%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN073+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 : n020.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 08:42:54 AM UTC 2026 % Result : Theorem 0.44s 0.64s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN073+1 : TPTP v9.2.1. Released v7.3.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n020.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 12:42:55 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.64 % SZS status Theorem % 0.44/0.64 % SZS output start Proof % 0.44/0.64 ( % 0.44/0.64 (declare-sort $$unsorted 0) % 0.44/0.64 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.r1 (-> $$unsorted Bool)) % 0.44/0.64 (declare-const tptp.id (-> $$unsorted $$unsorted Bool)) % 0.44/0.64 (define @t1 () (@var "Y24" $$unsorted)) % 0.44/0.64 (define @t2 () (@var "X19" $$unsorted)) % 0.44/0.64 (define @t3 () (tptp.id @t2 @t1)) % 0.44/0.64 (define @t4 () (tptp.r1 @t2)) % 0.44/0.64 (define @t5 () (not @t4)) % 0.44/0.64 (define @t6 () (@list @t2)) % 0.44/0.64 (define @t7 () (forall @t6 (or (and @t3 @t4) (and @t5 (not @t3))))) % 0.44/0.64 (define @t8 () (@list @t1)) % 0.44/0.64 (define @t9 () (exists @t8 @t7)) % 0.44/0.64 (define @t10 () (@var "Y21" $$unsorted)) % 0.44/0.64 (define @t11 () (@var "X12" $$unsorted)) % 0.44/0.64 (define @t12 () (tptp.id @t11 @t10)) % 0.44/0.64 (define @t13 () (@var "X11" $$unsorted)) % 0.44/0.64 (define @t14 () (tptp.r2 @t13 @t11)) % 0.44/0.64 (define @t15 () (@var "Y22" $$unsorted)) % 0.44/0.64 (define @t16 () (@var "X15" $$unsorted)) % 0.44/0.64 (define @t17 () (tptp.id @t16 @t15)) % 0.44/0.64 (define @t18 () (@var "X14" $$unsorted)) % 0.44/0.64 (define @t19 () (@var "X13" $$unsorted)) % 0.44/0.64 (define @t20 () (tptp.r3 @t19 @t18 @t16)) % 0.44/0.64 (define @t21 () (@var "Y23" $$unsorted)) % 0.44/0.64 (define @t22 () (@var "X18" $$unsorted)) % 0.44/0.64 (define @t23 () (tptp.id @t22 @t21)) % 0.44/0.64 (define @t24 () (@var "X17" $$unsorted)) % 0.44/0.64 (define @t25 () (@var "X16" $$unsorted)) % 0.44/0.64 (define @t26 () (tptp.r4 @t25 @t24 @t22)) % 0.44/0.64 (define @t27 () (@var "X20" $$unsorted)) % 0.44/0.64 (define @t28 () (@var "X21" $$unsorted)) % 0.44/0.64 (define @t29 () (@var "X22" $$unsorted)) % 0.44/0.64 (define @t30 () (@var "X25" $$unsorted)) % 0.44/0.64 (define @t31 () (@var "X24" $$unsorted)) % 0.44/0.64 (define @t32 () (@var "X23" $$unsorted)) % 0.44/0.64 (define @t33 () (@var "X27" $$unsorted)) % 0.44/0.64 (define @t34 () (tptp.r1 @t33)) % 0.44/0.64 (define @t35 () (@var "X26" $$unsorted)) % 0.44/0.64 (define @t36 () (tptp.r1 @t35)) % 0.44/0.64 (define @t37 () (@var "X31" $$unsorted)) % 0.44/0.64 (define @t38 () (@var "X30" $$unsorted)) % 0.44/0.64 (define @t39 () (tptp.r2 @t38 @t37)) % 0.44/0.64 (define @t40 () (@var "X29" $$unsorted)) % 0.44/0.64 (define @t41 () (@var "X28" $$unsorted)) % 0.44/0.64 (define @t42 () (tptp.r2 @t41 @t40)) % 0.44/0.64 (define @t43 () (@var "X37" $$unsorted)) % 0.44/0.64 (define @t44 () (@var "X36" $$unsorted)) % 0.44/0.64 (define @t45 () (@var "X35" $$unsorted)) % 0.44/0.64 (define @t46 () (tptp.r3 @t45 @t44 @t43)) % 0.44/0.64 (define @t47 () (@var "X34" $$unsorted)) % 0.44/0.64 (define @t48 () (@var "X33" $$unsorted)) % 0.44/0.64 (define @t49 () (@var "X32" $$unsorted)) % 0.44/0.64 (define @t50 () (tptp.r3 @t49 @t48 @t47)) % 0.44/0.64 (define @t51 () (@var "X43" $$unsorted)) % 0.44/0.64 (define @t52 () (@var "X42" $$unsorted)) % 0.44/0.64 (define @t53 () (@var "X41" $$unsorted)) % 0.44/0.64 (define @t54 () (tptp.r4 @t53 @t52 @t51)) % 0.44/0.64 (define @t55 () (@var "X40" $$unsorted)) % 0.44/0.64 (define @t56 () (@var "X39" $$unsorted)) % 0.44/0.64 (define @t57 () (@var "X38" $$unsorted)) % 0.44/0.64 (define @t58 () (tptp.r4 @t57 @t56 @t55)) % 0.44/0.64 (define @t59 () (@var "Y7" $$unsorted)) % 0.44/0.64 (define @t60 () (@var "X8" $$unsorted)) % 0.44/0.64 (define @t61 () (@var "X1" $$unsorted)) % 0.44/0.64 (define @t62 () (@var "Y4" $$unsorted)) % 0.44/0.64 (define @t63 () (@var "Y5" $$unsorted)) % 0.44/0.64 (define @t64 () (@var "Y15" $$unsorted)) % 0.44/0.64 (define @t65 () (@list @t63)) % 0.44/0.64 (define @t66 () (@list @t62)) % 0.44/0.64 (define @t67 () (@var "Y6" $$unsorted)) % 0.44/0.64 (define @t68 () (@var "X9" $$unsorted)) % 0.44/0.64 (define @t69 () (@var "X2" $$unsorted)) % 0.44/0.64 (define @t70 () (@var "Y2" $$unsorted)) % 0.44/0.64 (define @t71 () (@var "Y3" $$unsorted)) % 0.44/0.64 (define @t72 () (@var "Y14" $$unsorted)) % 0.44/0.64 (define @t73 () (@list @t71)) % 0.44/0.64 (define @t74 () (@list @t70)) % 0.44/0.64 (define @t75 () (@var "X10" $$unsorted)) % 0.44/0.64 (define @t76 () (@var "X3" $$unsorted)) % 0.44/0.64 (define @t77 () (tptp.id @t76 @t75)) % 0.44/0.64 (define @t78 () (@var "Y12" $$unsorted)) % 0.44/0.64 (define @t79 () (not (tptp.r2 @t75 @t78))) % 0.44/0.64 (define @t80 () (@var "Y13" $$unsorted)) % 0.44/0.64 (define @t81 () (@list @t78)) % 0.44/0.64 (define @t82 () (forall @t81 (or (forall (@list @t80) (or (not (tptp.id @t80 @t78)) (not (tptp.r2 @t76 @t80)))) @t79))) % 0.44/0.64 (define @t83 () (or @t82 @t77)) % 0.44/0.64 (define @t84 () (@list @t76 @t75)) % 0.44/0.64 (define @t85 () (forall @t84 @t83)) % 0.44/0.64 (define @t86 () (@var "Y9" $$unsorted)) % 0.44/0.64 (define @t87 () (@var "Y16" $$unsorted)) % 0.44/0.64 (define @t88 () (@var "X4" $$unsorted)) % 0.44/0.64 (define @t89 () (@var "Y18" $$unsorted)) % 0.44/0.64 (define @t90 () (@var "Y8" $$unsorted)) % 0.44/0.64 (define @t91 () (@var "Y17" $$unsorted)) % 0.44/0.64 (define @t92 () (@var "X5" $$unsorted)) % 0.44/0.64 (define @t93 () (@var "Y11" $$unsorted)) % 0.44/0.64 (define @t94 () (@var "Y1" $$unsorted)) % 0.44/0.64 (define @t95 () (@var "X6" $$unsorted)) % 0.44/0.64 (define @t96 () (@var "Y19" $$unsorted)) % 0.44/0.64 (define @t97 () (@var "Y10" $$unsorted)) % 0.44/0.64 (define @t98 () (@var "X7" $$unsorted)) % 0.44/0.64 (define @t99 () (not (tptp.r2 @t98 @t97))) % 0.44/0.64 (define @t100 () (@var "Y20" $$unsorted)) % 0.44/0.64 (define @t101 () (@list @t98 @t97)) % 0.44/0.64 (define @t102 () (forall @t101 (or (forall (@list @t100) (or (not (tptp.id @t100 @t97)) (not (tptp.r1 @t100)))) @t99))) % 0.44/0.64 (define @t103 () (not (tptp.r2 @t71 @t94))) % 0.44/0.64 (define @t104 () (forall @t73 (or (forall @t65 (or (not (tptp.r1 @t63)) (not (tptp.r2 @t63 @t71)))) @t103))) % 0.44/0.64 (define @t105 () (not (tptp.id @t70 @t94))) % 0.44/0.64 (define @t106 () (forall @t74 (or (forall @t66 (or (not (tptp.r1 @t62)) (not (tptp.r2 @t62 @t70)))) @t105))) % 0.44/0.64 (define @t107 () (or @t106 @t104)) % 0.44/0.64 (define @t108 () (@list @t94)) % 0.44/0.64 (define @t109 () (forall @t108 @t107)) % 0.44/0.64 (define @t110 () (not @t109)) % 0.44/0.64 (define @t111 () (@var "BOUND_VARIABLE_8017" $$unsorted)) % 0.44/0.64 (define @t112 () (not (tptp.r1 @t111))) % 0.44/0.64 (define @t113 () (not (tptp.id @t111 @t97))) % 0.44/0.64 (define @t114 () (or @t99 @t113 @t112)) % 0.44/0.64 (define @t115 () (or @t113 @t112)) % 0.44/0.64 (define @t116 () (or @t115 @t99)) % 0.44/0.64 (define @t117 () (@list @t98 @t97 @t111)) % 0.44/0.64 (define @t118 () (forall @t117 @t116)) % 0.44/0.64 (define @t119 () (@list @t111)) % 0.44/0.64 (define @t120 () (forall @t119 @t116)) % 0.44/0.64 (define @t121 () (forall @t119 @t115)) % 0.44/0.64 (define @t122 () (or @t121 @t99)) % 0.44/0.64 (define @t123 () (@var "BOUND_VARIABLE_7907" $$unsorted)) % 0.44/0.64 (define @t124 () (not (tptp.r2 @t76 @t123))) % 0.44/0.64 (define @t125 () (@var "BOUND_VARIABLE_7905" $$unsorted)) % 0.44/0.64 (define @t126 () (not (tptp.id @t123 @t125))) % 0.44/0.64 (define @t127 () (not (tptp.r2 @t75 @t125))) % 0.44/0.64 (define @t128 () (or @t127 @t126 @t124)) % 0.44/0.64 (define @t129 () (or @t128 @t77)) % 0.44/0.64 (define @t130 () (forall (@list @t76 @t75 @t125 @t123) @t129)) % 0.44/0.64 (define @t131 () (@list @t125 @t123)) % 0.44/0.64 (define @t132 () (forall @t131 @t129)) % 0.44/0.64 (define @t133 () (forall @t131 @t128)) % 0.44/0.64 (define @t134 () (@var "BOUND_VARIABLE_7891" $$unsorted)) % 0.44/0.64 (define @t135 () (or @t133 @t77)) % 0.44/0.64 (define @t136 () (not (tptp.r2 @t76 @t134))) % 0.44/0.64 (define @t137 () (not (tptp.id @t134 @t78))) % 0.44/0.64 (define @t138 () (or @t79 @t137 @t136)) % 0.44/0.64 (define @t139 () (@list @t78 @t134)) % 0.44/0.64 (define @t140 () (or @t137 @t136)) % 0.44/0.64 (define @t141 () (or @t140 @t79)) % 0.44/0.64 (define @t142 () (forall @t139 @t141)) % 0.44/0.64 (define @t143 () (@list @t134)) % 0.44/0.64 (define @t144 () (forall @t143 @t141)) % 0.44/0.64 (define @t145 () (forall @t143 @t140)) % 0.44/0.64 (define @t146 () (or @t145 @t79)) % 0.44/0.64 (define @t147 () (@var "BOUND_VARIABLE_8067" $$unsorted)) % 0.44/0.64 (define @t148 () (@var "BOUND_VARIABLE_8069" $$unsorted)) % 0.44/0.64 (define @t149 () (not (tptp.r2 @t148 @t147))) % 0.44/0.64 (define @t150 () (not (tptp.r1 @t148))) % 0.44/0.64 (define @t151 () (not (tptp.r2 @t147 @t94))) % 0.44/0.64 (define @t152 () (@var "BOUND_VARIABLE_8056" $$unsorted)) % 0.44/0.64 (define @t153 () (@var "BOUND_VARIABLE_8058" $$unsorted)) % 0.44/0.64 (define @t154 () (not (tptp.r2 @t153 @t152))) % 0.44/0.64 (define @t155 () (not (tptp.r1 @t153))) % 0.44/0.64 (define @t156 () (not (tptp.id @t152 @t94))) % 0.44/0.64 (define @t157 () (or @t156 @t155 @t154 @t151 @t150 @t149)) % 0.44/0.64 (define @t158 () (@list @t94 @t152 @t153 @t147 @t148)) % 0.44/0.64 (define @t159 () (forall @t158 @t157)) % 0.44/0.64 (define @t160 () (@quantifiers_skolemize @t159 1)) % 0.44/0.64 (define @t161 () (@quantifiers_skolemize @t159 0)) % 0.44/0.64 (define @t162 () (@quantifiers_skolemize @t159 3)) % 0.44/0.64 (define @t163 () (@quantifiers_skolemize @t159 4)) % 0.44/0.64 (define @t164 () (@quantifiers_skolemize @t159 2)) % 0.44/0.64 (define @t165 () (or @t151 @t150 @t149)) % 0.44/0.64 (define @t166 () (or @t156 @t155 @t154)) % 0.44/0.64 (define @t167 () (or @t166 @t165)) % 0.44/0.64 (define @t168 () (forall @t158 @t167)) % 0.44/0.64 (define @t169 () (forall (@list @t152 @t153 @t147 @t148) @t167)) % 0.44/0.64 (define @t170 () (forall (@list @t147 @t148) @t165)) % 0.44/0.64 (define @t171 () (@var "BOUND_VARIABLE_8042" $$unsorted)) % 0.44/0.64 (define @t172 () (forall (@list @t152 @t153) @t166)) % 0.44/0.64 (define @t173 () (@var "BOUND_VARIABLE_8030" $$unsorted)) % 0.44/0.64 (define @t174 () (or @t172 @t170)) % 0.44/0.64 (define @t175 () (not (tptp.r2 @t171 @t71))) % 0.44/0.64 (define @t176 () (not (tptp.r1 @t171))) % 0.44/0.64 (define @t177 () (or @t103 @t176 @t175)) % 0.44/0.64 (define @t178 () (@list @t71 @t171)) % 0.44/0.64 (define @t179 () (not (tptp.r2 @t173 @t70))) % 0.44/0.64 (define @t180 () (not (tptp.r1 @t173))) % 0.44/0.64 (define @t181 () (or @t105 @t180 @t179)) % 0.44/0.64 (define @t182 () (@list @t70 @t173)) % 0.44/0.64 (define @t183 () (or @t176 @t175)) % 0.44/0.64 (define @t184 () (or @t183 @t103)) % 0.44/0.64 (define @t185 () (forall @t178 @t184)) % 0.44/0.64 (define @t186 () (@list @t171)) % 0.44/0.64 (define @t187 () (forall @t186 @t184)) % 0.44/0.64 (define @t188 () (forall @t186 @t183)) % 0.44/0.64 (define @t189 () (or @t188 @t103)) % 0.44/0.64 (define @t190 () (or @t180 @t179)) % 0.44/0.64 (define @t191 () (or @t190 @t105)) % 0.44/0.64 (define @t192 () (forall @t182 @t191)) % 0.44/0.64 (define @t193 () (@list @t173)) % 0.44/0.64 (define @t194 () (forall @t193 @t191)) % 0.44/0.64 (define @t195 () (forall @t193 @t190)) % 0.44/0.64 (define @t196 () (or @t195 @t105)) % 0.44/0.64 (define @t197 () (tptp.r2 @t164 @t160)) % 0.44/0.64 (define @t198 () (tptp.r2 @t163 @t162)) % 0.44/0.64 (define @t199 () (not @t198)) % 0.44/0.64 (define @t200 () (tptp.r1 @t163)) % 0.44/0.64 (define @t201 () (not @t200)) % 0.44/0.64 (define @t202 () (tptp.r2 @t162 @t161)) % 0.44/0.64 (define @t203 () (not @t202)) % 0.44/0.64 (define @t204 () (not @t197)) % 0.44/0.64 (define @t205 () (tptp.r1 @t164)) % 0.44/0.64 (define @t206 () (not @t205)) % 0.44/0.64 (define @t207 () (tptp.id @t160 @t161)) % 0.44/0.64 (define @t208 () (not @t207)) % 0.44/0.64 (define @t209 () (or @t208 @t206 @t204 @t203 @t201 @t199)) % 0.44/0.64 (define @t210 () (@list true)) % 0.44/0.64 (define @t211 () (@list @t209)) % 0.44/0.64 (define @t212 () (tptp.r2 @t163 @t160)) % 0.44/0.64 (define @t213 () (not @t212)) % 0.44/0.64 (define @t214 () (and @t204 @t213)) % 0.44/0.64 (define @t215 () (not @t214)) % 0.44/0.64 (define @t216 () (@list false)) % 0.44/0.64 (define @t217 () (forall @t8 (not @t7))) % 0.44/0.64 (define @t218 () (@quantifiers_skolemize @t217 0)) % 0.44/0.64 (define @t219 () (not @t217)) % 0.44/0.64 (define @t220 () (tptp.id @t2 @t218)) % 0.44/0.64 (define @t221 () (forall @t6 (or (and @t220 @t4) (and @t5 (not @t220))))) % 0.44/0.64 (define @t222 () (not (not @t221))) % 0.44/0.64 (define @t223 () (tptp.id @t163 @t218)) % 0.44/0.64 (define @t224 () (not @t223)) % 0.44/0.64 (define @t225 () (and @t201 @t224)) % 0.44/0.64 (define @t226 () (not @t225)) % 0.44/0.64 (define @t227 () (and @t223 @t200)) % 0.44/0.64 (define @t228 () (or @t227 @t225)) % 0.44/0.64 (define @t229 () (@list true false)) % 0.44/0.64 (define @t230 () (tptp.id @t218 @t163)) % 0.44/0.64 (define @t231 () (or @t224 @t230)) % 0.44/0.64 (define @t232 () (@list false false)) % 0.44/0.64 (define @t233 () (tptp.id @t164 @t218)) % 0.44/0.64 (define @t234 () (not @t233)) % 0.44/0.64 (define @t235 () (and @t206 @t234)) % 0.44/0.64 (define @t236 () (not @t235)) % 0.44/0.64 (define @t237 () (and @t233 @t205)) % 0.44/0.64 (define @t238 () (or @t237 @t235)) % 0.44/0.64 (define @t239 () (not @t230)) % 0.44/0.64 (define @t240 () (tptp.id @t164 @t163)) % 0.44/0.64 (define @t241 () (or @t234 @t240 @t239)) % 0.44/0.64 (define @t242 () (@list false false false)) % 0.44/0.64 (define @t243 () (tptp.id @t161 @t160)) % 0.44/0.64 (define @t244 () (or @t208 @t243)) % 0.44/0.64 (define @t245 () (not @t243)) % 0.44/0.64 (define @t246 () (tptp.id @t160 @t160)) % 0.44/0.64 (define @t247 () (or @t208 @t246 @t245)) % 0.44/0.64 (define @t248 () (and @t197 @t212)) % 0.44/0.64 (define @t249 () (not @t246)) % 0.44/0.64 (define @t250 () (not @t240)) % 0.44/0.64 (define @t251 () (or @t250 @t249 @t214 @t248)) % 0.44/0.64 (define @t252 () (tptp.id @t163 @t162)) % 0.44/0.64 (define @t253 () (or @t252 @t203 @t208 @t213)) % 0.44/0.64 (define @t254 () (not @t252)) % 0.44/0.64 (define @t255 () (or @t199 @t254 @t201)) % 0.44/0.64 (define @t256 () (not @t255)) % 0.44/0.64 (define @t257 () (forall @t117 @t114)) % 0.44/0.64 (assume @p1 @t9) % 0.44/0.64 (assume @p2 (forall (@list @t13) (exists (@list @t10) (forall (@list @t11) (or (and @t12 @t14) (and (not @t14) (not @t12))))))) % 0.44/0.64 (assume @p3 (forall (@list @t19 @t18) (exists (@list @t15) (forall (@list @t16) (or (and @t17 @t20) (and (not @t20) (not @t17))))))) % 0.44/0.64 (assume @p4 (forall (@list @t25 @t24) (exists (@list @t21) (forall (@list @t22) (or (and @t23 @t26) (and (not @t26) (not @t23))))))) % 0.44/0.64 (assume @p5 (forall (@list @t27) (tptp.id @t27 @t27))) % 0.44/0.64 (assume @p6 (forall (@list @t28 @t29) (or (not (tptp.id @t28 @t29)) (tptp.id @t29 @t28)))) % 0.44/0.64 (assume @p7 (forall (@list @t32 @t31 @t30) (or (not (tptp.id @t32 @t31)) (tptp.id @t32 @t30) (not (tptp.id @t31 @t30))))) % 0.44/0.64 (assume @p8 (forall (@list @t35 @t33) (or (not (tptp.id @t35 @t33)) (and (not @t36) (not @t34)) (and @t36 @t34)))) % 0.44/0.64 (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)))) % 0.44/0.64 (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)))) % 0.44/0.64 (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)))) % 0.44/0.64 (assume @p12 (forall (@list @t61 @t60) (exists @t66 (and (exists @t65 (and (tptp.id @t63 @t62) (exists (@list @t64) (and (tptp.r2 @t60 @t64) (tptp.r3 @t61 @t64 @t63))))) (exists (@list @t59) (and (tptp.r2 @t59 @t62) (tptp.r3 @t61 @t60 @t59))))))) % 0.44/0.64 (assume @p13 (forall (@list @t69 @t68) (exists @t74 (and (exists @t73 (and (tptp.id @t71 @t70) (exists (@list @t72) (and (tptp.r2 @t68 @t72) (tptp.r4 @t69 @t72 @t71))))) (exists (@list @t67) (and (tptp.r3 @t67 @t69 @t70) (tptp.r4 @t69 @t68 @t67))))))) % 0.44/0.64 (assume @p14 @t85) % 0.44/0.64 (assume @p15 (forall (@list @t88) (exists (@list @t86) (and (tptp.id @t86 @t88) (exists (@list @t87) (and (tptp.r1 @t87) (tptp.r3 @t88 @t87 @t86))))))) % 0.44/0.64 (assume @p16 (forall (@list @t92) (exists (@list @t90) (and (exists (@list @t91) (and (tptp.r1 @t91) (tptp.r4 @t92 @t91 @t90))) (exists (@list @t89) (and (tptp.id @t90 @t89) (tptp.r1 @t89))))))) % 0.44/0.64 (assume @p17 (forall (@list @t95) (or (exists (@list @t96) (and (tptp.id @t95 @t96) (tptp.r1 @t96))) (exists (@list @t94 @t93) (and (tptp.id @t95 @t93) (tptp.r2 @t94 @t93)))))) % 0.44/0.64 (assume @p18 @t102) % 0.44/0.64 (assume @p19 @t110) % 0.44/0.64 (assume @p20 true) % 0.44/0.64 (step @p21 :rule aci_norm :args ((= @t116 @t114))) % 0.44/0.64 (step @p22 :rule cong :premises (@p21) :args (@t118)) % 0.44/0.64 (step @p23 :rule quant-merge-prenex :args ((= (forall @t101 @t120) @t118))) % 0.44/0.64 (step @p24 :rule refl :args (@t99)) % 0.44/0.64 (step @p25 :rule alpha_equiv :args (@t121 (@list @t111) (@list @t100))) % 0.44/0.64 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t122)) % 0.44/0.64 (step @p27 :rule quant-miniscope-or :args ((= @t120 @t122))) % 0.44/0.64 (step @p28 :rule trans :premises (@p27 @p26)) % 0.44/0.64 (step @p29 :rule symm :premises (@p28)) % 0.44/0.64 (step @p30 :rule cong :premises (@p29) :args (@t102)) % 0.44/0.64 (step @p31 :rule trans :premises (@p30 @p23)) % 0.44/0.64 (step @p32 :rule trans :premises (@p31 @p22)) % 0.44/0.64 (step @p33 :rule eq_resolve :premises (@p18 @p32)) % 0.44/0.64 (step @p34 :rule aci_norm :args ((= @t129 (or @t77 @t127 @t126 @t124)))) % 0.44/0.64 (step @p35 :rule cong :premises (@p34) :args (@t130)) % 0.44/0.64 (step @p36 :rule quant-merge-prenex :args ((= (forall @t84 @t132) @t130))) % 0.44/0.64 (step @p37 :rule refl :args (@t77)) % 0.44/0.64 (step @p38 :rule alpha_equiv :args (@t133 (@list @t125 @t123) (@list @t78 @t134))) % 0.44/0.64 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t135)) % 0.44/0.64 (step @p40 :rule quant-miniscope-or :args ((= @t132 @t135))) % 0.44/0.64 (step @p41 :rule trans :premises (@p40 @p39)) % 0.44/0.64 (step @p42 :rule symm :premises (@p41)) % 0.44/0.64 (step @p43 :rule cong :premises (@p42) :args ((forall @t84 (or (forall @t139 @t138) @t77)))) % 0.44/0.64 (step @p44 :rule trans :premises (@p43 @p36)) % 0.44/0.64 (step @p45 :rule trans :premises (@p44 @p35)) % 0.44/0.64 (step @p46 :rule refl :args (@t77)) % 0.44/0.64 (step @p47 :rule aci_norm :args ((= @t141 @t138))) % 0.44/0.64 (step @p48 :rule cong :premises (@p47) :args (@t142)) % 0.44/0.64 (step @p49 :rule quant-merge-prenex :args ((= (forall @t81 @t144) @t142))) % 0.44/0.64 (step @p50 :rule refl :args (@t79)) % 0.44/0.64 (step @p51 :rule alpha_equiv :args (@t145 (@list @t134) (@list @t80))) % 0.44/0.64 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t146)) % 0.44/0.64 (step @p53 :rule quant-miniscope-or :args ((= @t144 @t146))) % 0.44/0.64 (step @p54 :rule trans :premises (@p53 @p52)) % 0.44/0.64 (step @p55 :rule symm :premises (@p54)) % 0.44/0.64 (step @p56 :rule cong :premises (@p55) :args (@t82)) % 0.44/0.64 (step @p57 :rule trans :premises (@p56 @p49)) % 0.44/0.64 (step @p58 :rule trans :premises (@p57 @p48)) % 0.44/0.64 (step @p59 :rule nary_cong :premises (@p58 @p46) :args (@t83)) % 0.44/0.64 (step @p60 :rule cong :premises (@p59) :args (@t85)) % 0.44/0.64 (step @p61 :rule trans :premises (@p60 @p45)) % 0.44/0.64 (step @p62 :rule eq_resolve :premises (@p14 @p61)) % 0.44/0.64 (step @p63 :rule instantiate :premises (@p62) :args ((@list @t163 @t162 @t161 @t160))) % 0.44/0.64 (step @p64 :rule instantiate :premises (@p9) :args ((@list @t164 @t160 @t163 @t160))) % 0.44/0.64 (step @p65 :rule aci_norm :args ((= @t167 @t157))) % 0.44/0.64 (step @p66 :rule cong :premises (@p65) :args (@t168)) % 0.44/0.64 (step @p67 :rule quant-merge-prenex :args ((= (forall @t108 @t169) @t168))) % 0.44/0.64 (step @p68 :rule alpha_equiv :args (@t170 (@list @t147 @t148) (@list @t71 @t171))) % 0.44/0.64 (step @p69 :rule alpha_equiv :args (@t172 (@list @t152 @t153) (@list @t70 @t173))) % 0.44/0.64 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t174)) % 0.44/0.64 (step @p71 :rule quant-miniscope-or :args ((= @t169 @t174))) % 0.44/0.64 (step @p72 :rule trans :premises (@p71 @p70)) % 0.44/0.64 (step @p73 :rule symm :premises (@p72)) % 0.44/0.64 (step @p74 :rule cong :premises (@p73) :args ((forall @t108 (or (forall @t182 @t181) (forall @t178 @t177))))) % 0.44/0.64 (step @p75 :rule trans :premises (@p74 @p67)) % 0.44/0.64 (step @p76 :rule trans :premises (@p75 @p66)) % 0.44/0.64 (step @p77 :rule aci_norm :args ((= @t184 @t177))) % 0.44/0.64 (step @p78 :rule cong :premises (@p77) :args (@t185)) % 0.44/0.64 (step @p79 :rule quant-merge-prenex :args ((= (forall @t73 @t187) @t185))) % 0.44/0.64 (step @p80 :rule refl :args (@t103)) % 0.44/0.64 (step @p81 :rule alpha_equiv :args (@t188 (@list @t171) (@list @t63))) % 0.44/0.64 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t189)) % 0.44/0.64 (step @p83 :rule quant-miniscope-or :args ((= @t187 @t189))) % 0.44/0.64 (step @p84 :rule trans :premises (@p83 @p82)) % 0.44/0.64 (step @p85 :rule symm :premises (@p84)) % 0.44/0.64 (step @p86 :rule cong :premises (@p85) :args (@t104)) % 0.44/0.64 (step @p87 :rule trans :premises (@p86 @p79)) % 0.44/0.64 (step @p88 :rule trans :premises (@p87 @p78)) % 0.44/0.64 (step @p89 :rule aci_norm :args ((= @t191 @t181))) % 0.44/0.64 (step @p90 :rule cong :premises (@p89) :args (@t192)) % 0.44/0.64 (step @p91 :rule quant-merge-prenex :args ((= (forall @t74 @t194) @t192))) % 0.44/0.64 (step @p92 :rule refl :args (@t105)) % 0.44/0.64 (step @p93 :rule alpha_equiv :args (@t195 (@list @t173) (@list @t62))) % 0.44/0.64 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t196)) % 0.44/0.64 (step @p95 :rule quant-miniscope-or :args ((= @t194 @t196))) % 0.44/0.64 (step @p96 :rule trans :premises (@p95 @p94)) % 0.44/0.64 (step @p97 :rule symm :premises (@p96)) % 0.44/0.64 (step @p98 :rule cong :premises (@p97) :args (@t106)) % 0.44/0.64 (step @p99 :rule trans :premises (@p98 @p91)) % 0.44/0.64 (step @p100 :rule trans :premises (@p99 @p90)) % 0.44/0.64 (step @p101 :rule nary_cong :premises (@p100 @p88) :args (@t107)) % 0.44/0.64 (step @p102 :rule cong :premises (@p101) :args (@t109)) % 0.44/0.64 (step @p103 :rule trans :premises (@p102 @p76)) % 0.44/0.64 (step @p104 :rule cong :premises (@p103) :args (@t110)) % 0.44/0.64 (step @p105 :rule eq_resolve :premises (@p19 @p104)) % 0.44/0.64 (step @p106 :rule skolemize :premises (@p105)) % 0.44/0.64 (step @p107 :rule bool-double-not-elim :args (@t197)) % 0.44/0.64 (step @p108 :rule refl :args (@t209)) % 0.44/0.64 (step @p109 :rule nary_cong :premises (@p108 @p107) :args ((or @t209 (not @t204)))) % 0.44/0.64 (step @p110 :rule cnf_or_neg :args (@t209 2)) % 0.44/0.64 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 0.44/0.64 (step @p112 :rule reordering :premises (@p111) :args ((or @t197 @t209))) % 0.44/0.64 (step @p113 :rule chain_m_resolution :premises (@p112 @p106) :args (@t197 @t210 @t211)) % 0.44/0.64 (step @p114 :rule cnf_and_pos :args (@t214 0)) % 0.44/0.64 (step @p115 :rule reordering :premises (@p114) :args ((or @t204 @t215))) % 0.44/0.64 (step @p116 :rule chain_m_resolution :premises (@p115 @p113) :args (@t215 @t216 (@list @t197))) % 0.44/0.64 (step @p117 :rule instantiate :premises (@p7) :args ((@list @t164 @t218 @t163))) % 0.44/0.64 (step @p118 :rule instantiate :premises (@p6) :args ((@list @t163 @t218))) % 0.44/0.64 (step @p119 :rule exists-elim :args ((= @t9 @t219))) % 0.44/0.64 (step @p120 :rule eq_resolve :premises (@p1 @p119)) % 0.44/0.64 (step @p121 :rule refl :args (@t221)) % 0.44/0.64 (step @p122 :rule bool-double-not-elim :args (@t217)) % 0.44/0.64 (step @p123 :rule nary_cong :premises (@p122 @p121) :args ((or (not @t219) @t221))) % 0.44/0.64 (step @p124 :rule bool-double-not-elim :args (@t221)) % 0.44/0.64 (step @p125 :rule refl :args (@t219)) % 0.44/0.64 (step @p126 :rule cong :premises (@p125 @p124) :args ((=> @t219 @t222))) % 0.44/0.64 (assume-push @p217 @t219) % 0.44/0.64 (step @p128 :rule skolemize :premises (@p120)) % 0.44/0.64 (step-pop @p218 :rule scope :premises (@p128)) % 0.44/0.64 (step @p129 :rule process_scope :premises (@p218) :args (@t222)) % 0.44/0.64 (step @p131 :rule eq_resolve :premises (@p129 @p126)) % 0.44/0.64 (step @p132 :rule implies_elim :premises (@p131)) % 0.44/0.64 (step @p133 :rule eq_resolve :premises (@p132 @p123)) % 0.44/0.64 (step @p134 :rule chain_m_resolution :premises (@p133 @p120) :args (@t221 @t210 (@list @t217))) % 0.44/0.64 (step @p135 :rule instantiate :premises (@p134) :args ((@list @t163))) % 0.44/0.64 (step @p136 :rule bool-double-not-elim :args (@t200)) % 0.44/0.64 (step @p137 :rule nary_cong :premises (@p108 @p136) :args ((or @t209 (not @t201)))) % 0.44/0.64 (step @p138 :rule cnf_or_neg :args (@t209 4)) % 0.44/0.64 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.44/0.64 (step @p140 :rule reordering :premises (@p139) :args ((or @t200 @t209))) % 0.44/0.64 (step @p141 :rule chain_m_resolution :premises (@p140 @p106) :args (@t200 @t210 @t211)) % 0.44/0.64 (step @p142 :rule cnf_and_pos :args (@t225 0)) % 0.44/0.64 (step @p143 :rule reordering :premises (@p142) :args ((or @t201 @t226))) % 0.44/0.64 (step @p144 :rule chain_m_resolution :premises (@p143 @p141) :args (@t226 @t216 (@list @t200))) % 0.44/0.64 (step @p145 :rule cnf_or_pos :args (@t228)) % 0.44/0.64 (step @p146 :rule reordering :premises (@p145) :args ((or @t227 @t225 (not @t228)))) % 0.44/0.64 (step @p147 :rule chain_m_resolution :premises (@p146 @p144 @p135) :args (@t227 @t229 (@list @t225 @t228))) % 0.44/0.64 (step @p148 :rule cnf_and_pos :args (@t227 0)) % 0.44/0.64 (step @p149 :rule reordering :premises (@p148) :args ((or @t223 (not @t227)))) % 0.44/0.64 (step @p150 :rule chain_m_resolution :premises (@p149 @p147) :args (@t223 @t216 (@list @t227))) % 0.44/0.64 (step @p151 :rule cnf_or_pos :args (@t231)) % 0.44/0.64 (step @p152 :rule reordering :premises (@p151) :args ((or @t224 @t230 (not @t231)))) % 0.44/0.64 (step @p153 :rule chain_m_resolution :premises (@p152 @p150 @p118) :args (@t230 @t232 (@list @t223 @t231))) % 0.44/0.64 (step @p154 :rule instantiate :premises (@p134) :args ((@list @t164))) % 0.44/0.64 (step @p155 :rule bool-double-not-elim :args (@t205)) % 0.44/0.64 (step @p156 :rule nary_cong :premises (@p108 @p155) :args ((or @t209 (not @t206)))) % 0.44/0.64 (step @p157 :rule cnf_or_neg :args (@t209 1)) % 0.44/0.64 (step @p158 :rule eq_resolve :premises (@p157 @p156)) % 0.44/0.64 (step @p159 :rule reordering :premises (@p158) :args ((or @t205 @t209))) % 0.44/0.64 (step @p160 :rule chain_m_resolution :premises (@p159 @p106) :args (@t205 @t210 @t211)) % 0.44/0.64 (step @p161 :rule cnf_and_pos :args (@t235 0)) % 0.44/0.64 (step @p162 :rule reordering :premises (@p161) :args ((or @t206 @t236))) % 0.44/0.64 (step @p163 :rule chain_m_resolution :premises (@p162 @p160) :args (@t236 @t216 (@list @t205))) % 0.44/0.64 (step @p164 :rule cnf_or_pos :args (@t238)) % 0.44/0.64 (step @p165 :rule reordering :premises (@p164) :args ((or @t237 @t235 (not @t238)))) % 0.44/0.64 (step @p166 :rule chain_m_resolution :premises (@p165 @p163 @p154) :args (@t237 @t229 (@list @t235 @t238))) % 0.44/0.64 (step @p167 :rule cnf_and_pos :args (@t237 0)) % 0.44/0.64 (step @p168 :rule reordering :premises (@p167) :args ((or @t233 (not @t237)))) % 0.44/0.64 (step @p169 :rule chain_m_resolution :premises (@p168 @p166) :args (@t233 @t216 (@list @t237))) % 0.44/0.64 (step @p170 :rule cnf_or_pos :args (@t241)) % 0.44/0.64 (step @p171 :rule reordering :premises (@p170) :args ((or @t234 @t239 @t240 (not @t241)))) % 0.44/0.64 (step @p172 :rule chain_m_resolution :premises (@p171 @p169 @p153 @p117) :args (@t240 @t242 (@list @t233 @t230 @t241))) % 0.44/0.64 (step @p173 :rule instantiate :premises (@p7) :args ((@list @t160 @t161 @t160))) % 0.44/0.64 (step @p174 :rule instantiate :premises (@p6) :args ((@list @t160 @t161))) % 0.44/0.64 (step @p175 :rule bool-double-not-elim :args (@t207)) % 0.44/0.64 (step @p176 :rule nary_cong :premises (@p108 @p175) :args ((or @t209 (not @t208)))) % 0.44/0.64 (step @p177 :rule cnf_or_neg :args (@t209 0)) % 0.44/0.64 (step @p178 :rule eq_resolve :premises (@p177 @p176)) % 0.44/0.64 (step @p179 :rule reordering :premises (@p178) :args ((or @t207 @t209))) % 0.44/0.64 (step @p180 :rule chain_m_resolution :premises (@p179 @p106) :args (@t207 @t210 @t211)) % 0.44/0.64 (step @p181 :rule cnf_or_pos :args (@t244)) % 0.44/0.64 (step @p182 :rule reordering :premises (@p181) :args ((or @t208 @t243 (not @t244)))) % 0.44/0.64 (step @p183 :rule chain_m_resolution :premises (@p182 @p180 @p174) :args (@t243 @t232 (@list @t207 @t244))) % 0.44/0.64 (step @p184 :rule cnf_or_pos :args (@t247)) % 0.44/0.64 (step @p185 :rule reordering :premises (@p184) :args ((or @t208 @t245 @t246 (not @t247)))) % 0.44/0.64 (step @p186 :rule chain_m_resolution :premises (@p185 @p180 @p183 @p173) :args (@t246 @t242 (@list @t207 @t243 @t247))) % 0.44/0.64 (step @p187 :rule cnf_or_pos :args (@t251)) % 0.44/0.64 (step @p188 :rule reordering :premises (@p187) :args ((or @t249 @t250 @t214 @t248 (not @t251)))) % 0.44/0.64 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p172 @p116 @p64) :args (@t248 (@list false false true false) (@list @t246 @t240 @t214 @t251))) % 0.44/0.64 (step @p190 :rule cnf_and_pos :args (@t248 1)) % 0.44/0.64 (step @p191 :rule reordering :premises (@p190) :args ((or @t212 (not @t248)))) % 0.44/0.64 (step @p192 :rule chain_m_resolution :premises (@p191 @p189) :args (@t212 @t216 (@list @t248))) % 0.44/0.64 (step @p193 :rule bool-double-not-elim :args (@t202)) % 0.44/0.64 (step @p194 :rule nary_cong :premises (@p108 @p193) :args ((or @t209 (not @t203)))) % 0.44/0.64 (step @p195 :rule cnf_or_neg :args (@t209 3)) % 0.44/0.64 (step @p196 :rule eq_resolve :premises (@p195 @p194)) % 0.44/0.64 (step @p197 :rule reordering :premises (@p196) :args ((or @t202 @t209))) % 0.44/0.64 (step @p198 :rule chain_m_resolution :premises (@p197 @p106) :args (@t202 @t210 @t211)) % 0.44/0.64 (step @p199 :rule cnf_or_pos :args (@t253)) % 0.44/0.64 (step @p200 :rule reordering :premises (@p199) :args ((or @t208 @t203 @t252 @t213 (not @t253)))) % 0.44/0.64 (step @p201 :rule chain_m_resolution :premises (@p200 @p180 @p198 @p192 @p63) :args (@t252 (@list false false false false) (@list @t207 @t202 @t212 @t253))) % 0.44/0.64 (step @p202 :rule bool-double-not-elim :args (@t198)) % 0.44/0.64 (step @p203 :rule nary_cong :premises (@p108 @p202) :args ((or @t209 (not @t199)))) % 0.44/0.64 (step @p204 :rule cnf_or_neg :args (@t209 5)) % 0.44/0.64 (step @p205 :rule eq_resolve :premises (@p204 @p203)) % 0.44/0.64 (step @p206 :rule reordering :premises (@p205) :args ((or @t198 @t209))) % 0.44/0.64 (step @p207 :rule chain_m_resolution :premises (@p206 @p106) :args (@t198 @t210 @t211)) % 0.44/0.64 (step @p208 :rule cnf_or_pos :args (@t255)) % 0.44/0.64 (step @p209 :rule reordering :premises (@p208) :args ((or @t201 @t199 @t254 @t256))) % 0.44/0.64 (step @p210 :rule chain_m_resolution :premises (@p209 @p141 @p207 @p201) :args (@t256 @t242 (@list @t200 @t198 @t252))) % 0.44/0.64 (assume-push @p219 @t257) % 0.44/0.64 (step @p212 :rule instantiate :premises (@p33) :args ((@list @t163 @t162 @t163))) % 0.44/0.64 (step-pop @p220 :rule scope :premises (@p212)) % 0.44/0.64 (step @p213 :rule process_scope :premises (@p220) :args (@t255)) % 0.44/0.64 (step @p215 :rule implies_elim :premises (@p213)) % 0.44/0.64 (step @p216 false :rule chain_m_resolution :premises (@p215 @p210 @p33) :args (false @t229 (@list @t255 @t257))) % 0.44/0.64 ) % 0.44/0.64 % SZS output end Proof % 0.44/0.64 % cvc5 exiting %------------------------------------------------------------------------------