%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM528+1 : 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 : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:39:43 AM UTC 2026 % Result : Theorem 12.83s 13.02s % Output : Proof 12.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM528+1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 11:27:18 EDT 2026 % 0.07/0.25 % CPUTime : % 0.16/0.34 %----Proving TF0_NAR, FOF, or CNF % 12.83/13.02 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 12.83/13.02 % SZS status Theorem % 12.83/13.02 % SZS output start Proof % 12.83/13.02 ( % 12.83/13.02 (declare-sort $$unsorted 0) % 12.83/13.02 (declare-const tptp.xq $$unsorted) % 12.83/13.02 (declare-const tptp.xp $$unsorted) % 12.83/13.02 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 12.83/13.02 (declare-const tptp.sz10 $$unsorted) % 12.83/13.02 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 12.83/13.02 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 12.83/13.02 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 12.83/13.02 (declare-const tptp.sz00 $$unsorted) % 12.83/13.02 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 12.83/13.02 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 12.83/13.02 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 12.83/13.02 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 12.83/13.02 (declare-const tptp.xn $$unsorted) % 12.83/13.02 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 12.83/13.02 (declare-const tptp.xm $$unsorted) % 12.83/13.02 (define @t1 () (@var "W0" $$unsorted)) % 12.83/13.02 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 12.83/13.02 (define @t3 () (@list @t1)) % 12.83/13.02 (define @t4 () (tptp.aNaturalNumber0 tptp.sz10)) % 12.83/13.02 (define @t5 () (@var "W1" $$unsorted)) % 12.83/13.02 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 12.83/13.02 (define @t7 () (tptp.aNaturalNumber0 @t5)) % 12.83/13.02 (define @t8 () (and @t2 @t7)) % 12.83/13.02 (define @t9 () (@list @t1 @t5)) % 12.83/13.02 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 12.83/13.02 (define @t11 () (tptp.aNaturalNumber0 @t10)) % 12.83/13.02 (define @t12 () (forall @t9 (=> @t8 @t11))) % 12.83/13.02 (define @t13 () (tptp.sdtpldt0 @t5 @t1)) % 12.83/13.02 (define @t14 () (@var "W2" $$unsorted)) % 12.83/13.02 (define @t15 () (tptp.sdtpldt0 @t5 @t14)) % 12.83/13.02 (define @t16 () (tptp.aNaturalNumber0 @t14)) % 12.83/13.02 (define @t17 () (and @t2 @t7 @t16)) % 12.83/13.02 (define @t18 () (@list @t1 @t5 @t14)) % 12.83/13.02 (define @t19 () (tptp.sdtasdt0 @t5 @t1)) % 12.83/13.02 (define @t20 () (= @t10 @t19)) % 12.83/13.02 (define @t21 () (forall @t9 (=> @t8 @t20))) % 12.83/13.02 (define @t22 () (= (tptp.sdtasdt0 @t10 @t14) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t14)))) % 12.83/13.02 (define @t23 () (forall @t18 (=> @t17 @t22))) % 12.83/13.02 (define @t24 () (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1))) % 12.83/13.02 (define @t25 () (tptp.sdtasdt0 @t1 tptp.sz10)) % 12.83/13.02 (define @t26 () (and (= @t25 @t1) @t24)) % 12.83/13.02 (define @t27 () (=> @t2 @t26)) % 12.83/13.02 (define @t28 () (forall @t3 @t27)) % 12.83/13.02 (define @t29 () (tptp.sdtasdt0 @t14 @t1)) % 12.83/13.02 (define @t30 () (tptp.sdtasdt0 @t1 @t14)) % 12.83/13.02 (define @t31 () (= @t5 @t14)) % 12.83/13.02 (define @t32 () (tptp.sdtpldt0 @t14 @t1)) % 12.83/13.02 (define @t33 () (tptp.sdtpldt0 @t1 @t14)) % 12.83/13.02 (define @t34 () (= @t19 @t29)) % 12.83/13.02 (define @t35 () (= @t10 @t30)) % 12.83/13.02 (define @t36 () (or @t35 @t34)) % 12.83/13.02 (define @t37 () (=> @t36 @t31)) % 12.83/13.02 (define @t38 () (and @t7 @t16)) % 12.83/13.02 (define @t39 () (@list @t5 @t14)) % 12.83/13.02 (define @t40 () (forall @t39 (=> @t38 @t37))) % 12.83/13.02 (define @t41 () (= @t1 tptp.sz00)) % 12.83/13.02 (define @t42 () (not @t41)) % 12.83/13.02 (define @t43 () (=> @t42 @t40)) % 12.83/13.02 (define @t44 () (=> @t2 @t43)) % 12.83/13.02 (define @t45 () (forall @t3 @t44)) % 12.83/13.02 (define @t46 () (= @t5 tptp.sz00)) % 12.83/13.02 (define @t47 () (or @t41 @t46)) % 12.83/13.02 (define @t48 () (=> (= @t10 tptp.sz00) @t47)) % 12.83/13.02 (define @t49 () (=> @t8 @t48)) % 12.83/13.02 (define @t50 () (forall @t9 @t49)) % 12.83/13.02 (define @t51 () (and @t16 (= @t33 @t5))) % 12.83/13.02 (define @t52 () (@list @t14)) % 12.83/13.02 (define @t53 () (tptp.sdtlseqdt0 @t1 @t5)) % 12.83/13.02 (define @t54 () (= @t1 @t5)) % 12.83/13.02 (define @t55 () (tptp.sdtlseqdt0 @t5 @t1)) % 12.83/13.02 (define @t56 () (and @t53 @t55)) % 12.83/13.02 (define @t57 () (=> @t56 @t54)) % 12.83/13.02 (define @t58 () (forall @t9 (=> @t8 @t57))) % 12.83/13.02 (define @t59 () (tptp.sdtlseqdt0 @t5 @t14)) % 12.83/13.02 (define @t60 () (= @t5 @t1)) % 12.83/13.02 (define @t61 () (not @t60)) % 12.83/13.02 (define @t62 () (and @t61 @t55)) % 12.83/13.02 (define @t63 () (or @t53 @t62)) % 12.83/13.02 (define @t64 () (=> @t8 @t63)) % 12.83/13.02 (define @t65 () (forall @t9 @t64)) % 12.83/13.02 (define @t66 () (tptp.sdtpldt0 @t14 @t5)) % 12.83/13.02 (define @t67 () (not @t54)) % 12.83/13.02 (define @t68 () (and @t67 @t53)) % 12.83/13.02 (define @t69 () (not @t34)) % 12.83/13.02 (define @t70 () (not @t35)) % 12.83/13.02 (define @t71 () (= @t1 tptp.sz10)) % 12.83/13.02 (define @t72 () (tptp.sdtlseqdt0 @t5 @t19)) % 12.83/13.02 (define @t73 () (=> @t42 @t72)) % 12.83/13.02 (define @t74 () (forall @t9 (=> @t8 @t73))) % 12.83/13.02 (define @t75 () (tptp.iLess0 @t1 @t5)) % 12.83/13.02 (define @t76 () (and @t16 (= @t5 @t30))) % 12.83/13.02 (define @t77 () (tptp.doDivides0 @t1 @t5)) % 12.83/13.02 (define @t78 () (tptp.sdtsldt0 @t5 @t1)) % 12.83/13.02 (define @t79 () (and @t42 @t77)) % 12.83/13.02 (define @t80 () (tptp.doDivides0 @t1 @t14)) % 12.83/13.02 (define @t81 () (tptp.doDivides0 @t1 @t15)) % 12.83/13.02 (define @t82 () (not @t46)) % 12.83/13.02 (define @t83 () (or (= @t5 tptp.sz10) @t60)) % 12.83/13.02 (define @t84 () (tptp.doDivides0 @t5 @t1)) % 12.83/13.02 (define @t85 () (and @t7 @t84)) % 12.83/13.02 (define @t86 () (=> @t85 @t83)) % 12.83/13.02 (define @t87 () (@list @t5)) % 12.83/13.02 (define @t88 () (forall @t87 @t86)) % 12.83/13.02 (define @t89 () (not @t71)) % 12.83/13.02 (define @t90 () (and @t42 @t89 @t88)) % 12.83/13.02 (define @t91 () (tptp.isPrime0 @t1)) % 12.83/13.02 (define @t92 () (= @t91 @t90)) % 12.83/13.02 (define @t93 () (=> @t2 @t92)) % 12.83/13.02 (define @t94 () (forall @t3 @t93)) % 12.83/13.02 (define @t95 () (tptp.isPrime0 @t14)) % 12.83/13.02 (define @t96 () (= tptp.xp tptp.sz00)) % 12.83/13.02 (define @t97 () (not @t96)) % 12.83/13.02 (define @t98 () (= tptp.xm tptp.sz00)) % 12.83/13.02 (define @t99 () (tptp.aNaturalNumber0 tptp.xp)) % 12.83/13.02 (define @t100 () (tptp.aNaturalNumber0 tptp.xm)) % 12.83/13.02 (define @t101 () (tptp.aNaturalNumber0 tptp.xn)) % 12.83/13.02 (define @t102 () (tptp.sdtasdt0 tptp.xn tptp.xn)) % 12.83/13.02 (define @t103 () (tptp.sdtasdt0 tptp.xm tptp.xm)) % 12.83/13.02 (define @t104 () (tptp.sdtasdt0 tptp.xp @t103)) % 12.83/13.02 (define @t105 () (= @t104 @t102)) % 12.83/13.02 (define @t106 () (tptp.isPrime0 tptp.xp)) % 12.83/13.02 (define @t107 () (tptp.sdtlseqdt0 @t102 @t103)) % 12.83/13.02 (define @t108 () (tptp.sdtlseqdt0 tptp.xn tptp.xm)) % 12.83/13.02 (define @t109 () (tptp.sdtlseqdt0 tptp.xm tptp.xn)) % 12.83/13.02 (define @t110 () (not (= tptp.xm tptp.xn))) % 12.83/13.02 (define @t111 () (and @t110 @t109)) % 12.83/13.02 (define @t112 () (not @t111)) % 12.83/13.02 (define @t113 () (not @t7)) % 12.83/13.02 (define @t114 () (not @t2)) % 12.83/13.02 (define @t115 () (or @t114 @t113)) % 12.83/13.02 (define @t116 () (not @t8)) % 12.83/13.02 (define @t117 () (@list tptp.xp @t103)) % 12.83/13.02 (define @t118 () (@list tptp.xm tptp.xm)) % 12.83/13.02 (define @t119 () (tptp.aNaturalNumber0 @t103)) % 12.83/13.02 (define @t120 () (not @t100)) % 12.83/13.02 (define @t121 () (or @t120 @t120 @t119)) % 12.83/13.02 (define @t122 () (@list false false)) % 12.83/13.02 (define @t123 () (tptp.sdtasdt0 @t103 tptp.xp)) % 12.83/13.02 (define @t124 () (= @t104 @t123)) % 12.83/13.02 (define @t125 () (not @t119)) % 12.83/13.02 (define @t126 () (not @t99)) % 12.83/13.02 (define @t127 () (or @t126 @t125 @t124)) % 12.83/13.02 (define @t128 () (@list false false false)) % 12.83/13.02 (define @t129 () (and (= @t1 @t25) @t24)) % 12.83/13.02 (define @t130 () (tptp.sdtasdt0 tptp.xm tptp.sz10)) % 12.83/13.02 (define @t131 () (= tptp.xm @t130)) % 12.83/13.02 (define @t132 () (and @t131 (= tptp.xm (tptp.sdtasdt0 tptp.sz10 tptp.xm)))) % 12.83/13.02 (define @t133 () (or @t120 @t132)) % 12.83/13.02 (define @t134 () (@list false)) % 12.83/13.02 (define @t135 () (not @t16)) % 12.83/13.02 (define @t136 () (or @t114 @t113 @t135)) % 12.83/13.02 (define @t137 () (or @t113 @t135)) % 12.83/13.02 (define @t138 () (not @t38)) % 12.83/13.02 (define @t139 () (tptp.sdtasdt0 @t103 tptp.sz10)) % 12.83/13.02 (define @t140 () (= @t139 (tptp.sdtasdt0 tptp.xm @t130))) % 12.83/13.02 (define @t141 () (not @t4)) % 12.83/13.02 (define @t142 () (or @t120 @t120 @t141 @t140)) % 12.83/13.02 (define @t143 () (not @t55)) % 12.83/13.02 (define @t144 () (not @t53)) % 12.83/13.02 (define @t145 () (or @t144 @t143 @t54)) % 12.83/13.02 (define @t146 () (or @t114 @t113 @t41 @t72)) % 12.83/13.02 (define @t147 () (not @t42)) % 12.83/13.02 (define @t148 () (tptp.sdtlseqdt0 @t103 @t123)) % 12.83/13.02 (define @t149 () (or @t126 @t125 @t96 @t148)) % 12.83/13.02 (define @t150 () (forall @t9 @t146)) % 12.83/13.02 (define @t151 () (= tptp.sz00 tptp.xp)) % 12.83/13.02 (define @t152 () (or @t126 @t125 @t151 @t148)) % 12.83/13.02 (define @t153 () (tptp.sdtlseqdt0 @t103 @t102)) % 12.83/13.02 (define @t154 () (tptp.aNaturalNumber0 @t102)) % 12.83/13.02 (define @t155 () (not @t101)) % 12.83/13.02 (define @t156 () (or @t155 @t155 @t154)) % 12.83/13.02 (define @t157 () (= tptp.xn tptp.xm)) % 12.83/13.02 (define @t158 () (not @t157)) % 12.83/13.02 (define @t159 () (and @t158 @t108)) % 12.83/13.02 (define @t160 () (and @t67 @t55)) % 12.83/13.02 (define @t161 () (or @t114 @t113 @t53 @t160)) % 12.83/13.02 (define @t162 () (or @t53 @t160)) % 12.83/13.02 (define @t163 () (and @t158 @t109)) % 12.83/13.02 (define @t164 () (or @t155 @t120 @t108 @t163)) % 12.83/13.02 (define @t165 () (and @t110 @t108)) % 12.83/13.02 (define @t166 () (or @t120 @t155 @t109 @t165)) % 12.83/13.02 (define @t167 () (forall @t9 @t161)) % 12.83/13.02 (define @t168 () (or @t120 @t155 @t109 @t159)) % 12.83/13.02 (define @t169 () (not @t109)) % 12.83/13.02 (define @t170 () (= @t103 @t102)) % 12.83/13.02 (define @t171 () (not @t107)) % 12.83/13.02 (define @t172 () (not @t153)) % 12.83/13.02 (define @t173 () (not @t154)) % 12.83/13.02 (define @t174 () (or @t125 @t173 @t172 @t171 @t170)) % 12.83/13.02 (define @t175 () (@var "BOUND_VARIABLE_7818" $$unsorted)) % 12.83/13.02 (define @t176 () (@var "BOUND_VARIABLE_7816" $$unsorted)) % 12.83/13.02 (define @t177 () (= @t176 @t175)) % 12.83/13.02 (define @t178 () (and (not (= (tptp.sdtasdt0 @t1 @t176) (tptp.sdtasdt0 @t1 @t175))) (not (= (tptp.sdtasdt0 @t176 @t1) (tptp.sdtasdt0 @t175 @t1))))) % 12.83/13.02 (define @t179 () (not (tptp.aNaturalNumber0 @t175))) % 12.83/13.02 (define @t180 () (not (tptp.aNaturalNumber0 @t176))) % 12.83/13.02 (define @t181 () (or @t114 @t41 @t180 @t179 @t178 @t177)) % 12.83/13.02 (define @t182 () (or @t180 @t179 @t178 @t177)) % 12.83/13.02 (define @t183 () (or @t114 @t41 @t182)) % 12.83/13.02 (define @t184 () (@list @t1 @t176 @t175)) % 12.83/13.02 (define @t185 () (forall @t184 @t183)) % 12.83/13.02 (define @t186 () (@list @t176 @t175)) % 12.83/13.02 (define @t187 () (forall @t186 @t183)) % 12.83/13.02 (define @t188 () (forall @t186 @t182)) % 12.83/13.02 (define @t189 () (or @t114 @t41 @t188)) % 12.83/13.02 (define @t190 () (and @t70 @t69)) % 12.83/13.02 (define @t191 () (or @t113 @t135 @t190 @t31)) % 12.83/13.02 (define @t192 () (forall @t39 @t191)) % 12.83/13.02 (define @t193 () (or @t114 @t41 @t192)) % 12.83/13.02 (define @t194 () (=> @t42 @t192)) % 12.83/13.02 (define @t195 () (= tptp.sz10 tptp.xp)) % 12.83/13.02 (define @t196 () (tptp.sdtasdt0 tptp.sz10 @t103)) % 12.83/13.02 (define @t197 () (not (= @t196 @t104))) % 12.83/13.02 (define @t198 () (not (= @t139 @t123))) % 12.83/13.02 (define @t199 () (and @t198 @t197)) % 12.83/13.02 (define @t200 () (or @t125 (= @t103 tptp.sz00) @t141 @t126 @t199 @t195)) % 12.83/13.02 (define @t201 () (forall @t184 @t181)) % 12.83/13.02 (define @t202 () (= @t123 @t139)) % 12.83/13.02 (define @t203 () (not @t202)) % 12.83/13.02 (define @t204 () (and @t203 (not (= @t104 @t196)))) % 12.83/13.02 (define @t205 () (= tptp.sz00 @t103)) % 12.83/13.02 (define @t206 () (or @t125 @t205 @t141 @t126 @t204 @t195)) % 12.83/13.02 (define @t207 () (= tptp.sz10 @t5)) % 12.83/13.02 (define @t208 () (not @t84)) % 12.83/13.02 (define @t209 () (or @t113 @t208 @t207 @t54)) % 12.83/13.02 (define @t210 () (= @t91 (and @t42 @t89 (forall @t87 @t209)))) % 12.83/13.02 (define @t211 () (or @t207 @t54)) % 12.83/13.02 (define @t212 () (not (tptp.doDivides0 @t5 tptp.xp))) % 12.83/13.02 (define @t213 () (or @t113 @t212 @t207 (= tptp.xp @t5))) % 12.83/13.02 (define @t214 () (forall @t87 @t213)) % 12.83/13.02 (define @t215 () (not (= tptp.xp tptp.sz10))) % 12.83/13.02 (define @t216 () (and @t97 @t215 @t214)) % 12.83/13.02 (define @t217 () (= @t106 @t216)) % 12.83/13.02 (define @t218 () (or @t126 @t217)) % 12.83/13.02 (define @t219 () (forall @t3 (or @t114 @t210))) % 12.83/13.02 (define @t220 () (not @t195)) % 12.83/13.02 (define @t221 () (and (not @t151) @t220 (forall @t87 (or @t113 @t212 @t207 (= @t5 tptp.xp))))) % 12.83/13.02 (define @t222 () (= @t106 @t221)) % 12.83/13.02 (define @t223 () (or @t126 @t222)) % 12.83/13.02 (define @t224 () (= tptp.sz00 @t5)) % 12.83/13.02 (define @t225 () (= tptp.sz00 @t10)) % 12.83/13.02 (define @t226 () (not @t225)) % 12.83/13.02 (define @t227 () (or @t114 @t113 @t226 @t41 @t224)) % 12.83/13.02 (define @t228 () (or @t226 @t41 @t224)) % 12.83/13.02 (define @t229 () (or @t41 @t224)) % 12.83/13.02 (define @t230 () (=> @t225 @t229)) % 12.83/13.02 (define @t231 () (= tptp.sz00 tptp.xm)) % 12.83/13.02 (define @t232 () (not @t205)) % 12.83/13.02 (define @t233 () (or @t120 @t120 @t232 @t98 @t231)) % 12.83/13.02 (define @t234 () (forall @t9 @t227)) % 12.83/13.02 (define @t235 () (or @t120 @t120 @t232 @t231 @t231)) % 12.83/13.02 (define @t236 () (not @t140)) % 12.83/13.02 (define @t237 () (not @t170)) % 12.83/13.02 (define @t238 () (not @t131)) % 12.83/13.02 (define @t239 () (not @t124)) % 12.83/13.02 (define @t240 () (not @t105)) % 12.83/13.02 (define @t241 () (and @t203 @t202)) % 12.83/13.02 (assume @p1 (forall @t3 (=> @t2 true))) % 12.83/13.02 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 12.83/13.02 (assume @p3 (and @t4 (not (= tptp.sz10 tptp.sz00)))) % 12.83/13.02 (assume @p4 (forall @t9 (=> @t8 (tptp.aNaturalNumber0 @t6)))) % 12.83/13.02 (assume @p5 @t12) % 12.83/13.02 (assume @p6 (forall @t9 (=> @t8 (= @t6 @t13)))) % 12.83/13.02 (assume @p7 (forall @t18 (=> @t17 (= (tptp.sdtpldt0 @t6 @t14) (tptp.sdtpldt0 @t1 @t15))))) % 12.83/13.02 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 12.83/13.02 (assume @p9 @t21) % 12.83/13.02 (assume @p10 @t23) % 12.83/13.02 (assume @p11 @t28) % 12.83/13.02 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 12.83/13.02 (assume @p13 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t15) (tptp.sdtpldt0 @t10 @t30)) (= (tptp.sdtasdt0 @t15 @t1) (tptp.sdtpldt0 @t19 @t29)))))) % 12.83/13.02 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t6 @t33) (= @t13 @t32)) @t31)))) % 12.83/13.02 (assume @p15 @t45) % 12.83/13.02 (assume @p16 (forall @t9 (=> @t8 (=> (= @t6 tptp.sz00) (and @t41 @t46))))) % 12.83/13.02 (assume @p17 @t50) % 12.83/13.02 (assume @p18 (forall @t9 (=> @t8 (= @t53 (exists @t52 @t51))))) % 12.83/13.02 (assume @p19 (forall @t9 (=> @t8 (=> @t53 (forall @t52 (= (= @t14 (tptp.sdtmndt0 @t5 @t1)) @t51)))))) % 12.83/13.02 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 12.83/13.02 (assume @p21 @t58) % 12.83/13.02 (assume @p22 (forall @t18 (=> @t17 (=> (and @t53 @t59) (tptp.sdtlseqdt0 @t1 @t14))))) % 12.83/13.02 (assume @p23 @t65) % 12.83/13.02 (assume @p24 (forall @t9 (=> @t8 (=> @t68 (forall @t52 (=> @t16 (and (not (= @t32 @t66)) (tptp.sdtlseqdt0 @t32 @t66) (not (= @t33 @t15)) (tptp.sdtlseqdt0 @t33 @t15)))))))) % 12.83/13.02 (assume @p25 (forall @t18 (=> @t17 (=> (and @t42 (not @t31) @t59) (and @t70 (tptp.sdtlseqdt0 @t10 @t30) @t69 (tptp.sdtlseqdt0 @t19 @t29)))))) % 12.83/13.02 (assume @p26 (forall @t3 (=> @t2 (or @t41 @t71 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 12.83/13.02 (assume @p27 @t74) % 12.83/13.02 (assume @p28 (forall @t9 (=> @t8 (=> @t75 true)))) % 12.83/13.02 (assume @p29 (forall @t9 (=> @t8 (=> @t68 @t75)))) % 12.83/13.02 (assume @p30 (forall @t9 (=> @t8 (= @t77 (exists @t52 @t76))))) % 12.83/13.02 (assume @p31 (forall @t9 (=> @t8 (=> @t79 (forall @t52 (= (= @t14 @t78) @t76)))))) % 12.83/13.02 (assume @p32 (forall @t18 (=> @t17 (=> (and @t77 (tptp.doDivides0 @t5 @t14)) @t80)))) % 12.83/13.02 (assume @p33 (forall @t18 (=> @t17 (=> (and @t77 @t80) @t81)))) % 12.83/13.02 (assume @p34 (forall @t18 (=> @t17 (=> (and @t77 @t81) @t80)))) % 12.83/13.02 (assume @p35 (forall @t9 (=> @t8 (=> (and @t77 @t82) @t53)))) % 12.83/13.02 (assume @p36 (forall @t9 (=> @t8 (=> @t79 (forall @t52 (=> @t16 (= (tptp.sdtasdt0 @t14 @t78) (tptp.sdtsldt0 (tptp.sdtasdt0 @t14 @t5) @t1)))))))) % 12.83/13.02 (assume @p37 @t94) % 12.83/13.02 (assume @p38 (forall @t3 (=> (and @t2 @t42 @t89) (exists @t87 (and @t7 @t84 (tptp.isPrime0 @t5)))))) % 12.83/13.02 (assume @p39 (forall @t18 (=> @t17 (=> (and @t95 (tptp.doDivides0 @t14 @t10)) (or (tptp.doDivides0 @t14 @t1) (tptp.doDivides0 @t14 @t5)))))) % 12.83/13.02 (assume @p40 (and @t101 @t100 @t99 (not (= tptp.xn tptp.sz00)) (not @t98) @t97)) % 12.83/13.02 (assume @p41 (forall @t18 (=> (and @t2 @t7 @t16 @t42 @t82 (not (= @t14 tptp.sz00))) (=> (= (tptp.sdtasdt0 @t14 (tptp.sdtasdt0 @t5 @t5)) (tptp.sdtasdt0 @t1 @t1)) (=> (tptp.iLess0 @t1 tptp.xn) (not @t95)))))) % 12.83/13.02 (assume @p42 @t105) % 12.83/13.02 (assume @p43 @t106) % 12.83/13.02 (assume @p44 (and (tptp.doDivides0 tptp.xp @t102) (tptp.doDivides0 tptp.xp tptp.xn))) % 12.83/13.02 (assume @p45 (= tptp.xq (tptp.sdtsldt0 tptp.xn tptp.xp))) % 12.83/13.02 (assume @p46 (= @t103 (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xq tptp.xq)))) % 12.83/13.02 (assume @p47 (=> @t108 @t107)) % 12.83/13.02 (assume @p48 @t112) % 12.83/13.02 (assume @p49 true) % 12.83/13.02 (step @p50 :rule aci_norm :args ((= (or @t115 @t20) (or @t114 @t113 @t20)))) % 12.83/13.02 (step @p51 :rule refl :args (@t20)) % 12.83/13.02 (step @p52 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 12.83/13.02 (step @p53 :rule nary_cong :premises (@p52 @p51) :args ((or @t116 @t20))) % 12.83/13.02 (step @p54 :rule trans :premises (@p53 @p50)) % 12.83/13.02 (step @p55 :rule bool-impl-elim :args (@t8 @t20)) % 12.83/13.02 (step @p56 :rule trans :premises (@p55 @p54)) % 12.83/13.02 (step @p57 :rule cong :premises (@p56) :args (@t21)) % 12.83/13.02 (step @p58 :rule eq_resolve :premises (@p9 @p57)) % 12.83/13.02 (step @p59 :rule instantiate :premises (@p58) :args (@t117)) % 12.83/13.02 (step @p60 :rule aci_norm :args ((= (or @t115 @t11) (or @t114 @t113 @t11)))) % 12.83/13.02 (step @p61 :rule refl :args (@t11)) % 12.83/13.02 (step @p62 :rule nary_cong :premises (@p52 @p61) :args ((or @t116 @t11))) % 12.83/13.02 (step @p63 :rule trans :premises (@p62 @p60)) % 12.83/13.02 (step @p64 :rule bool-impl-elim :args (@t8 @t11)) % 12.83/13.02 (step @p65 :rule trans :premises (@p64 @p63)) % 12.83/13.02 (step @p66 :rule cong :premises (@p65) :args (@t12)) % 12.83/13.02 (step @p67 :rule eq_resolve :premises (@p5 @p66)) % 12.83/13.02 (step @p68 :rule instantiate :premises (@p67) :args (@t118)) % 12.83/13.02 (step @p69 :rule and_elim :premises (@p40) :args (1)) % 12.83/13.02 (step @p70 :rule cnf_or_pos :args (@t121)) % 12.83/13.02 (step @p71 :rule factoring :premises (@p70)) % 12.83/13.02 (step @p72 :rule reordering :premises (@p71) :args ((or @t120 @t119 (not @t121)))) % 12.83/13.02 (step @p73 :rule chain_m_resolution :premises (@p72 @p69 @p68) :args (@t119 @t122 (@list @t100 @t121))) % 12.83/13.02 (step @p74 :rule and_elim :premises (@p40) :args (2)) % 12.83/13.02 (step @p75 :rule cnf_or_pos :args (@t127)) % 12.83/13.02 (step @p76 :rule reordering :premises (@p75) :args ((or @t126 @t125 @t124 (not @t127)))) % 12.83/13.02 (step @p77 :rule chain_m_resolution :premises (@p76 @p74 @p73 @p59) :args (@t124 @t128 (@list @t99 @t119 @t127))) % 12.83/13.02 (step @p78 :rule bool-impl-elim :args (@t2 @t129)) % 12.83/13.02 (step @p79 :rule cong :premises (@p78) :args ((forall @t3 (=> @t2 @t129)))) % 12.83/13.02 (step @p80 :rule refl :args (@t24)) % 12.83/13.02 (step @p81 :rule eq-symm :args (@t25 @t1)) % 12.83/13.02 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t26)) % 12.83/13.02 (step @p83 :rule refl :args (@t2)) % 12.83/13.02 (step @p84 :rule cong :premises (@p83 @p82) :args (@t27)) % 12.83/13.02 (step @p85 :rule cong :premises (@p84) :args (@t28)) % 12.83/13.02 (step @p86 :rule trans :premises (@p85 @p79)) % 12.83/13.02 (step @p87 :rule eq_resolve :premises (@p11 @p86)) % 12.83/13.02 (step @p88 :rule instantiate :premises (@p87) :args ((@list tptp.xm))) % 12.83/13.02 (step @p89 :rule cnf_or_pos :args (@t133)) % 12.83/13.02 (step @p90 :rule reordering :premises (@p89) :args ((or @t120 @t132 (not @t133)))) % 12.83/13.02 (step @p91 :rule chain_m_resolution :premises (@p90 @p69 @p88) :args (@t132 @t122 (@list @t100 @t133))) % 12.83/13.02 (step @p92 :rule cnf_and_pos :args (@t132 0)) % 12.83/13.02 (step @p93 :rule reordering :premises (@p92) :args ((or @t131 (not @t132)))) % 12.83/13.02 (step @p94 :rule chain_m_resolution :premises (@p93 @p91) :args (@t131 @t134 (@list @t132))) % 12.83/13.02 (step @p95 :rule aci_norm :args ((= (or @t136 @t22) (or @t114 @t113 @t135 @t22)))) % 12.83/13.02 (step @p96 :rule refl :args (@t22)) % 12.83/13.02 (step @p97 :rule aci_norm :args ((= (or @t114 @t137) @t136))) % 12.83/13.02 (step @p98 :rule bool-and-de-morgan :args (@t7 @t16 true)) % 12.83/13.02 (step @p99 :rule refl :args (@t114)) % 12.83/13.02 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((or @t114 @t138))) % 12.83/13.02 (step @p101 :rule bool-and-de-morgan :args (@t2 @t7 (and @t16))) % 12.83/13.02 (step @p102 :rule trans :premises (@p101 @p100)) % 12.83/13.02 (step @p103 :rule trans :premises (@p102 @p97)) % 12.83/13.02 (step @p104 :rule nary_cong :premises (@p103 @p96) :args ((or (not @t17) @t22))) % 12.83/13.02 (step @p105 :rule trans :premises (@p104 @p95)) % 12.83/13.02 (step @p106 :rule bool-impl-elim :args (@t17 @t22)) % 12.83/13.02 (step @p107 :rule trans :premises (@p106 @p105)) % 12.83/13.02 (step @p108 :rule cong :premises (@p107) :args (@t23)) % 12.83/13.02 (step @p109 :rule eq_resolve :premises (@p10 @p108)) % 12.83/13.02 (step @p110 :rule instantiate :premises (@p109) :args ((@list tptp.xm tptp.xm tptp.sz10))) % 12.83/13.02 (step @p111 :rule and_elim :premises (@p3) :args (0)) % 12.83/13.02 (step @p112 :rule cnf_or_pos :args (@t142)) % 12.83/13.02 (step @p113 :rule factoring :premises (@p112)) % 12.83/13.02 (step @p114 :rule reordering :premises (@p113) :args ((or @t141 @t120 @t140 (not @t142)))) % 12.83/13.02 (step @p115 :rule chain_m_resolution :premises (@p114 @p111 @p69 @p110) :args (@t140 @t128 (@list @t4 @t100 @t142))) % 12.83/13.02 (step @p116 :rule aci_norm :args ((= (or @t115 @t145) (or @t114 @t113 @t144 @t143 @t54)))) % 12.83/13.02 (step @p117 :rule aci_norm :args ((= (or (or @t144 @t143) @t54) @t145))) % 12.83/13.02 (step @p118 :rule refl :args (@t54)) % 12.83/13.02 (step @p119 :rule bool-and-de-morgan :args (@t53 @t55 true)) % 12.83/13.02 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or (not @t56) @t54))) % 12.83/13.02 (step @p121 :rule trans :premises (@p120 @p117)) % 12.83/13.02 (step @p122 :rule bool-impl-elim :args (@t56 @t54)) % 12.83/13.02 (step @p123 :rule trans :premises (@p122 @p121)) % 12.83/13.02 (step @p124 :rule nary_cong :premises (@p52 @p123) :args ((or @t116 @t57))) % 12.83/13.02 (step @p125 :rule trans :premises (@p124 @p116)) % 12.83/13.02 (step @p126 :rule bool-impl-elim :args (@t8 @t57)) % 12.83/13.02 (step @p127 :rule trans :premises (@p126 @p125)) % 12.83/13.02 (step @p128 :rule cong :premises (@p127) :args (@t58)) % 12.83/13.02 (step @p129 :rule eq_resolve :premises (@p21 @p128)) % 12.83/13.02 (step @p130 :rule instantiate :premises (@p129) :args ((@list @t103 @t102))) % 12.83/13.02 (step @p131 :rule aci_norm :args ((= (or @t115 (or @t41 @t72)) @t146))) % 12.83/13.02 (step @p132 :rule refl :args (@t72)) % 12.83/13.02 (step @p133 :rule bool-double-not-elim :args (@t41)) % 12.83/13.02 (step @p134 :rule nary_cong :premises (@p133 @p132) :args ((or @t147 @t72))) % 12.83/13.02 (step @p135 :rule bool-impl-elim :args (@t42 @t72)) % 12.83/13.02 (step @p136 :rule trans :premises (@p135 @p134)) % 12.83/13.02 (step @p137 :rule nary_cong :premises (@p52 @p136) :args ((or @t116 @t73))) % 12.83/13.02 (step @p138 :rule trans :premises (@p137 @p131)) % 12.83/13.02 (step @p139 :rule bool-impl-elim :args (@t8 @t73)) % 12.83/13.02 (step @p140 :rule trans :premises (@p139 @p138)) % 12.83/13.02 (step @p141 :rule cong :premises (@p140) :args (@t74)) % 12.83/13.02 (step @p142 :rule eq_resolve :premises (@p27 @p141)) % 12.83/13.02 (step @p143 :rule refl :args (@t148)) % 12.83/13.02 (step @p144 :rule eq-symm :args (tptp.xp tptp.sz00)) % 12.83/13.02 (step @p145 :rule refl :args (@t125)) % 12.83/13.02 (step @p146 :rule refl :args (@t126)) % 12.83/13.02 (step @p147 :rule nary_cong :premises (@p146 @p145 @p144 @p143) :args (@t149)) % 12.83/13.02 (step @p148 :rule refl :args (@t150)) % 12.83/13.02 (step @p149 :rule cong :premises (@p148 @p147) :args ((=> @t150 @t149))) % 12.83/13.02 (assume-push @p435 @t150) % 12.83/13.02 (step @p151 :rule instantiate :premises (@p142) :args (@t117)) % 12.83/13.02 (step-pop @p436 :rule scope :premises (@p151)) % 12.83/13.02 (step @p152 :rule process_scope :premises (@p436) :args (@t149)) % 12.83/13.02 (step @p154 :rule eq_resolve :premises (@p152 @p149)) % 12.83/13.02 (step @p155 :rule implies_elim :premises (@p154)) % 12.83/13.02 (step @p156 :rule chain_m_resolution :premises (@p155 @p142) :args (@t152 @t134 (@list @t150))) % 12.83/13.02 (step @p157 :rule and_elim :premises (@p40) :args (5)) % 12.83/13.02 (step @p158 :rule symm :premises (@p157)) % 12.83/13.02 (step @p159 :rule cnf_or_pos :args (@t152)) % 12.83/13.02 (step @p160 :rule reordering :premises (@p159) :args ((or @t151 @t126 @t125 @t148 (not @t152)))) % 12.83/13.02 (step @p161 :rule chain_m_resolution :premises (@p160 @p158 @p74 @p73 @p156) :args (@t148 (@list true false false false) (@list @t151 @t99 @t119 @t152))) % 12.83/13.02 (step @p162 :rule true_intro :premises (@p161)) % 12.83/13.02 (step @p163 :rule symm :premises (@p42)) % 12.83/13.02 (step @p164 :rule trans :premises (@p163 @p77)) % 12.83/13.02 (step @p165 :rule refl :args (@t103)) % 12.83/13.02 (step @p166 :rule cong :premises (@p165 @p164) :args (@t153)) % 12.83/13.02 (step @p167 :rule trans :premises (@p166 @p162)) % 12.83/13.02 (step @p168 :rule true_elim :premises (@p167)) % 12.83/13.02 (step @p169 :rule instantiate :premises (@p67) :args ((@list tptp.xn tptp.xn))) % 12.83/13.02 (step @p170 :rule and_elim :premises (@p40) :args (0)) % 12.83/13.02 (step @p171 :rule cnf_or_pos :args (@t156)) % 12.83/13.02 (step @p172 :rule factoring :premises (@p171)) % 12.83/13.02 (step @p173 :rule reordering :premises (@p172) :args ((or @t155 @t154 (not @t156)))) % 12.83/13.02 (step @p174 :rule chain_m_resolution :premises (@p173 @p170 @p169) :args (@t154 @t122 (@list @t101 @t156))) % 12.83/13.02 (step @p175 :rule cnf_and_pos :args (@t159 1)) % 12.83/13.02 (step @p176 :rule reordering :premises (@p175) :args ((or @t108 (not @t159)))) % 12.83/13.02 (step @p177 :rule aci_norm :args ((= (or @t115 @t162) @t161))) % 12.83/13.02 (step @p178 :rule refl :args (@t162)) % 12.83/13.02 (step @p179 :rule nary_cong :premises (@p52 @p178) :args ((or @t116 @t162))) % 12.83/13.02 (step @p180 :rule trans :premises (@p179 @p177)) % 12.83/13.02 (step @p181 :rule bool-impl-elim :args (@t8 @t162)) % 12.83/13.02 (step @p182 :rule trans :premises (@p181 @p180)) % 12.83/13.02 (step @p183 :rule cong :premises (@p182) :args ((forall @t9 (=> @t8 @t162)))) % 12.83/13.02 (step @p184 :rule refl :args (@t55)) % 12.83/13.02 (step @p185 :rule eq-symm :args (@t5 @t1)) % 12.83/13.02 (step @p186 :rule cong :premises (@p185) :args (@t61)) % 12.83/13.02 (step @p187 :rule nary_cong :premises (@p186 @p184) :args (@t62)) % 12.83/13.02 (step @p188 :rule refl :args (@t53)) % 12.83/13.02 (step @p189 :rule nary_cong :premises (@p188 @p187) :args (@t63)) % 12.83/13.02 (step @p190 :rule refl :args (@t8)) % 12.83/13.02 (step @p191 :rule cong :premises (@p190 @p189) :args (@t64)) % 12.83/13.02 (step @p192 :rule cong :premises (@p191) :args (@t65)) % 12.83/13.02 (step @p193 :rule trans :premises (@p192 @p183)) % 12.83/13.02 (step @p194 :rule eq_resolve :premises (@p23 @p193)) % 12.83/13.02 (step @p195 :rule instantiate :premises (@p194) :args ((@list tptp.xn tptp.xm))) % 12.83/13.02 (step @p196 :rule cnf_or_pos :args (@t164)) % 12.83/13.02 (step @p197 :rule reordering :premises (@p196) :args ((or @t108 @t163 @t155 @t120 (not @t164)))) % 12.83/13.02 (step @p198 :rule refl :args (@t108)) % 12.83/13.02 (step @p199 :rule eq-symm :args (tptp.xm tptp.xn)) % 12.83/13.02 (step @p200 :rule cong :premises (@p199) :args (@t110)) % 12.83/13.02 (step @p201 :rule nary_cong :premises (@p200 @p198) :args (@t165)) % 12.83/13.02 (step @p202 :rule refl :args (@t109)) % 12.83/13.02 (step @p203 :rule refl :args (@t155)) % 12.83/13.02 (step @p204 :rule refl :args (@t120)) % 12.83/13.02 (step @p205 :rule nary_cong :premises (@p204 @p203 @p202 @p201) :args (@t166)) % 12.83/13.02 (step @p206 :rule refl :args (@t167)) % 12.83/13.02 (step @p207 :rule cong :premises (@p206 @p205) :args ((=> @t167 @t166))) % 12.83/13.02 (assume-push @p437 @t167) % 12.83/13.02 (step @p209 :rule instantiate :premises (@p194) :args ((@list tptp.xm tptp.xn))) % 12.83/13.02 (step-pop @p438 :rule scope :premises (@p209)) % 12.83/13.02 (step @p210 :rule process_scope :premises (@p438) :args (@t166)) % 12.83/13.02 (step @p212 :rule eq_resolve :premises (@p210 @p207)) % 12.83/13.02 (step @p213 :rule implies_elim :premises (@p212)) % 12.83/13.02 (step @p214 :rule chain_m_resolution :premises (@p213 @p194) :args (@t168 @t134 (@list @t167))) % 12.83/13.02 (step @p215 :rule cnf_or_pos :args (@t168)) % 12.83/13.02 (step @p216 :rule reordering :premises (@p215) :args ((or @t109 @t155 @t120 @t159 (not @t168)))) % 12.83/13.02 (step @p217 :rule cnf_and_pos :args (@t163 0)) % 12.83/13.02 (step @p218 :rule reordering :premises (@p217) :args ((or @t158 (not @t163)))) % 12.83/13.02 (step @p219 :rule refl :args (@t169)) % 12.83/13.02 (step @p220 :rule bool-double-not-elim :args (@t157)) % 12.83/13.02 (step @p221 :rule nary_cong :premises (@p220 @p219) :args ((or (not @t158) @t169))) % 12.83/13.02 (step @p222 :rule nary_cong :premises (@p200 @p202) :args (@t111)) % 12.83/13.02 (step @p223 :rule cong :premises (@p222) :args (@t112)) % 12.83/13.02 (step @p224 :rule eq_resolve :premises (@p48 @p223)) % 12.83/13.02 (step @p225 :rule not_and :premises (@p224)) % 12.83/13.02 (step @p226 :rule eq_resolve :premises (@p225 @p221)) % 12.83/13.02 (step @p227 :rule chain_m_resolution :premises (@p226 @p218 @p216 @p214 @p69 @p170 @p197 @p195 @p69 @p170 @p176) :args (@t108 (@list true false false false false false false false false true) (@list @t157 @t109 @t168 @t100 @t101 @t163 @t164 @t100 @t101 @t159))) % 12.83/13.02 (step @p228 :rule implies_elim :premises (@p47)) % 12.83/13.02 (step @p229 :rule reordering :premises (@p228) :args ((or @t107 (not @t108)))) % 12.83/13.02 (step @p230 :rule chain_m_resolution :premises (@p229 @p227) :args (@t107 @t134 (@list @t108))) % 12.83/13.02 (step @p231 :rule cnf_or_pos :args (@t174)) % 12.83/13.02 (step @p232 :rule reordering :premises (@p231) :args ((or @t171 @t125 @t173 @t170 @t172 (not @t174)))) % 12.83/13.02 (step @p233 :rule chain_m_resolution :premises (@p232 @p230 @p73 @p174 @p168 @p130) :args (@t170 (@list false false false false false) (@list @t107 @t119 @t154 @t153 @t174))) % 12.83/13.02 (step @p234 :rule aci_norm :args ((= @t183 @t181))) % 12.83/13.02 (step @p235 :rule cong :premises (@p234) :args (@t185)) % 12.83/13.02 (step @p236 :rule quant-merge-prenex :args ((= (forall @t3 @t187) @t185))) % 12.83/13.02 (step @p237 :rule alpha_equiv :args (@t188 (@list @t176 @t175) (@list @t5 @t14))) % 12.83/13.02 (step @p238 :rule refl :args (@t41)) % 12.83/13.02 (step @p239 :rule nary_cong :premises (@p99 @p238 @p237) :args (@t189)) % 12.83/13.02 (step @p240 :rule quant-miniscope-or :args ((= @t187 @t189))) % 12.83/13.02 (step @p241 :rule trans :premises (@p240 @p239)) % 12.83/13.02 (step @p242 :rule symm :premises (@p241)) % 12.83/13.02 (step @p243 :rule cong :premises (@p242) :args ((forall @t3 @t193))) % 12.83/13.02 (step @p244 :rule trans :premises (@p243 @p236)) % 12.83/13.02 (step @p245 :rule trans :premises (@p244 @p235)) % 12.83/13.02 (step @p246 :rule aci_norm :args ((= (or @t114 (or @t41 @t192)) @t193))) % 12.83/13.02 (step @p247 :rule refl :args (@t192)) % 12.83/13.02 (step @p248 :rule nary_cong :premises (@p133 @p247) :args ((or @t147 @t192))) % 12.83/13.02 (step @p249 :rule bool-impl-elim :args (@t42 @t192)) % 12.83/13.02 (step @p250 :rule trans :premises (@p249 @p248)) % 12.83/13.02 (step @p251 :rule nary_cong :premises (@p99 @p250) :args ((or @t114 @t194))) % 12.83/13.02 (step @p252 :rule trans :premises (@p251 @p246)) % 12.83/13.02 (step @p253 :rule bool-impl-elim :args (@t2 @t194)) % 12.83/13.02 (step @p254 :rule trans :premises (@p253 @p252)) % 12.83/13.02 (step @p255 :rule cong :premises (@p254) :args ((forall @t3 (=> @t2 @t194)))) % 12.83/13.02 (step @p256 :rule trans :premises (@p255 @p245)) % 12.83/13.02 (step @p257 :rule aci_norm :args ((= (or @t137 (or @t190 @t31)) @t191))) % 12.83/13.02 (step @p258 :rule refl :args (@t31)) % 12.83/13.02 (step @p259 :rule bool-or-de-morgan :args (@t35 @t34 false)) % 12.83/13.02 (step @p260 :rule nary_cong :premises (@p259 @p258) :args ((or (not @t36) @t31))) % 12.83/13.02 (step @p261 :rule bool-impl-elim :args (@t36 @t31)) % 12.83/13.02 (step @p262 :rule trans :premises (@p261 @p260)) % 12.83/13.02 (step @p263 :rule nary_cong :premises (@p98 @p262) :args ((or @t138 @t37))) % 12.83/13.02 (step @p264 :rule trans :premises (@p263 @p257)) % 12.83/13.02 (step @p265 :rule bool-impl-elim :args (@t38 @t37)) % 12.83/13.02 (step @p266 :rule trans :premises (@p265 @p264)) % 12.83/13.02 (step @p267 :rule cong :premises (@p266) :args (@t40)) % 12.83/13.02 (step @p268 :rule refl :args (@t42)) % 12.83/13.02 (step @p269 :rule cong :premises (@p268 @p267) :args (@t43)) % 12.83/13.02 (step @p270 :rule cong :premises (@p83 @p269) :args (@t44)) % 12.83/13.02 (step @p271 :rule cong :premises (@p270) :args (@t45)) % 12.83/13.02 (step @p272 :rule trans :premises (@p271 @p256)) % 12.83/13.02 (step @p273 :rule eq_resolve :premises (@p15 @p272)) % 12.83/13.02 (step @p274 :rule refl :args (@t195)) % 12.83/13.02 (step @p275 :rule eq-symm :args (@t196 @t104)) % 12.83/13.02 (step @p276 :rule cong :premises (@p275) :args (@t197)) % 12.83/13.02 (step @p277 :rule eq-symm :args (@t139 @t123)) % 12.83/13.02 (step @p278 :rule cong :premises (@p277) :args (@t198)) % 12.83/13.02 (step @p279 :rule nary_cong :premises (@p278 @p276) :args (@t199)) % 12.83/13.02 (step @p280 :rule refl :args (@t141)) % 12.83/13.02 (step @p281 :rule eq-symm :args (@t103 tptp.sz00)) % 12.83/13.02 (step @p282 :rule nary_cong :premises (@p145 @p281 @p280 @p146 @p279 @p274) :args (@t200)) % 12.83/13.02 (step @p283 :rule refl :args (@t201)) % 12.83/13.02 (step @p284 :rule cong :premises (@p283 @p282) :args ((=> @t201 @t200))) % 12.83/13.02 (assume-push @p439 @t201) % 12.83/13.02 (step @p286 :rule instantiate :premises (@p273) :args ((@list @t103 tptp.sz10 tptp.xp))) % 12.83/13.02 (step-pop @p440 :rule scope :premises (@p286)) % 12.83/13.02 (step @p287 :rule process_scope :premises (@p440) :args (@t200)) % 12.83/13.02 (step @p289 :rule eq_resolve :premises (@p287 @p284)) % 12.83/13.02 (step @p290 :rule implies_elim :premises (@p289)) % 12.83/13.02 (step @p291 :rule chain_m_resolution :premises (@p290 @p273) :args (@t206 @t134 (@list @t201))) % 12.83/13.02 (step @p292 :rule bool-impl-elim :args (@t2 @t210)) % 12.83/13.02 (step @p293 :rule cong :premises (@p292) :args ((forall @t3 (=> @t2 @t210)))) % 12.83/13.02 (step @p294 :rule aci_norm :args ((= (or (or @t113 @t208) @t211) @t209))) % 12.83/13.02 (step @p295 :rule refl :args (@t211)) % 12.83/13.02 (step @p296 :rule bool-and-de-morgan :args (@t7 @t84 true)) % 12.83/13.02 (step @p297 :rule nary_cong :premises (@p296 @p295) :args ((or (not @t85) @t211))) % 12.83/13.02 (step @p298 :rule trans :premises (@p297 @p294)) % 12.83/13.02 (step @p299 :rule bool-impl-elim :args (@t85 @t211)) % 12.83/13.02 (step @p300 :rule trans :premises (@p299 @p298)) % 12.83/13.02 (step @p301 :rule cong :premises (@p300) :args ((forall @t87 (=> @t85 @t211)))) % 12.83/13.02 (step @p302 :rule eq-symm :args (@t5 tptp.sz10)) % 12.83/13.02 (step @p303 :rule nary_cong :premises (@p302 @p185) :args (@t83)) % 12.83/13.02 (step @p304 :rule refl :args (@t85)) % 12.83/13.02 (step @p305 :rule cong :premises (@p304 @p303) :args (@t86)) % 12.83/13.02 (step @p306 :rule cong :premises (@p305) :args (@t88)) % 12.83/13.02 (step @p307 :rule trans :premises (@p306 @p301)) % 12.83/13.02 (step @p308 :rule refl :args (@t89)) % 12.83/13.02 (step @p309 :rule nary_cong :premises (@p268 @p308 @p307) :args (@t90)) % 12.83/13.02 (step @p310 :rule refl :args (@t91)) % 12.83/13.02 (step @p311 :rule cong :premises (@p310 @p309) :args (@t92)) % 12.83/13.02 (step @p312 :rule cong :premises (@p83 @p311) :args (@t93)) % 12.83/13.02 (step @p313 :rule cong :premises (@p312) :args (@t94)) % 12.83/13.02 (step @p314 :rule trans :premises (@p313 @p293)) % 12.83/13.02 (step @p315 :rule eq_resolve :premises (@p37 @p314)) % 12.83/13.02 (step @p316 :rule eq-symm :args (tptp.xp @t5)) % 12.83/13.02 (step @p317 :rule refl :args (@t207)) % 12.83/13.02 (step @p318 :rule refl :args (@t212)) % 12.83/13.02 (step @p319 :rule refl :args (@t113)) % 12.83/13.02 (step @p320 :rule nary_cong :premises (@p319 @p318 @p317 @p316) :args (@t213)) % 12.83/13.02 (step @p321 :rule cong :premises (@p320) :args (@t214)) % 12.83/13.02 (step @p322 :rule eq-symm :args (tptp.xp tptp.sz10)) % 12.83/13.02 (step @p323 :rule cong :premises (@p322) :args (@t215)) % 12.83/13.02 (step @p324 :rule cong :premises (@p144) :args (@t97)) % 12.83/13.02 (step @p325 :rule nary_cong :premises (@p324 @p323 @p321) :args (@t216)) % 12.83/13.02 (step @p326 :rule refl :args (@t106)) % 12.83/13.02 (step @p327 :rule cong :premises (@p326 @p325) :args (@t217)) % 12.83/13.02 (step @p328 :rule nary_cong :premises (@p146 @p327) :args (@t218)) % 12.83/13.02 (step @p329 :rule refl :args (@t219)) % 12.83/13.02 (step @p330 :rule cong :premises (@p329 @p328) :args ((=> @t219 @t218))) % 12.83/13.02 (assume-push @p441 @t219) % 12.83/13.02 (step @p332 :rule instantiate :premises (@p315) :args ((@list tptp.xp))) % 12.83/13.02 (step-pop @p442 :rule scope :premises (@p332)) % 12.83/13.02 (step @p333 :rule process_scope :premises (@p442) :args (@t218)) % 12.83/13.02 (step @p335 :rule eq_resolve :premises (@p333 @p330)) % 12.83/13.02 (step @p336 :rule implies_elim :premises (@p335)) % 12.83/13.02 (step @p337 :rule chain_m_resolution :premises (@p336 @p315) :args (@t223 @t134 (@list @t219))) % 12.83/13.02 (step @p338 :rule cnf_or_pos :args (@t223)) % 12.83/13.02 (step @p339 :rule reordering :premises (@p338) :args ((or @t126 @t222 (not @t223)))) % 12.83/13.02 (step @p340 :rule chain_m_resolution :premises (@p339 @p74 @p337) :args (@t222 @t122 (@list @t99 @t223))) % 12.83/13.02 (step @p341 :rule cnf_equiv_pos1 :args (@t222)) % 12.83/13.02 (step @p342 :rule reordering :premises (@p341) :args ((or (not @t106) @t221 (not @t222)))) % 12.83/13.02 (step @p343 :rule chain_m_resolution :premises (@p342 @p43 @p340) :args (@t221 @t122 (@list @t106 @t222))) % 12.83/13.02 (step @p344 :rule cnf_and_pos :args (@t221 1)) % 12.83/13.02 (step @p345 :rule reordering :premises (@p344) :args ((or @t220 (not @t221)))) % 12.83/13.02 (step @p346 :rule chain_m_resolution :premises (@p345 @p343) :args (@t220 @t134 (@list @t221))) % 12.83/13.02 (step @p347 :rule aci_norm :args ((= (or @t115 @t228) @t227))) % 12.83/13.02 (step @p348 :rule aci_norm :args ((= (or @t226 @t229) @t228))) % 12.83/13.02 (step @p349 :rule bool-impl-elim :args (@t225 @t229)) % 12.83/13.02 (step @p350 :rule trans :premises (@p349 @p348)) % 12.83/13.02 (step @p351 :rule nary_cong :premises (@p52 @p350) :args ((or @t116 @t230))) % 12.83/13.02 (step @p352 :rule trans :premises (@p351 @p347)) % 12.83/13.02 (step @p353 :rule bool-impl-elim :args (@t8 @t230)) % 12.83/13.02 (step @p354 :rule trans :premises (@p353 @p352)) % 12.83/13.02 (step @p355 :rule cong :premises (@p354) :args ((forall @t9 (=> @t8 @t230)))) % 12.83/13.02 (step @p356 :rule eq-symm :args (@t5 tptp.sz00)) % 12.83/13.02 (step @p357 :rule refl :args (@t41)) % 12.83/13.02 (step @p358 :rule nary_cong :premises (@p357 @p356) :args (@t47)) % 12.83/13.02 (step @p359 :rule eq-symm :args (@t10 tptp.sz00)) % 12.83/13.02 (step @p360 :rule cong :premises (@p359 @p358) :args (@t48)) % 12.83/13.02 (step @p361 :rule cong :premises (@p190 @p360) :args (@t49)) % 12.83/13.02 (step @p362 :rule cong :premises (@p361) :args (@t50)) % 12.83/13.02 (step @p363 :rule trans :premises (@p362 @p355)) % 12.83/13.02 (step @p364 :rule eq_resolve :premises (@p17 @p363)) % 12.83/13.02 (step @p365 :rule refl :args (@t231)) % 12.83/13.02 (step @p366 :rule eq-symm :args (tptp.xm tptp.sz00)) % 12.83/13.02 (step @p367 :rule refl :args (@t232)) % 12.83/13.02 (step @p368 :rule nary_cong :premises (@p204 @p204 @p367 @p366 @p365) :args (@t233)) % 12.83/13.02 (step @p369 :rule refl :args (@t234)) % 12.83/13.02 (step @p370 :rule cong :premises (@p369 @p368) :args ((=> @t234 @t233))) % 12.83/13.02 (assume-push @p443 @t234) % 12.83/13.02 (step @p372 :rule instantiate :premises (@p364) :args (@t118)) % 12.83/13.02 (step-pop @p444 :rule scope :premises (@p372)) % 12.83/13.02 (step @p373 :rule process_scope :premises (@p444) :args (@t233)) % 12.83/13.02 (step @p375 :rule eq_resolve :premises (@p373 @p370)) % 12.83/13.02 (step @p376 :rule implies_elim :premises (@p375)) % 12.83/13.02 (step @p377 :rule chain_m_resolution :premises (@p376 @p364) :args (@t235 @t134 (@list @t234))) % 12.83/13.02 (step @p378 :rule and_elim :premises (@p40) :args (4)) % 12.83/13.02 (step @p379 :rule symm :premises (@p378)) % 12.83/13.02 (step @p380 :rule cnf_or_pos :args (@t235)) % 12.83/13.02 (step @p381 :rule factoring :premises (@p380)) % 12.83/13.02 (step @p382 :rule reordering :premises (@p381) :args ((or @t231 @t120 @t232 (not @t235)))) % 12.83/13.02 (step @p383 :rule chain_m_resolution :premises (@p382 @p379 @p69 @p377) :args (@t232 (@list true false false) (@list @t231 @t100 @t235))) % 12.83/13.02 (step @p384 :rule cnf_or_pos :args (@t206)) % 12.83/13.02 (step @p385 :rule reordering :premises (@p384) :args ((or @t141 @t126 @t125 @t205 @t195 @t204 (not @t206)))) % 12.83/13.02 (step @p386 :rule chain_m_resolution :premises (@p385 @p111 @p74 @p73 @p383 @p346 @p291) :args (@t204 (@list false false false true true false) (@list @t4 @t99 @t119 @t205 @t195 @t206))) % 12.83/13.02 (step @p387 :rule cnf_and_pos :args (@t204 0)) % 12.83/13.02 (step @p388 :rule reordering :premises (@p387) :args ((or @t203 (not @t204)))) % 12.83/13.02 (step @p389 :rule chain_m_resolution :premises (@p388 @p386) :args (@t203 @t134 (@list @t204))) % 12.83/13.02 (step @p390 :rule bool-double-not-elim :args (@t202)) % 12.83/13.02 (step @p391 :rule refl :args (@t236)) % 12.83/13.02 (step @p392 :rule refl :args (@t237)) % 12.83/13.02 (step @p393 :rule refl :args (@t238)) % 12.83/13.02 (step @p394 :rule refl :args (@t239)) % 12.83/13.02 (step @p395 :rule refl :args (@t240)) % 12.83/13.02 (step @p396 :rule nary_cong :premises (@p395 @p394 @p393 @p392 @p391 @p390) :args ((or @t240 @t239 @t238 @t237 @t236 (not @t203)))) % 12.83/13.02 (assume-push @p445 @t203) % 12.83/13.02 (assume-push @p446 @t202) % 12.83/13.02 (step @p399 :rule evaluate :args ((= true false))) % 12.83/13.02 (step @p400 :rule false_intro :premises (@p389)) % 12.83/13.02 (step @p401 :rule symm :premises (@p115)) % 12.83/13.02 (step @p402 :rule refl :args (tptp.xm)) % 12.83/13.02 (step @p403 :rule cong :premises (@p402 @p94) :args (@t103)) % 12.83/13.02 (step @p404 :rule symm :premises (@p233)) % 12.83/13.02 (step @p405 :rule symm :premises (@p77)) % 12.83/13.02 (step @p406 :rule trans :premises (@p405 @p42 @p404 @p403 @p401)) % 12.83/13.02 (step @p407 :rule true_intro :premises (@p406)) % 12.83/13.02 (step @p408 :rule symm :premises (@p407)) % 12.83/13.02 (step @p409 :rule trans :premises (@p408 @p400)) % 12.83/13.02 (step @p410 false :rule eq_resolve :premises (@p409 @p399)) % 12.83/13.02 (step-pop @p447 :rule scope :premises (@p410)) % 12.83/13.02 (step-pop @p448 :rule scope :premises (@p447)) % 12.83/13.02 (step @p411 :rule process_scope :premises (@p448) :args (false)) % 12.83/13.02 (assume-push @p449 @t105) % 12.83/13.02 (assume-push @p450 @t124) % 12.83/13.02 (assume-push @p451 @t131) % 12.83/13.02 (assume-push @p452 @t170) % 12.83/13.02 (assume-push @p453 @t140) % 12.83/13.02 (assume-push @p454 @t203) % 12.83/13.02 (step @p401 :rule symm :premises (@p115)) % 12.83/13.02 (step @p402 :rule refl :args (tptp.xm)) % 12.83/13.02 (step @p403 :rule cong :premises (@p402 @p94) :args (@t103)) % 12.83/13.02 (step @p404 :rule symm :premises (@p233)) % 12.83/13.02 (step @p405 :rule symm :premises (@p77)) % 12.83/13.02 (step @p420 :rule trans :premises (@p405 @p42 @p404 @p403 @p401)) % 12.83/13.02 (step @p421 :rule and_intro :premises (@p389 @p420)) % 12.83/13.02 (step-pop @p455 :rule scope :premises (@p421)) % 12.83/13.02 (step-pop @p456 :rule scope :premises (@p455)) % 12.83/13.02 (step-pop @p457 :rule scope :premises (@p456)) % 12.83/13.02 (step-pop @p458 :rule scope :premises (@p457)) % 12.83/13.02 (step-pop @p459 :rule scope :premises (@p458)) % 12.83/13.02 (step-pop @p460 :rule scope :premises (@p459)) % 12.83/13.02 (step @p422 :rule process_scope :premises (@p460) :args (@t241)) % 12.83/13.02 (step @p429 :rule implies_elim :premises (@p422)) % 12.83/13.02 (step @p430 :rule resolution :premises (@p429 @p411) :args (true @t241)) % 12.83/13.02 (step @p431 :rule not_and :premises (@p430)) % 12.83/13.02 (step @p432 :rule eq_resolve :premises (@p431 @p396)) % 12.83/13.02 (step @p433 :rule reordering :premises (@p432) :args ((or @t240 @t237 @t239 @t238 @t236 @t202))) % 12.83/13.06 (step @p434 false :rule chain_m_resolution :premises (@p433 @p389 @p233 @p115 @p94 @p77 @p42) :args (false (@list true false false false false false) (@list @t202 @t170 @t140 @t131 @t124 @t105))) % 12.83/13.06 ) % 12.83/13.06 % SZS output end Proof % 12.83/13.06 % cvc5 exiting %------------------------------------------------------------------------------