%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC068+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n027.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 08:57:55 AM UTC 2026 % Result : Theorem 14.52s 14.75s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC068+1 : TPTP v9.2.1. Released v2.4.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n027.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 19:12:36 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.54 %----Proving TF0_NAR, FOF, or CNF % 14.52/14.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 14.52/14.75 % SZS status Theorem % 14.52/14.75 % SZS output start Proof % 14.52/14.75 ( % 14.52/14.75 (declare-sort $$unsorted 0) % 14.52/14.75 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 14.52/14.75 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 14.52/14.75 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 14.52/14.75 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 14.52/14.75 (declare-const tptp.nil $$unsorted) % 14.52/14.75 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.ssList (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 14.52/14.75 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 14.52/14.75 (define @t1 () (@var "V" $$unsorted)) % 14.52/14.75 (define @t2 () (@var "U" $$unsorted)) % 14.52/14.75 (define @t3 () (= @t2 @t1)) % 14.52/14.75 (define @t4 () (not @t3)) % 14.52/14.75 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 14.52/14.75 (define @t6 () (tptp.ssItem @t1)) % 14.52/14.75 (define @t7 () (@list @t1)) % 14.52/14.75 (define @t8 () (tptp.ssItem @t2)) % 14.52/14.75 (define @t9 () (@list @t2)) % 14.52/14.75 (define @t10 () (@var "X" $$unsorted)) % 14.52/14.75 (define @t11 () (tptp.cons @t1 @t10)) % 14.52/14.75 (define @t12 () (@var "W" $$unsorted)) % 14.52/14.75 (define @t13 () (tptp.ssList @t10)) % 14.52/14.75 (define @t14 () (@list @t10)) % 14.52/14.75 (define @t15 () (tptp.ssList @t12)) % 14.52/14.75 (define @t16 () (@list @t12)) % 14.52/14.75 (define @t17 () (tptp.ssList @t2)) % 14.52/14.75 (define @t18 () (tptp.cons @t1 tptp.nil)) % 14.52/14.75 (define @t19 () (tptp.app @t1 @t12)) % 14.52/14.75 (define @t20 () (tptp.frontsegP @t2 @t1)) % 14.52/14.75 (define @t21 () (tptp.ssList @t1)) % 14.52/14.75 (define @t22 () (tptp.app @t12 @t1)) % 14.52/14.75 (define @t23 () (tptp.rearsegP @t2 @t1)) % 14.52/14.75 (define @t24 () (tptp.app @t22 @t10)) % 14.52/14.75 (define @t25 () (and @t13 (= @t24 @t2))) % 14.52/14.75 (define @t26 () (exists @t14 @t25)) % 14.52/14.75 (define @t27 () (and @t15 @t26)) % 14.52/14.75 (define @t28 () (exists @t16 @t27)) % 14.52/14.75 (define @t29 () (tptp.segmentP @t2 @t1)) % 14.52/14.75 (define @t30 () (= @t29 @t28)) % 14.52/14.75 (define @t31 () (=> @t21 @t30)) % 14.52/14.75 (define @t32 () (forall @t7 @t31)) % 14.52/14.75 (define @t33 () (=> @t17 @t32)) % 14.52/14.75 (define @t34 () (forall @t9 @t33)) % 14.52/14.75 (define @t35 () (tptp.leq @t12 @t1)) % 14.52/14.75 (define @t36 () (tptp.leq @t1 @t12)) % 14.52/14.75 (define @t37 () (@var "Z" $$unsorted)) % 14.52/14.75 (define @t38 () (@var "Y" $$unsorted)) % 14.52/14.75 (define @t39 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t38)) (tptp.cons @t12 @t37)) @t2)) % 14.52/14.75 (define @t40 () (tptp.ssList @t37)) % 14.52/14.75 (define @t41 () (@list @t37)) % 14.52/14.75 (define @t42 () (tptp.ssList @t38)) % 14.52/14.75 (define @t43 () (@list @t38)) % 14.52/14.75 (define @t44 () (tptp.ssItem @t12)) % 14.52/14.75 (define @t45 () (tptp.lt @t1 @t12)) % 14.52/14.75 (define @t46 () (= @t1 @t12)) % 14.52/14.75 (define @t47 () (forall @t7 (=> @t21 @t5))) % 14.52/14.75 (define @t48 () (=> @t17 @t47)) % 14.52/14.75 (define @t49 () (forall @t9 @t48)) % 14.52/14.75 (define @t50 () (tptp.cons @t1 @t2)) % 14.52/14.75 (define @t51 () (tptp.ssList tptp.nil)) % 14.52/14.75 (define @t52 () (= @t1 @t2)) % 14.52/14.75 (define @t53 () (tptp.cons @t12 @t1)) % 14.52/14.75 (define @t54 () (= tptp.nil @t2)) % 14.52/14.75 (define @t55 () (tptp.hd @t2)) % 14.52/14.75 (define @t56 () (not @t54)) % 14.52/14.75 (define @t57 () (tptp.tl @t2)) % 14.52/14.75 (define @t58 () (tptp.app @t2 @t1)) % 14.52/14.75 (define @t59 () (tptp.app @t1 @t2)) % 14.52/14.75 (define @t60 () (tptp.leq @t1 @t2)) % 14.52/14.75 (define @t61 () (tptp.leq @t2 @t1)) % 14.52/14.75 (define @t62 () (tptp.geq @t2 @t1)) % 14.52/14.75 (define @t63 () (tptp.lt @t1 @t2)) % 14.52/14.75 (define @t64 () (tptp.lt @t2 @t1)) % 14.52/14.75 (define @t65 () (tptp.lt @t2 @t12)) % 14.52/14.75 (define @t66 () (tptp.gt @t2 @t1)) % 14.52/14.75 (define @t67 () (tptp.memberP @t12 @t2)) % 14.52/14.75 (define @t68 () (tptp.app @t12 @t2)) % 14.52/14.75 (define @t69 () (tptp.segmentP @t2 @t2)) % 14.52/14.75 (define @t70 () (forall @t9 (=> @t17 @t69))) % 14.52/14.75 (define @t71 () (tptp.cons @t2 tptp.nil)) % 14.52/14.75 (define @t72 () (tptp.hd @t1)) % 14.52/14.75 (define @t73 () (= tptp.nil @t1)) % 14.52/14.75 (define @t74 () (not @t73)) % 14.52/14.75 (define @t75 () (tptp.cons @t2 @t1)) % 14.52/14.75 (define @t76 () (= @t12 @t2)) % 14.52/14.75 (define @t77 () (and @t73 @t54)) % 14.52/14.75 (define @t78 () (= tptp.nil @t58)) % 14.52/14.75 (define @t79 () (= @t78 @t77)) % 14.52/14.75 (define @t80 () (=> @t21 @t79)) % 14.52/14.75 (define @t81 () (forall @t7 @t80)) % 14.52/14.75 (define @t82 () (=> @t17 @t81)) % 14.52/14.75 (define @t83 () (forall @t9 @t82)) % 14.52/14.75 (define @t84 () (tptp.app @t2 tptp.nil)) % 14.52/14.75 (define @t85 () (=> @t17 (= @t84 @t2))) % 14.52/14.75 (define @t86 () (forall @t9 @t85)) % 14.52/14.75 (define @t87 () (tptp.segmentP @t2 @t38)) % 14.52/14.75 (define @t88 () (tptp.segmentP @t1 @t38)) % 14.52/14.75 (define @t89 () (tptp.neq @t38 tptp.nil)) % 14.52/14.75 (define @t90 () (and @t42 @t89 @t88 @t87)) % 14.52/14.75 (define @t91 () (exists @t43 @t90)) % 14.52/14.75 (define @t92 () (not (= @t2 @t12))) % 14.52/14.75 (define @t93 () (not (= @t1 @t10))) % 14.52/14.75 (define @t94 () (tptp.app @t10 @t10)) % 14.52/14.75 (define @t95 () (not (= @t94 @t12))) % 14.52/14.75 (define @t96 () (or @t95 @t93 @t92 @t91 @t77)) % 14.52/14.75 (define @t97 () (=> @t13 @t96)) % 14.52/14.75 (define @t98 () (forall @t14 @t97)) % 14.52/14.75 (define @t99 () (=> @t15 @t98)) % 14.52/14.75 (define @t100 () (forall @t16 @t99)) % 14.52/14.75 (define @t101 () (=> @t21 @t100)) % 14.52/14.75 (define @t102 () (forall @t7 @t101)) % 14.52/14.75 (define @t103 () (=> @t17 @t102)) % 14.52/14.75 (define @t104 () (forall @t9 @t103)) % 14.52/14.75 (define @t105 () (not @t104)) % 14.52/14.75 (define @t106 () (= @t2 tptp.nil)) % 14.52/14.75 (define @t107 () (@var "BOUND_VARIABLE_10588" $$unsorted)) % 14.52/14.75 (define @t108 () (and (= @t107 tptp.nil) @t106)) % 14.52/14.75 (define @t109 () (= tptp.nil (tptp.app @t2 @t107))) % 14.52/14.75 (define @t110 () (= @t109 @t108)) % 14.52/14.75 (define @t111 () (not (tptp.ssList @t107))) % 14.52/14.75 (define @t112 () (not @t17)) % 14.52/14.75 (define @t113 () (or @t112 @t111 @t110)) % 14.52/14.75 (define @t114 () (or @t111 @t110)) % 14.52/14.75 (define @t115 () (or @t112 @t114)) % 14.52/14.75 (define @t116 () (@list @t2 @t107)) % 14.52/14.75 (define @t117 () (forall @t116 @t115)) % 14.52/14.75 (define @t118 () (@list @t107)) % 14.52/14.75 (define @t119 () (forall @t118 @t115)) % 14.52/14.75 (define @t120 () (forall @t118 @t114)) % 14.52/14.75 (define @t121 () (@list @t1)) % 14.52/14.75 (define @t122 () (or @t112 @t120)) % 14.52/14.75 (define @t123 () (and (= @t1 tptp.nil) @t106)) % 14.52/14.75 (define @t124 () (= @t78 @t123)) % 14.52/14.75 (define @t125 () (not @t21)) % 14.52/14.75 (define @t126 () (forall @t7 (or @t125 @t124))) % 14.52/14.75 (define @t127 () (@var "BOUND_VARIABLE_10971" $$unsorted)) % 14.52/14.75 (define @t128 () (tptp.app @t127 @t127)) % 14.52/14.75 (define @t129 () (= tptp.nil @t127)) % 14.52/14.75 (define @t130 () (and @t129 (= tptp.nil @t128))) % 14.52/14.75 (define @t131 () (not (tptp.segmentP @t127 @t38))) % 14.52/14.75 (define @t132 () (not @t89)) % 14.52/14.75 (define @t133 () (not @t42)) % 14.52/14.75 (define @t134 () (not (forall @t43 (or @t133 @t132 @t131 (not (tptp.segmentP @t128 @t38)))))) % 14.52/14.75 (define @t135 () (not (tptp.ssList @t127))) % 14.52/14.75 (define @t136 () (not (tptp.ssList @t128))) % 14.52/14.75 (define @t137 () (or @t136 @t135 @t134 @t130)) % 14.52/14.75 (define @t138 () (@list @t127)) % 14.52/14.75 (define @t139 () (@quantifiers_skolemize (forall @t138 @t137) 0)) % 14.52/14.75 (define @t140 () (tptp.app @t139 @t139)) % 14.52/14.75 (define @t141 () (= tptp.nil @t140)) % 14.52/14.75 (define @t142 () (= tptp.nil @t139)) % 14.52/14.75 (define @t143 () (= @t139 tptp.nil)) % 14.52/14.75 (define @t144 () (and @t142 @t143)) % 14.52/14.75 (define @t145 () (= @t141 @t144)) % 14.52/14.75 (define @t146 () (tptp.ssList @t139)) % 14.52/14.75 (define @t147 () (not @t146)) % 14.52/14.75 (define @t148 () (or @t147 @t147 @t145)) % 14.52/14.75 (define @t149 () (forall @t116 (or @t112 @t111 (= @t109 (and (= tptp.nil @t107) @t106))))) % 14.52/14.75 (define @t150 () (= @t142 @t141)) % 14.52/14.75 (define @t151 () (or @t147 @t147 @t150)) % 14.52/14.75 (define @t152 () (@list false)) % 14.52/14.75 (define @t153 () (not (= @t128 @t128))) % 14.52/14.75 (define @t154 () (and @t129 (= @t128 tptp.nil))) % 14.52/14.75 (define @t155 () (or @t136 @t135 @t134 @t154 @t153)) % 14.52/14.75 (define @t156 () (not (= @t2 @t128))) % 14.52/14.75 (define @t157 () (and @t129 @t106)) % 14.52/14.75 (define @t158 () (not @t87)) % 14.52/14.75 (define @t159 () (not (forall @t43 (or @t133 @t132 @t131 @t158)))) % 14.52/14.75 (define @t160 () (or @t156 @t112 @t135 @t159 @t157 @t156)) % 14.52/14.75 (define @t161 () (or @t112 @t135 @t159 @t157 @t156)) % 14.52/14.75 (define @t162 () (forall @t9 @t161)) % 14.52/14.75 (define @t163 () (forall @t138 @t162)) % 14.52/14.75 (define @t164 () (forall (@list @t127 @t2) @t161)) % 14.52/14.75 (define @t165 () (@list @t2 @t127)) % 14.52/14.75 (define @t166 () (and (= @t127 tptp.nil) @t106)) % 14.52/14.75 (define @t167 () (or @t112 @t135 @t159 @t166 @t156)) % 14.52/14.75 (define @t168 () (or @t135 @t159 @t166 @t156)) % 14.52/14.75 (define @t169 () (or @t112 @t168)) % 14.52/14.75 (define @t170 () (forall @t165 @t169)) % 14.52/14.75 (define @t171 () (forall @t138 @t169)) % 14.52/14.75 (define @t172 () (forall @t138 @t168)) % 14.52/14.75 (define @t173 () (or @t112 @t172)) % 14.52/14.75 (define @t174 () (tptp.app @t1 @t1)) % 14.52/14.75 (define @t175 () (not (= @t2 @t174))) % 14.52/14.75 (define @t176 () (not @t88)) % 14.52/14.75 (define @t177 () (or @t133 @t132 @t176 @t158)) % 14.52/14.75 (define @t178 () (not (forall @t43 @t177))) % 14.52/14.75 (define @t179 () (or @t125 @t178 @t123 @t175)) % 14.52/14.75 (define @t180 () (or @t112 (forall @t7 @t179))) % 14.52/14.75 (define @t181 () (or @t112 @t179)) % 14.52/14.75 (define @t182 () (or @t125 @t178 @t123 @t112 @t175)) % 14.52/14.75 (define @t183 () (or @t178 @t123 @t125 @t112 @t175)) % 14.52/14.75 (define @t184 () (or @t112 @t175)) % 14.52/14.75 (define @t185 () (not (= @t2 @t2))) % 14.52/14.75 (define @t186 () (or @t112 @t185 @t175)) % 14.52/14.75 (define @t187 () (not (= @t12 @t174))) % 14.52/14.75 (define @t188 () (not @t15)) % 14.52/14.75 (define @t189 () (or @t92 @t188 @t92 @t187)) % 14.52/14.75 (define @t190 () (or @t188 @t92 @t187)) % 14.52/14.75 (define @t191 () (forall @t16 @t190)) % 14.52/14.75 (define @t192 () (or @t178 @t123 @t125 @t191)) % 14.52/14.75 (define @t193 () (or @t178 @t123 @t125 @t190)) % 14.52/14.75 (define @t194 () (or @t188 @t92 @t178 @t123 @t125 @t187)) % 14.52/14.75 (define @t195 () (or @t92 @t178 @t123 @t125 @t187)) % 14.52/14.75 (define @t196 () (or @t125 @t187)) % 14.52/14.75 (define @t197 () (not (= @t1 @t1))) % 14.52/14.75 (define @t198 () (or @t125 @t187 @t197)) % 14.52/14.75 (define @t199 () (not (= @t12 @t94))) % 14.52/14.75 (define @t200 () (not @t13)) % 14.52/14.75 (define @t201 () (or @t93 @t200 @t199 @t93)) % 14.52/14.75 (define @t202 () (or @t200 @t199 @t93)) % 14.52/14.75 (define @t203 () (forall @t14 @t202)) % 14.52/14.75 (define @t204 () (or @t92 @t178 @t123 @t203)) % 14.52/14.75 (define @t205 () (or @t92 @t178 @t123 @t202)) % 14.52/14.75 (define @t206 () (or @t200 @t199 @t93 @t92 @t178 @t123)) % 14.52/14.75 (define @t207 () (or @t199 @t93 @t92 @t178 @t123)) % 14.52/14.75 (define @t208 () (forall @t43 (not @t90))) % 14.52/14.75 (define @t209 () (not @t208)) % 14.52/14.75 (define @t210 () (and @t142 @t141)) % 14.52/14.75 (define @t211 () (forall @t43 (or @t133 @t132 (not (tptp.segmentP @t139 @t38)) (not (tptp.segmentP @t140 @t38))))) % 14.52/14.75 (define @t212 () (not @t211)) % 14.52/14.75 (define @t213 () (tptp.ssList @t140)) % 14.52/14.75 (define @t214 () (not @t213)) % 14.52/14.75 (define @t215 () (or @t214 @t147 @t212 @t210)) % 14.52/14.75 (define @t216 () (@list true)) % 14.52/14.75 (define @t217 () (@list @t215)) % 14.52/14.75 (define @t218 () (@list false false)) % 14.52/14.75 (define @t219 () (@var "BOUND_VARIABLE_9095" $$unsorted)) % 14.52/14.75 (define @t220 () (= (tptp.neq @t2 @t219) (not (= @t2 @t219)))) % 14.52/14.75 (define @t221 () (not (tptp.ssList @t219))) % 14.52/14.75 (define @t222 () (or @t112 @t221 @t220)) % 14.52/14.75 (define @t223 () (or @t221 @t220)) % 14.52/14.75 (define @t224 () (or @t112 @t223)) % 14.52/14.75 (define @t225 () (@list @t2 @t219)) % 14.52/14.75 (define @t226 () (forall @t225 @t224)) % 14.52/14.75 (define @t227 () (@list @t219)) % 14.52/14.75 (define @t228 () (forall @t227 @t224)) % 14.52/14.75 (define @t229 () (forall @t227 @t223)) % 14.52/14.75 (define @t230 () (or @t112 @t229)) % 14.52/14.75 (define @t231 () (forall @t7 (or @t125 @t5))) % 14.52/14.75 (define @t232 () (tptp.neq @t139 tptp.nil)) % 14.52/14.75 (define @t233 () (not @t142)) % 14.52/14.75 (define @t234 () (not @t143)) % 14.52/14.75 (define @t235 () (= @t232 @t234)) % 14.52/14.75 (define @t236 () (not @t51)) % 14.52/14.75 (define @t237 () (or @t147 @t236 @t235)) % 14.52/14.75 (define @t238 () (forall @t225 @t222)) % 14.52/14.75 (define @t239 () (@list @t139 tptp.nil)) % 14.52/14.75 (define @t240 () (= @t233 @t232)) % 14.52/14.75 (define @t241 () (or @t147 @t236 @t240)) % 14.52/14.75 (define @t242 () (@list false false false)) % 14.52/14.75 (define @t243 () (@list @t139)) % 14.52/14.75 (define @t244 () (@var "BOUND_VARIABLE_8377" $$unsorted)) % 14.52/14.75 (define @t245 () (@var "BOUND_VARIABLE_8400" $$unsorted)) % 14.52/14.75 (define @t246 () (not (tptp.ssList @t244))) % 14.52/14.75 (define @t247 () (@list @t12 @t244)) % 14.52/14.75 (define @t248 () (= (tptp.segmentP @t2 @t245) (not (forall @t247 (or @t188 @t246 (not (= @t2 (tptp.app (tptp.app @t12 @t245) @t244)))))))) % 14.52/14.75 (define @t249 () (not (tptp.ssList @t245))) % 14.52/14.75 (define @t250 () (or @t249 @t248)) % 14.52/14.75 (define @t251 () (or @t112 @t250)) % 14.52/14.75 (define @t252 () (forall (@list @t2 @t245) @t251)) % 14.52/14.75 (define @t253 () (@list @t245)) % 14.52/14.75 (define @t254 () (forall @t253 @t251)) % 14.52/14.75 (define @t255 () (forall @t253 @t250)) % 14.52/14.75 (define @t256 () (or @t112 @t255)) % 14.52/14.75 (define @t257 () (not (= @t2 (tptp.app @t22 @t244)))) % 14.52/14.75 (define @t258 () (or @t188 @t246 @t257)) % 14.52/14.75 (define @t259 () (= @t29 (not (forall @t247 @t258)))) % 14.52/14.75 (define @t260 () (forall @t7 (or @t125 @t259))) % 14.52/14.75 (define @t261 () (or @t246 @t257)) % 14.52/14.75 (define @t262 () (or @t188 @t261)) % 14.52/14.75 (define @t263 () (forall @t247 @t262)) % 14.52/14.75 (define @t264 () (@list @t244)) % 14.52/14.75 (define @t265 () (forall @t264 @t262)) % 14.52/14.75 (define @t266 () (forall @t264 @t261)) % 14.52/14.75 (define @t267 () (or @t188 @t266)) % 14.52/14.75 (define @t268 () (= @t2 @t24)) % 14.52/14.75 (define @t269 () (forall @t14 (or @t200 (not @t268)))) % 14.52/14.75 (define @t270 () (not @t269)) % 14.52/14.75 (define @t271 () (and @t15 @t270)) % 14.52/14.75 (define @t272 () (forall @t16 (not @t271))) % 14.52/14.75 (define @t273 () (not @t272)) % 14.52/14.75 (define @t274 () (and @t13 @t268)) % 14.52/14.75 (define @t275 () (forall @t14 (not @t274))) % 14.52/14.75 (define @t276 () (not @t275)) % 14.52/14.75 (define @t277 () (forall @t247 (or @t188 @t246 (not (= @t140 (tptp.app (tptp.app @t12 @t139) @t244)))))) % 14.52/14.75 (define @t278 () (not @t277)) % 14.52/14.75 (define @t279 () (tptp.segmentP @t140 @t139)) % 14.52/14.75 (define @t280 () (= @t279 @t278)) % 14.52/14.75 (define @t281 () (or @t214 @t147 @t280)) % 14.52/14.75 (define @t282 () (= @t2 @t84)) % 14.52/14.75 (define @t283 () (= @t140 (tptp.app @t140 tptp.nil))) % 14.52/14.75 (define @t284 () (or @t214 @t283)) % 14.52/14.75 (define @t285 () (not @t283)) % 14.52/14.75 (define @t286 () (or @t147 @t236 @t285)) % 14.52/14.75 (define @t287 () (not @t286)) % 14.52/14.75 (define @t288 () (not @t280)) % 14.52/14.75 (define @t289 () (@list true false)) % 14.52/14.75 (define @t290 () (tptp.segmentP @t139 @t139)) % 14.52/14.75 (define @t291 () (or @t147 @t290)) % 14.52/14.75 (define @t292 () (not @t279)) % 14.52/14.75 (define @t293 () (not @t290)) % 14.52/14.75 (define @t294 () (not @t232)) % 14.52/14.75 (define @t295 () (or @t147 @t294 @t293 @t292)) % 14.52/14.75 (define @t296 () (not @t240)) % 14.52/14.75 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 14.52/14.75 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 14.52/14.75 (assume @p3 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.memberP @t2 @t1) (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t12 @t11) @t2))))))))))) % 14.52/14.75 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 14.52/14.75 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 14.52/14.75 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 14.52/14.75 (assume @p7 @t34) % 14.52/14.75 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 (not (and @t36 @t35))))))))))))))))) % 14.52/14.75 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 (or @t36 @t35)))))))))))))))) % 14.52/14.75 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 (or @t45 (tptp.lt @t12 @t1))))))))))))))))) % 14.52/14.75 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 @t36))))))))))))))) % 14.52/14.75 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 @t45))))))))))))))) % 14.52/14.75 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (forall @t41 (=> @t40 (=> @t39 (not @t46)))))))))))))))) % 14.52/14.75 (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t44 (forall @t14 (=> @t13 (forall @t43 (=> @t42 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t38))) @t2) @t46))))))))))))) % 14.52/14.75 (assume @p15 @t49) % 14.52/14.75 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t50)))))) % 14.52/14.75 (assume @p17 @t51) % 14.52/14.75 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t50 @t2))))))) % 14.52/14.75 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t44 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t52))))))))))) % 14.52/14.75 (assume @p20 (forall @t9 (=> @t17 (or @t54 (exists @t7 (and @t21 (exists @t16 (and @t44 (= @t53 @t2))))))))) % 14.52/14.75 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t50))))))) % 14.52/14.75 (assume @p22 (forall @t9 (=> @t17 (=> @t56 (tptp.ssItem @t55))))) % 14.52/14.75 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t50) @t1)))))) % 14.52/14.75 (assume @p24 (forall @t9 (=> @t17 (=> @t56 (tptp.ssList @t57))))) % 14.52/14.75 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t50) @t2)))))) % 14.52/14.75 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t58)))))) % 14.52/14.75 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t44 (= (tptp.cons @t12 @t59) (tptp.app @t53 @t2))))))))) % 14.52/14.75 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 14.52/14.75 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t61 @t60) @t3)))))) % 14.52/14.75 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t61 @t36) (tptp.leq @t2 @t12))))))))) % 14.52/14.75 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 14.52/14.75 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t62 @t60)))))) % 14.52/14.75 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t64 (not @t63))))))) % 14.52/14.75 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t64 @t45) @t65)))))))) % 14.52/14.75 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t66 @t63)))))) % 14.52/14.75 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t67))))))))) % 14.52/14.75 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t67))))))))) % 14.52/14.75 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 14.52/14.75 (assume @p39 (not (tptp.singletonP tptp.nil))) % 14.52/14.75 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 14.52/14.75 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 14.52/14.75 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 14.52/14.75 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 14.52/14.75 (assume @p44 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (= (tptp.frontsegP (tptp.cons @t2 @t12) @t11) (and @t3 (tptp.frontsegP @t12 @t10)))))))))))) % 14.52/14.75 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 14.52/14.75 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t54)))) % 14.52/14.75 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 14.52/14.75 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 14.52/14.75 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 14.52/14.75 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t68 @t1))))))))) % 14.52/14.75 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 14.52/14.75 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t54)))) % 14.52/14.75 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t29 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 14.52/14.75 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t29 (tptp.segmentP @t1 @t2)) @t3)))))) % 14.52/14.75 (assume @p55 @t70) % 14.52/14.75 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t29 (tptp.segmentP (tptp.app @t68 @t10) @t1))))))))))) % 14.52/14.75 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 14.52/14.75 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t54)))) % 14.52/14.75 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t71)))) % 14.52/14.75 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 14.52/14.75 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t71)))) % 14.52/14.75 (assume @p62 (tptp.totalorderP tptp.nil)) % 14.52/14.75 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t71)))) % 14.52/14.75 (assume @p64 (tptp.strictorderP tptp.nil)) % 14.52/14.75 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t71)))) % 14.52/14.75 (assume @p66 (tptp.totalorderedP tptp.nil)) % 14.52/14.75 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t75) (or @t73 (and @t74 (tptp.totalorderedP @t1) (tptp.leq @t2 @t72))))))))) % 14.52/14.75 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t71)))) % 14.52/14.75 (assume @p69 (tptp.strictorderedP tptp.nil)) % 14.52/14.75 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t75) (or @t73 (and @t74 (tptp.strictorderedP @t1) (tptp.lt @t2 @t72))))))))) % 14.52/14.75 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t71)))) % 14.52/14.75 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 14.52/14.75 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t71)))) % 14.52/14.75 (assume @p74 (tptp.equalelemsP tptp.nil)) % 14.52/14.75 (assume @p75 (forall @t9 (=> @t17 (=> @t56 (exists @t7 (and @t6 (= @t55 @t1))))))) % 14.52/14.75 (assume @p76 (forall @t9 (=> @t17 (=> @t56 (exists @t7 (and @t21 (= @t57 @t1))))))) % 14.52/14.75 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t74 @t56 (= @t72 @t55) (= (tptp.tl @t1) @t57)) @t52)))))) % 14.52/14.75 (assume @p78 (forall @t9 (=> @t17 (=> @t56 (= (tptp.cons @t55 @t57) @t2))))) % 14.52/14.75 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t58) @t76)))))))) % 14.52/14.75 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t59) @t76)))))))) % 14.52/14.75 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t50 (tptp.app @t18 @t2))))))) % 14.52/14.75 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t58 @t12) (tptp.app @t2 @t19))))))))) % 14.52/14.75 (assume @p83 @t83) % 14.52/14.75 (assume @p84 @t86) % 14.52/14.75 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t56 (= (tptp.hd @t58) @t55))))))) % 14.52/14.75 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t56 (= (tptp.tl @t58) (tptp.app @t57 @t1)))))))) % 14.52/14.75 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t62 (tptp.geq @t1 @t2)) @t3)))))) % 14.52/14.75 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t62 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 14.52/14.75 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 14.52/14.75 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 14.52/14.75 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t61 @t45) @t65)))))))) % 14.52/14.75 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t61 (or @t3 @t64))))))) % 14.52/14.75 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t64 (and @t4 @t61))))))) % 14.52/14.75 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t66 (not (tptp.gt @t1 @t2)))))))) % 14.52/14.75 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t44 (=> (and @t66 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 14.52/14.75 (assume @p96 @t105) % 14.52/14.75 (assume @p97 true) % 14.52/14.75 (step @p98 :rule refl :args (@t106)) % 14.52/14.75 (step @p99 :rule eq-symm :args (@t107 tptp.nil)) % 14.52/14.75 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t108)) % 14.52/14.75 (step @p101 :rule refl :args (@t109)) % 14.52/14.75 (step @p102 :rule cong :premises (@p101 @p100) :args (@t110)) % 14.52/14.75 (step @p103 :rule refl :args (@t111)) % 14.52/14.75 (step @p104 :rule refl :args (@t112)) % 14.52/14.75 (step @p105 :rule nary_cong :premises (@p104 @p103 @p102) :args (@t113)) % 14.52/14.75 (step @p106 :rule aci_norm :args ((= @t115 @t113))) % 14.52/14.75 (step @p107 :rule trans :premises (@p106 @p105)) % 14.52/14.75 (step @p108 :rule cong :premises (@p107) :args (@t117)) % 14.52/14.75 (step @p109 :rule quant-merge-prenex :args ((= (forall @t9 @t119) @t117))) % 14.52/14.75 (step @p110 :rule alpha_equiv :args (@t120 (@list @t107) @t121)) % 14.52/14.75 (step @p111 :rule refl :args (@t112)) % 14.52/14.75 (step @p112 :rule nary_cong :premises (@p111 @p110) :args (@t122)) % 14.52/14.75 (step @p113 :rule quant-miniscope-or :args ((= @t119 @t122))) % 14.52/14.75 (step @p114 :rule trans :premises (@p113 @p112)) % 14.52/14.75 (step @p115 :rule symm :premises (@p114)) % 14.52/14.75 (step @p116 :rule cong :premises (@p115) :args ((forall @t9 (or @t112 @t126)))) % 14.52/14.75 (step @p117 :rule trans :premises (@p116 @p109)) % 14.52/14.75 (step @p118 :rule trans :premises (@p117 @p108)) % 14.52/14.75 (step @p119 :rule bool-impl-elim :args (@t17 @t126)) % 14.52/14.75 (step @p120 :rule cong :premises (@p119) :args ((forall @t9 (=> @t17 @t126)))) % 14.52/14.75 (step @p121 :rule trans :premises (@p120 @p118)) % 14.52/14.75 (step @p122 :rule bool-impl-elim :args (@t21 @t124)) % 14.52/14.75 (step @p123 :rule cong :premises (@p122) :args ((forall @t7 (=> @t21 @t124)))) % 14.52/14.75 (step @p124 :rule eq-symm :args (tptp.nil @t2)) % 14.52/14.75 (step @p125 :rule eq-symm :args (tptp.nil @t1)) % 14.52/14.75 (step @p126 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@p253) :args (@t198)) % 14.52/14.75 (step @p256 :rule trans :premises (@p255 @p250)) % 14.52/14.75 (step @p257 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t200 @t199 @t93)) @t198))) % 14.52/14.75 (step @p258 :rule refl :args (@t93)) % 14.52/14.75 (step @p259 :rule refl :args (@t199)) % 14.52/14.75 (step @p260 :rule refl :args (@t200)) % 14.52/14.75 (step @p261 :rule eq-symm :args (@t1 @t10)) % 14.52/14.75 (step @p262 :rule cong :premises (@p261) :args (@t93)) % 14.52/14.75 (step @p263 :rule nary_cong :premises (@p262 @p260 @p259 @p258) :args (@t201)) % 14.52/14.75 (step @p264 :rule aci_norm :args ((= @t202 @t201))) % 14.52/14.75 (step @p265 :rule trans :premises (@p264 @p263)) % 14.52/14.75 (step @p266 :rule cong :premises (@p265) :args (@t203)) % 14.52/14.75 (step @p267 :rule trans :premises (@p266 @p257)) % 14.52/14.75 (step @p268 :rule trans :premises (@p267 @p256)) % 14.52/14.75 (step @p269 :rule refl :args (@t92)) % 14.52/14.75 (step @p270 :rule nary_cong :premises (@p269 @p236 @p235 @p268) :args (@t204)) % 14.52/14.75 (step @p271 :rule trans :premises (@p270 @p249)) % 14.52/14.75 (step @p272 :rule quant-miniscope-or :args ((= (forall @t14 @t205) @t204))) % 14.52/14.75 (step @p273 :rule aci_norm :args ((= @t206 @t205))) % 14.52/14.75 (step @p274 :rule cong :premises (@p273) :args ((forall @t14 @t206))) % 14.52/14.75 (step @p275 :rule trans :premises (@p274 @p272)) % 14.52/14.75 (step @p276 :rule trans :premises (@p275 @p271)) % 14.52/14.75 (step @p277 :rule aci_norm :args ((= (or @t200 @t207) @t206))) % 14.52/14.75 (step @p278 :rule bool-impl-elim :args (@t13 @t207)) % 14.52/14.75 (step @p279 :rule trans :premises (@p278 @p277)) % 14.52/14.75 (step @p280 :rule cong :premises (@p279) :args ((forall @t14 (=> @t13 @t207)))) % 14.52/14.75 (step @p281 :rule trans :premises (@p280 @p276)) % 14.52/14.75 (step @p282 :rule aci_norm :args ((= (or @t133 (or @t132 (or @t176 @t158))) @t177))) % 14.52/14.75 (step @p283 :rule bool-and-de-morgan :args (@t88 @t87 true)) % 14.52/14.75 (step @p284 :rule refl :args (@t132)) % 14.52/14.75 (step @p285 :rule nary_cong :premises (@p284 @p283) :args ((or @t132 (not (and @t88 @t87))))) % 14.52/14.75 (step @p286 :rule bool-and-de-morgan :args (@t89 @t88 (and @t87))) % 14.52/14.75 (step @p287 :rule trans :premises (@p286 @p285)) % 14.52/14.75 (step @p288 :rule refl :args (@t133)) % 14.52/14.75 (step @p289 :rule nary_cong :premises (@p288 @p287) :args ((or @t133 (not (and @t89 @t88 @t87))))) % 14.52/14.75 (step @p290 :rule bool-and-de-morgan :args (@t42 @t89 (and @t88 @t87))) % 14.52/14.75 (step @p291 :rule trans :premises (@p290 @p289)) % 14.52/14.75 (step @p292 :rule trans :premises (@p291 @p282)) % 14.52/14.75 (step @p293 :rule cong :premises (@p292) :args (@t208)) % 14.52/14.75 (step @p294 :rule cong :premises (@p293) :args (@t209)) % 14.52/14.75 (step @p295 :rule exists-elim :args ((= @t91 @t209))) % 14.52/14.75 (step @p296 :rule trans :premises (@p295 @p294)) % 14.52/14.75 (step @p297 :rule refl :args (@t93)) % 14.52/14.75 (step @p298 :rule eq-symm :args (@t94 @t12)) % 14.52/14.75 (step @p299 :rule cong :premises (@p298) :args (@t95)) % 14.52/14.75 (step @p300 :rule nary_cong :premises (@p299 @p297 @p269 @p296 @p126) :args (@t96)) % 14.52/14.75 (step @p301 :rule refl :args (@t13)) % 14.52/14.75 (step @p302 :rule cong :premises (@p301 @p300) :args (@t97)) % 14.52/14.75 (step @p303 :rule cong :premises (@p302) :args (@t98)) % 14.52/14.75 (step @p304 :rule trans :premises (@p303 @p281)) % 14.52/14.75 (step @p305 :rule refl :args (@t15)) % 14.52/14.75 (step @p306 :rule cong :premises (@p305 @p304) :args (@t99)) % 14.52/14.75 (step @p307 :rule cong :premises (@p306) :args (@t100)) % 14.52/14.75 (step @p308 :rule trans :premises (@p307 @p248)) % 14.52/14.75 (step @p309 :rule cong :premises (@p129 @p308) :args (@t101)) % 14.52/14.75 (step @p310 :rule cong :premises (@p309) :args (@t102)) % 14.52/14.75 (step @p311 :rule trans :premises (@p310 @p213)) % 14.52/14.75 (step @p312 :rule cong :premises (@p133 @p311) :args (@t103)) % 14.52/14.75 (step @p313 :rule cong :premises (@p312) :args (@t104)) % 14.52/14.75 (step @p314 :rule trans :premises (@p313 @p204)) % 14.52/14.75 (step @p315 :rule cong :premises (@p314) :args (@t105)) % 14.52/14.75 (step @p316 :rule eq_resolve :premises (@p96 @p315)) % 14.52/14.75 (step @p317 :rule skolemize :premises (@p316)) % 14.52/14.75 (step @p318 :rule bool-double-not-elim :args (@t146)) % 14.52/14.75 (step @p319 :rule refl :args (@t215)) % 14.52/14.75 (step @p320 :rule nary_cong :premises (@p319 @p318) :args ((or @t215 (not @t147)))) % 14.52/14.75 (step @p321 :rule cnf_or_neg :args (@t215 1)) % 14.52/14.75 (step @p322 :rule eq_resolve :premises (@p321 @p320)) % 14.52/14.75 (step @p323 :rule reordering :premises (@p322) :args ((or @t146 @t215))) % 14.52/14.75 (step @p324 :rule chain_m_resolution :premises (@p323 @p317) :args (@t146 @t216 @t217)) % 14.52/14.75 (step @p325 :rule cnf_or_pos :args (@t151)) % 14.52/14.75 (step @p326 :rule factoring :premises (@p325)) % 14.52/14.75 (step @p327 :rule reordering :premises (@p326) :args ((or @t147 @t150 (not @t151)))) % 14.52/14.75 (step @p328 :rule chain_m_resolution :premises (@p327 @p324 @p157) :args (@t150 @t218 (@list @t146 @t151))) % 14.52/14.75 (step @p329 :rule aci_norm :args ((= @t224 @t222))) % 14.52/14.75 (step @p330 :rule cong :premises (@p329) :args (@t226)) % 14.52/14.75 (step @p331 :rule quant-merge-prenex :args ((= (forall @t9 @t228) @t226))) % 14.52/14.75 (step @p332 :rule alpha_equiv :args (@t229 (@list @t219) @t121)) % 14.52/14.75 (step @p333 :rule nary_cong :premises (@p111 @p332) :args (@t230)) % 14.52/14.75 (step @p334 :rule quant-miniscope-or :args ((= @t228 @t230))) % 14.52/14.75 (step @p335 :rule trans :premises (@p334 @p333)) % 14.52/14.75 (step @p336 :rule symm :premises (@p335)) % 14.52/14.75 (step @p337 :rule cong :premises (@p336) :args ((forall @t9 (or @t112 @t231)))) % 14.52/14.75 (step @p338 :rule trans :premises (@p337 @p331)) % 14.52/14.75 (step @p339 :rule trans :premises (@p338 @p330)) % 14.52/14.75 (step @p340 :rule bool-impl-elim :args (@t17 @t231)) % 14.52/14.75 (step @p341 :rule cong :premises (@p340) :args ((forall @t9 (=> @t17 @t231)))) % 14.52/14.75 (step @p342 :rule trans :premises (@p341 @p339)) % 14.52/14.75 (step @p343 :rule bool-impl-elim :args (@t21 @t5)) % 14.52/14.75 (step @p344 :rule cong :premises (@p343) :args (@t47)) % 14.52/14.75 (step @p345 :rule cong :premises (@p133 @p344) :args (@t48)) % 14.52/14.75 (step @p346 :rule cong :premises (@p345) :args (@t49)) % 14.52/14.75 (step @p347 :rule trans :premises (@p346 @p342)) % 14.52/14.75 (step @p348 :rule eq_resolve :premises (@p15 @p347)) % 14.52/14.75 (step @p349 :rule eq-symm :args (@t232 @t233)) % 14.52/14.75 (step @p350 :rule cong :premises (@p140) :args (@t234)) % 14.52/14.75 (step @p351 :rule refl :args (@t232)) % 14.52/14.75 (step @p352 :rule cong :premises (@p351 @p350) :args (@t235)) % 14.52/14.75 (step @p353 :rule trans :premises (@p352 @p349)) % 14.52/14.75 (step @p354 :rule refl :args (@t236)) % 14.52/14.75 (step @p355 :rule nary_cong :premises (@p147 @p354 @p353) :args (@t237)) % 14.52/14.75 (step @p356 :rule refl :args (@t238)) % 14.52/14.75 (step @p357 :rule cong :premises (@p356 @p355) :args ((=> @t238 @t237))) % 14.52/14.75 (assume-push @p496 @t238) % 14.52/14.75 (step @p359 :rule instantiate :premises (@p348) :args (@t239)) % 14.52/14.75 (step-pop @p497 :rule scope :premises (@p359)) % 14.52/14.75 (step @p360 :rule process_scope :premises (@p497) :args (@t237)) % 14.52/14.75 (step @p362 :rule eq_resolve :premises (@p360 @p357)) % 14.52/14.75 (step @p363 :rule implies_elim :premises (@p362)) % 14.52/14.75 (step @p364 :rule chain_m_resolution :premises (@p363 @p348) :args (@t241 @t152 (@list @t238))) % 14.52/14.75 (step @p365 :rule cnf_or_pos :args (@t241)) % 14.52/14.75 (step @p366 :rule reordering :premises (@p365) :args ((or @t236 @t147 @t240 (not @t241)))) % 14.52/14.75 (step @p367 :rule chain_m_resolution :premises (@p366 @p17 @p324 @p364) :args (@t240 @t242 (@list @t51 @t146 @t241))) % 14.52/14.75 (step @p368 :rule bool-double-not-elim :args (@t211)) % 14.52/14.75 (step @p369 :rule nary_cong :premises (@p319 @p368) :args ((or @t215 (not @t212)))) % 14.52/14.75 (step @p370 :rule cnf_or_neg :args (@t215 2)) % 14.52/14.75 (step @p371 :rule eq_resolve :premises (@p370 @p369)) % 14.52/14.75 (step @p372 :rule reordering :premises (@p371) :args ((or @t211 @t215))) % 14.52/14.75 (step @p373 :rule chain_m_resolution :premises (@p372 @p317) :args (@t211 @t216 @t217)) % 14.52/14.75 (step @p374 :rule instantiate :premises (@p373) :args (@t243)) % 14.52/14.75 (step @p375 :rule aci_norm :args ((= @t251 (or @t112 @t249 @t248)))) % 14.52/14.75 (step @p376 :rule cong :premises (@p375) :args (@t252)) % 14.52/14.75 (step @p377 :rule quant-merge-prenex :args ((= (forall @t9 @t254) @t252))) % 14.52/14.75 (step @p378 :rule alpha_equiv :args (@t255 (@list @t245) @t121)) % 14.52/14.75 (step @p379 :rule nary_cong :premises (@p111 @p378) :args (@t256)) % 14.52/14.75 (step @p380 :rule quant-miniscope-or :args ((= @t254 @t256))) % 14.52/14.75 (step @p381 :rule trans :premises (@p380 @p379)) % 14.52/14.75 (step @p382 :rule symm :premises (@p381)) % 14.52/14.75 (step @p383 :rule cong :premises (@p382) :args ((forall @t9 (or @t112 @t260)))) % 14.52/14.75 (step @p384 :rule trans :premises (@p383 @p377)) % 14.52/14.75 (step @p385 :rule trans :premises (@p384 @p376)) % 14.52/14.75 (step @p386 :rule bool-impl-elim :args (@t17 @t260)) % 14.52/14.75 (step @p387 :rule cong :premises (@p386) :args ((forall @t9 (=> @t17 @t260)))) % 14.52/14.75 (step @p388 :rule trans :premises (@p387 @p385)) % 14.52/14.75 (step @p389 :rule bool-impl-elim :args (@t21 @t259)) % 14.52/14.75 (step @p390 :rule cong :premises (@p389) :args ((forall @t7 (=> @t21 @t259)))) % 14.52/14.75 (step @p391 :rule aci_norm :args ((= @t262 @t258))) % 14.52/14.75 (step @p392 :rule cong :premises (@p391) :args (@t263)) % 14.52/14.75 (step @p393 :rule quant-merge-prenex :args ((= (forall @t16 @t265) @t263))) % 14.52/14.75 (step @p394 :rule alpha_equiv :args (@t266 (@list @t244) (@list @t10))) % 14.52/14.75 (step @p395 :rule nary_cong :premises (@p225 @p394) :args (@t267)) % 14.52/14.75 (step @p396 :rule quant-miniscope-or :args ((= @t265 @t267))) % 14.52/14.75 (step @p397 :rule trans :premises (@p396 @p395)) % 14.52/14.75 (step @p398 :rule symm :premises (@p397)) % 14.52/14.75 (step @p399 :rule cong :premises (@p398) :args ((forall @t16 (or @t188 @t269)))) % 14.52/14.75 (step @p400 :rule trans :premises (@p399 @p393)) % 14.52/14.75 (step @p401 :rule trans :premises (@p400 @p392)) % 14.52/14.75 (step @p402 :rule bool-double-not-elim :args (@t269)) % 14.52/14.75 (step @p403 :rule nary_cong :premises (@p225 @p402) :args ((or @t188 (not @t270)))) % 14.52/14.75 (step @p404 :rule bool-and-de-morgan :args (@t15 @t270 true)) % 14.52/14.75 (step @p405 :rule trans :premises (@p404 @p403)) % 14.52/14.75 (step @p406 :rule cong :premises (@p405) :args (@t272)) % 14.52/14.75 (step @p407 :rule trans :premises (@p406 @p401)) % 14.52/14.75 (step @p408 :rule cong :premises (@p407) :args (@t273)) % 14.52/14.75 (step @p409 :rule exists-elim :args ((= (exists @t16 @t271) @t273))) % 14.52/14.75 (step @p410 :rule trans :premises (@p409 @p408)) % 14.52/14.75 (step @p411 :rule bool-and-de-morgan :args (@t13 @t268 true)) % 14.52/14.75 (step @p412 :rule cong :premises (@p411) :args (@t275)) % 14.52/14.75 (step @p413 :rule cong :premises (@p412) :args (@t276)) % 14.52/14.75 (step @p414 :rule exists-elim :args ((= (exists @t14 @t274) @t276))) % 14.52/14.75 (step @p415 :rule trans :premises (@p414 @p413)) % 14.52/14.75 (step @p416 :rule eq-symm :args (@t24 @t2)) % 14.52/14.75 (step @p417 :rule nary_cong :premises (@p301 @p416) :args (@t25)) % 14.52/14.75 (step @p418 :rule cong :premises (@p417) :args (@t26)) % 14.52/14.75 (step @p419 :rule trans :premises (@p418 @p415)) % 14.52/14.75 (step @p420 :rule nary_cong :premises (@p305 @p419) :args (@t27)) % 14.52/14.75 (step @p421 :rule cong :premises (@p420) :args (@t28)) % 14.52/14.75 (step @p422 :rule trans :premises (@p421 @p410)) % 14.52/14.75 (step @p423 :rule refl :args (@t29)) % 14.52/14.75 (step @p424 :rule cong :premises (@p423 @p422) :args (@t30)) % 14.52/14.75 (step @p425 :rule cong :premises (@p129 @p424) :args (@t31)) % 14.52/14.75 (step @p426 :rule cong :premises (@p425) :args (@t32)) % 14.52/14.75 (step @p427 :rule trans :premises (@p426 @p390)) % 14.52/14.75 (step @p428 :rule cong :premises (@p133 @p427) :args (@t33)) % 14.52/14.75 (step @p429 :rule cong :premises (@p428) :args (@t34)) % 14.52/14.75 (step @p430 :rule trans :premises (@p429 @p388)) % 14.52/14.75 (step @p431 :rule eq_resolve :premises (@p7 @p430)) % 14.52/14.75 (step @p432 :rule instantiate :premises (@p431) :args ((@list @t140 @t139))) % 14.52/14.75 (step @p433 :rule bool-double-not-elim :args (@t213)) % 14.52/14.75 (step @p434 :rule nary_cong :premises (@p319 @p433) :args ((or @t215 (not @t214)))) % 14.52/14.75 (step @p435 :rule cnf_or_neg :args (@t215 0)) % 14.52/14.75 (step @p436 :rule eq_resolve :premises (@p435 @p434)) % 14.52/14.75 (step @p437 :rule reordering :premises (@p436) :args ((or @t213 @t215))) % 14.52/14.75 (step @p438 :rule chain_m_resolution :premises (@p437 @p317) :args (@t213 @t216 @t217)) % 14.52/14.75 (step @p439 :rule cnf_or_pos :args (@t281)) % 14.52/14.75 (step @p440 :rule reordering :premises (@p439) :args ((or @t214 @t147 @t280 (not @t281)))) % 14.52/14.75 (step @p441 :rule chain_m_resolution :premises (@p440 @p438 @p324 @p432) :args (@t280 @t242 (@list @t213 @t146 @t281))) % 14.52/14.75 (step @p442 :rule bool-impl-elim :args (@t17 @t282)) % 14.52/14.75 (step @p443 :rule cong :premises (@p442) :args ((forall @t9 (=> @t17 @t282)))) % 14.52/14.75 (step @p444 :rule eq-symm :args (@t84 @t2)) % 14.52/14.75 (step @p445 :rule cong :premises (@p133 @p444) :args (@t85)) % 14.52/14.75 (step @p446 :rule cong :premises (@p445) :args (@t86)) % 14.52/14.75 (step @p447 :rule trans :premises (@p446 @p443)) % 14.52/14.75 (step @p448 :rule eq_resolve :premises (@p84 @p447)) % 14.52/14.75 (step @p449 :rule instantiate :premises (@p448) :args ((@list @t140))) % 14.52/14.75 (step @p450 :rule cnf_or_pos :args (@t284)) % 14.52/14.75 (step @p451 :rule reordering :premises (@p450) :args ((or @t214 @t283 (not @t284)))) % 14.52/14.75 (step @p452 :rule chain_m_resolution :premises (@p451 @p438 @p449) :args (@t283 @t218 (@list @t213 @t284))) % 14.52/14.75 (step @p453 :rule cnf_or_pos :args (@t286)) % 14.52/14.75 (step @p454 :rule reordering :premises (@p453) :args ((or @t236 @t147 @t285 @t287))) % 14.52/14.75 (step @p455 :rule chain_m_resolution :premises (@p454 @p17 @p324 @p452) :args (@t287 @t242 (@list @t51 @t146 @t283))) % 14.52/14.75 (assume-push @p498 @t277) % 14.52/14.75 (step @p457 :rule instantiate :premises (@p498) :args (@t239)) % 14.52/14.75 (step-pop @p499 :rule scope :premises (@p457)) % 14.52/14.75 (step @p458 :rule process_scope :premises (@p499) :args (@t286)) % 14.52/14.75 (step @p460 :rule implies_elim :premises (@p458)) % 14.52/14.75 (step @p461 :rule chain_m_resolution :premises (@p460 @p455) :args (@t278 @t216 (@list @t286))) % 14.52/14.75 (step @p462 :rule bool-double-not-elim :args (@t277)) % 14.52/14.75 (step @p463 :rule refl :args (@t279)) % 14.52/14.75 (step @p464 :rule refl :args (@t288)) % 14.52/14.75 (step @p465 :rule nary_cong :premises (@p464 @p463 @p462) :args ((or @t288 @t279 (not @t278)))) % 14.52/14.75 (step @p466 :rule cnf_equiv_pos2 :args (@t280)) % 14.52/14.75 (step @p467 :rule eq_resolve :premises (@p466 @p465)) % 14.52/14.75 (step @p468 :rule reordering :premises (@p467) :args ((or @t279 @t277 @t288))) % 14.52/14.75 (step @p469 :rule chain_m_resolution :premises (@p468 @p461 @p441) :args (@t279 @t289 (@list @t277 @t280))) % 14.52/14.75 (step @p470 :rule bool-impl-elim :args (@t17 @t69)) % 14.52/14.75 (step @p471 :rule cong :premises (@p470) :args (@t70)) % 14.52/14.75 (step @p472 :rule eq_resolve :premises (@p55 @p471)) % 14.52/14.75 (step @p473 :rule instantiate :premises (@p472) :args (@t243)) % 14.52/14.75 (step @p474 :rule cnf_or_pos :args (@t291)) % 14.52/14.75 (step @p475 :rule reordering :premises (@p474) :args ((or @t147 @t290 (not @t291)))) % 14.52/14.75 (step @p476 :rule chain_m_resolution :premises (@p475 @p324 @p473) :args (@t290 @t218 (@list @t146 @t291))) % 14.52/14.75 (step @p477 :rule cnf_or_pos :args (@t295)) % 14.52/14.75 (step @p478 :rule reordering :premises (@p477) :args ((or @t147 @t293 @t294 @t292 (not @t295)))) % 14.52/14.75 (step @p479 :rule chain_m_resolution :premises (@p478 @p324 @p476 @p469 @p374) :args (@t294 (@list false false false false) (@list @t146 @t290 @t279 @t295))) % 14.52/14.75 (step @p480 :rule bool-double-not-elim :args (@t142)) % 14.52/14.75 (step @p481 :rule refl :args (@t296)) % 14.52/14.75 (step @p482 :rule nary_cong :premises (@p481 @p480 @p351) :args ((or @t296 (not @t233) @t232))) % 14.52/14.75 (step @p483 :rule cnf_equiv_pos1 :args (@t240)) % 14.52/14.75 (step @p484 :rule eq_resolve :premises (@p483 @p482)) % 0.39/14.81 (step @p485 :rule reordering :premises (@p484) :args ((or @t142 @t232 @t296))) % 0.39/14.81 (step @p486 :rule chain_m_resolution :premises (@p485 @p479 @p367) :args (@t142 @t289 (@list @t232 @t240))) % 0.39/14.81 (step @p487 :rule cnf_or_neg :args (@t215 3)) % 0.39/14.81 (step @p488 :rule chain_m_resolution :premises (@p487 @p317) :args ((not @t210) @t216 @t217)) % 0.39/14.81 (step @p489 :rule cnf_and_neg :args (@t210)) % 0.39/14.81 (step @p490 :rule chain_m_resolution :premises (@p489 @p488 @p486) :args ((not @t141) @t289 (@list @t210 @t142))) % 0.39/14.81 (step @p491 :rule cnf_equiv_pos1 :args (@t150)) % 0.39/14.81 (step @p492 :rule reordering :premises (@p491) :args ((or @t141 @t233 (not @t150)))) % 0.39/14.81 (step @p493 false :rule chain_m_resolution :premises (@p492 @p490 @p486 @p328) :args (false (@list true false false) (@list @t141 @t142 @t150))) % 0.39/14.81 ) % 0.39/14.81 % SZS output end Proof % 0.39/14.82 % cvc5 exiting %------------------------------------------------------------------------------