%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET805+4 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n007.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 08:48:41 AM UTC 2026 % Result : Theorem 0.39s 0.62s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET805+4 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n007.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:11:56 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.62 % SZS status Theorem % 0.39/0.62 % SZS output start Proof % 0.39/0.62 ( % 0.39/0.62 (declare-sort $$unsorted 0) % 0.39/0.62 (declare-const tptp.min (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.max (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.lower_bound (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.order (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.least (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.greatest_lower_bound (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.least_upper_bound (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.greatest (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.upper_bound (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.empty_set $$unsorted) % 0.39/0.62 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.total_order (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (define @t1 () (@var "B" $$unsorted)) % 0.39/0.62 (define @t2 () (@var "X" $$unsorted)) % 0.39/0.62 (define @t3 () (tptp.member @t2 @t1)) % 0.39/0.62 (define @t4 () (@var "A" $$unsorted)) % 0.39/0.62 (define @t5 () (tptp.member @t2 @t4)) % 0.39/0.62 (define @t6 () (@list @t2)) % 0.39/0.62 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.39/0.62 (define @t8 () (tptp.subset @t4 @t1)) % 0.39/0.62 (define @t9 () (= @t8 @t7)) % 0.39/0.62 (define @t10 () (@list @t4 @t1)) % 0.39/0.62 (define @t11 () (forall @t10 @t9)) % 0.39/0.62 (define @t12 () (@list @t2 @t4)) % 0.39/0.62 (define @t13 () (@list @t2 @t4 @t1)) % 0.39/0.62 (define @t14 () (@var "E" $$unsorted)) % 0.39/0.62 (define @t15 () (= @t2 @t4)) % 0.39/0.62 (define @t16 () (@var "Y" $$unsorted)) % 0.39/0.62 (define @t17 () (tptp.member @t2 @t16)) % 0.39/0.62 (define @t18 () (tptp.member @t16 @t4)) % 0.39/0.62 (define @t19 () (@list @t16)) % 0.39/0.62 (define @t20 () (@var "Z" $$unsorted)) % 0.39/0.62 (define @t21 () (@var "R" $$unsorted)) % 0.39/0.62 (define @t22 () (tptp.apply @t21 @t2 @t20)) % 0.39/0.62 (define @t23 () (tptp.apply @t21 @t16 @t20)) % 0.39/0.62 (define @t24 () (tptp.apply @t21 @t2 @t16)) % 0.39/0.62 (define @t25 () (and @t24 @t23)) % 0.39/0.62 (define @t26 () (=> @t25 @t22)) % 0.39/0.62 (define @t27 () (tptp.member @t20 @t14)) % 0.39/0.62 (define @t28 () (tptp.member @t16 @t14)) % 0.39/0.62 (define @t29 () (tptp.member @t2 @t14)) % 0.39/0.62 (define @t30 () (and @t29 @t28 @t27)) % 0.39/0.62 (define @t31 () (@list @t2 @t16 @t20)) % 0.39/0.62 (define @t32 () (forall @t31 (=> @t30 @t26))) % 0.39/0.62 (define @t33 () (= @t2 @t16)) % 0.39/0.62 (define @t34 () (tptp.apply @t21 @t16 @t2)) % 0.39/0.62 (define @t35 () (and @t24 @t34)) % 0.39/0.62 (define @t36 () (=> @t35 @t33)) % 0.39/0.62 (define @t37 () (and @t29 @t28)) % 0.39/0.62 (define @t38 () (@list @t2 @t16)) % 0.39/0.62 (define @t39 () (forall @t38 (=> @t37 @t36))) % 0.39/0.62 (define @t40 () (tptp.apply @t21 @t2 @t2)) % 0.39/0.62 (define @t41 () (forall @t6 (=> @t29 @t40))) % 0.39/0.62 (define @t42 () (and @t41 @t39 @t32)) % 0.39/0.62 (define @t43 () (tptp.order @t21 @t14)) % 0.39/0.62 (define @t44 () (= @t43 @t42)) % 0.39/0.62 (define @t45 () (@list @t21 @t14)) % 0.39/0.62 (define @t46 () (forall @t45 @t44)) % 0.39/0.62 (define @t47 () (@var "M" $$unsorted)) % 0.39/0.62 (define @t48 () (tptp.apply @t21 @t2 @t47)) % 0.39/0.62 (define @t49 () (forall @t6 (=> @t29 @t48))) % 0.39/0.62 (define @t50 () (@list @t21 @t14 @t47)) % 0.39/0.62 (define @t51 () (tptp.apply @t21 @t47 @t2)) % 0.39/0.62 (define @t52 () (forall @t6 (=> @t29 @t51))) % 0.39/0.62 (define @t53 () (tptp.member @t47 @t14)) % 0.39/0.62 (define @t54 () (= @t47 @t2)) % 0.39/0.62 (define @t55 () (@list @t47)) % 0.39/0.62 (define @t56 () (tptp.member @t4 @t2)) % 0.39/0.62 (define @t57 () (@list @t4 @t2 @t21 @t14)) % 0.39/0.62 (define @t58 () (tptp.order @t21 @t2)) % 0.39/0.62 (define @t59 () (tptp.subset @t2 @t14)) % 0.39/0.62 (define @t60 () (forall @t6 (=> @t59 @t58))) % 0.39/0.62 (define @t61 () (=> @t43 @t60)) % 0.39/0.62 (define @t62 () (forall @t45 @t61)) % 0.39/0.62 (define @t63 () (not @t62)) % 0.39/0.62 (define @t64 () (not @t23)) % 0.39/0.62 (define @t65 () (not @t24)) % 0.39/0.62 (define @t66 () (not @t27)) % 0.39/0.62 (define @t67 () (not @t28)) % 0.39/0.62 (define @t68 () (not @t29)) % 0.39/0.62 (define @t69 () (or @t65 @t64 @t22)) % 0.39/0.62 (define @t70 () (or @t68 @t67 @t66)) % 0.39/0.62 (define @t71 () (not @t34)) % 0.39/0.62 (define @t72 () (or @t65 @t71 @t33)) % 0.39/0.62 (define @t73 () (@var "BOUND_VARIABLE_7745" $$unsorted)) % 0.39/0.62 (define @t74 () (tptp.order @t21 @t73)) % 0.39/0.62 (define @t75 () (not (tptp.subset @t73 @t14))) % 0.39/0.62 (define @t76 () (not @t43)) % 0.39/0.62 (define @t77 () (or @t76 @t75 @t74)) % 0.39/0.62 (define @t78 () (@list @t21 @t14 @t73)) % 0.39/0.62 (define @t79 () (forall @t78 @t77)) % 0.39/0.62 (define @t80 () (@quantifiers_skolemize @t79 1)) % 0.39/0.62 (define @t81 () (@quantifiers_skolemize @t79 0)) % 0.39/0.62 (define @t82 () (or @t75 @t74)) % 0.39/0.62 (define @t83 () (or @t76 @t82)) % 0.39/0.62 (define @t84 () (forall @t78 @t83)) % 0.39/0.62 (define @t85 () (@list @t73)) % 0.39/0.62 (define @t86 () (forall @t85 @t83)) % 0.39/0.62 (define @t87 () (forall @t85 @t82)) % 0.39/0.62 (define @t88 () (or @t76 @t87)) % 0.39/0.62 (define @t89 () (forall @t6 (or (not @t59) @t58))) % 0.39/0.62 (define @t90 () (tptp.order @t81 @t80)) % 0.39/0.62 (define @t91 () (@quantifiers_skolemize @t79 2)) % 0.39/0.62 (define @t92 () (tptp.order @t81 @t91)) % 0.39/0.62 (define @t93 () (tptp.subset @t91 @t80)) % 0.39/0.62 (define @t94 () (not @t93)) % 0.39/0.62 (define @t95 () (not @t90)) % 0.39/0.62 (define @t96 () (or @t95 @t94 @t92)) % 0.39/0.62 (define @t97 () (@list true)) % 0.39/0.62 (define @t98 () (@list @t96)) % 0.39/0.62 (define @t99 () (tptp.apply @t81 @t2 @t20)) % 0.39/0.62 (define @t100 () (not (tptp.apply @t81 @t16 @t20))) % 0.39/0.62 (define @t101 () (not (tptp.apply @t81 @t2 @t16))) % 0.39/0.62 (define @t102 () (not (tptp.member @t16 @t80))) % 0.39/0.62 (define @t103 () (tptp.member @t2 @t80)) % 0.39/0.62 (define @t104 () (not @t103)) % 0.39/0.62 (define @t105 () (forall @t31 (or @t104 @t102 (not (tptp.member @t20 @t80)) @t101 @t100 @t99))) % 0.39/0.62 (define @t106 () (not (tptp.apply @t81 @t16 @t2))) % 0.39/0.62 (define @t107 () (forall @t38 (or @t104 @t102 @t101 @t106 @t33))) % 0.39/0.62 (define @t108 () (tptp.apply @t81 @t2 @t2)) % 0.39/0.62 (define @t109 () (forall @t6 (or @t104 @t108))) % 0.39/0.62 (define @t110 () (and @t109 @t107 @t105)) % 0.39/0.62 (define @t111 () (= @t90 @t110)) % 0.39/0.62 (define @t112 () (@list false false)) % 0.39/0.62 (define @t113 () (not @t110)) % 0.39/0.62 (define @t114 () (@list false)) % 0.39/0.62 (define @t115 () (@list @t110)) % 0.39/0.62 (define @t116 () (not (tptp.member @t2 @t91))) % 0.39/0.62 (define @t117 () (forall @t6 (or @t116 @t103))) % 0.39/0.62 (define @t118 () (= @t93 @t117)) % 0.39/0.62 (define @t119 () (not (tptp.member @t16 @t91))) % 0.39/0.62 (define @t120 () (forall @t31 (or @t116 @t119 (not (tptp.member @t20 @t91)) @t101 @t100 @t99))) % 0.39/0.62 (define @t121 () (@quantifiers_skolemize @t120 2)) % 0.39/0.62 (define @t122 () (forall @t38 (or @t116 @t119 @t101 @t106 @t33))) % 0.39/0.62 (define @t123 () (@quantifiers_skolemize @t122 0)) % 0.39/0.62 (define @t124 () (tptp.member @t123 @t91)) % 0.39/0.62 (define @t125 () (@quantifiers_skolemize @t122 1)) % 0.39/0.62 (define @t126 () (= @t123 @t125)) % 0.39/0.62 (define @t127 () (tptp.apply @t81 @t125 @t123)) % 0.39/0.62 (define @t128 () (not @t127)) % 0.39/0.62 (define @t129 () (tptp.apply @t81 @t123 @t125)) % 0.39/0.62 (define @t130 () (not @t129)) % 0.39/0.62 (define @t131 () (tptp.member @t125 @t91)) % 0.39/0.62 (define @t132 () (not @t131)) % 0.39/0.62 (define @t133 () (not @t124)) % 0.39/0.62 (define @t134 () (or @t133 @t132 @t130 @t128 @t126)) % 0.39/0.62 (define @t135 () (tptp.member @t123 @t80)) % 0.39/0.62 (define @t136 () (or @t133 @t135)) % 0.39/0.62 (define @t137 () (tptp.member @t125 @t80)) % 0.39/0.62 (define @t138 () (or @t132 @t137)) % 0.39/0.62 (define @t139 () (not @t137)) % 0.39/0.62 (define @t140 () (not @t135)) % 0.39/0.62 (define @t141 () (or @t140 @t139 @t130 @t128 @t126)) % 0.39/0.62 (define @t142 () (not @t134)) % 0.39/0.62 (define @t143 () (not @t122)) % 0.39/0.62 (define @t144 () (forall @t6 (or @t116 @t108))) % 0.39/0.62 (define @t145 () (@quantifiers_skolemize @t144 0)) % 0.39/0.62 (define @t146 () (tptp.member @t145 @t91)) % 0.39/0.62 (define @t147 () (tptp.apply @t81 @t145 @t145)) % 0.39/0.62 (define @t148 () (not @t146)) % 0.39/0.62 (define @t149 () (or @t148 @t147)) % 0.39/0.62 (define @t150 () (@list @t145)) % 0.39/0.62 (define @t151 () (tptp.member @t145 @t80)) % 0.39/0.62 (define @t152 () (or @t148 @t151)) % 0.39/0.62 (define @t153 () (not @t151)) % 0.39/0.62 (define @t154 () (or @t153 @t147)) % 0.39/0.62 (define @t155 () (not @t149)) % 0.39/0.62 (define @t156 () (not @t144)) % 0.39/0.62 (define @t157 () (and @t144 @t122 @t120)) % 0.39/0.62 (define @t158 () (= @t92 @t157)) % 0.39/0.62 (define @t159 () (not @t157)) % 0.39/0.62 (define @t160 () (@list true false)) % 0.39/0.62 (define @t161 () (not @t120)) % 0.39/0.62 (define @t162 () (@quantifiers_skolemize @t120 0)) % 0.39/0.62 (define @t163 () (tptp.apply @t81 @t162 @t121)) % 0.39/0.62 (define @t164 () (@quantifiers_skolemize @t120 1)) % 0.39/0.62 (define @t165 () (tptp.apply @t81 @t164 @t121)) % 0.39/0.62 (define @t166 () (not @t165)) % 0.39/0.62 (define @t167 () (tptp.apply @t81 @t162 @t164)) % 0.39/0.62 (define @t168 () (not @t167)) % 0.39/0.62 (define @t169 () (tptp.member @t121 @t91)) % 0.39/0.62 (define @t170 () (not @t169)) % 0.39/0.62 (define @t171 () (tptp.member @t164 @t91)) % 0.39/0.62 (define @t172 () (not @t171)) % 0.39/0.62 (define @t173 () (tptp.member @t162 @t91)) % 0.39/0.62 (define @t174 () (not @t173)) % 0.39/0.62 (define @t175 () (or @t174 @t172 @t170 @t168 @t166 @t163)) % 0.39/0.62 (define @t176 () (not @t175)) % 0.39/0.62 (define @t177 () (@list @t175)) % 0.39/0.62 (define @t178 () (tptp.member @t121 @t80)) % 0.39/0.62 (define @t179 () (or @t170 @t178)) % 0.39/0.62 (define @t180 () (tptp.member @t164 @t80)) % 0.39/0.62 (define @t181 () (or @t172 @t180)) % 0.39/0.62 (define @t182 () (tptp.member @t162 @t80)) % 0.39/0.62 (define @t183 () (or @t174 @t182)) % 0.39/0.62 (define @t184 () (not @t178)) % 0.39/0.62 (define @t185 () (not @t180)) % 0.39/0.62 (define @t186 () (not @t182)) % 0.39/0.62 (define @t187 () (or @t186 @t185 @t184 @t168 @t166 @t163)) % 0.39/0.62 (define @t188 () (not @t187)) % 0.39/0.62 (assume @p1 @t11) % 0.39/0.62 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.39/0.62 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.39/0.62 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.39/0.62 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.39/0.62 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.39/0.62 (assume @p7 (forall (@list @t1 @t4 @t14) (= (tptp.member @t1 (tptp.difference @t14 @t4)) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.39/0.62 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t15))) % 0.39/0.62 (assume @p9 (forall @t13 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t15 (= @t2 @t1))))) % 0.39/0.62 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t19 (and @t18 @t17))))) % 0.39/0.62 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t19 (=> @t18 @t17))))) % 0.39/0.62 (assume @p12 @t46) % 0.39/0.62 (assume @p13 (forall @t45 (= (tptp.total_order @t21 @t14) (and @t43 (forall @t38 (=> @t37 (or @t24 @t34))))))) % 0.39/0.62 (assume @p14 (forall @t50 (= (tptp.upper_bound @t47 @t21 @t14) @t49))) % 0.39/0.62 (assume @p15 (forall @t50 (= (tptp.lower_bound @t47 @t21 @t14) @t52))) % 0.39/0.62 (assume @p16 (forall @t50 (= (tptp.greatest @t47 @t21 @t14) (and @t53 @t49)))) % 0.39/0.62 (assume @p17 (forall @t50 (= (tptp.least @t47 @t21 @t14) (and @t53 @t52)))) % 0.39/0.62 (assume @p18 (forall @t50 (= (tptp.max @t47 @t21 @t14) (and @t53 (forall @t6 (=> (and @t29 @t51) @t54)))))) % 0.39/0.62 (assume @p19 (forall @t50 (= (tptp.min @t47 @t21 @t14) (and @t53 (forall @t6 (=> (and @t29 @t48) @t54)))))) % 0.39/0.62 (assume @p20 (forall @t57 (= (tptp.least_upper_bound @t4 @t2 @t21 @t14) (and @t56 (tptp.upper_bound @t4 @t21 @t2) (forall @t55 (=> (and @t53 (tptp.upper_bound @t47 @t21 @t2)) (tptp.apply @t21 @t4 @t47))))))) % 0.39/0.62 (assume @p21 (forall @t57 (= (tptp.greatest_lower_bound @t4 @t2 @t21 @t14) (and @t56 (tptp.lower_bound @t4 @t21 @t2) (forall @t55 (=> (and @t53 (tptp.lower_bound @t47 @t21 @t2)) (tptp.apply @t21 @t47 @t4))))))) % 0.39/0.62 (assume @p22 @t63) % 0.39/0.62 (assume @p23 true) % 0.39/0.62 (step @p24 :rule aci_norm :args ((= (or @t70 @t69) (or @t68 @t67 @t66 @t65 @t64 @t22)))) % 0.39/0.62 (step @p25 :rule aci_norm :args ((= (or (or @t65 @t64) @t22) @t69))) % 0.39/0.62 (step @p26 :rule refl :args (@t22)) % 0.39/0.62 (step @p27 :rule bool-and-de-morgan :args (@t24 @t23 true)) % 0.39/0.62 (step @p28 :rule nary_cong :premises (@p27 @p26) :args ((or (not @t25) @t22))) % 0.39/0.62 (step @p29 :rule trans :premises (@p28 @p25)) % 0.39/0.62 (step @p30 :rule bool-impl-elim :args (@t25 @t22)) % 0.39/0.62 (step @p31 :rule trans :premises (@p30 @p29)) % 0.39/0.62 (step @p32 :rule aci_norm :args ((= (or @t68 (or @t67 @t66)) @t70))) % 0.39/0.62 (step @p33 :rule bool-and-de-morgan :args (@t28 @t27 true)) % 0.39/0.62 (step @p34 :rule refl :args (@t68)) % 0.39/0.62 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or @t68 (not (and @t28 @t27))))) % 0.39/0.62 (step @p36 :rule bool-and-de-morgan :args (@t29 @t28 (and @t27))) % 0.39/0.62 (step @p37 :rule trans :premises (@p36 @p35)) % 0.39/0.62 (step @p38 :rule trans :premises (@p37 @p32)) % 0.39/0.62 (step @p39 :rule nary_cong :premises (@p38 @p31) :args ((or (not @t30) @t26))) % 0.39/0.62 (step @p40 :rule trans :premises (@p39 @p24)) % 0.39/0.62 (step @p41 :rule bool-impl-elim :args (@t30 @t26)) % 0.39/0.62 (step @p42 :rule trans :premises (@p41 @p40)) % 0.39/0.62 (step @p43 :rule cong :premises (@p42) :args (@t32)) % 0.39/0.62 (step @p44 :rule aci_norm :args ((= (or (or @t68 @t67) @t72) (or @t68 @t67 @t65 @t71 @t33)))) % 0.39/0.62 (step @p45 :rule aci_norm :args ((= (or (or @t65 @t71) @t33) @t72))) % 0.39/0.62 (step @p46 :rule refl :args (@t33)) % 0.39/0.62 (step @p47 :rule bool-and-de-morgan :args (@t24 @t34 true)) % 0.39/0.62 (step @p48 :rule nary_cong :premises (@p47 @p46) :args ((or (not @t35) @t33))) % 0.39/0.62 (step @p49 :rule trans :premises (@p48 @p45)) % 0.39/0.62 (step @p50 :rule bool-impl-elim :args (@t35 @t33)) % 0.39/0.62 (step @p51 :rule trans :premises (@p50 @p49)) % 0.39/0.62 (step @p52 :rule bool-and-de-morgan :args (@t29 @t28 true)) % 0.39/0.62 (step @p53 :rule nary_cong :premises (@p52 @p51) :args ((or (not @t37) @t36))) % 0.39/0.62 (step @p54 :rule trans :premises (@p53 @p44)) % 0.39/0.62 (step @p55 :rule bool-impl-elim :args (@t37 @t36)) % 0.39/0.62 (step @p56 :rule trans :premises (@p55 @p54)) % 0.39/0.62 (step @p57 :rule cong :premises (@p56) :args (@t39)) % 0.39/0.62 (step @p58 :rule bool-impl-elim :args (@t29 @t40)) % 0.39/0.62 (step @p59 :rule cong :premises (@p58) :args (@t41)) % 0.39/0.62 (step @p60 :rule nary_cong :premises (@p59 @p57 @p43) :args (@t42)) % 0.39/0.62 (step @p61 :rule refl :args (@t43)) % 0.39/0.62 (step @p62 :rule cong :premises (@p61 @p60) :args (@t44)) % 0.39/0.62 (step @p63 :rule cong :premises (@p62) :args (@t46)) % 0.39/0.62 (step @p64 :rule eq_resolve :premises (@p12 @p63)) % 0.39/0.62 (step @p65 :rule instantiate :premises (@p64) :args ((@list @t81 @t80))) % 0.39/0.62 (step @p66 :rule aci_norm :args ((= @t83 @t77))) % 0.39/0.62 (step @p67 :rule cong :premises (@p66) :args (@t84)) % 0.39/0.62 (step @p68 :rule quant-merge-prenex :args ((= (forall @t45 @t86) @t84))) % 0.39/0.62 (step @p69 :rule alpha_equiv :args (@t87 (@list @t73) (@list @t2))) % 0.39/0.62 (step @p70 :rule refl :args (@t76)) % 0.39/0.62 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t88)) % 0.39/0.62 (step @p72 :rule quant-miniscope-or :args ((= @t86 @t88))) % 0.39/0.62 (step @p73 :rule trans :premises (@p72 @p71)) % 0.39/0.62 (step @p74 :rule symm :premises (@p73)) % 0.39/0.62 (step @p75 :rule cong :premises (@p74) :args ((forall @t45 (or @t76 @t89)))) % 0.39/0.62 (step @p76 :rule trans :premises (@p75 @p68)) % 0.39/0.62 (step @p77 :rule trans :premises (@p76 @p67)) % 0.39/0.62 (step @p78 :rule bool-impl-elim :args (@t43 @t89)) % 0.39/0.62 (step @p79 :rule cong :premises (@p78) :args ((forall @t45 (=> @t43 @t89)))) % 0.39/0.62 (step @p80 :rule trans :premises (@p79 @p77)) % 0.39/0.62 (step @p81 :rule bool-impl-elim :args (@t59 @t58)) % 0.39/0.62 (step @p82 :rule cong :premises (@p81) :args (@t60)) % 0.39/0.62 (step @p83 :rule cong :premises (@p61 @p82) :args (@t61)) % 0.39/0.62 (step @p84 :rule cong :premises (@p83) :args (@t62)) % 0.39/0.62 (step @p85 :rule trans :premises (@p84 @p80)) % 0.39/0.62 (step @p86 :rule cong :premises (@p85) :args (@t63)) % 0.39/0.62 (step @p87 :rule eq_resolve :premises (@p22 @p86)) % 0.39/0.62 (step @p88 :rule skolemize :premises (@p87)) % 0.39/0.62 (step @p89 :rule bool-double-not-elim :args (@t90)) % 0.39/0.62 (step @p90 :rule refl :args (@t96)) % 0.39/0.62 (step @p91 :rule nary_cong :premises (@p90 @p89) :args ((or @t96 (not @t95)))) % 0.39/0.62 (step @p92 :rule cnf_or_neg :args (@t96 0)) % 0.39/0.62 (step @p93 :rule eq_resolve :premises (@p92 @p91)) % 0.39/0.62 (step @p94 :rule reordering :premises (@p93) :args ((or @t90 @t96))) % 0.39/0.62 (step @p95 :rule chain_m_resolution :premises (@p94 @p88) :args (@t90 @t97 @t98)) % 0.39/0.62 (step @p96 :rule cnf_equiv_pos1 :args (@t111)) % 0.39/0.62 (step @p97 :rule reordering :premises (@p96) :args ((or @t95 @t110 (not @t111)))) % 0.39/0.62 (step @p98 :rule chain_m_resolution :premises (@p97 @p95 @p65) :args (@t110 @t112 (@list @t90 @t111))) % 0.39/0.62 (step @p99 :rule cnf_and_pos :args (@t110 2)) % 0.39/0.62 (step @p100 :rule reordering :premises (@p99) :args ((or @t105 @t113))) % 0.39/0.62 (step @p101 :rule chain_m_resolution :premises (@p100 @p98) :args (@t105 @t114 @t115)) % 0.39/0.62 (step @p102 :rule bool-impl-elim :args (@t5 @t3)) % 0.39/0.62 (step @p103 :rule cong :premises (@p102) :args (@t7)) % 0.39/0.62 (step @p104 :rule refl :args (@t8)) % 0.39/0.62 (step @p105 :rule cong :premises (@p104 @p103) :args (@t9)) % 0.39/0.62 (step @p106 :rule cong :premises (@p105) :args (@t11)) % 0.39/0.62 (step @p107 :rule eq_resolve :premises (@p1 @p106)) % 0.39/0.62 (step @p108 :rule instantiate :premises (@p107) :args ((@list @t91 @t80))) % 0.39/0.62 (step @p109 :rule bool-double-not-elim :args (@t93)) % 0.39/0.62 (step @p110 :rule nary_cong :premises (@p90 @p109) :args ((or @t96 (not @t94)))) % 0.39/0.62 (step @p111 :rule cnf_or_neg :args (@t96 1)) % 0.39/0.62 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.39/0.62 (step @p113 :rule reordering :premises (@p112) :args ((or @t93 @t96))) % 0.39/0.62 (step @p114 :rule chain_m_resolution :premises (@p113 @p88) :args (@t93 @t97 @t98)) % 0.39/0.62 (step @p115 :rule cnf_equiv_pos1 :args (@t118)) % 0.39/0.62 (step @p116 :rule reordering :premises (@p115) :args ((or @t94 @t117 (not @t118)))) % 0.39/0.62 (step @p117 :rule chain_m_resolution :premises (@p116 @p114 @p108) :args (@t117 @t112 (@list @t93 @t118))) % 0.39/0.62 (step @p118 :rule instantiate :premises (@p117) :args ((@list @t121))) % 0.39/0.62 (step @p119 :rule bool-double-not-elim :args (@t124)) % 0.39/0.62 (step @p120 :rule refl :args (@t134)) % 0.39/0.62 (step @p121 :rule nary_cong :premises (@p120 @p119) :args ((or @t134 (not @t133)))) % 0.39/0.62 (step @p122 :rule cnf_or_neg :args (@t134 0)) % 0.39/0.62 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.39/0.62 (step @p124 :rule reordering :premises (@p123) :args ((or @t124 @t134))) % 0.39/0.62 (step @p125 :rule bool-double-not-elim :args (@t131)) % 0.39/0.62 (step @p126 :rule nary_cong :premises (@p120 @p125) :args ((or @t134 (not @t132)))) % 0.39/0.62 (step @p127 :rule cnf_or_neg :args (@t134 1)) % 0.39/0.62 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 0.39/0.62 (step @p129 :rule reordering :premises (@p128) :args ((or @t131 @t134))) % 0.39/0.62 (step @p130 :rule bool-double-not-elim :args (@t129)) % 0.39/0.62 (step @p131 :rule nary_cong :premises (@p120 @p130) :args ((or @t134 (not @t130)))) % 0.39/0.62 (step @p132 :rule cnf_or_neg :args (@t134 2)) % 0.39/0.62 (step @p133 :rule eq_resolve :premises (@p132 @p131)) % 0.39/0.62 (step @p134 :rule reordering :premises (@p133) :args ((or @t129 @t134))) % 0.39/0.62 (step @p135 :rule bool-double-not-elim :args (@t127)) % 0.39/0.62 (step @p136 :rule nary_cong :premises (@p120 @p135) :args ((or @t134 (not @t128)))) % 0.39/0.62 (step @p137 :rule cnf_or_neg :args (@t134 3)) % 0.39/0.62 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.39/0.62 (step @p139 :rule reordering :premises (@p138) :args ((or @t127 @t134))) % 0.39/0.62 (step @p140 :rule cnf_or_neg :args (@t134 4)) % 0.39/0.62 (step @p141 :rule instantiate :premises (@p117) :args ((@list @t123))) % 0.39/0.62 (step @p142 :rule cnf_or_pos :args (@t136)) % 0.39/0.62 (step @p143 :rule reordering :premises (@p142) :args ((or @t133 @t135 (not @t136)))) % 0.39/0.62 (step @p144 :rule instantiate :premises (@p117) :args ((@list @t125))) % 0.39/0.62 (step @p145 :rule cnf_or_pos :args (@t138)) % 0.39/0.62 (step @p146 :rule reordering :premises (@p145) :args ((or @t132 @t137 (not @t138)))) % 0.39/0.62 (step @p147 :rule cnf_and_pos :args (@t110 1)) % 0.39/0.62 (step @p148 :rule reordering :premises (@p147) :args ((or @t107 @t113))) % 0.39/0.62 (step @p149 :rule chain_m_resolution :premises (@p148 @p98) :args (@t107 @t114 @t115)) % 0.39/0.62 (step @p150 :rule instantiate :premises (@p149) :args ((@list @t123 @t125))) % 0.39/0.62 (step @p151 :rule cnf_or_pos :args (@t141)) % 0.39/0.62 (step @p152 :rule reordering :premises (@p151) :args ((or @t130 @t128 @t126 @t140 @t139 (not @t141)))) % 0.39/0.62 (step @p153 :rule chain_m_resolution :premises (@p152 @p150 @p146 @p144 @p143 @p141 @p140 @p139 @p134 @p129 @p124) :args (@t134 (@list false false false false false true false false false false) (@list @t141 @t137 @t138 @t135 @t136 @t126 @t127 @t129 @t131 @t124))) % 0.39/0.62 (step @p154 :rule refl :args (@t142)) % 0.39/0.62 (step @p155 :rule bool-double-not-elim :args (@t122)) % 0.39/0.62 (step @p156 :rule nary_cong :premises (@p155 @p154) :args ((or (not @t143) @t142))) % 0.39/0.62 (assume-push @p262 @t143) % 0.39/0.62 (step @p158 :rule skolemize :premises (@p262)) % 0.39/0.62 (step-pop @p263 :rule scope :premises (@p158)) % 0.39/0.62 (step @p159 :rule process_scope :premises (@p263) :args (@t142)) % 0.39/0.62 (step @p161 :rule implies_elim :premises (@p159)) % 0.39/0.62 (step @p162 :rule eq_resolve :premises (@p161 @p156)) % 0.39/0.62 (step @p163 :rule chain_m_resolution :premises (@p162 @p153) :args (@t122 @t114 (@list @t134))) % 0.39/0.62 (step @p164 :rule bool-double-not-elim :args (@t146)) % 0.39/0.62 (step @p165 :rule refl :args (@t149)) % 0.39/0.62 (step @p166 :rule nary_cong :premises (@p165 @p164) :args ((or @t149 (not @t148)))) % 0.39/0.62 (step @p167 :rule cnf_or_neg :args (@t149 0)) % 0.39/0.62 (step @p168 :rule eq_resolve :premises (@p167 @p166)) % 0.39/0.62 (step @p169 :rule reordering :premises (@p168) :args ((or @t146 @t149))) % 0.39/0.62 (step @p170 :rule cnf_or_neg :args (@t149 1)) % 0.39/0.62 (step @p171 :rule instantiate :premises (@p117) :args (@t150)) % 0.39/0.62 (step @p172 :rule cnf_or_pos :args (@t152)) % 0.39/0.62 (step @p173 :rule reordering :premises (@p172) :args ((or @t148 @t151 (not @t152)))) % 0.39/0.62 (step @p174 :rule cnf_and_pos :args (@t110 0)) % 0.39/0.62 (step @p175 :rule reordering :premises (@p174) :args ((or @t109 @t113))) % 0.39/0.62 (step @p176 :rule chain_m_resolution :premises (@p175 @p98) :args (@t109 @t114 @t115)) % 0.39/0.62 (step @p177 :rule instantiate :premises (@p176) :args (@t150)) % 0.39/0.62 (step @p178 :rule cnf_or_pos :args (@t154)) % 0.39/0.62 (step @p179 :rule reordering :premises (@p178) :args ((or @t147 @t153 (not @t154)))) % 0.39/0.62 (step @p180 :rule chain_m_resolution :premises (@p179 @p177 @p173 @p171 @p170 @p169) :args (@t149 (@list false false false true false) (@list @t154 @t151 @t152 @t147 @t146))) % 0.39/0.62 (step @p181 :rule refl :args (@t155)) % 0.39/0.62 (step @p182 :rule bool-double-not-elim :args (@t144)) % 0.39/0.62 (step @p183 :rule nary_cong :premises (@p182 @p181) :args ((or (not @t156) @t155))) % 0.39/0.62 (assume-push @p264 @t156) % 0.39/0.62 (step @p185 :rule skolemize :premises (@p264)) % 0.39/0.62 (step-pop @p265 :rule scope :premises (@p185)) % 0.39/0.62 (step @p186 :rule process_scope :premises (@p265) :args (@t155)) % 0.39/0.62 (step @p188 :rule implies_elim :premises (@p186)) % 0.39/0.62 (step @p189 :rule eq_resolve :premises (@p188 @p183)) % 0.39/0.62 (step @p190 :rule chain_m_resolution :premises (@p189 @p180) :args (@t144 @t114 (@list @t149))) % 0.39/0.62 (step @p191 :rule instantiate :premises (@p64) :args ((@list @t81 @t91))) % 0.39/0.62 (step @p192 :rule cnf_or_neg :args (@t96 2)) % 0.39/0.62 (step @p193 :rule chain_m_resolution :premises (@p192 @p88) :args ((not @t92) @t97 @t98)) % 0.39/0.62 (step @p194 :rule cnf_equiv_pos2 :args (@t158)) % 0.39/0.62 (step @p195 :rule reordering :premises (@p194) :args ((or @t92 @t159 (not @t158)))) % 0.39/0.62 (step @p196 :rule chain_m_resolution :premises (@p195 @p193 @p191) :args (@t159 @t160 (@list @t92 @t158))) % 0.39/0.62 (step @p197 :rule cnf_and_neg :args (@t157)) % 0.39/0.62 (step @p198 :rule chain_m_resolution :premises (@p197 @p196 @p190 @p163) :args (@t161 (@list true false false) (@list @t157 @t144 @t122))) % 0.39/0.62 (step @p199 :rule refl :args (@t176)) % 0.39/0.62 (step @p200 :rule bool-double-not-elim :args (@t120)) % 0.39/0.62 (step @p201 :rule nary_cong :premises (@p200 @p199) :args ((or (not @t161) @t176))) % 0.39/0.62 (assume-push @p266 @t161) % 0.39/0.62 (step @p203 :rule skolemize :premises (@p266)) % 0.39/0.62 (step-pop @p267 :rule scope :premises (@p203)) % 0.39/0.62 (step @p204 :rule process_scope :premises (@p267) :args (@t176)) % 0.39/0.62 (step @p206 :rule implies_elim :premises (@p204)) % 0.39/0.62 (step @p207 :rule eq_resolve :premises (@p206 @p201)) % 0.39/0.62 (step @p208 :rule chain_m_resolution :premises (@p207 @p198) :args (@t176 @t97 (@list @t120))) % 0.39/0.62 (step @p209 :rule bool-double-not-elim :args (@t169)) % 0.39/0.62 (step @p210 :rule refl :args (@t175)) % 0.39/0.62 (step @p211 :rule nary_cong :premises (@p210 @p209) :args ((or @t175 (not @t170)))) % 0.39/0.62 (step @p212 :rule cnf_or_neg :args (@t175 2)) % 0.39/0.62 (step @p213 :rule eq_resolve :premises (@p212 @p211)) % 0.39/0.62 (step @p214 :rule reordering :premises (@p213) :args ((or @t169 @t175))) % 0.39/0.62 (step @p215 :rule chain_m_resolution :premises (@p214 @p208) :args (@t169 @t97 @t177)) % 0.39/0.62 (step @p216 :rule cnf_or_pos :args (@t179)) % 0.39/0.62 (step @p217 :rule reordering :premises (@p216) :args ((or @t170 @t178 (not @t179)))) % 0.39/0.62 (step @p218 :rule chain_m_resolution :premises (@p217 @p215 @p118) :args (@t178 @t112 (@list @t169 @t179))) % 0.39/0.62 (step @p219 :rule instantiate :premises (@p117) :args ((@list @t164))) % 0.39/0.62 (step @p220 :rule bool-double-not-elim :args (@t171)) % 0.39/0.62 (step @p221 :rule nary_cong :premises (@p210 @p220) :args ((or @t175 (not @t172)))) % 0.39/0.62 (step @p222 :rule cnf_or_neg :args (@t175 1)) % 0.39/0.62 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 0.39/0.62 (step @p224 :rule reordering :premises (@p223) :args ((or @t171 @t175))) % 0.39/0.62 (step @p225 :rule chain_m_resolution :premises (@p224 @p208) :args (@t171 @t97 @t177)) % 0.39/0.62 (step @p226 :rule cnf_or_pos :args (@t181)) % 0.39/0.62 (step @p227 :rule reordering :premises (@p226) :args ((or @t172 @t180 (not @t181)))) % 0.39/0.62 (step @p228 :rule chain_m_resolution :premises (@p227 @p225 @p219) :args (@t180 @t112 (@list @t171 @t181))) % 0.39/0.62 (step @p229 :rule instantiate :premises (@p117) :args ((@list @t162))) % 0.39/0.62 (step @p230 :rule bool-double-not-elim :args (@t173)) % 0.39/0.62 (step @p231 :rule nary_cong :premises (@p210 @p230) :args ((or @t175 (not @t174)))) % 0.39/0.62 (step @p232 :rule cnf_or_neg :args (@t175 0)) % 0.39/0.62 (step @p233 :rule eq_resolve :premises (@p232 @p231)) % 0.39/0.62 (step @p234 :rule reordering :premises (@p233) :args ((or @t173 @t175))) % 0.39/0.62 (step @p235 :rule chain_m_resolution :premises (@p234 @p208) :args (@t173 @t97 @t177)) % 0.39/0.62 (step @p236 :rule cnf_or_pos :args (@t183)) % 0.39/0.62 (step @p237 :rule reordering :premises (@p236) :args ((or @t174 @t182 (not @t183)))) % 0.39/0.62 (step @p238 :rule chain_m_resolution :premises (@p237 @p235 @p229) :args (@t182 @t112 (@list @t173 @t183))) % 0.39/0.62 (step @p239 :rule cnf_or_neg :args (@t175 5)) % 0.39/0.62 (step @p240 :rule chain_m_resolution :premises (@p239 @p208) :args ((not @t163) @t97 @t177)) % 0.39/0.62 (step @p241 :rule bool-double-not-elim :args (@t165)) % 0.39/0.62 (step @p242 :rule nary_cong :premises (@p210 @p241) :args ((or @t175 (not @t166)))) % 0.39/0.62 (step @p243 :rule cnf_or_neg :args (@t175 4)) % 0.39/0.62 (step @p244 :rule eq_resolve :premises (@p243 @p242)) % 0.39/0.62 (step @p245 :rule reordering :premises (@p244) :args ((or @t165 @t175))) % 0.39/0.62 (step @p246 :rule chain_m_resolution :premises (@p245 @p208) :args (@t165 @t97 @t177)) % 0.39/0.62 (step @p247 :rule bool-double-not-elim :args (@t167)) % 0.39/0.62 (step @p248 :rule nary_cong :premises (@p210 @p247) :args ((or @t175 (not @t168)))) % 0.39/0.62 (step @p249 :rule cnf_or_neg :args (@t175 3)) % 0.39/0.62 (step @p250 :rule eq_resolve :premises (@p249 @p248)) % 0.39/0.62 (step @p251 :rule reordering :premises (@p250) :args ((or @t167 @t175))) % 0.39/0.62 (step @p252 :rule chain_m_resolution :premises (@p251 @p208) :args (@t167 @t97 @t177)) % 0.39/0.62 (step @p253 :rule cnf_or_pos :args (@t187)) % 0.39/0.62 (step @p254 :rule reordering :premises (@p253) :args ((or @t168 @t166 @t163 @t186 @t185 @t184 @t188))) % 0.39/0.62 (step @p255 :rule chain_m_resolution :premises (@p254 @p252 @p246 @p240 @p238 @p228 @p218) :args (@t188 (@list false false true false false false) (@list @t167 @t165 @t163 @t182 @t180 @t178))) % 0.39/0.62 (assume-push @p268 @t105) % 0.39/0.62 (step @p257 :rule instantiate :premises (@p101) :args ((@list @t162 @t164 @t121))) % 0.39/0.62 (step-pop @p269 :rule scope :premises (@p257)) % 0.39/0.62 (step @p258 :rule process_scope :premises (@p269) :args (@t187)) % 0.39/0.62 (step @p260 :rule implies_elim :premises (@p258)) % 0.39/0.62 (step @p261 false :rule chain_m_resolution :premises (@p260 @p255 @p101) :args (false @t160 (@list @t187 @t105))) % 0.39/0.62 ) % 0.39/0.62 % SZS output end Proof % 0.39/0.62 % cvc5 exiting %------------------------------------------------------------------------------