 :rule symm :premises (@p1054)) % 0.39/0.61 (step @p612 :rule cong :premises (@p611) :args (@t86)) % 0.39/0.61 (step @p258 :rule false_intro :premises (@p164)) % 0.39/0.61 (step @p613 :rule symm :premises (@p258)) % 0.39/0.61 (step @p614 :rule trans :premises (@p613 @p612 @p298)) % 0.39/0.61 (step @p615 false :rule eq_resolve :premises (@p614 @p297)) % 0.39/0.61 (step-pop @p1056 :rule scope :premises (@p615)) % 0.39/0.61 (step-pop @p1057 :rule scope :premises (@p1056)) % 0.39/0.61 (step-pop @p1058 :rule scope :premises (@p1057)) % 0.39/0.61 (step @p616 :rule process_scope :premises (@p1058) :args (false)) % 0.39/0.61 (assume-push @p1059 @t88) % 0.39/0.61 (assume-push @p1060 @t99) % 0.39/0.61 (assume-push @p1061 @t208) % 0.39/0.61 (step @p623 :rule and_intro :premises (@p290 @p1061 @p164)) % 0.39/0.61 (step-pop @p1062 :rule scope :premises (@p623)) % 0.39/0.61 (step-pop @p1063 :rule scope :premises (@p1062)) % 0.39/0.61 (step-pop @p1064 :rule scope :premises (@p1063)) % 0.39/0.61 (step @p624 :rule process_scope :premises (@p1064) :args (@t210)) % 0.39/0.61 (step @p628 :rule implies_elim :premises (@p624)) % 0.39/0.61 (step @p629 :rule resolution :premises (@p628 @p616) :args (true @t210)) % 0.39/0.61 (step @p630 :rule not_and :premises (@p629)) % 0.39/0.61 (step @p631 :rule eq_resolve :premises (@p630 @p607)) % 0.39/0.61 (step @p632 :rule chain_m_resolution :premises (@p631 @p290 @p164) :args (@t209 (@list false true) (@list @t88 @t86))) % 0.39/0.61 (step @p633 :rule eq-symm :args (@t211 @t206)) % 0.39/0.61 (step @p634 :rule eq-refl :args (@t213)) % 0.39/0.61 (step @p635 :rule eq-symm :args (@t212 @t73)) % 0.39/0.61 (step @p636 :rule nary_cong :premises (@p222 @p635) :args (@t214)) % 0.39/0.61 (step @p637 :rule nary_cong :premises (@p224 @p636) :args (@t215)) % 0.39/0.61 (step @p638 :rule beta-reduce :args ((= @t216 @t215))) % 0.39/0.61 (step @p639 :rule trans :premises (@p638 @p637)) % 0.39/0.61 (step @p640 :rule refl :args (@t213)) % 0.39/0.61 (step @p641 :rule cong :premises (@p640 @p639) :args ((= @t213 @t216))) % 0.39/0.61 (step @p642 :rule trans :premises (@p641 @p634)) % 0.39/0.61 (step @p643 :rule eq-symm :args (@t216 @t213)) % 0.39/0.61 (step @p644 :rule trans :premises (@p643 @p642)) % 0.39/0.61 (step @p645 :rule skolem_intro :args (@t202)) % 0.39/0.61 (step @p646 :rule cong :premises (@p645) :args (@t203)) % 0.39/0.61 (step @p647 :rule cong :premises (@p133 @p646) :args (@t204)) % 0.39/0.61 (step @p648 :rule nary_cong :premises (@p135 @p647) :args (@t205)) % 0.39/0.61 (step @p649 :rule nary_cong :premises (@p140 @p648) :args (@t206)) % 0.39/0.61 (step @p650 :rule ho_cong :premises (@p144 @p645)) % 0.39/0.61 (step @p651 :rule cong :premises (@p650 @p649) :args ((= (_ @t85 @t202) @t206))) % 0.39/0.61 (step @p652 :rule trans :premises (@p651 @p644)) % 0.39/0.61 (step @p653 :rule true_elim :premises (@p652)) % 0.39/0.61 (step @p654 :rule eq-refl :args (@t201)) % 0.39/0.61 (step @p655 :rule refl :args (@t201)) % 0.39/0.61 (step @p656 :rule cong :premises (@p655 @p645) :args ((= @t201 @t202))) % 0.39/0.61 (step @p657 :rule trans :premises (@p656 @p654)) % 0.39/0.61 (step @p658 :rule true_elim :premises (@p657)) % 0.39/0.61 (step @p659 :rule cong :premises (@p658) :args (@t217)) % 0.39/0.61 (step @p660 :rule trans :premises (@p659 @p653)) % 0.39/0.61 (step @p661 :rule cong :premises (@p658) :args (@t218)) % 0.39/0.61 (step @p662 :rule cong :premises (@p661 @p660) :args (@t219)) % 0.39/0.61 (step @p663 :rule trans :premises (@p662 @p633)) % 0.39/0.61 (step @p664 :rule cong :premises (@p663) :args (@t220)) % 0.39/0.61 (step @p665 :rule refl :args (@t208)) % 0.39/0.61 (step @p666 :rule nary_cong :premises (@p665 @p664) :args (@t221)) % 0.39/0.61 ; trust TRUST THEORY_LEMMA % 0.39/0.61 (step @p667 :rule trust :premises () :args (@t221)) % 0.39/0.61 (step @p668 :rule eq_resolve :premises (@p667 @p666)) % 0.39/0.61 (step @p669 :rule chain_m_resolution :premises (@p668 @p632) :args ((not @t222) @t98 (@list @t208))) % 0.39/0.61 (step @p670 :rule cnf_equiv_neg2 :args (@t222)) % 0.39/0.61 (step @p671 :rule cnf_equiv_neg1 :args (@t223)) % 0.39/0.61 (step @p672 :rule reordering :premises (@p671) :args ((or @t191 @t190 @t223))) % 0.39/0.61 (step @p673 :rule refl :args (@t224)) % 0.39/0.61 (step @p674 :rule refl :args (@t191)) % 0.39/0.61 (step @p675 :rule bool-double-not-elim :args (@t211)) % 0.39/0.61 (step @p676 :rule refl :args (@t203)) % 0.39/0.61 (step @p677 :rule nary_cong :premises (@p676 @p675 @p674 @p673) :args ((or @t203 @t226 @t191 @t224))) % 0.39/0.61 (assume-push @p1065 @t202) % 0.39/0.61 (assume-push @p1066 @t225) % 0.39/0.61 (assume-push @p1067 @t189) % 0.39/0.61 (assume-push @p1068 @t225) % 0.39/0.61 (assume-push @p1069 @t202) % 0.39/0.61 (assume-push @p1070 @t189) % 0.39/0.61 (step @p684 :rule false_intro :premises (@p1066)) % 0.39/0.61 (step @p685 :rule true_intro :premises (@p1065)) % 0.39/0.61 (step @p686 :rule symm :premises (@p685)) % 0.39/0.61 (step @p687 :rule true_intro :premises (@p1067)) % 0.39/0.61 (step @p688 :rule trans :premises (@p687 @p686)) % 0.39/0.61 (step @p689 :rule cong :premises (@p688) :args (@t190)) % 0.39/0.61 (step @p690 :rule trans :premises (@p689 @p684)) % 0.39/0.61 (step @p691 :rule false_elim :premises (@p690)) % 0.39/0.61 (step-pop @p1071 :rule scope :premises (@p691)) % 0.39/0.61 (step-pop @p1072 :rule scope :premises (@p1071)) % 0.39/0.61 (step-pop @p1073 :rule scope :premises (@p1072)) % 0.39/0.61 (step @p692 :rule process_scope :premises (@p1073) :args (@t224)) % 0.39/0.61 (step @p696 :rule and_intro :premises (@p1066 @p1065 @p1067)) % 0.39/0.61 (step @p697 :rule modus_ponens :premises (@p696 @p692)) % 0.39/0.61 (step-pop @p1074 :rule scope :premises (@p697)) % 0.39/0.61 (step-pop @p1075 :rule scope :premises (@p1074)) % 0.39/0.61 (step-pop @p1076 :rule scope :premises (@p1075)) % 0.39/0.61 (step @p698 :rule process_scope :premises (@p1076) :args (@t224)) % 0.39/0.61 (step @p702 :rule implies_elim :premises (@p698)) % 0.39/0.61 (step @p703 :rule cnf_and_neg :args (@t227)) % 0.39/0.61 (step @p704 :rule resolution :premises (@p703 @p702) :args (true @t227)) % 0.39/0.61 (step @p705 :rule eq_resolve :premises (@p704 @p677)) % 0.39/0.61 (step @p706 :rule chain_m_resolution :premises (@p705 @p672) :args ((or @t203 @t211 @t191 @t223) @t228 @t229)) % 0.39/0.61 (step @p707 :rule bool-double-not-elim :args (@t189)) % 0.39/0.61 (step @p708 :rule refl :args (@t223)) % 0.39/0.61 (step @p709 :rule nary_cong :premises (@p708 @p707 @p673) :args ((or @t223 @t230 @t224))) % 0.39/0.61 (step @p710 :rule cnf_equiv_neg2 :args (@t223)) % 0.39/0.61 (step @p711 :rule eq_resolve :premises (@p710 @p709)) % 0.39/0.61 (step @p712 :rule reordering :premises (@p711) :args ((or @t189 @t223 @t224))) % 0.39/0.61 (step @p713 :rule refl :args (@t190)) % 0.39/0.61 (step @p714 :rule bool-double-not-elim :args (@t146)) % 0.39/0.61 (step @p715 :rule refl :args (@t231)) % 0.39/0.61 (step @p716 :rule nary_cong :premises (@p707 @p715 @p714 @p713) :args ((or @t230 @t231 (not @t232) @t190))) % 0.39/0.61 (assume-push @p1077 @t191) % 0.39/0.61 (assume-push @p1078 @t147) % 0.39/0.61 (assume-push @p1079 @t232) % 0.39/0.61 (assume-push @p1080 @t147) % 0.39/0.61 (assume-push @p1081 @t232) % 0.39/0.61 (assume-push @p1082 @t191) % 0.39/0.61 (step @p723 :rule true_intro :premises (@p1078)) % 0.39/0.61 (step @p724 :rule false_intro :premises (@p1079)) % 0.39/0.61 (step @p725 :rule symm :premises (@p724)) % 0.39/0.61 (step @p726 :rule false_intro :premises (@p1077)) % 0.39/0.61 (step @p727 :rule trans :premises (@p726 @p725)) % 0.39/0.61 (step @p728 :rule cong :premises (@p727) :args (@t190)) % 0.39/0.61 (step @p729 :rule trans :premises (@p728 @p723)) % 0.39/0.61 (step @p730 :rule true_elim :premises (@p729)) % 0.39/0.61 (step-pop @p1083 :rule scope :premises (@p730)) % 0.39/0.61 (step-pop @p1084 :rule scope :premises (@p1083)) % 0.39/0.61 (step-pop @p1085 :rule scope :premises (@p1084)) % 0.39/0.61 (step @p731 :rule process_scope :premises (@p1085) :args (@t190)) % 0.39/0.61 (step @p735 :rule and_intro :premises (@p1078 @p1079 @p1077)) % 0.39/0.61 (step @p736 :rule modus_ponens :premises (@p735 @p731)) % 0.39/0.61 (step-pop @p1086 :rule scope :premises (@p736)) % 0.39/0.61 (step-pop @p1087 :rule scope :premises (@p1086)) % 0.39/0.61 (step-pop @p1088 :rule scope :premises (@p1087)) % 0.39/0.61 (step @p737 :rule process_scope :premises (@p1088) :args (@t190)) % 0.39/0.61 (step @p741 :rule implies_elim :premises (@p737)) % 0.39/0.61 (step @p742 :rule cnf_and_neg :args (@t233)) % 0.39/0.61 (step @p743 :rule resolution :premises (@p742 @p741) :args (true @t233)) % 0.39/0.61 (step @p744 :rule eq_resolve :premises (@p743 @p716)) % 0.39/0.61 (step @p745 :rule reordering :premises (@p744) :args ((or @t189 @t190 @t146 @t231))) % 0.39/0.61 (step @p746 :rule chain_m_resolution :premises (@p745 @p712) :args ((or @t189 @t223 @t146 @t231) @t98 @t229)) % 0.39/0.61 (step @p747 :rule refl :args (@t232)) % 0.39/0.61 (step @p748 :rule nary_cong :premises (@p676 @p675 @p747 @p715) :args ((or @t203 @t226 @t232 @t231))) % 0.39/0.61 (assume-push @p1089 @t225) % 0.39/0.61 (assume-push @p1090 @t202) % 0.39/0.61 (assume-push @p1091 @t146) % 0.39/0.61 (assume-push @p1092 @t147) % 0.39/0.61 (step @p257 :rule evaluate :args (@t127)) % 0.39/0.61 (step @p753 :rule false_intro :premises (@p1089)) % 0.39/0.61 (step @p754 :rule true_intro :premises (@p1090)) % 0.39/0.61 (step @p755 :rule symm :premises (@p754)) % 0.39/0.61 (step @p756 :rule true_intro :premises (@p1091)) % 0.39/0.61 (step @p757 :rule trans :premises (@p756 @p755)) % 0.39/0.61 (step @p758 :rule cong :premises (@p757) :args (@t147)) % 0.39/0.61 (step @p759 :rule true_intro :premises (@p1092)) % 0.39/0.61 (step @p760 :rule symm :premises (@p759)) % 0.39/0.61 (step @p761 :rule trans :premises (@p760 @p758 @p753)) % 0.39/0.61 (step @p762 false :rule eq_resolve :premises (@p761 @p257)) % 0.39/0.61 (step-pop @p1093 :rule scope :premises (@p762)) % 0.39/0.61 (step-pop @p1094 :rule scope :premises (@p1093)) % 0.39/0.61 (step-pop @p1095 :rule scope :premises (@p1094)) % 0.39/0.61 (step-pop @p1096 :rule scope :premises (@p1095)) % 0.39/0.61 (step @p763 :rule process_scope :premises (@p1096) :args (false)) % 0.39/0.61 (assume-push @p1097 @t202) % 0.39/0.61 (assume-push @p1098 @t225) % 0.39/0.61 (assume-push @p1099 @t146) % 0.39/0.61 (assume-push @p1100 @t147) % 0.39/0.61 (step @p772 :rule and_intro :premises (@p1098 @p1097 @p1099 @p1100)) % 0.39/0.61 (step-pop @p1101 :rule scope :premises (@p772)) % 0.39/0.61 (step-pop @p1102 :rule scope :premises (@p1101)) % 0.39/0.61 (step-pop @p1103 :rule scope :premises (@p1102)) % 0.39/0.61 (step-pop @p1104 :rule scope :premises (@p1103)) % 0.39/0.61 (step @p773 :rule process_scope :premises (@p1104) :args (@t234)) % 0.39/0.61 (step @p778 :rule implies_elim :premises (@p773)) % 0.39/0.61 (step @p779 :rule resolution :premises (@p778 @p763) :args (true @t234)) % 0.39/0.61 (step @p780 :rule not_and :premises (@p779)) % 0.39/0.61 (step @p781 :rule eq_resolve :premises (@p780 @p748)) % 0.39/0.61 (step @p782 :rule reordering :premises (@p781) :args ((or @t203 @t211 @t231 @t232))) % 0.39/0.61 (step @p783 :rule chain_m_resolution :premises (@p782 @p746 @p706 @p670 @p669 @p605 @p603 @p602 @p600 @p564 @p536 @p535 @p398 @p370 @p289 @p161 @p128 @p183 @p166) :args ((or @t112 @t203) (@list false true true true false false false true true true true false true false true true true true) (@list @t146 @t189 @t211 @t222 @t206 @t205 @t204 @t223 @t185 @t156 @t74 @t147 @t141 @t88 @t90 @t42 @t102 @t80))) % 0.39/0.61 (step @p784 :rule bool-double-not-elim :args (@t202)) % 0.39/0.61 (step @p785 :rule refl :args (@t235)) % 0.39/0.61 (step @p786 :rule nary_cong :premises (@p785 @p400 @p784) :args ((or @t235 @t74 @t236))) % 0.39/0.61 (step @p787 :rule cnf_equiv_pos2 :args (@t204)) % 0.39/0.61 (step @p788 :rule eq_resolve :premises (@p787 @p786)) % 0.39/0.61 (step @p789 :rule reordering :premises (@p788) :args ((or @t74 @t202 @t235))) % 0.39/0.61 (step @p790 :rule cnf_or_pos :args (@t205)) % 0.39/0.61 (step @p791 :rule reordering :premises (@p790) :args ((or @t77 @t204 @t207))) % 0.39/0.61 (step @p792 :rule cnf_and_pos :args (@t206 1)) % 0.39/0.61 (step @p793 :rule reordering :premises (@p792) :args ((or @t205 (not @t206)))) % 0.39/0.61 (step @p794 :rule cnf_equiv_neg1 :args (@t222)) % 0.39/0.61 (step @p795 :rule reordering :premises (@p794) :args ((or @t206 @t211 @t222))) % 0.39/0.61 (step @p796 :rule bool-double-not-elim :args (@t135)) % 0.39/0.61 (step @p797 :rule refl :args (@t237)) % 0.39/0.61 (step @p798 :rule nary_cong :premises (@p797 @p796 @p747 @p715) :args ((or @t237 @t239 @t232 @t231))) % 0.39/0.61 (assume-push @p1105 @t238) % 0.39/0.61 (assume-push @p1106 @t134) % 0.39/0.61 (assume-push @p1107 @t146) % 0.39/0.61 (assume-push @p1108 @t147) % 0.39/0.61 (step @p257 :rule evaluate :args (@t127)) % 0.39/0.61 (step @p803 :rule false_intro :premises (@p1105)) % 0.39/0.61 (step @p804 :rule true_intro :premises (@p1106)) % 0.39/0.61 (step @p805 :rule symm :premises (@p804)) % 0.39/0.61 (step @p806 :rule true_intro :premises (@p1107)) % 0.39/0.61 (step @p807 :rule trans :premises (@p806 @p805)) % 0.39/0.61 (step @p808 :rule cong :premises (@p807) :args (@t147)) % 0.39/0.61 (step @p809 :rule true_intro :premises (@p1108)) % 0.39/0.61 (step @p810 :rule symm :premises (@p809)) % 0.39/0.61 (step @p811 :rule trans :premises (@p810 @p808 @p803)) % 0.39/0.61 (step @p812 false :rule eq_resolve :premises (@p811 @p257)) % 0.39/0.61 (step-pop @p1109 :rule scope :premises (@p812)) % 0.39/0.61 (step-pop @p1110 :rule scope :premises (@p1109)) % 0.39/0.61 (step-pop @p1111 :rule scope :premises (@p1110)) % 0.39/0.61 (step-pop @p1112 :rule scope :premises (@p1111)) % 0.39/0.61 (step @p813 :rule process_scope :premises (@p1112) :args (false)) % 0.39/0.61 (assume-push @p1113 @t134) % 0.39/0.61 (assume-push @p1114 @t238) % 0.39/0.61 (assume-push @p1115 @t146) % 0.39/0.61 (assume-push @p1116 @t147) % 0.39/0.61 (step @p822 :rule and_intro :premises (@p1114 @p1113 @p1115 @p1116)) % 0.39/0.61 (step-pop @p1117 :rule scope :premises (@p822)) % 0.39/0.61 (step-pop @p1118 :rule scope :premises (@p1117)) % 0.39/0.61 (step-pop @p1119 :rule scope :premises (@p1118)) % 0.39/0.61 (step-pop @p1120 :rule scope :premises (@p1119)) % 0.39/0.61 (step @p823 :rule process_scope :premises (@p1120) :args (@t240)) % 0.39/0.61 (step @p828 :rule implies_elim :premises (@p823)) % 0.39/0.61 (step @p829 :rule resolution :premises (@p828 @p813) :args (true @t240)) % 0.39/0.61 (step @p830 :rule not_and :premises (@p829)) % 0.39/0.61 (step @p831 :rule eq_resolve :premises (@p830 @p798)) % 0.39/0.61 (step @p832 :rule reordering :premises (@p831) :args ((or @t135 @t237 @t231 @t232))) % 0.39/0.61 (step @p833 :rule nary_cong :premises (@p674 @p797 @p796 @p673) :args ((or @t191 @t237 @t239 @t224))) % 0.39/0.61 (assume-push @p1121 @t189) % 0.39/0.61 (assume-push @p1122 @t134) % 0.39/0.61 (assume-push @p1123 @t238) % 0.39/0.61 (assume-push @p1124 @t238) % 0.39/0.61 (assume-push @p1125 @t134) % 0.39/0.61 (assume-push @p1126 @t189) % 0.39/0.61 (step @p840 :rule false_intro :premises (@p1123)) % 0.39/0.61 (step @p841 :rule true_intro :premises (@p1122)) % 0.39/0.61 (step @p842 :rule symm :premises (@p841)) % 0.39/0.61 (step @p843 :rule true_intro :premises (@p1121)) % 0.39/0.61 (step @p844 :rule trans :premises (@p843 @p842)) % 0.39/0.61 (step @p845 :rule cong :premises (@p844) :args (@t190)) % 0.39/0.61 (step @p846 :rule trans :premises (@p845 @p840)) % 0.39/0.61 (step @p847 :rule false_elim :premises (@p846)) % 0.39/0.61 (step-pop @p1127 :rule scope :premises (@p847)) % 0.39/0.61 (step-pop @p1128 :rule scope :premises (@p1127)) % 0.39/0.61 (step-pop @p1129 :rule scope :premises (@p1128)) % 0.39/0.61 (step @p848 :rule process_scope :premises (@p1129) :args (@t224)) % 0.39/0.61 (step @p852 :rule and_intro :premises (@p1123 @p1122 @p1121)) % 0.39/0.61 (step @p853 :rule modus_ponens :premises (@p852 @p848)) % 0.39/0.61 (step-pop @p1130 :rule scope :premises (@p853)) % 0.39/0.61 (step-pop @p1131 :rule scope :premises (@p1130)) % 0.39/0.61 (step-pop @p1132 :rule scope :premises (@p1131)) % 0.39/0.61 (step @p854 :rule process_scope :premises (@p1132) :args (@t224)) % 0.39/0.61 (step @p858 :rule implies_elim :premises (@p854)) % 0.39/0.61 (step @p859 :rule cnf_and_neg :args (@t241)) % 0.39/0.61 (step @p860 :rule resolution :premises (@p859 @p858) :args (true @t241)) % 0.39/0.61 (step @p861 :rule eq_resolve :premises (@p860 @p833)) % 0.39/0.61 (step @p862 :rule reordering :premises (@p861) :args ((or @t191 @t224 @t135 @t237))) % 0.39/0.61 (step @p863 :rule chain_m_resolution :premises (@p862 @p672 @p746 @p832) :args ((or @t223 @t135 @t237 @t231) @t242 (@list @t190 @t189 @t146))) % 0.39/0.61 (step @p864 :rule bool-double-not-elim :args (@t134)) % 0.39/0.61 (step @p865 :rule refl :args (@t225)) % 0.39/0.61 (step @p866 :rule nary_cong :premises (@p784 @p865 @p796 @p864) :args ((or @t236 @t225 @t239 (not @t237)))) % 0.39/0.61 (assume-push @p1133 @t211) % 0.39/0.61 (assume-push @p1134 @t203) % 0.39/0.61 (assume-push @p1135 @t237) % 0.39/0.61 (assume-push @p1136 @t238) % 0.39/0.61 (step @p297 :rule evaluate :args (@t131)) % 0.39/0.61 (step @p871 :rule true_intro :premises (@p1133)) % 0.39/0.61 (step @p872 :rule false_intro :premises (@p1134)) % 0.39/0.61 (step @p873 :rule symm :premises (@p872)) % 0.39/0.61 (step @p874 :rule false_intro :premises (@p1135)) % 0.39/0.61 (step @p875 :rule trans :premises (@p874 @p873)) % 0.39/0.61 (step @p876 :rule cong :premises (@p875) :args (@t135)) % 0.39/0.61 (step @p877 :rule false_intro :premises (@p1136)) % 0.39/0.61 (step @p878 :rule symm :premises (@p877)) % 0.39/0.61 (step @p879 :rule trans :premises (@p878 @p876 @p871)) % 0.39/0.61 (step @p880 false :rule eq_resolve :premises (@p879 @p297)) % 0.39/0.61 (step-pop @p1137 :rule scope :premises (@p880)) % 0.39/0.61 (step-pop @p1138 :rule scope :premises (@p1137)) % 0.39/0.61 (step-pop @p1139 :rule scope :premises (@p1138)) % 0.39/0.61 (step-pop @p1140 :rule scope :premises (@p1139)) % 0.39/0.61 (step @p881 :rule process_scope :premises (@p1140) :args (false)) % 0.39/0.61 (assume-push @p1141 @t203) % 0.39/0.61 (assume-push @p1142 @t211) % 0.39/0.61 (assume-push @p1143 @t238) % 0.39/0.61 (assume-push @p1144 @t237) % 0.39/0.61 (step @p890 :rule and_intro :premises (@p1142 @p1141 @p1144 @p1143)) % 0.39/0.61 (step-pop @p1145 :rule scope :premises (@p890)) % 0.39/0.61 (step-pop @p1146 :rule scope :premises (@p1145)) % 0.39/0.61 (step-pop @p1147 :rule scope :premises (@p1146)) % 0.39/0.61 (step-pop @p1148 :rule scope :premises (@p1147)) % 0.39/0.61 (step @p891 :rule process_scope :premises (@p1148) :args (@t243)) % 0.39/0.61 (step @p896 :rule implies_elim :premises (@p891)) % 0.39/0.61 (step @p897 :rule resolution :premises (@p896 @p881) :args (true @t243)) % 0.39/0.61 (step @p898 :rule not_and :premises (@p897)) % 0.39/0.61 (step @p899 :rule eq_resolve :premises (@p898 @p866)) % 0.39/0.61 (step @p900 :rule reordering :premises (@p899) :args ((or @t202 @t225 @t134 @t135))) % 0.39/0.61 (step @p901 :rule chain_m_resolution :premises (@p900 @p863 @p795 @p669 @p793 @p791 @p789 @p783 @p600 @p564 @p290 @p536 @p535 @p398 @p370 @p290 @p342 @p320 @p290 @p283 @p282 @p183 @p166) :args (@t112 (@list true false true true true true true true true false true true false true false true true false true true true true) (@list @t134 @t211 @t222 @t206 @t205 @t204 @t202 @t223 @t185 @t88 @t156 @t74 @t147 @t141 @t88 @t135 @t129 @t88 @t104 @t77 @t102 @t80))) % 0.39/0.61 (step @p902 :rule refl :args (@t82)) % 0.39/0.61 (step @p903 :rule bool-double-not-elim :args (@t80)) % 0.39/0.61 (step @p904 :rule nary_cong :premises (@p903 @p902) :args ((or (not @t81) @t82))) % 0.39/0.61 (step @p905 :rule equiv_elim1 :premises (@p165)) % 0.39/0.61 (step @p906 :rule eq_resolve :premises (@p905 @p904)) % 0.39/0.61 (step @p907 :rule chain_m_resolution :premises (@p906 @p901) :args (@t80 @t98 @t244)) % 0.39/0.61 (step @p908 :rule equiv_elim1 :premises (@p182)) % 0.39/0.61 (step @p909 :rule chain_m_resolution :premises (@p908 @p907) :args (@t102 @t228 (@list @t80))) % 0.39/0.61 (step @p910 :rule cnf_and_pos :args (@t250 0)) % 0.39/0.61 (step @p911 :rule reordering :premises (@p910) :args ((or @t82 @t251))) % 0.39/0.61 (step @p912 :rule chain_m_resolution :premises (@p911 @p901) :args (@t251 @t98 @t244)) % 0.39/0.61 (step @p913 :rule bool-double-not-elim :args (@t250)) % 0.39/0.61 (step @p914 :rule bool-eq-false :args (@t250)) % 0.39/0.61 (step @p915 :rule beta-reduce :args ((= @t252 false))) % 0.39/0.61 (step @p916 :rule cong :premises (@p915) :args ((not @t252))) % 0.39/0.61 (step @p917 :rule trans :premises (@p916 @p373)) % 0.39/0.61 (step @p918 :rule skolem_intro :args (@t246)) % 0.39/0.61 (step @p919 :rule ho_cong :premises (@p173 @p918)) % 0.39/0.61 (step @p920 :rule cong :premises (@p919) :args ((not @t253))) % 0.39/0.61 (step @p921 :rule bool-eq-false :args (@t253)) % 0.39/0.61 (step @p922 :rule trans :premises (@p921 @p920 @p917)) % 0.39/0.61 (step @p923 :rule true_elim :premises (@p922)) % 0.39/0.61 (step @p924 :rule eq-refl :args (@t245)) % 0.39/0.61 (step @p925 :rule refl :args (@t245)) % 0.39/0.61 (step @p926 :rule cong :premises (@p925 @p918) :args ((= @t245 @t246))) % 0.39/0.61 (step @p927 :rule trans :premises (@p926 @p924)) % 0.39/0.61 (step @p928 :rule true_elim :premises (@p927)) % 0.39/0.61 (step @p929 :rule cong :premises (@p928) :args (@t254)) % 0.39/0.61 (step @p930 :rule trans :premises (@p929 @p923)) % 0.39/0.61 (step @p931 :rule eq-refl :args (@t256)) % 0.39/0.61 (step @p932 :rule eq-symm :args (@t255 @t73)) % 0.39/0.61 (step @p933 :rule nary_cong :premises (@p222 @p932) :args (@t257)) % 0.39/0.61 (step @p934 :rule nary_cong :premises (@p224 @p933) :args (@t258)) % 0.39/0.61 (step @p935 :rule beta-reduce :args ((= @t259 @t258))) % 0.39/0.61 (step @p936 :rule trans :premises (@p935 @p934)) % 0.39/0.61 (step @p937 :rule refl :args (@t256)) % 0.39/0.61 (step @p938 :rule cong :premises (@p937 @p936) :args ((= @t256 @t259))) % 0.39/0.61 (step @p939 :rule trans :premises (@p938 @p931)) % 0.39/0.61 (step @p940 :rule eq-symm :args (@t259 @t256)) % 0.39/0.61 (step @p941 :rule trans :premises (@p940 @p939)) % 0.39/0.61 (step @p942 :rule cong :premises (@p918) :args (@t247)) % 0.39/0.61 (step @p943 :rule cong :premises (@p133 @p942) :args (@t248)) % 0.39/0.61 (step @p944 :rule nary_cong :premises (@p135 @p943) :args (@t249)) % 0.39/0.61 (step @p945 :rule nary_cong :premises (@p140 @p944) :args (@t250)) % 0.39/0.61 (step @p946 :rule ho_cong :premises (@p144 @p918)) % 0.39/0.61 (step @p947 :rule cong :premises (@p946 @p945) :args ((= (_ @t85 @t246) @t250))) % 0.39/0.61 (step @p948 :rule trans :premises (@p947 @p941)) % 0.39/0.61 (step @p949 :rule true_elim :premises (@p948)) % 0.39/0.61 (step @p950 :rule cong :premises (@p928) :args (@t260)) % 0.39/0.61 (step @p951 :rule trans :premises (@p950 @p949)) % 0.39/0.61 (step @p952 :rule cong :premises (@p951 @p930) :args (@t261)) % 0.39/0.61 (step @p953 :rule trans :premises (@p952 @p914)) % 0.39/0.61 (step @p954 :rule cong :premises (@p953) :args (@t262)) % 0.39/0.61 (step @p955 :rule trans :premises (@p954 @p913)) % 0.39/0.61 (step @p956 :rule refl :args (@t263)) % 0.39/0.61 (step @p957 :rule nary_cong :premises (@p956 @p955) :args (@t264)) % 0.39/0.61 ; trust TRUST THEORY_LEMMA % 0.39/0.61 (step @p958 :rule trust :premises () :args (@t264)) % 0.39/0.61 (step @p959 :rule eq_resolve :premises (@p958 @p957)) % 0.39/0.61 (step @p960 :rule chain_m_resolution :premises (@p959 @p912) :args (@t263 @t98 (@list @t250))) % 0.39/0.61 (step @p961 :rule refl :args (@t265)) % 0.39/0.61 (step @p962 :rule refl :args (@t143)) % 0.39/0.61 (step @p963 :rule nary_cong :premises (@p962 @p251 @p961) :args ((or @t143 @t126 @t265))) % 0.39/0.61 (assume-push @p1149 @t99) % 0.39/0.61 (assume-push @p1150 @t263) % 0.39/0.61 (assume-push @p1151 @t102) % 0.39/0.61 (step @p257 :rule evaluate :args (@t127)) % 0.39/0.61 (step @p258 :rule false_intro :premises (@p164)) % 0.39/0.61 (step @p967 :rule symm :premises (@p1150)) % 0.39/0.61 (step @p968 :rule cong :premises (@p967) :args (@t102)) % 0.39/0.61 (step @p969 :rule true_intro :premises (@p1151)) % 0.39/0.61 (step @p970 :rule symm :premises (@p969)) % 0.39/0.61 (step @p971 :rule trans :premises (@p970 @p968 @p258)) % 0.39/0.61 (step @p972 false :rule eq_resolve :premises (@p971 @p257)) % 0.39/0.61 (step-pop @p1152 :rule scope :premises (@p972)) % 0.39/0.61 (step-pop @p1153 :rule scope :premises (@p1152)) % 0.39/0.61 (step-pop @p1154 :rule scope :premises (@p1153)) % 0.39/0.61 (step @p973 :rule process_scope :premises (@p1154) :args (false)) % 0.39/0.61 (assume-push @p1155 @t102) % 0.39/0.61 (assume-push @p1156 @t99) % 0.39/0.61 (assume-push @p1157 @t263) % 0.39/0.61 (step @p980 :rule and_intro :premises (@p164 @p1157 @p1155)) % 0.39/0.61 (step-pop @p1158 :rule scope :premises (@p980)) % 0.39/0.61 (step-pop @p1159 :rule scope :premises (@p1158)) % 0.39/0.61 (step-pop @p1160 :rule scope :premises (@p1159)) % 0.39/0.61 (step @p981 :rule process_scope :premises (@p1160) :args (@t266)) % 0.39/0.61 (step @p985 :rule implies_elim :premises (@p981)) % 0.39/0.61 (step @p986 :rule resolution :premises (@p985 @p973) :args (true @t266)) % 0.39/0.61 (step @p987 :rule not_and :premises (@p986)) % 0.39/0.61 (step @p988 :rule eq_resolve :premises (@p987 @p963)) % 0.39/0.61 (step @p989 :rule reordering :premises (@p988) :args ((or @t86 @t143 @t265))) % 0.39/0.61 (step @p990 false :rule chain_m_resolution :premises (@p989 @p960 @p909 @p164) :args (false @t242 (@list @t263 @t102 @t86))) % 0.39/0.61 ) % 0.39/0.61 % SZS output end Proof % 0.39/0.61 % cvc5 exiting %------------------------------------------------------------------------------