%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU286+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 08:51:14 AM UTC 2026 % Result : Theorem 0.37s 0.62s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU286+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : 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 16:51:14 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.62 % SZS status Theorem % 0.37/0.62 % SZS output start Proof % 0.37/0.62 ( % 0.37/0.62 (declare-sort $$unsorted 0) % 0.37/0.62 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.function (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (define @t1 () (@var "B" $$unsorted)) % 0.37/0.62 (define @t2 () (@var "I" $$unsorted)) % 0.37/0.62 (define @t3 () (@var "G" $$unsorted)) % 0.37/0.62 (define @t4 () (tptp.in (tptp.ordered_pair @t3 @t2) @t1)) % 0.37/0.62 (define @t5 () (@var "H" $$unsorted)) % 0.37/0.62 (define @t6 () (tptp.in @t2 @t5)) % 0.37/0.62 (define @t7 () (@list @t2)) % 0.37/0.62 (define @t8 () (forall @t7 (=> @t6 @t4))) % 0.37/0.62 (define @t9 () (tptp.in @t3 @t5)) % 0.37/0.62 (define @t10 () (@var "F" $$unsorted)) % 0.37/0.62 (define @t11 () (= @t10 @t5)) % 0.37/0.62 (define @t12 () (and @t11 @t9 @t8)) % 0.37/0.62 (define @t13 () (@list @t5)) % 0.37/0.62 (define @t14 () (exists @t13 @t12)) % 0.37/0.62 (define @t15 () (@var "A" $$unsorted)) % 0.37/0.62 (define @t16 () (tptp.in @t10 @t15)) % 0.37/0.62 (define @t17 () (@var "E" $$unsorted)) % 0.37/0.62 (define @t18 () (tptp.ordered_pair @t10 @t3)) % 0.37/0.62 (define @t19 () (and (= @t18 @t17) @t16 @t14)) % 0.37/0.62 (define @t20 () (@list @t10 @t3)) % 0.37/0.62 (define @t21 () (exists @t20 @t19)) % 0.37/0.62 (define @t22 () (@var "C" $$unsorted)) % 0.37/0.62 (define @t23 () (tptp.cartesian_product2 @t15 @t22)) % 0.37/0.62 (define @t24 () (tptp.in @t17 @t23)) % 0.37/0.62 (define @t25 () (and @t24 @t21)) % 0.37/0.62 (define @t26 () (@var "D" $$unsorted)) % 0.37/0.62 (define @t27 () (tptp.in @t17 @t26)) % 0.37/0.62 (define @t28 () (= @t27 @t25)) % 0.37/0.62 (define @t29 () (@list @t17)) % 0.37/0.62 (define @t30 () (forall @t29 @t28)) % 0.37/0.62 (define @t31 () (@list @t26)) % 0.37/0.62 (define @t32 () (exists @t31 @t30)) % 0.37/0.62 (define @t33 () (@list @t22)) % 0.37/0.62 (define @t34 () (forall @t33 @t32)) % 0.37/0.62 (define @t35 () (tptp.relation @t1)) % 0.37/0.62 (define @t36 () (tptp.empty @t15)) % 0.37/0.62 (define @t37 () (not @t36)) % 0.37/0.62 (define @t38 () (and @t37 @t35)) % 0.37/0.62 (define @t39 () (=> @t38 @t34)) % 0.37/0.62 (define @t40 () (@list @t15 @t1)) % 0.37/0.62 (define @t41 () (forall @t40 @t39)) % 0.37/0.62 (define @t42 () (not @t41)) % 0.37/0.62 (define @t43 () (tptp.one_to_one @t15)) % 0.37/0.62 (define @t44 () (tptp.function @t15)) % 0.37/0.62 (define @t45 () (tptp.relation @t15)) % 0.37/0.62 (define @t46 () (and @t45 @t44 @t43)) % 0.37/0.62 (define @t47 () (@list @t15)) % 0.37/0.62 (define @t48 () (tptp.ordinal @t15)) % 0.37/0.62 (define @t49 () (tptp.epsilon_connected @t15)) % 0.37/0.62 (define @t50 () (tptp.epsilon_transitive @t15)) % 0.37/0.62 (define @t51 () (and @t45 @t36 @t44)) % 0.37/0.62 (define @t52 () (and @t50 @t49)) % 0.37/0.62 (define @t53 () (and @t50 @t49 @t48)) % 0.37/0.62 (define @t54 () (@var "R" $$unsorted)) % 0.37/0.62 (define @t55 () (@var "P" $$unsorted)) % 0.37/0.62 (define @t56 () (tptp.in (tptp.ordered_pair @t55 @t54) @t1)) % 0.37/0.62 (define @t57 () (@var "Q" $$unsorted)) % 0.37/0.62 (define @t58 () (tptp.in @t54 @t57)) % 0.37/0.62 (define @t59 () (@list @t54)) % 0.37/0.62 (define @t60 () (forall @t59 (=> @t58 @t56))) % 0.37/0.62 (define @t61 () (tptp.in @t55 @t57)) % 0.37/0.62 (define @t62 () (@var "O" $$unsorted)) % 0.37/0.62 (define @t63 () (= @t62 @t57)) % 0.37/0.62 (define @t64 () (and @t63 @t61 @t60)) % 0.37/0.62 (define @t65 () (@list @t57)) % 0.37/0.62 (define @t66 () (exists @t65 @t64)) % 0.37/0.62 (define @t67 () (tptp.in @t62 @t15)) % 0.37/0.62 (define @t68 () (tptp.ordered_pair @t62 @t55)) % 0.37/0.62 (define @t69 () (and (= @t68 @t17) @t67 @t66)) % 0.37/0.62 (define @t70 () (@list @t62 @t55)) % 0.37/0.62 (define @t71 () (exists @t70 @t69)) % 0.37/0.62 (define @t72 () (= @t10 @t17)) % 0.37/0.62 (define @t73 () (tptp.in @t10 @t23)) % 0.37/0.62 (define @t74 () (and @t73 @t72 @t71)) % 0.37/0.62 (define @t75 () (@list @t10)) % 0.37/0.62 (define @t76 () (exists @t75 @t74)) % 0.37/0.62 (define @t77 () (= @t27 @t76)) % 0.37/0.62 (define @t78 () (forall @t29 @t77)) % 0.37/0.62 (define @t79 () (exists @t31 @t78)) % 0.37/0.62 (define @t80 () (= @t17 @t10)) % 0.37/0.62 (define @t81 () (@var "N" $$unsorted)) % 0.37/0.62 (define @t82 () (@var "L" $$unsorted)) % 0.37/0.62 (define @t83 () (tptp.in (tptp.ordered_pair @t82 @t81) @t1)) % 0.37/0.62 (define @t84 () (@var "M" $$unsorted)) % 0.37/0.62 (define @t85 () (tptp.in @t81 @t84)) % 0.37/0.62 (define @t86 () (@list @t81)) % 0.37/0.62 (define @t87 () (forall @t86 (=> @t85 @t83))) % 0.37/0.62 (define @t88 () (tptp.in @t82 @t84)) % 0.37/0.62 (define @t89 () (@var "K" $$unsorted)) % 0.37/0.62 (define @t90 () (= @t89 @t84)) % 0.37/0.62 (define @t91 () (and @t90 @t88 @t87)) % 0.37/0.62 (define @t92 () (@list @t84)) % 0.37/0.62 (define @t93 () (exists @t92 @t91)) % 0.37/0.62 (define @t94 () (tptp.in @t89 @t15)) % 0.37/0.62 (define @t95 () (tptp.ordered_pair @t89 @t82)) % 0.37/0.62 (define @t96 () (and (= @t95 @t10) @t94 @t93)) % 0.37/0.62 (define @t97 () (@list @t89 @t82)) % 0.37/0.62 (define @t98 () (exists @t97 @t96)) % 0.37/0.62 (define @t99 () (= @t26 @t10)) % 0.37/0.62 (define @t100 () (@var "J" $$unsorted)) % 0.37/0.62 (define @t101 () (tptp.in (tptp.ordered_pair @t5 @t100) @t1)) % 0.37/0.62 (define @t102 () (tptp.in @t100 @t2)) % 0.37/0.62 (define @t103 () (@list @t100)) % 0.37/0.62 (define @t104 () (forall @t103 (=> @t102 @t101))) % 0.37/0.62 (define @t105 () (tptp.in @t5 @t2)) % 0.37/0.62 (define @t106 () (= @t3 @t2)) % 0.37/0.62 (define @t107 () (and @t106 @t105 @t104)) % 0.37/0.62 (define @t108 () (exists @t7 @t107)) % 0.37/0.62 (define @t109 () (tptp.in @t3 @t15)) % 0.37/0.62 (define @t110 () (tptp.ordered_pair @t3 @t5)) % 0.37/0.62 (define @t111 () (and (= @t110 @t17) @t109 @t108)) % 0.37/0.62 (define @t112 () (@list @t3 @t5)) % 0.37/0.62 (define @t113 () (exists @t112 @t111)) % 0.37/0.62 (define @t114 () (= @t26 @t17)) % 0.37/0.62 (define @t115 () (and @t114 @t113 @t99 @t98)) % 0.37/0.62 (define @t116 () (=> @t115 @t80)) % 0.37/0.62 (define @t117 () (@list @t26 @t17 @t10)) % 0.37/0.62 (define @t118 () (forall @t117 @t116)) % 0.37/0.62 (define @t119 () (=> @t118 @t79)) % 0.37/0.62 (define @t120 () (forall @t33 @t119)) % 0.37/0.62 (define @t121 () (=> @t38 @t120)) % 0.37/0.62 (define @t122 () (forall @t40 @t121)) % 0.37/0.62 (define @t123 () (not (forall @t7 (or (not (tptp.in @t2 @t10)) @t4)))) % 0.37/0.62 (define @t124 () (not (tptp.in @t3 @t10))) % 0.37/0.62 (define @t125 () (not @t16)) % 0.37/0.62 (define @t126 () (= @t17 @t18)) % 0.37/0.62 (define @t127 () (not @t126)) % 0.37/0.62 (define @t128 () (or @t127 @t125 @t124 @t123)) % 0.37/0.62 (define @t129 () (not (forall @t20 @t128))) % 0.37/0.62 (define @t130 () (@var "BOUND_VARIABLE_7636" $$unsorted)) % 0.37/0.62 (define @t131 () (not (forall @t31 (not (forall @t29 (= @t27 (and (tptp.in @t17 (tptp.cartesian_product2 @t15 @t130)) @t129))))))) % 0.37/0.62 (define @t132 () (not @t35)) % 0.37/0.62 (define @t133 () (or @t36 @t132 @t131)) % 0.37/0.62 (define @t134 () (forall (@list @t15 @t1 @t130) @t133)) % 0.37/0.62 (define @t135 () (@list @t130)) % 0.37/0.62 (define @t136 () (forall @t135 @t133)) % 0.37/0.62 (define @t137 () (forall @t135 @t131)) % 0.37/0.62 (define @t138 () (@list @t22)) % 0.37/0.62 (define @t139 () (or @t36 @t132 @t137)) % 0.37/0.62 (define @t140 () (forall @t29 (= @t27 (and @t24 @t129)))) % 0.37/0.62 (define @t141 () (not (forall @t31 (not @t140)))) % 0.37/0.62 (define @t142 () (forall @t33 @t141)) % 0.37/0.62 (define @t143 () (or @t36 @t132 @t142)) % 0.37/0.62 (define @t144 () (or @t36 @t132)) % 0.37/0.62 (define @t145 () (not @t38)) % 0.37/0.62 (define @t146 () (or @t124 @t123)) % 0.37/0.62 (define @t147 () (not @t146)) % 0.37/0.62 (define @t148 () (not @t147)) % 0.37/0.62 (define @t149 () (or @t127 @t125 @t148)) % 0.37/0.62 (define @t150 () (and @t126 @t16 @t147)) % 0.37/0.62 (define @t151 () (forall @t20 (not @t150))) % 0.37/0.62 (define @t152 () (not @t151)) % 0.37/0.62 (define @t153 () (not (= @t10 @t10))) % 0.37/0.62 (define @t154 () (or @t153 @t124 @t123)) % 0.37/0.62 (define @t155 () (forall @t7 (or (not @t6) @t4))) % 0.37/0.62 (define @t156 () (not @t155)) % 0.37/0.62 (define @t157 () (not @t9)) % 0.37/0.62 (define @t158 () (not @t11)) % 0.37/0.62 (define @t159 () (or @t158 @t158 @t157 @t156)) % 0.37/0.62 (define @t160 () (or @t158 @t157 @t156)) % 0.37/0.62 (define @t161 () (and @t11 @t9 @t155)) % 0.37/0.62 (define @t162 () (forall @t13 (not @t161))) % 0.37/0.62 (define @t163 () (not @t162)) % 0.37/0.62 (define @t164 () (not (forall @t59 (or (not (tptp.in @t54 @t62)) @t56)))) % 0.37/0.62 (define @t165 () (not (tptp.in @t55 @t62))) % 0.37/0.62 (define @t166 () (not @t67)) % 0.37/0.62 (define @t167 () (= @t17 @t68)) % 0.37/0.62 (define @t168 () (not @t167)) % 0.37/0.62 (define @t169 () (or @t168 @t166 @t165 @t164)) % 0.37/0.62 (define @t170 () (forall @t70 @t169)) % 0.37/0.62 (define @t171 () (not @t170)) % 0.37/0.62 (define @t172 () (@var "BOUND_VARIABLE_7933" $$unsorted)) % 0.37/0.62 (define @t173 () (tptp.in @t17 (tptp.cartesian_product2 @t15 @t172))) % 0.37/0.62 (define @t174 () (and @t173 @t171)) % 0.37/0.62 (define @t175 () (and @t171 @t173)) % 0.37/0.62 (define @t176 () (= @t27 @t175)) % 0.37/0.62 (define @t177 () (forall @t29 @t176)) % 0.37/0.62 (define @t178 () (not @t177)) % 0.37/0.62 (define @t179 () (forall @t31 @t178)) % 0.37/0.62 (define @t180 () (not @t179)) % 0.37/0.62 (define @t181 () (or @t36 @t132 @t180)) % 0.37/0.62 (define @t182 () (@list @t15 @t1 @t172)) % 0.37/0.62 (define @t183 () (forall @t182 @t181)) % 0.37/0.62 (define @t184 () (forall @t182 (or @t36 @t132 (not (forall @t31 (not (forall @t29 (= @t27 @t174)))))))) % 0.37/0.62 (define @t185 () (@var "BOUND_VARIABLE_8075" $$unsorted)) % 0.37/0.62 (define @t186 () (@var "BOUND_VARIABLE_8074" $$unsorted)) % 0.37/0.62 (define @t187 () (@var "BOUND_VARIABLE_8073" $$unsorted)) % 0.37/0.62 (define @t188 () (@var "BOUND_VARIABLE_8072" $$unsorted)) % 0.37/0.62 (define @t189 () (@var "BOUND_VARIABLE_8076" $$unsorted)) % 0.37/0.62 (define @t190 () (@var "BOUND_VARIABLE_8071" $$unsorted)) % 0.37/0.62 (define @t191 () (@var "BOUND_VARIABLE_8077" $$unsorted)) % 0.37/0.62 (define @t192 () (@var "BOUND_VARIABLE_8070" $$unsorted)) % 0.37/0.62 (define @t193 () (@list @t192 @t190 @t188 @t187 @t186 @t185 @t189 @t191)) % 0.37/0.62 (define @t194 () (@list true)) % 0.37/0.62 (define @t195 () (@list @t172)) % 0.37/0.62 (define @t196 () (forall @t195 @t181)) % 0.37/0.62 (define @t197 () (forall @t195 @t180)) % 0.37/0.62 (define @t198 () (or @t36 @t132 @t197)) % 0.37/0.62 (define @t199 () (forall @t29 (= @t27 (and @t171 @t24)))) % 0.37/0.62 (define @t200 () (not (forall @t31 (not @t199)))) % 0.37/0.62 (define @t201 () (forall @t33 @t200)) % 0.37/0.62 (define @t202 () (or @t36 @t132 @t201)) % 0.37/0.62 (define @t203 () (not @t24)) % 0.37/0.62 (define @t204 () (= @t27 (not (or @t170 @t203)))) % 0.37/0.62 (define @t205 () (not (= @t17 @t17))) % 0.37/0.62 (define @t206 () (or @t203 @t205)) % 0.37/0.62 (define @t207 () (not @t80)) % 0.37/0.62 (define @t208 () (not @t73)) % 0.37/0.62 (define @t209 () (or @t207 @t208 @t207)) % 0.37/0.62 (define @t210 () (or @t208 @t207)) % 0.37/0.62 (define @t211 () (forall @t75 @t210)) % 0.37/0.62 (define @t212 () (or @t170 @t211)) % 0.37/0.62 (define @t213 () (or @t170 @t210)) % 0.37/0.62 (define @t214 () (or @t208 @t207 @t170)) % 0.37/0.62 (define @t215 () (not @t171)) % 0.37/0.62 (define @t216 () (or @t208 @t207 @t215)) % 0.37/0.62 (define @t217 () (and @t73 @t80 @t171)) % 0.37/0.62 (define @t218 () (forall @t75 (not @t217))) % 0.37/0.62 (define @t219 () (not @t218)) % 0.37/0.62 (define @t220 () (or @t165 @t164)) % 0.37/0.62 (define @t221 () (not @t220)) % 0.37/0.62 (define @t222 () (not @t221)) % 0.37/0.62 (define @t223 () (or @t168 @t166 @t222)) % 0.37/0.62 (define @t224 () (and @t167 @t67 @t221)) % 0.37/0.62 (define @t225 () (forall @t70 (not @t224))) % 0.37/0.62 (define @t226 () (not @t225)) % 0.37/0.62 (define @t227 () (not (= @t62 @t62))) % 0.37/0.62 (define @t228 () (or @t227 @t165 @t164)) % 0.37/0.62 (define @t229 () (forall @t59 (or (not @t58) @t56))) % 0.37/0.62 (define @t230 () (not @t229)) % 0.37/0.62 (define @t231 () (not @t61)) % 0.37/0.62 (define @t232 () (not @t63)) % 0.37/0.62 (define @t233 () (or @t232 @t232 @t231 @t230)) % 0.37/0.62 (define @t234 () (or @t232 @t231 @t230)) % 0.37/0.62 (define @t235 () (and @t63 @t61 @t229)) % 0.37/0.62 (define @t236 () (forall @t65 (not @t235))) % 0.37/0.62 (define @t237 () (not @t236)) % 0.37/0.62 (define @t238 () (@var "BOUND_VARIABLE_7833" $$unsorted)) % 0.37/0.62 (define @t239 () (@var "BOUND_VARIABLE_7831" $$unsorted)) % 0.37/0.62 (define @t240 () (@var "BOUND_VARIABLE_7814" $$unsorted)) % 0.37/0.62 (define @t241 () (@var "BOUND_VARIABLE_7812" $$unsorted)) % 0.37/0.62 (define @t242 () (@list @t17 @t10 @t241 @t240 @t239 @t238)) % 0.37/0.62 (define @t243 () (not (forall @t86 (or (not (tptp.in @t81 @t239)) (tptp.in (tptp.ordered_pair @t238 @t81) @t1))))) % 0.37/0.62 (define @t244 () (not (tptp.in @t238 @t239))) % 0.37/0.62 (define @t245 () (not (tptp.in @t239 @t15))) % 0.37/0.62 (define @t246 () (not (= @t10 (tptp.ordered_pair @t239 @t238)))) % 0.37/0.62 (define @t247 () (not (forall @t103 (or (not (tptp.in @t100 @t241)) (tptp.in (tptp.ordered_pair @t240 @t100) @t1))))) % 0.37/0.62 (define @t248 () (not (tptp.in @t240 @t241))) % 0.37/0.62 (define @t249 () (not (tptp.in @t241 @t15))) % 0.37/0.62 (define @t250 () (not (= @t17 (tptp.ordered_pair @t241 @t240)))) % 0.37/0.62 (define @t251 () (or @t207 @t80 @t250 @t249 @t248 @t247 @t246 @t245 @t244 @t243)) % 0.37/0.62 (define @t252 () (or @t205 @t207 @t80 @t250 @t249 @t248 @t247 @t246 @t245 @t244 @t243)) % 0.37/0.62 (define @t253 () (not @t99)) % 0.37/0.62 (define @t254 () (not @t114)) % 0.37/0.62 (define @t255 () (or @t254 @t254 @t253 @t80 @t250 @t249 @t248 @t247 @t246 @t245 @t244 @t243)) % 0.37/0.62 (define @t256 () (or @t254 @t253 @t80 @t250 @t249 @t248 @t247 @t246 @t245 @t244 @t243)) % 0.37/0.62 (define @t257 () (forall @t31 @t256)) % 0.37/0.62 (define @t258 () (forall @t242 @t257)) % 0.37/0.62 (define @t259 () (forall (@list @t17 @t10 @t241 @t240 @t239 @t238 @t26) @t256)) % 0.37/0.62 (define @t260 () (@list @t26 @t17 @t10 @t241 @t240 @t239 @t238)) % 0.37/0.62 (define @t261 () (or @t246 @t245 @t244 @t243)) % 0.37/0.62 (define @t262 () (or @t250 @t249 @t248 @t247)) % 0.37/0.62 (define @t263 () (or @t254 @t262 @t253 @t261 @t80)) % 0.37/0.62 (define @t264 () (forall @t260 @t263)) % 0.37/0.62 (define @t265 () (forall (@list @t241 @t240 @t239 @t238) @t263)) % 0.37/0.62 (define @t266 () (forall (@list @t239 @t238) @t261)) % 0.37/0.62 (define @t267 () (forall (@list @t241 @t240) @t262)) % 0.37/0.62 (define @t268 () (or @t254 @t267 @t253 @t266 @t80)) % 0.37/0.62 (define @t269 () (not (forall @t86 (or (not (tptp.in @t81 @t89)) @t83)))) % 0.37/0.62 (define @t270 () (not (tptp.in @t82 @t89))) % 0.37/0.62 (define @t271 () (not @t94)) % 0.37/0.62 (define @t272 () (= @t10 @t95)) % 0.37/0.62 (define @t273 () (not @t272)) % 0.37/0.62 (define @t274 () (or @t273 @t271 @t270 @t269)) % 0.37/0.62 (define @t275 () (forall @t97 @t274)) % 0.37/0.62 (define @t276 () (not (forall @t103 (or (not (tptp.in @t100 @t3)) @t101)))) % 0.37/0.62 (define @t277 () (not (tptp.in @t5 @t3))) % 0.37/0.62 (define @t278 () (not @t109)) % 0.37/0.62 (define @t279 () (= @t17 @t110)) % 0.37/0.62 (define @t280 () (not @t279)) % 0.37/0.62 (define @t281 () (or @t280 @t278 @t277 @t276)) % 0.37/0.62 (define @t282 () (forall @t112 @t281)) % 0.37/0.62 (define @t283 () (or @t254 @t282 @t253 @t275 @t80)) % 0.37/0.62 (define @t284 () (not @t275)) % 0.37/0.62 (define @t285 () (not @t284)) % 0.37/0.62 (define @t286 () (not @t282)) % 0.37/0.62 (define @t287 () (not @t286)) % 0.37/0.62 (define @t288 () (or @t254 @t287 @t253 @t285)) % 0.37/0.62 (define @t289 () (and @t114 @t286 @t99 @t284)) % 0.37/0.62 (define @t290 () (or @t270 @t269)) % 0.37/0.62 (define @t291 () (not @t290)) % 0.37/0.62 (define @t292 () (not @t291)) % 0.37/0.62 (define @t293 () (or @t273 @t271 @t292)) % 0.37/0.62 (define @t294 () (and @t272 @t94 @t291)) % 0.37/0.62 (define @t295 () (forall @t97 (not @t294))) % 0.37/0.62 (define @t296 () (not @t295)) % 0.37/0.62 (define @t297 () (not (= @t89 @t89))) % 0.37/0.62 (define @t298 () (or @t297 @t270 @t269)) % 0.37/0.62 (define @t299 () (forall @t86 (or (not @t85) @t83))) % 0.37/0.62 (define @t300 () (not @t299)) % 0.37/0.62 (define @t301 () (not @t88)) % 0.37/0.62 (define @t302 () (not @t90)) % 0.37/0.62 (define @t303 () (or @t302 @t302 @t301 @t300)) % 0.37/0.62 (define @t304 () (or @t302 @t301 @t300)) % 0.37/0.62 (define @t305 () (and @t90 @t88 @t299)) % 0.37/0.62 (define @t306 () (forall @t92 (not @t305))) % 0.37/0.62 (define @t307 () (not @t306)) % 0.37/0.62 (define @t308 () (or @t277 @t276)) % 0.37/0.62 (define @t309 () (not @t308)) % 0.37/0.62 (define @t310 () (not @t309)) % 0.37/0.62 (define @t311 () (or @t280 @t278 @t310)) % 0.37/0.62 (define @t312 () (and @t279 @t109 @t309)) % 0.37/0.62 (define @t313 () (forall @t112 (not @t312))) % 0.37/0.62 (define @t314 () (not @t313)) % 0.37/0.62 (define @t315 () (not (= @t3 @t3))) % 0.37/0.62 (define @t316 () (or @t315 @t277 @t276)) % 0.37/0.62 (define @t317 () (forall @t103 (or (not @t102) @t101))) % 0.37/0.62 (define @t318 () (not @t317)) % 0.37/0.62 (define @t319 () (not @t105)) % 0.37/0.62 (define @t320 () (not @t106)) % 0.37/0.62 (define @t321 () (or @t320 @t320 @t319 @t318)) % 0.37/0.62 (define @t322 () (or @t320 @t319 @t318)) % 0.37/0.62 (define @t323 () (and @t106 @t105 @t317)) % 0.37/0.62 (define @t324 () (forall @t7 (not @t323))) % 0.37/0.62 (define @t325 () (not @t324)) % 0.37/0.62 (assume @p1 @t42) % 0.37/0.62 (assume @p2 (exists @t47 @t46)) % 0.37/0.62 (assume @p3 (exists @t47 (and @t45 @t44 @t43 @t36 @t50 @t49 @t48))) % 0.37/0.62 (assume @p4 (exists @t47 (and @t45 @t44))) % 0.37/0.62 (assume @p5 (exists @t47 @t51)) % 0.37/0.62 (assume @p6 (forall @t47 (=> @t51 @t46))) % 0.37/0.62 (assume @p7 (forall @t47 (=> @t48 @t52))) % 0.37/0.62 (assume @p8 (forall @t47 (=> @t52 @t48))) % 0.37/0.62 (assume @p9 (exists @t47 @t53)) % 0.37/0.62 (assume @p10 (exists @t47 (and @t37 @t50 @t49 @t48))) % 0.37/0.62 (assume @p11 (forall @t40 (=> (tptp.in @t15 @t1) (not (tptp.in @t1 @t15))))) % 0.37/0.62 (assume @p12 true) % 0.37/0.62 (assume @p13 (forall @t47 (=> @t36 @t44))) % 0.37/0.62 (assume @p14 (forall @t47 (=> @t36 @t53))) % 0.37/0.62 (assume @p15 (forall @t40 (not (tptp.empty (tptp.ordered_pair @t15 @t1))))) % 0.37/0.62 (assume @p16 (exists @t47 @t36)) % 0.37/0.62 (assume @p17 (exists @t47 @t37)) % 0.37/0.62 (assume @p18 @t122) % 0.37/0.62 (step @p19 :rule quant-merge-prenex :args ((= (forall @t40 @t136) @t134))) % 0.37/0.62 (step @p20 :rule alpha_equiv :args (@t137 (@list @t130) @t138)) % 0.37/0.62 (step @p21 :rule refl :args (@t132)) % 0.37/0.62 (step @p22 :rule refl :args (@t36)) % 0.37/0.62 (step @p23 :rule nary_cong :premises (@p22 @p21 @p20) :args (@t139)) % 0.37/0.62 (step @p24 :rule quant-miniscope-or :args ((= @t136 @t139))) % 0.37/0.62 (step @p25 :rule trans :premises (@p24 @p23)) % 0.37/0.62 (step @p26 :rule symm :premises (@p25)) % 0.37/0.62 (step @p27 :rule cong :premises (@p26) :args ((forall @t40 @t143))) % 0.37/0.62 (step @p28 :rule trans :premises (@p27 @p19)) % 0.37/0.62 (step @p29 :rule aci_norm :args ((= (or @t144 @t142) @t143))) % 0.37/0.62 (step @p30 :rule refl :args (@t142)) % 0.37/0.62 (step @p31 :rule bool-double-not-elim :args (@t36)) % 0.37/0.62 (step @p32 :rule nary_cong :premises (@p31 @p21) :args ((or (not @t37) @t132))) % 0.37/0.62 (step @p33 :rule bool-and-de-morgan :args (@t37 @t35 true)) % 0.37/0.62 (step @p34 :rule trans :premises (@p33 @p32)) % 0.37/0.62 (step @p35 :rule nary_cong :premises (@p34 @p30) :args ((or @t145 @t142))) % 0.37/0.62 (step @p36 :rule trans :premises (@p35 @p29)) % 0.37/0.62 (step @p37 :rule bool-impl-elim :args (@t38 @t142)) % 0.37/0.62 (step @p38 :rule trans :premises (@p37 @p36)) % 0.37/0.62 (step @p39 :rule cong :premises (@p38) :args ((forall @t40 (=> @t38 @t142)))) % 0.37/0.62 (step @p40 :rule trans :premises (@p39 @p28)) % 0.37/0.62 (step @p41 :rule exists-elim :args ((= (exists @t31 @t140) @t141))) % 0.37/0.62 (step @p42 :rule aci_norm :args ((= (or @t127 @t125 @t146) @t128))) % 0.37/0.62 (step @p43 :rule bool-double-not-elim :args (@t146)) % 0.37/0.62 (step @p44 :rule refl :args (@t125)) % 0.37/0.62 (step @p45 :rule refl :args (@t127)) % 0.37/0.62 (step @p46 :rule nary_cong :premises (@p45 @p44 @p43) :args (@t149)) % 0.37/0.62 (step @p47 :rule aci_norm :args ((= (or @t127 (or @t125 @t148)) @t149))) % 0.37/0.62 (step @p48 :rule trans :premises (@p47 @p46)) % 0.37/0.62 (step @p49 :rule bool-and-de-morgan :args (@t16 @t147 true)) % 0.37/0.62 (step @p50 :rule nary_cong :premises (@p45 @p49) :args ((or @t127 (not (and @t16 @t147))))) % 0.37/0.62 (step @p51 :rule bool-and-de-morgan :args (@t126 @t16 (and @t147))) % 0.37/0.62 (step @p52 :rule trans :premises (@p51 @p50)) % 0.37/0.62 (step @p53 :rule trans :premises (@p52 @p48)) % 0.37/0.62 (step @p54 :rule trans :premises (@p53 @p42)) % 0.37/0.62 (step @p55 :rule cong :premises (@p54) :args (@t151)) % 0.37/0.62 (step @p56 :rule cong :premises (@p55) :args (@t152)) % 0.37/0.62 (step @p57 :rule exists-elim :args ((= (exists @t20 @t150) @t152))) % 0.37/0.62 (step @p58 :rule trans :premises (@p57 @p56)) % 0.37/0.62 (step @p59 :rule aci_norm :args ((= (or false @t124 @t123) @t146))) % 0.37/0.62 (step @p60 :rule refl :args (@t123)) % 0.37/0.62 (step @p61 :rule refl :args (@t124)) % 0.37/0.62 (step @p62 :rule evaluate :args ((not true))) % 0.37/0.62 (step @p63 :rule eq-refl :args (@t10)) % 0.37/0.62 (step @p64 :rule cong :premises (@p63) :args (@t153)) % 0.37/0.62 (step @p65 :rule trans :premises (@p64 @p62)) % 0.37/0.62 (step @p66 :rule nary_cong :premises (@p65 @p61 @p60) :args (@t154)) % 0.37/0.62 (step @p67 :rule trans :premises (@p66 @p59)) % 0.37/0.62 (step @p68 :rule quant-var-elim-eq :args ((= (forall @t13 (or (not (= @t5 @t10)) @t158 @t157 @t156)) @t154))) % 0.37/0.62 (step @p69 :rule refl :args (@t156)) % 0.37/0.62 (step @p70 :rule refl :args (@t157)) % 0.37/0.62 (step @p71 :rule refl :args (@t158)) % 0.37/0.62 (step @p72 :rule eq-symm :args (@t10 @t5)) % 0.37/0.62 (step @p73 :rule cong :premises (@p72) :args (@t158)) % 0.37/0.62 (step @p74 :rule nary_cong :premises (@p73 @p71 @p70 @p69) :args (@t159)) % 0.37/0.62 (step @p75 :rule aci_norm :args ((= @t160 @t159))) % 0.37/0.62 (step @p76 :rule trans :premises (@p75 @p74)) % 0.37/0.62 (step @p77 :rule cong :premises (@p76) :args ((forall @t13 @t160))) % 0.37/0.62 (step @p78 :rule trans :premises (@p77 @p68)) % 0.37/0.62 (step @p79 :rule trans :premises (@p78 @p67)) % 0.37/0.62 (step @p80 :rule aci_norm :args ((= (or @t158 (or @t157 @t156)) @t160))) % 0.37/0.62 (step @p81 :rule bool-and-de-morgan :args (@t9 @t155 true)) % 0.37/0.62 (step @p82 :rule nary_cong :premises (@p71 @p81) :args ((or @t158 (not (and @t9 @t155))))) % 0.37/0.62 (step @p83 :rule bool-and-de-morgan :args (@t11 @t9 (and @t155))) % 0.37/0.62 (step @p84 :rule trans :premises (@p83 @p82)) % 0.37/0.62 (step @p85 :rule trans :premises (@p84 @p80)) % 0.37/0.62 (step @p86 :rule cong :premises (@p85) :args (@t162)) % 0.37/0.62 (step @p87 :rule trans :premises (@p86 @p79)) % 0.37/0.62 (step @p88 :rule cong :premises (@p87) :args (@t163)) % 0.37/0.62 (step @p89 :rule exists-elim :args ((= (exists @t13 @t161) @t163))) % 0.37/0.62 (step @p90 :rule trans :premises (@p89 @p88)) % 0.37/0.62 (step @p91 :rule bool-impl-elim :args (@t6 @t4)) % 0.37/0.62 (step @p92 :rule cong :premises (@p91) :args (@t8)) % 0.37/0.62 (step @p93 :rule refl :args (@t9)) % 0.37/0.62 (step @p94 :rule refl :args (@t11)) % 0.37/0.62 (step @p95 :rule nary_cong :premises (@p94 @p93 @p92) :args (@t12)) % 0.37/0.62 (step @p96 :rule cong :premises (@p95) :args (@t14)) % 0.37/0.62 (step @p97 :rule trans :premises (@p96 @p90)) % 0.37/0.62 (step @p98 :rule refl :args (@t16)) % 0.37/0.62 (step @p99 :rule eq-symm :args (@t18 @t17)) % 0.37/0.62 (step @p100 :rule nary_cong :premises (@p99 @p98 @p97) :args (@t19)) % 0.37/0.62 (step @p101 :rule cong :premises (@p100) :args (@t21)) % 0.37/0.62 (step @p102 :rule trans :premises (@p101 @p58)) % 0.37/0.62 (step @p103 :rule refl :args (@t24)) % 0.37/0.62 (step @p104 :rule nary_cong :premises (@p103 @p102) :args (@t25)) % 0.37/0.62 (step @p105 :rule refl :args (@t27)) % 0.37/0.62 (step @p106 :rule cong :premises (@p105 @p104) :args (@t28)) % 0.37/0.62 (step @p107 :rule cong :premises (@p106) :args (@t30)) % 0.37/0.62 (step @p108 :rule cong :premises (@p107) :args (@t32)) % 0.37/0.62 (step @p109 :rule trans :premises (@p108 @p41)) % 0.37/0.62 (step @p110 :rule cong :premises (@p109) :args (@t34)) % 0.37/0.62 (step @p111 :rule refl :args (@t38)) % 0.37/0.62 (step @p112 :rule cong :premises (@p111 @p110) :args (@t39)) % 0.37/0.62 (step @p113 :rule cong :premises (@p112) :args (@t41)) % 0.37/0.62 (step @p114 :rule trans :premises (@p113 @p40)) % 0.37/0.62 (step @p115 :rule cong :premises (@p114) :args (@t42)) % 0.37/0.62 (step @p116 :rule eq_resolve :premises (@p1 @p115)) % 0.37/0.62 (step @p117 :rule aci_norm :args ((= @t175 @t174))) % 0.37/0.62 (step @p118 :rule refl :args (@t27)) % 0.37/0.62 (step @p119 :rule cong :premises (@p118 @p117) :args (@t176)) % 0.37/0.62 (step @p120 :rule cong :premises (@p119) :args (@t177)) % 0.37/0.62 (step @p121 :rule cong :premises (@p120) :args (@t178)) % 0.37/0.62 (step @p122 :rule cong :premises (@p121) :args (@t179)) % 0.37/0.62 (step @p123 :rule cong :premises (@p122) :args (@t180)) % 0.37/0.62 (step @p124 :rule nary_cong :premises (@p22 @p21 @p123) :args (@t181)) % 0.37/0.62 (step @p125 :rule cong :premises (@p124) :args (@t183)) % 0.37/0.62 (step @p126 :rule symm :premises (@p125)) % 0.37/0.62 (step @p127 :rule true_intro :premises (@p126)) % 0.37/0.62 (step @p128 :rule eq-symm :args (@t183 @t184)) % 0.37/0.62 (step @p129 :rule trans :premises (@p128 @p127)) % 0.37/0.62 (step @p130 :rule cong :premises (@p126 @p125) :args ((= @t184 @t183))) % 0.37/0.62 (step @p131 :rule trans :premises (@p130 @p129)) % 0.37/0.62 (step @p132 :rule true_elim :premises (@p131)) % 0.37/0.62 (step @p133 :rule alpha_equiv :args ((forall (@list @t189 @t185 @t191) (or (tptp.empty @t189) (not (tptp.relation @t185)) (not (forall (@list @t192) (not (forall (@list @t190) (= (tptp.in @t190 @t192) (and (tptp.in @t190 (tptp.cartesian_product2 @t189 @t191)) (not (forall (@list @t188 @t187) (or (not (= @t190 (tptp.ordered_pair @t188 @t187))) (not (tptp.in @t188 @t189)) (not (tptp.in @t187 @t188)) (not (forall (@list @t186) (or (not (tptp.in @t186 @t188)) (tptp.in (tptp.ordered_pair @t187 @t186) @t185))))))))))))))) @t193 (@list @t26 @t17 @t62 @t55 @t54 @t1 @t15 @t172))) % 0.37/0.62 (step @p134 :rule alpha_equiv :args (@t134 (@list @t26 @t17 @t10 @t3 @t2 @t1 @t15 @t130) @t193)) % 0.37/0.62 (step @p135 :rule trans :premises (@p134 @p133 @p132)) % 0.37/0.62 (step @p136 :rule equiv_elim2 :premises (@p135)) % 0.37/0.62 (step @p137 :rule chain_m_resolution :premises (@p136 @p116) :args ((not @t183) @t194 (@list @t134))) % 0.37/0.62 (step @p138 :rule quant-merge-prenex :args ((= (forall @t40 @t196) @t183))) % 0.37/0.62 (step @p139 :rule alpha_equiv :args (@t197 (@list @t172) @t138)) % 0.37/0.62 (step @p140 :rule nary_cong :premises (@p22 @p21 @p139) :args (@t198)) % 0.37/0.62 (step @p141 :rule quant-miniscope-or :args ((= @t196 @t198))) % 0.37/0.62 (step @p142 :rule trans :premises (@p141 @p140)) % 0.37/0.62 (step @p143 :rule symm :premises (@p142)) % 0.37/0.62 (step @p144 :rule cong :premises (@p143) :args ((forall @t40 @t202))) % 0.37/0.62 (step @p145 :rule trans :premises (@p144 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trans :premises (@p404 @p403)) % 0.35/0.63 (step @p406 :rule bool-and-de-morgan :args (@t109 @t309 true)) % 0.35/0.63 (step @p407 :rule nary_cong :premises (@p402 @p406) :args ((or @t280 (not (and @t109 @t309))))) % 0.35/0.63 (step @p408 :rule bool-and-de-morgan :args (@t279 @t109 (and @t309))) % 0.35/0.63 (step @p409 :rule trans :premises (@p408 @p407)) % 0.35/0.63 (step @p410 :rule trans :premises (@p409 @p405)) % 0.35/0.63 (step @p411 :rule trans :premises (@p410 @p399)) % 0.35/0.63 (step @p412 :rule cong :premises (@p411) :args (@t313)) % 0.35/0.63 (step @p413 :rule cong :premises (@p412) :args (@t314)) % 0.35/0.63 (step @p414 :rule exists-elim :args ((= (exists @t112 @t312) @t314))) % 0.35/0.63 (step @p415 :rule trans :premises (@p414 @p413)) % 0.35/0.63 (step @p416 :rule aci_norm :args ((= (or false @t277 @t276) @t308))) % 0.35/0.63 (step @p417 :rule refl :args (@t276)) % 0.35/0.63 (step @p418 :rule refl :args (@t277)) % 0.35/0.63 (step @p419 :rule eq-refl :args (@t3)) % 0.35/0.63 (step @p420 :rule cong :premises (@p419) :args (@t315)) % 0.35/0.63 (step @p421 :rule trans :premises (@p420 @p62)) % 0.35/0.63 (step @p422 :rule nary_cong :premises (@p421 @p418 @p417) :args (@t316)) % 0.35/0.63 (step @p423 :rule trans :premises (@p422 @p416)) % 0.35/0.63 (step @p424 :rule quant-var-elim-eq :args ((= (forall @t7 (or (not (= @t2 @t3)) @t320 @t319 @t318)) @t316))) % 0.35/0.63 (step @p425 :rule refl :args (@t318)) % 0.35/0.63 (step @p426 :rule refl :args (@t319)) % 0.35/0.63 (step @p427 :rule refl :args (@t320)) % 0.35/0.63 (step @p428 :rule eq-symm :args (@t3 @t2)) % 0.35/0.63 (step @p429 :rule cong :premises (@p428) :args (@t320)) % 0.35/0.63 (step @p430 :rule nary_cong :premises (@p429 @p427 @p426 @p425) :args (@t321)) % 0.35/0.63 (step @p431 :rule aci_norm :args ((= @t322 @t321))) % 0.35/0.63 (step @p432 :rule trans :premises (@p431 @p430)) % 0.35/0.63 (step @p433 :rule cong :premises (@p432) :args ((forall @t7 @t322))) % 0.35/0.63 (step @p434 :rule trans :premises (@p433 @p424)) % 0.35/0.63 (step @p435 :rule trans :premises (@p434 @p423)) % 0.35/0.63 (step @p436 :rule aci_norm :args ((= (or @t320 (or @t319 @t318)) @t322))) % 0.35/0.63 (step @p437 :rule bool-and-de-morgan :args (@t105 @t317 true)) % 0.35/0.63 (step @p438 :rule nary_cong :premises (@p427 @p437) :args ((or @t320 (not (and @t105 @t317))))) % 0.35/0.63 (step @p439 :rule bool-and-de-morgan :args (@t106 @t105 (and @t317))) % 0.35/0.63 (step @p440 :rule trans :premises (@p439 @p438)) % 0.35/0.63 (step @p441 :rule trans :premises (@p440 @p436)) % 0.35/0.63 (step @p442 :rule cong :premises (@p441) :args (@t324)) % 0.35/0.63 (step @p443 :rule trans :premises (@p442 @p435)) % 0.35/0.63 (step @p444 :rule cong :premises (@p443) :args (@t325)) % 0.35/0.63 (step @p445 :rule exists-elim :args ((= (exists @t7 @t323) @t325))) % 0.35/0.63 (step @p446 :rule trans :premises (@p445 @p444)) % 0.35/0.63 (step @p447 :rule bool-impl-elim :args (@t102 @t101)) % 0.35/0.63 (step @p448 :rule cong :premises (@p447) :args (@t104)) % 0.35/0.63 (step @p449 :rule refl :args (@t105)) % 0.35/0.63 (step @p450 :rule refl :args (@t106)) % 0.35/0.63 (step @p451 :rule nary_cong :premises (@p450 @p449 @p448) :args (@t107)) % 0.35/0.63 (step @p452 :rule cong :premises (@p451) :args (@t108)) % 0.35/0.63 (step @p453 :rule trans :premises (@p452 @p446)) % 0.35/0.63 (step @p454 :rule refl :args (@t109)) % 0.35/0.63 (step @p455 :rule eq-symm :args (@t110 @t17)) % 0.35/0.63 (step @p456 :rule nary_cong :premises (@p455 @p454 @p453) :args (@t111)) % 0.35/0.63 (step @p457 :rule cong :premises (@p456) :args (@t113)) % 0.35/0.63 (step @p458 :rule trans :premises (@p457 @p415)) % 0.35/0.63 (step @p459 :rule refl :args (@t114)) % 0.35/0.63 (step @p460 :rule nary_cong :premises (@p459 @p458 @p398 @p397) :args (@t115)) % 0.35/0.63 (step @p461 :rule cong :premises (@p460 @p285) :args (@t116)) % 0.35/0.63 (step @p462 :rule cong :premises (@p461) :args (@t118)) % 0.35/0.63 (step @p463 :rule trans :premises (@p462 @p337)) % 0.35/0.63 (step @p464 :rule cong :premises (@p463 @p271) :args (@t119)) % 0.35/0.63 (step @p465 :rule trans :premises (@p464 @p154)) % 0.35/0.63 (step @p466 :rule cong :premises (@p465) :args (@t120)) % 0.35/0.63 (step @p467 :rule cong :premises (@p111 @p466) :args (@t121)) % 0.35/0.63 (step @p468 :rule cong :premises (@p467) :args (@t122)) % 0.35/0.63 (step @p469 :rule trans :premises (@p468 @p153)) % 0.35/0.63 (step @p470 :rule eq_resolve :premises (@p18 @p469)) % 0.35/0.63 (step @p471 false :rule chain_m_resolution :premises (@p470 @p137) :args (false @t194 (@list @t183))) % 0.35/0.63 ) % 0.35/0.63 % SZS output end Proof % 0.35/0.63 % cvc5 exiting %------------------------------------------------------------------------------