%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU785^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.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 08:53:11 AM UTC 2026 % Result : Theorem 0.37s 0.60s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU785^2 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:51:20 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.37/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.60 % SZS status Theorem % 0.37/0.60 % SZS output start Proof % 0.37/0.60 ( % 0.37/0.60 (declare-sort $$unsorted 0) % 0.37/0.60 (declare-const tptp.breln1unionIR Bool) % 0.37/0.60 (declare-const tptp.breln1unionIL Bool) % 0.37/0.60 (declare-const tptp.breln1 (-> $$unsorted $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (define @t1 () (@var "S" $$unsorted)) % 0.37/0.60 (define @t2 () (@var "R" $$unsorted)) % 0.37/0.60 (define @t3 () (_ (_ tptp.binunion @t2) @t1)) % 0.37/0.60 (define @t4 () (@var "Xy" $$unsorted)) % 0.37/0.60 (define @t5 () (@var "Xx" $$unsorted)) % 0.37/0.60 (define @t6 () (_ (_ tptp.kpair @t5) @t4)) % 0.37/0.60 (define @t7 () (_ tptp.in @t6)) % 0.37/0.60 (define @t8 () (_ @t7 @t3)) % 0.37/0.60 (define @t9 () (_ @t7 @t2)) % 0.37/0.60 (define @t10 () (=> @t9 @t8)) % 0.37/0.60 (define @t11 () (@var "A" $$unsorted)) % 0.37/0.60 (define @t12 () (_ (_ tptp.in @t4) @t11)) % 0.37/0.60 (define @t13 () (@list @t4)) % 0.37/0.60 (define @t14 () (forall @t13 (=> @t12 @t10))) % 0.37/0.60 (define @t15 () (_ (_ tptp.in @t5) @t11)) % 0.37/0.60 (define @t16 () (=> @t15 @t14)) % 0.37/0.60 (define @t17 () (@list @t5)) % 0.37/0.60 (define @t18 () (forall @t17 @t16)) % 0.37/0.60 (define @t19 () (_ tptp.breln1 @t11)) % 0.37/0.60 (define @t20 () (_ @t19 @t1)) % 0.37/0.60 (define @t21 () (=> @t20 @t18)) % 0.37/0.60 (define @t22 () (@list @t1)) % 0.37/0.60 (define @t23 () (forall @t22 @t21)) % 0.37/0.60 (define @t24 () (_ @t19 @t2)) % 0.37/0.60 (define @t25 () (=> @t24 @t23)) % 0.37/0.60 (define @t26 () (@list @t11 @t2)) % 0.37/0.60 (define @t27 () (forall @t26 @t25)) % 0.37/0.60 (define @t28 () (= tptp.breln1unionIL @t27)) % 0.37/0.60 (define @t29 () (_ @t7 @t1)) % 0.37/0.60 (define @t30 () (=> @t29 @t8)) % 0.37/0.60 (define @t31 () (forall @t13 (=> @t12 @t30))) % 0.37/0.60 (define @t32 () (=> @t15 @t31)) % 0.37/0.60 (define @t33 () (forall @t17 @t32)) % 0.37/0.60 (define @t34 () (=> @t20 @t33)) % 0.37/0.60 (define @t35 () (forall @t22 @t34)) % 0.37/0.60 (define @t36 () (=> @t24 @t35)) % 0.37/0.60 (define @t37 () (forall @t26 @t36)) % 0.37/0.60 (define @t38 () (= tptp.breln1unionIR @t37)) % 0.37/0.60 (define @t39 () (or @t9 @t29)) % 0.37/0.60 (define @t40 () (=> @t39 @t8)) % 0.37/0.60 (define @t41 () (forall @t13 (=> @t12 @t40))) % 0.37/0.60 (define @t42 () (=> @t15 @t41)) % 0.37/0.60 (define @t43 () (forall @t17 @t42)) % 0.37/0.60 (define @t44 () (=> @t20 @t43)) % 0.37/0.60 (define @t45 () (forall @t22 @t44)) % 0.37/0.60 (define @t46 () (=> @t24 @t45)) % 0.37/0.60 (define @t47 () (forall @t26 @t46)) % 0.37/0.60 (define @t48 () (=> tptp.breln1unionIR @t47)) % 0.37/0.60 (define @t49 () (=> tptp.breln1unionIL @t48)) % 0.37/0.60 (define @t50 () (not @t49)) % 0.37/0.60 (define @t51 () (@var "BOUND_VARIABLE_7722" $$unsorted)) % 0.37/0.60 (define @t52 () (@var "BOUND_VARIABLE_7726" $$unsorted)) % 0.37/0.60 (define @t53 () (@var "BOUND_VARIABLE_7724" $$unsorted)) % 0.37/0.60 (define @t54 () (tptp.kpair @t53 @t52)) % 0.37/0.60 (define @t55 () (tptp.in @t54 (tptp.binunion @t2 @t51))) % 0.37/0.60 (define @t56 () (and (not (tptp.in @t54 @t2)) (not (tptp.in @t54 @t51)))) % 0.37/0.60 (define @t57 () (not (tptp.in @t52 @t11))) % 0.37/0.60 (define @t58 () (not (tptp.in @t53 @t11))) % 0.37/0.60 (define @t59 () (not (tptp.breln1 @t11 @t51))) % 0.37/0.60 (define @t60 () (tptp.breln1 @t11 @t2)) % 0.37/0.60 (define @t61 () (not @t60)) % 0.37/0.60 (define @t62 () (or @t61 @t59 @t58 @t57 @t56 @t55)) % 0.37/0.60 (define @t63 () (@list @t11 @t2 @t51 @t53 @t52)) % 0.37/0.60 (define @t64 () (forall @t63 @t62)) % 0.37/0.60 (define @t65 () (@var "BOUND_VARIABLE_7633" $$unsorted)) % 0.37/0.60 (define @t66 () (@var "BOUND_VARIABLE_7637" $$unsorted)) % 0.37/0.60 (define @t67 () (@var "BOUND_VARIABLE_7635" $$unsorted)) % 0.37/0.60 (define @t68 () (tptp.kpair @t67 @t66)) % 0.37/0.60 (define @t69 () (tptp.in @t68 (tptp.binunion @t2 @t65))) % 0.37/0.60 (define @t70 () (not (tptp.in @t68 @t65))) % 0.37/0.60 (define @t71 () (not (tptp.in @t66 @t11))) % 0.37/0.60 (define @t72 () (not (tptp.in @t67 @t11))) % 0.37/0.60 (define @t73 () (not (tptp.breln1 @t11 @t65))) % 0.37/0.60 (define @t74 () (or @t61 @t73 @t72 @t71 @t70 @t69)) % 0.37/0.60 (define @t75 () (or @t73 @t72 @t71 @t70 @t69)) % 0.37/0.60 (define @t76 () (or @t61 @t75)) % 0.37/0.60 (define @t77 () (@list @t11 @t2 @t65 @t67 @t66)) % 0.37/0.60 (define @t78 () (forall @t77 @t76)) % 0.37/0.60 (define @t79 () (@list @t65 @t67 @t66)) % 0.37/0.60 (define @t80 () (forall @t79 @t76)) % 0.37/0.60 (define @t81 () (forall @t79 @t75)) % 0.37/0.60 (define @t82 () (@var "BOUND_VARIABLE_7611" $$unsorted)) % 0.37/0.60 (define @t83 () (@var "BOUND_VARIABLE_7609" $$unsorted)) % 0.37/0.60 (define @t84 () (or @t61 @t81)) % 0.37/0.60 (define @t85 () (tptp.binunion @t2 @t1)) % 0.37/0.60 (define @t86 () (tptp.kpair @t83 @t82)) % 0.37/0.60 (define @t87 () (tptp.in @t86 @t85)) % 0.37/0.60 (define @t88 () (not (tptp.in @t86 @t1))) % 0.37/0.60 (define @t89 () (not (tptp.in @t82 @t11))) % 0.37/0.60 (define @t90 () (not (tptp.in @t83 @t11))) % 0.37/0.60 (define @t91 () (tptp.breln1 @t11 @t1)) % 0.37/0.60 (define @t92 () (not @t91)) % 0.37/0.60 (define @t93 () (or @t92 @t90 @t89 @t88 @t87)) % 0.37/0.60 (define @t94 () (@list @t1 @t83 @t82)) % 0.37/0.60 (define @t95 () (forall @t94 @t93)) % 0.37/0.60 (define @t96 () (not @t24)) % 0.37/0.60 (define @t97 () (or @t96 @t95)) % 0.37/0.60 (define @t98 () (or @t90 @t89 @t88 @t87)) % 0.37/0.60 (define @t99 () (or @t92 @t98)) % 0.37/0.60 (define @t100 () (forall @t94 @t99)) % 0.37/0.60 (define @t101 () (@list @t83 @t82)) % 0.37/0.60 (define @t102 () (forall @t101 @t99)) % 0.37/0.60 (define @t103 () (forall @t101 @t98)) % 0.37/0.60 (define @t104 () (@var "BOUND_VARIABLE_7589" $$unsorted)) % 0.37/0.60 (define @t105 () (or @t92 @t103)) % 0.37/0.60 (define @t106 () (tptp.kpair @t5 @t104)) % 0.37/0.60 (define @t107 () (tptp.in @t106 @t85)) % 0.37/0.60 (define @t108 () (not (tptp.in @t106 @t1))) % 0.37/0.60 (define @t109 () (not (tptp.in @t104 @t11))) % 0.37/0.60 (define @t110 () (tptp.in @t5 @t11)) % 0.37/0.60 (define @t111 () (not @t110)) % 0.37/0.60 (define @t112 () (or @t111 @t109 @t108 @t107)) % 0.37/0.60 (define @t113 () (@list @t5 @t104)) % 0.37/0.60 (define @t114 () (forall @t113 @t112)) % 0.37/0.60 (define @t115 () (not @t20)) % 0.37/0.60 (define @t116 () (or @t115 @t114)) % 0.37/0.60 (define @t117 () (or @t109 @t108 @t107)) % 0.37/0.60 (define @t118 () (or @t111 @t117)) % 0.37/0.60 (define @t119 () (forall @t113 @t118)) % 0.37/0.60 (define @t120 () (@list @t104)) % 0.37/0.60 (define @t121 () (forall @t120 @t118)) % 0.37/0.60 (define @t122 () (forall @t120 @t117)) % 0.37/0.60 (define @t123 () (@list @t4)) % 0.37/0.60 (define @t124 () (or @t111 @t122)) % 0.37/0.60 (define @t125 () (tptp.kpair @t5 @t4)) % 0.37/0.60 (define @t126 () (tptp.in @t125 @t85)) % 0.37/0.60 (define @t127 () (tptp.in @t125 @t1)) % 0.37/0.60 (define @t128 () (not @t127)) % 0.37/0.60 (define @t129 () (tptp.in @t4 @t11)) % 0.37/0.60 (define @t130 () (not @t129)) % 0.37/0.60 (define @t131 () (forall @t13 (or @t130 @t128 @t126))) % 0.37/0.60 (define @t132 () (not @t15)) % 0.37/0.60 (define @t133 () (or @t132 @t131)) % 0.37/0.60 (define @t134 () (_ tptp.in @t125)) % 0.37/0.60 (define @t135 () (not @t29)) % 0.37/0.60 (define @t136 () (not @t12)) % 0.37/0.60 (define @t137 () (or @t136 @t135 @t8)) % 0.37/0.60 (define @t138 () (=> tptp.breln1unionIR @t64)) % 0.37/0.60 (define @t139 () (@var "BOUND_VARIABLE_7549" $$unsorted)) % 0.37/0.60 (define @t140 () (@var "BOUND_VARIABLE_7553" $$unsorted)) % 0.37/0.60 (define @t141 () (@var "BOUND_VARIABLE_7551" $$unsorted)) % 0.37/0.60 (define @t142 () (tptp.kpair @t141 @t140)) % 0.37/0.60 (define @t143 () (tptp.in @t142 (tptp.binunion @t2 @t139))) % 0.37/0.60 (define @t144 () (not (tptp.in @t142 @t2))) % 0.37/0.60 (define @t145 () (not (tptp.in @t140 @t11))) % 0.37/0.60 (define @t146 () (not (tptp.in @t141 @t11))) % 0.37/0.60 (define @t147 () (not (tptp.breln1 @t11 @t139))) % 0.37/0.60 (define @t148 () (or @t147 @t146 @t145 @t144 @t143)) % 0.37/0.60 (define @t149 () (or @t61 @t148)) % 0.37/0.60 (define @t150 () (forall (@list @t11 @t2 @t139 @t141 @t140) @t149)) % 0.37/0.60 (define @t151 () (@list @t139 @t141 @t140)) % 0.37/0.60 (define @t152 () (forall @t151 @t149)) % 0.37/0.60 (define @t153 () (forall @t151 @t148)) % 0.37/0.60 (define @t154 () (@var "BOUND_VARIABLE_7524" $$unsorted)) % 0.37/0.60 (define @t155 () (@var "BOUND_VARIABLE_7522" $$unsorted)) % 0.37/0.60 (define @t156 () (or @t61 @t153)) % 0.37/0.60 (define @t157 () (tptp.kpair @t155 @t154)) % 0.37/0.60 (define @t158 () (tptp.in @t157 @t85)) % 0.37/0.60 (define @t159 () (not (tptp.in @t157 @t2))) % 0.37/0.60 (define @t160 () (not (tptp.in @t154 @t11))) % 0.37/0.60 (define @t161 () (not (tptp.in @t155 @t11))) % 0.37/0.60 (define @t162 () (or @t92 @t161 @t160 @t159 @t158)) % 0.37/0.60 (define @t163 () (@list @t1 @t155 @t154)) % 0.37/0.60 (define @t164 () (forall @t163 @t162)) % 0.37/0.60 (define @t165 () (or @t96 @t164)) % 0.37/0.60 (define @t166 () (or @t161 @t160 @t159 @t158)) % 0.37/0.60 (define @t167 () (or @t92 @t166)) % 0.37/0.60 (define @t168 () (forall @t163 @t167)) % 0.37/0.60 (define @t169 () (@list @t155 @t154)) % 0.37/0.60 (define @t170 () (forall @t169 @t167)) % 0.37/0.60 (define @t171 () (forall @t169 @t166)) % 0.37/0.60 (define @t172 () (@var "BOUND_VARIABLE_7499" $$unsorted)) % 0.37/0.60 (define @t173 () (or @t92 @t171)) % 0.37/0.60 (define @t174 () (tptp.kpair @t5 @t172)) % 0.37/0.60 (define @t175 () (tptp.in @t174 @t85)) % 0.37/0.60 (define @t176 () (not (tptp.in @t174 @t2))) % 0.37/0.60 (define @t177 () (not (tptp.in @t172 @t11))) % 0.37/0.60 (define @t178 () (or @t111 @t177 @t176 @t175)) % 0.37/0.60 (define @t179 () (@list @t5 @t172)) % 0.37/0.60 (define @t180 () (forall @t179 @t178)) % 0.37/0.60 (define @t181 () (or @t115 @t180)) % 0.37/0.60 (define @t182 () (or @t177 @t176 @t175)) % 0.37/0.60 (define @t183 () (or @t111 @t182)) % 0.37/0.60 (define @t184 () (forall @t179 @t183)) % 0.37/0.60 (define @t185 () (@list @t172)) % 0.37/0.60 (define @t186 () (forall @t185 @t183)) % 0.37/0.60 (define @t187 () (forall @t185 @t182)) % 0.37/0.60 (define @t188 () (or @t111 @t187)) % 0.37/0.60 (define @t189 () (tptp.in @t125 @t2)) % 0.37/0.60 (define @t190 () (not @t189)) % 0.37/0.60 (define @t191 () (forall @t13 (or @t130 @t190 @t126))) % 0.37/0.60 (define @t192 () (or @t132 @t191)) % 0.37/0.60 (define @t193 () (not @t9)) % 0.37/0.60 (define @t194 () (or @t136 @t193 @t8)) % 0.37/0.60 (define @t195 () (=> tptp.breln1unionIL @t138)) % 0.37/0.60 (define @t196 () (or @t59 @t58 @t57 @t56 @t55)) % 0.37/0.60 (define @t197 () (or @t61 @t196)) % 0.37/0.60 (define @t198 () (forall @t63 @t197)) % 0.37/0.60 (define @t199 () (@list @t51 @t53 @t52)) % 0.37/0.60 (define @t200 () (forall @t199 @t197)) % 0.37/0.60 (define @t201 () (forall @t199 @t196)) % 0.37/0.60 (define @t202 () (@var "BOUND_VARIABLE_7697" $$unsorted)) % 0.37/0.60 (define @t203 () (@var "BOUND_VARIABLE_7695" $$unsorted)) % 0.37/0.60 (define @t204 () (or @t61 @t201)) % 0.37/0.60 (define @t205 () (tptp.kpair @t203 @t202)) % 0.37/0.60 (define @t206 () (tptp.in @t205 @t85)) % 0.37/0.60 (define @t207 () (and (not (tptp.in @t205 @t2)) (not (tptp.in @t205 @t1)))) % 0.37/0.60 (define @t208 () (not (tptp.in @t202 @t11))) % 0.37/0.60 (define @t209 () (not (tptp.in @t203 @t11))) % 0.37/0.60 (define @t210 () (or @t92 @t209 @t208 @t207 @t206)) % 0.37/0.60 (define @t211 () (@list @t1 @t203 @t202)) % 0.37/0.60 (define @t212 () (forall @t211 @t210)) % 0.37/0.60 (define @t213 () (or @t96 @t212)) % 0.37/0.60 (define @t214 () (or @t209 @t208 @t207 @t206)) % 0.37/0.60 (define @t215 () (or @t92 @t214)) % 0.37/0.60 (define @t216 () (forall @t211 @t215)) % 0.37/0.60 (define @t217 () (@list @t203 @t202)) % 0.37/0.60 (define @t218 () (forall @t217 @t215)) % 0.37/0.60 (define @t219 () (forall @t217 @t214)) % 0.37/0.60 (define @t220 () (@var "BOUND_VARIABLE_7672" $$unsorted)) % 0.37/0.60 (define @t221 () (or @t92 @t219)) % 0.37/0.60 (define @t222 () (tptp.kpair @t5 @t220)) % 0.37/0.60 (define @t223 () (tptp.in @t222 @t85)) % 0.37/0.60 (define @t224 () (and (not (tptp.in @t222 @t2)) (not (tptp.in @t222 @t1)))) % 0.37/0.60 (define @t225 () (not (tptp.in @t220 @t11))) % 0.37/0.60 (define @t226 () (or @t111 @t225 @t224 @t223)) % 0.37/0.60 (define @t227 () (@list @t5 @t220)) % 0.37/0.60 (define @t228 () (forall @t227 @t226)) % 0.37/0.60 (define @t229 () (or @t115 @t228)) % 0.37/0.60 (define @t230 () (or @t225 @t224 @t223)) % 0.37/0.60 (define @t231 () (or @t111 @t230)) % 0.37/0.60 (define @t232 () (forall @t227 @t231)) % 0.37/0.60 (define @t233 () (@list @t220)) % 0.37/0.60 (define @t234 () (forall @t233 @t231)) % 0.37/0.60 (define @t235 () (forall @t233 @t230)) % 0.37/0.60 (define @t236 () (or @t111 @t235)) % 0.37/0.60 (define @t237 () (forall @t13 (or @t130 (and @t190 @t128) @t126))) % 0.37/0.60 (define @t238 () (or @t132 @t237)) % 0.37/0.60 (define @t239 () (and @t193 @t135)) % 0.37/0.60 (define @t240 () (or @t136 @t239 @t8)) % 0.37/0.60 (define @t241 () (@quantifiers_skolemize @t64 2)) % 0.37/0.60 (define @t242 () (@quantifiers_skolemize @t64 1)) % 0.37/0.60 (define @t243 () (@quantifiers_skolemize @t64 4)) % 0.37/0.60 (define @t244 () (@quantifiers_skolemize @t64 3)) % 0.37/0.60 (define @t245 () (tptp.kpair @t244 @t243)) % 0.37/0.60 (define @t246 () (tptp.in @t245 (tptp.binunion @t242 @t241))) % 0.37/0.60 (define @t247 () (tptp.in @t245 @t241)) % 0.37/0.60 (define @t248 () (not @t247)) % 0.37/0.60 (define @t249 () (tptp.in @t245 @t242)) % 0.37/0.60 (define @t250 () (not @t249)) % 0.37/0.60 (define @t251 () (and @t250 @t248)) % 0.37/0.60 (define @t252 () (@quantifiers_skolemize @t64 0)) % 0.37/0.60 (define @t253 () (tptp.in @t243 @t252)) % 0.37/0.60 (define @t254 () (not @t253)) % 0.37/0.60 (define @t255 () (tptp.in @t244 @t252)) % 0.37/0.60 (define @t256 () (not @t255)) % 0.37/0.60 (define @t257 () (tptp.breln1 @t252 @t241)) % 0.37/0.60 (define @t258 () (not @t257)) % 0.37/0.60 (define @t259 () (tptp.breln1 @t252 @t242)) % 0.37/0.60 (define @t260 () (not @t259)) % 0.37/0.60 (define @t261 () (or @t260 @t258 @t256 @t254 @t251 @t246)) % 0.37/0.60 (define @t262 () (@list true)) % 0.37/0.60 (define @t263 () (@list @t261)) % 0.37/0.60 (define @t264 () (@list @t252 @t242 @t241 @t244 @t243)) % 0.37/0.60 (define @t265 () (or @t260 @t258 @t256 @t254 @t250 @t246)) % 0.37/0.60 (define @t266 () (or @t260 @t258 @t256 @t254 @t248 @t246)) % 0.37/0.60 (define @t267 () (not @t266)) % 0.37/0.60 (define @t268 () (forall @t77 @t74)) % 0.37/0.60 (assume @p1 @t28) % 0.37/0.60 (assume @p2 @t38) % 0.37/0.60 (assume @p3 @t50) % 0.37/0.60 (assume @p4 true) % 0.37/0.60 (step @p5 :rule refl :args (@t64)) % 0.37/0.60 (step @p6 :rule aci_norm :args ((= @t76 @t74))) % 0.37/0.60 (step @p7 :rule cong :premises (@p6) :args (@t78)) % 0.37/0.60 (step @p8 :rule quant-merge-prenex :args ((= (forall @t26 @t80) @t78))) % 0.37/0.60 (step @p9 :rule alpha_equiv :args (@t81 (@list @t65 @t67 @t66) (@list @t1 @t83 @t82))) % 0.37/0.60 (step @p10 :rule refl :args (@t61)) % 0.37/0.60 (step @p11 :rule nary_cong 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(step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.37/0.60 (step @p74 :rule cong :premises (@p73) :args (@t132)) % 0.37/0.60 (step @p75 :rule nary_cong :premises (@p74 @p68) :args (@t133)) % 0.37/0.60 (step @p76 :rule cong :premises (@p75) :args ((forall @t17 @t133))) % 0.37/0.60 (step @p77 :rule trans :premises (@p76 @p67)) % 0.37/0.60 (step @p78 :rule bool-impl-elim :args (@t15 @t131)) % 0.37/0.60 (step @p79 :rule cong :premises (@p78) :args ((forall @t17 (=> @t15 @t131)))) % 0.37/0.60 (step @p80 :rule trans :premises (@p79 @p77)) % 0.37/0.60 (step @p81 :rule refl :args ((tptp.in @t6 @t3))) % 0.37/0.60 (step @p82 :rule refl :args (@t85)) % 0.37/0.60 (step @p83 :rule refl :args (@t125)) % 0.37/0.60 (step @p84 :rule cong :premises (@p83 @p82) :args (@t126)) % 0.37/0.60 (step @p85 :rule trans :premises (@p84 @p81)) % 0.37/0.60 (step @p86 :rule refl :args (tptp.in)) % 0.37/0.60 (step @p87 :rule ho_cong :premises (@p86 @p83)) % 0.37/0.60 (step @p88 :rule ho_cong :premises (@p87 @p82)) 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:rule ho_cong :premises (@p87 @p204)) % 0.37/0.60 (step @p208 :rule cong :premises (@p207 @p206) :args ((= (_ @t134 @t2) @t189))) % 0.37/0.60 (step @p209 :rule symm :premises (@p208)) % 0.37/0.60 (step @p210 :rule refl :args (@t9)) % 0.37/0.60 (step @p211 :rule eq_resolve :premises (@p210 @p209)) % 0.37/0.60 (step @p212 :rule ho_cong :premises (@p101 @p204)) % 0.37/0.60 (step @p213 :rule trans :premises (@p212 @p211)) % 0.37/0.60 (step @p214 :rule cong :premises (@p213) :args (@t193)) % 0.37/0.60 (step @p215 :rule nary_cong :premises (@p121 @p214 @p103) :args (@t194)) % 0.37/0.60 (step @p216 :rule cong :premises (@p215) :args ((forall @t13 @t194))) % 0.37/0.60 (step @p217 :rule aci_norm :args ((= (or @t136 (or @t193 @t8)) @t194))) % 0.37/0.60 (step @p218 :rule bool-impl-elim :args (@t9 @t8)) % 0.37/0.60 (step @p219 :rule nary_cong :premises (@p126 @p218) :args ((or @t136 @t10))) % 0.37/0.60 (step @p220 :rule trans :premises (@p219 @p217)) % 0.37/0.60 (step @p221 :rule bool-impl-elim 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@p264 :rule symm :premises (@p263)) % 0.37/0.60 (step @p265 :rule cong :premises (@p264) :args ((forall @t22 (or @t92 @t228)))) % 0.37/0.60 (step @p266 :rule trans :premises (@p265 @p259)) % 0.37/0.60 (step @p267 :rule trans :premises (@p266 @p258)) % 0.37/0.60 (step @p268 :rule refl :args (@t228)) % 0.37/0.60 (step @p269 :rule nary_cong :premises (@p49 @p268) :args (@t229)) % 0.37/0.60 (step @p270 :rule cong :premises (@p269) :args ((forall @t22 @t229))) % 0.37/0.60 (step @p271 :rule trans :premises (@p270 @p267)) % 0.37/0.60 (step @p272 :rule bool-impl-elim :args (@t20 @t228)) % 0.37/0.60 (step @p273 :rule cong :premises (@p272) :args ((forall @t22 (=> @t20 @t228)))) % 0.37/0.60 (step @p274 :rule trans :premises (@p273 @p271)) % 0.37/0.60 (step @p275 :rule aci_norm :args ((= @t231 @t226))) % 0.37/0.60 (step @p276 :rule cong :premises (@p275) :args (@t232)) % 0.37/0.60 (step @p277 :rule quant-merge-prenex :args ((= (forall @t17 @t234) @t232))) % 0.37/0.60 (step @p278 :rule alpha_equiv 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@p289)) % 0.37/0.60 (step @p293 :rule nary_cong :premises (@p214 @p115) :args (@t239)) % 0.37/0.60 (step @p294 :rule nary_cong :premises (@p121 @p293 @p103) :args (@t240)) % 0.37/0.60 (step @p295 :rule cong :premises (@p294) :args ((forall @t13 @t240))) % 0.37/0.60 (step @p296 :rule aci_norm :args ((= (or @t136 (or @t239 @t8)) @t240))) % 0.37/0.60 (step @p297 :rule bool-or-de-morgan :args (@t9 @t29 false)) % 0.37/0.60 (step @p298 :rule nary_cong :premises (@p297 @p91) :args ((or (not @t39) @t8))) % 0.37/0.60 (step @p299 :rule bool-impl-elim :args (@t39 @t8)) % 0.37/0.60 (step @p300 :rule trans :premises (@p299 @p298)) % 0.37/0.60 (step @p301 :rule nary_cong :premises (@p126 @p300) :args ((or @t136 @t40))) % 0.37/0.60 (step @p302 :rule trans :premises (@p301 @p296)) % 0.37/0.60 (step @p303 :rule bool-impl-elim :args (@t12 @t40)) % 0.37/0.60 (step @p304 :rule trans :premises (@p303 @p302)) % 0.37/0.60 (step @p305 :rule cong :premises (@p304) :args (@t41)) % 0.37/0.60 (step @p306 :rule trans :premises (@p305 @p295)) % 0.37/0.60 (step @p307 :rule cong :premises (@p133 @p306) :args (@t42)) % 0.37/0.60 (step @p308 :rule cong :premises (@p307) :args (@t43)) % 0.37/0.60 (step @p309 :rule trans :premises (@p308 @p292)) % 0.37/0.60 (step @p310 :rule cong :premises (@p137 @p309) :args (@t44)) % 0.37/0.60 (step @p311 :rule cong :premises (@p310) :args (@t45)) % 0.37/0.60 (step @p312 :rule trans :premises (@p311 @p274)) % 0.37/0.60 (step @p313 :rule cong :premises (@p141 @p312) :args (@t46)) % 0.37/0.60 (step @p314 :rule cong :premises (@p313) :args (@t47)) % 0.37/0.60 (step @p315 :rule trans :premises (@p314 @p256)) % 0.37/0.60 (step @p316 :rule cong :premises (@p145 @p315) :args (@t48)) % 0.37/0.60 (step @p317 :rule cong :premises (@p234 @p316) :args (@t49)) % 0.37/0.60 (step @p318 :rule cong :premises (@p317) :args (@t50)) % 0.37/0.60 (step @p319 :rule trans :premises (@p318 @p238)) % 0.37/0.60 (step @p320 :rule eq_resolve :premises (@p3 @p319)) % 0.37/0.60 (step @p321 :rule not_implies_elim2 :premises (@p320)) % 0.37/0.60 (step @p322 :rule not_implies_elim1 :premises (@p321)) % 0.37/0.60 (step @p323 :rule not_implies_elim2 :premises (@p321)) % 0.37/0.60 (step @p324 :rule skolemize :premises (@p323)) % 0.37/0.60 (step @p325 :rule cnf_or_neg :args (@t261 5)) % 0.37/0.60 (step @p326 :rule chain_m_resolution :premises (@p325 @p324) :args ((not @t246) @t262 @t263)) % 0.37/0.60 (step @p327 :rule cnf_or_neg :args (@t261 4)) % 0.37/0.60 (step @p328 :rule chain_m_resolution :premises (@p327 @p324) :args ((not @t251) @t262 @t263)) % 0.37/0.60 (step @p329 :rule not_implies_elim1 :premises (@p320)) % 0.37/0.60 (step @p330 :rule instantiate :premises (@p329) :args (@t264)) % 0.37/0.60 (step @p331 :rule bool-double-not-elim :args (@t253)) % 0.37/0.60 (step @p332 :rule refl :args (@t261)) % 0.37/0.60 (step @p333 :rule nary_cong :premises (@p332 @p331) :args ((or @t261 (not @t254)))) % 0.37/0.60 (step @p334 :rule cnf_or_neg :args (@t261 3)) % 0.37/0.60 (step @p335 :rule eq_resolve :premises (@p334 @p333)) % 0.37/0.60 (step @p336 :rule reordering :premises (@p335) :args ((or @t253 @t261))) % 0.37/0.60 (step @p337 :rule chain_m_resolution :premises (@p336 @p324) :args (@t253 @t262 @t263)) % 0.37/0.60 (step @p338 :rule bool-double-not-elim :args (@t255)) % 0.37/0.60 (step @p339 :rule nary_cong :premises (@p332 @p338) :args ((or @t261 (not @t256)))) % 0.37/0.60 (step @p340 :rule cnf_or_neg :args (@t261 2)) % 0.37/0.60 (step @p341 :rule eq_resolve :premises (@p340 @p339)) % 0.37/0.60 (step @p342 :rule reordering :premises (@p341) :args ((or @t255 @t261))) % 0.37/0.60 (step @p343 :rule chain_m_resolution :premises (@p342 @p324) :args (@t255 @t262 @t263)) % 0.37/0.60 (step @p344 :rule bool-double-not-elim :args (@t257)) % 0.37/0.60 (step @p345 :rule nary_cong :premises (@p332 @p344) :args ((or @t261 (not @t258)))) % 0.37/0.60 (step @p346 :rule cnf_or_neg :args (@t261 1)) % 0.37/0.60 (step @p347 :rule eq_resolve :premises (@p346 @p345)) % 0.37/0.60 (step @p348 :rule reordering :premises (@p347) :args ((or @t257 @t261))) % 0.37/0.60 (step @p349 :rule chain_m_resolution :premises (@p348 @p324) :args (@t257 @t262 @t263)) % 0.37/0.60 (step @p350 :rule bool-double-not-elim :args (@t259)) % 0.37/0.60 (step @p351 :rule nary_cong :premises (@p332 @p350) :args ((or @t261 (not @t260)))) % 0.37/0.60 (step @p352 :rule cnf_or_neg :args (@t261 0)) % 0.37/0.60 (step @p353 :rule eq_resolve :premises (@p352 @p351)) % 0.37/0.60 (step @p354 :rule reordering :premises (@p353) :args ((or @t259 @t261))) % 0.37/0.60 (step @p355 :rule chain_m_resolution :premises (@p354 @p324) :args (@t259 @t262 @t263)) % 0.37/0.60 (step @p356 :rule cnf_or_pos :args (@t265)) % 0.37/0.60 (step @p357 :rule reordering :premises (@p356) :args ((or @t260 @t258 @t256 @t254 @t250 @t246 (not @t265)))) % 0.37/0.60 (step @p358 :rule chain_m_resolution :premises (@p357 @p355 @p349 @p343 @p337 @p326 @p330) :args (@t250 (@list false false false false true false) (@list @t259 @t257 @t255 @t253 @t246 @t265))) % 0.37/0.60 (step @p359 :rule bool-double-not-elim :args (@t247)) % 0.37/0.60 (step @p360 :rule bool-double-not-elim :args (@t249)) % 0.37/0.60 (step @p361 :rule refl :args (@t251)) % 0.37/0.60 (step @p362 :rule nary_cong :premises (@p361 @p360 @p359) :args ((or @t251 (not @t250) (not @t248)))) % 0.37/0.60 (step @p363 :rule cnf_and_neg :args (@t251)) % 0.37/0.60 (step @p364 :rule eq_resolve :premises (@p363 @p362)) % 0.37/0.60 (step @p365 :rule reordering :premises (@p364) :args ((or @t249 @t247 @t251))) % 0.37/0.60 (step @p366 :rule chain_m_resolution :premises (@p365 @p358 @p328) :args (@t247 (@list true true) (@list @t249 @t251))) % 0.37/0.60 (step @p367 :rule cnf_or_pos :args (@t266)) % 0.37/0.60 (step @p368 :rule reordering :premises (@p367) :args ((or @t260 @t258 @t256 @t254 @t248 @t246 @t267))) % 0.37/0.60 (step @p369 :rule chain_m_resolution :premises (@p368 @p355 @p349 @p343 @p337 @p366 @p326) :args (@t267 (@list false false false false false true) (@list @t259 @t257 @t255 @t253 @t247 @t246))) % 0.37/0.60 (assume-push @p376 @t268) % 0.37/0.60 (step @p371 :rule instantiate :premises (@p322) :args (@t264)) % 0.37/0.60 (step-pop @p377 :rule scope :premises (@p371)) % 0.37/0.60 (step @p372 :rule process_scope :premises (@p377) :args (@t266)) % 0.37/0.60 (step @p374 :rule implies_elim :premises (@p372)) % 0.37/0.60 (step @p375 false :rule chain_m_resolution :premises (@p374 @p369 @p322) :args (false (@list true false) (@list @t266 @t268))) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------