%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV300^5 : TPTP v9.2.1. Bugfixed v6.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:55:44 AM UTC 2026 % Result : Theorem 0.61s 0.89s % Output : Proof 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV300^5 : TPTP v9.2.1. Bugfixed v6.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n021.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 : Tue Jun 2 18:28:05 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.61/0.89 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.61/0.89 % SZS status Theorem % 0.61/0.89 % SZS output start Proof % 0.61/0.89 ( % 0.61/0.89 (declare-sort $$unsorted 0) % 0.61/0.89 (declare-const tptp.cONE (-> (-> $$unsorted Bool) Bool)) % 0.61/0.89 (define tptp.cZERO () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (lambda (@list _let_2) (not (exists (@list _let_1) (_ _let_2 _let_1))))))) % 0.61/0.89 (define tptp.cSUCC () (let ((_let_1 (@var "Xt" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "Xn" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_4 _let_2) (exists (@list _let_3) (and (_ _let_2 _let_3) (_ _let_4 (lambda (@list _let_1) (and (not (= _let_1 _let_3)) (_ _let_2 _let_1)))))))))))) % 0.61/0.89 (define @t1 () (= tptp.cONE (_ tptp.cSUCC tptp.cZERO))) % 0.61/0.89 (define @t2 () (@var "Xy" $$unsorted)) % 0.61/0.89 (define @t3 () (@var "Xx" $$unsorted)) % 0.61/0.89 (define @t4 () (lambda (@list @t3 @t2) (= @t3 @t2))) % 0.61/0.89 (define @t5 () (@var "P" (-> $$unsorted Bool))) % 0.61/0.89 (define @t6 () (= @t5 (_ @t4 @t2))) % 0.61/0.89 (define @t7 () (@list @t2)) % 0.61/0.89 (define @t8 () (exists @t7 @t6)) % 0.61/0.89 (define @t9 () (@list @t5)) % 0.61/0.89 (define @t10 () (lambda @t9 @t8)) % 0.61/0.89 (define @t11 () (= tptp.cONE @t10)) % 0.61/0.89 (define @t12 () (@var "Xg" (-> $$unsorted $$unsorted))) % 0.61/0.89 (define @t13 () (@var "Xf" (-> $$unsorted $$unsorted))) % 0.61/0.89 (define @t14 () (= @t13 @t12)) % 0.61/0.89 (define @t15 () (_ @t12 @t3)) % 0.61/0.89 (define @t16 () (_ @t13 @t3)) % 0.61/0.89 (define @t17 () (= @t16 @t15)) % 0.61/0.89 (define @t18 () (@list @t3)) % 0.61/0.89 (define @t19 () (forall @t18 @t17)) % 0.61/0.89 (define @t20 () (=> @t19 @t14)) % 0.61/0.89 (define @t21 () (@list @t13 @t12)) % 0.61/0.89 (define @t22 () (forall @t21 @t20)) % 0.61/0.89 (define @t23 () (=> @t22 @t11)) % 0.61/0.89 (define @t24 () (not @t23)) % 0.61/0.89 (define @t25 () (@var "Xp" (-> $$unsorted Bool))) % 0.61/0.89 (define @t26 () (_ @t25 @t3)) % 0.61/0.89 (define @t27 () (exists @t18 @t26)) % 0.61/0.89 (define @t28 () (not @t27)) % 0.61/0.89 (define @t29 () (@list @t25)) % 0.61/0.89 (define @t30 () (lambda @t29 @t28)) % 0.61/0.89 (define @t31 () (@var "Xt" $$unsorted)) % 0.61/0.89 (define @t32 () (_ @t25 @t31)) % 0.61/0.89 (define @t33 () (not (= @t31 @t3))) % 0.61/0.89 (define @t34 () (and @t33 @t32)) % 0.61/0.89 (define @t35 () (@list @t31)) % 0.61/0.89 (define @t36 () (lambda @t35 @t34)) % 0.61/0.89 (define @t37 () (@var "Xn" (-> (-> $$unsorted Bool) Bool))) % 0.61/0.89 (define @t38 () (and @t26 (_ @t37 @t36))) % 0.61/0.89 (define @t39 () (exists @t18 @t38)) % 0.61/0.89 (define @t40 () (@list @t37 @t25)) % 0.61/0.89 (define @t41 () (lambda @t40 @t39)) % 0.61/0.89 (define @t42 () (@var "BOUND_VARIABLE_7522" $$unsorted)) % 0.61/0.89 (define @t43 () (_ @t25 @t42)) % 0.61/0.89 (define @t44 () (not @t43)) % 0.61/0.89 (define @t45 () (= @t3 @t42)) % 0.61/0.89 (define @t46 () (@list @t42)) % 0.61/0.89 (define @t47 () (_ @t25 @t3)) % 0.61/0.89 (define @t48 () (not @t47)) % 0.61/0.89 (define @t49 () (lambda @t29 (not (forall @t18 (or @t48 (not (forall @t46 (or @t45 @t44)))))))) % 0.61/0.89 (define @t50 () (@purify @t49)) % 0.61/0.89 (define @t51 () (@var "BOUND_VARIABLE_7560" $$unsorted)) % 0.61/0.89 (define @t52 () (@list @t51)) % 0.61/0.89 (define @t53 () (lambda @t52 (= @t2 @t51))) % 0.61/0.89 (define @t54 () (= @t5 @t53)) % 0.61/0.89 (define @t55 () (not (forall @t7 (not @t54)))) % 0.61/0.89 (define @t56 () (lambda @t9 @t55)) % 0.61/0.89 (define @t57 () (@purify @t56)) % 0.61/0.89 (define @t58 () (= @t49 @t56)) % 0.61/0.89 (define @t59 () (_ @t12 @t3)) % 0.61/0.89 (define @t60 () (_ @t13 @t3)) % 0.61/0.89 (define @t61 () (forall @t18 (= @t60 @t59))) % 0.61/0.89 (define @t62 () (forall @t21 (or (not @t61) @t14))) % 0.61/0.89 (define @t63 () (=> @t62 @t58)) % 0.61/0.89 (define @t64 () (not @t45)) % 0.61/0.89 (define @t65 () (and @t64 @t43)) % 0.61/0.89 (define @t66 () (_ @t25 @t31)) % 0.61/0.89 (define @t67 () (not (= @t3 @t31))) % 0.61/0.89 (define @t68 () (and @t67 @t66)) % 0.61/0.89 (define @t69 () (lambda @t35 @t68)) % 0.61/0.89 (define @t70 () (_ @t69 @t42)) % 0.61/0.89 (define @t71 () (not @t70)) % 0.61/0.89 (define @t72 () (forall @t46 @t71)) % 0.61/0.89 (define @t73 () (forall @t18 @t48)) % 0.61/0.89 (define @t74 () (lambda @t29 @t73)) % 0.61/0.89 (define @t75 () (not (_ @t74 @t69))) % 0.61/0.89 (define @t76 () (or @t48 @t75)) % 0.61/0.89 (define @t77 () (forall @t18 @t76)) % 0.61/0.89 (define @t78 () (not @t77)) % 0.61/0.89 (define @t79 () (lambda @t29 @t78)) % 0.61/0.89 (define @t80 () (_ @t37 @t69)) % 0.61/0.89 (define @t81 () (_ (lambda @t40 (not (forall @t18 (or @t48 (not @t80))))) @t74)) % 0.61/0.89 (define @t82 () (not @t26)) % 0.61/0.89 (define @t83 () (forall @t18 @t82)) % 0.61/0.89 (define @t84 () (not @t83)) % 0.61/0.89 (define @t85 () (and @t67 @t32)) % 0.61/0.89 (define @t86 () (lambda @t35 @t85)) % 0.61/0.89 (define @t87 () (_ @t37 @t86)) % 0.61/0.89 (define @t88 () (not @t87)) % 0.61/0.89 (define @t89 () (or @t82 @t88)) % 0.61/0.89 (define @t90 () (and @t26 @t87)) % 0.61/0.89 (define @t91 () (forall @t18 (not @t90))) % 0.61/0.89 (define @t92 () (not @t91)) % 0.61/0.89 (define @t93 () (= tptp.cONE @t56)) % 0.61/0.89 (define @t94 () (=> @t62 @t93)) % 0.61/0.89 (define @t95 () (@const 0 (-> $$unsorted Bool))) % 0.61/0.89 (define @t96 () (forall @t7 (not (= @t53 @t95)))) % 0.61/0.89 (define @t97 () (not @t96)) % 0.61/0.89 (define @t98 () (not (_ @t95 @t42))) % 0.61/0.89 (define @t99 () (forall @t18 (or (not (_ @t95 @t3)) (not (forall @t46 (or @t45 @t98)))))) % 0.61/0.89 (define @t100 () (not @t99)) % 0.61/0.89 (define @t101 () (_ @t49 @t95)) % 0.61/0.89 (define @t102 () (_ @t50 @t95)) % 0.61/0.89 (define @t103 () (not (= @t95 @t53))) % 0.61/0.89 (define @t104 () (forall @t7 @t103)) % 0.61/0.89 (define @t105 () (not @t104)) % 0.61/0.89 (define @t106 () (_ @t56 @t95)) % 0.61/0.89 (define @t107 () (_ @t57 @t95)) % 0.61/0.89 (define @t108 () (= @t107 @t102)) % 0.61/0.89 (define @t109 () (not @t108)) % 0.61/0.89 (define @t110 () (= @t57 @t50)) % 0.61/0.89 (define @t111 () (or @t110 @t109)) % 0.61/0.89 (define @t112 () (= @t100 @t97)) % 0.61/0.89 (define @t113 () (@list true)) % 0.61/0.89 (define @t114 () (not @t97)) % 0.61/0.89 (define @t115 () (not @t100)) % 0.61/0.89 (define @t116 () (@quantifiers_skolemize @t99 0)) % 0.61/0.89 (define @t117 () (forall @t46 (or (= @t42 @t116) @t98))) % 0.61/0.89 (define @t118 () (not @t117)) % 0.61/0.89 (define @t119 () (_ @t95 @t116)) % 0.61/0.89 (define @t120 () (not @t119)) % 0.61/0.89 (define @t121 () (or @t120 @t118)) % 0.61/0.89 (define @t122 () (not @t121)) % 0.61/0.89 (define @t123 () (or (= @t116 @t42) @t98)) % 0.61/0.89 (define @t124 () (forall @t46 @t123)) % 0.61/0.89 (define @t125 () (not @t124)) % 0.61/0.89 (define @t126 () (or @t120 @t125)) % 0.61/0.89 (define @t127 () (not @t126)) % 0.61/0.89 (define @t128 () (not @t118)) % 0.61/0.89 (define @t129 () (lambda @t52 (= @t51 @t116))) % 0.61/0.89 (define @t130 () (@purify @t129)) % 0.61/0.89 (define @t131 () (= @t95 @t129)) % 0.61/0.89 (define @t132 () (not @t131)) % 0.61/0.89 (define @t133 () (lambda @t52 (= @t116 @t51))) % 0.61/0.89 (define @t134 () (= @t133 @t95)) % 0.61/0.89 (define @t135 () (not @t134)) % 0.61/0.89 (define @t136 () (@list @t116)) % 0.61/0.89 (define @t137 () (@const 1 $$unsorted)) % 0.61/0.89 (define @t138 () (= @t116 @t137)) % 0.61/0.89 (define @t139 () (= @t137 @t116)) % 0.61/0.89 (define @t140 () (_ @t129 @t137)) % 0.61/0.89 (define @t141 () (_ @t130 @t137)) % 0.61/0.89 (define @t142 () (_ @t95 @t137)) % 0.61/0.89 (define @t143 () (= @t142 @t141)) % 0.61/0.89 (define @t144 () (not @t143)) % 0.61/0.89 (define @t145 () (= @t95 @t130)) % 0.61/0.89 (define @t146 () (or @t145 @t144)) % 0.61/0.89 (define @t147 () (not @t142)) % 0.61/0.89 (define @t148 () (or @t139 @t147)) % 0.61/0.89 (define @t149 () (@list @t137)) % 0.61/0.89 (define @t150 () (= @t142 @t138)) % 0.61/0.89 (define @t151 () (or @t138 @t147)) % 0.61/0.89 (define @t152 () (not @t151)) % 0.61/0.89 (define @t153 () (not @t138)) % 0.61/0.89 (define @t154 () (@list false true)) % 0.61/0.89 (define @t155 () (@quantifiers_skolemize @t96 0)) % 0.61/0.89 (define @t156 () (lambda @t52 (= @t51 @t155))) % 0.61/0.89 (define @t157 () (@purify @t156)) % 0.61/0.89 (define @t158 () (= @t95 @t157)) % 0.61/0.89 (define @t159 () (= @t95 @t156)) % 0.61/0.89 (define @t160 () (lambda @t52 (= @t155 @t51))) % 0.61/0.89 (define @t161 () (= @t160 @t95)) % 0.61/0.89 (define @t162 () (not (not @t161))) % 0.61/0.89 (define @t163 () (@quantifiers_skolemize @t117 0)) % 0.61/0.89 (define @t164 () (= @t155 @t163)) % 0.61/0.89 (define @t165 () (_ @t95 @t163)) % 0.61/0.89 (define @t166 () (= @t165 @t164)) % 0.61/0.89 (define @t167 () (@list false)) % 0.61/0.89 (define @t168 () (@list @t158)) % 0.61/0.89 (define @t169 () (not @t165)) % 0.61/0.89 (define @t170 () (or (= @t163 @t42) @t98)) % 0.61/0.89 (define @t171 () (forall @t46 @t170)) % 0.61/0.89 (define @t172 () (not @t171)) % 0.61/0.89 (define @t173 () (or @t169 @t172)) % 0.61/0.89 (define @t174 () (forall @t46 (or (= @t42 @t163) @t98))) % 0.61/0.89 (define @t175 () (not @t174)) % 0.61/0.89 (define @t176 () (or @t169 @t175)) % 0.61/0.89 (define @t177 () (@list @t99)) % 0.61/0.89 (define @t178 () (@quantifiers_skolemize @t174 0)) % 0.61/0.89 (define @t179 () (_ @t95 @t178)) % 0.61/0.89 (define @t180 () (not @t179)) % 0.61/0.89 (define @t181 () (= @t163 @t178)) % 0.61/0.89 (define @t182 () (or @t181 @t180)) % 0.61/0.89 (define @t183 () (not @t182)) % 0.61/0.89 (define @t184 () (or (= @t178 @t163) @t180)) % 0.61/0.89 (define @t185 () (not @t184)) % 0.61/0.89 (define @t186 () (= @t155 @t178)) % 0.61/0.89 (define @t187 () (= @t179 @t186)) % 0.61/0.89 (define @t188 () (not @t186)) % 0.61/0.89 (define @t189 () (not @t164)) % 0.61/0.89 (define @t190 () (not @t181)) % 0.61/0.89 (define @t191 () (and @t164 @t190)) % 0.61/0.89 (define @t192 () (= @t116 @t163)) % 0.61/0.89 (define @t193 () (or @t192 @t169)) % 0.61/0.89 (define @t194 () (not @t193)) % 0.61/0.89 (define @t195 () (or (= @t163 @t116) @t169)) % 0.61/0.89 (define @t196 () (not @t195)) % 0.61/0.89 (define @t197 () (_ @t95 @t155)) % 0.61/0.89 (define @t198 () (not @t197)) % 0.61/0.89 (define @t199 () (or (= @t155 @t116) @t198)) % 0.61/0.89 (define @t200 () (= @t116 @t155)) % 0.61/0.89 (define @t201 () (or @t200 @t198)) % 0.61/0.89 (define @t202 () (= @t119 @t200)) % 0.61/0.89 (define @t203 () (= @t165 @t192)) % 0.61/0.89 (define @t204 () (=> @t145 (= @t119 true))) % 0.61/0.89 (define @t205 () (not @t145)) % 0.61/0.89 (define @t206 () (not @t203)) % 0.61/0.89 (define @t207 () (or (= @t137 @t42) @t98)) % 0.61/0.89 (define @t208 () (forall @t46 @t207)) % 0.61/0.89 (define @t209 () (not @t208)) % 0.61/0.89 (define @t210 () (or @t147 @t209)) % 0.61/0.89 (define @t211 () (forall @t46 (or (= @t42 @t137) @t98))) % 0.61/0.89 (define @t212 () (not @t211)) % 0.61/0.89 (define @t213 () (or @t147 @t212)) % 0.61/0.89 (define @t214 () (= @t137 @t155)) % 0.61/0.89 (define @t215 () (= @t142 @t214)) % 0.61/0.89 (define @t216 () (@quantifiers_skolemize @t211 0)) % 0.61/0.89 (define @t217 () (_ @t95 @t216)) % 0.61/0.89 (define @t218 () (not @t217)) % 0.61/0.89 (define @t219 () (= @t137 @t216)) % 0.61/0.89 (define @t220 () (or @t219 @t218)) % 0.61/0.89 (define @t221 () (not @t220)) % 0.61/0.89 (define @t222 () (or (= @t216 @t137) @t218)) % 0.61/0.89 (define @t223 () (not @t222)) % 0.61/0.89 (define @t224 () (= @t155 @t216)) % 0.61/0.89 (define @t225 () (= @t217 @t224)) % 0.61/0.89 (define @t226 () (not @t224)) % 0.61/0.89 (define @t227 () (not @t214)) % 0.61/0.89 (define @t228 () (not @t219)) % 0.61/0.89 (define @t229 () (and @t228 @t214)) % 0.61/0.89 (define @t230 () (@list true false)) % 0.61/0.89 (define @t231 () (not @t200)) % 0.61/0.89 (define @t232 () (=> @t158 (= @t197 true))) % 0.61/0.89 (assume @p1 @t1) % 0.61/0.89 (assume @p2 @t24) % 0.61/0.89 (assume @p3 true) % 0.61/0.89 (step @p4 (= tptp.cZERO @t30) :rule refl :args (@t30)) % 0.61/0.89 (step @p5 (= tptp.cSUCC @t41) :rule refl :args (@t41)) % 0.61/0.89 (step @p6 :rule eq-symm :args (@t50 @t57)) % 0.61/0.89 (step @p7 :rule eq-refl :args (@t56)) % 0.61/0.89 (step @p8 :rule skolem_intro :args (@t57)) % 0.61/0.89 (step @p9 :rule refl :args (@t56)) % 0.61/0.89 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t56 @t57))) % 0.61/0.89 (step @p11 :rule trans :premises (@p10 @p7)) % 0.61/0.89 (step @p12 :rule true_elim :premises (@p11)) % 0.61/0.89 (step @p13 :rule eq-refl :args (@t49)) % 0.61/0.89 (step @p14 :rule skolem_intro :args (@t50)) % 0.61/0.89 (step @p15 :rule refl :args (@t49)) % 0.61/0.89 (step @p16 :rule cong :premises (@p15 @p14) :args ((= @t49 @t50))) % 0.61/0.89 (step @p17 :rule trans :premises (@p16 @p13)) % 0.61/0.89 (step @p18 :rule true_elim :premises (@p17)) % 0.61/0.89 (step @p19 :rule cong :premises (@p18 @p12) :args (@t58)) % 0.61/0.89 (step @p20 :rule trans :premises (@p19 @p6)) % 0.61/0.89 (step @p21 :rule refl :args (@t62)) % 0.61/0.89 (step @p22 :rule cong :premises (@p21 @p20) :args (@t63)) % 0.61/0.89 (step @p23 :rule cong :premises (@p22) :args ((not @t63))) % 0.61/0.89 (step @p24 :rule refl :args (@t44)) % 0.61/0.89 (step @p25 :rule bool-double-not-elim :args (@t45)) % 0.61/0.89 (step @p26 :rule nary_cong :premises (@p25 @p24) :args ((or (not @t64) @t44))) % 0.61/0.89 (step @p27 :rule bool-and-de-morgan :args (@t64 @t43 true)) % 0.61/0.89 (step @p28 :rule trans :premises (@p27 @p26)) % 0.61/0.89 (step @p29 :rule cong :premises (@p28) :args ((forall @t46 (not @t65)))) % 0.61/0.89 (step @p30 :rule beta-reduce :args ((= @t70 @t65))) % 0.61/0.89 (step @p31 :rule cong :premises (@p30) :args (@t71)) % 0.61/0.89 (step @p32 :rule cong :premises (@p31) :args (@t72)) % 0.61/0.89 (step @p33 :rule trans :premises (@p32 @p29)) % 0.61/0.89 (step @p34 :rule beta-reduce :args ((= (_ (lambda @t29 (forall @t46 @t44)) @t69) @t72))) % 0.61/0.89 (step @p35 :rule trans :premises (@p34 @p33)) % 0.61/0.89 (step @p36 :rule refl :args (@t69)) % 0.61/0.89 (step @p37 :rule alpha_equiv :args (@t73 (@list @t3) (@list @t42))) % 0.61/0.89 (step @p38 :rule cong :premises (@p37) :args (@t74)) % 0.61/0.89 (step @p39 :rule ho_cong :premises (@p38 @p36)) % 0.61/0.89 (step @p40 :rule trans :premises (@p39 @p35)) % 0.61/0.89 (step @p41 :rule cong :premises (@p40) :args (@t75)) % 0.61/0.89 (step @p42 :rule refl :args (@t48)) % 0.61/0.89 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t76)) % 0.61/0.89 (step @p44 :rule cong :premises (@p43) :args (@t77)) % 0.61/0.89 (step @p45 :rule cong :premises (@p44) :args (@t78)) % 0.61/0.89 (step @p46 :rule cong :premises (@p45) :args (@t79)) % 0.61/0.89 (step @p47 :rule beta-reduce :args ((= @t81 @t79))) % 0.61/0.89 (step @p48 :rule trans :premises (@p47 @p46)) % 0.61/0.89 (step @p49 :rule refl :args (tptp.cONE)) % 0.61/0.89 (step @p50 :rule cong :premises (@p49 @p48) :args ((= tptp.cONE @t81))) % 0.61/0.89 (step @p51 :rule bool-double-not-elim :args (@t73)) % 0.61/0.89 (step @p52 :rule refl :args (@t47)) % 0.61/0.89 (step @p53 :rule refl :args (@t26)) % 0.61/0.89 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t26 @t47))) % 0.61/0.89 (step @p55 :rule symm :premises 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0.61/0.89 (step @p72 :rule trans :premises (@p71 @p66)) % 0.61/0.89 (step @p73 :rule refl :args (@t37)) % 0.61/0.89 (step @p74 :rule ho_cong :premises (@p73 @p70)) % 0.61/0.89 (step @p75 :rule cong :premises (@p74 @p72) :args ((= (_ @t37 @t69) @t80))) % 0.61/0.89 (step @p76 :rule symm :premises (@p75)) % 0.61/0.89 (step @p77 :rule refl :args (@t87)) % 0.61/0.89 (step @p78 :rule eq_resolve :premises (@p77 @p76)) % 0.61/0.89 (step @p79 :rule refl :args (@t32)) % 0.61/0.89 (step @p80 :rule cong :premises (@p79 @p67) :args ((= @t32 @t66))) % 0.61/0.89 (step @p81 :rule symm :premises (@p80)) % 0.61/0.89 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.61/0.89 (step @p83 :rule nary_cong :premises (@p68 @p82) :args (@t85)) % 0.61/0.89 (step @p84 :rule cong :premises (@p83) :args (@t86)) % 0.61/0.89 (step @p85 :rule ho_cong :premises (@p73 @p84)) % 0.61/0.89 (step @p86 :rule trans :premises (@p85 @p78)) % 0.61/0.89 (step @p87 :rule cong :premises (@p86) :args (@t88)) % 0.61/0.89 (step @p88 :rule nary_cong :premises (@p57 @p87) :args (@t89)) % 0.61/0.89 (step @p89 :rule cong :premises (@p88) :args ((forall @t18 @t89))) % 0.61/0.89 (step @p90 :rule bool-and-de-morgan :args (@t26 @t87 true)) % 0.61/0.89 (step @p91 :rule cong :premises (@p90) :args (@t91)) % 0.61/0.89 (step @p92 :rule trans :premises (@p91 @p89)) % 0.61/0.89 (step @p93 :rule cong :premises (@p92) :args (@t92)) % 0.61/0.89 (step @p94 :rule exists-elim :args ((= (exists @t18 @t90) @t92))) % 0.61/0.89 (step @p95 :rule trans :premises (@p94 @p93)) % 0.61/0.89 (step @p96 :rule refl :args (@t32)) % 0.61/0.89 (step @p97 :rule eq-symm :args (@t31 @t3)) % 0.61/0.89 (step @p98 :rule cong :premises (@p97) :args (@t33)) % 0.61/0.89 (step @p99 :rule nary_cong :premises (@p98 @p96) :args (@t34)) % 0.61/0.89 (step @p100 :rule cong :premises (@p99) :args (@t36)) % 0.61/0.89 (step @p101 :rule refl :args (@t37)) % 0.61/0.89 (step @p102 :rule ho_cong :premises (@p101 @p100)) % 0.61/0.89 (step @p103 :rule refl :args 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0.61/0.89 (step @p118 :rule refl :args (@t2)) % 0.61/0.89 (step @p119 :rule alpha_equiv :args (@t4 (@list @t2) (@list @t51))) % 0.61/0.89 (step @p120 :rule ho_cong :premises (@p119 @p118)) % 0.61/0.89 (step @p121 :rule trans :premises (@p120 @p117)) % 0.61/0.89 (step @p122 :rule refl :args (@t5)) % 0.61/0.89 (step @p123 :rule cong :premises (@p122 @p121) :args (@t6)) % 0.61/0.89 (step @p124 :rule cong :premises (@p123) :args (@t8)) % 0.61/0.89 (step @p125 :rule trans :premises (@p124 @p116)) % 0.61/0.89 (step @p126 :rule cong :premises (@p125) :args (@t10)) % 0.61/0.89 (step @p127 :rule cong :premises (@p49 @p126) :args (@t11)) % 0.61/0.89 (step @p128 :rule bool-impl-elim :args (@t61 @t14)) % 0.61/0.89 (step @p129 :rule cong :premises (@p128) :args ((forall @t21 (=> @t61 @t14)))) % 0.61/0.89 (step @p130 :rule refl :args (@t14)) % 0.61/0.89 (step @p131 :rule refl :args (@t59)) % 0.61/0.89 (step @p132 :rule refl :args (@t15)) % 0.61/0.89 (step @p133 :rule cong :premises (@p132 @p131) :args ((= @t15 @t59))) % 0.61/0.89 (step @p134 :rule symm :premises (@p133)) % 0.61/0.89 (step @p135 :rule eq_resolve :premises (@p132 @p134)) % 0.61/0.89 (step @p136 :rule refl :args (@t60)) % 0.61/0.89 (step @p137 :rule refl :args (@t16)) % 0.61/0.89 (step @p138 :rule cong :premises (@p137 @p136) :args ((= @t16 @t60))) % 0.61/0.89 (step @p139 :rule symm :premises (@p138)) % 0.61/0.89 (step @p140 :rule eq_resolve :premises (@p137 @p139)) % 0.61/0.89 (step @p141 :rule cong :premises (@p140 @p135) :args (@t17)) % 0.61/0.89 (step @p142 :rule cong :premises (@p141) :args (@t19)) % 0.61/0.89 (step @p143 :rule cong :premises (@p142 @p130) :args (@t20)) % 0.61/0.89 (step @p144 :rule cong :premises (@p143) :args (@t22)) % 0.61/0.89 (step @p145 :rule trans :premises (@p144 @p129)) % 0.61/0.89 (step @p146 :rule cong :premises (@p145 @p127) :args (@t23)) % 0.61/0.89 (step @p147 :rule cong :premises (@p146) :args (@t24)) % 0.61/0.89 (step @p148 :rule trans :premises (@p147 @p115 @p23)) % 0.61/0.89 (step @p149 :rule eq_resolve :premises (@p2 @p148)) % 0.61/0.89 (step @p150 :rule not_implies_elim2 :premises (@p149)) % 0.61/0.89 (step @p151 :rule eq-symm :args (@t97 @t100)) % 0.61/0.89 (step @p152 :rule eq-refl :args (@t100)) % 0.61/0.89 (step @p153 :rule beta-reduce :args ((= @t101 @t100))) % 0.61/0.89 (step @p154 :rule refl :args (@t100)) % 0.61/0.89 (step @p155 :rule cong :premises (@p154 @p153) :args ((= @t100 @t101))) % 0.61/0.89 (step @p156 :rule trans :premises (@p155 @p152)) % 0.61/0.89 (step @p157 :rule eq-symm :args (@t101 @t100)) % 0.61/0.89 (step @p158 :rule trans :premises (@p157 @p156)) % 0.61/0.89 (step @p159 :rule refl :args (@t95)) % 0.61/0.89 (step @p160 :rule ho_cong :premises (@p14 @p159)) % 0.61/0.89 (step @p161 :rule cong :premises (@p160 @p154) :args ((= @t102 @t100))) % 0.61/0.89 (step @p162 :rule trans :premises (@p161 @p158)) % 0.61/0.89 (step @p163 :rule true_elim :premises (@p162)) % 0.61/0.89 (step @p164 :rule eq-refl :args (@t97)) % 0.61/0.89 (step @p165 :rule eq-symm :args (@t95 @t53)) % 0.61/0.89 (step @p166 :rule cong :premises (@p165) :args (@t103)) % 0.61/0.89 (step @p167 :rule cong :premises (@p166) :args (@t104)) % 0.61/0.89 (step @p168 :rule cong :premises (@p167) :args (@t105)) % 0.61/0.89 (step @p169 :rule beta-reduce :args ((= @t106 @t105))) % 0.61/0.89 (step @p170 :rule trans :premises (@p169 @p168)) % 0.61/0.89 (step @p171 :rule refl :args (@t97)) % 0.61/0.89 (step @p172 :rule cong :premises (@p171 @p170) :args ((= @t97 @t106))) % 0.61/0.89 (step @p173 :rule trans :premises (@p172 @p164)) % 0.61/0.89 (step @p174 :rule eq-symm :args (@t106 @t97)) % 0.61/0.89 (step @p175 :rule trans :premises (@p174 @p173)) % 0.61/0.89 (step @p176 :rule ho_cong :premises (@p8 @p159)) % 0.61/0.89 (step @p177 :rule cong :premises (@p176 @p171) :args ((= @t107 @t97))) % 0.61/0.89 (step @p178 :rule trans :premises (@p177 @p175)) % 0.61/0.89 (step @p179 :rule true_elim :premises (@p178)) % 0.61/0.89 (step @p180 :rule cong :premises (@p179 @p163) :args (@t108)) % 0.61/0.89 (step @p181 :rule trans :premises (@p180 @p151)) % 0.61/0.89 (step @p182 :rule cong :premises (@p181) :args (@t109)) % 0.61/0.89 (step @p183 :rule refl :args (@t110)) % 0.61/0.89 (step @p184 :rule nary_cong :premises (@p183 @p182) :args (@t111)) % 0.61/0.89 ; WARNING: add trust step for TRUST % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p185 :rule trust :premises () :args (@t111)) % 0.61/0.89 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.61/0.89 (step @p187 :rule chain_m_resolution :premises (@p186 @p150) :args ((not @t112) @t113 (@list @t110))) % 0.61/0.89 (step @p188 :rule bool-double-not-elim :args (@t96)) % 0.61/0.89 (step @p189 :rule bool-double-not-elim :args (@t99)) % 0.61/0.89 (step @p190 :rule refl :args (@t112)) % 0.61/0.89 (step @p191 :rule nary_cong :premises (@p190 @p189 @p188) :args ((or @t112 @t115 @t114))) % 0.61/0.89 (step @p192 :rule cnf_equiv_neg2 :args (@t112)) % 0.61/0.89 (step @p193 :rule eq_resolve 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0.61/0.89 (step @p223 :rule reordering :premises (@p222) :args ((or @t117 @t121))) % 0.61/0.89 (step @p224 :rule eq-refl :args (@t129)) % 0.61/0.89 (step @p225 :rule skolem_intro :args (@t130)) % 0.61/0.89 (step @p226 :rule refl :args (@t129)) % 0.61/0.89 (step @p227 :rule cong :premises (@p226 @p225) :args ((= @t129 @t130))) % 0.61/0.89 (step @p228 :rule trans :premises (@p227 @p224)) % 0.61/0.89 (step @p229 :rule true_elim :premises (@p228)) % 0.61/0.89 (step @p230 :rule cong :premises (@p159 @p229) :args (@t131)) % 0.61/0.89 (step @p231 :rule cong :premises (@p230) :args (@t132)) % 0.61/0.89 (step @p232 :rule refl :args (@t96)) % 0.61/0.89 (step @p233 :rule cong :premises (@p232 @p231) :args ((=> @t96 @t132))) % 0.61/0.89 (step @p234 :rule eq-symm :args (@t129 @t95)) % 0.61/0.89 (step @p235 :rule eq-symm :args (@t116 @t51)) % 0.61/0.89 (step @p236 :rule cong :premises (@p235) :args (@t133)) % 0.61/0.89 (step @p237 :rule cong :premises (@p236 @p159) :args (@t134)) % 0.61/0.89 (step @p238 :rule trans :premises (@p237 @p234)) % 0.61/0.89 (step @p239 :rule cong :premises (@p238) :args (@t135)) % 0.61/0.89 (step @p240 :rule cong :premises (@p232 @p239) :args ((=> @t96 @t135))) % 0.61/0.89 (assume-push @p565 @t96) % 0.61/0.89 (step @p242 :rule instantiate :premises (@p565) :args (@t136)) % 0.61/0.89 (step-pop @p566 :rule scope :premises (@p242)) % 0.61/0.89 (step @p243 :rule process_scope :premises (@p566) :args (@t135)) % 0.61/0.89 (step @p245 :rule eq_resolve :premises (@p243 @p240)) % 0.61/0.89 (step @p246 :rule eq_resolve :premises (@p245 @p233)) % 0.61/0.89 (step @p247 :rule implies_elim :premises (@p246)) % 0.61/0.89 (step @p248 :rule eq-refl :args (@t138)) % 0.61/0.89 (step @p249 :rule eq-symm :args (@t137 @t116)) % 0.61/0.89 (step @p250 :rule beta-reduce :args ((= @t140 @t139))) % 0.61/0.89 (step @p251 :rule trans :premises (@p250 @p249)) % 0.61/0.89 (step @p252 :rule refl :args (@t138)) % 0.61/0.89 (step @p253 :rule cong :premises (@p252 @p251) :args ((= @t138 @t140))) % 0.61/0.89 (step @p254 :rule trans :premises (@p253 @p248)) % 0.61/0.89 (step @p255 :rule eq-symm :args (@t140 @t138)) % 0.61/0.89 (step @p256 :rule trans :premises (@p255 @p254)) % 0.61/0.89 (step @p257 :rule refl :args (@t137)) % 0.61/0.89 (step @p258 :rule ho_cong :premises (@p225 @p257)) % 0.61/0.89 (step @p259 :rule cong :premises (@p258 @p252) :args ((= @t141 @t138))) % 0.61/0.89 (step @p260 :rule trans :premises (@p259 @p256)) % 0.61/0.89 (step @p261 :rule true_elim :premises (@p260)) % 0.61/0.89 (step @p262 :rule refl :args (@t142)) % 0.61/0.89 (step @p263 :rule cong :premises (@p262 @p261) :args (@t143)) % 0.61/0.89 (step @p264 :rule cong :premises (@p263) :args (@t144)) % 0.61/0.89 (step @p265 :rule refl :args (@t145)) % 0.61/0.89 (step @p266 :rule nary_cong :premises (@p265 @p264) :args (@t146)) % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p267 :rule trust :premises () :args (@t146)) % 0.61/0.89 (step @p268 :rule eq_resolve :premises (@p267 @p266)) % 0.61/0.89 (step @p269 :rule refl :args (@t147)) % 0.61/0.89 (step @p270 :rule nary_cong :premises (@p249 @p269) :args (@t148)) % 0.61/0.89 (step @p271 :rule refl :args (@t117)) % 0.61/0.89 (step @p272 :rule cong :premises (@p271 @p270) :args ((=> @t117 @t148))) % 0.61/0.89 (assume-push @p567 @t117) % 0.61/0.89 (step @p274 :rule instantiate :premises (@p567) :args (@t149)) % 0.61/0.89 (step-pop @p568 :rule scope :premises (@p274)) % 0.61/0.89 (step @p275 :rule process_scope :premises (@p568) :args (@t148)) % 0.61/0.89 (step @p277 :rule eq_resolve :premises (@p275 @p272)) % 0.61/0.89 (step @p278 :rule implies_elim :premises (@p277)) % 0.61/0.89 (step @p279 :rule cnf_equiv_neg2 :args (@t150)) % 0.61/0.89 (step @p280 :rule cnf_or_pos :args (@t151)) % 0.61/0.89 (step @p281 :rule reordering :premises (@p280) :args ((or @t138 @t147 @t152))) % 0.61/0.89 (step @p282 :rule chain_m_resolution :premises (@p281 @p279) :args ((or @t150 @t147 @t152) @t113 (@list @t138))) % 0.61/0.89 (step @p283 :rule cnf_equiv_neg1 :args (@t150)) % 0.61/0.89 (step @p284 :rule reordering :premises (@p283) :args ((or @t142 @t138 @t150))) % 0.61/0.89 (step @p285 :rule bool-double-not-elim :args (@t142)) % 0.61/0.89 (step @p286 :rule refl :args (@t153)) % 0.61/0.89 (step @p287 :rule nary_cong :premises (@p202 @p286 @p285) :args ((or @t120 @t153 (not @t147)))) % 0.61/0.89 (assume-push @p569 @t119) % 0.61/0.89 (assume-push @p570 @t138) % 0.61/0.89 (assume-push @p571 @t147) % 0.61/0.89 (step @p291 :rule evaluate :args ((= false true))) % 0.61/0.89 (step @p292 :rule true_intro :premises (@p569)) % 0.61/0.89 (step @p293 :rule symm :premises (@p570)) % 0.61/0.89 (step @p294 :rule cong :premises (@p293) :args (@t142)) % 0.61/0.89 (step @p295 :rule false_intro :premises (@p571)) % 0.61/0.89 (step @p296 :rule symm :premises (@p295)) % 0.61/0.89 (step @p297 :rule trans :premises (@p296 @p294 @p292)) % 0.61/0.89 (step @p298 false :rule eq_resolve :premises (@p297 @p291)) % 0.61/0.89 (step-pop @p572 :rule scope :premises (@p298)) % 0.61/0.89 (step-pop @p573 :rule scope :premises (@p572)) % 0.61/0.89 (step-pop @p574 :rule scope :premises (@p573)) % 0.61/0.89 (step @p299 :rule process_scope :premises (@p574) :args (false)) % 0.61/0.89 (step @p303 :rule not_and :premises (@p299)) % 0.61/0.89 (step @p304 :rule eq_resolve :premises (@p303 @p287)) % 0.61/0.89 (step @p305 :rule reordering :premises (@p304) :args ((or @t120 @t142 @t153))) % 0.61/0.89 (step @p306 :rule chain_m_resolution :premises (@p305 @p284 @p282 @p278 @p268 @p247 @p223 @p218 @p212 @p194 @p187) :args (@t99 (@list false true false true true false false true false true) (@list @t138 @t142 @t151 @t150 @t145 @t117 @t119 @t121 @t96 @t112))) % 0.61/0.89 (step @p307 :rule cnf_equiv_neg1 :args (@t112)) % 0.61/0.89 (step @p308 :rule reordering :premises (@p307) :args ((or @t100 @t97 @t112))) % 0.61/0.89 (step @p309 :rule chain_m_resolution :premises (@p308 @p306 @p187) :args (@t97 @t154 (@list @t99 @t112))) % 0.61/0.89 (step @p310 :rule refl :args (@t158)) % 0.61/0.89 (step @p311 :rule nary_cong :premises (@p188 @p310) :args ((or @t114 @t158))) % 0.61/0.89 (step @p312 :rule eq-refl :args (@t156)) % 0.61/0.89 (step @p313 :rule skolem_intro :args (@t157)) % 0.61/0.89 (step @p314 :rule refl :args (@t156)) % 0.61/0.89 (step @p315 :rule cong :premises (@p314 @p313) :args ((= @t156 @t157))) % 0.61/0.89 (step @p316 :rule trans :premises (@p315 @p312)) % 0.61/0.89 (step @p317 :rule true_elim :premises (@p316)) % 0.61/0.89 (step @p318 :rule cong :premises (@p159 @p317) :args (@t159)) % 0.61/0.89 (step @p319 :rule cong :premises (@p171 @p318) :args ((=> @t97 @t159))) % 0.61/0.89 (step @p320 :rule eq-symm :args (@t156 @t95)) % 0.61/0.89 (step @p321 :rule eq-symm :args (@t155 @t51)) % 0.61/0.89 (step @p322 :rule cong :premises (@p321) :args (@t160)) % 0.61/0.89 (step @p323 :rule cong :premises (@p322 @p159) :args (@t161)) % 0.61/0.89 (step @p324 :rule trans :premises (@p323 @p320)) % 0.61/0.89 (step @p325 :rule bool-double-not-elim :args (@t161)) % 0.61/0.89 (step @p326 :rule trans :premises (@p325 @p324)) % 0.61/0.89 (step @p327 :rule cong :premises (@p171 @p326) :args ((=> @t97 @t162))) % 0.61/0.89 (step @p328 :rule trans :premises (@p327 @p319)) % 0.61/0.89 (assume-push @p575 @t97) % 0.61/0.89 (step @p330 :rule skolemize :premises (@p575)) % 0.61/0.89 (step-pop @p576 :rule scope :premises (@p330)) % 0.61/0.89 (step @p331 :rule process_scope :premises (@p576) :args (@t162)) % 0.61/0.89 (step @p333 :rule eq_resolve :premises (@p331 @p328)) % 0.61/0.89 (step @p334 :rule implies_elim :premises (@p333)) % 0.61/0.89 (step @p335 :rule eq_resolve :premises (@p334 @p311)) % 0.61/0.89 (step @p336 :rule chain_m_resolution :premises (@p335 @p309) :args (@t158 @t113 (@list @t96))) % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p337 :rule trust :premises () :args ((=> @t158 @t166))) % 0.61/0.89 (step @p338 :rule implies_elim :premises (@p337)) % 0.61/0.89 (step @p339 :rule chain_m_resolution :premises (@p338 @p336) :args (@t166 @t167 @t168)) % 0.61/0.89 (step @p340 :rule cnf_equiv_pos1 :args (@t166)) % 0.61/0.89 (step @p341 :rule reordering :premises (@p340) :args ((or @t169 @t164 (not @t166)))) % 0.61/0.89 (step @p342 :rule eq-symm :args (@t163 @t42)) % 0.61/0.89 (step @p343 :rule nary_cong :premises (@p342 @p197) :args (@t170)) % 0.61/0.89 (step @p344 :rule cong :premises (@p343) :args (@t171)) % 0.61/0.89 (step @p345 :rule cong :premises (@p344) :args (@t172)) % 0.61/0.89 (step @p346 :rule refl :args (@t169)) % 0.61/0.89 (step @p347 :rule nary_cong :premises (@p346 @p345) :args (@t173)) % 0.61/0.89 (step @p348 :rule refl :args (@t99)) % 0.61/0.89 (step @p349 :rule cong :premises (@p348 @p347) :args ((=> @t99 @t173))) % 0.61/0.89 (assume-push @p577 @t99) % 0.61/0.89 (step @p351 :rule instantiate :premises (@p577) :args ((@list @t163))) % 0.61/0.89 (step-pop @p578 :rule scope :premises (@p351)) % 0.61/0.89 (step @p352 :rule process_scope :premises (@p578) :args (@t173)) % 0.61/0.89 (step @p354 :rule eq_resolve :premises (@p352 @p349)) % 0.61/0.89 (step @p355 :rule implies_elim :premises (@p354)) % 0.61/0.89 (step @p356 :rule chain_m_resolution :premises (@p355 @p306) :args (@t176 @t167 @t177)) % 0.61/0.89 (step @p357 :rule cnf_or_pos :args (@t176)) % 0.61/0.89 (step @p358 :rule reordering :premises (@p357) :args ((or @t169 @t175 (not @t176)))) % 0.61/0.89 (step @p359 :rule refl :args (@t183)) % 0.61/0.89 (step @p360 :rule bool-double-not-elim :args (@t174)) % 0.61/0.89 (step @p361 :rule nary_cong :premises (@p360 @p359) :args ((or (not @t175) @t183))) % 0.61/0.89 (step @p362 :rule refl :args (@t180)) % 0.61/0.89 (step @p363 :rule eq-symm :args (@t178 @t163)) % 0.61/0.89 (step @p364 :rule nary_cong :premises (@p363 @p362) :args (@t184)) % 0.61/0.89 (step @p365 :rule cong :premises (@p364) :args (@t185)) % 0.61/0.89 (step @p366 :rule refl :args (@t175)) % 0.61/0.89 (step @p367 :rule cong :premises (@p366 @p365) :args ((=> @t175 @t185))) % 0.61/0.89 (assume-push @p579 @t175) % 0.61/0.89 (step @p369 :rule skolemize :premises (@p579)) % 0.61/0.89 (step-pop @p580 :rule scope :premises (@p369)) % 0.61/0.89 (step @p370 :rule process_scope :premises (@p580) :args (@t185)) % 0.61/0.89 (step @p372 :rule eq_resolve :premises (@p370 @p367)) % 0.61/0.89 (step @p373 :rule implies_elim :premises (@p372)) % 0.61/0.89 (step @p374 :rule eq_resolve :premises (@p373 @p361)) % 0.61/0.89 (step @p375 :rule cnf_or_neg :args (@t182 0)) % 0.61/0.89 (step @p376 :rule bool-double-not-elim :args (@t179)) % 0.61/0.89 (step @p377 :rule refl :args (@t182)) % 0.61/0.89 (step @p378 :rule nary_cong :premises (@p377 @p376) :args ((or @t182 (not @t180)))) % 0.61/0.89 (step @p379 :rule cnf_or_neg :args (@t182 1)) % 0.61/0.89 (step @p380 :rule eq_resolve :premises (@p379 @p378)) % 0.61/0.89 (step @p381 :rule reordering :premises (@p380) :args ((or @t179 @t182))) % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p382 :rule trust :premises () :args ((=> @t158 @t187))) % 0.61/0.89 (step @p383 :rule implies_elim :premises (@p382)) % 0.61/0.89 (step @p384 :rule chain_m_resolution :premises (@p383 @p336) :args (@t187 @t167 @t168)) % 0.61/0.89 (step @p385 :rule cnf_equiv_pos1 :args (@t187)) % 0.61/0.89 (step @p386 :rule reordering :premises (@p385) :args ((or @t180 @t186 (not @t187)))) % 0.61/0.89 (step @p387 :rule refl :args (@t188)) % 0.61/0.89 (step @p388 :rule bool-double-not-elim :args (@t181)) % 0.61/0.89 (step @p389 :rule refl :args (@t189)) % 0.61/0.89 (step @p390 :rule nary_cong :premises (@p389 @p388 @p387) :args ((or @t189 (not @t190) @t188))) % 0.61/0.89 (assume-push @p581 @t164) % 0.61/0.89 (assume-push @p582 @t190) % 0.61/0.89 (assume-push @p583 @t190) % 0.61/0.89 (assume-push @p584 @t164) % 0.61/0.89 (step @p395 :rule false_intro :premises (@p582)) % 0.61/0.89 (step @p396 :rule refl :args (@t178)) % 0.61/0.89 (step @p397 :rule cong :premises (@p581 @p396) :args (@t186)) % 0.61/0.89 (step @p398 :rule trans :premises (@p397 @p395)) % 0.61/0.89 (step @p399 :rule false_elim :premises (@p398)) % 0.61/0.89 (step-pop @p585 :rule scope :premises (@p399)) % 0.61/0.89 (step-pop @p586 :rule scope :premises (@p585)) % 0.61/0.89 (step @p400 :rule process_scope :premises (@p586) :args (@t188)) % 0.61/0.89 (step @p403 :rule and_intro :premises (@p582 @p581)) % 0.61/0.89 (step @p404 :rule modus_ponens :premises (@p403 @p400)) % 0.61/0.89 (step-pop @p587 :rule scope :premises (@p404)) % 0.61/0.89 (step-pop @p588 :rule scope :premises (@p587)) % 0.61/0.89 (step @p405 :rule process_scope :premises (@p588) :args (@t188)) % 0.61/0.89 (step @p408 :rule implies_elim :premises (@p405)) % 0.61/0.89 (step @p409 :rule cnf_and_neg :args (@t191)) % 0.61/0.89 (step @p410 :rule resolution :premises (@p409 @p408) :args (true @t191)) % 0.61/0.89 (step @p411 :rule eq_resolve :premises (@p410 @p390)) % 0.61/0.89 (step @p412 :rule chain_m_resolution :premises (@p411 @p386 @p384 @p381 @p375 @p374 @p358 @p356 @p341 @p339) :args (@t169 (@list false false false true true true false false false) (@list @t186 @t187 @t179 @t181 @t182 @t174 @t176 @t164 @t166))) % 0.61/0.89 (step @p413 :rule bool-double-not-elim :args (@t165)) % 0.61/0.89 (step @p414 :rule refl :args (@t193)) % 0.61/0.89 (step @p415 :rule nary_cong :premises (@p414 @p413) :args ((or @t193 (not @t169)))) % 0.61/0.89 (step @p416 :rule cnf_or_neg :args (@t193 1)) % 0.61/0.89 (step @p417 :rule eq_resolve :premises (@p416 @p415)) % 0.61/0.89 (step @p418 :rule reordering :premises (@p417) :args ((or @t165 @t193))) % 0.61/0.89 (step @p419 :rule chain_m_resolution :premises (@p418 @p412) :args (@t193 @t113 (@list @t165))) % 0.61/0.89 (step @p420 :rule refl :args (@t194)) % 0.61/0.89 (step @p421 :rule nary_cong :premises (@p219 @p420) :args ((or @t128 @t194))) % 0.61/0.89 (step @p422 :rule eq-symm :args (@t163 @t116)) % 0.61/0.89 (step @p423 :rule nary_cong :premises (@p422 @p346) :args (@t195)) % 0.61/0.89 (step @p424 :rule cong :premises (@p423) :args (@t196)) % 0.61/0.89 (step @p425 :rule refl :args (@t118)) % 0.61/0.89 (step @p426 :rule cong :premises (@p425 @p424) :args ((=> @t118 @t196))) % 0.61/0.89 (assume-push @p589 @t118) % 0.61/0.89 (step @p428 :rule skolemize :premises (@p589)) % 0.61/0.89 (step-pop @p590 :rule scope :premises (@p428)) % 0.61/0.89 (step @p429 :rule process_scope :premises (@p590) :args (@t196)) % 0.61/0.89 (step @p431 :rule eq_resolve :premises (@p429 @p426)) % 0.61/0.89 (step @p432 :rule implies_elim :premises (@p431)) % 0.61/0.89 (step @p433 :rule eq_resolve :premises (@p432 @p421)) % 0.61/0.89 (step @p434 :rule chain_m_resolution :premises (@p433 @p419) :args (@t117 @t167 (@list @t193))) % 0.61/0.89 (step @p435 :rule refl :args (@t198)) % 0.61/0.89 (step @p436 :rule eq-symm :args (@t155 @t116)) % 0.61/0.89 (step @p437 :rule nary_cong :premises (@p436 @p435) :args (@t199)) % 0.61/0.89 (step @p438 :rule cong :premises (@p271 @p437) :args ((=> @t117 @t199))) % 0.61/0.89 (assume-push @p591 @t117) % 0.61/0.89 (step @p440 :rule instantiate :premises (@p591) :args ((@list @t155))) % 0.61/0.89 (step-pop @p592 :rule scope :premises (@p440)) % 0.61/0.89 (step @p441 :rule process_scope :premises (@p592) :args (@t199)) % 0.61/0.89 (step @p443 :rule eq_resolve :premises (@p441 @p438)) % 0.61/0.89 (step @p444 :rule implies_elim :premises (@p443)) % 0.61/0.89 (step @p445 :rule chain_m_resolution :premises (@p444 @p434) :args (@t201 @t167 (@list @t117))) % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p446 :rule trust :premises () :args ((=> @t158 @t202))) % 0.61/0.89 (step @p447 :rule implies_elim :premises (@p446)) % 0.61/0.89 (step @p448 :rule chain_m_resolution :premises (@p447 @p336) :args (@t202 @t167 @t168)) % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p449 :rule trust :premises () :args ((=> @t145 @t203))) % 0.61/0.89 (step @p450 :rule implies_elim :premises (@p449)) % 0.61/0.89 (step @p451 :rule bool-eq-true :args (@t119)) % 0.61/0.89 (step @p452 :rule cong :premises (@p265 @p451) :args (@t204)) % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p453 :rule trust :premises () :args (@t204)) % 0.61/0.89 (step @p454 :rule eq_resolve :premises (@p453 @p452)) % 0.61/0.89 (step @p455 :rule implies_elim :premises (@p454)) % 0.61/0.89 (step @p456 :rule reordering :premises (@p455) :args ((or @t119 @t205))) % 0.61/0.89 (step @p457 :rule cnf_or_neg :args (@t193 0)) % 0.61/0.89 (step @p458 :rule cnf_equiv_pos1 :args (@t203)) % 0.61/0.89 (step @p459 :rule reordering :premises (@p458) :args ((or @t169 @t192 @t206))) % 0.61/0.89 (step @p460 :rule chain_m_resolution :premises (@p459 @p418 @p457) :args ((or @t193 @t206) @t154 (@list @t165 @t192))) % 0.61/0.89 (step @p461 :rule cong :premises (@p348 @p203) :args ((=> @t99 @t126))) % 0.61/0.89 (assume-push @p593 @t99) % 0.61/0.89 (step @p463 :rule instantiate :premises (@p593) :args (@t136)) % 0.61/0.89 (step-pop @p594 :rule scope :premises (@p463)) % 0.61/0.89 (step @p464 :rule process_scope :premises (@p594) :args (@t126)) % 0.61/0.89 (step @p466 :rule eq_resolve :premises (@p464 @p461)) % 0.61/0.89 (step @p467 :rule implies_elim :premises (@p466)) % 0.61/0.89 (step @p468 :rule chain_m_resolution :premises (@p467 @p306) :args (@t121 @t167 @t177)) % 0.61/0.89 (step @p469 :rule cnf_or_pos :args (@t121)) % 0.61/0.89 (step @p470 :rule reordering :premises (@p469) :args ((or @t120 @t118 @t122))) % 0.61/0.89 (step @p471 :rule chain_m_resolution :premises (@p433 @p470 @p468 @p460 @p456 @p450) :args (@t205 (@list true false false false false) (@list @t117 @t121 @t193 @t119 @t203))) % 0.61/0.89 (step @p472 :rule chain_m_resolution :premises (@p268 @p471) :args ((not @t150) @t113 (@list @t145))) % 0.61/0.89 (step @p473 :rule eq-symm :args (@t137 @t42)) % 0.61/0.89 (step @p474 :rule nary_cong :premises (@p473 @p197) :args (@t207)) % 0.61/0.89 (step @p475 :rule cong :premises (@p474) :args (@t208)) % 0.61/0.89 (step @p476 :rule cong :premises (@p475) :args (@t209)) % 0.61/0.89 (step @p477 :rule nary_cong :premises (@p269 @p476) :args (@t210)) % 0.61/0.89 (step @p478 :rule cong :premises (@p348 @p477) :args ((=> @t99 @t210))) % 0.61/0.89 (assume-push @p595 @t99) % 0.61/0.89 (step @p480 :rule instantiate :premises (@p595) :args (@t149)) % 0.61/0.89 (step-pop @p596 :rule scope :premises (@p480)) % 0.61/0.89 (step @p481 :rule process_scope :premises (@p596) :args (@t210)) % 0.61/0.89 (step @p483 :rule eq_resolve :premises (@p481 @p478)) % 0.61/0.89 (step @p484 :rule implies_elim :premises (@p483)) % 0.61/0.89 (step @p485 :rule chain_m_resolution :premises (@p484 @p306) :args (@t213 @t167 @t177)) % 0.61/0.89 (step @p486 :rule cnf_or_pos :args (@t213)) % 0.61/0.89 (step @p487 :rule reordering :premises (@p486) :args ((or @t147 @t212 (not @t213)))) % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p488 :rule trust :premises () :args ((=> @t158 @t215))) % 0.61/0.89 (step @p489 :rule implies_elim :premises (@p488)) % 0.61/0.89 (step @p490 :rule chain_m_resolution :premises (@p489 @p336) :args (@t215 @t167 @t168)) % 0.61/0.89 (step @p491 :rule cnf_equiv_pos1 :args (@t215)) % 0.61/0.89 (step @p492 :rule reordering :premises (@p491) :args ((or @t147 @t214 (not @t215)))) % 0.61/0.89 (step @p493 :rule refl :args (@t221)) % 0.61/0.89 (step @p494 :rule bool-double-not-elim :args (@t211)) % 0.61/0.89 (step @p495 :rule nary_cong :premises (@p494 @p493) :args ((or (not @t212) @t221))) % 0.61/0.89 (step @p496 :rule refl :args (@t218)) % 0.61/0.89 (step @p497 :rule eq-symm :args (@t216 @t137)) % 0.61/0.89 (step @p498 :rule nary_cong :premises (@p497 @p496) :args (@t222)) % 0.61/0.89 (step @p499 :rule cong :premises (@p498) :args (@t223)) % 0.61/0.89 (step @p500 :rule refl :args (@t212)) % 0.61/0.89 (step @p501 :rule cong :premises (@p500 @p499) :args ((=> @t212 @t223))) % 0.61/0.89 (assume-push @p597 @t212) % 0.61/0.89 (step @p503 :rule skolemize :premises (@p597)) % 0.61/0.89 (step-pop @p598 :rule scope :premises (@p503)) % 0.61/0.89 (step @p504 :rule process_scope :premises (@p598) :args (@t223)) % 0.61/0.89 (step @p506 :rule eq_resolve :premises (@p504 @p501)) % 0.61/0.89 (step @p507 :rule implies_elim :premises (@p506)) % 0.61/0.89 (step @p508 :rule eq_resolve :premises (@p507 @p495)) % 0.61/0.89 (step @p509 :rule cnf_or_neg :args (@t220 0)) % 0.61/0.89 (step @p510 :rule bool-double-not-elim :args (@t217)) % 0.61/0.89 (step @p511 :rule refl :args (@t220)) % 0.61/0.89 (step @p512 :rule nary_cong :premises (@p511 @p510) :args ((or @t220 (not @t218)))) % 0.61/0.89 (step @p513 :rule cnf_or_neg :args (@t220 1)) % 0.61/0.89 (step @p514 :rule eq_resolve :premises (@p513 @p512)) % 0.61/0.89 (step @p515 :rule reordering :premises (@p514) :args ((or @t217 @t220))) % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p516 :rule trust :premises () :args ((=> @t158 @t225))) % 0.61/0.89 (step @p517 :rule implies_elim :premises (@p516)) % 0.61/0.89 (step @p518 :rule chain_m_resolution :premises (@p517 @p336) :args (@t225 @t167 @t168)) % 0.61/0.89 (step @p519 :rule cnf_equiv_pos1 :args (@t225)) % 0.61/0.89 (step @p520 :rule reordering :premises (@p519) :args ((or @t218 @t224 (not @t225)))) % 0.61/0.89 (step @p521 :rule refl :args (@t226)) % 0.61/0.89 (step @p522 :rule refl :args (@t227)) % 0.61/0.89 (step @p523 :rule bool-double-not-elim :args (@t219)) % 0.61/0.89 (step @p524 :rule nary_cong :premises (@p523 @p522 @p521) :args ((or (not @t228) @t227 @t226))) % 0.61/0.89 (assume-push @p599 @t228) % 0.61/0.89 (assume-push @p600 @t214) % 0.61/0.89 (assume-push @p601 @t228) % 0.61/0.89 (assume-push @p602 @t214) % 0.61/0.89 (step @p529 :rule false_intro :premises (@p599)) % 0.61/0.89 (step @p530 :rule refl :args (@t216)) % 0.61/0.89 (step @p531 :rule symm :premises (@p600)) % 0.61/0.89 (step @p532 :rule cong :premises (@p531 @p530) :args (@t224)) % 0.61/0.89 (step @p533 :rule trans :premises (@p532 @p529)) % 0.61/0.89 (step @p534 :rule false_elim :premises (@p533)) % 0.61/0.89 (step-pop @p603 :rule scope :premises (@p534)) % 0.61/0.89 (step-pop @p604 :rule scope :premises (@p603)) % 0.61/0.89 (step @p535 :rule process_scope :premises (@p604) :args (@t226)) % 0.61/0.89 (step @p538 :rule and_intro :premises (@p599 @p600)) % 0.61/0.89 (step @p539 :rule modus_ponens :premises (@p538 @p535)) % 0.61/0.89 (step-pop @p605 :rule scope :premises (@p539)) % 0.61/0.89 (step-pop @p606 :rule scope :premises (@p605)) % 0.61/0.89 (step @p540 :rule process_scope :premises (@p606) :args (@t226)) % 0.61/0.89 (step @p543 :rule implies_elim :premises (@p540)) % 0.61/0.89 (step @p544 :rule cnf_and_neg :args (@t229)) % 0.61/0.89 (step @p545 :rule resolution :premises (@p544 @p543) :args (true @t229)) % 0.61/0.89 (step @p546 :rule eq_resolve :premises (@p545 @p524)) % 0.61/0.89 (step @p547 :rule reordering :premises (@p546) :args ((or @t219 @t226 @t227))) % 0.61/0.89 (step @p548 :rule chain_m_resolution :premises (@p547 @p520 @p518 @p515 @p509 @p508 @p492 @p490 @p487 @p485) :args (@t147 (@list false false false true true false false true false) (@list @t224 @t225 @t217 @t219 @t220 @t214 @t215 @t211 @t213))) % 0.61/0.89 (step @p549 :rule chain_m_resolution :premises (@p284 @p548 @p472) :args (@t138 (@list true true) (@list @t142 @t150))) % 0.61/0.89 (step @p550 :rule chain_m_resolution :premises (@p305 @p548 @p549) :args (@t120 @t230 (@list @t142 @t138))) % 0.61/0.89 (step @p551 :rule cnf_equiv_pos2 :args (@t202)) % 0.61/0.89 (step @p552 :rule reordering :premises (@p551) :args ((or @t119 @t231 (not @t202)))) % 0.61/0.89 (step @p553 :rule chain_m_resolution :premises (@p552 @p550 @p448) :args (@t231 @t230 (@list @t119 @t202))) % 0.61/0.89 (step @p554 :rule cnf_or_pos :args (@t201)) % 0.61/0.89 (step @p555 :rule reordering :premises (@p554) :args ((or @t200 @t198 (not @t201)))) % 0.61/0.89 (step @p556 :rule chain_m_resolution :premises (@p555 @p553 @p445) :args (@t198 @t230 (@list @t200 @t201))) % 0.61/0.89 (step @p557 :rule bool-eq-true :args (@t197)) % 0.61/0.89 (step @p558 :rule cong :premises (@p310 @p557) :args (@t232)) % 0.61/0.89 ; trust TRUST THEORY_LEMMA % 0.61/0.89 (step @p559 :rule trust :premises () :args (@t232)) % 0.61/0.89 (step @p560 :rule eq_resolve :premises (@p559 @p558)) % 0.61/0.89 (step @p561 :rule implies_elim :premises (@p560)) % 0.61/0.89 (step @p562 false :rule chain_m_resolution :premises (@p561 @p556 @p336) :args (false @t230 (@list @t197 @t158))) % 0.61/0.89 ) % 0.61/0.89 % SZS output end Proof % 0.61/0.89 % cvc5 exiting %------------------------------------------------------------------------------