%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN069+1 : TPTP v9.2.1. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n012.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 08:42:53 AM UTC 2026 % Result : Theorem 27.93s 28.16s % Output : Proof 27.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUN069+1 : TPTP v9.2.1. Released v7.3.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.08/0.25 % Computer : n012.cluster.edu % 0.08/0.25 % Model : x86_64 x86_64 % 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.25 % Memory : 8042.1875MB % 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.25 % CPULimit : 300 % 0.08/0.25 % WCLimit : 300 % 0.08/0.25 % DateTime : Tue Jun 2 12:38:33 EDT 2026 % 0.08/0.25 % CPUTime : % 0.15/0.34 %----Proving TF0_NAR, FOF, or CNF % 27.93/28.16 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 27.93/28.16 --- Run --no-e-matching --full-saturate-quant at 6... % 27.93/28.16 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 27.93/28.16 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 27.93/28.16 % SZS status Theorem % 27.93/28.16 % SZS output start Proof % 27.93/28.16 ( % 27.93/28.16 (declare-sort $$unsorted 0) % 27.93/28.16 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 27.93/28.16 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 27.93/28.16 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 27.93/28.16 (declare-const tptp.r1 (-> $$unsorted Bool)) % 27.93/28.16 (declare-const tptp.id (-> $$unsorted $$unsorted Bool)) % 27.93/28.16 (define @t1 () (@var "Y24" $$unsorted)) % 27.93/28.16 (define @t2 () (@var "X19" $$unsorted)) % 27.93/28.16 (define @t3 () (tptp.id @t2 @t1)) % 27.93/28.16 (define @t4 () (tptp.r1 @t2)) % 27.93/28.16 (define @t5 () (not @t4)) % 27.93/28.16 (define @t6 () (@list @t2)) % 27.93/28.16 (define @t7 () (forall @t6 (or (and @t3 @t4) (and @t5 (not @t3))))) % 27.93/28.16 (define @t8 () (@list @t1)) % 27.93/28.16 (define @t9 () (exists @t8 @t7)) % 27.93/28.16 (define @t10 () (@var "Y21" $$unsorted)) % 27.93/28.16 (define @t11 () (@var "X12" $$unsorted)) % 27.93/28.16 (define @t12 () (tptp.id @t11 @t10)) % 27.93/28.16 (define @t13 () (@var "X11" $$unsorted)) % 27.93/28.16 (define @t14 () (tptp.r2 @t13 @t11)) % 27.93/28.16 (define @t15 () (@var "Y22" $$unsorted)) % 27.93/28.16 (define @t16 () (@var "X15" $$unsorted)) % 27.93/28.16 (define @t17 () (tptp.id @t16 @t15)) % 27.93/28.16 (define @t18 () (@var "X14" $$unsorted)) % 27.93/28.16 (define @t19 () (@var "X13" $$unsorted)) % 27.93/28.16 (define @t20 () (tptp.r3 @t19 @t18 @t16)) % 27.93/28.16 (define @t21 () (@var "Y23" $$unsorted)) % 27.93/28.16 (define @t22 () (@var "X18" $$unsorted)) % 27.93/28.16 (define @t23 () (tptp.id @t22 @t21)) % 27.93/28.16 (define @t24 () (@var "X17" $$unsorted)) % 27.93/28.16 (define @t25 () (@var "X16" $$unsorted)) % 27.93/28.16 (define @t26 () (tptp.r4 @t25 @t24 @t22)) % 27.93/28.16 (define @t27 () (@var "X20" $$unsorted)) % 27.93/28.16 (define @t28 () (@var "X21" $$unsorted)) % 27.93/28.16 (define @t29 () (@var "X22" $$unsorted)) % 27.93/28.16 (define @t30 () (@var "X25" $$unsorted)) % 27.93/28.16 (define @t31 () (@var "X24" $$unsorted)) % 27.93/28.16 (define @t32 () (@var "X23" $$unsorted)) % 27.93/28.16 (define @t33 () (@var "X27" $$unsorted)) % 27.93/28.16 (define @t34 () (tptp.r1 @t33)) % 27.93/28.16 (define @t35 () (@var "X26" $$unsorted)) % 27.93/28.16 (define @t36 () (tptp.r1 @t35)) % 27.93/28.16 (define @t37 () (@var "X31" $$unsorted)) % 27.93/28.16 (define @t38 () (@var "X30" $$unsorted)) % 27.93/28.16 (define @t39 () (tptp.r2 @t38 @t37)) % 27.93/28.16 (define @t40 () (@var "X29" $$unsorted)) % 27.93/28.16 (define @t41 () (@var "X28" $$unsorted)) % 27.93/28.16 (define @t42 () (tptp.r2 @t41 @t40)) % 27.93/28.16 (define @t43 () (@var "X37" $$unsorted)) % 27.93/28.16 (define @t44 () (@var "X36" $$unsorted)) % 27.93/28.16 (define @t45 () (@var "X35" $$unsorted)) % 27.93/28.16 (define @t46 () (tptp.r3 @t45 @t44 @t43)) % 27.93/28.16 (define @t47 () (@var "X34" $$unsorted)) % 27.93/28.16 (define @t48 () (@var "X33" $$unsorted)) % 27.93/28.16 (define @t49 () (@var "X32" $$unsorted)) % 27.93/28.16 (define @t50 () (tptp.r3 @t49 @t48 @t47)) % 27.93/28.16 (define @t51 () (@var "X43" $$unsorted)) % 27.93/28.16 (define @t52 () (@var "X42" $$unsorted)) % 27.93/28.16 (define @t53 () (@var "X41" $$unsorted)) % 27.93/28.16 (define @t54 () (tptp.r4 @t53 @t52 @t51)) % 27.93/28.16 (define @t55 () (@var "X40" $$unsorted)) % 27.93/28.16 (define @t56 () (@var "X39" $$unsorted)) % 27.93/28.16 (define @t57 () (@var "X38" $$unsorted)) % 27.93/28.16 (define @t58 () (tptp.r4 @t57 @t56 @t55)) % 27.93/28.16 (define @t59 () (@var "Y7" $$unsorted)) % 27.93/28.16 (define @t60 () (@var "X8" $$unsorted)) % 27.93/28.16 (define @t61 () (@var "X1" $$unsorted)) % 27.93/28.16 (define @t62 () (tptp.r3 @t61 @t60 @t59)) % 27.93/28.16 (define @t63 () (@var "Y4" $$unsorted)) % 27.93/28.16 (define @t64 () (tptp.r2 @t59 @t63)) % 27.93/28.16 (define @t65 () (and @t64 @t62)) % 27.93/28.16 (define @t66 () (@list @t59)) % 27.93/28.16 (define @t67 () (exists @t66 @t65)) % 27.93/28.16 (define @t68 () (@var "Y5" $$unsorted)) % 27.93/28.16 (define @t69 () (@var "Y15" $$unsorted)) % 27.93/28.16 (define @t70 () (tptp.r3 @t61 @t69 @t68)) % 27.93/28.16 (define @t71 () (tptp.r2 @t60 @t69)) % 27.93/28.16 (define @t72 () (and @t71 @t70)) % 27.93/28.16 (define @t73 () (@list @t69)) % 27.93/28.16 (define @t74 () (exists @t73 @t72)) % 27.93/28.16 (define @t75 () (tptp.id @t68 @t63)) % 27.93/28.16 (define @t76 () (and @t75 @t74)) % 27.93/28.16 (define @t77 () (@list @t68)) % 27.93/28.16 (define @t78 () (exists @t77 @t76)) % 27.93/28.16 (define @t79 () (and @t78 @t67)) % 27.93/28.16 (define @t80 () (@list @t63)) % 27.93/28.16 (define @t81 () (exists @t80 @t79)) % 27.93/28.16 (define @t82 () (forall (@list @t61 @t60) @t81)) % 27.93/28.16 (define @t83 () (@var "Y6" $$unsorted)) % 27.93/28.16 (define @t84 () (@var "X9" $$unsorted)) % 27.93/28.16 (define @t85 () (@var "X2" $$unsorted)) % 27.93/28.16 (define @t86 () (@var "Y2" $$unsorted)) % 27.93/28.16 (define @t87 () (@var "Y3" $$unsorted)) % 27.93/28.16 (define @t88 () (@var "Y14" $$unsorted)) % 27.93/28.16 (define @t89 () (@list @t86)) % 27.93/28.16 (define @t90 () (@var "X10" $$unsorted)) % 27.93/28.16 (define @t91 () (@var "X3" $$unsorted)) % 27.93/28.16 (define @t92 () (tptp.id @t91 @t90)) % 27.93/28.16 (define @t93 () (@var "Y12" $$unsorted)) % 27.93/28.16 (define @t94 () (not (tptp.r2 @t90 @t93))) % 27.93/28.16 (define @t95 () (@var "Y13" $$unsorted)) % 27.93/28.16 (define @t96 () (@list @t93)) % 27.93/28.16 (define @t97 () (forall @t96 (or (forall (@list @t95) (or (not (tptp.id @t95 @t93)) (not (tptp.r2 @t91 @t95)))) @t94))) % 27.93/28.16 (define @t98 () (or @t97 @t92)) % 27.93/28.16 (define @t99 () (@list @t91 @t90)) % 27.93/28.16 (define @t100 () (forall @t99 @t98)) % 27.93/28.16 (define @t101 () (@var "Y9" $$unsorted)) % 27.93/28.16 (define @t102 () (@var "Y16" $$unsorted)) % 27.93/28.16 (define @t103 () (@var "X4" $$unsorted)) % 27.93/28.16 (define @t104 () (@var "Y18" $$unsorted)) % 27.93/28.16 (define @t105 () (@var "Y8" $$unsorted)) % 27.93/28.16 (define @t106 () (@var "Y17" $$unsorted)) % 27.93/28.16 (define @t107 () (@var "X5" $$unsorted)) % 27.93/28.16 (define @t108 () (@var "Y11" $$unsorted)) % 27.93/28.16 (define @t109 () (@var "Y1" $$unsorted)) % 27.93/28.16 (define @t110 () (@var "X6" $$unsorted)) % 27.93/28.16 (define @t111 () (@var "Y19" $$unsorted)) % 27.93/28.16 (define @t112 () (@var "Y10" $$unsorted)) % 27.93/28.16 (define @t113 () (@var "X7" $$unsorted)) % 27.93/28.16 (define @t114 () (@var "Y20" $$unsorted)) % 27.93/28.16 (define @t115 () (tptp.r2 @t86 @t109)) % 27.93/28.16 (define @t116 () (tptp.r1 @t86)) % 27.93/28.16 (define @t117 () (and @t116 @t115)) % 27.93/28.16 (define @t118 () (exists @t89 @t117)) % 27.93/28.16 (define @t119 () (tptp.id @t109 @t109)) % 27.93/28.16 (define @t120 () (and @t119 @t118)) % 27.93/28.16 (define @t121 () (@list @t109)) % 27.93/28.16 (define @t122 () (exists @t121 @t120)) % 27.93/28.16 (define @t123 () (not @t122)) % 27.93/28.16 (define @t124 () (@var "BOUND_VARIABLE_7892" $$unsorted)) % 27.93/28.16 (define @t125 () (not (tptp.r2 @t91 @t124))) % 27.93/28.16 (define @t126 () (@var "BOUND_VARIABLE_7890" $$unsorted)) % 27.93/28.16 (define @t127 () (not (tptp.id @t124 @t126))) % 27.93/28.16 (define @t128 () (not (tptp.r2 @t90 @t126))) % 27.93/28.16 (define @t129 () (or @t92 @t128 @t127 @t125)) % 27.93/28.16 (define @t130 () (or @t128 @t127 @t125)) % 27.93/28.16 (define @t131 () (or @t130 @t92)) % 27.93/28.16 (define @t132 () (@list @t91 @t90 @t126 @t124)) % 27.93/28.16 (define @t133 () (forall @t132 @t131)) % 27.93/28.16 (define @t134 () (@list @t126 @t124)) % 27.93/28.16 (define @t135 () (forall @t134 @t131)) % 27.93/28.16 (define @t136 () (forall @t134 @t130)) % 27.93/28.16 (define @t137 () (@var "BOUND_VARIABLE_7876" $$unsorted)) % 27.93/28.16 (define @t138 () (or @t136 @t92)) % 27.93/28.16 (define @t139 () (not (tptp.r2 @t91 @t137))) % 27.93/28.16 (define @t140 () (not (tptp.id @t137 @t93))) % 27.93/28.16 (define @t141 () (or @t94 @t140 @t139)) % 27.93/28.16 (define @t142 () (@list @t93 @t137)) % 27.93/28.16 (define @t143 () (or @t140 @t139)) % 27.93/28.16 (define @t144 () (or @t143 @t94)) % 27.93/28.16 (define @t145 () (forall @t142 @t144)) % 27.93/28.16 (define @t146 () (@list @t137)) % 27.93/28.16 (define @t147 () (forall @t146 @t144)) % 27.93/28.16 (define @t148 () (forall @t146 @t143)) % 27.93/28.16 (define @t149 () (or @t148 @t94)) % 27.93/28.16 (define @t150 () (@var "BOUND_VARIABLE_7791" $$unsorted)) % 27.93/28.16 (define @t151 () (forall @t8 (not @t7))) % 27.93/28.16 (define @t152 () (@quantifiers_skolemize @t151 0)) % 27.93/28.16 (define @t153 () (not (tptp.r2 @t150 @t63))) % 27.93/28.16 (define @t154 () (@var "BOUND_VARIABLE_7780" $$unsorted)) % 27.93/28.16 (define @t155 () (@var "BOUND_VARIABLE_7782" $$unsorted)) % 27.93/28.16 (define @t156 () (not (tptp.id @t154 @t63))) % 27.93/28.16 (define @t157 () (@list @t63 @t154 @t155 @t150)) % 27.93/28.16 (define @t158 () (forall @t157 (or @t156 (not (tptp.r2 @t152 @t155)) (not (tptp.r3 @t152 @t155 @t154)) @t153 (not (tptp.r3 @t152 @t152 @t150))))) % 27.93/28.16 (define @t159 () (@quantifiers_skolemize @t158 2)) % 27.93/28.16 (define @t160 () (not @t151)) % 27.93/28.16 (define @t161 () (tptp.id @t2 @t152)) % 27.93/28.16 (define @t162 () (forall @t6 (or (and @t161 @t4) (and @t5 (not @t161))))) % 27.93/28.16 (define @t163 () (not (not @t162))) % 27.93/28.16 (define @t164 () (@list true)) % 27.93/28.16 (define @t165 () (@var "BOUND_VARIABLE_8031" $$unsorted)) % 27.93/28.16 (define @t166 () (not (tptp.r2 @t165 @t109))) % 27.93/28.16 (define @t167 () (not (tptp.r1 @t165))) % 27.93/28.16 (define @t168 () (not @t119)) % 27.93/28.16 (define @t169 () (or @t168 @t167 @t166)) % 27.93/28.16 (define @t170 () (@list @t109 @t165)) % 27.93/28.16 (define @t171 () (or @t167 @t166)) % 27.93/28.16 (define @t172 () (or @t168 @t171)) % 27.93/28.16 (define @t173 () (forall @t170 @t172)) % 27.93/28.16 (define @t174 () (@list @t165)) % 27.93/28.16 (define @t175 () (forall @t174 @t172)) % 27.93/28.16 (define @t176 () (forall @t174 @t171)) % 27.93/28.16 (define @t177 () (or @t168 @t176)) % 27.93/28.16 (define @t178 () (forall @t89 (or (not @t116) (not @t115)))) % 27.93/28.16 (define @t179 () (not @t178)) % 27.93/28.16 (define @t180 () (and @t119 @t179)) % 27.93/28.16 (define @t181 () (forall @t121 (not @t180))) % 27.93/28.16 (define @t182 () (not @t181)) % 27.93/28.16 (define @t183 () (forall @t89 (not @t117))) % 27.93/28.16 (define @t184 () (not @t183)) % 27.93/28.16 (define @t185 () (not (tptp.r3 @t61 @t60 @t150))) % 27.93/28.16 (define @t186 () (not (tptp.r3 @t61 @t155 @t154))) % 27.93/28.16 (define @t187 () (not (tptp.r2 @t60 @t155))) % 27.93/28.16 (define @t188 () (or @t153 @t185)) % 27.93/28.16 (define @t189 () (or @t156 @t187 @t186)) % 27.93/28.16 (define @t190 () (or @t189 @t188)) % 27.93/28.16 (define @t191 () (forall @t157 @t190)) % 27.93/28.16 (define @t192 () (forall (@list @t154 @t155 @t150) @t190)) % 27.93/28.16 (define @t193 () (forall (@list @t150) @t188)) % 27.93/28.16 (define @t194 () (forall (@list @t154 @t155) @t189)) % 27.93/28.16 (define @t195 () (@var "BOUND_VARIABLE_7752" $$unsorted)) % 27.93/28.16 (define @t196 () (or @t194 @t193)) % 27.93/28.16 (define @t197 () (forall @t66 (or (not @t64) (not @t62)))) % 27.93/28.16 (define @t198 () (not (tptp.r3 @t61 @t195 @t68))) % 27.93/28.16 (define @t199 () (not (tptp.r2 @t60 @t195))) % 27.93/28.16 (define @t200 () (not @t75)) % 27.93/28.16 (define @t201 () (or @t200 @t199 @t198)) % 27.93/28.16 (define @t202 () (@list @t68 @t195)) % 27.93/28.16 (define @t203 () (forall @t202 @t201)) % 27.93/28.16 (define @t204 () (not @t197)) % 27.93/28.16 (define @t205 () (not @t203)) % 27.93/28.16 (define @t206 () (and @t205 @t204)) % 27.93/28.16 (define @t207 () (forall @t80 (not @t206))) % 27.93/28.16 (define @t208 () (not @t207)) % 27.93/28.16 (define @t209 () (forall @t66 (not @t65))) % 27.93/28.16 (define @t210 () (not @t209)) % 27.93/28.16 (define @t211 () (or @t199 @t198)) % 27.93/28.16 (define @t212 () (or @t200 @t211)) % 27.93/28.16 (define @t213 () (forall @t202 @t212)) % 27.93/28.16 (define @t214 () (@list @t195)) % 27.93/28.16 (define @t215 () (forall @t214 @t212)) % 27.93/28.16 (define @t216 () (forall @t214 @t211)) % 27.93/28.16 (define @t217 () (or @t200 @t216)) % 27.93/28.16 (define @t218 () (forall @t73 (or (not @t71) (not @t70)))) % 27.93/28.16 (define @t219 () (not @t218)) % 27.93/28.16 (define @t220 () (and @t75 @t219)) % 27.93/28.16 (define @t221 () (forall @t77 (not @t220))) % 27.93/28.16 (define @t222 () (not @t221)) % 27.93/28.16 (define @t223 () (forall @t73 (not @t72))) % 27.93/28.16 (define @t224 () (not @t223)) % 27.93/28.16 (define @t225 () (tptp.r2 @t152 @t159)) % 27.93/28.16 (define @t226 () (@quantifiers_skolemize @t158 3)) % 27.93/28.16 (define @t227 () (@quantifiers_skolemize @t158 0)) % 27.93/28.16 (define @t228 () (@quantifiers_skolemize @t158 1)) % 27.93/28.16 (define @t229 () (not @t225)) % 27.93/28.16 (define @t230 () (or (not (tptp.id @t228 @t227)) @t229 (not (tptp.r3 @t152 @t159 @t228)) (not (tptp.r2 @t226 @t227)) (not (tptp.r3 @t152 @t152 @t226)))) % 27.93/28.16 (define @t231 () (tptp.r1 @t152)) % 27.93/28.16 (define @t232 () (not @t231)) % 27.93/28.16 (define @t233 () (tptp.id @t159 @t159)) % 27.93/28.16 (define @t234 () (not @t233)) % 27.93/28.16 (define @t235 () (or @t234 @t232 @t229)) % 27.93/28.16 (define @t236 () (tptp.id @t152 @t152)) % 27.93/28.16 (define @t237 () (and @t236 @t231)) % 27.93/28.16 (define @t238 () (not @t237)) % 27.93/28.16 (define @t239 () (not @t236)) % 27.93/28.16 (define @t240 () (and @t232 @t239)) % 27.93/28.16 (define @t241 () (or @t237 @t240)) % 27.93/28.16 (define @t242 () (@list true false)) % 27.93/28.16 (define @t243 () (or @t236 @t229 @t234 @t229)) % 27.93/28.16 (define @t244 () (not @t243)) % 27.93/28.16 (define @t245 () (forall @t132 @t129)) % 27.93/28.16 (assume @p1 @t9) % 27.93/28.16 (assume @p2 (forall (@list @t13) (exists (@list @t10) (forall (@list @t11) (or (and @t12 @t14) (and (not @t14) (not @t12))))))) % 27.93/28.16 (assume @p3 (forall (@list @t19 @t18) (exists (@list @t15) (forall (@list @t16) (or (and @t17 @t20) (and (not @t20) (not @t17))))))) % 27.93/28.16 (assume @p4 (forall (@list @t25 @t24) (exists (@list @t21) (forall (@list @t22) (or (and @t23 @t26) (and (not @t26) (not @t23))))))) % 27.93/28.16 (assume @p5 (forall (@list @t27) (tptp.id @t27 @t27))) % 27.93/28.16 (assume @p6 (forall (@list @t28 @t29) (or (not (tptp.id @t28 @t29)) (tptp.id @t29 @t28)))) % 27.93/28.16 (assume @p7 (forall (@list @t32 @t31 @t30) (or (not (tptp.id @t32 @t31)) (tptp.id @t32 @t30) (not (tptp.id @t31 @t30))))) % 27.93/28.16 (assume @p8 (forall (@list @t35 @t33) (or (not (tptp.id @t35 @t33)) (and (not @t36) (not @t34)) (and @t36 @t34)))) % 27.93/28.16 (assume @p9 (forall (@list @t41 @t40 @t38 @t37) (or (not (tptp.id @t41 @t38)) (not (tptp.id @t40 @t37)) (and (not @t42) (not @t39)) (and @t42 @t39)))) % 27.93/28.16 (assume @p10 (forall (@list @t49 @t48 @t47 @t45 @t44 @t43) (or (not (tptp.id @t49 @t45)) (not (tptp.id @t48 @t44)) (not (tptp.id @t47 @t43)) (and (not @t50) (not @t46)) (and @t50 @t46)))) % 27.93/28.16 (assume @p11 (forall (@list @t57 @t56 @t55 @t53 @t52 @t51) (or (not (tptp.id @t57 @t53)) (not (tptp.id @t56 @t52)) (not (tptp.id @t55 @t51)) (and (not @t58) (not @t54)) (and @t58 @t54)))) % 27.93/28.16 (assume @p12 @t82) % 27.93/28.16 (assume @p13 (forall (@list @t85 @t84) (exists @t89 (and (exists (@list @t87) (and (tptp.id @t87 @t86) (exists (@list @t88) (and (tptp.r2 @t84 @t88) (tptp.r4 @t85 @t88 @t87))))) (exists (@list @t83) (and (tptp.r3 @t83 @t85 @t86) (tptp.r4 @t85 @t84 @t83))))))) % 27.93/28.16 (assume @p14 @t100) % 27.93/28.16 (assume @p15 (forall (@list @t103) (exists (@list @t101) (and (tptp.id @t101 @t103) (exists (@list @t102) (and (tptp.r1 @t102) (tptp.r3 @t103 @t102 @t101))))))) % 27.93/28.16 (assume @p16 (forall (@list @t107) (exists (@list @t105) (and (exists (@list @t106) (and (tptp.r1 @t106) (tptp.r4 @t107 @t106 @t105))) (exists (@list @t104) (and (tptp.id @t105 @t104) (tptp.r1 @t104))))))) % 27.93/28.16 (assume @p17 (forall (@list @t110) (or (exists (@list @t111) (and (tptp.id @t110 @t111) (tptp.r1 @t111))) (exists (@list @t109 @t108) (and (tptp.id @t110 @t108) (tptp.r2 @t109 @t108)))))) % 27.93/28.16 (assume @p18 (forall (@list @t113 @t112) (or (forall (@list @t114) (or (not (tptp.id @t114 @t112)) (not (tptp.r1 @t114)))) (not (tptp.r2 @t113 @t112))))) % 27.93/28.16 (assume @p19 @t123) % 27.93/28.16 (assume @p20 true) % 27.93/28.16 (step @p21 :rule aci_norm :args ((= @t131 @t129))) % 27.93/28.16 (step @p22 :rule cong :premises (@p21) :args (@t133)) % 27.93/28.16 (step @p23 :rule quant-merge-prenex :args ((= (forall @t99 @t135) @t133))) % 27.93/28.16 (step @p24 :rule refl :args (@t92)) % 27.93/28.16 (step @p25 :rule alpha_equiv :args (@t136 (@list @t126 @t124) (@list @t93 @t137))) % 27.93/28.17 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t138)) % 27.93/28.17 (step @p27 :rule quant-miniscope-or :args ((= @t135 @t138))) % 27.93/28.17 (step @p28 :rule trans :premises (@p27 @p26)) % 27.93/28.17 (step @p29 :rule symm :premises (@p28)) % 27.93/28.17 (step @p30 :rule cong :premises (@p29) :args ((forall @t99 (or (forall @t142 @t141) @t92)))) % 27.93/28.17 (step @p31 :rule trans :premises (@p30 @p23)) % 27.93/28.17 (step @p32 :rule trans :premises (@p31 @p22)) % 27.93/28.17 (step @p33 :rule refl :args (@t92)) % 27.93/28.17 (step @p34 :rule aci_norm :args ((= @t144 @t141))) % 27.93/28.17 (step @p35 :rule cong :premises (@p34) :args (@t145)) % 27.93/28.17 (step @p36 :rule quant-merge-prenex :args ((= (forall @t96 @t147) @t145))) % 27.93/28.17 (step @p37 :rule refl :args (@t94)) % 27.93/28.17 (step @p38 :rule alpha_equiv :args (@t148 (@list @t137) (@list @t95))) % 27.93/28.17 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t149)) % 27.93/28.17 (step @p40 :rule quant-miniscope-or :args ((= @t147 @t149))) % 27.93/28.17 (step @p41 :rule trans :premises (@p40 @p39)) % 27.93/28.17 (step @p42 :rule symm :premises (@p41)) % 27.93/28.17 (step @p43 :rule cong :premises (@p42) :args (@t97)) % 27.93/28.17 (step @p44 :rule trans :premises (@p43 @p36)) % 27.93/28.17 (step @p45 :rule trans :premises (@p44 @p35)) % 27.93/28.17 (step @p46 :rule nary_cong :premises (@p45 @p33) :args (@t98)) % 27.93/28.17 (step @p47 :rule cong :premises (@p46) :args (@t100)) % 27.93/28.17 (step @p48 :rule trans :premises (@p47 @p32)) % 27.93/28.17 (step @p49 :rule eq_resolve :premises (@p14 @p48)) % 27.93/28.17 (step @p50 :rule instantiate :premises (@p5) :args ((@list @t159))) % 27.93/28.17 (step @p51 :rule exists-elim :args ((= @t9 @t160))) % 27.93/28.17 (step @p52 :rule eq_resolve :premises (@p1 @p51)) % 27.93/28.17 (step @p53 :rule refl :args (@t162)) % 27.93/28.17 (step @p54 :rule bool-double-not-elim :args (@t151)) % 27.93/28.17 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or (not @t160) @t162))) % 27.93/28.17 (step @p56 :rule bool-double-not-elim :args (@t162)) % 27.93/28.17 (step @p57 :rule refl :args (@t160)) % 27.93/28.17 (step @p58 :rule cong :premises (@p57 @p56) :args ((=> @t160 @t163))) % 27.93/28.17 (assume-push @p196 @t160) % 27.93/28.17 (step @p60 :rule skolemize :premises (@p52)) % 27.93/28.17 (step-pop @p197 :rule scope :premises (@p60)) % 27.93/28.17 (step @p61 :rule process_scope :premises (@p197) :args (@t163)) % 27.93/28.17 (step @p63 :rule eq_resolve :premises (@p61 @p58)) % 27.93/28.17 (step @p64 :rule implies_elim :premises (@p63)) % 27.93/28.17 (step @p65 :rule eq_resolve :premises (@p64 @p55)) % 27.93/28.17 (step @p66 :rule chain_m_resolution :premises (@p65 @p52) :args (@t162 @t164 (@list @t151))) % 27.93/28.17 (step @p67 :rule instantiate :premises (@p66) :args ((@list @t152))) % 27.93/28.17 (step @p68 :rule bool-double-not-elim :args ((forall @t170 @t169))) % 27.93/28.17 (step @p69 :rule aci_norm :args ((= @t172 @t169))) % 27.93/28.17 (step @p70 :rule cong :premises (@p69) :args (@t173)) % 27.93/28.17 (step @p71 :rule quant-merge-prenex :args ((= (forall @t121 @t175) @t173))) % 27.93/28.17 (step @p72 :rule alpha_equiv :args (@t176 (@list @t165) (@list @t86))) % 27.93/28.17 (step @p73 :rule refl :args (@t168)) % 27.93/28.17 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t177)) % 27.93/28.17 (step @p75 :rule quant-miniscope-or :args ((= @t175 @t177))) % 27.93/28.17 (step @p76 :rule trans :premises (@p75 @p74)) % 27.93/28.17 (step @p77 :rule symm :premises (@p76)) % 27.93/28.17 (step @p78 :rule cong :premises (@p77) :args ((forall @t121 (or @t168 @t178)))) % 27.93/28.17 (step @p79 :rule trans :premises (@p78 @p71)) % 27.93/28.17 (step @p80 :rule trans :premises (@p79 @p70)) % 27.93/28.17 (step @p81 :rule bool-double-not-elim :args (@t178)) % 27.93/28.17 (step @p82 :rule nary_cong :premises (@p73 @p81) :args ((or @t168 (not @t179)))) % 27.93/28.17 (step @p83 :rule bool-and-de-morgan :args (@t119 @t179 true)) % 27.93/28.17 (step @p84 :rule trans :premises (@p83 @p82)) % 27.93/28.17 (step @p85 :rule cong :premises (@p84) :args (@t181)) % 27.93/28.17 (step @p86 :rule trans :premises (@p85 @p80)) % 27.93/28.17 (step @p87 :rule cong :premises (@p86) :args (@t182)) % 27.93/28.17 (step @p88 :rule exists-elim :args ((= (exists @t121 @t180) @t182))) % 27.93/28.17 (step @p89 :rule trans :premises (@p88 @p87)) % 27.93/28.17 (step @p90 :rule bool-and-de-morgan :args (@t116 @t115 true)) % 27.93/28.17 (step @p91 :rule cong :premises (@p90) :args (@t183)) % 27.93/28.17 (step @p92 :rule cong :premises (@p91) :args (@t184)) % 27.93/28.17 (step @p93 :rule exists-elim :args ((= @t118 @t184))) % 27.93/28.17 (step @p94 :rule trans :premises (@p93 @p92)) % 27.93/28.17 (step @p95 :rule refl :args (@t119)) % 27.93/28.17 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t120)) % 27.93/28.17 (step @p97 :rule cong :premises (@p96) :args (@t122)) % 27.93/28.17 (step @p98 :rule trans :premises (@p97 @p89)) % 27.93/28.17 (step @p99 :rule cong :premises (@p98) :args (@t123)) % 27.93/28.17 (step @p100 :rule trans :premises (@p99 @p68)) % 27.93/28.17 (step @p101 :rule eq_resolve :premises (@p19 @p100)) % 27.93/28.17 (step @p102 :rule instantiate :premises (@p101) :args ((@list @t159 @t152))) % 27.93/28.17 (step @p103 :rule aci_norm :args ((= @t190 (or @t156 @t187 @t186 @t153 @t185)))) % 27.93/28.17 (step @p104 :rule cong :premises (@p103) :args (@t191)) % 27.93/28.17 (step @p105 :rule quant-merge-prenex :args ((= (forall @t80 @t192) @t191))) % 27.93/28.17 (step @p106 :rule alpha_equiv :args (@t193 (@list @t150) (@list @t59))) % 27.93/28.17 (step @p107 :rule alpha_equiv :args (@t194 (@list @t154 @t155) (@list @t68 @t195))) % 27.93/28.17 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t196)) % 27.93/28.17 (step @p109 :rule quant-miniscope-or :args ((= @t192 @t196))) % 27.93/28.17 (step @p110 :rule trans :premises (@p109 @p108)) % 27.93/28.17 (step @p111 :rule symm :premises (@p110)) % 27.93/28.17 (step @p112 :rule cong :premises (@p111) :args ((forall @t80 (or @t203 @t197)))) % 27.93/28.17 (step @p113 :rule trans :premises (@p112 @p105)) % 27.93/28.17 (step @p114 :rule trans :premises (@p113 @p104)) % 27.93/28.17 (step @p115 :rule bool-double-not-elim :args (@t197)) % 27.93/28.17 (step @p116 :rule bool-double-not-elim :args (@t203)) % 27.93/28.17 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or (not @t205) (not @t204)))) % 27.93/28.17 (step @p118 :rule bool-and-de-morgan :args (@t205 @t204 true)) % 27.93/28.17 (step @p119 :rule trans :premises (@p118 @p117)) % 27.93/28.17 (step @p120 :rule cong :premises (@p119) :args (@t207)) % 27.93/28.17 (step @p121 :rule trans :premises (@p120 @p114)) % 27.93/28.17 (step @p122 :rule cong :premises (@p121) :args (@t208)) % 27.93/28.17 (step @p123 :rule exists-elim :args ((= (exists @t80 @t206) @t208))) % 27.93/28.17 (step @p124 :rule trans :premises (@p123 @p122)) % 27.93/28.17 (step @p125 :rule bool-and-de-morgan :args (@t64 @t62 true)) % 27.93/28.17 (step @p126 :rule cong :premises (@p125) :args (@t209)) % 27.93/28.17 (step @p127 :rule cong :premises (@p126) :args (@t210)) % 27.93/28.17 (step @p128 :rule exists-elim :args ((= @t67 @t210))) % 27.93/28.17 (step @p129 :rule trans :premises (@p128 @p127)) % 27.93/28.17 (step @p130 :rule aci_norm :args ((= @t212 @t201))) % 27.93/28.17 (step @p131 :rule cong :premises (@p130) :args (@t213)) % 27.93/28.17 (step @p132 :rule quant-merge-prenex :args ((= (forall @t77 @t215) @t213))) % 27.93/28.17 (step @p133 :rule alpha_equiv :args (@t216 (@list @t195) (@list @t69))) % 27.93/28.17 (step @p134 :rule refl :args (@t200)) % 27.93/28.17 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t217)) % 27.93/28.17 (step @p136 :rule quant-miniscope-or :args ((= @t215 @t217))) % 27.93/28.17 (step @p137 :rule trans :premises (@p136 @p135)) % 27.93/28.17 (step @p138 :rule symm :premises (@p137)) % 27.93/28.17 (step @p139 :rule cong :premises (@p138) :args ((forall @t77 (or @t200 @t218)))) % 27.93/28.17 (step @p140 :rule trans :premises (@p139 @p132)) % 27.93/28.17 (step @p141 :rule trans :premises (@p140 @p131)) % 27.93/28.17 (step @p142 :rule bool-double-not-elim :args (@t218)) % 27.93/28.17 (step @p143 :rule nary_cong :premises (@p134 @p142) :args ((or @t200 (not @t219)))) % 27.93/28.17 (step @p144 :rule bool-and-de-morgan :args (@t75 @t219 true)) % 27.93/28.17 (step @p145 :rule trans :premises (@p144 @p143)) % 27.93/28.17 (step @p146 :rule cong :premises (@p145) :args (@t221)) % 27.93/28.17 (step @p147 :rule trans :premises (@p146 @p141)) % 27.93/28.17 (step @p148 :rule cong :premises (@p147) :args (@t222)) % 27.93/28.17 (step @p149 :rule exists-elim :args ((= (exists @t77 @t220) @t222))) % 27.93/28.17 (step @p150 :rule trans :premises (@p149 @p148)) % 27.93/28.17 (step @p151 :rule bool-and-de-morgan :args (@t71 @t70 true)) % 27.93/28.17 (step @p152 :rule cong :premises (@p151) :args (@t223)) % 27.93/28.17 (step @p153 :rule cong :premises (@p152) :args (@t224)) % 27.93/28.17 (step @p154 :rule exists-elim :args ((= @t74 @t224))) % 27.93/28.17 (step @p155 :rule trans :premises (@p154 @p153)) % 27.93/28.17 (step @p156 :rule refl :args (@t75)) % 27.93/28.17 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t76)) % 27.93/28.17 (step @p158 :rule cong :premises (@p157) :args (@t78)) % 27.93/28.17 (step @p159 :rule trans :premises (@p158 @p150)) % 27.93/28.17 (step @p160 :rule nary_cong :premises (@p159 @p129) :args (@t79)) % 27.93/28.17 (step @p161 :rule cong :premises (@p160) :args (@t81)) % 27.93/28.17 (step @p162 :rule trans :premises (@p161 @p124)) % 27.93/28.17 (step @p163 :rule cong :premises (@p162) :args (@t82)) % 27.93/28.17 (step @p164 :rule eq_resolve :premises (@p12 @p163)) % 27.93/28.17 (step @p165 :rule instantiate :premises (@p164) :args ((@list @t152 @t152))) % 27.93/28.17 (step @p166 :rule skolemize :premises (@p165)) % 27.93/28.17 (step @p167 :rule bool-double-not-elim :args (@t225)) % 27.93/28.17 (step @p168 :rule refl :args (@t230)) % 27.93/28.17 (step @p169 :rule nary_cong :premises (@p168 @p167) :args ((or @t230 (not @t229)))) % 27.93/28.17 (step @p170 :rule cnf_or_neg :args (@t230 1)) % 27.93/28.17 (step @p171 :rule eq_resolve :premises (@p170 @p169)) % 27.93/28.17 (step @p172 :rule reordering :premises (@p171) :args ((or @t225 @t230))) % 27.93/28.17 (step @p173 :rule chain_m_resolution :premises (@p172 @p166) :args (@t225 @t164 (@list @t230))) % 27.93/28.17 (step @p174 :rule cnf_or_pos :args (@t235)) % 27.93/28.17 (step @p175 :rule reordering :premises (@p174) :args ((or @t232 @t229 @t234 (not @t235)))) % 27.93/28.17 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p50 @p102) :args (@t232 (@list false false false) (@list @t225 @t233 @t235))) % 27.93/28.17 (step @p177 :rule cnf_and_pos :args (@t237 1)) % 27.93/28.17 (step @p178 :rule reordering :premises (@p177) :args ((or @t231 @t238))) % 27.93/28.17 (step @p179 :rule chain_m_resolution :premises (@p178 @p176) :args (@t238 @t164 (@list @t231))) % 27.93/28.17 (step @p180 :rule cnf_or_pos :args (@t241)) % 27.93/28.17 (step @p181 :rule reordering :premises (@p180) :args ((or @t237 @t240 (not @t241)))) % 27.93/28.17 (step @p182 :rule chain_m_resolution :premises (@p181 @p179 @p67) :args (@t240 @t242 (@list @t237 @t241))) % 27.93/28.17 (step @p183 :rule cnf_and_pos :args (@t240 1)) % 27.93/28.17 (step @p184 :rule reordering :premises (@p183) :args ((or @t239 (not @t240)))) % 27.93/28.17 (step @p185 :rule chain_m_resolution :premises (@p184 @p182) :args (@t239 (@list false) (@list @t240))) % 27.93/28.17 (step @p186 :rule cnf_or_pos :args (@t243)) % 27.93/28.17 (step @p187 :rule factoring :premises (@p186)) % 27.93/28.17 (step @p188 :rule reordering :premises (@p187) :args ((or @t229 @t236 @t234 @t244))) % 27.93/28.17 (step @p189 :rule chain_m_resolution :premises (@p188 @p173 @p185 @p50) :args (@t244 (@list false true false) (@list @t225 @t236 @t233))) % 27.93/28.17 (assume-push @p198 @t245) % 27.93/28.17 (step @p191 :rule instantiate :premises (@p49) :args ((@list @t152 @t152 @t159 @t159))) % 27.93/28.17 (step-pop @p199 :rule scope :premises (@p191)) % 27.93/28.17 (step @p192 :rule process_scope :premises (@p199) :args (@t243)) % 27.93/28.17 (step @p194 :rule implies_elim :premises (@p192)) % 27.93/28.17 (step @p195 false :rule chain_m_resolution :premises (@p194 @p189 @p49) :args (false @t242 (@list @t243 @t245))) % 27.93/28.17 ) % 27.93/28.17 % SZS output end Proof % 27.93/28.17 % cvc5 exiting %------------------------------------------------------------------------------