%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM507+3 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n023.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 08:39:39 AM UTC 2026 % Result : Theorem 9.02s 9.26s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM507+3 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n023.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 11:26:28 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 9.02/9.26 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 9.02/9.26 % SZS status Theorem % 9.02/9.26 % SZS output start Proof % 9.02/9.26 ( % 9.02/9.26 (declare-sort $$unsorted 0) % 9.02/9.26 (declare-const tptp.xr $$unsorted) % 9.02/9.26 (declare-const tptp.xk $$unsorted) % 9.02/9.26 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 9.02/9.26 (declare-const tptp.xm $$unsorted) % 9.02/9.26 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 9.02/9.26 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 9.02/9.26 (declare-const tptp.xn $$unsorted) % 9.02/9.26 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 9.02/9.26 (declare-const tptp.sz00 $$unsorted) % 9.02/9.26 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 9.02/9.26 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 9.02/9.26 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 9.02/9.26 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 9.02/9.26 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 9.02/9.26 (declare-const tptp.sz10 $$unsorted) % 9.02/9.26 (declare-const tptp.xp $$unsorted) % 9.02/9.26 (define @t1 () (@var "W0" $$unsorted)) % 9.02/9.27 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 9.02/9.27 (define @t3 () (@list @t1)) % 9.02/9.27 (define @t4 () (@var "W1" $$unsorted)) % 9.02/9.27 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 9.02/9.27 (define @t6 () (tptp.aNaturalNumber0 @t5)) % 9.02/9.27 (define @t7 () (tptp.aNaturalNumber0 @t4)) % 9.02/9.27 (define @t8 () (and @t2 @t7)) % 9.02/9.27 (define @t9 () (@list @t1 @t4)) % 9.02/9.27 (define @t10 () (forall @t9 (=> @t8 @t6))) % 9.02/9.27 (define @t11 () (tptp.sdtasdt0 @t1 @t4)) % 9.02/9.27 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 9.02/9.27 (define @t13 () (@var "W2" $$unsorted)) % 9.02/9.27 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 9.02/9.27 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 9.02/9.27 (define @t16 () (= @t15 (tptp.sdtpldt0 @t1 @t14))) % 9.02/9.27 (define @t17 () (tptp.aNaturalNumber0 @t13)) % 9.02/9.27 (define @t18 () (and @t2 @t7 @t17)) % 9.02/9.27 (define @t19 () (@list @t1 @t4 @t13)) % 9.02/9.27 (define @t20 () (forall @t19 (=> @t18 @t16))) % 9.02/9.27 (define @t21 () (tptp.sdtasdt0 @t4 @t1)) % 9.02/9.27 (define @t22 () (tptp.sdtasdt0 @t13 @t1)) % 9.02/9.27 (define @t23 () (tptp.sdtasdt0 @t1 @t13)) % 9.02/9.27 (define @t24 () (= @t4 @t13)) % 9.02/9.27 (define @t25 () (tptp.sdtpldt0 @t13 @t1)) % 9.02/9.27 (define @t26 () (tptp.sdtpldt0 @t1 @t13)) % 9.02/9.27 (define @t27 () (= @t21 @t22)) % 9.02/9.27 (define @t28 () (= @t11 @t23)) % 9.02/9.27 (define @t29 () (and @t7 @t17)) % 9.02/9.27 (define @t30 () (= @t1 tptp.sz00)) % 9.02/9.27 (define @t31 () (not @t30)) % 9.02/9.27 (define @t32 () (= @t4 tptp.sz00)) % 9.02/9.27 (define @t33 () (and @t17 (= @t26 @t4))) % 9.02/9.27 (define @t34 () (@list @t13)) % 9.02/9.27 (define @t35 () (exists @t34 @t33)) % 9.02/9.27 (define @t36 () (tptp.sdtlseqdt0 @t1 @t4)) % 9.02/9.27 (define @t37 () (= @t36 @t35)) % 9.02/9.27 (define @t38 () (=> @t8 @t37)) % 9.02/9.27 (define @t39 () (forall @t9 @t38)) % 9.02/9.27 (define @t40 () (= @t1 @t4)) % 9.02/9.27 (define @t41 () (tptp.sdtlseqdt0 @t4 @t1)) % 9.02/9.27 (define @t42 () (and @t36 @t41)) % 9.02/9.27 (define @t43 () (=> @t42 @t40)) % 9.02/9.27 (define @t44 () (forall @t9 (=> @t8 @t43))) % 9.02/9.27 (define @t45 () (tptp.sdtlseqdt0 @t4 @t13)) % 9.02/9.27 (define @t46 () (= @t4 @t1)) % 9.02/9.27 (define @t47 () (not @t46)) % 9.02/9.27 (define @t48 () (and @t47 @t41)) % 9.02/9.27 (define @t49 () (or @t36 @t48)) % 9.02/9.27 (define @t50 () (=> @t8 @t49)) % 9.02/9.27 (define @t51 () (forall @t9 @t50)) % 9.02/9.27 (define @t52 () (tptp.sdtlseqdt0 @t26 @t14)) % 9.02/9.27 (define @t53 () (not (= @t26 @t14))) % 9.02/9.27 (define @t54 () (tptp.sdtpldt0 @t13 @t4)) % 9.02/9.27 (define @t55 () (tptp.sdtlseqdt0 @t25 @t54)) % 9.02/9.27 (define @t56 () (not (= @t25 @t54))) % 9.02/9.27 (define @t57 () (and @t56 @t55 @t53 @t52)) % 9.02/9.27 (define @t58 () (=> @t17 @t57)) % 9.02/9.27 (define @t59 () (forall @t34 @t58)) % 9.02/9.27 (define @t60 () (not @t40)) % 9.02/9.27 (define @t61 () (and @t60 @t36)) % 9.02/9.27 (define @t62 () (=> @t61 @t59)) % 9.02/9.27 (define @t63 () (=> @t8 @t62)) % 9.02/9.27 (define @t64 () (forall @t9 @t63)) % 9.02/9.27 (define @t65 () (= @t1 tptp.sz10)) % 9.02/9.27 (define @t66 () (tptp.iLess0 @t1 @t4)) % 9.02/9.27 (define @t67 () (and @t17 (= @t4 @t23))) % 9.02/9.27 (define @t68 () (tptp.doDivides0 @t1 @t4)) % 9.02/9.27 (define @t69 () (tptp.sdtsldt0 @t4 @t1)) % 9.02/9.27 (define @t70 () (and @t31 @t68)) % 9.02/9.27 (define @t71 () (tptp.doDivides0 @t1 @t13)) % 9.02/9.27 (define @t72 () (tptp.doDivides0 @t1 @t14)) % 9.02/9.27 (define @t73 () (not @t32)) % 9.02/9.27 (define @t74 () (and @t68 @t73)) % 9.02/9.27 (define @t75 () (=> @t74 @t36)) % 9.02/9.27 (define @t76 () (=> @t8 @t75)) % 9.02/9.27 (define @t77 () (forall @t9 @t76)) % 9.02/9.27 (define @t78 () (tptp.doDivides0 @t4 @t1)) % 9.02/9.27 (define @t79 () (@list @t4)) % 9.02/9.27 (define @t80 () (not @t65)) % 9.02/9.27 (define @t81 () (tptp.aNaturalNumber0 tptp.xp)) % 9.02/9.27 (define @t82 () (tptp.aNaturalNumber0 tptp.xm)) % 9.02/9.27 (define @t83 () (tptp.aNaturalNumber0 tptp.xn)) % 9.02/9.27 (define @t84 () (@var "W3" $$unsorted)) % 9.02/9.27 (define @t85 () (tptp.sdtasdt0 @t13 @t84)) % 9.02/9.27 (define @t86 () (tptp.aNaturalNumber0 @t84)) % 9.02/9.27 (define @t87 () (@list @t84)) % 9.02/9.27 (define @t88 () (tptp.sdtpldt0 tptp.xn tptp.xm)) % 9.02/9.27 (define @t89 () (tptp.sdtpldt0 @t88 tptp.xp)) % 9.02/9.27 (define @t90 () (@var "W4" $$unsorted)) % 9.02/9.27 (define @t91 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 9.02/9.27 (define @t92 () (tptp.sdtpldt0 tptp.xp @t1)) % 9.02/9.27 (define @t93 () (tptp.aNaturalNumber0 tptp.xk)) % 9.02/9.27 (define @t94 () (= tptp.xk tptp.sz10)) % 9.02/9.27 (define @t95 () (= tptp.xk tptp.sz00)) % 9.02/9.27 (define @t96 () (or @t95 @t94)) % 9.02/9.27 (define @t97 () (not @t96)) % 9.02/9.27 (define @t98 () (tptp.doDivides0 tptp.xr tptp.xk)) % 9.02/9.27 (define @t99 () (tptp.sdtasdt0 tptp.xr @t1)) % 9.02/9.27 (define @t100 () (= tptp.xk @t99)) % 9.02/9.27 (define @t101 () (and @t2 @t100)) % 9.02/9.27 (define @t102 () (exists @t3 @t101)) % 9.02/9.27 (define @t103 () (tptp.aNaturalNumber0 tptp.xr)) % 9.02/9.27 (define @t104 () (tptp.sdtpldt0 tptp.xr @t1)) % 9.02/9.27 (define @t105 () (and @t2 (= @t104 tptp.xk))) % 9.02/9.27 (define @t106 () (exists @t3 @t105)) % 9.02/9.27 (define @t107 () (tptp.sdtlseqdt0 tptp.xk tptp.xp)) % 9.02/9.27 (define @t108 () (tptp.sdtpldt0 tptp.xk @t1)) % 9.02/9.27 (define @t109 () (and @t2 (= @t108 tptp.xp))) % 9.02/9.27 (define @t110 () (exists @t3 @t109)) % 9.02/9.27 (define @t111 () (= tptp.xk tptp.xp)) % 9.02/9.27 (define @t112 () (tptp.sdtpldt0 @t88 tptp.xr)) % 9.02/9.27 (define @t113 () (tptp.sdtlseqdt0 @t112 @t89)) % 9.02/9.27 (define @t114 () (tptp.sdtpldt0 @t112 @t1)) % 9.02/9.27 (define @t115 () (and @t2 (= @t114 @t89))) % 9.02/9.27 (define @t116 () (exists @t3 @t115)) % 9.02/9.27 (define @t117 () (or @t116 @t113)) % 9.02/9.27 (define @t118 () (not (= @t112 @t89))) % 9.02/9.27 (define @t119 () (and @t118 @t117)) % 9.02/9.27 (define @t120 () (not @t119)) % 9.02/9.27 (define @t121 () (= tptp.xk @t104)) % 9.02/9.27 (define @t122 () (and @t2 @t121)) % 9.02/9.27 (define @t123 () (forall @t3 (not @t122))) % 9.02/9.27 (define @t124 () (not @t123)) % 9.02/9.27 (define @t125 () (not @t2)) % 9.02/9.27 (define @t126 () (@quantifiers_skolemize (forall @t3 (or @t125 (not @t121))) 0)) % 9.02/9.27 (define @t127 () (tptp.sdtpldt0 tptp.xr @t126)) % 9.02/9.27 (define @t128 () (= tptp.xk @t127)) % 9.02/9.27 (define @t129 () (not @t128)) % 9.02/9.27 (define @t130 () (tptp.aNaturalNumber0 @t126)) % 9.02/9.27 (define @t131 () (not @t130)) % 9.02/9.27 (define @t132 () (or @t131 @t129)) % 9.02/9.27 (define @t133 () (@list true)) % 9.02/9.27 (define @t134 () (@list @t132)) % 9.02/9.27 (define @t135 () (= tptp.xp @t108)) % 9.02/9.27 (define @t136 () (and @t2 @t135)) % 9.02/9.27 (define @t137 () (forall @t3 (not @t136))) % 9.02/9.27 (define @t138 () (not @t137)) % 9.02/9.27 (define @t139 () (@quantifiers_skolemize (forall @t3 (or @t125 (not @t135))) 0)) % 9.02/9.27 (define @t140 () (tptp.sdtpldt0 tptp.xk @t139)) % 9.02/9.27 (define @t141 () (= tptp.xp @t140)) % 9.02/9.27 (define @t142 () (not @t141)) % 9.02/9.27 (define @t143 () (tptp.aNaturalNumber0 @t139)) % 9.02/9.27 (define @t144 () (not @t143)) % 9.02/9.27 (define @t145 () (or @t144 @t142)) % 9.02/9.27 (define @t146 () (@list @t145)) % 9.02/9.27 (define @t147 () (not @t17)) % 9.02/9.27 (define @t148 () (not @t7)) % 9.02/9.27 (define @t149 () (or @t125 @t148 @t147)) % 9.02/9.27 (define @t150 () (tptp.sdtpldt0 @t126 @t139)) % 9.02/9.27 (define @t151 () (tptp.sdtpldt0 tptp.xr @t150)) % 9.02/9.27 (define @t152 () (= (tptp.sdtpldt0 @t127 @t139) @t151)) % 9.02/9.27 (define @t153 () (not @t103)) % 9.02/9.27 (define @t154 () (or @t153 @t131 @t144 @t152)) % 9.02/9.27 (define @t155 () (@list false false false false)) % 9.02/9.27 (define @t156 () (@list @t103 @t130 @t143 @t154)) % 9.02/9.27 (define @t157 () (= @t4 @t26)) % 9.02/9.27 (define @t158 () (= @t36 (not (forall @t34 (or @t147 (not @t157)))))) % 9.02/9.27 (define @t159 () (or @t125 @t148)) % 9.02/9.27 (define @t160 () (not @t8)) % 9.02/9.27 (define @t161 () (and @t17 @t157)) % 9.02/9.27 (define @t162 () (forall @t34 (not @t161))) % 9.02/9.27 (define @t163 () (not @t162)) % 9.02/9.27 (define @t164 () (@list tptp.xr tptp.xp)) % 9.02/9.27 (define @t165 () (forall @t34 (or @t147 (not (= tptp.xp (tptp.sdtpldt0 tptp.xr @t13)))))) % 9.02/9.27 (define @t166 () (not @t165)) % 9.02/9.27 (define @t167 () (tptp.sdtlseqdt0 tptp.xr tptp.xp)) % 9.02/9.27 (define @t168 () (= @t167 @t166)) % 9.02/9.27 (define @t169 () (not @t81)) % 9.02/9.27 (define @t170 () (or @t153 @t169 @t168)) % 9.02/9.27 (define @t171 () (@list false false false)) % 9.02/9.27 (define @t172 () (tptp.sdtpldt0 tptp.xp @t88)) % 9.02/9.27 (define @t173 () (tptp.sdtpldt0 tptp.xr @t88)) % 9.02/9.27 (define @t174 () (tptp.sdtlseqdt0 @t173 @t172)) % 9.02/9.27 (define @t175 () (not (= @t172 @t173))) % 9.02/9.27 (define @t176 () (= @t89 @t112)) % 9.02/9.27 (define @t177 () (not @t176)) % 9.02/9.27 (define @t178 () (and @t177 @t113 @t175 @t174)) % 9.02/9.27 (define @t179 () (not @t178)) % 9.02/9.27 (define @t180 () (tptp.sdtlseqdt0 @t172 @t173)) % 9.02/9.27 (define @t181 () (tptp.sdtlseqdt0 @t89 @t112)) % 9.02/9.27 (define @t182 () (and @t177 @t181 @t175 @t180)) % 9.02/9.27 (define @t183 () (@var "BOUND_VARIABLE_8074" $$unsorted)) % 9.02/9.27 (define @t184 () (tptp.sdtpldt0 @t4 @t183)) % 9.02/9.27 (define @t185 () (tptp.sdtpldt0 @t1 @t183)) % 9.02/9.27 (define @t186 () (tptp.sdtpldt0 @t183 @t4)) % 9.02/9.27 (define @t187 () (tptp.sdtpldt0 @t183 @t1)) % 9.02/9.27 (define @t188 () (and (not (= @t187 @t186)) (tptp.sdtlseqdt0 @t187 @t186) (not (= @t184 @t185)) (tptp.sdtlseqdt0 @t185 @t184))) % 9.02/9.27 (define @t189 () (not (tptp.aNaturalNumber0 @t183))) % 9.02/9.27 (define @t190 () (not @t36)) % 9.02/9.27 (define @t191 () (or @t125 @t148 @t40 @t190 @t189 @t188)) % 9.02/9.27 (define @t192 () (or @t189 @t188)) % 9.02/9.27 (define @t193 () (or @t125 @t148 @t40 @t190 @t192)) % 9.02/9.27 (define @t194 () (@list @t1 @t4 @t183)) % 9.02/9.27 (define @t195 () (forall @t194 @t193)) % 9.02/9.27 (define @t196 () (@list @t183)) % 9.02/9.27 (define @t197 () (forall @t196 @t193)) % 9.02/9.27 (define @t198 () (forall @t196 @t192)) % 9.02/9.27 (define @t199 () (or @t125 @t148 @t40 @t190 @t198)) % 9.02/9.27 (define @t200 () (and @t56 @t55 (not (= @t14 @t26)) @t52)) % 9.02/9.27 (define @t201 () (forall @t34 (or @t147 @t200))) % 9.02/9.27 (define @t202 () (or @t125 @t148 @t40 @t190 @t201)) % 9.02/9.27 (define @t203 () (or @t40 @t190 @t201)) % 9.02/9.27 (define @t204 () (=> @t61 @t201)) % 9.02/9.27 (define @t205 () (and @t118 @t113 @t175 @t174)) % 9.02/9.27 (define @t206 () (tptp.aNaturalNumber0 @t88)) % 9.02/9.27 (define @t207 () (not @t206)) % 9.02/9.27 (define @t208 () (not @t167)) % 9.02/9.27 (define @t209 () (= tptp.xr tptp.xp)) % 9.02/9.27 (define @t210 () (or @t153 @t169 @t209 @t208 @t207 @t205)) % 9.02/9.27 (define @t211 () (forall @t194 @t191)) % 9.02/9.27 (define @t212 () (= tptp.xp tptp.xr)) % 9.02/9.27 (define @t213 () (or @t153 @t169 @t212 @t208 @t207 @t178)) % 9.02/9.27 (define @t214 () (@list false)) % 9.02/9.27 (define @t215 () (@list @t211)) % 9.02/9.27 (define @t216 () (= tptp.sz00 @t4)) % 9.02/9.27 (define @t217 () (not @t68)) % 9.02/9.27 (define @t218 () (or @t217 @t216 @t36)) % 9.02/9.27 (define @t219 () (not @t216)) % 9.02/9.27 (define @t220 () (and @t68 @t219)) % 9.02/9.27 (define @t221 () (=> @t220 @t36)) % 9.02/9.27 (define @t222 () (tptp.sdtlseqdt0 tptp.xr tptp.xk)) % 9.02/9.27 (define @t223 () (= tptp.sz00 tptp.xk)) % 9.02/9.27 (define @t224 () (not @t98)) % 9.02/9.27 (define @t225 () (not @t93)) % 9.02/9.27 (define @t226 () (or @t153 @t225 @t224 @t223 @t222)) % 9.02/9.27 (define @t227 () (@list true false false false false)) % 9.02/9.27 (define @t228 () (not @t41)) % 9.02/9.27 (define @t229 () (or @t125 @t148 @t190 @t228 @t40)) % 9.02/9.27 (define @t230 () (or @t190 @t228 @t40)) % 9.02/9.27 (define @t231 () (tptp.sdtlseqdt0 tptp.xp tptp.xk)) % 9.02/9.27 (define @t232 () (not @t231)) % 9.02/9.27 (define @t233 () (not @t107)) % 9.02/9.27 (define @t234 () (or @t225 @t169 @t233 @t232 @t111)) % 9.02/9.27 (define @t235 () (forall @t9 @t229)) % 9.02/9.27 (define @t236 () (= tptp.xp tptp.xk)) % 9.02/9.27 (define @t237 () (or @t225 @t169 @t233 @t232 @t236)) % 9.02/9.27 (define @t238 () (forall @t3 (not @t101))) % 9.02/9.27 (define @t239 () (not @t238)) % 9.02/9.27 (define @t240 () (@quantifiers_skolemize (forall @t3 (or @t125 (not @t100))) 0)) % 9.02/9.27 (define @t241 () (tptp.sdtasdt0 tptp.xr @t240)) % 9.02/9.27 (define @t242 () (= tptp.xk @t241)) % 9.02/9.27 (define @t243 () (not @t242)) % 9.02/9.27 (define @t244 () (or (not (tptp.aNaturalNumber0 @t240)) @t243)) % 9.02/9.27 (define @t245 () (not @t222)) % 9.02/9.27 (define @t246 () (not @t212)) % 9.02/9.27 (define @t247 () (= true false)) % 9.02/9.27 (define @t248 () (and @t232 @t212 @t242 @t222)) % 9.02/9.27 (define @t249 () (not @t82)) % 9.02/9.27 (define @t250 () (not @t83)) % 9.02/9.27 (define @t251 () (or @t250 @t249 @t206)) % 9.02/9.27 (define @t252 () (not (= @t173 @t172))) % 9.02/9.27 (define @t253 () (and @t177 @t181 @t252 @t180)) % 9.02/9.27 (define @t254 () (tptp.sdtlseqdt0 tptp.xp tptp.xr)) % 9.02/9.27 (define @t255 () (not @t254)) % 9.02/9.27 (define @t256 () (or @t169 @t153 @t212 @t255 @t207 @t253)) % 9.02/9.27 (define @t257 () (or @t169 @t153 @t212 @t255 @t207 @t182)) % 9.02/9.27 (define @t258 () (and @t60 @t41)) % 9.02/9.27 (define @t259 () (or @t125 @t148 @t36 @t258)) % 9.02/9.27 (define @t260 () (or @t36 @t258)) % 9.02/9.27 (define @t261 () (not @t209)) % 9.02/9.27 (define @t262 () (and @t261 @t254)) % 9.02/9.27 (define @t263 () (or @t153 @t169 @t167 @t262)) % 9.02/9.27 (define @t264 () (forall @t9 @t259)) % 9.02/9.27 (define @t265 () (and @t246 @t254)) % 9.02/9.27 (define @t266 () (or @t153 @t169 @t167 @t265)) % 9.02/9.27 (define @t267 () (= @t89 @t114)) % 9.02/9.27 (define @t268 () (or (not (forall @t3 (or @t125 (not @t267)))) @t113)) % 9.02/9.27 (define @t269 () (not @t268)) % 9.02/9.27 (define @t270 () (and @t2 @t267)) % 9.02/9.27 (define @t271 () (forall @t3 (not @t270))) % 9.02/9.27 (define @t272 () (not @t271)) % 9.02/9.27 (define @t273 () (not @t168)) % 9.02/9.27 (define @t274 () (= tptp.xp @t151)) % 9.02/9.27 (define @t275 () (not @t274)) % 9.02/9.27 (define @t276 () (tptp.aNaturalNumber0 @t150)) % 9.02/9.27 (define @t277 () (not @t276)) % 9.02/9.27 (define @t278 () (or @t277 @t275)) % 9.02/9.27 (define @t279 () (or @t131 @t144 @t276)) % 9.02/9.27 (define @t280 () (not @t152)) % 9.02/9.27 (define @t281 () (and @t274 @t275)) % 9.02/9.27 (assume @p1 (forall @t3 (=> @t2 true))) % 9.02/9.27 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 9.02/9.27 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 9.02/9.27 (assume @p4 @t10) % 9.02/9.27 (assume @p5 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t11)))) % 9.02/9.27 (assume @p6 (forall @t9 (=> @t8 (= @t5 @t12)))) % 9.02/9.27 (assume @p7 @t20) % 9.02/9.27 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 9.02/9.27 (assume @p9 (forall @t9 (=> @t8 (= @t11 @t21)))) % 9.02/9.27 (assume @p10 (forall @t19 (=> @t18 (= (tptp.sdtasdt0 @t11 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 9.02/9.27 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 9.02/9.27 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 9.02/9.27 (assume @p13 (forall @t19 (=> @t18 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t11 @t23)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t21 @t22)))))) % 9.02/9.27 (assume @p14 (forall @t19 (=> @t18 (=> (or (= @t5 @t26) (= @t12 @t25)) @t24)))) % 9.02/9.27 (assume @p15 (forall @t3 (=> @t2 (=> @t31 (forall (@list @t4 @t13) (=> @t29 (=> (or @t28 @t27) @t24))))))) % 9.02/9.27 (assume @p16 (forall @t9 (=> @t8 (=> (= @t5 tptp.sz00) (and @t30 @t32))))) % 9.02/9.27 (assume @p17 (forall @t9 (=> @t8 (=> (= @t11 tptp.sz00) (or @t30 @t32))))) % 9.02/9.27 (assume @p18 @t39) % 9.02/9.27 (assume @p19 (forall @t9 (=> @t8 (=> @t36 (forall @t34 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t33)))))) % 9.02/9.27 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 9.02/9.27 (assume @p21 @t44) % 9.02/9.27 (assume @p22 (forall @t19 (=> @t18 (=> (and @t36 @t45) (tptp.sdtlseqdt0 @t1 @t13))))) % 9.02/9.27 (assume @p23 @t51) % 9.02/9.27 (assume @p24 @t64) % 9.02/9.27 (assume @p25 (forall @t19 (=> @t18 (=> (and @t31 (not @t24) @t45) (and (not @t28) (tptp.sdtlseqdt0 @t11 @t23) (not @t27) (tptp.sdtlseqdt0 @t21 @t22)))))) % 9.02/9.27 (assume @p26 (forall @t3 (=> @t2 (or @t30 @t65 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 9.02/9.27 (assume @p27 (forall @t9 (=> @t8 (=> @t31 (tptp.sdtlseqdt0 @t4 @t21))))) % 9.02/9.27 (assume @p28 (forall @t9 (=> @t8 (=> @t66 true)))) % 9.02/9.27 (assume @p29 (forall @t9 (=> @t8 (=> @t61 @t66)))) % 9.02/9.27 (assume @p30 (forall @t9 (=> @t8 (= @t68 (exists @t34 @t67))))) % 9.02/9.27 (assume @p31 (forall @t9 (=> @t8 (=> @t70 (forall @t34 (= (= @t13 @t69) @t67)))))) % 9.02/9.27 (assume @p32 (forall @t19 (=> @t18 (=> (and @t68 (tptp.doDivides0 @t4 @t13)) @t71)))) % 9.02/9.27 (assume @p33 (forall @t19 (=> @t18 (=> (and @t68 @t71) @t72)))) % 9.02/9.27 (assume @p34 (forall @t19 (=> @t18 (=> (and @t68 @t72) @t71)))) % 9.02/9.27 (assume @p35 @t77) % 9.02/9.27 (assume @p36 (forall @t9 (=> @t8 (=> @t70 (forall @t34 (=> @t17 (= (tptp.sdtasdt0 @t13 @t69) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 9.02/9.27 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t31 @t80 (forall @t79 (=> (and @t7 @t78) (or (= @t4 tptp.sz10) @t46)))))))) % 9.02/9.27 (assume @p38 (forall @t3 (=> (and @t2 @t31 @t80) (exists @t79 (and @t7 @t78 (tptp.isPrime0 @t4)))))) % 9.02/9.27 (assume @p39 (and @t83 @t82 @t81)) % 9.02/9.27 (assume @p40 (forall @t19 (=> @t18 (=> (and (or (and (not (= @t13 tptp.sz00)) (not (= @t13 tptp.sz10)) (forall @t87 (=> (and @t86 (exists (@list @t90) (and (tptp.aNaturalNumber0 @t90) (= @t13 (tptp.sdtasdt0 @t84 @t90)))) (tptp.doDivides0 @t84 @t13)) (or (= @t84 tptp.sz10) (= @t84 @t13))))) (tptp.isPrime0 @t13)) (or (exists @t87 (and @t86 (= @t11 @t85))) (tptp.doDivides0 @t13 @t11))) (=> (tptp.iLess0 @t15 @t89) (or (and (exists @t87 (and @t86 (= @t1 @t85))) (tptp.doDivides0 @t13 @t1)) (and (exists @t87 (and @t86 (= @t4 @t85))) (tptp.doDivides0 @t13 @t4)))))))) % 9.02/9.27 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t79 (and @t7 (= tptp.xp @t11))) (tptp.doDivides0 @t1 tptp.xp))) (or @t65 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t91 (tptp.sdtasdt0 tptp.xp @t1)))) (tptp.doDivides0 tptp.xp @t91))) % 9.02/9.27 (assume @p42 (not (or (exists @t3 (and @t2 (= @t92 tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn)))) % 9.02/9.27 (assume @p43 (not (or (exists @t3 (and @t2 (= @t92 tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm)))) % 9.02/9.27 (assume @p44 (and (not (= tptp.xn tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xn @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xm @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp))) % 9.02/9.27 (assume @p45 (and @t93 (= @t91 (tptp.sdtasdt0 tptp.xp tptp.xk)) (= tptp.xk (tptp.sdtsldt0 @t91 tptp.xp)))) % 9.02/9.27 (assume @p46 @t97) % 9.02/9.27 (assume @p47 (and (not @t95) (not @t94))) % 9.02/9.27 (assume @p48 (and @t103 @t102 @t98 (not (= tptp.xr tptp.sz00)) (not (= tptp.xr tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t79 (and @t7 (= tptp.xr @t11))) (tptp.doDivides0 @t1 tptp.xr))) (or @t65 (= @t1 tptp.xr)))) (tptp.isPrime0 tptp.xr))) % 9.02/9.27 (assume @p49 (and @t106 (exists @t3 (and @t2 (= @t91 @t99))) (tptp.doDivides0 tptp.xr @t91))) % 9.02/9.27 (assume @p50 (and (not @t111) @t110 @t107)) % 9.02/9.27 (assume @p51 @t120) % 9.02/9.27 (assume @p52 true) % 9.02/9.27 (step @p53 :rule bool-and-de-morgan :args (@t2 @t121 true)) % 9.02/9.27 (step @p54 :rule cong :premises (@p53) :args (@t123)) % 9.02/9.27 (step @p55 :rule cong :premises (@p54) :args (@t124)) % 9.02/9.27 (step @p56 :rule exists-elim :args ((= (exists @t3 @t122) @t124))) % 9.02/9.27 (step @p57 :rule trans :premises (@p56 @p55)) % 9.02/9.27 (step @p58 :rule eq-symm :args (@t104 tptp.xk)) % 9.02/9.27 (step @p59 :rule refl :args (@t2)) % 9.02/9.27 (step @p60 :rule nary_cong :premises (@p59 @p58) :args (@t105)) % 9.02/9.27 (step @p61 :rule cong :premises (@p60) :args (@t106)) % 9.02/9.27 (step @p62 :rule trans :premises (@p61 @p57)) % 9.02/9.27 (step @p63 :rule and_elim :premises (@p49) :args (0)) % 9.02/9.27 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 9.02/9.27 (step @p65 :rule skolemize :premises (@p64)) % 9.02/9.27 (step @p66 :rule bool-double-not-elim :args (@t128)) % 9.02/9.27 (step @p67 :rule refl :args (@t132)) % 9.02/9.27 (step @p68 :rule nary_cong :premises (@p67 @p66) :args ((or @t132 (not @t129)))) % 9.02/9.27 (step @p69 :rule cnf_or_neg :args (@t132 1)) % 9.02/9.27 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 9.02/9.27 (step @p71 :rule reordering :premises (@p70) :args ((or @t128 @t132))) % 9.02/9.27 (step @p72 :rule chain_m_resolution :premises (@p71 @p65) :args (@t128 @t133 @t134)) % 9.02/9.27 (step @p73 :rule bool-and-de-morgan :args (@t2 @t135 true)) % 9.02/9.27 (step @p74 :rule cong :premises (@p73) :args (@t137)) % 9.02/9.27 (step @p75 :rule cong :premises (@p74) :args (@t138)) % 9.02/9.27 (step @p76 :rule exists-elim :args ((= (exists @t3 @t136) @t138))) % 9.02/9.27 (step @p77 :rule trans :premises (@p76 @p75)) % 9.02/9.27 (step @p78 :rule eq-symm :args (@t108 tptp.xp)) % 9.02/9.27 (step @p79 :rule nary_cong :premises (@p59 @p78) :args (@t109)) % 9.02/9.27 (step @p80 :rule cong :premises (@p79) :args (@t110)) % 9.02/9.27 (step @p81 :rule trans :premises (@p80 @p77)) % 9.02/9.27 (step @p82 :rule and_elim :premises (@p50) :args (1)) % 9.02/9.27 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 9.02/9.27 (step @p84 :rule skolemize :premises (@p83)) % 9.02/9.27 (step @p85 :rule bool-double-not-elim :args (@t141)) % 9.02/9.27 (step @p86 :rule refl :args (@t145)) % 9.02/9.27 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or @t145 (not @t142)))) % 9.02/9.27 (step @p88 :rule cnf_or_neg :args (@t145 1)) % 9.02/9.27 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 9.02/9.27 (step @p90 :rule reordering :premises (@p89) :args ((or @t141 @t145))) % 9.02/9.27 (step @p91 :rule chain_m_resolution :premises (@p90 @p84) :args (@t141 @t133 @t146)) % 9.02/9.27 (step @p92 :rule aci_norm :args ((= (or @t149 @t16) (or @t125 @t148 @t147 @t16)))) % 9.02/9.27 (step @p93 :rule refl :args (@t16)) % 9.02/9.27 (step @p94 :rule aci_norm :args ((= (or @t125 (or @t148 @t147)) @t149))) % 9.02/9.27 (step @p95 :rule bool-and-de-morgan :args (@t7 @t17 true)) % 9.02/9.27 (step @p96 :rule refl :args (@t125)) % 9.02/9.27 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or @t125 (not @t29)))) % 9.02/9.27 (step @p98 :rule bool-and-de-morgan :args (@t2 @t7 (and @t17))) % 9.02/9.27 (step @p99 :rule trans :premises (@p98 @p97)) % 9.02/9.27 (step @p100 :rule trans :premises (@p99 @p94)) % 9.02/9.27 (step @p101 :rule nary_cong :premises (@p100 @p93) :args ((or (not @t18) @t16))) % 9.02/9.27 (step @p102 :rule trans :premises (@p101 @p92)) % 9.02/9.27 (step @p103 :rule bool-impl-elim :args (@t18 @t16)) % 9.02/9.27 (step @p104 :rule trans :premises (@p103 @p102)) % 9.02/9.27 (step @p105 :rule cong :premises (@p104) :args (@t20)) % 9.02/9.27 (step @p106 :rule eq_resolve :premises (@p7 @p105)) % 9.02/9.27 (step @p107 :rule instantiate :premises (@p106) :args ((@list tptp.xr @t126 @t139))) % 9.02/9.27 (step @p108 :rule bool-double-not-elim :args (@t143)) % 9.02/9.27 (step @p109 :rule nary_cong :premises (@p86 @p108) :args ((or @t145 (not @t144)))) % 9.02/9.27 (step @p110 :rule cnf_or_neg :args (@t145 0)) % 9.02/9.27 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 9.02/9.27 (step @p112 :rule reordering :premises (@p111) :args ((or @t143 @t145))) % 9.02/9.27 (step @p113 :rule chain_m_resolution :premises (@p112 @p84) :args (@t143 @t133 @t146)) % 9.02/9.27 (step @p114 :rule bool-double-not-elim :args (@t130)) % 9.02/9.27 (step @p115 :rule nary_cong :premises (@p67 @p114) :args ((or @t132 (not @t131)))) % 9.02/9.27 (step @p116 :rule cnf_or_neg :args (@t132 0)) % 9.02/9.27 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 9.02/9.27 (step @p118 :rule reordering :premises (@p117) :args ((or @t130 @t132))) % 9.02/9.27 (step @p119 :rule chain_m_resolution :premises (@p118 @p65) :args (@t130 @t133 @t134)) % 9.02/9.27 (step @p120 :rule and_elim :premises (@p48) :args (0)) % 9.02/9.27 (step @p121 :rule cnf_or_pos :args (@t154)) % 9.02/9.27 (step @p122 :rule reordering :premises (@p121) :args ((or @t153 @t131 @t144 @t152 (not @t154)))) % 9.02/9.27 (step @p123 :rule chain_m_resolution :premises (@p122 @p120 @p119 @p113 @p107) :args (@t152 @t155 @t156)) % 9.02/9.27 (step @p124 :rule aci_norm :args ((= (or @t159 @t158) (or @t125 @t148 @t158)))) % 9.02/9.27 (step @p125 :rule refl :args (@t158)) % 9.02/9.27 (step @p126 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 9.02/9.27 (step @p127 :rule nary_cong :premises (@p126 @p125) :args ((or @t160 @t158))) % 9.02/9.27 (step @p128 :rule trans :premises (@p127 @p124)) % 9.02/9.27 (step @p129 :rule bool-impl-elim :args (@t8 @t158)) % 9.02/9.27 (step @p130 :rule trans :premises (@p129 @p128)) % 9.02/9.27 (step @p131 :rule cong :premises (@p130) :args ((forall @t9 (=> @t8 @t158)))) % 9.02/9.27 (step @p132 :rule bool-and-de-morgan :args (@t17 @t157 true)) % 9.02/9.27 (step @p133 :rule cong :premises (@p132) :args (@t162)) % 9.02/9.27 (step @p134 :rule cong :premises (@p133) :args (@t163)) % 9.02/9.27 (step @p135 :rule exists-elim :args ((= (exists @t34 @t161) @t163))) % 9.02/9.27 (step @p136 :rule trans :premises (@p135 @p134)) % 9.02/9.27 (step @p137 :rule eq-symm :args (@t26 @t4)) % 9.02/9.27 (step @p138 :rule refl :args (@t17)) % 9.02/9.27 (step @p139 :rule nary_cong :premises (@p138 @p137) :args (@t33)) % 9.02/9.27 (step @p140 :rule cong :premises (@p139) :args (@t35)) % 9.02/9.27 (step @p141 :rule trans :premises (@p140 @p136)) % 9.02/9.27 (step @p142 :rule refl :args (@t36)) % 9.02/9.27 (step @p143 :rule cong :premises (@p142 @p141) :args (@t37)) % 9.02/9.27 (step @p144 :rule refl :args (@t8)) % 9.02/9.27 (step @p145 :rule cong :premises (@p144 @p143) :args (@t38)) % 9.02/9.27 (step @p146 :rule cong :premises (@p145) :args (@t39)) % 9.02/9.27 (step @p147 :rule trans :premises (@p146 @p131)) % 9.02/9.27 (step @p148 :rule eq_resolve :premises (@p18 @p147)) % 9.02/9.27 (step @p149 :rule instantiate :premises (@p148) :args (@t164)) % 9.02/9.27 (step @p150 :rule and_elim :premises (@p39) :args (2)) % 9.02/9.27 (step @p151 :rule cnf_or_pos :args (@t170)) % 9.02/9.27 (step @p152 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:premises (@p534) :args (@t256)) % 9.02/9.27 (step @p383 :rule eq_resolve :premises (@p381 @p378)) % 9.02/9.27 (step @p384 :rule implies_elim :premises (@p383)) % 9.02/9.27 (step @p385 :rule chain_m_resolution :premises (@p384 @p205) :args (@t257 @t214 @t215)) % 9.02/9.27 (step @p386 :rule cnf_or_pos :args (@t257)) % 9.02/9.27 (step @p387 :rule reordering :premises (@p386) :args ((or @t169 @t153 @t207 @t212 @t255 @t182 (not @t257)))) % 9.02/9.27 (step @p388 :rule aci_norm :args ((= (or @t159 @t260) @t259))) % 9.02/9.27 (step @p389 :rule refl :args (@t260)) % 9.02/9.27 (step @p390 :rule nary_cong :premises (@p126 @p389) :args ((or @t160 @t260))) % 9.02/9.27 (step @p391 :rule trans :premises (@p390 @p388)) % 9.02/9.27 (step @p392 :rule bool-impl-elim :args (@t8 @t260)) % 9.02/9.27 (step @p393 :rule trans :premises (@p392 @p391)) % 9.02/9.27 (step @p394 :rule cong :premises (@p393) :args ((forall @t9 (=> @t8 @t260)))) % 9.02/9.27 (step @p395 :rule refl :args (@t41)) % 9.02/9.27 (step @p396 :rule eq-symm :args (@t4 @t1)) % 9.02/9.27 (step @p397 :rule cong :premises (@p396) :args (@t47)) % 9.02/9.27 (step @p398 :rule nary_cong :premises (@p397 @p395) :args (@t48)) % 9.02/9.27 (step @p399 :rule nary_cong :premises (@p142 @p398) :args (@t49)) % 9.02/9.27 (step @p400 :rule cong :premises (@p144 @p399) :args (@t50)) % 9.02/9.27 (step @p401 :rule cong :premises (@p400) :args (@t51)) % 9.02/9.27 (step @p402 :rule trans :premises (@p401 @p394)) % 9.02/9.27 (step @p403 :rule eq_resolve :premises (@p23 @p402)) % 9.02/9.27 (step @p404 :rule refl :args (@t254)) % 9.02/9.27 (step @p405 :rule cong :premises (@p214) :args (@t261)) % 9.02/9.27 (step @p406 :rule nary_cong :premises (@p405 @p404) :args (@t262)) % 9.02/9.27 (step @p407 :rule refl :args (@t167)) % 9.02/9.27 (step @p408 :rule nary_cong :premises (@p216 @p215 @p407 @p406) :args (@t263)) % 9.02/9.27 (step @p409 :rule refl :args (@t264)) % 9.02/9.27 (step @p410 :rule cong :premises (@p409 @p408) :args ((=> @t264 @t263))) % 9.02/9.27 (assume-push @p535 @t264) % 9.02/9.27 (step @p412 :rule instantiate :premises (@p403) :args (@t164)) % 9.02/9.27 (step-pop @p536 :rule scope :premises (@p412)) % 9.02/9.27 (step @p413 :rule process_scope :premises (@p536) :args (@t263)) % 9.02/9.27 (step @p415 :rule eq_resolve :premises (@p413 @p410)) % 9.02/9.27 (step @p416 :rule implies_elim :premises (@p415)) % 9.02/9.27 (step @p417 :rule chain_m_resolution :premises (@p416 @p403) :args (@t266 @t214 (@list @t264))) % 9.02/9.27 (step @p418 :rule cnf_or_pos :args (@t266)) % 9.02/9.27 (step @p419 :rule reordering :premises (@p418) :args ((or @t169 @t153 @t167 @t265 (not @t266)))) % 9.02/9.27 (step @p420 :rule cnf_and_pos :args (@t265 1)) % 9.02/9.27 (step @p421 :rule reordering :premises (@p420) :args ((or @t254 (not @t265)))) % 9.02/9.27 (step @p422 :rule chain_m_resolution :premises (@p421 @p419 @p417 @p120 @p150 @p387 @p385 @p352 @p366 @p120 @p150 @p368 @p366 @p352 @p226 @p120 @p150 @p157 @p155) :args (@t177 (@list false false false false true false true false false false true false true false false false true true) (@list @t265 @t266 @t103 @t81 @t254 @t257 @t212 @t206 @t103 @t81 @t167 @t206 @t212 @t213 @t103 @t81 @t182 @t178))) % 9.02/9.27 (step @p423 :rule refl :args (@t269)) % 9.02/9.27 (step @p424 :rule bool-double-not-elim :args (@t176)) % 9.02/9.27 (step @p425 :rule nary_cong :premises (@p424 @p423) :args ((or (not @t177) @t269))) % 9.02/9.27 (step @p426 :rule bool-and-de-morgan :args (@t2 @t267 true)) % 9.02/9.27 (step @p427 :rule cong :premises (@p426) :args (@t271)) % 9.02/9.27 (step @p428 :rule cong :premises (@p427) :args (@t272)) % 9.02/9.27 (step @p429 :rule exists-elim :args ((= (exists @t3 @t270) @t272))) % 9.02/9.27 (step @p430 :rule trans :premises (@p429 @p428)) % 9.02/9.27 (step @p431 :rule eq-symm :args (@t114 @t89)) % 9.02/9.27 (step @p432 :rule nary_cong :premises (@p59 @p431) :args (@t115)) % 9.02/9.27 (step @p433 :rule cong :premises (@p432) :args (@t116)) % 9.02/9.27 (step @p434 :rule trans :premises (@p433 @p430)) % 9.02/9.27 (step @p435 :rule nary_cong :premises (@p434 @p208) :args (@t117)) % 9.02/9.27 (step @p436 :rule nary_cong :premises (@p210 @p435) :args (@t119)) % 9.02/9.27 (step @p437 :rule cong :premises (@p436) :args (@t120)) % 9.02/9.27 (step @p438 :rule eq_resolve :premises (@p51 @p437)) % 9.02/9.27 (step @p439 :rule not_and :premises (@p438)) % 9.02/9.27 (step @p440 :rule eq_resolve :premises (@p439 @p425)) % 9.02/9.27 (assume-push @p537 @t212) % 9.02/9.27 (assume-push @p538 @t212) % 9.02/9.27 (step @p443 :rule refl :args (@t88)) % 9.02/9.27 (step @p444 :rule cong :premises (@p443 @p537) :args (@t89)) % 9.02/9.27 (step-pop @p539 :rule scope :premises (@p444)) % 9.02/9.27 (step @p445 :rule process_scope :premises (@p539) :args (@t176)) % 9.02/9.27 (step @p447 :rule modus_ponens :premises (@p537 @p445)) % 9.02/9.27 (step-pop @p540 :rule scope :premises (@p447)) % 9.02/9.27 (step @p448 :rule process_scope :premises (@p540) :args (@t176)) % 9.02/9.27 (step @p450 :rule implies_elim :premises (@p448)) % 9.02/9.27 (step @p451 :rule reordering :premises (@p450) :args ((or @t176 @t246))) % 9.02/9.27 (step @p452 :rule cnf_or_neg :args (@t268 1)) % 9.02/9.27 (step @p453 :rule cnf_and_pos :args (@t178 1)) % 9.02/9.27 (step @p454 :rule reordering :premises (@p453) :args ((or @t113 @t179))) % 9.02/9.27 (step @p455 :rule chain_m_resolution :premises (@p454 @p368 @p366 @p226 @p120 @p150 @p452 @p451 @p440) :args ((or @t176 @t208) (@list false false false false false true true true) (@list @t178 @t206 @t213 @t103 @t81 @t113 @t212 @t268))) % 9.02/9.27 (step @p456 :rule chain_m_resolution :premises (@p455 @p422) :args (@t208 @t133 (@list @t176))) % 9.02/9.27 (step @p457 :rule bool-double-not-elim :args (@t165)) % 0.36/9.32 (step @p458 :rule refl :args (@t273)) % 0.36/9.32 (step @p459 :rule nary_cong :premises (@p458 @p407 @p457) :args ((or @t273 @t167 (not @t166)))) % 0.36/9.32 (step @p460 :rule cnf_equiv_pos2 :args (@t168)) % 0.36/9.32 (step @p461 :rule eq_resolve :premises (@p460 @p459)) % 0.36/9.32 (step @p462 :rule reordering :premises (@p461) :args ((or @t167 @t165 @t273))) % 0.36/9.32 (step @p463 :rule chain_m_resolution :premises (@p462 @p456 @p153) :args (@t165 (@list true false) (@list @t167 @t168))) % 0.36/9.32 (assume-push @p541 @t165) % 0.36/9.32 (step @p465 :rule instantiate :premises (@p541) :args ((@list @t150))) % 0.36/9.32 (step-pop @p542 :rule scope :premises (@p465)) % 0.36/9.32 (step @p466 :rule process_scope :premises (@p542) :args (@t278)) % 0.36/9.32 (step @p468 :rule implies_elim :premises (@p466)) % 0.36/9.32 (step @p469 :rule chain_m_resolution :premises (@p468 @p463) :args (@t278 @t214 (@list @t165))) % 0.36/9.32 (step @p470 :rule instantiate :premises (@p360) :args ((@list @t126 @t139))) % 0.36/9.32 (step @p471 :rule cnf_or_pos :args (@t279)) % 0.36/9.32 (step @p472 :rule reordering :premises (@p471) :args ((or @t131 @t144 @t276 (not @t279)))) % 0.36/9.32 (step @p473 :rule chain_m_resolution :premises (@p472 @p119 @p113 @p470) :args (@t276 @t171 (@list @t130 @t143 @t279))) % 0.36/9.32 (step @p474 :rule cnf_or_pos :args (@t278)) % 0.36/9.32 (step @p475 :rule reordering :premises (@p474) :args ((or @t277 @t275 (not @t278)))) % 0.36/9.32 (step @p476 :rule chain_m_resolution :premises (@p475 @p473 @p469) :args (@t275 (@list false false) (@list @t276 @t278))) % 0.36/9.32 (step @p477 :rule bool-double-not-elim :args (@t274)) % 0.36/9.32 (step @p478 :rule refl :args (@t280)) % 0.36/9.32 (step @p479 :rule refl :args (@t142)) % 0.36/9.32 (step @p480 :rule refl :args (@t129)) % 0.36/9.32 (step @p481 :rule nary_cong :premises (@p480 @p479 @p478 @p477) :args ((or @t129 @t142 @t280 (not @t275)))) % 0.36/9.32 (assume-push @p543 @t274) % 0.36/9.32 (assume-push @p544 @t275) % 0.36/9.32 (step @p322 :rule evaluate :args (@t247)) % 0.36/9.32 (step @p484 :rule false_intro :premises (@p544)) % 0.36/9.32 (step @p485 :rule chain_m_resolution :premises (@p122 @p120 @p119 @p113 @p107) :args (@t152 @t155 @t156)) % 0.36/9.32 (step @p486 :rule refl :args (@t139)) % 0.36/9.32 (step @p487 :rule cong :premises (@p72 @p486) :args (@t140)) % 0.36/9.32 (step @p488 :rule chain_m_resolution :premises (@p90 @p84) :args (@t141 @t133 @t146)) % 0.36/9.32 (step @p489 :rule trans :premises (@p488 @p487 @p485)) % 0.36/9.32 (step @p490 :rule true_intro :premises (@p489)) % 0.36/9.32 (step @p491 :rule symm :premises (@p490)) % 0.36/9.32 (step @p492 :rule trans :premises (@p491 @p484)) % 0.36/9.32 (step @p493 false :rule eq_resolve :premises (@p492 @p322)) % 0.36/9.32 (step-pop @p545 :rule scope :premises (@p493)) % 0.36/9.32 (step-pop @p546 :rule scope :premises (@p545)) % 0.36/9.32 (step @p494 :rule process_scope :premises (@p546) :args (false)) % 0.36/9.32 (assume-push @p547 @t128) % 0.36/9.32 (assume-push @p548 @t141) % 0.36/9.32 (assume-push @p549 @t152) % 0.36/9.32 (assume-push @p550 @t275) % 0.36/9.32 (step @p486 :rule refl :args (@t139)) % 0.36/9.32 (step @p487 :rule cong :premises (@p72 @p486) :args (@t140)) % 0.36/9.32 (step @p501 :rule trans :premises (@p91 @p487 @p123)) % 0.36/9.32 (step @p502 :rule and_intro :premises (@p501 @p550)) % 0.36/9.32 (step-pop @p551 :rule scope :premises (@p502)) % 0.36/9.32 (step-pop @p552 :rule scope :premises (@p551)) % 0.36/9.32 (step-pop @p553 :rule scope :premises (@p552)) % 0.36/9.32 (step-pop @p554 :rule scope :premises (@p553)) % 0.36/9.32 (step @p503 :rule process_scope :premises (@p554) :args (@t281)) % 0.36/9.32 (step @p508 :rule implies_elim :premises (@p503)) % 0.36/9.32 (step @p509 :rule resolution :premises (@p508 @p494) :args (true @t281)) % 0.36/9.32 (step @p510 :rule not_and :premises (@p509)) % 0.36/9.32 (step @p511 :rule eq_resolve :premises (@p510 @p481)) % 0.36/9.32 (step @p512 false :rule chain_m_resolution :premises (@p511 @p476 @p123 @p91 @p72) :args (false (@list true false false false) (@list @t274 @t152 @t141 @t128))) % 0.36/9.32 ) % 0.36/9.32 % SZS output end Proof % 0.36/9.32 % cvc5 exiting %------------------------------------------------------------------------------