%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV009^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n015.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 08:55:18 AM UTC 2026 % Result : Theorem 120.83s 121.13s % Output : Proof 120.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV009^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n015.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 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 18:07:34 EDT 2026 % 0.16/0.35 % CPUTime : % 0.30/0.50 %----Proving TH0 % 120.83/121.13 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 120.83/121.13 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 120.83/121.13 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 120.83/121.13 --- Run --ho-elim --full-saturate-quant at 18s... % 120.83/121.13 % SZS status Theorem % 120.83/121.13 % SZS output start Proof % 120.83/121.13 ( % 120.83/121.13 (declare-sort tptp.a 0) % 120.83/121.13 (define @t1 () (@var "Xz" tptp.a)) % 120.83/121.13 (define @t2 () (@var "S" (-> tptp.a Bool))) % 120.83/121.13 (define @t3 () (_ @t2 @t1)) % 120.83/121.13 (define @t4 () (@var "Xx" tptp.a)) % 120.83/121.13 (define @t5 () (_ @t2 @t4)) % 120.83/121.13 (define @t6 () (@var "P" (-> (-> tptp.a Bool) Bool))) % 120.83/121.13 (define @t7 () (_ @t6 @t2)) % 120.83/121.13 (define @t8 () (and @t7 @t5 @t3)) % 120.83/121.13 (define @t9 () (@list @t2)) % 120.83/121.13 (define @t10 () (exists @t9 @t8)) % 120.83/121.13 (define @t11 () (@var "Xy" tptp.a)) % 120.83/121.13 (define @t12 () (_ @t2 @t11)) % 120.83/121.13 (define @t13 () (and @t7 @t12 @t3)) % 120.83/121.13 (define @t14 () (exists @t9 @t13)) % 120.83/121.13 (define @t15 () (and @t7 @t5 @t12)) % 120.83/121.13 (define @t16 () (exists @t9 @t15)) % 120.83/121.13 (define @t17 () (and @t16 @t14)) % 120.83/121.13 (define @t18 () (=> @t17 @t10)) % 120.83/121.13 (define @t19 () (@list @t4 @t11 @t1)) % 120.83/121.13 (define @t20 () (forall @t19 @t18)) % 120.83/121.13 (define @t21 () (and @t7 @t12 @t5)) % 120.83/121.13 (define @t22 () (exists @t9 @t21)) % 120.83/121.13 (define @t23 () (=> @t16 @t22)) % 120.83/121.13 (define @t24 () (@list @t4 @t11)) % 120.83/121.13 (define @t25 () (forall @t24 @t23)) % 120.83/121.13 (define @t26 () (and @t7 @t5 @t5)) % 120.83/121.13 (define @t27 () (exists @t9 @t26)) % 120.83/121.13 (define @t28 () (@list @t4)) % 120.83/121.13 (define @t29 () (forall @t28 @t27)) % 120.83/121.13 (define @t30 () (and @t29 @t25 @t20)) % 120.83/121.13 (define @t31 () (@var "Xp" (-> tptp.a Bool))) % 120.83/121.13 (define @t32 () (@var "Xq" (-> tptp.a Bool))) % 120.83/121.13 (define @t33 () (_ @t32 @t4)) % 120.83/121.13 (define @t34 () (_ @t6 @t32)) % 120.83/121.13 (define @t35 () (and @t34 @t33)) % 120.83/121.13 (define @t36 () (=> @t35 (= @t32 @t31))) % 120.83/121.13 (define @t37 () (@list @t32)) % 120.83/121.13 (define @t38 () (forall @t37 @t36)) % 120.83/121.13 (define @t39 () (_ @t31 @t4)) % 120.83/121.13 (define @t40 () (_ @t6 @t31)) % 120.83/121.13 (define @t41 () (and @t40 @t39 @t38)) % 120.83/121.13 (define @t42 () (@list @t31)) % 120.83/121.13 (define @t43 () (exists @t42 @t41)) % 120.83/121.13 (define @t44 () (forall @t28 @t43)) % 120.83/121.13 (define @t45 () (=> @t44 @t30)) % 120.83/121.13 (define @t46 () (@list @t6)) % 120.83/121.13 (define @t47 () (forall @t46 @t45)) % 120.83/121.13 (define @t48 () (not @t47)) % 120.83/121.13 (define @t49 () (@var "BOUND_VARIABLE_7630" tptp.a)) % 120.83/121.13 (define @t50 () (@var "BOUND_VARIABLE_7663" (@ho-elim-sort (-> tptp.a Bool)))) % 120.83/121.13 (define @t51 () (@const 0 (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a Bool))) % 120.83/121.13 (define @t52 () (@var "BOUND_VARIABLE_7628" tptp.a)) % 120.83/121.13 (define @t53 () (@var "BOUND_VARIABLE_7674" (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.a Bool)) Bool)))) % 120.83/121.13 (define @t54 () (@const 1 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.a Bool)) Bool)) (@ho-elim-sort (-> tptp.a Bool)) Bool))) % 120.83/121.13 (define @t55 () (@var "BOUND_VARIABLE_7680" (@ho-elim-sort (-> tptp.a Bool)))) % 120.83/121.13 (define @t56 () (@var "BOUND_VARIABLE_7626" tptp.a)) % 120.83/121.13 (define @t57 () (@var "BOUND_VARIABLE_7690" (@ho-elim-sort (-> tptp.a Bool)))) % 120.83/121.13 (define @t58 () (not (_ @t54 @t53 @t57))) % 120.83/121.13 (define @t59 () (@list @t57)) % 120.83/121.13 (define @t60 () (@var "BOUND_VARIABLE_7608" tptp.a)) % 120.83/121.13 (define @t61 () (@var "BOUND_VARIABLE_7704" (@ho-elim-sort (-> tptp.a Bool)))) % 120.83/121.13 (define @t62 () (@var "BOUND_VARIABLE_7606" tptp.a)) % 120.83/121.13 (define @t63 () (@var "BOUND_VARIABLE_7599" tptp.a)) % 120.83/121.13 (define @t64 () (and (not (forall @t59 (or @t58 (not (_ @t51 @t57 @t63))))) (or (not (forall @t59 (or @t58 (not (_ @t51 @t57 @t60)) (not (_ @t51 @t57 @t62))))) (not (_ @t54 @t53 @t61)) (not (_ @t51 @t61 @t62)) (not (_ @t51 @t61 @t60))) (or (not (forall @t59 (or @t58 (not (_ @t51 @t57 @t56)) (not (_ @t51 @t57 @t49))))) (not (_ @t54 @t53 @t55)) (not (_ @t51 @t55 @t56)) (not (_ @t51 @t55 @t52)) (not (_ @t54 @t53 @t50)) (not (_ @t51 @t50 @t52)) (not (_ @t51 @t50 @t49))))) % 120.83/121.13 (define @t65 () (@var "BOUND_VARIABLE_7731" (@ho-elim-sort (-> tptp.a Bool)))) % 120.83/121.13 (define @t66 () (@var "BOUND_VARIABLE_7730" (@ho-elim-sort (-> tptp.a Bool)))) % 120.83/121.13 (define @t67 () (= @t66 @t65)) % 120.83/121.13 (define @t68 () (not (_ @t51 @t66 @t4))) % 120.83/121.13 (define @t69 () (not (_ @t54 @t53 @t66))) % 120.83/121.13 (define @t70 () (@list @t66)) % 120.83/121.13 (define @t71 () (not (_ @t51 @t65 @t4))) % 120.83/121.13 (define @t72 () (not (_ @t54 @t53 @t65))) % 120.83/121.13 (define @t73 () (@list @t65)) % 120.83/121.13 (define @t74 () (@list @t53 @t63 @t62 @t60 @t61 @t56 @t52 @t49 @t55 @t50)) % 120.83/121.13 (define @t75 () (forall @t74 (or (not (forall @t28 (not (forall @t73 (or @t72 @t71 (not (forall @t70 (or @t69 @t68 @t67)))))))) @t64))) % 120.83/121.13 (define @t76 () (@quantifiers_skolemize @t75 7)) % 120.83/121.13 (define @t77 () (@quantifiers_skolemize @t75 5)) % 120.83/121.13 (define @t78 () (@quantifiers_skolemize @t75 0)) % 120.83/121.13 (define @t79 () (not (_ @t54 @t78 @t57))) % 120.83/121.13 (define @t80 () (forall @t59 (or @t79 (not (_ @t51 @t57 @t77)) (not (_ @t51 @t57 @t76))))) % 120.83/121.13 (define @t81 () (@quantifiers_skolemize @t75 9)) % 120.83/121.13 (define @t82 () (_ @t51 @t81 @t76)) % 120.83/121.13 (define @t83 () (not @t82)) % 120.83/121.13 (define @t84 () (@quantifiers_skolemize @t75 6)) % 120.83/121.13 (define @t85 () (_ @t51 @t81 @t84)) % 120.83/121.13 (define @t86 () (not @t85)) % 120.83/121.13 (define @t87 () (_ @t54 @t78 @t81)) % 120.83/121.13 (define @t88 () (not @t87)) % 120.83/121.13 (define @t89 () (@quantifiers_skolemize @t75 8)) % 120.83/121.13 (define @t90 () (_ @t51 @t89 @t84)) % 120.83/121.13 (define @t91 () (not @t90)) % 120.83/121.13 (define @t92 () (_ @t51 @t89 @t77)) % 120.83/121.13 (define @t93 () (not @t92)) % 120.83/121.13 (define @t94 () (_ @t54 @t78 @t89)) % 120.83/121.13 (define @t95 () (not @t94)) % 120.83/121.13 (define @t96 () (not @t80)) % 120.83/121.13 (define @t97 () (or @t96 @t95 @t93 @t91 @t88 @t86 @t83)) % 120.83/121.13 (define @t98 () (or @t69 @t68 (= @t65 @t66))) % 120.83/121.13 (define @t99 () (forall @t70 @t98)) % 120.83/121.13 (define @t100 () (not @t99)) % 120.83/121.13 (define @t101 () (or @t72 @t71 @t100)) % 120.83/121.13 (define @t102 () (forall @t73 @t101)) % 120.83/121.13 (define @t103 () (not @t102)) % 120.83/121.13 (define @t104 () (forall @t28 @t103)) % 120.83/121.13 (define @t105 () (not @t104)) % 120.83/121.13 (define @t106 () (or @t105 @t64)) % 120.83/121.13 (define @t107 () (forall @t74 @t106)) % 120.83/121.13 (define @t108 () (not @t107)) % 120.83/121.13 (define @t109 () (@var "BOUND_VARIABLE_7634" (-> tptp.a Bool))) % 120.83/121.13 (define @t110 () (@var "BOUND_VARIABLE_7632" (-> tptp.a Bool))) % 120.83/121.13 (define @t111 () (_ @t6 @t2)) % 120.83/121.13 (define @t112 () (not @t111)) % 120.83/121.13 (define @t113 () (or (not (forall @t9 (or @t112 (not (_ @t2 @t56)) (not (_ @t2 @t49))))) (not (_ @t6 @t110)) (not (_ @t110 @t56)) (not (_ @t110 @t52)) (not (_ @t6 @t109)) (not (_ @t109 @t52)) (not (_ @t109 @t49)))) % 120.83/121.13 (define @t114 () (@var "BOUND_VARIABLE_7610" (-> tptp.a Bool))) % 120.83/121.13 (define @t115 () (or (not (forall @t9 (or @t112 (not (_ @t2 @t60)) (not (_ @t2 @t62))))) (not (_ @t6 @t114)) (not (_ @t114 @t62)) (not (_ @t114 @t60)))) % 120.83/121.13 (define @t116 () (not (forall @t9 (or @t112 (not (_ @t2 @t63)))))) % 120.83/121.13 (define @t117 () (and @t116 @t115 @t113)) % 120.83/121.13 (define @t118 () (= @t31 @t32)) % 120.83/121.13 (define @t119 () (_ @t32 @t4)) % 120.83/121.13 (define @t120 () (_ @t6 @t32)) % 120.83/121.13 (define @t121 () (forall @t37 (or (not @t120) (not @t119) @t118))) % 120.83/121.13 (define @t122 () (not @t121)) % 120.83/121.13 (define @t123 () (_ @t31 @t4)) % 120.83/121.13 (define @t124 () (_ @t6 @t31)) % 120.83/121.13 (define @t125 () (forall @t28 (not (forall @t42 (or (not @t124) (not @t123) @t122))))) % 120.83/121.13 (define @t126 () (not @t125)) % 120.83/121.13 (define @t127 () (or @t126 @t117)) % 120.83/121.13 (define @t128 () (forall (@list @t6 @t63 @t62 @t60 @t114 @t56 @t52 @t49 @t110 @t109) @t127)) % 120.83/121.13 (define @t129 () (@list @t63 @t62 @t60 @t114 @t56 @t52 @t49 @t110 @t109)) % 120.83/121.13 (define @t130 () (forall @t129 @t127)) % 120.83/121.13 (define @t131 () (forall (@list @t56 @t52 @t49 @t110 @t109) @t113)) % 120.83/121.13 (define @t132 () (@var "BOUND_VARIABLE_7579" (-> tptp.a Bool))) % 120.83/121.13 (define @t133 () (@var "BOUND_VARIABLE_7570" (-> tptp.a Bool))) % 120.83/121.13 (define @t134 () (forall @t129 @t113)) % 120.83/121.13 (define @t135 () (forall (@list @t62 @t60 @t114) @t115)) % 120.83/121.13 (define @t136 () (@var "BOUND_VARIABLE_7530" (-> tptp.a Bool))) % 120.83/121.13 (define @t137 () (forall @t129 @t115)) % 120.83/121.13 (define @t138 () (forall (@list @t63) @t116)) % 120.83/121.13 (define @t139 () (forall @t129 @t116)) % 120.83/121.13 (define @t140 () (and @t139 @t137 @t134)) % 120.83/121.13 (define @t141 () (forall @t129 @t117)) % 120.83/121.13 (define @t142 () (or @t126 @t141)) % 120.83/121.13 (define @t143 () (not (_ @t132 @t1))) % 120.83/121.13 (define @t144 () (not (_ @t132 @t11))) % 120.83/121.13 (define @t145 () (not (_ @t6 @t132))) % 120.83/121.13 (define @t146 () (not (_ @t133 @t11))) % 120.83/121.13 (define @t147 () (not (_ @t133 @t4))) % 120.83/121.13 (define @t148 () (not (_ @t6 @t133))) % 120.83/121.13 (define @t149 () (_ @t2 @t1)) % 120.83/121.13 (define @t150 () (not @t149)) % 120.83/121.13 (define @t151 () (_ @t2 @t4)) % 120.83/121.13 (define @t152 () (not @t151)) % 120.83/121.13 (define @t153 () (not (forall @t9 (or @t112 @t152 @t150)))) % 120.83/121.13 (define @t154 () (or @t153 @t148 @t147 @t146 @t145 @t144 @t143)) % 120.83/121.13 (define @t155 () (@list @t4 @t11 @t1 @t133 @t132)) % 120.83/121.13 (define @t156 () (not (_ @t136 @t11))) % 120.83/121.13 (define @t157 () (not (_ @t136 @t4))) % 120.83/121.13 (define @t158 () (not (_ @t6 @t136))) % 120.83/121.13 (define @t159 () (_ @t2 @t11)) % 120.83/121.13 (define @t160 () (not @t159)) % 120.83/121.13 (define @t161 () (not (forall @t9 (or @t112 @t160 @t152)))) % 120.83/121.13 (define @t162 () (or @t161 @t158 @t157 @t156)) % 120.83/121.13 (define @t163 () (@list @t4 @t11 @t136)) % 120.83/121.13 (define @t164 () (and (forall @t28 (not (forall @t9 (or @t112 @t152)))) (forall @t163 @t162) (forall @t155 @t154))) % 120.83/121.13 (define @t165 () (or @t145 @t144 @t143)) % 120.83/121.13 (define @t166 () (or @t148 @t147 @t146)) % 120.83/121.13 (define @t167 () (or @t166 @t165 @t153)) % 120.83/121.13 (define @t168 () (forall @t155 @t167)) % 120.83/121.13 (define @t169 () (forall (@list @t133 @t132) @t167)) % 120.83/121.13 (define @t170 () (forall (@list @t132) @t165)) % 120.83/121.13 (define @t171 () (@list @t2)) % 120.83/121.13 (define @t172 () (forall (@list @t133) @t166)) % 120.83/121.13 (define @t173 () (or @t172 @t170 @t153)) % 120.83/121.13 (define @t174 () (forall @t9 (or @t112 @t160 @t150))) % 120.83/121.13 (define @t175 () (forall @t9 (or @t112 @t152 @t160))) % 120.83/121.13 (define @t176 () (or @t175 @t174 @t153)) % 120.83/121.13 (define @t177 () (not @t174)) % 120.83/121.13 (define @t178 () (not @t175)) % 120.83/121.13 (define @t179 () (not @t178)) % 120.83/121.13 (define @t180 () (and @t178 @t177)) % 120.83/121.13 (define @t181 () (not @t3)) % 120.83/121.13 (define @t182 () (not @t5)) % 120.83/121.13 (define @t183 () (not @t7)) % 120.83/121.13 (define @t184 () (or @t183 @t182 @t181)) % 120.83/121.13 (define @t185 () (forall @t9 (not @t8))) % 120.83/121.13 (define @t186 () (not @t185)) % 120.83/121.13 (define @t187 () (not @t12)) % 120.83/121.13 (define @t188 () (or @t183 @t187 @t181)) % 120.83/121.13 (define @t189 () (forall @t9 (not @t13))) % 120.83/121.13 (define @t190 () (not @t189)) % 120.83/121.13 (define @t191 () (or @t183 @t182 @t187)) % 120.83/121.13 (define @t192 () (forall @t9 (not @t15))) % 120.83/121.13 (define @t193 () (not @t192)) % 120.83/121.13 (define @t194 () (or @t158 @t157 @t156)) % 120.83/121.13 (define @t195 () (or @t194 @t161)) % 120.83/121.13 (define @t196 () (forall @t163 @t195)) % 120.83/121.13 (define @t197 () (@list @t136)) % 120.83/121.13 (define @t198 () (forall @t197 @t195)) % 120.83/121.13 (define @t199 () (forall @t197 @t194)) % 120.83/121.13 (define @t200 () (or @t199 @t161)) % 120.83/121.13 (define @t201 () (or @t183 @t187 @t182)) % 120.83/121.13 (define @t202 () (forall @t9 (not @t21))) % 120.83/121.13 (define @t203 () (not @t202)) % 120.83/121.13 (define @t204 () (or @t183 @t182)) % 120.83/121.13 (define @t205 () (or @t183 @t182 @t182)) % 120.83/121.13 (define @t206 () (forall @t9 (not @t26))) % 120.83/121.13 (define @t207 () (not @t206)) % 120.83/121.13 (define @t208 () (not @t39)) % 120.83/121.13 (define @t209 () (not @t40)) % 120.83/121.13 (define @t210 () (or @t209 @t208 @t122)) % 120.83/121.13 (define @t211 () (and @t40 @t39 @t121)) % 120.83/121.13 (define @t212 () (forall @t42 (not @t211))) % 120.83/121.13 (define @t213 () (not @t212)) % 120.83/121.13 (define @t214 () (not @t33)) % 120.83/121.13 (define @t215 () (not @t34)) % 120.83/121.13 (define @t216 () (or @t215 @t214 @t118)) % 120.83/121.13 (define @t217 () (not (_ @t54 @t78 @t66))) % 120.83/121.13 (define @t218 () (not (_ @t54 @t78 @t65))) % 120.83/121.13 (define @t219 () (forall @t28 (not (forall @t73 (or @t218 @t71 (not (forall @t70 (or @t217 @t68 @t67)))))))) % 120.83/121.13 (define @t220 () (@quantifiers_skolemize @t75 3)) % 120.83/121.13 (define @t221 () (@quantifiers_skolemize @t75 4)) % 120.83/121.13 (define @t222 () (_ @t51 @t221 @t220)) % 120.83/121.13 (define @t223 () (not @t222)) % 120.83/121.13 (define @t224 () (@quantifiers_skolemize @t75 2)) % 120.83/121.13 (define @t225 () (_ @t51 @t221 @t224)) % 120.83/121.13 (define @t226 () (not @t225)) % 120.83/121.13 (define @t227 () (_ @t54 @t78 @t221)) % 120.83/121.13 (define @t228 () (not @t227)) % 120.83/121.13 (define @t229 () (forall @t59 (or @t79 (not (_ @t51 @t57 @t220)) (not (_ @t51 @t57 @t224))))) % 120.83/121.13 (define @t230 () (not @t229)) % 120.83/121.13 (define @t231 () (or @t230 @t228 @t226 @t223)) % 120.83/121.13 (define @t232 () (@quantifiers_skolemize @t75 1)) % 120.83/121.13 (define @t233 () (forall @t59 (or @t79 (not (_ @t51 @t57 @t232))))) % 120.83/121.13 (define @t234 () (not @t233)) % 120.83/121.13 (define @t235 () (and @t234 @t231 @t97)) % 120.83/121.13 (define @t236 () (not @t219)) % 120.83/121.13 (define @t237 () (or @t236 @t235)) % 120.83/121.13 (define @t238 () (@list true)) % 120.83/121.13 (define @t239 () (@list @t237)) % 120.83/121.13 (define @t240 () (not (_ @t51 @t66 @t84))) % 120.83/121.13 (define @t241 () (@quantifiers_skolemize (forall @t73 (or @t218 (not (_ @t51 @t65 @t84)) (not (forall @t70 (or @t217 @t240 @t67))))) 0)) % 120.83/121.13 (define @t242 () (forall @t70 (or @t217 @t240 (= @t66 @t241)))) % 120.83/121.13 (define @t243 () (not @t242)) % 120.83/121.13 (define @t244 () (or (not (_ @t54 @t78 @t241)) (not (_ @t51 @t241 @t84)) @t243)) % 120.83/121.13 (define @t245 () (@list @t89)) % 120.83/121.13 (define @t246 () (= @t89 @t241)) % 120.83/121.13 (define @t247 () (or @t95 @t91 @t246)) % 120.83/121.13 (define @t248 () (= @t81 @t241)) % 120.83/121.13 (define @t249 () (or @t88 @t86 @t248)) % 120.83/121.13 (define @t250 () (_ @t51 @t89 @t76)) % 120.83/121.13 (define @t251 () (and @t82 @t246 @t248)) % 120.83/121.13 (define @t252 () (not @t250)) % 120.83/121.13 (define @t253 () (or @t95 @t93 @t252)) % 120.83/121.13 (define @t254 () (not (_ @t51 @t66 @t232))) % 120.83/121.13 (define @t255 () (@quantifiers_skolemize (forall @t73 (or @t218 (not (_ @t51 @t65 @t232)) (not (forall @t70 (or @t217 @t254 @t67))))) 0)) % 120.74/121.13 (define @t256 () (_ @t51 @t255 @t232)) % 120.74/121.13 (define @t257 () (not @t256)) % 120.74/121.13 (define @t258 () (_ @t54 @t78 @t255)) % 120.74/121.13 (define @t259 () (not @t258)) % 120.74/121.13 (define @t260 () (or @t259 @t257 (not (forall @t70 (or @t217 @t254 (= @t66 @t255)))))) % 120.74/121.13 (define @t261 () (@list @t260)) % 120.74/121.13 (define @t262 () (or @t259 @t257)) % 120.74/121.13 (define @t263 () (not @t262)) % 120.74/121.13 (define @t264 () (not @t97)) % 120.74/121.13 (define @t265 () (not @t231)) % 120.74/121.13 (define @t266 () (@list @t231)) % 120.74/121.13 (define @t267 () (or @t228 @t223 @t226)) % 120.74/121.13 (assume @p1 @t48) % 120.74/121.13 (assume @p2 true) % 120.74/121.13 (step @p3 :rule bool-double-not-elim :args (@t80)) % 120.74/121.13 (step @p4 :rule refl :args (@t97)) % 120.74/121.13 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t97 (not @t96)))) % 120.74/121.13 (step @p6 :rule cnf_or_neg :args (@t97 0)) % 120.74/121.13 (step @p7 :rule eq_resolve :premises (@p6 @p5)) % 120.74/121.13 (step @p8 :rule reordering :premises (@p7) :args ((or @t80 @t97))) % 120.74/121.13 (step @p9 :rule bool-double-not-elim :args (@t94)) % 120.74/121.13 (step @p10 :rule nary_cong :premises (@p4 @p9) :args ((or @t97 (not @t95)))) % 120.74/121.13 (step @p11 :rule cnf_or_neg :args (@t97 1)) % 120.74/121.13 (step @p12 :rule eq_resolve :premises (@p11 @p10)) % 120.74/121.13 (step @p13 :rule reordering :premises (@p12) :args ((or @t94 @t97))) % 120.74/121.13 (step @p14 :rule bool-double-not-elim :args (@t92)) % 120.74/121.13 (step @p15 :rule nary_cong :premises (@p4 @p14) :args ((or @t97 (not @t93)))) % 120.74/121.13 (step @p16 :rule cnf_or_neg :args (@t97 2)) % 120.74/121.13 (step @p17 :rule eq_resolve :premises (@p16 @p15)) % 120.74/121.13 (step @p18 :rule reordering :premises (@p17) :args ((or @t92 @t97))) % 120.74/121.13 (step @p19 :rule bool-double-not-elim :args (@t90)) % 120.74/121.13 (step @p20 :rule nary_cong :premises (@p4 @p19) :args ((or @t97 (not @t91)))) % 120.74/121.13 (step @p21 :rule cnf_or_neg :args (@t97 3)) % 120.74/121.13 (step @p22 :rule eq_resolve :premises (@p21 @p20)) % 120.74/121.13 (step @p23 :rule reordering :premises (@p22) :args ((or @t90 @t97))) % 120.74/121.13 (step @p24 :rule bool-double-not-elim :args (@t87)) % 120.74/121.13 (step @p25 :rule nary_cong :premises (@p4 @p24) :args ((or @t97 (not @t88)))) % 120.74/121.13 (step @p26 :rule cnf_or_neg :args (@t97 4)) % 120.74/121.13 (step @p27 :rule eq_resolve :premises (@p26 @p25)) % 120.74/121.13 (step @p28 :rule reordering :premises (@p27) :args ((or @t87 @t97))) % 120.74/121.13 (step @p29 :rule bool-double-not-elim :args (@t85)) % 120.74/121.13 (step @p30 :rule nary_cong :premises (@p4 @p29) :args ((or @t97 (not @t86)))) % 120.74/121.13 (step @p31 :rule cnf_or_neg :args (@t97 5)) % 120.74/121.13 (step @p32 :rule eq_resolve :premises (@p31 @p30)) % 120.74/121.13 (step @p33 :rule reordering :premises (@p32) :args ((or @t85 @t97))) % 120.74/121.13 (step @p34 :rule bool-double-not-elim :args (@t82)) % 120.74/121.13 (step @p35 :rule nary_cong :premises (@p4 @p34) :args ((or @t97 (not @t83)))) % 120.74/121.13 (step @p36 :rule cnf_or_neg :args (@t97 6)) % 120.74/121.13 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 120.74/121.13 (step @p38 :rule reordering :premises (@p37) :args ((or @t82 @t97))) % 120.74/121.13 (step @p39 :rule refl :args (@t64)) % 120.74/121.13 (step @p40 :rule eq-symm :args (@t65 @t66)) % 120.74/121.13 (step @p41 :rule refl :args (@t68)) % 120.74/121.13 (step @p42 :rule refl :args (@t69)) % 120.74/121.13 (step @p43 :rule nary_cong :premises (@p42 @p41 @p40) :args (@t98)) % 120.74/121.13 (step @p44 :rule cong :premises (@p43) :args (@t99)) % 120.74/121.13 (step @p45 :rule cong :premises (@p44) :args (@t100)) % 120.74/121.13 (step @p46 :rule refl :args (@t71)) % 120.74/121.13 (step @p47 :rule refl :args (@t72)) % 120.74/121.13 (step @p48 :rule nary_cong :premises (@p47 @p46 @p45) :args (@t101)) % 120.74/121.13 (step @p49 :rule cong :premises (@p48) :args (@t102)) % 120.74/121.13 (step @p50 :rule cong :premises (@p49) :args (@t103)) % 120.74/121.13 (step @p51 :rule cong :premises (@p50) :args (@t104)) % 120.74/121.13 (step @p52 :rule cong :premises (@p51) :args (@t105)) % 120.74/121.13 (step @p53 :rule nary_cong :premises (@p52 @p39) :args (@t106)) % 120.74/121.13 (step @p54 :rule cong :premises (@p53) :args (@t107)) % 120.74/121.13 (step @p55 :rule cong :premises (@p54) :args (@t108)) % 120.74/121.13 ; WARNING: add trust step for TRUST % 120.74/121.13 ; trust TRUST PREPROCESS_HO_ELIM % 120.74/121.13 (step @p56 :rule trust :premises () :args ((= (not @t128) @t108))) % 120.74/121.13 (step @p57 :rule quant-merge-prenex :args ((= (forall @t46 @t130) @t128))) % 120.74/121.13 (step @p58 :rule alpha_equiv :args (@t131 (@list @t56 @t52 @t49 @t110 @t109) (@list @t4 @t11 @t1 @t133 @t132))) % 120.74/121.13 (step @p59 :rule quant-unused-vars :args ((= @t134 @t131))) % 120.74/121.13 (step @p60 :rule trans :premises (@p59 @p58)) % 120.74/121.13 (step @p61 :rule alpha_equiv :args (@t135 (@list @t62 @t60 @t114) (@list @t4 @t11 @t136))) % 120.74/121.13 (step @p62 :rule quant-unused-vars :args ((= @t137 @t135))) % 120.74/121.13 (step @p63 :rule trans :premises (@p62 @p61)) % 120.74/121.13 (step @p64 :rule alpha_equiv :args (@t138 (@list @t63) (@list @t4))) % 120.74/121.13 (step @p65 :rule quant-unused-vars :args ((= @t139 @t138))) % 120.74/121.13 (step @p66 :rule trans :premises (@p65 @p64)) % 120.74/121.13 (step @p67 :rule nary_cong :premises (@p66 @p63 @p60) :args (@t140)) % 120.74/121.13 (step @p68 :rule quant-miniscope-and :args ((= @t141 @t140))) % 120.74/121.13 (step @p69 :rule trans :premises (@p68 @p67)) % 120.74/121.13 (step @p70 :rule refl :args (@t126)) % 120.74/121.13 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t142)) % 120.74/121.13 (step @p72 :rule quant-miniscope-or :args ((= @t130 @t142))) % 120.74/121.13 (step @p73 :rule trans :premises (@p72 @p71)) % 120.74/121.13 (step @p74 :rule symm :premises (@p73)) % 120.74/121.13 (step @p75 :rule cong :premises (@p74) :args ((forall @t46 (or @t126 @t164)))) % 120.74/121.13 (step @p76 :rule trans :premises (@p75 @p57)) % 120.74/121.13 (step @p77 :rule bool-impl-elim :args (@t125 @t164)) % 120.74/121.13 (step @p78 :rule cong :premises (@p77) :args ((forall @t46 (=> @t125 @t164)))) % 120.74/121.13 (step @p79 :rule trans :premises (@p78 @p76)) % 120.74/121.13 (step @p80 :rule aci_norm :args ((= @t167 @t154))) % 120.74/121.13 (step @p81 :rule cong :premises (@p80) :args (@t168)) % 120.74/121.13 (step @p82 :rule quant-merge-prenex :args ((= (forall @t19 @t169) @t168))) % 120.74/121.13 (step @p83 :rule refl :args (@t153)) % 120.74/121.13 (step @p84 :rule alpha_equiv :args (@t170 (@list @t132) @t171)) % 120.74/121.13 (step @p85 :rule alpha_equiv :args (@t172 (@list @t133) @t171)) % 120.74/121.13 (step @p86 :rule nary_cong :premises (@p85 @p84 @p83) :args (@t173)) % 120.74/121.13 (step @p87 :rule quant-miniscope-or :args ((= @t169 @t173))) % 120.74/121.13 (step @p88 :rule trans :premises (@p87 @p86)) % 120.74/121.13 (step @p89 :rule symm :premises (@p88)) % 120.74/121.13 (step @p90 :rule cong :premises (@p89) :args ((forall @t19 @t176))) % 120.74/121.13 (step @p91 :rule trans :premises (@p90 @p82)) % 120.74/121.13 (step @p92 :rule trans :premises (@p91 @p81)) % 120.74/121.13 (step @p93 :rule aci_norm :args ((= (or (or @t175 @t174) @t153) @t176))) % 120.74/121.13 (step @p94 :rule bool-double-not-elim :args (@t174)) % 120.74/121.13 (step @p95 :rule bool-double-not-elim :args (@t175)) % 120.74/121.13 (step @p96 :rule nary_cong :premises (@p95 @p94) :args ((or @t179 (not @t177)))) % 120.74/121.13 (step @p97 :rule bool-and-de-morgan :args (@t178 @t177 true)) % 120.74/121.13 (step @p98 :rule trans :premises (@p97 @p96)) % 120.74/121.13 (step @p99 :rule nary_cong :premises (@p98 @p83) :args ((or (not @t180) @t153))) % 120.74/121.13 (step @p100 :rule trans :premises (@p99 @p93)) % 120.74/121.13 (step @p101 :rule bool-impl-elim :args (@t180 @t153)) % 120.74/121.13 (step @p102 :rule trans :premises (@p101 @p100)) % 120.74/121.13 (step @p103 :rule cong :premises (@p102) :args ((forall @t19 (=> @t180 @t153)))) % 120.74/121.13 (step @p104 :rule trans :premises (@p103 @p92)) % 120.74/121.13 (step @p105 :rule refl :args (@t149)) % 120.74/121.13 (step @p106 :rule refl :args (@t3)) % 120.74/121.13 (step @p107 :rule cong :premises (@p106 @p105) :args ((= @t3 @t149))) % 120.74/121.13 (step @p108 :rule symm :premises (@p107)) % 120.74/121.13 (step @p109 :rule eq_resolve :premises (@p106 @p108)) % 120.74/121.13 (step @p110 :rule cong :premises (@p109) :args (@t181)) % 120.74/121.13 (step @p111 :rule refl :args (@t151)) % 120.74/121.13 (step @p112 :rule refl :args (@t5)) % 120.74/121.13 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t5 @t151))) % 120.74/121.13 (step @p114 :rule symm :premises (@p113)) % 120.74/121.13 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 120.74/121.13 (step @p116 :rule cong :premises (@p115) :args (@t182)) % 120.74/121.13 (step @p117 :rule refl :args (@t111)) % 120.74/121.13 (step @p118 :rule refl :args (@t7)) % 120.74/121.13 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t7 @t111))) % 120.74/121.13 (step @p120 :rule symm :premises (@p119)) % 120.74/121.13 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 120.74/121.13 (step @p122 :rule cong :premises (@p121) :args (@t183)) % 120.74/121.13 (step @p123 :rule nary_cong :premises (@p122 @p116 @p110) :args (@t184)) % 120.74/121.13 (step @p124 :rule cong :premises (@p123) :args ((forall @t9 @t184))) % 120.74/121.13 (step @p125 :rule aci_norm :args ((= (or @t183 (or @t182 @t181)) @t184))) % 120.74/121.13 (step @p126 :rule bool-and-de-morgan :args (@t5 @t3 true)) % 120.74/121.13 (step @p127 :rule refl :args (@t183)) % 120.74/121.13 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or @t183 (not (and @t5 @t3))))) % 120.74/121.13 (step @p129 :rule bool-and-de-morgan :args (@t7 @t5 (and @t3))) % 120.74/121.13 (step @p130 :rule trans :premises (@p129 @p128)) % 120.74/121.13 (step @p131 :rule trans :premises (@p130 @p125)) % 120.74/121.13 (step @p132 :rule cong :premises (@p131) :args (@t185)) % 120.74/121.13 (step @p133 :rule trans :premises (@p132 @p124)) % 120.74/121.13 (step @p134 :rule cong :premises (@p133) :args (@t186)) % 120.74/121.13 (step @p135 :rule exists-elim :args ((= @t10 @t186))) % 120.74/121.13 (step @p136 :rule trans :premises (@p135 @p134)) % 120.74/121.13 (step @p137 :rule refl :args (@t159)) % 120.74/121.13 (step @p138 :rule refl :args (@t12)) % 120.74/121.13 (step @p139 :rule cong :premises (@p138 @p137) :args ((= @t12 @t159))) % 120.74/121.13 (step @p140 :rule symm :premises (@p139)) % 120.74/121.13 (step @p141 :rule eq_resolve :premises (@p138 @p140)) % 120.74/121.13 (step @p142 :rule cong :premises (@p141) :args (@t187)) % 120.74/121.13 (step @p143 :rule nary_cong :premises (@p122 @p142 @p110) :args (@t188)) % 120.74/121.13 (step @p144 :rule cong :premises (@p143) :args ((forall @t9 @t188))) % 120.74/121.13 (step @p145 :rule aci_norm :args ((= (or @t183 (or @t187 @t181)) @t188))) % 120.74/121.13 (step @p146 :rule bool-and-de-morgan :args (@t12 @t3 true)) % 120.74/121.13 (step @p147 :rule nary_cong :premises (@p127 @p146) :args ((or @t183 (not (and @t12 @t3))))) % 120.74/121.13 (step @p148 :rule bool-and-de-morgan :args (@t7 @t12 (and @t3))) % 120.74/121.13 (step @p149 :rule trans :premises (@p148 @p147)) % 120.74/121.13 (step @p150 :rule trans :premises (@p149 @p145)) % 120.74/121.13 (step @p151 :rule cong :premises (@p150) :args (@t189)) % 120.74/121.13 (step @p152 :rule trans :premises (@p151 @p144)) % 120.74/121.13 (step @p153 :rule cong :premises (@p152) :args (@t190)) % 120.74/121.13 (step @p154 :rule exists-elim :args ((= @t14 @t190))) % 120.74/121.13 (step @p155 :rule trans :premises (@p154 @p153)) % 120.74/121.13 (step @p156 :rule nary_cong :premises (@p122 @p116 @p142) :args (@t191)) % 120.74/121.13 (step @p157 :rule cong :premises (@p156) :args ((forall @t9 @t191))) % 120.74/121.13 (step @p158 :rule aci_norm :args ((= (or @t183 (or @t182 @t187)) @t191))) % 120.74/121.13 (step @p159 :rule bool-and-de-morgan :args (@t5 @t12 true)) % 120.74/121.13 (step @p160 :rule nary_cong :premises (@p127 @p159) :args ((or @t183 (not (and @t5 @t12))))) % 120.74/121.13 (step @p161 :rule bool-and-de-morgan :args (@t7 @t5 (and @t12))) % 120.74/121.13 (step @p162 :rule trans :premises (@p161 @p160)) % 120.74/121.13 (step @p163 :rule trans :premises (@p162 @p158)) % 120.74/121.13 (step @p164 :rule cong :premises (@p163) :args (@t192)) % 120.74/121.13 (step @p165 :rule trans :premises (@p164 @p157)) % 120.74/121.13 (step @p166 :rule cong :premises (@p165) :args (@t193)) % 120.74/121.13 (step @p167 :rule exists-elim :args ((= @t16 @t193))) % 120.74/121.13 (step @p168 :rule trans :premises (@p167 @p166)) % 120.74/121.13 (step @p169 :rule nary_cong :premises (@p168 @p155) :args (@t17)) % 120.74/121.13 (step @p170 :rule cong :premises (@p169 @p136) :args (@t18)) % 120.74/121.13 (step @p171 :rule cong :premises (@p170) :args (@t20)) % 120.74/121.13 (step @p172 :rule trans :premises (@p171 @p104)) % 120.74/121.13 (step @p173 :rule aci_norm :args ((= @t195 @t162))) % 120.74/121.13 (step @p174 :rule cong :premises (@p173) :args (@t196)) % 120.74/121.13 (step @p175 :rule quant-merge-prenex :args ((= (forall @t24 @t198) @t196))) % 120.74/121.13 (step @p176 :rule refl :args (@t161)) % 120.74/121.13 (step @p177 :rule alpha_equiv :args (@t199 (@list @t136) @t171)) % 120.74/121.13 (step @p178 :rule nary_cong :premises (@p177 @p176) :args (@t200)) % 120.74/121.13 (step @p179 :rule quant-miniscope-or :args ((= @t198 @t200))) % 120.74/121.13 (step @p180 :rule trans :premises (@p179 @p178)) % 120.74/121.13 (step @p181 :rule symm :premises (@p180)) % 120.74/121.13 (step @p182 :rule cong :premises (@p181) :args ((forall @t24 (or @t175 @t161)))) % 120.74/121.13 (step @p183 :rule trans :premises (@p182 @p175)) % 120.74/121.13 (step @p184 :rule trans :premises (@p183 @p174)) % 120.74/121.13 (step @p185 :rule nary_cong :premises (@p95 @p176) :args ((or @t179 @t161))) % 120.74/121.13 (step @p186 :rule bool-impl-elim :args (@t178 @t161)) % 120.74/121.13 (step @p187 :rule trans :premises (@p186 @p185)) % 120.74/121.13 (step @p188 :rule cong :premises (@p187) :args ((forall @t24 (=> @t178 @t161)))) % 120.74/121.13 (step @p189 :rule trans :premises (@p188 @p184)) % 120.74/121.13 (step @p190 :rule nary_cong :premises (@p122 @p142 @p116) :args (@t201)) % 120.74/121.13 (step @p191 :rule cong :premises (@p190) :args ((forall @t9 @t201))) % 120.74/121.13 (step @p192 :rule aci_norm :args ((= (or @t183 (or @t187 @t182)) @t201))) % 120.74/121.13 (step @p193 :rule bool-and-de-morgan :args (@t12 @t5 true)) % 120.74/121.13 (step @p194 :rule nary_cong :premises (@p127 @p193) :args ((or @t183 (not (and @t12 @t5))))) % 120.74/121.13 (step @p195 :rule bool-and-de-morgan :args (@t7 @t12 (and @t5))) % 120.74/121.13 (step @p196 :rule trans :premises (@p195 @p194)) % 120.74/121.13 (step @p197 :rule trans :premises (@p196 @p192)) % 120.74/121.13 (step @p198 :rule cong :premises (@p197) :args (@t202)) % 120.74/121.13 (step @p199 :rule trans :premises (@p198 @p191)) % 120.74/121.13 (step @p200 :rule cong :premises (@p199) :args (@t203)) % 120.74/121.13 (step @p201 :rule exists-elim :args ((= @t22 @t203))) % 120.74/121.13 (step @p202 :rule trans :premises (@p201 @p200)) % 120.74/121.13 (step @p203 :rule cong :premises (@p168 @p202) :args (@t23)) % 120.74/121.13 (step @p204 :rule cong :premises (@p203) :args (@t25)) % 120.74/121.13 (step @p205 :rule trans :premises (@p204 @p189)) % 120.74/121.13 (step @p206 :rule nary_cong :premises (@p122 @p116) :args (@t204)) % 120.74/121.13 (step @p207 :rule cong :premises (@p206) :args ((forall @t9 @t204))) % 120.74/121.13 (step @p208 :rule aci_norm :args ((= @t205 @t204))) % 120.74/121.13 (step @p209 :rule aci_norm :args ((= (or @t183 (or @t182 @t182)) @t205))) % 120.74/121.13 (step @p210 :rule bool-and-de-morgan :args (@t5 @t5 true)) % 120.74/121.13 (step @p211 :rule nary_cong :premises (@p127 @p210) :args ((or @t183 (not (and @t5 @t5))))) % 120.74/121.13 (step @p212 :rule bool-and-de-morgan :args (@t7 @t5 (and @t5))) % 120.74/121.13 (step @p213 :rule trans :premises (@p212 @p211)) % 120.74/121.13 (step @p214 :rule trans :premises (@p213 @p209)) % 120.74/121.13 (step @p215 :rule trans :premises (@p214 @p208)) % 120.74/121.13 (step @p216 :rule cong :premises (@p215) :args (@t206)) % 120.74/121.13 (step @p217 :rule trans :premises (@p216 @p207)) % 120.74/121.13 (step @p218 :rule cong :premises (@p217) :args (@t207)) % 120.74/121.13 (step @p219 :rule exists-elim :args ((= @t27 @t207))) % 120.74/121.13 (step @p220 :rule trans :premises (@p219 @p218)) % 120.74/121.13 (step @p221 :rule cong :premises (@p220) :args (@t29)) % 120.74/121.13 (step @p222 :rule nary_cong :premises (@p221 @p205 @p172) :args (@t30)) % 120.74/121.13 (step @p223 :rule refl :args (@t122)) % 120.74/121.13 (step @p224 :rule refl :args (@t123)) % 120.74/121.13 (step @p225 :rule refl :args (@t39)) % 120.74/121.13 (step @p226 :rule cong :premises (@p225 @p224) :args ((= @t39 @t123))) % 120.74/121.13 (step @p227 :rule symm :premises (@p226)) % 120.74/121.13 (step @p228 :rule eq_resolve :premises (@p225 @p227)) % 120.74/121.13 (step @p229 :rule cong :premises (@p228) :args (@t208)) % 120.74/121.13 (step @p230 :rule refl :args (@t124)) % 120.74/121.13 (step @p231 :rule refl :args (@t40)) % 120.74/121.13 (step @p232 :rule cong :premises (@p231 @p230) :args ((= @t40 @t124))) % 120.74/121.13 (step @p233 :rule symm :premises (@p232)) % 120.74/121.13 (step @p234 :rule eq_resolve :premises (@p231 @p233)) % 120.74/121.13 (step @p235 :rule cong :premises (@p234) :args (@t209)) % 120.74/121.13 (step @p236 :rule nary_cong :premises (@p235 @p229 @p223) :args (@t210)) % 120.74/121.13 (step @p237 :rule cong :premises (@p236) :args ((forall @t42 @t210))) % 120.74/121.13 (step @p238 :rule aci_norm :args ((= (or @t209 (or @t208 @t122)) @t210))) % 120.74/121.13 (step @p239 :rule bool-and-de-morgan :args (@t39 @t121 true)) % 120.74/121.13 (step @p240 :rule refl :args (@t209)) % 120.74/121.13 (step @p241 :rule nary_cong :premises (@p240 @p239) :args ((or @t209 (not (and @t39 @t121))))) % 120.74/121.13 (step @p242 :rule bool-and-de-morgan :args (@t40 @t39 (and @t121))) % 120.74/121.13 (step @p243 :rule trans :premises (@p242 @p241)) % 120.74/121.13 (step @p244 :rule trans :premises (@p243 @p238)) % 120.74/121.13 (step @p245 :rule cong :premises (@p244) :args (@t212)) % 120.74/121.13 (step @p246 :rule trans :premises (@p245 @p237)) % 120.74/121.13 (step @p247 :rule cong :premises (@p246) :args (@t213)) % 120.74/121.13 (step @p248 :rule exists-elim :args ((= (exists @t42 @t211) @t213))) % 120.74/121.13 (step @p249 :rule trans :premises (@p248 @p247)) % 120.74/121.13 (step @p250 :rule refl :args (@t118)) % 120.74/121.13 (step @p251 :rule refl :args (@t119)) % 120.74/121.13 (step @p252 :rule refl :args (@t33)) % 120.74/121.13 (step @p253 :rule cong :premises (@p252 @p251) :args ((= @t33 @t119))) % 120.74/121.13 (step @p254 :rule symm :premises (@p253)) % 120.74/121.13 (step @p255 :rule eq_resolve :premises (@p252 @p254)) % 120.74/121.13 (step @p256 :rule cong :premises (@p255) :args (@t214)) % 120.74/121.13 (step @p257 :rule refl :args (@t120)) % 120.74/121.13 (step @p258 :rule refl :args (@t34)) % 120.74/121.13 (step @p259 :rule cong :premises (@p258 @p257) :args ((= @t34 @t120))) % 120.74/121.13 (step @p260 :rule symm :premises (@p259)) % 120.74/121.13 (step @p261 :rule eq_resolve :premises (@p258 @p260)) % 120.74/121.13 (step @p262 :rule cong :premises (@p261) :args (@t215)) % 120.74/121.13 (step @p263 :rule nary_cong :premises (@p262 @p256 @p250) :args (@t216)) % 120.74/121.13 (step @p264 :rule cong :premises (@p263) :args ((forall @t37 @t216))) % 120.74/121.13 (step @p265 :rule aci_norm :args ((= (or (or @t215 @t214) @t118) @t216))) % 120.74/121.13 (step @p266 :rule bool-and-de-morgan :args (@t34 @t33 true)) % 120.74/121.13 (step @p267 :rule nary_cong :premises (@p266 @p250) :args ((or (not @t35) @t118))) % 120.74/121.13 (step @p268 :rule trans :premises (@p267 @p265)) % 120.74/121.13 (step @p269 :rule bool-impl-elim :args (@t35 @t118)) % 120.74/121.13 (step @p270 :rule trans :premises (@p269 @p268)) % 120.74/121.13 (step @p271 :rule cong :premises (@p270) :args ((forall @t37 (=> @t35 @t118)))) % 120.74/121.13 (step @p272 :rule trans :premises (@p271 @p264)) % 120.74/121.13 (step @p273 :rule eq-symm :args (@t32 @t31)) % 120.74/121.13 (step @p274 :rule refl :args (@t35)) % 120.74/121.13 (step @p275 :rule cong :premises (@p274 @p273) :args (@t36)) % 120.74/121.13 (step @p276 :rule cong :premises (@p275) :args (@t38)) % 120.74/121.13 (step @p277 :rule trans :premises (@p276 @p272)) % 120.74/121.13 (step @p278 :rule refl :args (@t39)) % 120.74/121.13 (step @p279 :rule refl :args (@t40)) % 120.74/121.13 (step @p280 :rule nary_cong :premises (@p279 @p278 @p277) :args (@t41)) % 120.74/121.13 (step @p281 :rule cong :premises (@p280) :args (@t43)) % 120.74/121.13 (step @p282 :rule trans :premises (@p281 @p249)) % 120.74/121.13 (step @p283 :rule cong :premises (@p282) :args (@t44)) % 120.74/121.13 (step @p284 :rule cong :premises (@p283 @p222) :args (@t45)) % 120.74/121.13 (step @p285 :rule cong :premises (@p284) :args (@t47)) % 120.74/121.13 (step @p286 :rule trans :premises (@p285 @p79)) % 120.74/121.13 (step @p287 :rule cong :premises (@p286) :args (@t48)) % 120.74/121.13 (step @p288 :rule trans :premises (@p287 @p56 @p55)) % 120.74/121.13 (step @p289 :rule eq_resolve :premises (@p1 @p288)) % 120.74/121.13 (step @p290 :rule skolemize :premises (@p289)) % 120.74/121.13 (step @p291 :rule bool-double-not-elim :args (@t219)) % 120.74/121.13 (step @p292 :rule refl :args (@t237)) % 120.74/121.13 (step @p293 :rule nary_cong :premises (@p292 @p291) :args ((or @t237 (not @t236)))) % 120.74/121.13 (step @p294 :rule cnf_or_neg :args (@t237 0)) % 120.74/121.13 (step @p295 :rule eq_resolve :premises (@p294 @p293)) % 120.74/121.13 (step @p296 :rule reordering :premises (@p295) :args ((or @t219 @t237))) % 120.74/121.13 (step @p297 :rule chain_m_resolution :premises (@p296 @p290) :args (@t219 @t238 @t239)) % 120.74/121.13 (step @p298 :rule instantiate :premises (@p297) :args ((@list @t84))) % 120.74/121.13 (step @p299 :rule skolemize :premises (@p298)) % 120.74/121.13 (step @p300 :rule bool-double-not-elim :args (@t242)) % 120.74/121.13 (step @p301 :rule refl :args (@t244)) % 120.74/121.13 (step @p302 :rule nary_cong :premises (@p301 @p300) :args ((or @t244 (not @t243)))) % 120.74/121.13 (step @p303 :rule cnf_or_neg :args (@t244 2)) % 120.74/121.13 (step @p304 :rule eq_resolve :premises (@p303 @p302)) % 120.74/121.13 (step @p305 :rule reordering :premises (@p304) :args ((or @t242 @t244))) % 120.74/121.13 (step @p306 :rule chain_m_resolution :premises (@p305 @p299) :args (@t242 @t238 (@list @t244))) % 120.74/121.13 (step @p307 :rule instantiate :premises (@p306) :args (@t245)) % 120.74/121.13 (step @p308 :rule cnf_or_pos :args (@t247)) % 120.74/121.13 (step @p309 :rule reordering :premises (@p308) :args ((or @t95 @t91 @t246 (not @t247)))) % 120.74/121.13 (step @p310 :rule instantiate :premises (@p306) :args ((@list @t81))) % 120.74/121.13 (step @p311 :rule cnf_or_pos :args (@t249)) % 120.74/121.13 (step @p312 :rule reordering :premises (@p311) :args ((or @t88 @t86 @t248 (not @t249)))) % 120.74/121.13 (assume-push @p416 @t82) % 120.74/121.13 (assume-push @p417 @t246) % 120.74/121.13 (assume-push @p418 @t248) % 120.74/121.13 (assume-push @p419 @t82) % 120.74/121.13 (assume-push @p420 @t248) % 120.74/121.13 (assume-push @p421 @t246) % 120.74/121.13 (step @p319 :rule true_intro :premises (@p416)) % 120.74/121.13 (step @p320 :rule refl :args (@t76)) % 120.74/121.13 (step @p321 :rule symm :premises (@p418)) % 120.74/121.13 (step @p322 :rule trans :premises (@p417 @p321)) % 120.74/121.13 (step @p323 :rule cong :premises (@p322 @p320) :args (@t250)) % 120.74/121.13 (step @p324 :rule trans :premises (@p323 @p319)) % 120.74/121.13 (step @p325 :rule true_elim :premises (@p324)) % 120.74/121.13 (step-pop @p422 :rule scope :premises (@p325)) % 120.74/121.13 (step-pop @p423 :rule scope :premises (@p422)) % 120.74/121.13 (step-pop @p424 :rule scope :premises (@p423)) % 120.74/121.13 (step @p326 :rule process_scope :premises (@p424) :args (@t250)) % 120.74/121.13 (step @p330 :rule and_intro :premises (@p416 @p418 @p417)) % 120.74/121.13 (step @p331 :rule modus_ponens :premises (@p330 @p326)) % 120.74/121.13 (step-pop @p425 :rule scope :premises (@p331)) % 120.74/121.13 (step-pop @p426 :rule scope :premises (@p425)) % 120.74/121.13 (step-pop @p427 :rule scope :premises (@p426)) % 120.74/121.13 (step @p332 :rule process_scope :premises (@p427) :args (@t250)) % 120.74/121.13 (step @p336 :rule implies_elim :premises (@p332)) % 120.74/121.13 (step @p337 :rule cnf_and_neg :args (@t251)) % 120.74/121.13 (step @p338 :rule resolution :premises (@p337 @p336) :args (true @t251)) % 120.74/121.13 (step @p339 :rule cnf_or_pos :args (@t253)) % 120.74/121.13 (step @p340 :rule reordering :premises (@p339) :args ((or @t95 @t93 @t252 (not @t253)))) % 120.74/121.13 (assume-push @p428 @t80) % 120.74/121.13 (step @p342 :rule instantiate :premises (@p428) :args (@t245)) % 120.74/121.13 (step-pop @p429 :rule scope :premises (@p342)) % 120.74/121.13 (step @p343 :rule process_scope :premises (@p429) :args (@t253)) % 120.74/121.13 (step @p345 :rule implies_elim :premises (@p343)) % 120.74/121.13 (step @p346 :rule chain_m_resolution :premises (@p345 @p340 @p338 @p312 @p310 @p309 @p307 @p38 @p33 @p28 @p23 @p18 @p13 @p8) :args (@t97 (@list true false false false false false false false false false false false false) (@list @t253 @t250 @t248 @t249 @t246 @t247 @t82 @t85 @t87 @t90 @t92 @t94 @t80))) % 120.74/121.13 (step @p347 :rule cnf_or_neg :args (@t237 1)) % 120.74/121.13 (step @p348 :rule chain_m_resolution :premises (@p347 @p290) :args ((not @t235) @t238 @t239)) % 120.74/121.13 (step @p349 :rule instantiate :premises (@p297) :args ((@list @t232))) % 120.74/121.13 (step @p350 :rule skolemize :premises (@p349)) % 120.74/121.13 (step @p351 :rule bool-double-not-elim :args (@t256)) % 120.74/121.13 (step @p352 :rule refl :args (@t260)) % 120.74/121.13 (step @p353 :rule nary_cong :premises (@p352 @p351) :args ((or @t260 (not @t257)))) % 120.74/121.13 (step @p354 :rule cnf_or_neg :args (@t260 1)) % 120.74/121.13 (step @p355 :rule eq_resolve :premises (@p354 @p353)) % 120.74/121.13 (step @p356 :rule reordering :premises (@p355) :args ((or @t256 @t260))) % 120.74/121.13 (step @p357 :rule chain_m_resolution :premises (@p356 @p350) :args (@t256 @t238 @t261)) % 120.74/121.13 (step @p358 :rule bool-double-not-elim :args (@t258)) % 120.74/121.13 (step @p359 :rule nary_cong :premises (@p352 @p358) :args ((or @t260 (not @t259)))) % 120.74/121.13 (step @p360 :rule cnf_or_neg :args (@t260 0)) % 120.74/121.13 (step @p361 :rule eq_resolve :premises (@p360 @p359)) % 120.74/121.13 (step @p362 :rule reordering :premises (@p361) :args ((or @t258 @t260))) % 120.74/121.13 (step @p363 :rule chain_m_resolution :premises (@p362 @p350) :args (@t258 @t238 @t261)) % 120.74/121.13 (step @p364 :rule cnf_or_pos :args (@t262)) % 120.74/121.13 (step @p365 :rule reordering :premises (@p364) :args ((or @t259 @t257 @t263))) % 120.74/121.13 (step @p366 :rule chain_m_resolution :premises (@p365 @p363 @p357) :args (@t263 (@list false false) (@list @t258 @t256))) % 120.74/121.13 (assume-push @p430 @t233) % 120.74/121.13 (step @p368 :rule instantiate :premises (@p430) :args ((@list @t255))) % 120.74/121.13 (step-pop @p431 :rule scope :premises (@p368)) % 120.74/121.13 (step @p369 :rule process_scope :premises (@p431) :args (@t262)) % 120.74/121.13 (step @p371 :rule implies_elim :premises (@p369)) % 120.74/121.13 (step @p372 :rule chain_m_resolution :premises (@p371 @p366) :args (@t234 @t238 (@list @t262))) % 120.74/121.13 (step @p373 :rule refl :args (@t264)) % 120.74/121.13 (step @p374 :rule refl :args (@t265)) % 120.74/121.13 (step @p375 :rule bool-double-not-elim :args (@t233)) % 120.74/121.13 (step @p376 :rule refl :args (@t235)) % 120.74/121.13 (step @p377 :rule nary_cong :premises (@p376 @p375 @p374 @p373) :args ((or @t235 (not @t234) @t265 @t264))) % 120.74/121.13 (step @p378 :rule cnf_and_neg :args (@t235)) % 120.74/121.13 (step @p379 :rule eq_resolve :premises (@p378 @p377)) % 120.74/121.13 (step @p380 :rule reordering :premises (@p379) :args ((or @t233 @t235 @t265 @t264))) % 120.74/121.13 (step @p381 :rule chain_m_resolution :premises (@p380 @p372 @p348 @p346) :args (@t265 (@list true true false) (@list @t233 @t235 @t97))) % 120.74/121.13 (step @p382 :rule bool-double-not-elim :args (@t227)) % 120.74/121.13 (step @p383 :rule refl :args (@t231)) % 120.74/121.13 (step @p384 :rule nary_cong :premises (@p383 @p382) :args ((or @t231 (not @t228)))) % 120.74/121.13 (step @p385 :rule cnf_or_neg :args (@t231 1)) % 120.74/121.13 (step @p386 :rule eq_resolve :premises (@p385 @p384)) % 120.74/121.13 (step @p387 :rule reordering :premises (@p386) :args ((or @t227 @t231))) % 120.74/121.13 (step @p388 :rule chain_m_resolution :premises (@p387 @p381) :args (@t227 @t238 @t266)) % 120.74/121.13 (step @p389 :rule bool-double-not-elim :args (@t229)) % 120.74/121.13 (step @p390 :rule nary_cong :premises (@p383 @p389) :args ((or @t231 (not @t230)))) % 120.74/121.13 (step @p391 :rule cnf_or_neg :args (@t231 0)) % 120.74/121.13 (step @p392 :rule eq_resolve :premises (@p391 @p390)) % 120.74/121.13 (step @p393 :rule reordering :premises (@p392) :args ((or @t229 @t231))) % 120.74/121.13 (step @p394 :rule chain_m_resolution :premises (@p393 @p381) :args (@t229 @t238 @t266)) % 120.74/121.13 (assume-push @p432 @t229) % 120.74/121.13 (step @p396 :rule instantiate :premises (@p432) :args ((@list @t221))) % 120.74/121.13 (step-pop @p433 :rule scope :premises (@p396)) % 120.74/121.13 (step @p397 :rule process_scope :premises (@p433) :args (@t267)) % 120.74/121.13 (step @p399 :rule implies_elim :premises (@p397)) % 120.74/121.13 (step @p400 :rule chain_m_resolution :premises (@p399 @p394) :args (@t267 (@list false) (@list @t229))) % 120.74/121.13 (step @p401 :rule bool-double-not-elim :args (@t225)) % 120.74/121.13 (step @p402 :rule nary_cong :premises (@p383 @p401) :args ((or @t231 (not @t226)))) % 120.74/121.13 (step @p403 :rule cnf_or_neg :args (@t231 2)) % 120.74/121.13 (step @p404 :rule eq_resolve :premises (@p403 @p402)) % 120.74/121.13 (step @p405 :rule reordering :premises (@p404) :args ((or @t225 @t231))) % 120.74/121.13 (step @p406 :rule chain_m_resolution :premises (@p405 @p381) :args (@t225 @t238 @t266)) % 120.74/121.13 (step @p407 :rule bool-double-not-elim :args (@t222)) % 120.74/121.13 (step @p408 :rule nary_cong :premises (@p383 @p407) :args ((or @t231 (not @t223)))) % 120.74/121.13 (step @p409 :rule cnf_or_neg :args (@t231 3)) % 120.74/121.13 (step @p410 :rule eq_resolve :premises (@p409 @p408)) % 120.74/121.13 (step @p411 :rule reordering :premises (@p410) :args ((or @t222 @t231))) % 120.74/121.13 (step @p412 :rule chain_m_resolution :premises (@p411 @p381) :args (@t222 @t238 @t266)) % 120.74/121.13 (step @p413 :rule cnf_or_pos :args (@t267)) % 120.74/121.13 (step @p414 :rule reordering :premises (@p413) :args ((or @t228 @t226 @t223 (not @t267)))) % 120.74/121.13 (step @p415 false :rule chain_m_resolution :premises (@p414 @p412 @p406 @p400 @p388) :args (false (@list false false false false) (@list @t222 @t225 @t267 @t227))) % 120.74/121.13 ) % 120.74/121.13 % SZS output end Proof % 120.74/121.13 % cvc5 exiting %------------------------------------------------------------------------------