%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV293^5 : TPTP v9.2.1. Bugfixed v6.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n003.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 0.63s 0.82s % Output : Proof 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV293^5 : TPTP v9.2.1. Bugfixed v6.2.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n003.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 18:25:44 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.63/0.82 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.63/0.82 % SZS status Theorem % 0.63/0.82 % SZS output start Proof % 0.63/0.82 ( % 0.63/0.82 (declare-sort $$unsorted 0) % 0.63/0.82 (declare-const tptp.cONE (-> (-> $$unsorted Bool) Bool)) % 0.63/0.82 (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))))))) % 0.63/0.82 (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)))))))))))) % 0.63/0.82 (define @t1 () (= tptp.cONE (_ tptp.cSUCC tptp.cZERO))) % 0.63/0.82 (define @t2 () (@var "Xy" $$unsorted)) % 0.63/0.82 (define @t3 () (@var "Xx" $$unsorted)) % 0.63/0.82 (define @t4 () (lambda (@list @t3 @t2) (= @t3 @t2))) % 0.63/0.82 (define @t5 () (@var "P" (-> $$unsorted Bool))) % 0.63/0.82 (define @t6 () (= @t5 (_ @t4 @t2))) % 0.63/0.82 (define @t7 () (@list @t2)) % 0.63/0.82 (define @t8 () (exists @t7 @t6)) % 0.63/0.82 (define @t9 () (@list @t5)) % 0.63/0.82 (define @t10 () (lambda @t9 @t8)) % 0.63/0.82 (define @t11 () (= tptp.cONE @t10)) % 0.63/0.82 (define @t12 () (not @t11)) % 0.63/0.82 (define @t13 () (@var "Xp" (-> $$unsorted Bool))) % 0.63/0.82 (define @t14 () (_ @t13 @t3)) % 0.63/0.82 (define @t15 () (@list @t3)) % 0.63/0.82 (define @t16 () (exists @t15 @t14)) % 0.63/0.82 (define @t17 () (not @t16)) % 0.63/0.82 (define @t18 () (@list @t13)) % 0.63/0.82 (define @t19 () (lambda @t18 @t17)) % 0.63/0.82 (define @t20 () (@var "Xt" $$unsorted)) % 0.63/0.82 (define @t21 () (_ @t13 @t20)) % 0.63/0.82 (define @t22 () (not (= @t20 @t3))) % 0.63/0.82 (define @t23 () (and @t22 @t21)) % 0.63/0.82 (define @t24 () (@list @t20)) % 0.63/0.82 (define @t25 () (lambda @t24 @t23)) % 0.63/0.82 (define @t26 () (@var "Xn" (-> (-> $$unsorted Bool) Bool))) % 0.63/0.82 (define @t27 () (and @t14 (_ @t26 @t25))) % 0.63/0.82 (define @t28 () (exists @t15 @t27)) % 0.63/0.82 (define @t29 () (@list @t26 @t13)) % 0.63/0.82 (define @t30 () (lambda @t29 @t28)) % 0.63/0.82 (define @t31 () (@var "BOUND_VARIABLE_7508" $$unsorted)) % 0.63/0.82 (define @t32 () (_ @t13 @t31)) % 0.63/0.82 (define @t33 () (not @t32)) % 0.63/0.82 (define @t34 () (= @t3 @t31)) % 0.63/0.82 (define @t35 () (@list @t31)) % 0.63/0.82 (define @t36 () (_ @t13 @t3)) % 0.63/0.82 (define @t37 () (not @t36)) % 0.63/0.82 (define @t38 () (lambda @t18 (not (forall @t15 (or @t37 (not (forall @t35 (or @t34 @t33)))))))) % 0.63/0.82 (define @t39 () (@purify @t38)) % 0.63/0.82 (define @t40 () (@var "BOUND_VARIABLE_7539" $$unsorted)) % 0.63/0.82 (define @t41 () (@list @t40)) % 0.63/0.82 (define @t42 () (lambda @t41 (= @t2 @t40))) % 0.63/0.82 (define @t43 () (= @t5 @t42)) % 0.63/0.82 (define @t44 () (not (forall @t7 (not @t43)))) % 0.63/0.82 (define @t45 () (lambda @t9 @t44)) % 0.63/0.82 (define @t46 () (@purify @t45)) % 0.63/0.82 (define @t47 () (= @t38 @t45)) % 0.63/0.82 (define @t48 () (not @t34)) % 0.63/0.82 (define @t49 () (and @t48 @t32)) % 0.63/0.82 (define @t50 () (_ @t13 @t20)) % 0.63/0.82 (define @t51 () (not (= @t3 @t20))) % 0.63/0.82 (define @t52 () (and @t51 @t50)) % 0.63/0.82 (define @t53 () (lambda @t24 @t52)) % 0.63/0.82 (define @t54 () (_ @t53 @t31)) % 0.63/0.82 (define @t55 () (not @t54)) % 0.63/0.82 (define @t56 () (forall @t35 @t55)) % 0.63/0.82 (define @t57 () (forall @t15 @t37)) % 0.63/0.82 (define @t58 () (lambda @t18 @t57)) % 0.63/0.82 (define @t59 () (not (_ @t58 @t53))) % 0.63/0.82 (define @t60 () (or @t37 @t59)) % 0.63/0.82 (define @t61 () (forall @t15 @t60)) % 0.63/0.82 (define @t62 () (not @t61)) % 0.63/0.82 (define @t63 () (lambda @t18 @t62)) % 0.63/0.82 (define @t64 () (_ @t26 @t53)) % 0.63/0.82 (define @t65 () (_ (lambda @t29 (not (forall @t15 (or @t37 (not @t64))))) @t58)) % 0.63/0.82 (define @t66 () (not @t14)) % 0.63/0.82 (define @t67 () (forall @t15 @t66)) % 0.63/0.82 (define @t68 () (not @t67)) % 0.63/0.82 (define @t69 () (and @t51 @t21)) % 0.63/0.82 (define @t70 () (lambda @t24 @t69)) % 0.63/0.82 (define @t71 () (_ @t26 @t70)) % 0.63/0.82 (define @t72 () (not @t71)) % 0.63/0.82 (define @t73 () (or @t66 @t72)) % 0.63/0.82 (define @t74 () (and @t14 @t71)) % 0.63/0.82 (define @t75 () (forall @t15 (not @t74))) % 0.63/0.82 (define @t76 () (not @t75)) % 0.63/0.82 (define @t77 () (= tptp.cONE @t45)) % 0.63/0.82 (define @t78 () (@const 0 (-> $$unsorted Bool))) % 0.63/0.82 (define @t79 () (forall @t7 (not (= @t42 @t78)))) % 0.63/0.82 (define @t80 () (not @t79)) % 0.63/0.82 (define @t81 () (not (_ @t78 @t31))) % 0.63/0.82 (define @t82 () (forall @t15 (or (not (_ @t78 @t3)) (not (forall @t35 (or @t34 @t81)))))) % 0.63/0.82 (define @t83 () (not @t82)) % 0.63/0.82 (define @t84 () (_ @t38 @t78)) % 0.63/0.82 (define @t85 () (_ @t39 @t78)) % 0.63/0.82 (define @t86 () (not (= @t78 @t42))) % 0.63/0.82 (define @t87 () (forall @t7 @t86)) % 0.63/0.82 (define @t88 () (not @t87)) % 0.63/0.82 (define @t89 () (_ @t45 @t78)) % 0.63/0.82 (define @t90 () (_ @t46 @t78)) % 0.63/0.82 (define @t91 () (= @t90 @t85)) % 0.63/0.82 (define @t92 () (not @t91)) % 0.63/0.82 (define @t93 () (= @t46 @t39)) % 0.63/0.82 (define @t94 () (or @t93 @t92)) % 0.63/0.82 (define @t95 () (= @t83 @t80)) % 0.63/0.82 (define @t96 () (@list true)) % 0.63/0.82 (define @t97 () (not @t80)) % 0.63/0.82 (define @t98 () (not @t83)) % 0.63/0.82 (define @t99 () (@quantifiers_skolemize @t82 0)) % 0.63/0.82 (define @t100 () (forall @t35 (or (= @t31 @t99) @t81))) % 0.63/0.82 (define @t101 () (not @t100)) % 0.63/0.82 (define @t102 () (_ @t78 @t99)) % 0.63/0.82 (define @t103 () (not @t102)) % 0.63/0.82 (define @t104 () (or @t103 @t101)) % 0.63/0.82 (define @t105 () (not @t104)) % 0.63/0.82 (define @t106 () (or (= @t99 @t31) @t81)) % 0.63/0.82 (define @t107 () (forall @t35 @t106)) % 0.63/0.82 (define @t108 () (not @t107)) % 0.63/0.82 (define @t109 () (or @t103 @t108)) % 0.63/0.82 (define @t110 () (not @t109)) % 0.63/0.82 (define @t111 () (not @t101)) % 0.63/0.82 (define @t112 () (lambda @t41 (= @t40 @t99))) % 0.63/0.82 (define @t113 () (@purify @t112)) % 0.63/0.82 (define @t114 () (= @t78 @t112)) % 0.63/0.82 (define @t115 () (not @t114)) % 0.63/0.82 (define @t116 () (lambda @t41 (= @t99 @t40))) % 0.63/0.82 (define @t117 () (= @t116 @t78)) % 0.63/0.82 (define @t118 () (not @t117)) % 0.63/0.82 (define @t119 () (@list @t99)) % 0.63/0.82 (define @t120 () (@const 1 $$unsorted)) % 0.63/0.82 (define @t121 () (= @t99 @t120)) % 0.63/0.82 (define @t122 () (= @t120 @t99)) % 0.63/0.82 (define @t123 () (_ @t112 @t120)) % 0.63/0.82 (define @t124 () (_ @t113 @t120)) % 0.63/0.82 (define @t125 () (_ @t78 @t120)) % 0.63/0.82 (define @t126 () (= @t125 @t124)) % 0.63/0.82 (define @t127 () (not @t126)) % 0.63/0.82 (define @t128 () (= @t78 @t113)) % 0.63/0.82 (define @t129 () (or @t128 @t127)) % 0.63/0.82 (define @t130 () (not @t125)) % 0.63/0.82 (define @t131 () (or @t122 @t130)) % 0.63/0.82 (define @t132 () (@list @t120)) % 0.63/0.82 (define @t133 () (= @t125 @t121)) % 0.63/0.82 (define @t134 () (or @t121 @t130)) % 0.63/0.82 (define @t135 () (not @t134)) % 0.63/0.82 (define @t136 () (not @t121)) % 0.63/0.82 (define @t137 () (@list false true)) % 0.63/0.82 (define @t138 () (@quantifiers_skolemize @t79 0)) % 0.63/0.82 (define @t139 () (lambda @t41 (= @t40 @t138))) % 0.63/0.82 (define @t140 () (@purify @t139)) % 0.63/0.82 (define @t141 () (= @t78 @t140)) % 0.63/0.82 (define @t142 () (= @t78 @t139)) % 0.63/0.82 (define @t143 () (lambda @t41 (= @t138 @t40))) % 0.63/0.82 (define @t144 () (= @t143 @t78)) % 0.63/0.82 (define @t145 () (not (not @t144))) % 0.63/0.82 (define @t146 () (@quantifiers_skolemize @t100 0)) % 0.63/0.82 (define @t147 () (= @t138 @t146)) % 0.63/0.82 (define @t148 () (_ @t78 @t146)) % 0.63/0.82 (define @t149 () (= @t148 @t147)) % 0.63/0.82 (define @t150 () (@list false)) % 0.63/0.82 (define @t151 () (@list @t141)) % 0.63/0.82 (define @t152 () (not @t148)) % 0.63/0.82 (define @t153 () (or (= @t146 @t31) @t81)) % 0.63/0.82 (define @t154 () (forall @t35 @t153)) % 0.63/0.82 (define @t155 () (not @t154)) % 0.63/0.82 (define @t156 () (or @t152 @t155)) % 0.63/0.82 (define @t157 () (forall @t35 (or (= @t31 @t146) @t81))) % 0.63/0.82 (define @t158 () (not @t157)) % 0.63/0.82 (define @t159 () (or @t152 @t158)) % 0.63/0.82 (define @t160 () (@list @t82)) % 0.63/0.82 (define @t161 () (@quantifiers_skolemize @t157 0)) % 0.63/0.82 (define @t162 () (_ @t78 @t161)) % 0.63/0.82 (define @t163 () (not @t162)) % 0.63/0.82 (define @t164 () (= @t146 @t161)) % 0.63/0.82 (define @t165 () (or @t164 @t163)) % 0.63/0.82 (define @t166 () (not @t165)) % 0.63/0.82 (define @t167 () (or (= @t161 @t146) @t163)) % 0.63/0.82 (define @t168 () (not @t167)) % 0.63/0.82 (define @t169 () (= @t138 @t161)) % 0.63/0.82 (define @t170 () (= @t162 @t169)) % 0.63/0.82 (define @t171 () (not @t169)) % 0.63/0.82 (define @t172 () (not @t147)) % 0.63/0.82 (define @t173 () (not @t164)) % 0.63/0.82 (define @t174 () (and @t147 @t173)) % 0.63/0.82 (define @t175 () (= @t99 @t146)) % 0.63/0.82 (define @t176 () (or @t175 @t152)) % 0.63/0.82 (define @t177 () (not @t176)) % 0.63/0.82 (define @t178 () (or (= @t146 @t99) @t152)) % 0.63/0.82 (define @t179 () (not @t178)) % 0.63/0.82 (define @t180 () (_ @t78 @t138)) % 0.63/0.82 (define @t181 () (not @t180)) % 0.63/0.82 (define @t182 () (or (= @t138 @t99) @t181)) % 0.63/0.82 (define @t183 () (= @t99 @t138)) % 0.63/0.82 (define @t184 () (or @t183 @t181)) % 0.63/0.82 (define @t185 () (= @t102 @t183)) % 0.63/0.82 (define @t186 () (= @t148 @t175)) % 0.63/0.82 (define @t187 () (=> @t128 (= @t102 true))) % 0.63/0.82 (define @t188 () (not @t128)) % 0.63/0.82 (define @t189 () (not @t186)) % 0.63/0.82 (define @t190 () (or (= @t120 @t31) @t81)) % 0.63/0.82 (define @t191 () (forall @t35 @t190)) % 0.63/0.82 (define @t192 () (not @t191)) % 0.63/0.82 (define @t193 () (or @t130 @t192)) % 0.63/0.82 (define @t194 () (forall @t35 (or (= @t31 @t120) @t81))) % 0.63/0.82 (define @t195 () (not @t194)) % 0.63/0.82 (define @t196 () (or @t130 @t195)) % 0.63/0.82 (define @t197 () (= @t120 @t138)) % 0.63/0.82 (define @t198 () (= @t125 @t197)) % 0.63/0.82 (define @t199 () (@quantifiers_skolemize @t194 0)) % 0.63/0.82 (define @t200 () (_ @t78 @t199)) % 0.63/0.82 (define @t201 () (not @t200)) % 0.63/0.82 (define @t202 () (= @t120 @t199)) % 0.63/0.82 (define @t203 () (or @t202 @t201)) % 0.63/0.82 (define @t204 () (not @t203)) % 0.63/0.82 (define @t205 () (or (= @t199 @t120) @t201)) % 0.63/0.82 (define @t206 () (not @t205)) % 0.63/0.82 (define @t207 () (= @t138 @t199)) % 0.63/0.82 (define @t208 () (= @t200 @t207)) % 0.63/0.82 (define @t209 () (not @t207)) % 0.63/0.82 (define @t210 () (not @t197)) % 0.63/0.82 (define @t211 () (not @t202)) % 0.63/0.82 (define @t212 () (and @t211 @t197)) % 0.63/0.82 (define @t213 () (@list true false)) % 0.63/0.82 (define @t214 () (not @t183)) % 0.63/0.82 (define @t215 () (=> @t141 (= @t180 true))) % 0.63/0.82 (assume @p1 @t1) % 0.63/0.82 (assume @p2 @t12) % 0.63/0.82 (assume @p3 true) % 0.63/0.82 (step @p4 (= tptp.cZERO @t19) :rule refl :args (@t19)) % 0.63/0.82 (step @p5 (= tptp.cSUCC @t30) :rule refl :args (@t30)) % 0.63/0.82 (step @p6 :rule eq-symm :args (@t39 @t46)) % 0.63/0.82 (step @p7 :rule eq-refl :args (@t45)) % 0.63/0.82 (step @p8 :rule skolem_intro :args (@t46)) % 0.63/0.82 (step @p9 :rule refl :args (@t45)) % 0.63/0.82 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t45 @t46))) % 0.63/0.82 (step @p11 :rule trans :premises (@p10 @p7)) % 0.63/0.82 (step @p12 :rule true_elim :premises (@p11)) % 0.63/0.82 (step @p13 :rule eq-refl :args (@t38)) % 0.63/0.82 (step @p14 :rule skolem_intro :args (@t39)) % 0.63/0.82 (step @p15 :rule refl :args (@t38)) % 0.63/0.82 (step @p16 :rule cong :premises (@p15 @p14) :args ((= @t38 @t39))) % 0.63/0.82 (step @p17 :rule trans :premises (@p16 @p13)) % 0.63/0.82 (step @p18 :rule true_elim :premises (@p17)) % 0.63/0.82 (step @p19 :rule cong :premises (@p18 @p12) :args (@t47)) % 0.63/0.82 (step @p20 :rule trans :premises (@p19 @p6)) % 0.63/0.82 (step @p21 :rule cong :premises (@p20) :args ((not @t47))) % 0.63/0.82 (step @p22 :rule refl :args (@t33)) % 0.63/0.82 (step @p23 :rule bool-double-not-elim :args (@t34)) % 0.63/0.82 (step @p24 :rule nary_cong :premises (@p23 @p22) :args ((or (not @t48) @t33))) % 0.63/0.82 (step @p25 :rule bool-and-de-morgan :args (@t48 @t32 true)) % 0.63/0.82 (step @p26 :rule trans :premises (@p25 @p24)) % 0.63/0.82 (step @p27 :rule cong :premises (@p26) :args ((forall @t35 (not @t49)))) % 0.63/0.82 (step @p28 :rule beta-reduce :args ((= @t54 @t49))) % 0.63/0.82 (step @p29 :rule cong :premises (@p28) :args (@t55)) % 0.63/0.82 (step @p30 :rule cong :premises (@p29) :args (@t56)) % 0.63/0.82 (step @p31 :rule trans :premises (@p30 @p27)) % 0.63/0.82 (step @p32 :rule beta-reduce :args ((= (_ (lambda @t18 (forall @t35 @t33)) @t53) @t56))) % 0.63/0.82 (step @p33 :rule trans :premises (@p32 @p31)) % 0.63/0.82 (step @p34 :rule refl :args (@t53)) % 0.63/0.82 (step @p35 :rule alpha_equiv :args (@t57 (@list @t3) (@list @t31))) % 0.63/0.82 (step @p36 :rule cong :premises (@p35) :args (@t58)) % 0.63/0.82 (step @p37 :rule ho_cong :premises (@p36 @p34)) % 0.63/0.82 (step @p38 :rule trans :premises (@p37 @p33)) % 0.63/0.82 (step @p39 :rule cong :premises (@p38) :args (@t59)) % 0.63/0.82 (step @p40 :rule refl :args (@t37)) % 0.63/0.82 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t60)) % 0.63/0.82 (step @p42 :rule cong :premises (@p41) :args (@t61)) % 0.63/0.82 (step @p43 :rule cong :premises (@p42) :args (@t62)) % 0.63/0.82 (step @p44 :rule cong :premises (@p43) :args (@t63)) % 0.63/0.82 (step @p45 :rule beta-reduce :args ((= @t65 @t63))) % 0.63/0.82 (step @p46 :rule trans :premises (@p45 @p44)) % 0.63/0.82 (step @p47 :rule refl :args (tptp.cONE)) % 0.63/0.82 (step @p48 :rule cong :premises (@p47 @p46) :args ((= tptp.cONE @t65))) % 0.63/0.82 (step @p49 :rule bool-double-not-elim :args (@t57)) % 0.63/0.82 (step @p50 :rule refl :args (@t36)) % 0.63/0.82 (step @p51 :rule refl :args (@t14)) % 0.63/0.82 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t14 @t36))) % 0.63/0.82 (step @p53 :rule symm :premises (@p52)) % 0.63/0.82 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 0.63/0.82 (step @p55 :rule cong :premises (@p54) :args (@t66)) % 0.63/0.82 (step @p56 :rule cong :premises (@p55) :args (@t67)) % 0.63/0.82 (step @p57 :rule cong :premises (@p56) :args (@t68)) % 0.63/0.82 (step @p58 :rule exists-elim :args ((= @t16 @t68))) % 0.63/0.82 (step @p59 :rule trans :premises (@p58 @p57)) % 0.63/0.82 (step @p60 :rule cong :premises (@p59) :args (@t17)) % 0.63/0.82 (step @p61 :rule trans :premises (@p60 @p49)) % 0.63/0.82 (step @p62 :rule cong :premises (@p61) :args (@t19)) % 0.63/0.82 (step @p63 :rule trans :premises (@p4 @p62)) % 0.63/0.82 (step @p64 :rule refl :args ((_ @t26 @t70))) % 0.63/0.82 (step @p65 :rule refl :args (@t50)) % 0.63/0.82 (step @p66 :rule refl :args (@t51)) % 0.63/0.82 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t52)) % 0.63/0.82 (step @p68 :rule cong :premises (@p67) :args (@t53)) % 0.63/0.82 (step @p69 :rule cong :premises (@p68) :args (@t64)) % 0.63/0.82 (step @p70 :rule trans :premises (@p69 @p64)) % 0.63/0.82 (step @p71 :rule refl :args (@t26)) % 0.63/0.82 (step @p72 :rule ho_cong :premises (@p71 @p68)) % 0.63/0.82 (step @p73 :rule cong :premises (@p72 @p70) :args ((= (_ @t26 @t53) @t64))) % 0.63/0.82 (step @p74 :rule symm :premises (@p73)) % 0.63/0.82 (step @p75 :rule refl :args (@t71)) % 0.63/0.82 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.63/0.82 (step @p77 :rule refl :args (@t21)) % 0.63/0.82 (step @p78 :rule cong :premises (@p77 @p65) :args ((= @t21 @t50))) % 0.63/0.82 (step @p79 :rule symm :premises (@p78)) % 0.63/0.82 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 0.63/0.82 (step @p81 :rule nary_cong :premises (@p66 @p80) :args (@t69)) % 0.63/0.82 (step @p82 :rule cong :premises (@p81) :args (@t70)) % 0.63/0.82 (step @p83 :rule ho_cong :premises (@p71 @p82)) % 0.63/0.82 (step @p84 :rule trans :premises (@p83 @p76)) % 0.63/0.82 (step @p85 :rule cong :premises (@p84) :args (@t72)) % 0.63/0.82 (step @p86 :rule nary_cong :premises (@p55 @p85) :args (@t73)) % 0.63/0.82 (step @p87 :rule cong :premises (@p86) :args ((forall @t15 @t73))) % 0.63/0.82 (step @p88 :rule bool-and-de-morgan :args (@t14 @t71 true)) % 0.63/0.82 (step @p89 :rule cong :premises (@p88) :args (@t75)) % 0.63/0.82 (step @p90 :rule trans :premises (@p89 @p87)) % 0.63/0.82 (step @p91 :rule cong :premises (@p90) :args (@t76)) % 0.63/0.82 (step @p92 :rule exists-elim :args ((= (exists @t15 @t74) @t76))) % 0.63/0.82 (step @p93 :rule trans :premises (@p92 @p91)) % 0.63/0.82 (step @p94 :rule refl :args (@t21)) % 0.63/0.82 (step @p95 :rule eq-symm :args (@t20 @t3)) % 0.63/0.82 (step @p96 :rule cong :premises (@p95) :args (@t22)) % 0.63/0.82 (step @p97 :rule nary_cong :premises (@p96 @p94) :args (@t23)) % 0.63/0.82 (step @p98 :rule cong :premises (@p97) :args (@t25)) % 0.63/0.82 (step @p99 :rule refl :args (@t26)) % 0.63/0.82 (step @p100 :rule ho_cong :premises (@p99 @p98)) % 0.63/0.82 (step @p101 :rule refl :args (@t14)) % 0.63/0.82 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t27)) % 0.63/0.82 (step @p103 :rule cong :premises (@p102) :args (@t28)) % 0.63/0.82 (step @p104 :rule trans :premises (@p103 @p93)) % 0.63/0.82 (step @p105 :rule cong :premises (@p104) :args (@t30)) % 0.63/0.82 (step @p106 :rule trans :premises (@p5 @p105)) % 0.63/0.82 (step @p107 :rule ho_cong :premises (@p106 @p63)) % 0.63/0.82 (step @p108 :rule cong :premises (@p47 @p107) :args (@t1)) % 0.63/0.82 (step @p109 :rule trans :premises (@p108 @p48)) % 0.63/0.82 (step @p110 :rule eq_resolve :premises (@p1 @p109)) % 0.63/0.82 (step @p111 :rule cong :premises (@p110 @p9) :args (@t77)) % 0.63/0.82 (step @p112 :rule cong :premises (@p111) :args ((not @t77))) % 0.63/0.82 (step @p113 :rule exists-elim :args ((= (exists @t7 @t43) @t44))) % 0.63/0.82 (step @p114 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t40) (= @t3 @t40)) @t2) @t42))) % 0.63/0.82 (step @p115 :rule refl :args (@t2)) % 0.63/0.82 (step @p116 :rule alpha_equiv :args (@t4 (@list @t2) (@list @t40))) % 0.63/0.82 (step @p117 :rule ho_cong :premises (@p116 @p115)) % 0.63/0.82 (step @p118 :rule trans :premises (@p117 @p114)) % 0.63/0.82 (step @p119 :rule refl :args (@t5)) % 0.63/0.82 (step @p120 :rule cong :premises (@p119 @p118) :args (@t6)) % 0.63/0.82 (step @p121 :rule cong :premises (@p120) :args (@t8)) % 0.63/0.82 (step @p122 :rule trans :premises (@p121 @p113)) % 0.63/0.82 (step @p123 :rule cong :premises (@p122) :args (@t10)) % 0.63/0.82 (step @p124 :rule cong :premises (@p47 @p123) :args (@t11)) % 0.63/0.82 (step @p125 :rule cong :premises (@p124) :args (@t12)) % 0.63/0.82 (step @p126 :rule trans :premises (@p125 @p112 @p21)) % 0.63/0.82 (step @p127 :rule eq_resolve :premises (@p2 @p126)) % 0.63/0.82 (step @p128 :rule eq-symm :args (@t80 @t83)) % 0.63/0.82 (step @p129 :rule eq-refl :args (@t83)) % 0.63/0.82 (step @p130 :rule beta-reduce :args ((= @t84 @t83))) % 0.63/0.82 (step @p131 :rule refl :args (@t83)) % 0.63/0.82 (step @p132 :rule cong :premises (@p131 @p130) :args ((= @t83 @t84))) % 0.63/0.82 (step @p133 :rule trans :premises (@p132 @p129)) % 0.63/0.82 (step @p134 :rule eq-symm :args (@t84 @t83)) % 0.63/0.82 (step @p135 :rule trans :premises (@p134 @p133)) % 0.63/0.82 (step @p136 :rule refl :args (@t78)) % 0.63/0.82 (step @p137 :rule ho_cong :premises (@p14 @p136)) % 0.63/0.82 (step @p138 :rule cong :premises (@p137 @p131) :args ((= @t85 @t83))) % 0.63/0.82 (step @p139 :rule trans :premises (@p138 @p135)) % 0.63/0.82 (step @p140 :rule true_elim :premises (@p139)) % 0.63/0.82 (step @p141 :rule eq-refl :args (@t80)) % 0.63/0.82 (step @p142 :rule eq-symm :args (@t78 @t42)) % 0.63/0.82 (step @p143 :rule cong :premises (@p142) :args (@t86)) % 0.63/0.82 (step @p144 :rule cong :premises (@p143) :args (@t87)) % 0.63/0.82 (step @p145 :rule cong :premises (@p144) :args (@t88)) % 0.63/0.82 (step @p146 :rule beta-reduce :args ((= @t89 @t88))) % 0.63/0.82 (step @p147 :rule trans :premises (@p146 @p145)) % 0.63/0.82 (step @p148 :rule refl :args (@t80)) % 0.63/0.82 (step @p149 :rule cong :premises (@p148 @p147) :args ((= @t80 @t89))) % 0.63/0.82 (step @p150 :rule trans :premises (@p149 @p141)) % 0.63/0.82 (step @p151 :rule eq-symm :args (@t89 @t80)) % 0.63/0.82 (step @p152 :rule trans :premises (@p151 @p150)) % 0.63/0.82 (step @p153 :rule ho_cong :premises (@p8 @p136)) % 0.63/0.82 (step @p154 :rule cong :premises (@p153 @p148) :args ((= @t90 @t80))) % 0.63/0.82 (step @p155 :rule trans :premises (@p154 @p152)) % 0.63/0.82 (step @p156 :rule true_elim :premises (@p155)) % 0.63/0.82 (step @p157 :rule cong :premises (@p156 @p140) :args (@t91)) % 0.63/0.82 (step @p158 :rule trans :premises (@p157 @p128)) % 0.63/0.82 (step @p159 :rule cong :premises (@p158) :args (@t92)) % 0.63/0.82 (step @p160 :rule refl :args (@t93)) % 0.63/0.82 (step @p161 :rule nary_cong :premises (@p160 @p159) :args (@t94)) % 0.63/0.82 ; WARNING: add trust step for TRUST % 0.63/0.82 ; trust TRUST THEORY_LEMMA % 0.63/0.82 (step @p162 :rule trust :premises () :args (@t94)) % 0.63/0.82 (step @p163 :rule eq_resolve :premises (@p162 @p161)) % 0.63/0.82 (step @p164 :rule chain_m_resolution :premises (@p163 @p127) :args ((not @t95) @t96 (@list @t93))) % 0.63/0.82 (step @p165 :rule bool-double-not-elim :args (@t79)) % 0.63/0.82 (step @p166 :rule bool-double-not-elim :args (@t82)) % 0.63/0.82 (step @p167 :rule refl :args (@t95)) % 0.63/0.82 (step @p168 :rule nary_cong :premises (@p167 @p166 @p165) :args ((or @t95 @t98 @t97))) % 0.63/0.82 (step @p169 :rule cnf_equiv_neg2 :args (@t95)) % 0.63/0.82 (step @p170 :rule eq_resolve :premises (@p169 @p168)) % 0.63/0.82 (step @p171 :rule reordering :premises (@p170) :args ((or @t82 @t79 @t95))) % 0.63/0.82 (step @p172 :rule refl :args (@t105)) % 0.63/0.82 (step @p173 :rule nary_cong :premises (@p166 @p172) :args ((or @t98 @t105))) % 0.63/0.82 (step @p174 :rule refl :args (@t81)) % 0.63/0.82 (step @p175 :rule eq-symm :args (@t99 @t31)) % 0.63/0.82 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t106)) % 0.63/0.82 (step @p177 :rule cong :premises (@p176) :args (@t107)) % 0.63/0.82 (step @p178 :rule cong :premises (@p177) :args (@t108)) % 0.63/0.82 (step @p179 :rule refl :args (@t103)) % 0.63/0.82 (step @p180 :rule nary_cong :premises (@p179 @p178) :args (@t109)) % 0.63/0.82 (step @p181 :rule cong :premises (@p180) :args (@t110)) % 0.63/0.82 (step @p182 :rule cong :premises (@p131 @p181) :args ((=> @t83 @t110))) % 0.63/0.82 (assume-push @p540 @t83) % 0.63/0.82 (step @p184 :rule skolemize :premises (@p540)) % 0.63/0.82 (step-pop @p541 :rule scope :premises (@p184)) % 0.63/0.82 (step @p185 :rule process_scope :premises (@p541) :args (@t110)) % 0.63/0.82 (step @p187 :rule eq_resolve :premises (@p185 @p182)) % 0.63/0.82 (step @p188 :rule implies_elim :premises (@p187)) % 0.63/0.82 (step @p189 :rule eq_resolve :premises (@p188 @p173)) % 0.63/0.82 (step @p190 :rule bool-double-not-elim :args (@t102)) % 0.63/0.82 (step @p191 :rule refl :args (@t104)) % 0.63/0.82 (step @p192 :rule nary_cong :premises (@p191 @p190) :args ((or @t104 (not @t103)))) % 0.63/0.82 (step @p193 :rule cnf_or_neg :args (@t104 0)) % 0.63/0.82 (step @p194 :rule eq_resolve :premises (@p193 @p192)) % 0.63/0.82 (step @p195 :rule reordering :premises (@p194) :args ((or @t102 @t104))) % 0.63/0.82 (step @p196 :rule bool-double-not-elim :args (@t100)) % 0.63/0.82 (step @p197 :rule nary_cong :premises (@p191 @p196) :args ((or @t104 @t111))) % 0.63/0.82 (step @p198 :rule cnf_or_neg :args (@t104 1)) % 0.63/0.82 (step @p199 :rule eq_resolve :premises (@p198 @p197)) % 0.63/0.82 (step @p200 :rule reordering :premises (@p199) :args ((or @t100 @t104))) % 0.63/0.82 (step @p201 :rule eq-refl :args (@t112)) % 0.63/0.82 (step @p202 :rule skolem_intro :args (@t113)) % 0.63/0.82 (step @p203 :rule refl :args (@t112)) % 0.63/0.82 (step @p204 :rule cong :premises (@p203 @p202) :args ((= @t112 @t113))) % 0.63/0.82 (step @p205 :rule trans :premises (@p204 @p201)) % 0.63/0.82 (step @p206 :rule true_elim :premises (@p205)) % 0.63/0.82 (step @p207 :rule cong :premises (@p136 @p206) :args (@t114)) % 0.63/0.82 (step @p208 :rule cong :premises (@p207) :args (@t115)) % 0.63/0.82 (step @p209 :rule refl :args (@t79)) % 0.63/0.82 (step @p210 :rule cong :premises (@p209 @p208) :args ((=> @t79 @t115))) % 0.63/0.82 (step @p211 :rule eq-symm :args (@t112 @t78)) % 0.63/0.82 (step @p212 :rule eq-symm :args (@t99 @t40)) % 0.63/0.82 (step @p213 :rule cong :premises (@p212) :args (@t116)) % 0.63/0.82 (step @p214 :rule cong :premises (@p213 @p136) :args (@t117)) % 0.63/0.82 (step @p215 :rule trans :premises (@p214 @p211)) % 0.63/0.82 (step @p216 :rule cong :premises (@p215) :args (@t118)) % 0.63/0.82 (step @p217 :rule cong :premises (@p209 @p216) :args ((=> @t79 @t118))) % 0.63/0.82 (assume-push @p542 @t79) % 0.63/0.82 (step @p219 :rule instantiate :premises (@p542) :args (@t119)) % 0.63/0.82 (step-pop @p543 :rule scope :premises (@p219)) % 0.63/0.82 (step @p220 :rule process_scope :premises (@p543) :args (@t118)) % 0.63/0.82 (step @p222 :rule eq_resolve :premises (@p220 @p217)) % 0.63/0.82 (step @p223 :rule eq_resolve :premises (@p222 @p210)) % 0.63/0.82 (step @p224 :rule implies_elim :premises (@p223)) % 0.63/0.82 (step @p225 :rule eq-refl :args (@t121)) % 0.63/0.82 (step @p226 :rule eq-symm :args (@t120 @t99)) % 0.63/0.82 (step @p227 :rule beta-reduce :args ((= @t123 @t122))) % 0.63/0.82 (step @p228 :rule trans :premises (@p227 @p226)) % 0.63/0.82 (step @p229 :rule refl :args (@t121)) % 0.63/0.82 (step @p230 :rule cong :premises (@p229 @p228) :args ((= @t121 @t123))) % 0.63/0.82 (step @p231 :rule trans :premises (@p230 @p225)) % 0.63/0.82 (step @p232 :rule eq-symm :args (@t123 @t121)) % 0.63/0.82 (step @p233 :rule trans :premises (@p232 @p231)) % 0.63/0.82 (step @p234 :rule refl :args (@t120)) % 0.63/0.82 (step @p235 :rule ho_cong :premises (@p202 @p234)) % 0.63/0.82 (step @p236 :rule cong :premises (@p235 @p229) :args ((= @t124 @t121))) % 0.63/0.82 (step @p237 :rule trans :premises (@p236 @p233)) % 0.63/0.82 (step @p238 :rule true_elim :premises (@p237)) % 0.63/0.82 (step @p239 :rule refl :args (@t125)) % 0.63/0.82 (step @p240 :rule cong :premises (@p239 @p238) :args (@t126)) % 0.63/0.82 (step @p241 :rule cong :premises (@p240) :args (@t127)) % 0.63/0.82 (step @p242 :rule refl :args (@t128)) % 0.63/0.82 (step @p243 :rule nary_cong :premises (@p242 @p241) :args (@t129)) % 0.63/0.82 ; trust TRUST THEORY_LEMMA % 0.63/0.82 (step @p244 :rule trust :premises () :args (@t129)) % 0.63/0.82 (step @p245 :rule eq_resolve :premises (@p244 @p243)) % 0.63/0.82 (step @p246 :rule refl :args (@t130)) % 0.63/0.82 (step @p247 :rule nary_cong :premises (@p226 @p246) :args (@t131)) % 0.63/0.82 (step @p248 :rule refl :args (@t100)) % 0.63/0.82 (step @p249 :rule cong :premises (@p248 @p247) :args ((=> @t100 @t131))) % 0.63/0.82 (assume-push @p544 @t100) % 0.63/0.82 (step @p251 :rule instantiate :premises (@p544) :args (@t132)) % 0.63/0.82 (step-pop @p545 :rule scope :premises (@p251)) % 0.63/0.82 (step @p252 :rule process_scope :premises (@p545) :args (@t131)) % 0.63/0.82 (step @p254 :rule eq_resolve :premises (@p252 @p249)) % 0.63/0.82 (step @p255 :rule implies_elim :premises (@p254)) % 0.63/0.82 (step @p256 :rule cnf_equiv_neg2 :args (@t133)) % 0.63/0.82 (step @p257 :rule cnf_or_pos :args (@t134)) % 0.63/0.82 (step @p258 :rule reordering :premises (@p257) :args ((or @t121 @t130 @t135))) % 0.63/0.82 (step @p259 :rule chain_m_resolution :premises (@p258 @p256) :args ((or @t133 @t130 @t135) @t96 (@list @t121))) % 0.63/0.82 (step @p260 :rule cnf_equiv_neg1 :args (@t133)) % 0.63/0.82 (step @p261 :rule reordering :premises (@p260) :args ((or @t125 @t121 @t133))) % 0.63/0.82 (step @p262 :rule bool-double-not-elim :args (@t125)) % 0.63/0.82 (step @p263 :rule refl :args (@t136)) % 0.63/0.82 (step @p264 :rule nary_cong :premises (@p179 @p263 @p262) :args ((or @t103 @t136 (not @t130)))) % 0.63/0.82 (assume-push @p546 @t102) % 0.63/0.82 (assume-push @p547 @t121) % 0.63/0.82 (assume-push @p548 @t130) % 0.63/0.82 (step @p268 :rule evaluate :args ((= false true))) % 0.63/0.82 (step @p269 :rule true_intro :premises (@p546)) % 0.63/0.82 (step @p270 :rule symm :premises (@p547)) % 0.63/0.82 (step @p271 :rule cong :premises (@p270) :args (@t125)) % 0.63/0.82 (step @p272 :rule false_intro :premises (@p548)) % 0.63/0.82 (step @p273 :rule symm :premises (@p272)) % 0.63/0.82 (step @p274 :rule trans :premises (@p273 @p271 @p269)) % 0.63/0.82 (step @p275 false :rule eq_resolve :premises (@p274 @p268)) % 0.63/0.82 (step-pop @p549 :rule scope :premises (@p275)) % 0.63/0.82 (step-pop @p550 :rule scope :premises (@p549)) % 0.63/0.82 (step-pop @p551 :rule scope :premises (@p550)) % 0.63/0.82 (step @p276 :rule process_scope :premises (@p551) :args (false)) % 0.63/0.82 (step @p280 :rule not_and :premises (@p276)) % 0.63/0.82 (step @p281 :rule eq_resolve :premises (@p280 @p264)) % 0.63/0.82 (step @p282 :rule reordering :premises (@p281) :args ((or @t103 @t125 @t136))) % 0.63/0.82 (step @p283 :rule chain_m_resolution :premises (@p282 @p261 @p259 @p255 @p245 @p224 @p200 @p195 @p189 @p171 @p164) :args (@t82 (@list false true false true true false false true false true) (@list @t121 @t125 @t134 @t133 @t128 @t100 @t102 @t104 @t79 @t95))) % 0.63/0.82 (step @p284 :rule cnf_equiv_neg1 :args (@t95)) % 0.63/0.82 (step @p285 :rule reordering :premises (@p284) :args ((or @t83 @t80 @t95))) % 0.63/0.82 (step @p286 :rule chain_m_resolution :premises (@p285 @p283 @p164) :args (@t80 @t137 (@list @t82 @t95))) % 0.63/0.82 (step @p287 :rule refl :args (@t141)) % 0.63/0.82 (step @p288 :rule nary_cong :premises (@p165 @p287) :args ((or @t97 @t141))) % 0.63/0.82 (step @p289 :rule eq-refl :args (@t139)) % 0.63/0.82 (step @p290 :rule skolem_intro :args (@t140)) % 0.63/0.82 (step @p291 :rule refl :args (@t139)) % 0.63/0.82 (step @p292 :rule cong :premises (@p291 @p290) :args ((= @t139 @t140))) % 0.63/0.82 (step @p293 :rule trans :premises (@p292 @p289)) % 0.63/0.82 (step @p294 :rule true_elim :premises (@p293)) % 0.63/0.82 (step @p295 :rule cong :premises (@p136 @p294) :args (@t142)) % 0.63/0.82 (step @p296 :rule cong :premises (@p148 @p295) :args ((=> @t80 @t142))) % 0.63/0.82 (step @p297 :rule eq-symm :args (@t139 @t78)) % 0.63/0.82 (step @p298 :rule eq-symm :args (@t138 @t40)) % 0.63/0.82 (step @p299 :rule cong :premises (@p298) :args (@t143)) % 0.63/0.82 (step @p300 :rule cong :premises (@p299 @p136) :args (@t144)) % 0.63/0.82 (step @p301 :rule trans :premises (@p300 @p297)) % 0.63/0.82 (step @p302 :rule bool-double-not-elim :args (@t144)) % 0.63/0.82 (step @p303 :rule trans :premises (@p302 @p301)) % 0.63/0.82 (step @p304 :rule cong :premises (@p148 @p303) :args ((=> @t80 @t145))) % 0.63/0.82 (step @p305 :rule trans :premises (@p304 @p296)) % 0.63/0.82 (assume-push @p552 @t80) % 0.63/0.82 (step @p307 :rule skolemize :premises (@p552)) % 0.63/0.82 (step-pop @p553 :rule scope :premises (@p307)) % 0.63/0.82 (step @p308 :rule process_scope :premises (@p553) :args (@t145)) % 0.63/0.82 (step @p310 :rule eq_resolve :premises (@p308 @p305)) % 0.63/0.82 (step @p311 :rule implies_elim :premises (@p310)) % 0.63/0.82 (step @p312 :rule eq_resolve :premises (@p311 @p288)) % 0.63/0.82 (step @p313 :rule chain_m_resolution :premises (@p312 @p286) :args (@t141 @t96 (@list @t79))) % 0.63/0.82 ; trust TRUST THEORY_LEMMA % 0.63/0.82 (step @p314 :rule trust :premises () :args ((=> @t141 @t149))) % 0.63/0.82 (step @p315 :rule implies_elim :premises (@p314)) % 0.63/0.82 (step @p316 :rule chain_m_resolution :premises (@p315 @p313) :args (@t149 @t150 @t151)) % 0.63/0.82 (step @p317 :rule cnf_equiv_pos1 :args (@t149)) % 0.63/0.82 (step @p318 :rule reordering :premises (@p317) :args ((or @t152 @t147 (not @t149)))) % 0.63/0.82 (step @p319 :rule eq-symm :args (@t146 @t31)) % 0.63/0.82 (step @p320 :rule nary_cong :premises (@p319 @p174) :args (@t153)) % 0.63/0.82 (step @p321 :rule cong :premises (@p320) :args (@t154)) % 0.63/0.82 (step @p322 :rule cong :premises (@p321) :args (@t155)) % 0.63/0.82 (step @p323 :rule refl :args (@t152)) % 0.63/0.82 (step @p324 :rule nary_cong :premises (@p323 @p322) :args (@t156)) % 0.63/0.82 (step @p325 :rule refl :args (@t82)) % 0.63/0.82 (step @p326 :rule cong :premises (@p325 @p324) :args ((=> @t82 @t156))) % 0.63/0.82 (assume-push @p554 @t82) % 0.63/0.82 (step @p328 :rule instantiate :premises (@p554) :args ((@list @t146))) % 0.63/0.82 (step-pop @p555 :rule scope :premises (@p328)) % 0.63/0.82 (step @p329 :rule process_scope :premises (@p555) :args (@t156)) % 0.63/0.82 (step @p331 :rule eq_resolve :premises (@p329 @p326)) % 0.63/0.82 (step @p332 :rule implies_elim :premises (@p331)) % 0.63/0.82 (step @p333 :rule chain_m_resolution :premises (@p332 @p283) :args (@t159 @t150 @t160)) % 0.63/0.82 (step @p334 :rule cnf_or_pos :args (@t159)) % 0.63/0.82 (step @p335 :rule reordering :premises (@p334) :args ((or @t152 @t158 (not @t159)))) % 0.63/0.82 (step @p336 :rule refl :args (@t166)) % 0.63/0.82 (step @p337 :rule bool-double-not-elim :args (@t157)) % 0.63/0.82 (step @p338 :rule nary_cong :premises (@p337 @p336) :args ((or (not @t158) @t166))) % 0.63/0.82 (step @p339 :rule refl :args (@t163)) % 0.63/0.82 (step @p340 :rule eq-symm :args (@t161 @t146)) % 0.63/0.82 (step @p341 :rule nary_cong :premises (@p340 @p339) :args (@t167)) % 0.63/0.82 (step @p342 :rule cong :premises (@p341) :args (@t168)) % 0.63/0.82 (step @p343 :rule refl :args (@t158)) % 0.63/0.82 (step @p344 :rule cong :premises (@p343 @p342) :args ((=> @t158 @t168))) % 0.63/0.82 (assume-push @p556 @t158) % 0.63/0.82 (step @p346 :rule skolemize :premises (@p556)) % 0.63/0.82 (step-pop @p557 :rule scope :premises (@p346)) % 0.63/0.82 (step @p347 :rule process_scope :premises (@p557) :args (@t168)) % 0.63/0.82 (step @p349 :rule eq_resolve :premises (@p347 @p344)) % 0.63/0.82 (step @p350 :rule implies_elim :premises (@p349)) % 0.63/0.82 (step @p351 :rule eq_resolve :premises (@p350 @p338)) % 0.63/0.82 (step @p352 :rule cnf_or_neg :args (@t165 0)) % 0.63/0.82 (step @p353 :rule bool-double-not-elim :args (@t162)) % 0.63/0.82 (step @p354 :rule refl :args (@t165)) % 0.63/0.82 (step @p355 :rule nary_cong :premises (@p354 @p353) :args ((or @t165 (not @t163)))) % 0.63/0.82 (step @p356 :rule cnf_or_neg :args (@t165 1)) % 0.63/0.82 (step @p357 :rule eq_resolve :premises (@p356 @p355)) % 0.63/0.82 (step @p358 :rule reordering :premises (@p357) :args ((or @t162 @t165))) % 0.63/0.82 ; trust TRUST THEORY_LEMMA % 0.63/0.82 (step @p359 :rule trust :premises () :args ((=> @t141 @t170))) % 0.63/0.82 (step @p360 :rule implies_elim :premises (@p359)) % 0.63/0.82 (step @p361 :rule chain_m_resolution :premises (@p360 @p313) :args (@t170 @t150 @t151)) % 0.63/0.82 (step @p362 :rule cnf_equiv_pos1 :args (@t170)) % 0.63/0.82 (step @p363 :rule reordering :premises (@p362) :args ((or @t163 @t169 (not @t170)))) % 0.63/0.82 (step @p364 :rule refl :args (@t171)) % 0.63/0.82 (step @p365 :rule bool-double-not-elim :args (@t164)) % 0.63/0.82 (step @p366 :rule refl :args (@t172)) % 0.63/0.82 (step @p367 :rule nary_cong :premises (@p366 @p365 @p364) :args ((or @t172 (not @t173) @t171))) % 0.63/0.82 (assume-push @p558 @t147) % 0.63/0.82 (assume-push @p559 @t173) % 0.63/0.82 (assume-push @p560 @t173) % 0.63/0.82 (assume-push @p561 @t147) % 0.63/0.82 (step @p372 :rule false_intro :premises (@p559)) % 0.63/0.82 (step @p373 :rule refl :args (@t161)) % 0.63/0.82 (step @p374 :rule cong :premises (@p558 @p373) :args (@t169)) % 0.63/0.82 (step @p375 :rule trans :premises (@p374 @p372)) % 0.63/0.82 (step @p376 :rule false_elim :premises (@p375)) % 0.63/0.82 (step-pop @p562 :rule scope :premises (@p376)) % 0.63/0.82 (step-pop @p563 :rule scope :premises (@p562)) % 0.63/0.82 (step @p377 :rule process_scope :premises (@p563) :args (@t171)) % 0.63/0.82 (step @p380 :rule and_intro :premises (@p559 @p558)) % 0.63/0.82 (step @p381 :rule modus_ponens :premises (@p380 @p377)) % 0.63/0.82 (step-pop @p564 :rule scope :premises (@p381)) % 0.63/0.82 (step-pop @p565 :rule scope :premises (@p564)) % 0.63/0.82 (step @p382 :rule process_scope :premises (@p565) :args (@t171)) % 0.63/0.82 (step @p385 :rule implies_elim :premises (@p382)) % 0.63/0.82 (step @p386 :rule cnf_and_neg :args (@t174)) % 0.63/0.82 (step @p387 :rule resolution :premises (@p386 @p385) :args (true @t174)) % 0.63/0.82 (step @p388 :rule eq_resolve :premises (@p387 @p367)) % 0.63/0.82 (step @p389 :rule chain_m_resolution :premises (@p388 @p363 @p361 @p358 @p352 @p351 @p335 @p333 @p318 @p316) :args (@t152 (@list false false false true true true false false false) (@list @t169 @t170 @t162 @t164 @t165 @t157 @t159 @t147 @t149))) % 0.63/0.82 (step @p390 :rule bool-double-not-elim :args (@t148)) % 0.63/0.82 (step @p391 :rule refl :args (@t176)) % 0.63/0.82 (step @p392 :rule nary_cong :premises (@p391 @p390) :args ((or @t176 (not @t152)))) % 0.63/0.82 (step @p393 :rule cnf_or_neg :args (@t176 1)) % 0.63/0.82 (step @p394 :rule eq_resolve :premises (@p393 @p392)) % 0.63/0.82 (step @p395 :rule reordering :premises (@p394) :args ((or @t148 @t176))) % 0.63/0.82 (step @p396 :rule chain_m_resolution :premises (@p395 @p389) :args (@t176 @t96 (@list @t148))) % 0.63/0.82 (step @p397 :rule refl :args (@t177)) % 0.63/0.82 (step @p398 :rule nary_cong :premises (@p196 @p397) :args ((or @t111 @t177))) % 0.63/0.82 (step @p399 :rule eq-symm :args (@t146 @t99)) % 0.63/0.82 (step @p400 :rule nary_cong :premises (@p399 @p323) :args (@t178)) % 0.63/0.82 (step @p401 :rule cong :premises (@p400) :args (@t179)) % 0.63/0.82 (step @p402 :rule refl :args (@t101)) % 0.63/0.82 (step @p403 :rule cong :premises (@p402 @p401) :args ((=> @t101 @t179))) % 0.63/0.82 (assume-push @p566 @t101) % 0.63/0.82 (step @p405 :rule skolemize :premises (@p566)) % 0.63/0.82 (step-pop @p567 :rule scope :premises (@p405)) % 0.63/0.82 (step @p406 :rule process_scope :premises (@p567) :args (@t179)) % 0.63/0.82 (step @p408 :rule eq_resolve :premises (@p406 @p403)) % 0.63/0.82 (step @p409 :rule implies_elim :premises (@p408)) % 0.63/0.82 (step @p410 :rule eq_resolve :premises (@p409 @p398)) % 0.63/0.82 (step @p411 :rule chain_m_resolution :premises (@p410 @p396) :args (@t100 @t150 (@list @t176))) % 0.63/0.82 (step @p412 :rule refl :args (@t181)) % 0.63/0.82 (step @p413 :rule eq-symm :args (@t138 @t99)) % 0.63/0.82 (step @p414 :rule nary_cong :premises (@p413 @p412) :args (@t182)) % 0.63/0.82 (step @p415 :rule cong :premises (@p248 @p414) :args ((=> @t100 @t182))) % 0.63/0.82 (assume-push @p568 @t100) % 0.63/0.82 (step @p417 :rule instantiate :premises (@p568) :args ((@list @t138))) % 0.63/0.82 (step-pop @p569 :rule scope :premises (@p417)) % 0.63/0.82 (step @p418 :rule process_scope :premises (@p569) :args (@t182)) % 0.63/0.82 (step @p420 :rule eq_resolve :premises (@p418 @p415)) % 0.63/0.82 (step @p421 :rule implies_elim :premises (@p420)) % 0.63/0.82 (step @p422 :rule chain_m_resolution :premises (@p421 @p411) :args (@t184 @t150 (@list @t100))) % 0.63/0.82 ; trust TRUST THEORY_LEMMA % 0.63/0.82 (step @p423 :rule trust :premises () :args ((=> @t141 @t185))) % 0.63/0.82 (step @p424 :rule implies_elim :premises (@p423)) % 0.63/0.82 (step @p425 :rule chain_m_resolution :premises (@p424 @p313) :args (@t185 @t150 @t151)) % 0.63/0.82 ; trust TRUST THEORY_LEMMA % 0.63/0.82 (step @p426 :rule trust :premises () :args ((=> @t128 @t186))) % 0.63/0.82 (step @p427 :rule implies_elim :premises (@p426)) % 0.63/0.82 (step @p428 :rule bool-eq-true :args (@t102)) % 0.63/0.82 (step @p429 :rule cong :premises (@p242 @p428) :args (@t187)) % 0.63/0.82 ; trust TRUST THEORY_LEMMA % 0.63/0.82 (step @p430 :rule trust :premises () :args (@t187)) % 0.63/0.82 (step @p431 :rule eq_resolve :premises (@p430 @p429)) % 0.63/0.82 (step @p432 :rule implies_elim :premises (@p431)) % 0.63/0.82 (step @p433 :rule reordering :premises (@p432) :args ((or @t102 @t188))) % 0.63/0.82 (step @p434 :rule cnf_or_neg :args (@t176 0)) % 0.63/0.82 (step @p435 :rule cnf_equiv_pos1 :args (@t186)) % 0.63/0.82 (step @p436 :rule reordering :premises (@p435) :args ((or @t152 @t175 @t189))) % 0.63/0.82 (step @p437 :rule chain_m_resolution :premises (@p436 @p395 @p434) :args ((or @t176 @t189) @t137 (@list @t148 @t175))) % 0.63/0.82 (step @p438 :rule cong :premises (@p325 @p180) :args ((=> @t82 @t109))) % 0.63/0.82 (assume-push @p570 @t82) % 0.63/0.82 (step @p440 :rule instantiate :premises (@p570) :args (@t119)) % 0.63/0.82 (step-pop @p571 :rule scope :premises (@p440)) % 0.63/0.82 (step @p441 :rule process_scope :premises (@p571) :args (@t109)) % 0.63/0.82 (step @p443 :rule eq_resolve :premises (@p441 @p438)) % 0.63/0.82 (step @p444 :rule implies_elim :premises (@p443)) % 0.63/0.82 (step @p445 :rule chain_m_resolution :premises (@p444 @p283) :args (@t104 @t150 @t160)) % 0.63/0.82 (step @p446 :rule cnf_or_pos :args (@t104)) % 0.63/0.82 (step @p447 :rule reordering :premises (@p446) :args ((or @t103 @t101 @t105))) % 0.63/0.82 (step @p448 :rule chain_m_resolution :premises (@p410 @p447 @p445 @p437 @p433 @p427) :args (@t188 (@list true false false false false) (@list @t100 @t104 @t176 @t102 @t186))) % 0.63/0.82 (step @p449 :rule chain_m_resolution :premises (@p245 @p448) :args ((not @t133) @t96 (@list @t128))) % 0.63/0.82 (step @p450 :rule eq-symm :args (@t120 @t31)) % 0.63/0.82 (step @p451 :rule nary_cong :premises (@p450 @p174) :args (@t190)) % 0.63/0.82 (step @p452 :rule cong :premises (@p451) :args (@t191)) % 0.63/0.82 (step @p453 :rule cong :premises (@p452) :args (@t192)) % 0.63/0.82 (step @p454 :rule nary_cong :premises (@p246 @p453) :args (@t193)) % 0.63/0.82 (step @p455 :rule cong :premises (@p325 @p454) :args ((=> @t82 @t193))) % 0.63/0.82 (assume-push @p572 @t82) % 0.63/0.82 (step @p457 :rule instantiate :premises (@p572) :args (@t132)) % 0.63/0.82 (step-pop @p573 :rule scope :premises (@p457)) % 0.63/0.82 (step @p458 :rule process_scope :premises (@p573) :args (@t193)) % 0.63/0.82 (step @p460 :rule eq_resolve :premises (@p458 @p455)) % 0.63/0.82 (step @p461 :rule implies_elim :premises (@p460)) % 0.63/0.82 (step @p462 :rule chain_m_resolution :premises (@p461 @p283) :args (@t196 @t150 @t160)) % 0.63/0.82 (step @p463 :rule cnf_or_pos :args (@t196)) % 0.63/0.82 (step @p464 :rule reordering :premises (@p463) :args ((or @t130 @t195 (not @t196)))) % 0.63/0.82 ; trust TRUST THEORY_LEMMA % 0.63/0.82 (step @p465 :rule trust :premises () :args ((=> @t141 @t198))) % 0.63/0.82 (step @p466 :rule implies_elim :premises (@p465)) % 0.63/0.82 (step @p467 :rule chain_m_resolution :premises (@p466 @p313) :args (@t198 @t150 @t151)) % 0.63/0.82 (step @p468 :rule cnf_equiv_pos1 :args (@t198)) % 0.63/0.82 (step @p469 :rule reordering :premises (@p468) :args ((or @t130 @t197 (not @t198)))) % 0.63/0.82 (step @p470 :rule refl :args (@t204)) % 0.63/0.82 (step @p471 :rule bool-double-not-elim :args (@t194)) % 0.63/0.82 (step @p472 :rule nary_cong :premises (@p471 @p470) :args ((or (not @t195) @t204))) % 0.63/0.82 (step @p473 :rule refl :args (@t201)) % 0.63/0.82 (step @p474 :rule eq-symm :args (@t199 @t120)) % 0.63/0.82 (step @p475 :rule nary_cong :premises (@p474 @p473) :args (@t205)) % 0.63/0.82 (step @p476 :rule cong :premises (@p475) :args (@t206)) % 0.63/0.82 (step @p477 :rule refl :args (@t195)) % 0.63/0.82 (step @p478 :rule cong :premises (@p477 @p476) :args ((=> @t195 @t206))) % 0.63/0.82 (assume-push @p574 @t195) % 0.63/0.82 (step @p480 :rule skolemize :premises (@p574)) % 0.63/0.82 (step-pop @p575 :rule scope :premises (@p480)) % 0.63/0.82 (step @p481 :rule process_scope :premises (@p575) :args (@t206)) % 0.63/0.82 (step @p483 :rule eq_resolve :premises (@p481 @p478)) % 0.63/0.82 (step @p484 :rule implies_elim :premises (@p483)) % 0.63/0.82 (step @p485 :rule eq_resolve :premises (@p484 @p472)) % 0.63/0.82 (step @p486 :rule cnf_or_neg :args (@t203 0)) % 0.63/0.82 (step @p487 :rule bool-double-not-elim :args (@t200)) % 0.63/0.82 (step @p488 :rule refl :args (@t203)) % 0.63/0.82 (step @p489 :rule nary_cong :premises (@p488 @p487) :args ((or @t203 (not @t201)))) % 0.63/0.82 (step @p490 :rule cnf_or_neg :args (@t203 1)) % 0.63/0.82 (step @p491 :rule eq_resolve :premises (@p490 @p489)) % 0.63/0.82 (step @p492 :rule reordering :premises (@p491) :args ((or @t200 @t203))) % 0.63/0.82 ; trust TRUST THEORY_LEMMA % 0.63/0.82 (step @p493 :rule trust :premises () :args ((=> @t141 @t208))) % 0.63/0.82 (step @p494 :rule implies_elim :premises (@p493)) % 0.63/0.82 (step @p495 :rule chain_m_resolution :premises (@p494 @p313) :args (@t208 @t150 @t151)) % 0.63/0.82 (step @p496 :rule cnf_equiv_pos1 :args (@t208)) % 0.63/0.82 (step @p497 :rule reordering :premises (@p496) :args ((or @t201 @t207 (not @t208)))) % 0.63/0.82 (step @p498 :rule refl :args (@t209)) % 0.63/0.82 (step @p499 :rule refl :args (@t210)) % 0.63/0.82 (step @p500 :rule bool-double-not-elim :args (@t202)) % 0.63/0.82 (step @p501 :rule nary_cong :premises (@p500 @p499 @p498) :args ((or (not @t211) @t210 @t209))) % 0.63/0.82 (assume-push @p576 @t211) % 0.63/0.82 (assume-push @p577 @t197) % 0.63/0.82 (assume-push @p578 @t211) % 0.63/0.82 (assume-push @p579 @t197) % 0.63/0.82 (step @p506 :rule false_intro :premises (@p576)) % 0.63/0.82 (step @p507 :rule refl :args (@t199)) % 0.63/0.82 (step @p508 :rule symm :premises (@p577)) % 0.63/0.82 (step @p509 :rule cong :premises (@p508 @p507) :args (@t207)) % 0.63/0.82 (step @p510 :rule trans :premises (@p509 @p506)) % 0.63/0.83 (step @p511 :rule false_elim :premises (@p510)) % 0.63/0.83 (step-pop @p580 :rule scope :premises (@p511)) % 0.63/0.83 (step-pop @p581 :rule scope :premises (@p580)) % 0.63/0.83 (step @p512 :rule process_scope :premises (@p581) :args (@t209)) % 0.63/0.83 (step @p515 :rule and_intro :premises (@p576 @p577)) % 0.63/0.83 (step @p516 :rule modus_ponens :premises (@p515 @p512)) % 0.63/0.83 (step-pop @p582 :rule scope :premises (@p516)) % 0.63/0.83 (step-pop @p583 :rule scope :premises (@p582)) % 0.63/0.83 (step @p517 :rule process_scope :premises (@p583) :args (@t209)) % 0.63/0.83 (step @p520 :rule implies_elim :premises (@p517)) % 0.63/0.83 (step @p521 :rule cnf_and_neg :args (@t212)) % 0.63/0.83 (step @p522 :rule resolution :premises (@p521 @p520) :args (true @t212)) % 0.63/0.83 (step @p523 :rule eq_resolve :premises (@p522 @p501)) % 0.63/0.83 (step @p524 :rule reordering :premises (@p523) :args ((or @t202 @t209 @t210))) % 0.63/0.83 (step @p525 :rule chain_m_resolution :premises (@p524 @p497 @p495 @p492 @p486 @p485 @p469 @p467 @p464 @p462) :args (@t130 (@list false false false true true false false true false) (@list @t207 @t208 @t200 @t202 @t203 @t197 @t198 @t194 @t196))) % 0.63/0.83 (step @p526 :rule chain_m_resolution :premises (@p261 @p525 @p449) :args (@t121 (@list true true) (@list @t125 @t133))) % 0.63/0.83 (step @p527 :rule chain_m_resolution :premises (@p282 @p525 @p526) :args (@t103 @t213 (@list @t125 @t121))) % 0.63/0.83 (step @p528 :rule cnf_equiv_pos2 :args (@t185)) % 0.63/0.83 (step @p529 :rule reordering :premises (@p528) :args ((or @t102 @t214 (not @t185)))) % 0.63/0.83 (step @p530 :rule chain_m_resolution :premises (@p529 @p527 @p425) :args (@t214 @t213 (@list @t102 @t185))) % 0.63/0.83 (step @p531 :rule cnf_or_pos :args (@t184)) % 0.63/0.83 (step @p532 :rule reordering :premises (@p531) :args ((or @t183 @t181 (not @t184)))) % 0.63/0.83 (step @p533 :rule chain_m_resolution :premises (@p532 @p530 @p422) :args (@t181 @t213 (@list @t183 @t184))) % 0.63/0.83 (step @p534 :rule bool-eq-true :args (@t180)) % 0.63/0.83 (step @p535 :rule cong :premises (@p287 @p534) :args (@t215)) % 0.63/0.83 ; trust TRUST THEORY_LEMMA % 0.63/0.83 (step @p536 :rule trust :premises () :args (@t215)) % 0.63/0.83 (step @p537 :rule eq_resolve :premises (@p536 @p535)) % 0.63/0.83 (step @p538 :rule implies_elim :premises (@p537)) % 0.63/0.83 (step @p539 false :rule chain_m_resolution :premises (@p538 @p533 @p313) :args (false @t213 (@list @t180 @t141))) % 0.63/0.83 ) % 0.63/0.83 % SZS output end Proof % 0.63/0.83 % cvc5 exiting %------------------------------------------------------------------------------