%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LAT385+4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:30:36 AM UTC 2026 % Result : Theorem 0.74s 0.98s % Output : Proof 0.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : LAT385+4 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n014.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 07:01:13 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.74/0.98 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.74/0.98 % SZS status Theorem % 0.74/0.98 % SZS output start Proof % 0.74/0.98 ( % 0.74/0.98 (declare-sort $$unsorted 0) % 0.74/0.98 (declare-const tptp.xP $$unsorted) % 0.74/0.98 (declare-const tptp.xT $$unsorted) % 0.74/0.98 (declare-const tptp.xS $$unsorted) % 0.74/0.98 (declare-const tptp.cS1142 (-> $$unsorted $$unsorted)) % 0.74/0.98 (declare-const tptp.isMonotone0 (-> $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.aFixedPointOf0 (-> $$unsorted $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.xU $$unsorted) % 0.74/0.98 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.74/0.98 (declare-const tptp.isOn0 (-> $$unsorted $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.szRzazndt0 (-> $$unsorted $$unsorted)) % 0.74/0.98 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.aCompleteLattice0 (-> $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.isEmpty0 (-> $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.cS1241 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.74/0.98 (declare-const tptp.xf $$unsorted) % 0.74/0.98 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.aLowerBoundOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.aSupremumOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.aUpperBoundOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.aInfimumOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.74/0.98 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.74/0.98 (define @t1 () (@var "W0" $$unsorted)) % 0.74/0.98 (define @t2 () (tptp.aSet0 @t1)) % 0.74/0.98 (define @t3 () (@list @t1)) % 0.74/0.98 (define @t4 () (tptp.aElement0 @t1)) % 0.74/0.98 (define @t5 () (@var "W1" $$unsorted)) % 0.74/0.98 (define @t6 () (tptp.aElement0 @t5)) % 0.74/0.98 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.74/0.98 (define @t8 () (@list @t5)) % 0.74/0.98 (define @t9 () (@var "W2" $$unsorted)) % 0.74/0.98 (define @t10 () (tptp.aElementOf0 @t9 @t1)) % 0.74/0.98 (define @t11 () (@list @t9)) % 0.74/0.98 (define @t12 () (tptp.aSet0 @t5)) % 0.74/0.98 (define @t13 () (tptp.aSubsetOf0 @t5 @t1)) % 0.74/0.98 (define @t14 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.74/0.98 (define @t15 () (and @t4 @t6)) % 0.74/0.98 (define @t16 () (@list @t1 @t5)) % 0.74/0.98 (define @t17 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.74/0.98 (define @t18 () (tptp.sdtlseqdt0 @t5 @t9)) % 0.74/0.98 (define @t19 () (@var "W3" $$unsorted)) % 0.74/0.98 (define @t20 () (tptp.sdtlseqdt0 @t9 @t19)) % 0.74/0.98 (define @t21 () (tptp.aElementOf0 @t19 @t5)) % 0.74/0.98 (define @t22 () (@list @t19)) % 0.74/0.98 (define @t23 () (tptp.aLowerBoundOfIn0 @t9 @t5 @t1)) % 0.74/0.98 (define @t24 () (tptp.sdtlseqdt0 @t19 @t9)) % 0.74/0.98 (define @t25 () (tptp.aUpperBoundOfIn0 @t9 @t5 @t1)) % 0.74/0.98 (define @t26 () (tptp.aInfimumOfIn0 @t9 @t5 @t1)) % 0.74/0.98 (define @t27 () (tptp.aSupremumOfIn0 @t9 @t5 @t1)) % 0.74/0.98 (define @t28 () (= @t9 @t19)) % 0.74/0.98 (define @t29 () (tptp.aSupremumOfIn0 @t19 @t5 @t1)) % 0.74/0.98 (define @t30 () (@list @t9 @t19)) % 0.74/0.98 (define @t31 () (tptp.aFunction0 @t1)) % 0.74/0.98 (define @t32 () (tptp.szDzozmdt0 @t1)) % 0.74/0.98 (define @t33 () (tptp.szRzazndt0 @t1)) % 0.74/0.98 (define @t34 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.74/0.98 (define @t35 () (tptp.aElementOf0 @t5 @t32)) % 0.74/0.98 (define @t36 () (tptp.szRzazndt0 tptp.xf)) % 0.74/0.98 (define @t37 () (tptp.szDzozmdt0 tptp.xf)) % 0.74/0.98 (define @t38 () (tptp.sdtlpdtrp0 tptp.xf @t1)) % 0.74/0.98 (define @t39 () (tptp.aElementOf0 @t1 @t37)) % 0.74/0.98 (define @t40 () (tptp.aSupremumOfIn0 @t9 @t1 tptp.xU)) % 0.74/0.98 (define @t41 () (tptp.aUpperBoundOfIn0 @t19 @t1 tptp.xU)) % 0.74/0.98 (define @t42 () (@var "W4" $$unsorted)) % 0.74/0.98 (define @t43 () (tptp.sdtlseqdt0 @t42 @t19)) % 0.74/0.98 (define @t44 () (tptp.aElementOf0 @t42 @t1)) % 0.74/0.98 (define @t45 () (@list @t42)) % 0.74/0.98 (define @t46 () (forall @t45 (=> @t44 @t43))) % 0.74/0.98 (define @t47 () (tptp.aElementOf0 @t19 tptp.xU)) % 0.74/0.98 (define @t48 () (and @t47 @t46)) % 0.74/0.98 (define @t49 () (or @t48 @t41)) % 0.74/0.98 (define @t50 () (=> @t49 @t20)) % 0.74/0.98 (define @t51 () (forall @t22 @t50)) % 0.74/0.98 (define @t52 () (tptp.aUpperBoundOfIn0 @t9 @t1 tptp.xU)) % 0.74/0.98 (define @t53 () (tptp.aElementOf0 @t19 @t1)) % 0.74/0.98 (define @t54 () (forall @t22 (=> @t53 @t24))) % 0.74/0.98 (define @t55 () (tptp.aElementOf0 @t9 tptp.xU)) % 0.74/0.98 (define @t56 () (and @t55 @t55 @t54 @t52 @t51 @t40)) % 0.74/0.98 (define @t57 () (exists @t11 @t56)) % 0.74/0.98 (define @t58 () (tptp.aInfimumOfIn0 @t5 @t1 tptp.xU)) % 0.74/0.98 (define @t59 () (tptp.sdtlseqdt0 @t9 @t5)) % 0.74/0.98 (define @t60 () (tptp.aLowerBoundOfIn0 @t9 @t1 tptp.xU)) % 0.74/0.98 (define @t61 () (forall @t22 (=> @t53 @t20))) % 0.74/0.98 (define @t62 () (and @t55 @t61)) % 0.74/0.98 (define @t63 () (or @t62 @t60)) % 0.74/0.98 (define @t64 () (=> @t63 @t59)) % 0.74/0.98 (define @t65 () (forall @t11 @t64)) % 0.74/0.98 (define @t66 () (tptp.aLowerBoundOfIn0 @t5 @t1 tptp.xU)) % 0.74/0.98 (define @t67 () (forall @t11 (=> @t10 @t18))) % 0.74/0.98 (define @t68 () (tptp.aElementOf0 @t5 tptp.xU)) % 0.74/0.98 (define @t69 () (and @t68 @t68 @t67 @t66 @t65 @t58 @t57)) % 0.74/0.98 (define @t70 () (exists @t8 @t69)) % 0.74/0.98 (define @t71 () (tptp.aSubsetOf0 @t1 tptp.xU)) % 0.74/0.98 (define @t72 () (forall @t8 (=> @t7 @t68))) % 0.74/0.98 (define @t73 () (and @t2 @t72)) % 0.74/0.98 (define @t74 () (or @t73 @t71)) % 0.74/0.98 (define @t75 () (=> @t74 @t70)) % 0.74/0.98 (define @t76 () (forall @t3 @t75)) % 0.74/0.98 (define @t77 () (tptp.aElementOf0 @t1 tptp.xS)) % 0.74/0.98 (define @t78 () (tptp.aFixedPointOf0 @t1 tptp.xf)) % 0.74/0.98 (define @t79 () (= @t38 @t1)) % 0.74/0.98 (define @t80 () (tptp.aElementOf0 @t1 tptp.xP)) % 0.74/0.98 (define @t81 () (tptp.aUpperBoundOfIn0 @t1 tptp.xT tptp.xU)) % 0.74/0.98 (define @t82 () (tptp.aElementOf0 @t5 tptp.xT)) % 0.74/0.98 (define @t83 () (forall @t8 (=> @t82 @t17))) % 0.74/0.98 (define @t84 () (or @t83 @t81)) % 0.74/0.98 (define @t85 () (tptp.sdtlseqdt0 @t38 @t1)) % 0.74/0.98 (define @t86 () (tptp.aElementOf0 @t1 tptp.xU)) % 0.74/0.98 (define @t87 () (and @t86 @t85 @t84)) % 0.74/0.98 (define @t88 () (=> @t87 @t80)) % 0.74/0.98 (define @t89 () (and @t86 @t85 @t83 @t81)) % 0.74/0.98 (define @t90 () (=> @t80 @t89)) % 0.74/0.98 (define @t91 () (and @t90 @t88)) % 0.74/0.98 (define @t92 () (forall @t3 @t91)) % 0.74/0.98 (define @t93 () (tptp.aSet0 tptp.xP)) % 0.74/0.98 (define @t94 () (tptp.aInfimumOfIn0 @t1 tptp.xP tptp.xU)) % 0.74/0.98 (define @t95 () (tptp.aLowerBoundOfIn0 @t5 tptp.xP tptp.xU)) % 0.74/0.98 (define @t96 () (tptp.aElementOf0 @t9 tptp.xP)) % 0.74/0.98 (define @t97 () (forall @t11 (=> @t96 @t18))) % 0.74/0.98 (define @t98 () (and @t68 @t97 @t95)) % 0.74/0.98 (define @t99 () (=> @t98 @t17)) % 0.74/0.98 (define @t100 () (forall @t8 @t99)) % 0.74/0.98 (define @t101 () (tptp.aLowerBoundOfIn0 @t1 tptp.xP tptp.xU)) % 0.74/0.98 (define @t102 () (tptp.aElementOf0 @t5 tptp.xP)) % 0.74/0.98 (define @t103 () (forall @t8 (=> @t102 @t14))) % 0.74/0.98 (define @t104 () (and @t86 @t103)) % 0.74/0.98 (define @t105 () (or @t104 @t101)) % 0.74/0.98 (define @t106 () (and @t86 @t105 @t100)) % 0.74/0.98 (define @t107 () (or @t106 @t94)) % 0.74/0.98 (define @t108 () (exists @t3 @t107)) % 0.74/0.98 (define @t109 () (not @t108)) % 0.74/0.98 (define @t110 () (not @t40)) % 0.74/0.98 (define @t111 () (not @t41)) % 0.74/0.98 (define @t112 () (forall @t45 (or (not @t44) @t43))) % 0.74/0.98 (define @t113 () (not @t47)) % 0.74/0.98 (define @t114 () (forall @t22 (or (and (or @t113 (not @t112)) @t111) @t20))) % 0.74/0.98 (define @t115 () (not @t114)) % 0.74/0.98 (define @t116 () (not @t52)) % 0.74/0.98 (define @t117 () (not @t53)) % 0.74/0.98 (define @t118 () (forall @t22 (or @t117 @t24))) % 0.74/0.98 (define @t119 () (not @t118)) % 0.74/0.98 (define @t120 () (not @t55)) % 0.74/0.98 (define @t121 () (or @t120 @t119 @t116 @t115 @t110)) % 0.74/0.98 (define @t122 () (forall @t11 @t121)) % 0.74/0.98 (define @t123 () (not @t58)) % 0.74/0.98 (define @t124 () (not @t60)) % 0.74/0.98 (define @t125 () (forall @t22 (or @t117 @t20))) % 0.74/0.98 (define @t126 () (forall @t11 (or (and (or @t120 (not @t125)) @t124) @t59))) % 0.74/0.98 (define @t127 () (not @t126)) % 0.74/0.98 (define @t128 () (not @t66)) % 0.74/0.98 (define @t129 () (forall @t11 (or (not @t10) @t18))) % 0.74/0.98 (define @t130 () (not @t129)) % 0.74/0.98 (define @t131 () (not @t68)) % 0.74/0.98 (define @t132 () (or @t131 @t130 @t128 @t127 @t123)) % 0.74/0.98 (define @t133 () (forall @t8 @t132)) % 0.74/0.98 (define @t134 () (not @t71)) % 0.74/0.98 (define @t135 () (forall @t8 (or (not @t7) @t68))) % 0.74/0.98 (define @t136 () (and @t2 @t135)) % 0.74/0.98 (define @t137 () (or @t122 @t133)) % 0.74/0.98 (define @t138 () (not @t137)) % 0.74/0.98 (define @t139 () (or @t136 @t71)) % 0.74/0.98 (define @t140 () (or @t122 @t132)) % 0.74/0.98 (define @t141 () (or @t131 @t130 @t128 @t127 @t123 @t122)) % 0.74/0.98 (define @t142 () (not @t122)) % 0.74/0.98 (define @t143 () (not @t142)) % 0.74/0.98 (define @t144 () (or @t131 @t131 @t130 @t128 @t127 @t123 @t143)) % 0.74/0.98 (define @t145 () (and @t68 @t68 @t129 @t66 @t126 @t58 @t142)) % 0.74/0.98 (define @t146 () (forall @t8 (not @t145))) % 0.74/0.98 (define @t147 () (not @t146)) % 0.74/0.98 (define @t148 () (or @t120 @t120 @t119 @t116 @t115 @t110)) % 0.74/0.98 (define @t149 () (and @t55 @t55 @t118 @t52 @t114 @t40)) % 0.74/0.98 (define @t150 () (forall @t11 (not @t149))) % 0.74/0.98 (define @t151 () (not @t150)) % 0.74/0.98 (define @t152 () (and @t47 @t112)) % 0.74/0.98 (define @t153 () (or @t152 @t41)) % 0.74/0.98 (define @t154 () (and @t55 @t125)) % 0.74/0.98 (define @t155 () (or @t154 @t60)) % 0.74/0.98 (define @t156 () (@var "BOUND_VARIABLE_8479" $$unsorted)) % 0.74/0.98 (define @t157 () (@var "BOUND_VARIABLE_8460" $$unsorted)) % 0.74/0.98 (define @t158 () (not @t95)) % 0.74/0.98 (define @t159 () (not @t96)) % 0.74/0.98 (define @t160 () (forall @t11 (or @t159 @t18))) % 0.74/0.98 (define @t161 () (not @t160)) % 0.74/0.98 (define @t162 () (not @t102)) % 0.74/0.98 (define @t163 () (not (tptp.aElementOf0 @t157 tptp.xU))) % 0.74/0.98 (define @t164 () (not @t94)) % 0.74/0.98 (define @t165 () (forall @t3 @t164)) % 0.74/0.98 (define @t166 () (@list @t1)) % 0.74/0.98 (define @t167 () (or @t131 @t161 @t158 @t17)) % 0.74/0.98 (define @t168 () (forall @t8 @t167)) % 0.74/0.98 (define @t169 () (not @t168)) % 0.74/0.98 (define @t170 () (not @t101)) % 0.74/0.98 (define @t171 () (forall @t8 (or @t162 @t14))) % 0.74/0.98 (define @t172 () (not @t86)) % 0.74/0.98 (define @t173 () (or @t172 (and (or @t172 (not @t171)) @t170) @t169)) % 0.74/0.98 (define @t174 () (forall @t3 @t173)) % 0.74/0.98 (define @t175 () (and @t174 @t165)) % 0.74/0.98 (define @t176 () (and @t86 @t171)) % 0.74/0.98 (define @t177 () (or @t176 @t101)) % 0.74/0.98 (define @t178 () (not @t177)) % 0.74/0.98 (define @t179 () (or @t172 @t178 @t169)) % 0.74/0.98 (define @t180 () (and @t86 @t177 @t168)) % 0.74/0.98 (define @t181 () (or @t180 @t94)) % 0.74/0.98 (define @t182 () (forall @t3 (not @t181))) % 0.74/0.98 (define @t183 () (not @t182)) % 0.74/0.98 (define @t184 () (or @t131 @t161 @t158)) % 0.74/0.98 (define @t185 () (and @t68 @t160 @t95)) % 0.74/0.98 (define @t186 () (not (tptp.aElementOf0 @t19 tptp.xP))) % 0.74/0.98 (define @t187 () (and (or @t120 (not (forall @t22 (or @t186 @t20)))) (not (tptp.aLowerBoundOfIn0 @t9 tptp.xP tptp.xU)))) % 0.74/0.98 (define @t188 () (forall @t8 (or @t131 @t161 @t158 (not (forall @t11 (or @t187 @t59))) (not (tptp.aInfimumOfIn0 @t5 tptp.xP tptp.xU))))) % 0.74/0.98 (define @t189 () (@quantifiers_skolemize @t188 0)) % 0.74/0.98 (define @t190 () (tptp.aInfimumOfIn0 @t189 tptp.xP tptp.xU)) % 0.74/0.98 (define @t191 () (not @t190)) % 0.74/0.98 (define @t192 () (or (not (tptp.aElementOf0 @t189 tptp.xU)) (not (forall @t11 (or @t159 (tptp.sdtlseqdt0 @t189 @t9)))) (not (tptp.aLowerBoundOfIn0 @t189 tptp.xP tptp.xU)) (not (forall @t11 (or @t187 (tptp.sdtlseqdt0 @t9 @t189)))) @t191)) % 0.74/0.98 (define @t193 () (@list true)) % 0.74/0.98 (define @t194 () (not @t192)) % 0.74/0.98 (define @t195 () (not @t188)) % 0.74/0.98 (define @t196 () (@list false)) % 0.74/0.98 (define @t197 () (and (not (forall @t11 (or @t120 (not (forall @t22 (or @t186 @t24))) (not (tptp.aUpperBoundOfIn0 @t9 tptp.xP tptp.xU)) (not (forall @t22 (or (and (or @t113 (not (forall @t45 (or (not (tptp.aElementOf0 @t42 tptp.xP)) @t43)))) (not (tptp.aUpperBoundOfIn0 @t19 tptp.xP tptp.xU))) @t20))) (not (tptp.aSupremumOfIn0 @t9 tptp.xP tptp.xU))))) @t195)) % 0.74/0.98 (define @t198 () (not @t197)) % 0.74/0.98 (define @t199 () (forall @t8 (or @t162 @t68))) % 0.74/0.98 (define @t200 () (not @t199)) % 0.74/0.98 (define @t201 () (not @t93)) % 0.74/0.98 (define @t202 () (or @t201 @t200)) % 0.74/0.98 (define @t203 () (and @t202 (not (tptp.aSubsetOf0 tptp.xP tptp.xU)))) % 0.74/0.98 (define @t204 () (or @t203 @t197)) % 0.74/0.98 (define @t205 () (@quantifiers_skolemize @t199 0)) % 0.74/0.98 (define @t206 () (tptp.aElementOf0 @t205 tptp.xU)) % 0.74/0.98 (define @t207 () (tptp.aElementOf0 @t205 tptp.xP)) % 0.74/0.98 (define @t208 () (not @t207)) % 0.74/0.98 (define @t209 () (or @t208 @t206)) % 0.74/0.98 (define @t210 () (not @t209)) % 0.74/0.98 (define @t211 () (@list @t209)) % 0.74/0.98 (define @t212 () (@quantifiers_skolemize (forall @t11 (or @t120 (not (forall @t22 (or @t113 @t24))) (not (tptp.aUpperBoundOfIn0 @t9 tptp.xU tptp.xU)) (not (forall @t22 (or (and (or @t113 (not (forall @t45 (or (not (tptp.aElementOf0 @t42 tptp.xU)) @t43)))) (not (tptp.aUpperBoundOfIn0 @t19 tptp.xU tptp.xU))) @t20))) (not (tptp.aSupremumOfIn0 @t9 tptp.xU tptp.xU)))) 0)) % 0.74/0.98 (define @t213 () (and @t206 (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf @t205) @t205) (or (not (tptp.aElementOf0 @t212 tptp.xT)) (tptp.sdtlseqdt0 @t212 @t205)) (tptp.aUpperBoundOfIn0 @t205 tptp.xT tptp.xU))) % 0.74/0.98 (define @t214 () (not @t213)) % 0.74/0.98 (define @t215 () (@var "BOUND_VARIABLE_8394" $$unsorted)) % 0.74/0.98 (define @t216 () (not @t82)) % 0.74/0.98 (define @t217 () (forall (@list @t215) (or (not (tptp.aElementOf0 @t215 tptp.xU)) (not (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf @t215) @t215)) (and (not (forall @t8 (or @t216 (tptp.sdtlseqdt0 @t5 @t215)))) (not (tptp.aUpperBoundOfIn0 @t215 tptp.xT tptp.xU))) (tptp.aElementOf0 @t215 tptp.xP)))) % 0.74/0.98 (define @t218 () (@var "BOUND_VARIABLE_8379" $$unsorted)) % 0.74/0.98 (define @t219 () (tptp.aUpperBoundOfIn0 @t218 tptp.xT tptp.xU)) % 0.74/0.98 (define @t220 () (@var "BOUND_VARIABLE_8413" $$unsorted)) % 0.74/0.98 (define @t221 () (or (not (tptp.aElementOf0 @t220 tptp.xT)) (tptp.sdtlseqdt0 @t220 @t218))) % 0.74/0.98 (define @t222 () (tptp.sdtlseqdt0 (tptp.sdtlpdtrp0 tptp.xf @t218) @t218)) % 0.74/0.98 (define @t223 () (tptp.aElementOf0 @t218 tptp.xU)) % 0.74/0.98 (define @t224 () (and @t223 @t222 @t221 @t219)) % 0.74/0.98 (define @t225 () (not (tptp.aElementOf0 @t218 tptp.xP))) % 0.74/0.98 (define @t226 () (or @t225 @t224)) % 0.74/0.98 (define @t227 () (@list @t220)) % 0.74/0.98 (define @t228 () (forall @t227 @t226)) % 0.74/0.98 (define @t229 () (@list @t218)) % 0.74/0.98 (define @t230 () (forall @t227 @t219)) % 0.74/0.98 (define @t231 () (forall @t227 @t221)) % 0.74/0.98 (define @t232 () (forall @t227 @t222)) % 0.74/0.98 (define @t233 () (forall @t227 @t223)) % 0.74/0.98 (define @t234 () (and @t233 @t232 @t231 @t230)) % 0.74/0.98 (define @t235 () (forall @t227 @t224)) % 0.74/0.98 (define @t236 () (or @t225 @t235)) % 0.74/0.98 (define @t237 () (forall @t229 (or @t225 (and @t223 @t222 (forall @t8 (or @t216 (tptp.sdtlseqdt0 @t5 @t218))) @t219)))) % 0.74/0.98 (define @t238 () (forall @t8 (or @t216 @t17))) % 0.74/0.98 (define @t239 () (and (not @t238) (not @t81))) % 0.74/0.98 (define @t240 () (not @t85)) % 0.74/0.98 (define @t241 () (or @t172 @t240 @t239 @t80)) % 0.74/0.98 (define @t242 () (forall @t3 @t241)) % 0.74/0.98 (define @t243 () (and @t86 @t85 @t238 @t81)) % 0.74/0.98 (define @t244 () (or (not @t80) @t243)) % 0.74/0.98 (define @t245 () (forall @t3 @t244)) % 0.74/0.98 (define @t246 () (and @t245 @t242)) % 0.74/0.98 (define @t247 () (or @t238 @t81)) % 0.74/0.98 (define @t248 () (not @t247)) % 0.74/0.98 (define @t249 () (or @t172 @t240 @t248)) % 0.74/0.98 (define @t250 () (and @t86 @t85 @t247)) % 0.74/0.98 (define @t251 () (and (=> @t80 @t243) (=> @t250 @t80))) % 0.74/0.98 (define @t252 () (or @t208 @t213)) % 0.74/0.98 (assume @p1 (forall @t3 (=> @t2 true))) % 0.74/0.98 (assume @p2 (forall @t3 (=> @t4 true))) % 0.74/0.98 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.74/0.98 (assume @p4 (forall @t3 (=> @t2 (= (tptp.isEmpty0 @t1) (not (exists @t8 @t7)))))) % 0.74/0.98 (assume @p5 (forall @t3 (=> @t2 (forall @t8 (= @t13 (and @t12 (forall @t11 (=> (tptp.aElementOf0 @t9 @t5) @t10)))))))) % 0.74/0.98 (assume @p6 (forall @t16 (=> @t15 (=> @t14 true)))) % 0.74/0.98 (assume @p7 (forall @t3 (=> @t4 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.74/0.98 (assume @p8 (forall @t16 (=> @t15 (=> (and @t14 @t17) (= @t1 @t5))))) % 0.74/0.98 (assume @p9 (forall (@list @t1 @t5 @t9) (=> (and @t4 @t6 (tptp.aElement0 @t9)) (=> (and @t14 @t18) (tptp.sdtlseqdt0 @t1 @t9))))) % 0.74/0.98 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (=> @t13 (forall @t11 (= @t23 (and @t10 (forall @t22 (=> @t21 @t20)))))))))) % 0.74/0.98 (assume @p11 (forall @t3 (=> @t2 (forall @t8 (=> @t13 (forall @t11 (= @t25 (and @t10 (forall @t22 (=> @t21 @t24)))))))))) % 0.74/0.98 (assume @p12 (forall @t3 (=> @t2 (forall @t8 (=> @t13 (forall @t11 (= @t26 (and @t10 @t23 (forall @t22 (=> (tptp.aLowerBoundOfIn0 @t19 @t5 @t1) @t24)))))))))) % 0.74/0.98 (assume @p13 (forall @t3 (=> @t2 (forall @t8 (=> @t13 (forall @t11 (= @t27 (and @t10 @t25 (forall @t22 (=> (tptp.aUpperBoundOfIn0 @t19 @t5 @t1) @t20)))))))))) % 0.74/0.98 (assume @p14 (forall @t3 (=> @t2 (forall @t8 (=> @t13 (forall @t30 (=> (and @t27 @t29) @t28))))))) % 0.74/0.98 (assume @p15 (forall @t3 (=> @t2 (forall @t8 (=> @t13 (forall @t30 (=> (and @t26 (tptp.aInfimumOfIn0 @t19 @t5 @t1)) @t28))))))) % 0.74/0.98 (assume @p16 (forall @t3 (= (tptp.aCompleteLattice0 @t1) (and @t2 (forall @t8 (=> @t13 (exists @t11 (and @t26 (exists @t22 @t29))))))))) % 0.74/0.98 (assume @p17 (forall @t3 (=> @t31 true))) % 0.74/0.98 (assume @p18 (forall @t3 (=> @t31 (tptp.aSet0 @t32)))) % 0.74/0.98 (assume @p19 (forall @t3 (=> @t31 (tptp.aSet0 @t33)))) % 0.74/0.98 (assume @p20 (forall @t16 (=> (and @t31 @t12) (= (tptp.isOn0 @t1 @t5) (and (= @t32 @t33) (= @t33 @t5)))))) % 0.74/0.98 (assume @p21 (forall @t3 (=> @t31 (forall @t8 (=> @t35 (tptp.aElementOf0 @t34 @t33)))))) % 0.74/0.98 (assume @p22 (forall @t3 (=> @t31 (forall @t8 (= (tptp.aFixedPointOf0 @t5 @t1) (and @t35 (= @t34 @t5))))))) % 0.74/0.98 (assume @p23 (forall @t3 (=> @t31 (= (tptp.isMonotone0 @t1) (forall (@list @t5 @t9) (=> (and @t35 (tptp.aElementOf0 @t9 @t32)) (=> @t18 (tptp.sdtlseqdt0 @t34 (tptp.sdtlpdtrp0 @t1 @t9))))))))) % 0.74/0.98 (assume @p24 (and (tptp.aSet0 tptp.xU) @t76 (tptp.aCompleteLattice0 tptp.xU) (tptp.aFunction0 tptp.xf) (forall @t16 (=> (and @t39 (tptp.aElementOf0 @t5 @t37)) (=> @t14 (tptp.sdtlseqdt0 @t38 (tptp.sdtlpdtrp0 tptp.xf @t5))))) (tptp.isMonotone0 tptp.xf) (= @t37 @t36) (= @t36 tptp.xU) (tptp.isOn0 tptp.xf tptp.xU))) % 0.74/0.98 (assume @p25 (and (tptp.aSet0 tptp.xS) (forall @t3 (and (=> @t77 (and @t39 @t79 @t78)) (=> (or (and @t39 @t79) @t78) @t77))) (= tptp.xS (tptp.cS1142 tptp.xf)))) % 0.74/0.98 (assume @p26 (and (tptp.aSet0 tptp.xT) (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xT) @t77)) (tptp.aSubsetOf0 tptp.xT tptp.xS))) % 0.74/0.98 (assume @p27 (and @t93 @t92 (= tptp.xP (tptp.cS1241 tptp.xU tptp.xf tptp.xT)))) % 0.74/0.98 (assume @p28 @t109) % 0.74/0.98 (assume @p29 true) % 0.74/0.98 (step @p30 :rule bool-or-de-morgan :args (@t122 @t133 false)) % 0.74/0.98 (step @p31 :rule refl :args (@t134)) % 0.74/0.98 (step @p32 :rule bool-and-de-morgan :args (@t2 @t135 true)) % 0.74/0.98 (step @p33 :rule nary_cong :premises (@p32 @p31) :args ((and (not @t136) @t134))) % 0.74/0.98 (step @p34 :rule bool-or-de-morgan :args (@t136 @t71 false)) % 0.74/0.98 (step @p35 :rule trans :premises (@p34 @p33)) % 0.74/0.98 (step @p36 :rule nary_cong :premises (@p35 @p30) :args ((or (not @t139) @t138))) % 0.74/0.98 (step @p37 :rule bool-impl-elim :args (@t139 @t138)) % 0.74/0.98 (step @p38 :rule trans :premises (@p37 @p36)) % 0.74/0.98 (step @p39 :rule cong :premises (@p38) :args ((forall @t3 (=> @t139 @t138)))) % 0.74/0.98 (step @p40 :rule quant-miniscope-or :args ((= (forall @t8 @t140) @t137))) % 0.74/0.98 (step @p41 :rule aci_norm :args ((= @t141 @t140))) % 0.74/0.98 (step @p42 :rule cong :premises (@p41) :args ((forall @t8 @t141))) % 0.74/0.98 (step @p43 :rule trans :premises (@p42 @p40)) % 0.74/0.98 (step @p44 :rule aci_norm :args ((= (or @t131 @t131 @t130 @t128 @t127 @t123 @t122) @t141))) % 0.74/0.98 (step @p45 :rule bool-double-not-elim :args (@t122)) % 0.74/0.98 (step @p46 :rule refl :args (@t123)) % 0.74/0.98 (step @p47 :rule refl :args (@t127)) % 0.74/0.98 (step @p48 :rule refl :args (@t128)) % 0.74/0.98 (step @p49 :rule refl :args (@t130)) % 0.74/0.98 (step @p50 :rule refl :args (@t131)) % 0.74/0.98 (step @p51 :rule nary_cong :premises (@p50 @p50 @p49 @p48 @p47 @p46 @p45) :args (@t144)) % 0.74/0.98 (step @p52 :rule aci_norm :args ((= (or @t131 (or @t131 (or @t130 (or @t128 (or @t127 (or @t123 @t143)))))) @t144))) % 0.74/0.98 (step @p53 :rule trans :premises (@p52 @p51)) % 0.74/0.98 (step @p54 :rule bool-and-de-morgan :args (@t58 @t142 true)) % 0.74/0.98 (step @p55 :rule nary_cong :premises (@p47 @p54) :args ((or @t127 (not (and @t58 @t142))))) % 0.74/0.98 (step @p56 :rule bool-and-de-morgan :args (@t126 @t58 (and @t142))) % 0.74/0.98 (step @p57 :rule trans :premises (@p56 @p55)) % 0.74/0.98 (step @p58 :rule nary_cong :premises (@p48 @p57) :args ((or @t128 (not (and @t126 @t58 @t142))))) % 0.74/0.98 (step @p59 :rule bool-and-de-morgan :args (@t66 @t126 (and @t58 @t142))) % 0.74/0.98 (step @p60 :rule trans :premises (@p59 @p58)) % 0.74/0.98 (step @p61 :rule nary_cong :premises (@p49 @p60) :args ((or @t130 (not (and @t66 @t126 @t58 @t142))))) % 0.74/0.98 (step @p62 :rule bool-and-de-morgan :args (@t129 @t66 (and @t126 @t58 @t142))) % 0.74/0.98 (step @p63 :rule trans :premises (@p62 @p61)) % 0.74/0.98 (step @p64 :rule nary_cong :premises (@p50 @p63) :args ((or @t131 (not (and @t129 @t66 @t126 @t58 @t142))))) % 0.74/0.98 (step @p65 :rule bool-and-de-morgan :args (@t68 @t129 (and @t66 @t126 @t58 @t142))) % 0.74/0.98 (step @p66 :rule trans :premises (@p65 @p64)) % 0.74/0.98 (step @p67 :rule nary_cong :premises (@p50 @p66) :args ((or @t131 (not (and @t68 @t129 @t66 @t126 @t58 @t142))))) % 0.74/0.98 (step @p68 :rule bool-and-de-morgan :args (@t68 @t68 (and @t129 @t66 @t126 @t58 @t142))) % 0.74/0.98 (step @p69 :rule trans :premises (@p68 @p67)) % 0.74/0.98 (step @p70 :rule trans :premises (@p69 @p53)) % 0.74/0.98 (step @p71 :rule trans :premises (@p70 @p44)) % 0.74/0.98 (step @p72 :rule cong :premises (@p71) :args (@t146)) % 0.74/0.98 (step @p73 :rule trans :premises (@p72 @p43)) % 0.74/0.98 (step @p74 :rule cong :premises (@p73) :args (@t147)) % 0.74/0.98 (step @p75 :rule exists-elim :args ((= (exists @t8 @t145) @t147))) % 0.74/0.98 (step @p76 :rule trans :premises (@p75 @p74)) % 0.74/0.98 (step @p77 :rule aci_norm :args ((= @t148 @t121))) % 0.74/0.98 (step @p78 :rule aci_norm :args ((= (or @t120 (or @t120 (or @t119 (or @t116 (or @t115 @t110))))) @t148))) % 0.74/0.98 (step @p79 :rule bool-and-de-morgan :args (@t114 @t40 true)) % 0.74/0.98 (step @p80 :rule refl :args (@t116)) % 0.74/0.98 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or @t116 (not (and @t114 @t40))))) % 0.74/0.98 (step @p82 :rule bool-and-de-morgan :args (@t52 @t114 (and @t40))) % 0.74/0.98 (step @p83 :rule trans :premises (@p82 @p81)) % 0.74/0.98 (step @p84 :rule refl :args (@t119)) % 0.74/0.98 (step @p85 :rule nary_cong :premises (@p84 @p83) :args ((or @t119 (not (and @t52 @t114 @t40))))) % 0.74/0.98 (step @p86 :rule bool-and-de-morgan :args (@t118 @t52 (and @t114 @t40))) % 0.74/0.98 (step @p87 :rule trans :premises (@p86 @p85)) % 0.74/0.98 (step @p88 :rule refl :args (@t120)) % 0.74/0.98 (step @p89 :rule nary_cong :premises (@p88 @p87) :args ((or @t120 (not (and @t118 @t52 @t114 @t40))))) % 0.74/0.98 (step @p90 :rule bool-and-de-morgan :args (@t55 @t118 (and @t52 @t114 @t40))) % 0.74/0.98 (step @p91 :rule trans :premises (@p90 @p89)) % 0.74/0.98 (step @p92 :rule nary_cong :premises (@p88 @p91) :args ((or @t120 (not (and @t55 @t118 @t52 @t114 @t40))))) % 0.74/0.98 (step @p93 :rule bool-and-de-morgan :args (@t55 @t55 (and @t118 @t52 @t114 @t40))) % 0.74/0.98 (step @p94 :rule trans :premises (@p93 @p92)) % 0.74/0.98 (step @p95 :rule trans :premises (@p94 @p78)) % 0.74/0.98 (step @p96 :rule trans :premises (@p95 @p77)) % 0.74/0.98 (step @p97 :rule cong :premises (@p96) :args (@t150)) % 0.74/0.98 (step @p98 :rule cong :premises (@p97) :args (@t151)) % 0.74/0.98 (step @p99 :rule exists-elim :args ((= (exists @t11 @t149) @t151))) % 0.74/0.98 (step @p100 :rule trans :premises (@p99 @p98)) % 0.74/0.98 (step @p101 :rule refl :args (@t40)) % 0.74/0.98 (step @p102 :rule refl :args (@t20)) % 0.74/0.98 (step @p103 :rule refl :args (@t111)) % 0.74/0.98 (step @p104 :rule bool-and-de-morgan :args (@t47 @t112 true)) % 0.74/0.98 (step @p105 :rule nary_cong :premises (@p104 @p103) :args ((and (not @t152) @t111))) % 0.74/0.98 (step @p106 :rule bool-or-de-morgan :args (@t152 @t41 false)) % 0.74/0.98 (step @p107 :rule trans :premises (@p106 @p105)) % 0.74/0.98 (step @p108 :rule nary_cong :premises (@p107 @p102) :args ((or (not @t153) @t20))) % 0.74/0.98 (step @p109 :rule bool-impl-elim :args (@t153 @t20)) % 0.74/0.98 (step @p110 :rule trans :premises (@p109 @p108)) % 0.74/0.98 (step @p111 :rule cong :premises (@p110) :args ((forall @t22 (=> @t153 @t20)))) % 0.74/0.98 (step @p112 :rule refl :args (@t20)) % 0.74/0.98 (step @p113 :rule refl :args (@t41)) % 0.74/0.98 (step @p114 :rule bool-impl-elim :args (@t44 @t43)) % 0.74/0.98 (step @p115 :rule cong :premises (@p114) :args (@t46)) % 0.74/0.98 (step @p116 :rule refl :args (@t47)) % 0.74/0.98 (step @p117 :rule nary_cong :premises (@p116 @p115) :args (@t48)) % 0.74/0.98 (step @p118 :rule nary_cong :premises (@p117 @p113) :args (@t49)) % 0.74/0.98 (step @p119 :rule cong :premises (@p118 @p112) :args (@t50)) % 0.74/0.98 (step @p120 :rule cong :premises (@p119) :args (@t51)) % 0.74/0.98 (step @p121 :rule trans :premises (@p120 @p111)) % 0.74/0.98 (step @p122 :rule refl :args (@t52)) % 0.74/0.98 (step @p123 :rule bool-impl-elim :args (@t53 @t24)) % 0.74/0.98 (step @p124 :rule cong :premises (@p123) :args (@t54)) % 0.74/0.98 (step @p125 :rule refl :args (@t55)) % 0.74/0.98 (step @p126 :rule nary_cong :premises (@p125 @p125 @p124 @p122 @p121 @p101) :args (@t56)) % 0.74/0.98 (step @p127 :rule cong :premises (@p126) :args (@t57)) % 0.74/0.98 (step @p128 :rule trans :premises (@p127 @p100)) % 0.74/0.98 (step @p129 :rule refl :args (@t58)) % 0.74/0.98 (step @p130 :rule refl :args (@t59)) % 0.74/0.98 (step @p131 :rule refl :args (@t124)) % 0.74/0.98 (step @p132 :rule bool-and-de-morgan :args (@t55 @t125 true)) % 0.74/0.98 (step @p133 :rule nary_cong :premises (@p132 @p131) :args ((and (not @t154) @t124))) % 0.74/0.98 (step @p134 :rule bool-or-de-morgan :args (@t154 @t60 false)) % 0.74/0.98 (step @p135 :rule trans :premises (@p134 @p133)) % 0.74/0.98 (step @p136 :rule nary_cong :premises (@p135 @p130) :args ((or (not @t155) @t59))) % 0.74/0.98 (step @p137 :rule bool-impl-elim :args (@t155 @t59)) % 0.74/0.98 (step @p138 :rule trans :premises (@p137 @p136)) % 0.74/0.98 (step @p139 :rule cong :premises (@p138) :args ((forall @t11 (=> @t155 @t59)))) % 0.74/0.98 (step @p140 :rule refl :args (@t59)) % 0.74/0.98 (step @p141 :rule refl :args (@t60)) % 0.74/0.98 (step @p142 :rule 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:args ((or @t172 (not (and @t85 @t247))))) % 0.74/0.99 (step @p318 :rule bool-and-de-morgan :args (@t86 @t85 (and @t247))) % 0.74/0.99 (step @p319 :rule trans :premises (@p318 @p317)) % 0.74/0.99 (step @p320 :rule trans :premises (@p319 @p315)) % 0.74/0.99 (step @p321 :rule trans :premises (@p320 @p314)) % 0.74/0.99 (step @p322 :rule nary_cong :premises (@p321 @p311) :args ((or (not @t250) @t80))) % 0.74/0.99 (step @p323 :rule trans :premises (@p322 @p310)) % 0.74/0.99 (step @p324 :rule bool-impl-elim :args (@t250 @t80)) % 0.74/0.99 (step @p325 :rule trans :premises (@p324 @p323)) % 0.74/0.99 (step @p326 :rule bool-impl-elim :args (@t80 @t243)) % 0.74/0.99 (step @p327 :rule nary_cong :premises (@p326 @p325) :args (@t251)) % 0.74/0.99 (step @p328 :rule cong :premises (@p327) :args ((forall @t3 @t251))) % 0.74/0.99 (step @p329 :rule trans :premises (@p328 @p309)) % 0.74/0.99 (step @p330 :rule refl :args (@t80)) % 0.74/0.99 (step @p331 :rule refl :args (@t81)) % 0.74/0.99 (step @p332 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instantiate :premises (@p345) :args ((@list @t205 @t212))) % 0.74/0.99 (step @p347 :rule cnf_or_pos :args (@t252)) % 0.74/0.99 (step @p348 :rule reordering :premises (@p347) :args ((or @t208 @t213 (not @t252)))) % 0.74/0.99 (step @p349 false :rule chain_m_resolution :premises (@p348 @p346 @p286 @p281) :args (false (@list false true false) (@list @t252 @t213 @t207))) % 0.74/0.99 ) % 0.74/0.99 % SZS output end Proof % 0.74/0.99 % cvc5 exiting %------------------------------------------------------------------------------