%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN066+2 : TPTP v9.2.1. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n028.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 08:42:52 AM UTC 2026 % Result : Theorem 0.36s 0.62s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN066+2 : TPTP v9.2.1. Released v7.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n028.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 12:38:50 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.62 % SZS status Theorem % 0.36/0.62 % SZS output start Proof % 0.36/0.62 ( % 0.36/0.62 (declare-sort $$unsorted 0) % 0.36/0.62 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.r1 (-> $$unsorted Bool)) % 0.36/0.62 (define @t1 () (@var "Y24" $$unsorted)) % 0.36/0.62 (define @t2 () (@var "X19" $$unsorted)) % 0.36/0.62 (define @t3 () (= @t2 @t1)) % 0.36/0.62 (define @t4 () (tptp.r1 @t2)) % 0.36/0.62 (define @t5 () (and @t4 @t3)) % 0.36/0.62 (define @t6 () (not @t3)) % 0.36/0.62 (define @t7 () (not @t4)) % 0.36/0.62 (define @t8 () (and @t7 @t6)) % 0.36/0.62 (define @t9 () (or @t8 @t5)) % 0.36/0.62 (define @t10 () (@list @t2)) % 0.36/0.62 (define @t11 () (forall @t10 @t9)) % 0.36/0.62 (define @t12 () (@list @t1)) % 0.36/0.62 (define @t13 () (exists @t12 @t11)) % 0.36/0.62 (define @t14 () (@var "Y21" $$unsorted)) % 0.36/0.62 (define @t15 () (@var "X12" $$unsorted)) % 0.36/0.62 (define @t16 () (= @t15 @t14)) % 0.36/0.62 (define @t17 () (@var "X11" $$unsorted)) % 0.36/0.62 (define @t18 () (tptp.r2 @t17 @t15)) % 0.36/0.62 (define @t19 () (@var "Y22" $$unsorted)) % 0.36/0.62 (define @t20 () (@var "X15" $$unsorted)) % 0.36/0.62 (define @t21 () (= @t20 @t19)) % 0.36/0.62 (define @t22 () (@var "X14" $$unsorted)) % 0.36/0.62 (define @t23 () (@var "X13" $$unsorted)) % 0.36/0.62 (define @t24 () (tptp.r3 @t23 @t22 @t20)) % 0.36/0.62 (define @t25 () (@var "Y23" $$unsorted)) % 0.36/0.62 (define @t26 () (@var "X18" $$unsorted)) % 0.36/0.62 (define @t27 () (= @t26 @t25)) % 0.36/0.62 (define @t28 () (@var "X17" $$unsorted)) % 0.36/0.62 (define @t29 () (@var "X16" $$unsorted)) % 0.36/0.62 (define @t30 () (tptp.r4 @t29 @t28 @t26)) % 0.36/0.62 (define @t31 () (@var "Y7" $$unsorted)) % 0.36/0.62 (define @t32 () (@var "X8" $$unsorted)) % 0.36/0.62 (define @t33 () (@var "X1" $$unsorted)) % 0.36/0.62 (define @t34 () (@var "Y4" $$unsorted)) % 0.36/0.62 (define @t35 () (@var "Y5" $$unsorted)) % 0.36/0.62 (define @t36 () (@var "Y15" $$unsorted)) % 0.36/0.62 (define @t37 () (@list @t35)) % 0.36/0.62 (define @t38 () (@list @t34)) % 0.36/0.62 (define @t39 () (@var "Y6" $$unsorted)) % 0.36/0.62 (define @t40 () (@var "X9" $$unsorted)) % 0.36/0.62 (define @t41 () (@var "X2" $$unsorted)) % 0.36/0.62 (define @t42 () (tptp.r4 @t41 @t40 @t39)) % 0.36/0.62 (define @t43 () (@var "Y2" $$unsorted)) % 0.36/0.62 (define @t44 () (tptp.r3 @t39 @t41 @t43)) % 0.36/0.62 (define @t45 () (and @t44 @t42)) % 0.36/0.62 (define @t46 () (@list @t39)) % 0.36/0.62 (define @t47 () (exists @t46 @t45)) % 0.36/0.62 (define @t48 () (@var "Y3" $$unsorted)) % 0.36/0.62 (define @t49 () (= @t48 @t43)) % 0.36/0.62 (define @t50 () (@var "Y14" $$unsorted)) % 0.36/0.62 (define @t51 () (tptp.r4 @t41 @t50 @t48)) % 0.36/0.62 (define @t52 () (tptp.r2 @t40 @t50)) % 0.36/0.62 (define @t53 () (and @t52 @t51)) % 0.36/0.62 (define @t54 () (@list @t50)) % 0.36/0.62 (define @t55 () (exists @t54 @t53)) % 0.36/0.62 (define @t56 () (and @t55 @t49)) % 0.36/0.62 (define @t57 () (@list @t48)) % 0.36/0.62 (define @t58 () (exists @t57 @t56)) % 0.36/0.62 (define @t59 () (and @t58 @t47)) % 0.36/0.62 (define @t60 () (@list @t43)) % 0.36/0.62 (define @t61 () (exists @t60 @t59)) % 0.36/0.62 (define @t62 () (forall (@list @t41 @t40) @t61)) % 0.36/0.62 (define @t63 () (@var "X10" $$unsorted)) % 0.36/0.62 (define @t64 () (@var "X3" $$unsorted)) % 0.36/0.62 (define @t65 () (= @t64 @t63)) % 0.36/0.62 (define @t66 () (@var "Y12" $$unsorted)) % 0.36/0.62 (define @t67 () (not (tptp.r2 @t63 @t66))) % 0.36/0.62 (define @t68 () (@var "Y13" $$unsorted)) % 0.36/0.62 (define @t69 () (not (= @t68 @t66))) % 0.36/0.62 (define @t70 () (not (tptp.r2 @t64 @t68))) % 0.36/0.62 (define @t71 () (or @t70 @t69)) % 0.36/0.62 (define @t72 () (@list @t68)) % 0.36/0.62 (define @t73 () (forall @t72 @t71)) % 0.36/0.62 (define @t74 () (or @t73 @t67)) % 0.36/0.62 (define @t75 () (@list @t66)) % 0.36/0.62 (define @t76 () (forall @t75 @t74)) % 0.36/0.62 (define @t77 () (or @t76 @t65)) % 0.36/0.62 (define @t78 () (@list @t64 @t63)) % 0.36/0.62 (define @t79 () (forall @t78 @t77)) % 0.36/0.62 (define @t80 () (@var "X4" $$unsorted)) % 0.36/0.62 (define @t81 () (@var "Y9" $$unsorted)) % 0.36/0.62 (define @t82 () (@var "Y16" $$unsorted)) % 0.36/0.62 (define @t83 () (@var "Y18" $$unsorted)) % 0.36/0.62 (define @t84 () (@var "Y8" $$unsorted)) % 0.36/0.62 (define @t85 () (@var "Y17" $$unsorted)) % 0.36/0.62 (define @t86 () (@var "X5" $$unsorted)) % 0.36/0.62 (define @t87 () (@var "Y11" $$unsorted)) % 0.36/0.62 (define @t88 () (@var "X6" $$unsorted)) % 0.36/0.62 (define @t89 () (@var "Y1" $$unsorted)) % 0.36/0.62 (define @t90 () (@var "Y19" $$unsorted)) % 0.36/0.62 (define @t91 () (@var "Y10" $$unsorted)) % 0.36/0.62 (define @t92 () (@var "X7" $$unsorted)) % 0.36/0.62 (define @t93 () (not (tptp.r2 @t92 @t91))) % 0.36/0.62 (define @t94 () (@var "Y20" $$unsorted)) % 0.36/0.62 (define @t95 () (not (= @t94 @t91))) % 0.36/0.62 (define @t96 () (not (tptp.r1 @t94))) % 0.36/0.62 (define @t97 () (or @t96 @t95)) % 0.36/0.62 (define @t98 () (@list @t94)) % 0.36/0.62 (define @t99 () (forall @t98 @t97)) % 0.36/0.62 (define @t100 () (or @t99 @t93)) % 0.36/0.62 (define @t101 () (forall (@list @t92 @t91) @t100)) % 0.36/0.62 (define @t102 () (not (= @t89 @t35))) % 0.36/0.62 (define @t103 () (not (tptp.r1 @t35))) % 0.36/0.62 (define @t104 () (or @t103 @t102)) % 0.36/0.62 (define @t105 () (forall @t37 @t104)) % 0.36/0.62 (define @t106 () (not (= @t89 @t43))) % 0.36/0.62 (define @t107 () (not (tptp.r2 @t48 @t43))) % 0.36/0.62 (define @t108 () (forall @t57 (or (forall @t38 (or (not (tptp.r1 @t34)) (not (tptp.r2 @t34 @t48)))) @t107))) % 0.36/0.62 (define @t109 () (or @t108 @t106)) % 0.36/0.62 (define @t110 () (forall @t60 @t109)) % 0.36/0.62 (define @t111 () (and @t110 @t105)) % 0.36/0.62 (define @t112 () (@list @t89)) % 0.36/0.62 (define @t113 () (exists @t112 @t111)) % 0.36/0.62 (define @t114 () (not @t113)) % 0.36/0.62 (define @t115 () (not (tptp.r1 @t91))) % 0.36/0.62 (define @t116 () (not (= @t91 @t91))) % 0.36/0.62 (define @t117 () (or @t115 @t116)) % 0.36/0.62 (define @t118 () (not (= @t91 @t94))) % 0.36/0.62 (define @t119 () (or @t118 @t96 @t118)) % 0.36/0.62 (define @t120 () (or @t96 @t118)) % 0.36/0.62 (define @t121 () (tptp.r1 @t1)) % 0.36/0.62 (define @t122 () (@var "BOUND_VARIABLE_7646" $$unsorted)) % 0.36/0.62 (define @t123 () (tptp.r1 @t122)) % 0.36/0.62 (define @t124 () (not @t123)) % 0.36/0.62 (define @t125 () (@list @t122)) % 0.36/0.62 (define @t126 () (forall @t125 (or @t124 (and @t123 (= @t1 @t122))))) % 0.36/0.62 (define @t127 () (forall @t12 (or (not @t126) (not @t121)))) % 0.36/0.62 (define @t128 () (@quantifiers_skolemize @t127 0)) % 0.36/0.62 (define @t129 () (@list @t128 @t128)) % 0.36/0.62 (define @t130 () (and @t126 @t121)) % 0.36/0.62 (define @t131 () (forall @t12 (not @t130))) % 0.36/0.62 (define @t132 () (not @t131)) % 0.36/0.62 (define @t133 () (= @t1 @t1)) % 0.36/0.62 (define @t134 () (and @t121 @t133)) % 0.36/0.62 (define @t135 () (not @t133)) % 0.36/0.62 (define @t136 () (or @t135 @t134)) % 0.36/0.62 (define @t137 () (@var "BOUND_VARIABLE_7655" $$unsorted)) % 0.36/0.62 (define @t138 () (= @t1 @t137)) % 0.36/0.62 (define @t139 () (and (tptp.r1 @t137) @t138)) % 0.36/0.62 (define @t140 () (not @t138)) % 0.36/0.62 (define @t141 () (@list @t137)) % 0.36/0.62 (define @t142 () (or @t140 @t140 @t139)) % 0.36/0.62 (define @t143 () (or @t140 @t139)) % 0.36/0.62 (define @t144 () (forall @t141 @t143)) % 0.36/0.62 (define @t145 () (= @t1 @t2)) % 0.36/0.62 (define @t146 () (and @t4 @t145)) % 0.36/0.62 (define @t147 () (not @t145)) % 0.36/0.62 (define @t148 () (or @t147 @t146)) % 0.36/0.62 (define @t149 () (forall @t10 @t148)) % 0.36/0.62 (define @t150 () (@list @t2)) % 0.36/0.62 (define @t151 () (or @t7 @t146)) % 0.36/0.62 (define @t152 () (forall @t10 @t151)) % 0.36/0.62 (define @t153 () (and @t152 @t149)) % 0.36/0.62 (define @t154 () (tptp.r1 @t128)) % 0.36/0.62 (define @t155 () (not @t154)) % 0.36/0.62 (define @t156 () (forall @t125 (or @t124 (and @t123 (= @t122 @t128))))) % 0.36/0.62 (define @t157 () (not @t156)) % 0.36/0.62 (define @t158 () (or @t157 @t155)) % 0.36/0.62 (define @t159 () (not @t158)) % 0.36/0.62 (define @t160 () (not @t127)) % 0.36/0.62 (define @t161 () (and @t123 (= @t128 @t122))) % 0.36/0.62 (define @t162 () (or @t124 @t161)) % 0.36/0.62 (define @t163 () (forall @t125 @t162)) % 0.36/0.62 (define @t164 () (not @t163)) % 0.36/0.62 (define @t165 () (or @t164 @t155)) % 0.36/0.62 (define @t166 () (not @t165)) % 0.36/0.62 (define @t167 () (@list true)) % 0.36/0.62 (define @t168 () (@list @t158)) % 0.36/0.62 (define @t169 () (not (tptp.r2 @t128 @t128))) % 0.36/0.62 (define @t170 () (or @t155 @t169)) % 0.36/0.62 (define @t171 () (@list false false)) % 0.36/0.62 (define @t172 () (@var "BOUND_VARIABLE_7995" $$unsorted)) % 0.36/0.62 (define @t173 () (not (tptp.r2 @t63 @t172))) % 0.36/0.62 (define @t174 () (not (tptp.r2 @t64 @t172))) % 0.36/0.62 (define @t175 () (or @t65 @t174 @t173)) % 0.36/0.62 (define @t176 () (or @t174 @t173)) % 0.36/0.62 (define @t177 () (or @t176 @t65)) % 0.36/0.62 (define @t178 () (@list @t64 @t63 @t172)) % 0.36/0.62 (define @t179 () (forall @t178 @t177)) % 0.36/0.62 (define @t180 () (@list @t172)) % 0.36/0.62 (define @t181 () (forall @t180 @t177)) % 0.36/0.62 (define @t182 () (forall @t180 @t176)) % 0.36/0.62 (define @t183 () (or @t182 @t65)) % 0.36/0.62 (define @t184 () (not (tptp.r2 @t64 @t66))) % 0.36/0.62 (define @t185 () (not (= @t66 @t66))) % 0.36/0.62 (define @t186 () (or @t184 @t185)) % 0.36/0.62 (define @t187 () (not (= @t66 @t68))) % 0.36/0.62 (define @t188 () (or @t187 @t70 @t187)) % 0.36/0.62 (define @t189 () (or @t70 @t187)) % 0.36/0.62 (define @t190 () (@var "BOUND_VARIABLE_7966" $$unsorted)) % 0.36/0.62 (define @t191 () (@var "BOUND_VARIABLE_7959" $$unsorted)) % 0.36/0.62 (define @t192 () (@list @t43 @t191 @t190)) % 0.36/0.62 (define @t193 () (forall @t192 (or (not (tptp.r2 @t128 @t191)) (not (tptp.r4 @t128 @t191 @t43)) (not (tptp.r3 @t190 @t128 @t43)) (not (tptp.r4 @t128 @t128 @t190))))) % 0.36/0.62 (define @t194 () (@quantifiers_skolemize @t193 1)) % 0.36/0.62 (define @t195 () (tptp.r2 @t128 @t194)) % 0.36/0.62 (define @t196 () (not @t195)) % 0.36/0.62 (define @t197 () (@var "BOUND_VARIABLE_8154" $$unsorted)) % 0.36/0.62 (define @t198 () (@var "BOUND_VARIABLE_8156" $$unsorted)) % 0.36/0.62 (define @t199 () (not (tptp.r2 @t198 @t197))) % 0.36/0.62 (define @t200 () (not (tptp.r1 @t198))) % 0.36/0.62 (define @t201 () (@list @t197 @t198)) % 0.36/0.62 (define @t202 () (forall @t201 (or (not (tptp.r2 @t197 @t194)) @t200 @t199))) % 0.36/0.62 (define @t203 () (@quantifiers_skolemize @t202 0)) % 0.36/0.62 (define @t204 () (tptp.r2 @t203 @t194)) % 0.36/0.62 (define @t205 () (not @t204)) % 0.36/0.62 (define @t206 () (or (= @t203 @t128) @t205 @t196)) % 0.36/0.62 (define @t207 () (forall @t178 @t175)) % 0.36/0.62 (define @t208 () (= @t128 @t203)) % 0.36/0.62 (define @t209 () (or @t208 @t205 @t196)) % 0.36/0.62 (define @t210 () (@list false)) % 0.36/0.62 (define @t211 () (tptp.r1 @t89)) % 0.36/0.62 (define @t212 () (not (tptp.r2 @t197 @t89))) % 0.36/0.62 (define @t213 () (or @t212 @t200 @t199)) % 0.36/0.62 (define @t214 () (forall @t201 @t213)) % 0.36/0.62 (define @t215 () (not @t214)) % 0.36/0.62 (define @t216 () (not @t211)) % 0.36/0.62 (define @t217 () (and @t214 @t216)) % 0.36/0.62 (define @t218 () (forall @t112 (not @t217))) % 0.36/0.62 (define @t219 () (not @t218)) % 0.36/0.62 (define @t220 () (not (= @t89 @t89))) % 0.36/0.62 (define @t221 () (or @t216 @t220)) % 0.36/0.62 (define @t222 () (not (= @t35 @t89))) % 0.36/0.62 (define @t223 () (or @t222 @t103 @t222)) % 0.36/0.62 (define @t224 () (or @t103 @t222)) % 0.36/0.62 (define @t225 () (or @t220 @t212 @t200 @t199)) % 0.36/0.62 (define @t226 () (not (tptp.r2 @t197 @t43))) % 0.36/0.62 (define @t227 () (not (= @t43 @t89))) % 0.36/0.62 (define @t228 () (or @t227 @t227 @t226 @t200 @t199)) % 0.36/0.62 (define @t229 () (or @t227 @t226 @t200 @t199)) % 0.36/0.62 (define @t230 () (forall @t60 @t229)) % 0.36/0.62 (define @t231 () (forall @t201 @t230)) % 0.36/0.62 (define @t232 () (forall (@list @t197 @t198 @t43) @t229)) % 0.36/0.62 (define @t233 () (@list @t43 @t197 @t198)) % 0.36/0.62 (define @t234 () (or @t226 @t200 @t199)) % 0.36/0.62 (define @t235 () (or @t234 @t227)) % 0.36/0.62 (define @t236 () (forall @t233 @t235)) % 0.36/0.62 (define @t237 () (forall @t201 @t235)) % 0.36/0.62 (define @t238 () (forall @t201 @t234)) % 0.36/0.62 (define @t239 () (@var "BOUND_VARIABLE_8138" $$unsorted)) % 0.36/0.62 (define @t240 () (or @t238 @t227)) % 0.36/0.62 (define @t241 () (not (tptp.r2 @t239 @t48))) % 0.36/0.62 (define @t242 () (not (tptp.r1 @t239))) % 0.36/0.62 (define @t243 () (or @t107 @t242 @t241)) % 0.36/0.62 (define @t244 () (@list @t48 @t239)) % 0.36/0.62 (define @t245 () (or @t242 @t241)) % 0.36/0.62 (define @t246 () (or @t245 @t107)) % 0.36/0.62 (define @t247 () (forall @t244 @t246)) % 0.36/0.62 (define @t248 () (@list @t239)) % 0.36/0.62 (define @t249 () (forall @t248 @t246)) % 0.36/0.62 (define @t250 () (forall @t248 @t245)) % 0.36/0.62 (define @t251 () (or @t250 @t107)) % 0.36/0.62 (define @t252 () (not (tptp.r4 @t41 @t40 @t190))) % 0.36/0.62 (define @t253 () (not (tptp.r3 @t190 @t41 @t43))) % 0.36/0.62 (define @t254 () (not (tptp.r4 @t41 @t191 @t43))) % 0.36/0.62 (define @t255 () (not (tptp.r2 @t40 @t191))) % 0.36/0.62 (define @t256 () (or @t253 @t252)) % 0.36/0.62 (define @t257 () (or @t255 @t254)) % 0.36/0.62 (define @t258 () (or @t257 @t256)) % 0.36/0.62 (define @t259 () (forall @t192 @t258)) % 0.36/0.62 (define @t260 () (forall (@list @t191 @t190) @t258)) % 0.36/0.62 (define @t261 () (forall (@list @t190) @t256)) % 0.36/0.62 (define @t262 () (forall (@list @t191) @t257)) % 0.36/0.62 (define @t263 () (@var "BOUND_VARIABLE_7921" $$unsorted)) % 0.36/0.62 (define @t264 () (@list @t263)) % 0.36/0.62 (define @t265 () (or @t262 @t261)) % 0.36/0.62 (define @t266 () (forall @t46 (or (not @t44) (not @t42)))) % 0.36/0.62 (define @t267 () (not (tptp.r4 @t41 @t263 @t43))) % 0.36/0.62 (define @t268 () (not (tptp.r2 @t40 @t263))) % 0.36/0.62 (define @t269 () (or @t268 @t267)) % 0.36/0.62 (define @t270 () (@list @t263)) % 0.36/0.62 (define @t271 () (forall @t270 @t269)) % 0.36/0.62 (define @t272 () (not @t266)) % 0.36/0.62 (define @t273 () (not @t271)) % 0.36/0.62 (define @t274 () (and @t273 @t272)) % 0.36/0.62 (define @t275 () (forall @t60 (not @t274))) % 0.36/0.62 (define @t276 () (not @t275)) % 0.36/0.62 (define @t277 () (forall @t46 (not @t45))) % 0.36/0.62 (define @t278 () (not @t277)) % 0.36/0.62 (define @t279 () (not (= @t43 @t43))) % 0.36/0.62 (define @t280 () (or @t279 @t268 @t267)) % 0.36/0.62 (define @t281 () (not (tptp.r4 @t41 @t263 @t48))) % 0.36/0.62 (define @t282 () (= @t43 @t48)) % 0.36/0.62 (define @t283 () (not @t282)) % 0.36/0.62 (define @t284 () (or @t283 @t283 @t268 @t281)) % 0.36/0.62 (define @t285 () (or @t283 @t268 @t281)) % 0.36/0.62 (define @t286 () (forall @t57 @t285)) % 0.36/0.62 (define @t287 () (forall @t270 @t286)) % 0.36/0.62 (define @t288 () (forall (@list @t263 @t48) @t285)) % 0.36/0.62 (define @t289 () (@list @t48 @t263)) % 0.36/0.62 (define @t290 () (or @t268 @t281)) % 0.36/0.62 (define @t291 () (or @t290 @t283)) % 0.36/0.62 (define @t292 () (forall @t289 @t291)) % 0.36/0.62 (define @t293 () (forall @t270 @t291)) % 0.36/0.62 (define @t294 () (forall @t270 @t290)) % 0.36/0.62 (define @t295 () (or @t294 @t283)) % 0.36/0.62 (define @t296 () (forall @t54 (or (not @t52) (not @t51)))) % 0.36/0.62 (define @t297 () (not @t296)) % 0.36/0.62 (define @t298 () (and @t297 @t282)) % 0.36/0.62 (define @t299 () (forall @t57 (not @t298))) % 0.36/0.62 (define @t300 () (not @t299)) % 0.36/0.62 (define @t301 () (forall @t54 (not @t53))) % 0.36/0.62 (define @t302 () (not @t301)) % 0.36/0.62 (define @t303 () (@quantifiers_skolemize @t193 2)) % 0.36/0.62 (define @t304 () (@quantifiers_skolemize @t193 0)) % 0.36/0.62 (define @t305 () (or @t196 (not (tptp.r4 @t128 @t194 @t304)) (not (tptp.r3 @t303 @t128 @t304)) (not (tptp.r4 @t128 @t128 @t303)))) % 0.36/0.62 (define @t306 () (tptp.r1 @t194)) % 0.36/0.62 (define @t307 () (not @t306)) % 0.36/0.62 (define @t308 () (or @t307 @t196)) % 0.36/0.62 (define @t309 () (not @t202)) % 0.36/0.62 (define @t310 () (or @t309 @t306)) % 0.36/0.62 (define @t311 () (@quantifiers_skolemize @t202 1)) % 0.36/0.62 (define @t312 () (tptp.r2 @t311 @t203)) % 0.36/0.62 (define @t313 () (not @t312)) % 0.36/0.62 (define @t314 () (tptp.r1 @t311)) % 0.36/0.62 (define @t315 () (not @t314)) % 0.36/0.62 (define @t316 () (or @t205 @t315 @t313)) % 0.36/0.62 (define @t317 () (@list @t316)) % 0.36/0.62 (define @t318 () (and @t314 (= @t311 @t128))) % 0.36/0.62 (define @t319 () (or @t315 @t318)) % 0.36/0.62 (define @t320 () (= @t128 @t311)) % 0.36/0.62 (define @t321 () (and @t314 @t320)) % 0.36/0.62 (define @t322 () (or @t315 @t321)) % 0.36/0.62 (assume @p1 @t13) % 0.36/0.62 (assume @p2 (forall (@list @t17) (exists (@list @t14) (forall (@list @t15) (or (and (not @t18) (not @t16)) (and @t18 @t16)))))) % 0.36/0.62 (assume @p3 (forall (@list @t23 @t22) (exists (@list @t19) (forall (@list @t20) (or (and (not @t24) (not @t21)) (and @t24 @t21)))))) % 0.36/0.62 (assume @p4 (forall (@list @t29 @t28) (exists (@list @t25) (forall (@list @t26) (or (and (not @t30) (not @t27)) (and @t30 @t27)))))) % 0.36/0.62 (assume @p5 (forall (@list @t33 @t32) (exists @t38 (and (exists @t37 (and (exists (@list @t36) (and (tptp.r2 @t32 @t36) (tptp.r3 @t33 @t36 @t35))) (= @t35 @t34))) (exists (@list @t31) (and (tptp.r2 @t31 @t34) (tptp.r3 @t33 @t32 @t31))))))) % 0.36/0.62 (assume @p6 @t62) % 0.36/0.62 (assume @p7 @t79) % 0.36/0.62 (assume @p8 (forall (@list @t80) (exists (@list @t81) (and (exists (@list @t82) (and (tptp.r1 @t82) (tptp.r3 @t80 @t82 @t81))) (= @t81 @t80))))) % 0.36/0.62 (assume @p9 (forall (@list @t86) (exists (@list @t84) (and (exists (@list @t85) (and (tptp.r1 @t85) (tptp.r4 @t86 @t85 @t84))) (exists (@list @t83) (and (tptp.r1 @t83) (= @t84 @t83))))))) % 0.36/0.62 (assume @p10 (forall (@list @t88) (or (exists (@list @t90) (and (tptp.r1 @t90) (= @t88 @t90))) (exists (@list @t89 @t87) (and (tptp.r2 @t89 @t87) (= @t88 @t87)))))) % 0.36/0.62 (assume @p11 @t101) % 0.36/0.62 (assume @p12 @t114) % 0.36/0.62 (assume @p13 true) % 0.36/0.62 (step @p14 :rule evaluate :args ((= true false))) % 0.36/0.62 (step @p15 :rule refl :args (@t93)) % 0.36/0.62 (step @p16 :rule aci_norm :args ((= (or @t115 false) @t115))) % 0.36/0.62 (step @p17 :rule evaluate :args ((not true))) % 0.36/0.62 (step @p18 :rule eq-refl :args (@t91)) % 0.36/0.62 (step @p19 :rule cong :premises (@p18) :args (@t116)) % 0.36/0.62 (step @p20 :rule trans :premises (@p19 @p17)) % 0.36/0.62 (step @p21 :rule refl :args (@t115)) % 0.36/0.62 (step @p22 :rule nary_cong :premises (@p21 @p20) :args (@t117)) % 0.36/0.62 (step @p23 :rule trans :premises (@p22 @p16)) % 0.36/0.62 (step @p24 :rule quant-var-elim-eq :args ((= (forall @t98 (or @t95 @t96 @t118)) @t117))) % 0.36/0.62 (step @p25 :rule refl :args (@t118)) % 0.36/0.62 (step @p26 :rule refl :args (@t96)) % 0.36/0.62 (step @p27 :rule eq-symm :args (@t91 @t94)) % 0.36/0.62 (step @p28 :rule cong :premises (@p27) :args (@t118)) % 0.36/0.62 (step @p29 :rule nary_cong :premises (@p28 @p26 @p25) :args (@t119)) % 0.36/0.62 (step @p30 :rule aci_norm :args ((= @t120 @t119))) % 0.36/0.62 (step @p31 :rule trans :premises (@p30 @p29)) % 0.36/0.62 (step @p32 :rule cong :premises (@p31) :args ((forall @t98 @t120))) % 0.36/0.62 (step @p33 :rule trans :premises (@p32 @p24)) % 0.36/0.62 (step @p34 :rule trans :premises (@p33 @p23)) % 0.36/0.62 (step @p35 :rule eq-symm :args (@t94 @t91)) % 0.36/0.62 (step @p36 :rule cong :premises (@p35) :args (@t95)) % 0.36/0.62 (step @p37 :rule refl :args (@t96)) % 0.36/0.62 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t97)) % 0.36/0.62 (step @p39 :rule cong :premises (@p38) :args (@t99)) % 0.36/0.62 (step @p40 :rule trans :premises (@p39 @p34)) % 0.36/0.62 (step @p41 :rule nary_cong :premises (@p40 @p15) :args (@t100)) % 0.36/0.62 (step @p42 :rule cong :premises (@p41) :args (@t101)) % 0.36/0.62 (step @p43 :rule eq_resolve :premises (@p11 @p42)) % 0.36/0.62 (step @p44 :rule instantiate :premises (@p43) :args (@t129)) % 0.36/0.62 (step @p45 :rule bool-and-de-morgan :args (@t126 @t121 true)) % 0.36/0.62 (step @p46 :rule cong :premises (@p45) :args (@t131)) % 0.36/0.62 (step @p47 :rule cong :premises (@p46) :args (@t132)) % 0.36/0.62 (step @p48 :rule exists-elim :args ((= (exists @t12 @t130) @t132))) % 0.36/0.62 (step @p49 :rule trans :premises (@p48 @p47)) % 0.36/0.62 (step @p50 :rule aci_norm :args ((= (or false @t121) @t121))) % 0.36/0.62 (step @p51 :rule aci_norm :args ((= (and @t121 true) @t121))) % 0.36/0.62 (step @p52 :rule eq-refl :args (@t1)) % 0.36/0.62 (step @p53 :rule refl :args (@t121)) % 0.36/0.62 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t134)) % 0.36/0.62 (step @p55 :rule trans :premises (@p54 @p51)) % 0.36/0.62 (step @p56 :rule cong :premises (@p52) :args (@t135)) % 0.36/0.62 (step @p57 :rule trans :premises (@p56 @p17)) % 0.36/0.62 (step @p58 :rule nary_cong :premises (@p57 @p55) :args (@t136)) % 0.36/0.62 (step @p59 :rule trans :premises (@p58 @p50)) % 0.36/0.62 (step @p60 :rule quant-var-elim-eq :args ((= (forall @t141 (or (not (= @t137 @t1)) @t140 @t139)) @t136))) % 0.36/0.62 (step @p61 :rule refl :args (@t139)) % 0.36/0.62 (step @p62 :rule refl :args (@t140)) % 0.36/0.62 (step @p63 :rule eq-symm :args (@t1 @t137)) % 0.36/0.62 (step @p64 :rule cong :premises (@p63) :args (@t140)) % 0.36/0.62 (step @p65 :rule nary_cong :premises (@p64 @p62 @p61) :args (@t142)) % 0.36/0.62 (step @p66 :rule aci_norm :args ((= @t143 @t142))) % 0.36/0.62 (step @p67 :rule trans :premises (@p66 @p65)) % 0.36/0.62 (step @p68 :rule cong :premises (@p67) :args (@t144)) % 0.36/0.62 (step @p69 :rule trans :premises (@p68 @p60)) % 0.36/0.62 (step @p70 :rule trans :premises (@p69 @p59)) % 0.36/0.62 (step @p71 :rule refl :args (@t126)) % 0.36/0.62 (step @p72 :rule nary_cong :premises (@p71 @p70) :args ((and @t126 @t144))) % 0.36/0.62 (step @p73 :rule alpha_equiv :args (@t149 @t150 (@list @t137))) % 0.36/0.62 (step @p74 :rule alpha_equiv :args (@t152 @t150 (@list @t122))) % 0.36/0.62 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t153)) % 0.36/0.62 (step @p76 :rule quant-miniscope-and :args ((= (forall @t10 (and @t151 @t148)) @t153))) % 0.36/0.62 (step @p77 :rule trans :premises (@p76 @p75)) % 0.36/0.62 (step @p78 :rule trans :premises (@p77 @p72)) % 0.36/0.62 (step @p79 :rule bool-or-and-distrib :args (@t7 @t147 true @t146 false)) % 0.36/0.62 (step @p80 :rule cong :premises (@p79) :args ((forall @t10 (or (and @t7 @t147) @t146)))) % 0.36/0.62 (step @p81 :rule trans :premises (@p80 @p78)) % 0.36/0.62 (step @p82 :rule eq-symm :args (@t2 @t1)) % 0.36/0.62 (step @p83 :rule refl :args (@t4)) % 0.36/0.62 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t5)) % 0.36/0.62 (step @p85 :rule cong :premises (@p82) :args (@t6)) % 0.36/0.62 (step @p86 :rule refl :args (@t7)) % 0.36/0.62 (step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t8)) % 0.36/0.62 (step @p88 :rule nary_cong :premises (@p87 @p84) :args (@t9)) % 0.36/0.62 (step @p89 :rule cong :premises (@p88) :args (@t11)) % 0.36/0.62 (step @p90 :rule trans :premises (@p89 @p81)) % 0.36/0.62 (step @p91 :rule cong :premises (@p90) :args (@t13)) % 0.36/0.62 (step @p92 :rule trans :premises (@p91 @p49)) % 0.36/0.62 (step @p93 :rule eq_resolve :premises (@p1 @p92)) % 0.36/0.62 (step @p94 :rule refl :args (@t159)) % 0.36/0.62 (step @p95 :rule bool-double-not-elim :args (@t127)) % 0.36/0.62 (step @p96 :rule nary_cong :premises (@p95 @p94) :args ((or (not @t160) @t159))) % 0.36/0.62 (step @p97 :rule refl :args (@t155)) % 0.36/0.62 (step @p98 :rule eq-symm :args (@t128 @t122)) % 0.36/0.62 (step @p99 :rule refl :args (@t123)) % 0.36/0.62 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t161)) % 0.36/0.62 (step @p101 :rule refl :args (@t124)) % 0.36/0.62 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t162)) % 0.36/0.62 (step @p103 :rule cong :premises (@p102) :args (@t163)) % 0.36/0.62 (step @p104 :rule cong :premises (@p103) :args (@t164)) % 0.36/0.62 (step @p105 :rule nary_cong :premises (@p104 @p97) :args (@t165)) % 0.36/0.62 (step @p106 :rule cong :premises (@p105) :args (@t166)) % 0.36/0.62 (step @p107 :rule refl :args (@t160)) % 0.36/0.62 (step @p108 :rule cong :premises (@p107 @p106) :args ((=> @t160 @t166))) % 0.36/0.62 (assume-push @p430 @t160) % 0.36/0.62 (step @p110 :rule skolemize :premises (@p93)) % 0.36/0.62 (step-pop @p431 :rule scope :premises (@p110)) % 0.36/0.62 (step @p111 :rule process_scope :premises (@p431) :args (@t166)) % 0.36/0.62 (step @p113 :rule eq_resolve :premises (@p111 @p108)) % 0.36/0.62 (step @p114 :rule implies_elim :premises (@p113)) % 0.36/0.62 (step @p115 :rule eq_resolve :premises (@p114 @p96)) % 0.36/0.62 (step @p116 :rule chain_m_resolution :premises (@p115 @p93) :args (@t159 @t167 (@list @t127))) % 0.36/0.62 (step @p117 :rule bool-double-not-elim :args (@t154)) % 0.36/0.62 (step @p118 :rule refl :args (@t158)) % 0.36/0.62 (step @p119 :rule nary_cong :premises (@p118 @p117) :args ((or @t158 (not @t155)))) % 0.36/0.62 (step @p120 :rule cnf_or_neg :args (@t158 1)) % 0.36/0.62 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.36/0.62 (step @p122 :rule reordering :premises (@p121) :args ((or @t154 @t158))) % 0.36/0.62 (step @p123 :rule chain_m_resolution :premises (@p122 @p116) :args (@t154 @t167 @t168)) % 0.36/0.62 (step @p124 :rule cnf_or_pos :args (@t170)) % 0.36/0.62 (step @p125 :rule reordering :premises (@p124) :args ((or @t155 @t169 (not @t170)))) % 0.36/0.62 (step @p126 :rule chain_m_resolution :premises (@p125 @p123 @p44) :args (@t169 @t171 (@list @t154 @t170))) % 0.36/0.62 (step @p127 :rule false_intro :premises (@p126)) % 0.36/0.62 (step @p128 :rule aci_norm :args ((= @t177 @t175))) % 0.36/0.62 (step @p129 :rule cong :premises (@p128) :args (@t179)) % 0.36/0.62 (step @p130 :rule quant-merge-prenex :args ((= (forall @t78 @t181) @t179))) % 0.36/0.62 (step @p131 :rule refl :args (@t65)) % 0.36/0.62 (step @p132 :rule alpha_equiv :args (@t182 (@list @t172) (@list @t66))) % 0.36/0.62 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t183)) % 0.36/0.62 (step @p134 :rule quant-miniscope-or :args ((= @t181 @t183))) % 0.36/0.62 (step @p135 :rule trans :premises (@p134 @p133)) % 0.36/0.62 (step @p136 :rule symm :premises (@p135)) % 0.36/0.62 (step @p137 :rule cong :premises (@p136) :args ((forall @t78 (or (forall @t75 (or @t184 @t67)) @t65)))) % 0.36/0.62 (step @p138 :rule trans :premises (@p137 @p130)) % 0.36/0.62 (step @p139 :rule trans :premises (@p138 @p129)) % 0.36/0.62 (step @p140 :rule refl :args (@t65)) % 0.36/0.62 (step @p141 :rule refl :args (@t67)) % 0.36/0.62 (step @p142 :rule aci_norm :args ((= (or @t184 false) @t184))) % 0.36/0.62 (step @p143 :rule eq-refl :args (@t66)) % 0.36/0.62 (step @p144 :rule cong :premises (@p143) :args (@t185)) % 0.36/0.62 (step @p145 :rule trans :premises (@p144 @p17)) % 0.36/0.62 (step @p146 :rule refl :args (@t184)) % 0.36/0.62 (step @p147 :rule nary_cong :premises (@p146 @p145) :args (@t186)) % 0.36/0.62 (step @p148 :rule trans :premises (@p147 @p142)) % 0.36/0.62 (step @p149 :rule quant-var-elim-eq :args ((= (forall @t72 (or @t69 @t70 @t187)) @t186))) % 0.36/0.62 (step @p150 :rule refl :args (@t187)) % 0.36/0.62 (step @p151 :rule refl :args (@t70)) % 0.36/0.62 (step @p152 :rule eq-symm :args (@t66 @t68)) % 0.36/0.62 (step @p153 :rule cong :premises (@p152) :args (@t187)) % 0.36/0.62 (step @p154 :rule nary_cong :premises (@p153 @p151 @p150) :args (@t188)) % 0.36/0.62 (step @p155 :rule aci_norm :args ((= @t189 @t188))) % 0.36/0.62 (step @p156 :rule trans :premises (@p155 @p154)) % 0.36/0.62 (step @p157 :rule cong :premises (@p156) :args ((forall @t72 @t189))) % 0.36/0.62 (step @p158 :rule trans :premises (@p157 @p149)) % 0.36/0.62 (step @p159 :rule trans :premises (@p158 @p148)) % 0.36/0.62 (step @p160 :rule eq-symm :args (@t68 @t66)) % 0.36/0.62 (step @p161 :rule cong 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0.36/0.62 (step @p416 :rule reordering :premises (@p415) :args ((or @t320 (not @t321)))) % 0.36/0.62 (step @p417 :rule chain_m_resolution :premises (@p416 @p414) :args (@t320 @t210 (@list @t321))) % 0.36/0.62 (step @p418 :rule symm :premises (@p417)) % 0.36/0.62 (step @p419 :rule cong :premises (@p418 @p385) :args (@t312)) % 0.36/0.62 (step @p420 :rule bool-double-not-elim :args (@t312)) % 0.36/0.62 (step @p421 :rule nary_cong :premises (@p373 @p420) :args ((or @t316 (not @t313)))) % 0.36/0.62 (step @p422 :rule cnf_or_neg :args (@t316 2)) % 0.36/0.62 (step @p423 :rule eq_resolve :premises (@p422 @p421)) % 0.36/0.62 (step @p424 :rule reordering :premises (@p423) :args ((or @t312 @t316))) % 0.36/0.62 (step @p425 :rule chain_m_resolution :premises (@p424 @p371) :args (@t312 @t167 @t317)) % 0.36/0.62 (step @p426 :rule true_intro :premises (@p425)) % 0.36/0.62 (step @p427 :rule symm :premises (@p426)) % 0.36/0.62 (step @p428 :rule trans :premises (@p427 @p419 @p384 @p127)) % 0.36/0.62 (step @p429 false :rule eq_resolve :premises (@p428 @p14)) % 0.36/0.62 ) % 0.36/0.62 % SZS output end Proof % 0.36/0.62 % cvc5 exiting %------------------------------------------------------------------------------