%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM493+3 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:39:36 AM UTC 2026 % Result : Theorem 132.28s 132.55s % Output : Proof 132.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM493+3 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.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 11:24:22 EDT 2026 % 0.16/0.35 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 132.28/132.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 132.28/132.55 --- Run --no-e-matching --full-saturate-quant at 6... % 132.28/132.55 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 132.28/132.55 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 132.28/132.55 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 132.28/132.55 --- Run --trigger-sel=max --full-saturate-quant at 15... % 132.28/132.55 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 132.28/132.55 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 132.28/132.55 --- Run --prenex-quant=none --full-saturate-quant at 30... % 132.28/132.55 % SZS status Theorem % 132.28/132.55 % SZS output start Proof % 132.28/132.55 ( % 132.28/132.55 (declare-sort $$unsorted 0) % 132.28/132.55 (declare-const tptp.xr $$unsorted) % 132.28/132.55 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 132.28/132.55 (declare-const tptp.xm $$unsorted) % 132.28/132.55 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 132.28/132.55 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 132.28/132.55 (declare-const tptp.xn $$unsorted) % 132.28/132.55 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 132.28/132.55 (declare-const tptp.sz00 $$unsorted) % 132.28/132.55 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 132.28/132.55 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 132.28/132.55 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 132.28/132.55 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 132.28/132.55 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 132.28/132.55 (declare-const tptp.sz10 $$unsorted) % 132.28/132.55 (declare-const tptp.xp $$unsorted) % 132.28/132.55 (define @t1 () (@var "W0" $$unsorted)) % 132.28/132.55 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 132.28/132.55 (define @t3 () (@list @t1)) % 132.28/132.55 (define @t4 () (tptp.aNaturalNumber0 tptp.sz00)) % 132.28/132.55 (define @t5 () (@var "W1" $$unsorted)) % 132.28/132.55 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 132.28/132.55 (define @t7 () (tptp.aNaturalNumber0 @t6)) % 132.28/132.55 (define @t8 () (tptp.aNaturalNumber0 @t5)) % 132.28/132.55 (define @t9 () (and @t2 @t8)) % 132.28/132.55 (define @t10 () (@list @t1 @t5)) % 132.28/132.55 (define @t11 () (forall @t10 (=> @t9 @t7))) % 132.28/132.55 (define @t12 () (tptp.sdtasdt0 @t1 @t5)) % 132.28/132.55 (define @t13 () (tptp.sdtpldt0 @t5 @t1)) % 132.28/132.55 (define @t14 () (= @t6 @t13)) % 132.28/132.55 (define @t15 () (forall @t10 (=> @t9 @t14))) % 132.28/132.55 (define @t16 () (@var "W2" $$unsorted)) % 132.28/132.55 (define @t17 () (tptp.sdtpldt0 @t5 @t16)) % 132.28/132.55 (define @t18 () (tptp.sdtpldt0 @t6 @t16)) % 132.28/132.55 (define @t19 () (= @t18 (tptp.sdtpldt0 @t1 @t17))) % 132.28/132.55 (define @t20 () (tptp.aNaturalNumber0 @t16)) % 132.28/132.55 (define @t21 () (and @t2 @t8 @t20)) % 132.28/132.55 (define @t22 () (@list @t1 @t5 @t16)) % 132.28/132.55 (define @t23 () (forall @t22 (=> @t21 @t19))) % 132.28/132.55 (define @t24 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 132.28/132.55 (define @t25 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 132.28/132.55 (define @t26 () (and (= @t25 @t1) @t24)) % 132.28/132.55 (define @t27 () (=> @t2 @t26)) % 132.28/132.55 (define @t28 () (forall @t3 @t27)) % 132.28/132.55 (define @t29 () (tptp.sdtasdt0 @t5 @t1)) % 132.28/132.55 (define @t30 () (tptp.sdtasdt0 @t16 @t1)) % 132.28/132.55 (define @t31 () (tptp.sdtasdt0 @t1 @t16)) % 132.28/132.55 (define @t32 () (= @t5 @t16)) % 132.28/132.55 (define @t33 () (tptp.sdtpldt0 @t16 @t1)) % 132.28/132.55 (define @t34 () (= @t13 @t33)) % 132.28/132.55 (define @t35 () (tptp.sdtpldt0 @t1 @t16)) % 132.28/132.55 (define @t36 () (= @t6 @t35)) % 132.28/132.55 (define @t37 () (or @t36 @t34)) % 132.28/132.55 (define @t38 () (=> @t37 @t32)) % 132.28/132.55 (define @t39 () (forall @t22 (=> @t21 @t38))) % 132.28/132.55 (define @t40 () (= @t29 @t30)) % 132.28/132.55 (define @t41 () (= @t12 @t31)) % 132.28/132.55 (define @t42 () (and @t8 @t20)) % 132.28/132.55 (define @t43 () (= @t1 tptp.sz00)) % 132.28/132.55 (define @t44 () (not @t43)) % 132.28/132.55 (define @t45 () (= @t5 tptp.sz00)) % 132.28/132.55 (define @t46 () (and @t20 (= @t35 @t5))) % 132.28/132.55 (define @t47 () (@list @t16)) % 132.28/132.55 (define @t48 () (tptp.sdtlseqdt0 @t1 @t5)) % 132.28/132.55 (define @t49 () (= @t1 @t5)) % 132.28/132.55 (define @t50 () (tptp.sdtlseqdt0 @t5 @t1)) % 132.28/132.55 (define @t51 () (tptp.sdtlseqdt0 @t5 @t16)) % 132.28/132.55 (define @t52 () (= @t5 @t1)) % 132.28/132.55 (define @t53 () (tptp.sdtlseqdt0 @t35 @t17)) % 132.28/132.55 (define @t54 () (not (= @t35 @t17))) % 132.28/132.55 (define @t55 () (tptp.sdtpldt0 @t16 @t5)) % 132.28/132.55 (define @t56 () (tptp.sdtlseqdt0 @t33 @t55)) % 132.28/132.55 (define @t57 () (not (= @t33 @t55))) % 132.28/132.55 (define @t58 () (and @t57 @t56 @t54 @t53)) % 132.28/132.55 (define @t59 () (=> @t20 @t58)) % 132.28/132.55 (define @t60 () (forall @t47 @t59)) % 132.28/132.55 (define @t61 () (not @t49)) % 132.28/132.55 (define @t62 () (and @t61 @t48)) % 132.28/132.55 (define @t63 () (=> @t62 @t60)) % 132.28/132.55 (define @t64 () (=> @t9 @t63)) % 132.28/132.55 (define @t65 () (forall @t10 @t64)) % 132.28/132.55 (define @t66 () (= @t1 tptp.sz10)) % 132.28/132.55 (define @t67 () (tptp.iLess0 @t1 @t5)) % 132.28/132.55 (define @t68 () (=> @t62 @t67)) % 132.28/132.55 (define @t69 () (forall @t10 (=> @t9 @t68))) % 132.28/132.55 (define @t70 () (and @t20 (= @t5 @t31))) % 132.28/132.55 (define @t71 () (tptp.doDivides0 @t1 @t5)) % 132.28/132.55 (define @t72 () (tptp.sdtsldt0 @t5 @t1)) % 132.28/132.55 (define @t73 () (and @t44 @t71)) % 132.28/132.55 (define @t74 () (tptp.doDivides0 @t1 @t16)) % 132.28/132.55 (define @t75 () (tptp.doDivides0 @t1 @t17)) % 132.28/132.55 (define @t76 () (tptp.doDivides0 @t5 @t1)) % 132.28/132.55 (define @t77 () (@list @t5)) % 132.28/132.55 (define @t78 () (not @t66)) % 132.28/132.55 (define @t79 () (tptp.aNaturalNumber0 tptp.xp)) % 132.28/132.55 (define @t80 () (tptp.aNaturalNumber0 tptp.xm)) % 132.28/132.55 (define @t81 () (tptp.aNaturalNumber0 tptp.xn)) % 132.28/132.55 (define @t82 () (tptp.doDivides0 @t16 @t5)) % 132.28/132.55 (define @t83 () (@var "W3" $$unsorted)) % 132.28/132.55 (define @t84 () (tptp.sdtasdt0 @t16 @t83)) % 132.28/132.55 (define @t85 () (= @t5 @t84)) % 132.28/132.55 (define @t86 () (tptp.aNaturalNumber0 @t83)) % 132.28/132.55 (define @t87 () (and @t86 @t85)) % 132.28/132.55 (define @t88 () (@list @t83)) % 132.28/132.55 (define @t89 () (exists @t88 @t87)) % 132.28/132.55 (define @t90 () (and @t89 @t82)) % 132.28/132.55 (define @t91 () (tptp.doDivides0 @t16 @t1)) % 132.28/132.55 (define @t92 () (= @t1 @t84)) % 132.28/132.55 (define @t93 () (and @t86 @t92)) % 132.28/132.55 (define @t94 () (exists @t88 @t93)) % 132.28/132.55 (define @t95 () (and @t94 @t91)) % 132.28/132.55 (define @t96 () (or @t95 @t90)) % 132.28/132.55 (define @t97 () (tptp.sdtpldt0 tptp.xn tptp.xm)) % 132.28/132.55 (define @t98 () (tptp.sdtpldt0 @t97 tptp.xp)) % 132.28/132.55 (define @t99 () (tptp.iLess0 @t18 @t98)) % 132.28/132.55 (define @t100 () (=> @t99 @t96)) % 132.28/132.55 (define @t101 () (tptp.doDivides0 @t16 @t12)) % 132.28/132.55 (define @t102 () (= @t12 @t84)) % 132.28/132.55 (define @t103 () (and @t86 @t102)) % 132.28/132.55 (define @t104 () (exists @t88 @t103)) % 132.28/132.55 (define @t105 () (or @t104 @t101)) % 132.28/132.55 (define @t106 () (tptp.isPrime0 @t16)) % 132.28/132.55 (define @t107 () (or (= @t83 tptp.sz10) (= @t83 @t16))) % 132.28/132.55 (define @t108 () (tptp.doDivides0 @t83 @t16)) % 132.28/132.55 (define @t109 () (@var "W4" $$unsorted)) % 132.28/132.55 (define @t110 () (tptp.sdtasdt0 @t83 @t109)) % 132.28/132.55 (define @t111 () (= @t16 @t110)) % 132.28/132.55 (define @t112 () (tptp.aNaturalNumber0 @t109)) % 132.28/132.55 (define @t113 () (and @t112 @t111)) % 132.28/132.55 (define @t114 () (@list @t109)) % 132.28/132.55 (define @t115 () (exists @t114 @t113)) % 132.28/132.55 (define @t116 () (and @t86 @t115 @t108)) % 132.28/132.55 (define @t117 () (=> @t116 @t107)) % 132.28/132.55 (define @t118 () (forall @t88 @t117)) % 132.28/132.55 (define @t119 () (not (= @t16 tptp.sz10))) % 132.28/132.55 (define @t120 () (not (= @t16 tptp.sz00))) % 132.28/132.55 (define @t121 () (and @t120 @t119 @t118)) % 132.28/132.55 (define @t122 () (or @t121 @t106)) % 132.28/132.55 (define @t123 () (and @t122 @t105)) % 132.28/132.55 (define @t124 () (=> @t123 @t100)) % 132.28/132.55 (define @t125 () (=> @t21 @t124)) % 132.28/132.55 (define @t126 () (forall @t22 @t125)) % 132.28/132.55 (define @t127 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 132.28/132.55 (define @t128 () (tptp.sdtasdt0 tptp.xp @t1)) % 132.28/132.55 (define @t129 () (tptp.isPrime0 tptp.xp)) % 132.28/132.55 (define @t130 () (tptp.sdtpldt0 tptp.xp tptp.xr)) % 132.28/132.55 (define @t131 () (tptp.aNaturalNumber0 tptp.xr)) % 132.28/132.55 (define @t132 () (tptp.sdtlseqdt0 tptp.xr tptp.xn)) % 132.28/132.55 (define @t133 () (not (= tptp.xr tptp.xn))) % 132.28/132.55 (define @t134 () (tptp.sdtasdt0 tptp.xr tptp.xm)) % 132.28/132.55 (define @t135 () (tptp.doDivides0 tptp.xp @t134)) % 132.28/132.55 (define @t136 () (tptp.doDivides0 tptp.xp tptp.xm)) % 132.28/132.55 (define @t137 () (= tptp.xm @t128)) % 132.28/132.55 (define @t138 () (and @t2 @t137)) % 132.28/132.55 (define @t139 () (exists @t3 @t138)) % 132.28/132.55 (define @t140 () (tptp.doDivides0 tptp.xp tptp.xr)) % 132.28/132.55 (define @t141 () (and @t2 (= tptp.xr @t128))) % 132.28/132.55 (define @t142 () (exists @t3 @t141)) % 132.28/132.55 (define @t143 () (or @t142 @t140 @t139 @t136)) % 132.28/132.55 (define @t144 () (not @t143)) % 132.28/132.55 (define @t145 () (not @t8)) % 132.28/132.55 (define @t146 () (not @t2)) % 132.28/132.55 (define @t147 () (or @t146 @t145 @t14)) % 132.28/132.55 (define @t148 () (or @t146 @t145)) % 132.28/132.55 (define @t149 () (not @t9)) % 132.28/132.55 (define @t150 () (@list tptp.xp tptp.xm)) % 132.28/132.55 (define @t151 () (tptp.sdtpldt0 tptp.xm tptp.xp)) % 132.28/132.55 (define @t152 () (tptp.sdtpldt0 tptp.xp tptp.xm)) % 132.28/132.55 (define @t153 () (= @t152 @t151)) % 132.28/132.55 (define @t154 () (not @t80)) % 132.28/132.55 (define @t155 () (not @t79)) % 132.28/132.55 (define @t156 () (or @t155 @t154 @t153)) % 132.28/132.55 (define @t157 () (@list false false false)) % 132.28/132.55 (define @t158 () (not @t20)) % 132.28/132.55 (define @t159 () (or @t146 @t145 @t158)) % 132.28/132.55 (define @t160 () (not @t21)) % 132.28/132.55 (define @t161 () (tptp.sdtpldt0 @t130 @t151)) % 132.28/132.55 (define @t162 () (tptp.sdtpldt0 @t130 tptp.xm)) % 132.28/132.55 (define @t163 () (tptp.sdtpldt0 @t162 tptp.xp)) % 132.28/132.55 (define @t164 () (= @t163 @t161)) % 132.28/132.55 (define @t165 () (tptp.aNaturalNumber0 @t130)) % 132.28/132.55 (define @t166 () (not @t165)) % 132.28/132.55 (define @t167 () (or @t166 @t154 @t155 @t164)) % 132.28/132.55 (define @t168 () (@list false false false false)) % 132.28/132.55 (define @t169 () (@list tptp.xr tptp.xm tptp.xp)) % 132.28/132.55 (define @t170 () (tptp.sdtpldt0 tptp.xr @t151)) % 132.28/132.55 (define @t171 () (tptp.sdtpldt0 tptp.xr tptp.xm)) % 132.28/132.55 (define @t172 () (tptp.sdtpldt0 @t171 tptp.xp)) % 132.28/132.55 (define @t173 () (= @t172 @t170)) % 132.28/132.55 (define @t174 () (not @t131)) % 132.28/132.55 (define @t175 () (or @t174 @t154 @t155 @t173)) % 132.28/132.55 (define @t176 () (not @t48)) % 132.28/132.55 (define @t177 () (or @t146 @t145 @t49 @t176 @t67)) % 132.28/132.55 (define @t178 () (or @t49 @t176 @t67)) % 132.28/132.55 (define @t179 () (or @t49 @t176)) % 132.28/132.55 (define @t180 () (not @t62)) % 132.28/132.55 (define @t181 () (tptp.iLess0 @t172 @t163)) % 132.28/132.55 (define @t182 () (tptp.sdtlseqdt0 @t172 @t163)) % 132.28/132.55 (define @t183 () (not @t182)) % 132.28/132.55 (define @t184 () (tptp.aNaturalNumber0 @t163)) % 132.28/132.55 (define @t185 () (not @t184)) % 132.28/132.55 (define @t186 () (tptp.aNaturalNumber0 @t172)) % 132.28/132.55 (define @t187 () (not @t186)) % 132.28/132.55 (define @t188 () (or @t187 @t185 (= @t172 @t163) @t183 @t181)) % 132.28/132.55 (define @t189 () (forall @t10 @t177)) % 132.28/132.55 (define @t190 () (= @t163 @t172)) % 132.28/132.55 (define @t191 () (or @t187 @t185 @t190 @t183 @t181)) % 132.28/132.55 (define @t192 () (@list false)) % 132.28/132.55 (define @t193 () (and (= @t1 @t25) @t24)) % 132.28/132.55 (define @t194 () (tptp.sdtpldt0 tptp.xm tptp.sz00)) % 132.28/132.55 (define @t195 () (= tptp.xm @t194)) % 132.28/132.55 (define @t196 () (and @t195 (= tptp.xm (tptp.sdtpldt0 tptp.sz00 tptp.xm)))) % 132.28/132.55 (define @t197 () (or @t154 @t196)) % 132.28/132.55 (define @t198 () (@list false false)) % 132.28/132.55 (define @t199 () (tptp.sdtpldt0 tptp.xm tptp.xr)) % 132.28/132.55 (define @t200 () (or @t154 @t174 (= @t199 @t171))) % 132.28/132.55 (define @t201 () (forall @t10 @t147)) % 132.28/132.55 (define @t202 () (= @t171 @t199)) % 132.28/132.55 (define @t203 () (or @t154 @t174 @t202)) % 132.28/132.55 (define @t204 () (@list @t201)) % 132.28/132.55 (define @t205 () (tptp.sdtpldt0 tptp.xm @t130)) % 132.28/132.55 (define @t206 () (or @t154 @t166 (= @t205 @t162))) % 132.28/132.55 (define @t207 () (= @t162 @t205)) % 132.28/132.55 (define @t208 () (or @t154 @t166 @t207)) % 132.28/132.55 (define @t209 () (tptp.sdtpldt0 tptp.xr tptp.xp)) % 132.28/132.55 (define @t210 () (= @t130 @t209)) % 132.28/132.55 (define @t211 () (or @t155 @t174 @t210)) % 132.28/132.55 (define @t212 () (tptp.sdtpldt0 @t199 tptp.xp)) % 132.28/132.55 (define @t213 () (= @t212 (tptp.sdtpldt0 tptp.xm @t209))) % 132.28/132.55 (define @t214 () (or @t154 @t174 @t155 @t213)) % 132.28/132.55 (define @t215 () (tptp.sdtpldt0 @t130 @t194)) % 132.28/132.55 (define @t216 () (= (tptp.sdtpldt0 @t162 tptp.sz00) @t215)) % 132.28/132.55 (define @t217 () (not @t4)) % 132.28/132.55 (define @t218 () (or @t166 @t154 @t217 @t216)) % 132.28/132.55 (define @t219 () (and (not @t36) (not @t34))) % 132.28/132.55 (define @t220 () (tptp.aNaturalNumber0 @t171)) % 132.28/132.55 (define @t221 () (or @t174 @t154 @t220)) % 132.28/132.55 (define @t222 () (not @t220)) % 132.28/132.55 (define @t223 () (or @t222 @t155 @t186)) % 132.28/132.55 (define @t224 () (= tptp.sz00 tptp.xp)) % 132.28/132.55 (define @t225 () (tptp.sdtpldt0 @t172 tptp.sz00)) % 132.28/132.55 (define @t226 () (= @t225 (tptp.sdtpldt0 @t172 tptp.xp))) % 132.28/132.55 (define @t227 () (not @t226)) % 132.28/132.55 (define @t228 () (and @t227 (not (= (tptp.sdtpldt0 tptp.sz00 @t172) (tptp.sdtpldt0 tptp.xp @t172))))) % 132.28/132.55 (define @t229 () (or @t187 @t217 @t155 @t228 @t224)) % 132.28/132.55 (define @t230 () (@list true false false false false)) % 132.28/132.55 (define @t231 () (and @t195 @t202 @t207 @t210 @t213 @t216 @t190)) % 132.28/132.55 (define @t232 () (tptp.aNaturalNumber0 @t162)) % 132.28/132.55 (define @t233 () (or @t166 @t154 @t232)) % 132.28/132.55 (define @t234 () (not @t232)) % 132.28/132.55 (define @t235 () (or @t234 @t155 @t184)) % 132.28/132.55 (define @t236 () (not @t86)) % 132.28/132.55 (define @t237 () (and (not (forall @t88 (or @t236 (not @t85)))) @t82)) % 132.28/132.55 (define @t238 () (and (not (forall @t88 (or @t236 (not @t92)))) @t91)) % 132.28/132.55 (define @t239 () (not @t99)) % 132.28/132.55 (define @t240 () (not @t101)) % 132.28/132.55 (define @t241 () (forall @t88 (or @t236 (not @t102)))) % 132.28/132.55 (define @t242 () (and @t241 @t240)) % 132.28/132.55 (define @t243 () (not @t106)) % 132.28/132.55 (define @t244 () (= @t16 @t83)) % 132.28/132.55 (define @t245 () (= tptp.sz10 @t83)) % 132.28/132.55 (define @t246 () (not @t108)) % 132.28/132.55 (define @t247 () (not @t112)) % 132.28/132.55 (define @t248 () (forall @t114 (or @t247 (not @t111)))) % 132.28/132.55 (define @t249 () (or @t236 @t248 @t246 @t245 @t244)) % 132.28/132.55 (define @t250 () (forall @t88 @t249)) % 132.28/132.55 (define @t251 () (not @t250)) % 132.28/132.55 (define @t252 () (= tptp.sz10 @t16)) % 132.28/132.55 (define @t253 () (= tptp.sz00 @t16)) % 132.28/132.55 (define @t254 () (and (or @t253 @t252 @t251) @t243)) % 132.28/132.55 (define @t255 () (or @t146 @t145 @t158 @t254 @t242 @t239 @t238 @t237)) % 132.28/132.55 (define @t256 () (or @t254 @t242 @t239 @t238 @t237)) % 132.28/132.55 (define @t257 () (or @t239 @t238 @t237)) % 132.28/132.55 (define @t258 () (or @t238 @t237)) % 132.28/132.55 (define @t259 () (not @t241)) % 132.28/132.55 (define @t260 () (not @t252)) % 132.28/132.55 (define @t261 () (not @t260)) % 132.28/132.55 (define @t262 () (not @t253)) % 132.28/132.55 (define @t263 () (not @t262)) % 132.28/132.55 (define @t264 () (or @t263 @t261 @t251)) % 132.28/132.55 (define @t265 () (and @t262 @t260 @t250)) % 132.28/132.55 (define @t266 () (or @t259 @t101)) % 132.28/132.55 (define @t267 () (or @t265 @t106)) % 132.28/132.55 (define @t268 () (=> @t99 @t258)) % 132.28/132.55 (define @t269 () (and @t267 @t266)) % 132.28/132.55 (define @t270 () (=> @t269 @t268)) % 132.28/132.55 (define @t271 () (forall @t88 (not @t87))) % 132.28/132.55 (define @t272 () (not @t271)) % 132.28/132.55 (define @t273 () (forall @t88 (not @t93))) % 132.28/132.55 (define @t274 () (not @t273)) % 132.28/132.55 (define @t275 () (forall @t88 (not @t103))) % 132.28/132.55 (define @t276 () (not @t275)) % 132.28/132.55 (define @t277 () (or @t245 @t244)) % 132.28/132.55 (define @t278 () (not @t248)) % 132.28/132.55 (define @t279 () (not @t278)) % 132.28/132.55 (define @t280 () (or @t236 @t279 @t246)) % 132.28/132.55 (define @t281 () (and @t86 @t278 @t108)) % 132.28/132.55 (define @t282 () (forall @t114 (not @t113))) % 132.28/132.55 (define @t283 () (not @t282)) % 132.28/132.55 (define @t284 () (forall @t3 (not @t138))) % 132.28/132.55 (define @t285 () (not @t284)) % 132.28/132.55 (define @t286 () (= @t128 tptp.xr)) % 132.28/132.55 (define @t287 () (and @t2 @t286)) % 132.28/132.55 (define @t288 () (forall @t3 (not @t287))) % 132.28/132.55 (define @t289 () (not @t288)) % 132.28/132.55 (define @t290 () (tptp.sdtasdt0 tptp.xp @t83)) % 132.28/132.55 (define @t291 () (and (not (forall @t88 (or @t236 (not (= tptp.xr @t290))))) @t140)) % 132.28/132.55 (define @t292 () (not @t291)) % 132.28/132.55 (define @t293 () (@list true)) % 132.28/132.55 (define @t294 () (not @t135)) % 132.28/132.55 (define @t295 () (and (forall @t88 (or @t236 (not (= @t134 @t290)))) @t294)) % 132.28/132.55 (define @t296 () (not @t295)) % 132.28/132.55 (define @t297 () (and (not (forall @t88 (or @t236 (not (= tptp.xm @t290))))) @t136)) % 132.28/132.55 (define @t298 () (not @t297)) % 132.28/132.55 (define @t299 () (not @t129)) % 132.28/132.55 (define @t300 () (and (or @t224 (= tptp.sz10 tptp.xp) (not (forall @t88 (or @t236 (forall @t114 (or @t247 (not (= tptp.xp @t110)))) (not (tptp.doDivides0 @t83 tptp.xp)) @t245 (= tptp.xp @t83))))) @t299)) % 132.28/132.55 (define @t301 () (not @t300)) % 132.28/132.55 (define @t302 () (not @t181)) % 132.28/132.55 (define @t303 () (or @t174 @t154 @t155 @t300 @t295 @t302 @t291 @t297)) % 132.28/132.55 (define @t304 () (and @t57 @t56 (not (= @t17 @t35)) @t53)) % 132.28/132.55 (define @t305 () (forall @t47 (or @t158 @t304))) % 132.28/132.55 (define @t306 () (or @t146 @t145 @t49 @t176 @t305)) % 132.28/132.55 (define @t307 () (or @t49 @t176 @t305)) % 132.28/132.55 (define @t308 () (=> @t62 @t305)) % 132.28/132.55 (define @t309 () (tptp.sdtpldt0 @t130 @t16)) % 132.28/132.55 (define @t310 () (tptp.sdtpldt0 tptp.xr @t16)) % 132.28/132.55 (define @t311 () (tptp.sdtlseqdt0 @t310 @t309)) % 132.28/132.55 (define @t312 () (not (= @t309 @t310))) % 132.28/132.55 (define @t313 () (tptp.sdtpldt0 @t16 @t130)) % 132.28/132.55 (define @t314 () (tptp.sdtpldt0 @t16 tptp.xr)) % 132.28/132.55 (define @t315 () (tptp.sdtlseqdt0 @t314 @t313)) % 132.28/132.55 (define @t316 () (not (= @t314 @t313))) % 132.28/132.55 (define @t317 () (and @t316 @t315 @t312 @t311)) % 132.28/132.55 (define @t318 () (or @t158 @t317)) % 132.28/132.55 (define @t319 () (forall @t47 @t318)) % 132.28/132.55 (define @t320 () (tptp.sdtlseqdt0 tptp.xr @t130)) % 132.28/132.55 (define @t321 () (not @t320)) % 132.28/132.55 (define @t322 () (= tptp.xr @t130)) % 132.28/132.55 (define @t323 () (or @t174 @t166 @t322 @t321 @t319)) % 132.28/132.55 (define @t324 () (forall @t10 @t306)) % 132.28/132.55 (define @t325 () (forall @t47 (or @t158 (and (not (= @t313 @t314)) @t315 @t312 @t311)))) % 132.28/132.55 (define @t326 () (or @t174 @t166 @t322 @t321 @t325)) % 132.28/132.55 (define @t327 () (= tptp.xn tptp.xr)) % 132.28/132.55 (define @t328 () (tptp.aNaturalNumber0 @t152)) % 132.28/132.55 (define @t329 () (or @t155 @t154 @t328)) % 132.28/132.55 (define @t330 () (tptp.sdtpldt0 @t130 @t152)) % 132.28/132.55 (define @t331 () (tptp.sdtpldt0 tptp.xr @t152)) % 132.28/132.55 (define @t332 () (tptp.sdtlseqdt0 @t331 @t330)) % 132.28/132.55 (define @t333 () (tptp.sdtpldt0 @t152 @t130)) % 132.28/132.55 (define @t334 () (tptp.sdtpldt0 @t152 tptp.xr)) % 132.28/132.55 (define @t335 () (and (not (= @t333 @t334)) (tptp.sdtlseqdt0 @t334 @t333) (not (= @t330 @t331)) @t332)) % 132.28/132.55 (define @t336 () (not @t328)) % 132.28/132.55 (define @t337 () (or @t336 @t335)) % 132.28/132.55 (define @t338 () (not @t332)) % 132.28/132.55 (define @t339 () (not @t173)) % 132.28/132.55 (define @t340 () (not @t164)) % 132.28/132.55 (define @t341 () (not @t153)) % 132.28/132.55 (define @t342 () (and @t332 @t153 @t173 @t164 @t183)) % 132.28/132.55 (assume @p1 (forall @t3 (=> @t2 true))) % 132.28/132.55 (assume @p2 @t4) % 132.28/132.55 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 132.28/132.55 (assume @p4 @t11) % 132.28/132.55 (assume @p5 (forall @t10 (=> @t9 (tptp.aNaturalNumber0 @t12)))) % 132.28/132.55 (assume @p6 @t15) % 132.28/132.55 (assume @p7 @t23) % 132.28/132.55 (assume @p8 @t28) % 132.28/132.55 (assume @p9 (forall @t10 (=> @t9 (= @t12 @t29)))) % 132.28/132.55 (assume @p10 (forall @t22 (=> @t21 (= (tptp.sdtasdt0 @t12 @t16) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t16)))))) % 132.28/132.55 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 132.28/132.55 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 132.28/132.55 (assume @p13 (forall @t22 (=> @t21 (and (= (tptp.sdtasdt0 @t1 @t17) (tptp.sdtpldt0 @t12 @t31)) (= (tptp.sdtasdt0 @t17 @t1) (tptp.sdtpldt0 @t29 @t30)))))) % 132.28/132.55 (assume @p14 @t39) % 132.28/132.55 (assume @p15 (forall @t3 (=> @t2 (=> @t44 (forall (@list @t5 @t16) (=> @t42 (=> (or @t41 @t40) @t32))))))) % 132.28/132.55 (assume @p16 (forall @t10 (=> @t9 (=> (= @t6 tptp.sz00) (and @t43 @t45))))) % 132.28/132.55 (assume @p17 (forall @t10 (=> @t9 (=> (= @t12 tptp.sz00) (or @t43 @t45))))) % 132.28/132.55 (assume @p18 (forall @t10 (=> @t9 (= @t48 (exists @t47 @t46))))) % 132.28/132.55 (assume @p19 (forall @t10 (=> @t9 (=> @t48 (forall @t47 (= (= @t16 (tptp.sdtmndt0 @t5 @t1)) @t46)))))) % 132.28/132.55 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 132.28/132.55 (assume @p21 (forall @t10 (=> @t9 (=> (and @t48 @t50) @t49)))) % 132.28/132.55 (assume @p22 (forall @t22 (=> @t21 (=> (and @t48 @t51) (tptp.sdtlseqdt0 @t1 @t16))))) % 132.28/132.55 (assume @p23 (forall @t10 (=> @t9 (or @t48 (and (not @t52) @t50))))) % 132.28/132.55 (assume @p24 @t65) % 132.28/132.55 (assume @p25 (forall @t22 (=> @t21 (=> (and @t44 (not @t32) @t51) (and (not @t41) (tptp.sdtlseqdt0 @t12 @t31) (not @t40) (tptp.sdtlseqdt0 @t29 @t30)))))) % 132.28/132.55 (assume @p26 (forall @t3 (=> @t2 (or @t43 @t66 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 132.28/132.55 (assume @p27 (forall @t10 (=> @t9 (=> @t44 (tptp.sdtlseqdt0 @t5 @t29))))) % 132.28/132.55 (assume @p28 (forall @t10 (=> @t9 (=> @t67 true)))) % 132.28/132.55 (assume @p29 @t69) % 132.28/132.55 (assume @p30 (forall @t10 (=> @t9 (= @t71 (exists @t47 @t70))))) % 132.28/132.55 (assume @p31 (forall @t10 (=> @t9 (=> @t73 (forall @t47 (= (= @t16 @t72) @t70)))))) % 132.28/132.55 (assume @p32 (forall @t22 (=> @t21 (=> (and @t71 (tptp.doDivides0 @t5 @t16)) @t74)))) % 132.28/132.55 (assume @p33 (forall @t22 (=> @t21 (=> (and @t71 @t74) @t75)))) % 132.28/132.55 (assume @p34 (forall @t22 (=> @t21 (=> (and @t71 @t75) @t74)))) % 132.28/132.55 (assume @p35 (forall @t10 (=> @t9 (=> (and @t71 (not @t45)) @t48)))) % 132.28/132.55 (assume @p36 (forall @t10 (=> @t9 (=> @t73 (forall @t47 (=> @t20 (= (tptp.sdtasdt0 @t16 @t72) (tptp.sdtsldt0 (tptp.sdtasdt0 @t16 @t5) @t1)))))))) % 132.28/132.55 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t44 @t78 (forall @t77 (=> (and @t8 @t76) (or (= @t5 tptp.sz10) @t52)))))))) % 132.28/132.55 (assume @p38 (forall @t3 (=> (and @t2 @t44 @t78) (exists @t77 (and @t8 @t76 (tptp.isPrime0 @t5)))))) % 132.28/132.55 (assume @p39 (and @t81 @t80 @t79)) % 132.28/132.55 (assume @p40 @t126) % 132.28/132.55 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t77 (and @t8 (= tptp.xp @t12))) (tptp.doDivides0 @t1 tptp.xp))) (or @t66 (= @t1 tptp.xp)))) @t129 (exists @t3 (and @t2 (= @t127 @t128))) (tptp.doDivides0 tptp.xp @t127))) % 132.28/132.55 (assume @p42 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xp @t1) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn))) % 132.28/132.55 (assume @p43 (and @t131 (= @t130 tptp.xn) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) % 132.28/132.55 (assume @p44 (and @t133 (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xr @t1) tptp.xn))) @t132)) % 132.28/132.55 (assume @p45 (and (exists @t3 (and @t2 (= @t134 @t128))) @t135)) % 132.28/132.55 (assume @p46 @t144) % 132.28/132.55 (assume @p47 true) % 132.28/132.55 (step @p48 :rule aci_norm :args ((= (or @t148 @t14) @t147))) % 132.28/132.55 (step @p49 :rule refl :args (@t14)) % 132.28/132.55 (step @p50 :rule bool-and-de-morgan :args (@t2 @t8 true)) % 132.28/132.55 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or @t149 @t14))) % 132.28/132.55 (step @p52 :rule trans :premises (@p51 @p48)) % 132.28/132.55 (step @p53 :rule bool-impl-elim :args (@t9 @t14)) % 132.28/132.55 (step @p54 :rule trans :premises (@p53 @p52)) % 132.28/132.55 (step @p55 :rule cong :premises (@p54) :args (@t15)) % 132.28/132.55 (step @p56 :rule eq_resolve :premises (@p6 @p55)) % 132.28/132.55 (step @p57 :rule instantiate :premises (@p56) :args (@t150)) % 132.28/132.55 (step @p58 :rule and_elim :premises (@p39) :args (2)) % 132.28/132.55 (step @p59 :rule and_elim :premises (@p39) :args (1)) % 132.28/132.55 (step @p60 :rule cnf_or_pos :args (@t156)) % 132.28/132.55 (step @p61 :rule reordering :premises (@p60) :args ((or @t154 @t155 @t153 (not @t156)))) % 132.28/132.55 (step @p62 :rule chain_m_resolution :premises (@p61 @p59 @p58 @p57) :args (@t153 @t157 (@list @t80 @t79 @t156))) % 132.28/132.55 (step @p63 :rule aci_norm :args ((= (or @t159 @t19) (or @t146 @t145 @t158 @t19)))) % 132.28/132.55 (step @p64 :rule refl :args (@t19)) % 132.28/132.55 (step @p65 :rule aci_norm :args ((= (or @t146 (or @t145 @t158)) @t159))) % 132.28/132.55 (step @p66 :rule bool-and-de-morgan :args (@t8 @t20 true)) % 132.28/132.55 (step @p67 :rule refl :args (@t146)) % 132.28/132.55 (step @p68 :rule nary_cong :premises (@p67 @p66) :args ((or @t146 (not @t42)))) % 132.28/132.55 (step @p69 :rule bool-and-de-morgan :args (@t2 @t8 (and @t20))) % 132.28/132.55 (step @p70 :rule trans :premises (@p69 @p68)) % 132.28/132.55 (step @p71 :rule trans :premises (@p70 @p65)) % 132.28/132.55 (step @p72 :rule nary_cong :premises (@p71 @p64) :args ((or @t160 @t19))) % 132.28/132.55 (step @p73 :rule trans :premises (@p72 @p63)) % 132.28/132.55 (step @p74 :rule bool-impl-elim :args (@t21 @t19)) % 132.28/132.55 (step @p75 :rule trans :premises (@p74 @p73)) % 132.28/132.55 (step @p76 :rule cong :premises (@p75) :args (@t23)) % 132.28/132.55 (step @p77 :rule eq_resolve :premises (@p7 @p76)) % 132.28/132.55 (step @p78 :rule instantiate :premises (@p77) :args ((@list @t130 tptp.xm tptp.xp))) % 132.28/132.55 (step @p79 :rule and_elim :premises (@p43) :args (1)) % 132.28/132.55 (step @p80 :rule symm :premises (@p79)) % 132.28/132.55 (step @p81 :rule cong :premises (@p80) :args (@t81)) % 132.28/132.55 (step @p82 :rule and_elim :premises (@p39) :args (0)) % 132.28/132.55 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 132.28/132.55 (step @p84 :rule cnf_or_pos :args (@t167)) % 132.28/132.55 (step @p85 :rule reordering :premises (@p84) :args ((or @t166 @t154 @t155 @t164 (not @t167)))) % 132.28/132.55 (step @p86 :rule chain_m_resolution :premises (@p85 @p83 @p59 @p58 @p78) :args (@t164 @t168 (@list @t165 @t80 @t79 @t167))) % 132.28/132.55 (step @p87 :rule instantiate :premises (@p77) :args (@t169)) % 132.28/132.55 (step @p88 :rule and_elim :premises (@p43) :args (0)) % 132.28/132.55 (step @p89 :rule cnf_or_pos :args (@t175)) % 132.28/132.55 (step @p90 :rule reordering :premises (@p89) :args ((or @t154 @t155 @t174 @t173 (not @t175)))) % 132.28/132.55 (step @p91 :rule chain_m_resolution :premises (@p90 @p59 @p58 @p88 @p87) :args (@t173 @t168 (@list @t80 @t79 @t131 @t175))) % 132.28/132.55 (step @p92 :rule aci_norm :args ((= (or @t148 @t178) @t177))) % 132.28/132.55 (step @p93 :rule aci_norm :args ((= (or @t179 @t67) @t178))) % 132.28/132.55 (step @p94 :rule refl :args (@t67)) % 132.28/132.55 (step @p95 :rule refl :args (@t176)) % 132.28/132.55 (step @p96 :rule bool-double-not-elim :args (@t49)) % 132.28/132.55 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or (not @t61) @t176))) % 132.28/132.55 (step @p98 :rule bool-and-de-morgan :args (@t61 @t48 true)) % 132.28/132.55 (step @p99 :rule trans :premises (@p98 @p97)) % 132.28/132.55 (step @p100 :rule nary_cong :premises (@p99 @p94) :args ((or @t180 @t67))) % 132.28/132.55 (step @p101 :rule trans :premises (@p100 @p93)) % 132.28/132.55 (step @p102 :rule bool-impl-elim :args (@t62 @t67)) % 132.28/132.55 (step @p103 :rule trans :premises (@p102 @p101)) % 132.28/132.55 (step @p104 :rule nary_cong :premises (@p50 @p103) :args ((or @t149 @t68))) % 132.28/132.55 (step @p105 :rule trans :premises (@p104 @p92)) % 132.28/132.55 (step @p106 :rule bool-impl-elim :args 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chain_m_resolution :premises (@p523 @p521) :args (@t332 @t192 (@list @t335))) % 132.28/132.55 (step @p525 :rule refl :args (@t338)) % 132.28/132.55 (step @p526 :rule bool-double-not-elim :args (@t182)) % 132.28/132.55 (step @p527 :rule refl :args (@t339)) % 132.28/132.55 (step @p528 :rule refl :args (@t340)) % 132.28/132.55 (step @p529 :rule refl :args (@t341)) % 132.28/132.55 (step @p530 :rule nary_cong :premises (@p529 @p528 @p527 @p526 @p525) :args ((or @t341 @t340 @t339 (not @t183) @t338))) % 132.28/132.55 (assume-push @p608 @t332) % 132.28/132.55 (assume-push @p609 @t153) % 132.28/132.55 (assume-push @p610 @t173) % 132.28/132.55 (assume-push @p611 @t164) % 132.28/132.55 (assume-push @p612 @t183) % 132.28/132.55 (step @p536 :rule evaluate :args ((= false true))) % 132.28/132.55 (step @p537 :rule true_intro :premises (@p524)) % 132.28/132.55 (step @p538 :rule symm :premises (@p62)) % 132.28/132.55 (step @p245 :rule refl :args (@t130)) % 132.28/132.55 (step @p539 :rule cong :premises (@p245 @p538) :args (@t161)) % 132.28/132.55 (step @p540 :rule trans :premises (@p86 @p539)) % 132.28/132.55 (step @p541 :rule cong :premises (@p497 @p538) :args (@t170)) % 132.28/132.55 (step @p542 :rule trans :premises (@p91 @p541)) % 132.28/132.55 (step @p543 :rule cong :premises (@p542 @p540) :args (@t182)) % 132.28/132.55 (step @p544 :rule false_intro :premises (@p612)) % 132.28/132.55 (step @p545 :rule symm :premises (@p544)) % 132.28/132.55 (step @p546 :rule trans :premises (@p545 @p543 @p537)) % 132.28/132.55 (step @p547 false :rule eq_resolve :premises (@p546 @p536)) % 132.28/132.55 (step-pop @p613 :rule scope :premises (@p547)) % 132.28/132.55 (step-pop @p614 :rule scope :premises (@p613)) % 132.28/132.55 (step-pop @p615 :rule scope :premises (@p614)) % 132.28/132.55 (step-pop @p616 :rule scope :premises (@p615)) % 132.28/132.55 (step-pop @p617 :rule scope :premises (@p616)) % 132.28/132.55 (step @p548 :rule process_scope :premises (@p617) :args (false)) % 132.28/132.55 (assume-push @p618 @t153) % 132.28/132.55 (assume-push @p619 @t164) % 132.28/132.55 (assume-push @p620 @t173) % 132.28/132.55 (assume-push @p621 @t183) % 132.28/132.55 (assume-push @p622 @t332) % 132.28/132.55 (step @p559 :rule and_intro :premises (@p524 @p62 @p91 @p86 @p621)) % 132.28/132.55 (step-pop @p623 :rule scope :premises (@p559)) % 132.28/132.55 (step-pop @p624 :rule scope :premises (@p623)) % 132.28/132.55 (step-pop @p625 :rule scope :premises (@p624)) % 132.28/132.55 (step-pop @p626 :rule scope :premises (@p625)) % 132.28/132.55 (step-pop @p627 :rule scope :premises (@p626)) % 132.28/132.55 (step @p560 :rule process_scope :premises (@p627) :args (@t342)) % 132.28/132.55 (step @p566 :rule implies_elim :premises (@p560)) % 132.28/132.55 (step @p567 :rule resolution :premises (@p566 @p548) :args (true @t342)) % 132.28/132.55 (step @p568 :rule not_and :premises (@p567)) % 132.28/132.55 (step @p569 :rule eq_resolve :premises (@p568 @p530)) % 132.28/132.55 (step @p570 :rule reordering :premises (@p569) :args ((or @t182 @t341 @t340 @t339 @t338))) % 132.28/132.55 (step @p571 false :rule chain_m_resolution :premises (@p570 @p524 @p445 @p91 @p86 @p62) :args (false (@list false true false false false) (@list @t332 @t182 @t173 @t164 @t153))) % 132.28/132.55 ) % 132.28/132.55 % SZS output end Proof % 132.28/132.55 % cvc5 exiting %------------------------------------------------------------------------------