%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM396+1 : 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 : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:39:18 AM UTC 2026 % Result : Theorem 33.86s 34.05s % Output : Proof 33.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM396+1 : 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 % 0.15/0.33 % Computer : n021.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 11:17:35 EDT 2026 % 0.15/0.33 % CPUTime : % 0.29/0.48 %----Proving TF0_NAR, FOF, or CNF % 33.86/34.05 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 33.86/34.05 --- Run --no-e-matching --full-saturate-quant at 6... % 33.86/34.05 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 33.86/34.05 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.86/34.05 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 33.86/34.05 % SZS status Theorem % 33.86/34.05 % SZS output start Proof % 33.86/34.05 ( % 33.86/34.05 (declare-sort $$unsorted 0) % 33.86/34.05 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 33.86/34.05 (declare-const tptp.relation_non_empty (-> $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.empty_set $$unsorted) % 33.86/34.05 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.function (-> $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 33.86/34.05 (declare-const tptp.empty (-> $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.relation (-> $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 33.86/34.05 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 33.86/34.05 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 33.86/34.05 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 33.86/34.05 (define @t1 () (@var "A" $$unsorted)) % 33.86/34.05 (define @t2 () (@var "B" $$unsorted)) % 33.86/34.05 (define @t3 () (tptp.in @t2 @t1)) % 33.86/34.05 (define @t4 () (not @t3)) % 33.86/34.05 (define @t5 () (tptp.in @t1 @t2)) % 33.86/34.05 (define @t6 () (@list @t1 @t2)) % 33.86/34.05 (define @t7 () (tptp.function @t1)) % 33.86/34.05 (define @t8 () (tptp.empty @t1)) % 33.86/34.05 (define @t9 () (@list @t1)) % 33.86/34.05 (define @t10 () (tptp.epsilon_connected @t1)) % 33.86/34.05 (define @t11 () (tptp.epsilon_transitive @t1)) % 33.86/34.05 (define @t12 () (and @t11 @t10)) % 33.86/34.05 (define @t13 () (tptp.ordinal @t1)) % 33.86/34.05 (define @t14 () (forall @t9 (=> @t13 @t12))) % 33.86/34.05 (define @t15 () (tptp.relation @t1)) % 33.86/34.05 (define @t16 () (tptp.one_to_one @t1)) % 33.86/34.05 (define @t17 () (and @t15 @t7 @t16)) % 33.86/34.05 (define @t18 () (and @t15 @t8 @t7)) % 33.86/34.05 (define @t19 () (forall @t9 (=> @t12 @t13))) % 33.86/34.05 (define @t20 () (and @t11 @t10 @t13)) % 33.86/34.05 (define @t21 () (tptp.set_union2 @t2 @t1)) % 33.86/34.05 (define @t22 () (tptp.set_union2 @t1 @t2)) % 33.86/34.05 (define @t23 () (tptp.singleton @t1)) % 33.86/34.05 (define @t24 () (tptp.succ @t1)) % 33.86/34.05 (define @t25 () (@var "C" $$unsorted)) % 33.86/34.05 (define @t26 () (tptp.in @t25 @t2)) % 33.86/34.05 (define @t27 () (= @t26 (= @t25 @t1))) % 33.86/34.05 (define @t28 () (@list @t25)) % 33.86/34.05 (define @t29 () (forall @t28 @t27)) % 33.86/34.05 (define @t30 () (= @t2 @t23)) % 33.86/34.05 (define @t31 () (= @t30 @t29)) % 33.86/34.05 (define @t32 () (forall @t6 @t31)) % 33.86/34.05 (define @t33 () (tptp.subset @t2 @t1)) % 33.86/34.05 (define @t34 () (@list @t2)) % 33.86/34.05 (define @t35 () (forall @t34 (=> @t3 @t33))) % 33.86/34.05 (define @t36 () (= @t11 @t35)) % 33.86/34.05 (define @t37 () (forall @t9 @t36)) % 33.86/34.05 (define @t38 () (@var "D" $$unsorted)) % 33.86/34.05 (define @t39 () (@list @t38)) % 33.86/34.05 (define @t40 () (forall @t39 (= (tptp.in @t38 @t25) (or (tptp.in @t38 @t1) (tptp.in @t38 @t2))))) % 33.86/34.05 (define @t41 () (= (= @t25 @t22) @t40)) % 33.86/34.05 (define @t42 () (@list @t1 @t2 @t25)) % 33.86/34.05 (define @t43 () (forall @t42 @t41)) % 33.86/34.05 (define @t44 () (not @t26)) % 33.86/34.05 (define @t45 () (= @t2 @t25)) % 33.86/34.05 (define @t46 () (not @t45)) % 33.86/34.05 (define @t47 () (tptp.in @t2 @t25)) % 33.86/34.05 (define @t48 () (not @t47)) % 33.86/34.05 (define @t49 () (tptp.in @t25 @t1)) % 33.86/34.05 (define @t50 () (@list @t2 @t25)) % 33.86/34.05 (define @t51 () (forall @t50 (not (and @t3 @t49 @t48 @t46 @t44)))) % 33.86/34.05 (define @t52 () (= @t10 @t51)) % 33.86/34.05 (define @t53 () (forall @t9 @t52)) % 33.86/34.05 (define @t54 () (tptp.relation_empty_yielding tptp.empty_set)) % 33.86/34.05 (define @t55 () (tptp.relation tptp.empty_set)) % 33.86/34.05 (define @t56 () (tptp.empty tptp.empty_set)) % 33.86/34.05 (define @t57 () (not @t8)) % 33.86/34.05 (define @t58 () (tptp.relation_empty_yielding @t1)) % 33.86/34.05 (define @t59 () (tptp.element @t1 @t2)) % 33.86/34.05 (define @t60 () (tptp.subset @t1 @t25)) % 33.86/34.05 (define @t61 () (tptp.subset @t2 @t25)) % 33.86/34.05 (define @t62 () (tptp.subset @t1 @t2)) % 33.86/34.05 (define @t63 () (and @t62 @t61)) % 33.86/34.05 (define @t64 () (forall @t42 (=> @t63 @t60))) % 33.86/34.05 (define @t65 () (tptp.ordinal @t24)) % 33.86/34.05 (define @t66 () (forall @t9 (=> @t13 @t65))) % 33.86/34.05 (define @t67 () (not @t66)) % 33.86/34.05 (define @t68 () (tptp.empty @t2)) % 33.86/34.05 (define @t69 () (tptp.element @t2 (tptp.powerset @t25))) % 33.86/34.05 (define @t70 () (not @t49)) % 33.86/34.05 (define @t71 () (not @t44)) % 33.86/34.05 (define @t72 () (not @t46)) % 33.86/34.05 (define @t73 () (not @t48)) % 33.86/34.05 (define @t74 () (or @t4 @t70 @t73 @t72 @t71)) % 33.86/34.05 (define @t75 () (@quantifiers_skolemize (forall @t9 (or (not @t13) @t65)) 0)) % 33.86/34.05 (define @t76 () (tptp.succ @t75)) % 33.86/34.05 (define @t77 () (@list @t76)) % 33.86/34.05 (define @t78 () (not @t10)) % 33.86/34.05 (define @t79 () (not @t11)) % 33.86/34.05 (define @t80 () (not (tptp.in @t2 @t76))) % 33.86/34.05 (define @t81 () (forall @t34 (or @t80 (tptp.subset @t2 @t76)))) % 33.86/34.05 (define @t82 () (@quantifiers_skolemize @t81 0)) % 33.86/34.05 (define @t83 () (tptp.in @t82 @t76)) % 33.86/34.05 (define @t84 () (tptp.subset @t82 @t76)) % 33.86/34.05 (define @t85 () (not @t83)) % 33.86/34.05 (define @t86 () (or @t85 @t84)) % 33.86/34.05 (define @t87 () (= @t22 @t25)) % 33.86/34.05 (define @t88 () (tptp.singleton @t75)) % 33.86/34.05 (define @t89 () (forall @t39 (= (tptp.in @t38 @t76) (or (tptp.in @t38 @t75) (tptp.in @t38 @t88))))) % 33.86/34.05 (define @t90 () (tptp.set_union2 @t75 @t88)) % 33.86/34.05 (define @t91 () (= @t90 @t76)) % 33.86/34.05 (define @t92 () (forall @t42 (= @t40 @t87))) % 33.86/34.05 (define @t93 () (= @t89 @t91)) % 33.86/34.05 (define @t94 () (= @t76 @t90)) % 33.86/34.05 (define @t95 () (= @t94 @t89)) % 33.86/34.05 (define @t96 () (@list false)) % 33.86/34.05 (define @t97 () (@list @t75)) % 33.86/34.05 (define @t98 () (not @t94)) % 33.86/34.05 (define @t99 () (@list false false)) % 33.86/34.05 (define @t100 () (@list @t82)) % 33.86/34.05 (define @t101 () (tptp.in @t82 @t88)) % 33.86/34.05 (define @t102 () (tptp.in @t82 @t75)) % 33.86/34.05 (define @t103 () (or @t102 @t101)) % 33.86/34.05 (define @t104 () (= @t83 @t103)) % 33.86/34.05 (define @t105 () (tptp.subset @t82 @t90)) % 33.86/34.05 (define @t106 () (not @t105)) % 33.86/34.05 (define @t107 () (not @t84)) % 33.86/34.05 (define @t108 () (not @t107)) % 33.86/34.05 (define @t109 () (and @t94 @t107)) % 33.86/34.05 (define @t110 () (@list @t75 @t88)) % 33.86/34.05 (define @t111 () (not @t61)) % 33.86/34.05 (define @t112 () (not @t62)) % 33.86/34.05 (define @t113 () (tptp.subset @t75 @t90)) % 33.86/34.05 (define @t114 () (not @t113)) % 33.86/34.05 (define @t115 () (tptp.subset @t82 @t75)) % 33.86/34.05 (define @t116 () (not @t115)) % 33.86/34.05 (define @t117 () (or @t116 @t114 @t105)) % 33.86/34.05 (define @t118 () (tptp.ordinal @t75)) % 33.86/34.05 (define @t119 () (tptp.ordinal @t76)) % 33.86/34.05 (define @t120 () (not @t118)) % 33.86/34.05 (define @t121 () (or @t120 @t119)) % 33.86/34.05 (define @t122 () (@list true)) % 33.86/34.05 (define @t123 () (@list @t121)) % 33.86/34.05 (define @t124 () (tptp.epsilon_connected @t75)) % 33.86/34.05 (define @t125 () (tptp.epsilon_transitive @t75)) % 33.86/34.05 (define @t126 () (and @t125 @t124)) % 33.86/34.05 (define @t127 () (or @t120 @t126)) % 33.86/34.05 (define @t128 () (not @t126)) % 33.86/34.05 (define @t129 () (@list @t126)) % 33.86/34.05 (define @t130 () (not (tptp.in @t2 @t75))) % 33.86/34.05 (define @t131 () (forall @t34 (or @t130 (tptp.subset @t2 @t75)))) % 33.86/34.05 (define @t132 () (= @t125 @t131)) % 33.86/34.05 (define @t133 () (not @t102)) % 33.86/34.05 (define @t134 () (or @t133 @t115)) % 33.86/34.05 (define @t135 () (tptp.in @t25 @t88)) % 33.86/34.05 (define @t136 () (forall @t28 (= @t135 (= @t25 @t75)))) % 33.86/34.05 (define @t137 () (= @t135 (= @t75 @t25))) % 33.86/34.05 (define @t138 () (forall @t28 @t137)) % 33.86/34.05 (define @t139 () (= (= @t88 @t88) @t138)) % 33.86/34.05 (define @t140 () (forall @t6 (= @t30 (forall @t28 (= @t26 (= @t1 @t25)))))) % 33.86/34.05 (define @t141 () (= @t101 (= @t82 @t75))) % 33.86/34.05 (define @t142 () (= @t75 @t82)) % 33.86/34.05 (define @t143 () (= @t101 @t142)) % 33.86/34.05 (define @t144 () (@list @t136)) % 33.86/34.05 (define @t145 () (not @t142)) % 33.86/34.05 (define @t146 () (and @t107 @t142 @t94 @t113)) % 33.86/34.05 (define @t147 () (not @t86)) % 33.86/34.05 (define @t148 () (not @t81)) % 33.86/34.05 (define @t149 () (tptp.epsilon_transitive @t76)) % 33.86/34.05 (define @t150 () (= @t149 @t81)) % 33.86/34.05 (define @t151 () (tptp.epsilon_connected @t76)) % 33.86/34.05 (define @t152 () (not @t151)) % 33.86/34.05 (define @t153 () (not @t149)) % 33.86/34.05 (define @t154 () (or @t153 @t152 @t119)) % 33.86/34.05 (define @t155 () (forall @t50 (or @t80 (not (tptp.in @t25 @t76)) @t47 @t45 @t26))) % 33.86/34.05 (define @t156 () (= @t151 @t155)) % 33.86/34.05 (define @t157 () (not @t155)) % 33.86/34.05 (define @t158 () (@list true false)) % 33.86/34.05 (define @t159 () (@quantifiers_skolemize @t155 0)) % 33.86/34.05 (define @t160 () (@quantifiers_skolemize @t155 1)) % 33.86/34.05 (define @t161 () (tptp.in @t160 @t159)) % 33.86/34.05 (define @t162 () (= @t159 @t160)) % 33.86/34.05 (define @t163 () (tptp.in @t159 @t160)) % 33.86/34.05 (define @t164 () (tptp.in @t160 @t76)) % 33.86/34.05 (define @t165 () (not @t164)) % 33.86/34.05 (define @t166 () (tptp.in @t159 @t76)) % 33.86/34.05 (define @t167 () (not @t166)) % 33.86/34.05 (define @t168 () (or @t167 @t165 @t163 @t162 @t161)) % 33.86/34.05 (define @t169 () (not @t168)) % 33.86/34.05 (define @t170 () (not @t163)) % 33.86/34.05 (define @t171 () (@list @t168)) % 33.86/34.05 (define @t172 () (@list @t159)) % 33.86/34.05 (define @t173 () (tptp.in @t159 @t88)) % 33.86/34.05 (define @t174 () (tptp.in @t159 @t75)) % 33.86/34.05 (define @t175 () (or @t174 @t173)) % 33.86/34.05 (define @t176 () (= @t166 @t175)) % 33.86/34.05 (define @t177 () (= @t173 (= @t159 @t75))) % 33.86/34.05 (define @t178 () (= @t75 @t159)) % 33.86/34.05 (define @t179 () (= @t173 @t178)) % 33.86/34.05 (define @t180 () (not @t162)) % 33.86/34.05 (define @t181 () (= @t75 @t160)) % 33.86/34.05 (define @t182 () (not @t181)) % 33.86/34.05 (define @t183 () (not @t178)) % 33.86/34.05 (define @t184 () (and @t180 @t178)) % 33.86/34.05 (define @t185 () (not @t161)) % 33.86/34.05 (define @t186 () (tptp.in @t160 @t75)) % 33.86/34.05 (define @t187 () (not @t186)) % 33.86/34.05 (define @t188 () (and @t185 @t178)) % 33.86/34.05 (define @t189 () (tptp.in @t160 @t88)) % 33.86/34.05 (define @t190 () (= @t189 (= @t160 @t75))) % 33.86/34.05 (define @t191 () (@list @t160)) % 33.86/34.05 (define @t192 () (= @t189 @t181)) % 33.86/34.05 (define @t193 () (or @t186 @t189)) % 33.86/34.05 (define @t194 () (= @t164 @t193)) % 33.86/34.05 (define @t195 () (not @t173)) % 33.86/34.05 (define @t196 () (forall @t50 (or @t130 (not (tptp.in @t25 @t75)) @t47 @t45 @t26))) % 33.86/34.05 (define @t197 () (= @t124 @t196)) % 33.86/34.05 (define @t198 () (not @t174)) % 33.86/34.05 (define @t199 () (or @t198 @t187 @t163 @t162 @t161)) % 33.86/34.05 (define @t200 () (and @t174 @t181 @t170)) % 33.86/34.05 (assume @p1 (forall @t6 (=> @t5 @t4))) % 33.86/34.05 (assume @p2 (forall @t9 (=> @t8 @t7))) % 33.86/34.05 (assume @p3 @t14) % 33.86/34.05 (assume @p4 (forall @t9 (=> @t8 @t15))) % 33.86/34.05 (assume @p5 (forall @t9 (=> @t18 @t17))) % 33.86/34.05 (assume @p6 @t19) % 33.86/34.05 (assume @p7 (forall @t9 (=> @t8 @t20))) % 33.86/34.05 (assume @p8 (forall @t6 (= @t22 @t21))) % 33.86/34.05 (assume @p9 (forall @t9 (= @t24 (tptp.set_union2 @t1 @t23)))) % 33.86/34.05 (assume @p10 @t32) % 33.86/34.05 (assume @p11 @t37) % 33.86/34.05 (assume @p12 @t43) % 33.86/34.05 (assume @p13 @t53) % 33.86/34.05 (assume @p14 (forall @t9 (= @t13 @t12))) % 33.86/34.05 (assume @p15 (forall @t9 (exists @t34 (tptp.element @t2 @t1)))) % 33.86/34.05 (assume @p16 (and @t56 @t55 @t54)) % 33.86/34.05 (assume @p17 (forall @t9 (not (tptp.empty @t24)))) % 33.86/34.05 (assume @p18 @t56) % 33.86/34.05 (assume @p19 (and @t55 @t54 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) @t56 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set))) % 33.86/34.05 (assume @p20 (forall @t6 (=> (and @t15 (tptp.relation @t2)) (tptp.relation @t22)))) % 33.86/34.05 (assume @p21 (forall @t6 (=> @t57 (not (tptp.empty @t22))))) % 33.86/34.05 (assume @p22 (forall @t6 (=> @t57 (not (tptp.empty @t21))))) % 33.86/34.05 (assume @p23 (and @t56 @t55)) % 33.86/34.05 (assume @p24 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 33.86/34.05 (assume @p25 (exists @t9 (and @t15 @t7))) % 33.86/34.05 (assume @p26 (exists @t9 @t20)) % 33.86/34.05 (assume @p27 (exists @t9 (and @t8 @t15))) % 33.86/34.05 (assume @p28 (exists @t9 @t8)) % 33.86/34.05 (assume @p29 (exists @t9 @t18)) % 33.86/34.05 (assume @p30 (exists @t9 (and @t15 @t7 @t16 @t8 @t11 @t10 @t13))) % 33.86/34.05 (assume @p31 (exists @t9 (and @t57 @t15))) % 33.86/34.05 (assume @p32 (exists @t9 @t57)) % 33.86/34.05 (assume @p33 (exists @t9 @t17)) % 33.86/34.05 (assume @p34 (exists @t9 (and @t15 @t58))) % 33.86/34.05 (assume @p35 (exists @t9 (and @t15 @t58 @t7))) % 33.86/34.05 (assume @p36 (exists @t9 (and @t15 (tptp.relation_non_empty @t1) @t7))) % 33.86/34.05 (assume @p37 (forall @t6 (tptp.subset @t1 @t1))) % 33.86/34.05 (assume @p38 (forall @t9 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 33.86/34.05 (assume @p39 (forall @t6 (=> @t5 @t59))) % 33.86/34.05 (assume @p40 @t64) % 33.86/34.05 (assume @p41 @t67) % 33.86/34.05 (assume @p42 (forall @t6 (=> @t59 (or @t68 @t5)))) % 33.86/34.05 (assume @p43 (forall @t6 (= (tptp.element @t1 (tptp.powerset @t2)) @t62))) % 33.86/34.05 (assume @p44 (forall @t42 (=> (and @t5 @t69) (tptp.element @t1 @t25)))) % 33.86/34.05 (assume @p45 (forall @t42 (not (and @t5 @t69 (tptp.empty @t25))))) % 33.86/34.05 (assume @p46 (forall @t9 (=> @t8 (= @t1 tptp.empty_set)))) % 33.86/34.05 (assume @p47 (forall @t6 (not (and @t5 @t68)))) % 33.86/34.05 (assume @p48 (forall @t6 (tptp.subset @t1 @t22))) % 33.86/34.06 (assume @p49 (forall @t6 (not (and @t8 (not (= @t1 @t2)) @t68)))) % 33.86/34.06 (assume @p50 true) % 33.86/34.06 (step @p51 :rule bool-double-not-elim :args (@t26)) % 33.86/34.06 (step @p52 :rule bool-double-not-elim :args (@t45)) % 33.86/34.06 (step @p53 :rule bool-double-not-elim :args (@t47)) % 33.86/34.06 (step @p54 :rule refl :args (@t70)) % 33.86/34.06 (step @p55 :rule refl :args (@t4)) % 33.86/34.06 (step @p56 :rule nary_cong :premises (@p55 @p54 @p53 @p52 @p51) :args (@t74)) % 33.86/34.06 (step @p57 :rule aci_norm :args ((= (or @t4 (or @t70 (or @t73 (or @t72 @t71)))) @t74))) % 33.86/34.06 (step @p58 :rule trans :premises (@p57 @p56)) % 33.86/34.06 (step @p59 :rule bool-and-de-morgan :args (@t46 @t44 true)) % 33.86/34.06 (step @p60 :rule refl :args (@t73)) % 33.86/34.06 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or @t73 (not (and @t46 @t44))))) % 33.86/34.06 (step @p62 :rule bool-and-de-morgan :args (@t48 @t46 (and @t44))) % 33.86/34.06 (step @p63 :rule trans :premises (@p62 @p61)) % 33.86/34.06 (step @p64 :rule nary_cong :premises (@p54 @p63) :args ((or @t70 (not (and @t48 @t46 @t44))))) % 33.86/34.06 (step @p65 :rule bool-and-de-morgan :args (@t49 @t48 (and @t46 @t44))) % 33.86/34.06 (step @p66 :rule trans :premises (@p65 @p64)) % 33.86/34.06 (step @p67 :rule nary_cong :premises (@p55 @p66) :args ((or @t4 (not (and @t49 @t48 @t46 @t44))))) % 33.86/34.06 (step @p68 :rule bool-and-de-morgan :args (@t3 @t49 (and @t48 @t46 @t44))) % 33.86/34.06 (step @p69 :rule trans :premises (@p68 @p67)) % 33.86/34.06 (step @p70 :rule trans :premises (@p69 @p58)) % 33.86/34.06 (step @p71 :rule cong :premises (@p70) :args (@t51)) % 33.86/34.06 (step @p72 :rule refl :args (@t10)) % 33.86/34.06 (step @p73 :rule cong :premises (@p72 @p71) :args (@t52)) % 33.86/34.06 (step @p74 :rule cong :premises (@p73) :args (@t53)) % 33.86/34.06 (step @p75 :rule eq_resolve :premises (@p13 @p74)) % 33.86/34.06 (step @p76 :rule instantiate :premises (@p75) :args (@t77)) % 33.86/34.06 (step @p77 :rule aci_norm :args ((= (or (or @t79 @t78) @t13) (or @t79 @t78 @t13)))) % 33.86/34.06 (step @p78 :rule refl :args (@t13)) % 33.86/34.06 (step @p79 :rule bool-and-de-morgan :args (@t11 @t10 true)) % 33.86/34.06 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or (not @t12) @t13))) % 33.86/34.06 (step @p81 :rule trans :premises (@p80 @p77)) % 33.86/34.06 (step @p82 :rule bool-impl-elim :args (@t12 @t13)) % 33.86/34.06 (step @p83 :rule trans :premises (@p82 @p81)) % 33.86/34.06 (step @p84 :rule cong :premises (@p83) :args (@t19)) % 33.86/34.06 (step @p85 :rule eq_resolve :premises (@p6 @p84)) % 33.86/34.06 (step @p86 :rule instantiate :premises (@p85) :args (@t77)) % 33.86/34.06 (step @p87 :rule bool-impl-elim :args (@t3 @t33)) % 33.86/34.06 (step @p88 :rule cong :premises (@p87) :args (@t35)) % 33.86/34.06 (step @p89 :rule refl :args (@t11)) % 33.86/34.06 (step @p90 :rule cong :premises (@p89 @p88) :args (@t36)) % 33.86/34.06 (step @p91 :rule cong :premises (@p90) :args (@t37)) % 33.86/34.06 (step @p92 :rule eq_resolve :premises (@p11 @p91)) % 33.86/34.06 (step @p93 :rule instantiate :premises (@p92) :args (@t77)) % 33.86/34.06 (step @p94 :rule bool-double-not-elim :args (@t83)) % 33.86/34.06 (step @p95 :rule refl :args (@t86)) % 33.86/34.06 (step @p96 :rule nary_cong :premises (@p95 @p94) :args ((or @t86 (not @t85)))) % 33.86/34.06 (step @p97 :rule cnf_or_neg :args (@t86 0)) % 33.86/34.06 (step @p98 :rule eq_resolve :premises (@p97 @p96)) % 33.86/34.06 (step @p99 :rule reordering :premises (@p98) :args ((or @t83 @t86))) % 33.86/34.06 (step @p100 :rule cnf_or_neg :args (@t86 1)) % 33.86/34.06 (step @p101 :rule eq-symm :args (@t87 @t40)) % 33.86/34.06 (step @p102 :rule refl :args (@t40)) % 33.86/34.06 (step @p103 :rule eq-symm :args (@t25 @t22)) % 33.86/34.06 (step @p104 :rule cong :premises (@p103 @p102) :args (@t41)) % 33.86/34.06 (step @p105 :rule trans :premises (@p104 @p101)) % 33.86/34.06 (step @p106 :rule cong :premises (@p105) :args (@t43)) % 33.86/34.06 (step @p107 :rule eq_resolve :premises (@p12 @p106)) % 33.86/34.06 (step @p108 :rule refl :args (@t89)) % 33.86/34.06 (step @p109 :rule eq-symm :args (@t90 @t76)) % 33.86/34.06 (step @p110 :rule cong :premises (@p109 @p108) :args ((= @t91 @t89))) % 33.86/34.06 (step @p111 :rule eq-symm :args (@t89 @t91)) % 33.86/34.06 (step @p112 :rule trans :premises (@p111 @p110)) % 33.86/34.06 (step @p113 :rule refl :args (@t92)) % 33.86/34.06 (step @p114 :rule cong :premises (@p113 @p112) :args ((=> @t92 @t93))) % 33.86/34.06 (assume-push @p459 @t92) % 33.86/34.06 (step @p116 :rule instantiate :premises (@p107) :args ((@list @t75 @t88 @t76))) % 33.86/34.06 (step-pop @p460 :rule scope :premises (@p116)) % 33.86/34.06 (step @p117 :rule process_scope :premises (@p460) :args (@t93)) % 33.86/34.06 (step @p119 :rule eq_resolve :premises (@p117 @p114)) % 33.86/34.06 (step @p120 :rule implies_elim :premises (@p119)) % 33.86/34.06 (step @p121 :rule chain_m_resolution :premises (@p120 @p107) :args (@t95 @t96 (@list @t92))) % 33.86/34.06 (step @p122 :rule instantiate :premises (@p9) :args (@t97)) % 33.86/34.06 (step @p123 :rule cnf_equiv_pos1 :args (@t95)) % 33.86/34.06 (step @p124 :rule reordering :premises (@p123) :args ((or @t98 @t89 (not @t95)))) % 33.86/34.06 (step @p125 :rule chain_m_resolution :premises (@p124 @p122 @p121) :args (@t89 @t99 (@list @t94 @t95))) % 33.86/34.06 (step @p126 :rule instantiate :premises (@p125) :args (@t100)) % 33.86/34.06 (step @p127 :rule cnf_equiv_pos1 :args (@t104)) % 33.86/34.06 (step @p128 :rule reordering :premises (@p127) :args ((or @t85 @t103 (not @t104)))) % 33.86/34.06 (step @p129 :rule refl :args (@t106)) % 33.86/34.06 (step @p130 :rule bool-double-not-elim :args (@t84)) % 33.86/34.06 (step @p131 :rule refl :args (@t98)) % 33.86/34.06 (step @p132 :rule nary_cong :premises (@p131 @p130 @p129) :args ((or @t98 @t108 @t106))) % 33.86/34.06 (assume-push @p461 @t94) % 33.86/34.06 (assume-push @p462 @t107) % 33.86/34.06 (assume-push @p463 @t107) % 33.86/34.06 (assume-push @p464 @t94) % 33.86/34.06 (step @p137 :rule false_intro :premises (@p462)) % 33.86/34.06 (step @p138 :rule symm :premises (@p122)) % 33.86/34.06 (step @p139 :rule refl :args (@t82)) % 33.86/34.06 (step @p140 :rule cong :premises (@p139 @p138) :args (@t105)) % 33.86/34.06 (step @p141 :rule trans :premises (@p140 @p137)) % 33.86/34.06 (step @p142 :rule false_elim :premises (@p141)) % 33.86/34.06 (step-pop @p465 :rule scope :premises (@p142)) % 33.86/34.06 (step-pop @p466 :rule scope :premises (@p465)) % 33.86/34.06 (step @p143 :rule process_scope :premises (@p466) :args (@t106)) % 33.86/34.06 (step @p146 :rule and_intro :premises (@p462 @p122)) % 33.86/34.06 (step @p147 :rule modus_ponens :premises (@p146 @p143)) % 33.86/34.06 (step-pop @p467 :rule scope :premises (@p147)) % 33.86/34.06 (step-pop @p468 :rule scope :premises (@p467)) % 33.86/34.06 (step @p148 :rule process_scope :premises (@p468) :args (@t106)) % 33.86/34.06 (step @p151 :rule implies_elim :premises (@p148)) % 33.86/34.06 (step @p152 :rule cnf_and_neg :args (@t109)) % 33.86/34.06 (step @p153 :rule resolution :premises (@p152 @p151) :args (true @t109)) % 33.86/34.06 (step @p154 :rule eq_resolve :premises (@p153 @p132)) % 33.86/34.06 (step @p155 :rule instantiate :premises (@p48) :args (@t110)) % 33.86/34.06 (step @p156 :rule aci_norm :args ((= (or (or @t112 @t111) @t60) (or @t112 @t111 @t60)))) % 33.86/34.06 (step @p157 :rule refl :args (@t60)) % 33.86/34.06 (step @p158 :rule bool-and-de-morgan :args (@t62 @t61 true)) % 33.86/34.06 (step @p159 :rule nary_cong :premises (@p158 @p157) :args ((or (not @t63) @t60))) % 33.86/34.06 (step @p160 :rule trans :premises (@p159 @p156)) % 33.86/34.06 (step @p161 :rule bool-impl-elim :args (@t63 @t60)) % 33.86/34.06 (step @p162 :rule trans :premises (@p161 @p160)) % 33.86/34.06 (step @p163 :rule cong :premises (@p162) :args (@t64)) % 33.86/34.06 (step @p164 :rule eq_resolve :premises (@p40 @p163)) % 33.86/34.06 (step @p165 :rule instantiate :premises (@p164) :args ((@list @t82 @t75 @t90))) % 33.86/34.06 (step @p166 :rule cnf_or_pos :args (@t117)) % 33.86/34.06 (step @p167 :rule reordering :premises (@p166) :args ((or @t114 @t116 @t105 (not @t117)))) % 33.86/34.06 (step @p168 :rule instantiate :premises (@p92) :args (@t97)) % 33.86/34.06 (step @p169 :rule bool-impl-elim :args (@t13 @t12)) % 33.86/34.06 (step @p170 :rule cong :premises (@p169) :args (@t14)) % 33.86/34.06 (step @p171 :rule eq_resolve :premises (@p3 @p170)) % 33.86/34.06 (step @p172 :rule instantiate :premises (@p171) :args (@t97)) % 33.86/34.06 (step @p173 :rule bool-impl-elim :args (@t13 @t65)) % 33.86/34.06 (step @p174 :rule cong :premises (@p173) :args (@t66)) % 33.86/34.06 (step @p175 :rule cong :premises (@p174) :args (@t67)) % 33.86/34.06 (step @p176 :rule eq_resolve :premises (@p41 @p175)) % 33.86/34.06 (step @p177 :rule skolemize :premises (@p176)) % 33.86/34.06 (step @p178 :rule bool-double-not-elim :args (@t118)) % 33.86/34.06 (step @p179 :rule refl :args (@t121)) % 33.86/34.06 (step @p180 :rule nary_cong :premises (@p179 @p178) :args ((or @t121 (not @t120)))) % 33.86/34.06 (step @p181 :rule cnf_or_neg :args (@t121 0)) % 33.86/34.06 (step @p182 :rule eq_resolve :premises (@p181 @p180)) % 33.86/34.06 (step @p183 :rule reordering :premises (@p182) :args ((or @t118 @t121))) % 33.86/34.06 (step @p184 :rule chain_m_resolution :premises (@p183 @p177) :args (@t118 @t122 @t123)) % 33.86/34.06 (step @p185 :rule cnf_or_pos :args (@t127)) % 33.86/34.06 (step @p186 :rule reordering :premises (@p185) :args ((or @t120 @t126 (not @t127)))) % 33.86/34.06 (step @p187 :rule chain_m_resolution :premises (@p186 @p184 @p172) :args (@t126 @t99 (@list @t118 @t127))) % 33.86/34.06 (step @p188 :rule cnf_and_pos :args (@t126 0)) % 33.86/34.06 (step @p189 :rule reordering :premises (@p188) :args ((or @t125 @t128))) % 33.86/34.06 (step @p190 :rule chain_m_resolution :premises (@p189 @p187) :args (@t125 @t96 @t129)) % 33.86/34.06 (step @p191 :rule cnf_equiv_pos1 :args (@t132)) % 33.86/34.06 (step @p192 :rule reordering :premises (@p191) :args ((or (not @t125) @t131 (not @t132)))) % 33.86/34.06 (step @p193 :rule chain_m_resolution :premises (@p192 @p190 @p168) :args (@t131 @t99 (@list @t125 @t132))) % 33.86/34.06 (step @p194 :rule instantiate :premises (@p193) :args (@t100)) % 33.86/34.06 (step @p195 :rule cnf_or_pos :args (@t134)) % 33.86/34.06 (step @p196 :rule reordering :premises (@p195) :args ((or @t133 @t115 (not @t134)))) % 33.86/34.06 (step @p197 :rule cnf_or_pos :args (@t103)) % 33.86/34.06 (step @p198 :rule reordering :premises (@p197) :args ((or @t102 @t101 (not @t103)))) % 33.86/34.06 (step @p199 :rule eq-symm :args (@t25 @t1)) % 33.86/34.06 (step @p200 :rule refl :args (@t26)) % 33.86/34.06 (step @p201 :rule cong :premises (@p200 @p199) :args (@t27)) % 33.86/34.06 (step @p202 :rule cong :premises (@p201) :args (@t29)) % 33.86/34.06 (step @p203 :rule refl :args (@t30)) % 33.86/34.06 (step @p204 :rule cong :premises (@p203 @p202) :args (@t31)) % 33.86/34.06 (step @p205 :rule cong :premises (@p204) :args (@t32)) % 33.86/34.06 (step @p206 :rule eq_resolve :premises (@p10 @p205)) % 33.86/34.06 (step @p207 :rule bool-eq-true :args (@t136)) % 33.86/34.06 (step @p208 :rule eq-symm :args (true @t136)) % 33.86/34.06 (step @p209 :rule trans :premises (@p208 @p207)) % 33.86/34.06 (step @p210 :rule eq-symm :args (@t75 @t25)) % 33.86/34.06 (step @p211 :rule refl :args (@t135)) % 33.86/34.06 (step @p212 :rule cong :premises (@p211 @p210) :args (@t137)) % 33.86/34.06 (step @p213 :rule cong :premises (@p212) :args (@t138)) % 33.86/34.06 (step @p214 :rule eq-refl :args (@t88)) % 33.86/34.06 (step @p215 :rule cong :premises (@p214 @p213) :args (@t139)) % 33.86/34.06 (step @p216 :rule trans :premises (@p215 @p209)) % 33.86/34.06 (step @p217 :rule refl :args (@t140)) % 33.86/34.06 (step @p218 :rule cong :premises (@p217 @p216) :args ((=> @t140 @t139))) % 33.86/34.06 (assume-push @p469 @t140) % 33.86/34.06 (step @p220 :rule instantiate :premises (@p206) :args (@t110)) % 33.86/34.06 (step-pop @p470 :rule scope :premises (@p220)) % 33.86/34.06 (step @p221 :rule process_scope :premises (@p470) :args (@t139)) % 33.86/34.06 (step @p223 :rule eq_resolve :premises (@p221 @p218)) % 33.86/34.06 (step @p224 :rule implies_elim :premises (@p223)) % 33.86/34.06 (step @p225 :rule chain_m_resolution :premises (@p224 @p206) :args (@t136 @t96 (@list @t140))) % 33.86/34.06 (step @p226 :rule eq-symm :args (@t82 @t75)) % 33.86/34.06 (step @p227 :rule refl :args (@t101)) % 33.86/34.06 (step @p228 :rule cong :premises (@p227 @p226) :args (@t141)) % 33.86/34.06 (step @p229 :rule refl :args (@t136)) % 33.86/34.06 (step @p230 :rule cong :premises (@p229 @p228) :args ((=> @t136 @t141))) % 33.86/34.06 (assume-push @p471 @t136) % 33.86/34.06 (step @p232 :rule instantiate :premises (@p225) :args (@t100)) % 33.86/34.06 (step-pop @p472 :rule scope :premises (@p232)) % 33.86/34.06 (step @p233 :rule process_scope :premises (@p472) :args (@t141)) % 33.86/34.06 (step @p235 :rule eq_resolve :premises (@p233 @p230)) % 33.86/34.06 (step @p236 :rule implies_elim :premises (@p235)) % 33.86/34.06 (step @p237 :rule chain_m_resolution :premises (@p236 @p225) :args (@t143 @t96 @t144)) % 33.86/34.06 (step @p238 :rule cnf_equiv_pos1 :args (@t143)) % 33.86/34.06 (step @p239 :rule reordering :premises (@p238) :args ((or (not @t101) @t142 (not @t143)))) % 33.86/34.06 (step @p240 :rule refl :args (@t145)) % 33.86/34.06 (step @p241 :rule refl :args (@t114)) % 33.86/34.06 (step @p242 :rule nary_cong :premises (@p131 @p241 @p130 @p240) :args ((or @t98 @t114 @t108 @t145))) % 33.86/34.06 (assume-push @p473 @t107) % 33.86/34.06 (assume-push @p474 @t142) % 33.86/34.06 (assume-push @p475 @t94) % 33.86/34.06 (assume-push @p476 @t113) % 33.86/34.06 (step @p247 :rule evaluate :args ((= true false))) % 33.86/34.06 (step @p248 :rule false_intro :premises (@p473)) % 33.86/34.06 (step @p138 :rule symm :premises (@p122)) % 33.86/34.06 (step @p249 :rule cong :premises (@p474 @p138) :args (@t113)) % 33.86/34.06 (step @p250 :rule true_intro :premises (@p155)) % 33.86/34.06 (step @p251 :rule symm :premises (@p250)) % 33.86/34.06 (step @p252 :rule trans :premises (@p251 @p249 @p248)) % 33.86/34.06 (step @p253 false :rule eq_resolve :premises (@p252 @p247)) % 33.86/34.06 (step-pop @p477 :rule scope :premises (@p253)) % 33.86/34.06 (step-pop @p478 :rule scope :premises (@p477)) % 33.86/34.06 (step-pop @p479 :rule scope :premises (@p478)) % 33.86/34.06 (step-pop @p480 :rule scope :premises (@p479)) % 33.86/34.06 (step @p254 :rule process_scope :premises (@p480) :args (false)) % 33.86/34.06 (assume-push @p481 @t94) % 33.86/34.06 (assume-push @p482 @t113) % 33.86/34.06 (assume-push @p483 @t107) % 33.86/34.06 (assume-push @p484 @t142) % 33.86/34.06 (step @p263 :rule and_intro :premises (@p483 @p484 @p122 @p155)) % 33.86/34.06 (step-pop @p485 :rule scope :premises (@p263)) % 33.86/34.06 (step-pop @p486 :rule scope :premises (@p485)) % 33.86/34.06 (step-pop @p487 :rule scope :premises (@p486)) % 33.86/34.06 (step-pop @p488 :rule scope :premises (@p487)) % 33.86/34.06 (step @p264 :rule process_scope :premises (@p488) :args (@t146)) % 33.86/34.06 (step @p269 :rule implies_elim :premises (@p264)) % 33.86/34.06 (step @p270 :rule resolution :premises (@p269 @p254) :args (true @t146)) % 33.86/34.06 (step @p271 :rule not_and :premises (@p270)) % 33.86/34.06 (step @p272 :rule eq_resolve :premises (@p271 @p242)) % 33.86/34.06 (step @p273 :rule chain_m_resolution :premises (@p272 @p155 @p122 @p239 @p237 @p198 @p196 @p194 @p167 @p165 @p155 @p154 @p122 @p128 @p126 @p100 @p99) :args (@t86 (@list false false false false false true false true false false true false false false true false) (@list @t113 @t94 @t142 @t143 @t101 @t102 @t134 @t115 @t117 @t113 @t105 @t94 @t103 @t104 @t84 @t83))) % 33.86/34.06 (step @p274 :rule refl :args (@t147)) % 33.86/34.06 (step @p275 :rule bool-double-not-elim :args (@t81)) % 33.86/34.06 (step @p276 :rule nary_cong :premises (@p275 @p274) :args ((or (not @t148) @t147))) % 33.86/34.06 (assume-push @p489 @t148) % 33.86/34.06 (step @p278 :rule skolemize :premises (@p489)) % 33.86/34.06 (step-pop @p490 :rule scope :premises (@p278)) % 33.86/34.06 (step @p279 :rule process_scope :premises (@p490) :args (@t147)) % 33.86/34.06 (step @p281 :rule implies_elim :premises (@p279)) % 33.86/34.06 (step @p282 :rule eq_resolve :premises (@p281 @p276)) % 33.86/34.06 (step @p283 :rule chain_m_resolution :premises (@p282 @p273) :args (@t81 @t96 (@list @t86))) % 33.86/34.06 (step @p284 :rule cnf_equiv_pos2 :args (@t150)) % 33.86/34.06 (step @p285 :rule reordering :premises (@p284) :args ((or @t149 @t148 (not @t150)))) % 33.86/34.06 (step @p286 :rule chain_m_resolution :premises (@p285 @p283 @p93) :args (@t149 @t99 (@list @t81 @t150))) % 33.86/34.06 (step @p287 :rule cnf_or_neg :args (@t121 1)) % 33.86/34.06 (step @p288 :rule chain_m_resolution :premises (@p287 @p177) :args ((not @t119) @t122 @t123)) % 33.86/34.06 (step @p289 :rule cnf_or_pos :args (@t154)) % 33.86/34.06 (step @p290 :rule reordering :premises (@p289) :args ((or @t119 @t153 @t152 (not @t154)))) % 33.86/34.06 (step @p291 :rule chain_m_resolution :premises (@p290 @p288 @p286 @p86) :args (@t152 (@list true false false) (@list @t119 @t149 @t154))) % 33.86/34.06 (step @p292 :rule cnf_equiv_pos2 :args (@t156)) % 33.86/34.06 (step @p293 :rule reordering :premises (@p292) :args ((or @t151 @t157 (not @t156)))) % 33.86/34.06 (step @p294 :rule chain_m_resolution :premises (@p293 @p291 @p76) :args (@t157 @t158 (@list @t151 @t156))) % 33.86/34.06 (step @p295 :rule refl :args (@t169)) % 33.86/34.06 (step @p296 :rule bool-double-not-elim :args (@t155)) % 33.86/34.06 (step @p297 :rule nary_cong :premises (@p296 @p295) :args ((or (not @t157) @t169))) % 33.86/34.06 (assume-push @p491 @t157) % 33.86/34.06 (step @p299 :rule skolemize :premises (@p491)) % 33.86/34.06 (step-pop @p492 :rule scope :premises (@p299)) % 33.86/34.06 (step @p300 :rule process_scope :premises (@p492) :args (@t169)) % 33.86/34.06 (step @p302 :rule implies_elim :premises (@p300)) % 33.86/34.06 (step @p303 :rule eq_resolve :premises (@p302 @p297)) % 33.86/34.06 (step @p304 :rule chain_m_resolution :premises (@p303 @p294) :args (@t169 @t122 (@list @t155))) % 33.86/34.06 (step @p305 :rule cnf_or_neg :args (@t168 2)) % 33.86/34.06 (step @p306 :rule chain_m_resolution :premises (@p305 @p304) :args (@t170 @t122 @t171)) % 33.86/34.06 (step @p307 :rule instantiate :premises (@p125) :args (@t172)) % 33.86/34.06 (step @p308 :rule bool-double-not-elim :args (@t166)) % 33.86/34.06 (step @p309 :rule refl :args (@t168)) % 33.86/34.06 (step @p310 :rule nary_cong :premises (@p309 @p308) :args ((or @t168 (not @t167)))) % 33.86/34.06 (step @p311 :rule cnf_or_neg :args (@t168 0)) % 33.86/34.06 (step @p312 :rule eq_resolve :premises (@p311 @p310)) % 33.86/34.06 (step @p313 :rule reordering :premises (@p312) :args ((or @t166 @t168))) % 33.86/34.06 (step @p314 :rule chain_m_resolution :premises (@p313 @p304) :args (@t166 @t122 @t171)) % 33.86/34.06 (step @p315 :rule cnf_equiv_pos1 :args (@t176)) % 33.86/34.06 (step @p316 :rule reordering :premises (@p315) :args ((or @t167 @t175 (not @t176)))) % 33.86/34.06 (step @p317 :rule chain_m_resolution :premises (@p316 @p314 @p307) :args (@t175 @t99 (@list @t166 @t176))) % 33.86/34.06 (step @p318 :rule eq-symm :args (@t159 @t75)) % 33.86/34.06 (step @p319 :rule refl :args (@t173)) % 33.86/34.06 (step @p320 :rule cong :premises (@p319 @p318) :args (@t177)) % 33.86/34.06 (step @p321 :rule cong :premises (@p229 @p320) :args ((=> @t136 @t177))) % 33.86/34.06 (assume-push @p493 @t136) % 33.86/34.06 (step @p323 :rule instantiate :premises (@p225) :args (@t172)) % 33.86/34.06 (step-pop @p494 :rule scope :premises (@p323)) % 33.86/34.06 (step @p324 :rule process_scope :premises (@p494) :args (@t177)) % 33.86/34.06 (step @p326 :rule eq_resolve :premises (@p324 @p321)) % 33.86/34.06 (step @p327 :rule implies_elim :premises (@p326)) % 33.86/34.06 (step @p328 :rule chain_m_resolution :premises (@p327 @p225) :args (@t179 @t96 @t144)) % 33.86/34.06 (step @p329 :rule cnf_or_neg :args (@t168 3)) % 33.86/34.06 (step @p330 :rule chain_m_resolution :premises (@p329 @p304) :args (@t180 @t122 @t171)) % 33.86/34.06 (step @p331 :rule refl :args (@t182)) % 33.86/34.06 (step @p332 :rule refl :args (@t183)) % 33.86/34.06 (step @p333 :rule bool-double-not-elim :args (@t162)) % 33.86/34.06 (step @p334 :rule nary_cong :premises (@p333 @p332 @p331) :args ((or (not @t180) @t183 @t182))) % 33.86/34.06 (assume-push @p495 @t180) % 33.86/34.06 (assume-push @p496 @t178) % 33.86/34.06 (assume-push @p497 @t180) % 33.86/34.06 (assume-push @p498 @t178) % 33.86/34.06 (step @p339 :rule false_intro :premises (@p495)) % 33.86/34.06 (step @p340 :rule refl :args (@t160)) % 33.86/34.06 (step @p341 :rule cong :premises (@p496 @p340) :args (@t181)) % 33.86/34.06 (step @p342 :rule trans :premises (@p341 @p339)) % 33.86/34.06 (step @p343 :rule false_elim :premises (@p342)) % 33.86/34.06 (step-pop @p499 :rule scope :premises (@p343)) % 33.86/34.06 (step-pop @p500 :rule scope :premises (@p499)) % 33.86/34.06 (step @p344 :rule process_scope :premises (@p500) :args (@t182)) % 33.86/34.06 (step @p347 :rule and_intro :premises (@p495 @p496)) % 33.86/34.06 (step @p348 :rule modus_ponens :premises (@p347 @p344)) % 33.86/34.06 (step-pop @p501 :rule scope :premises (@p348)) % 33.86/34.06 (step-pop @p502 :rule scope :premises (@p501)) % 33.86/34.06 (step @p349 :rule process_scope :premises (@p502) :args (@t182)) % 33.86/34.06 (step @p352 :rule implies_elim :premises (@p349)) % 33.86/34.06 (step @p353 :rule cnf_and_neg :args (@t184)) % 33.86/34.06 (step @p354 :rule resolution :premises (@p353 @p352) :args (true @t184)) % 33.86/34.06 (step @p355 :rule eq_resolve :premises (@p354 @p334)) % 33.86/34.06 (step @p356 :rule cnf_or_neg :args (@t168 4)) % 33.86/34.06 (step @p357 :rule chain_m_resolution :premises (@p356 @p304) :args (@t185 @t122 @t171)) % 33.86/34.06 (step @p358 :rule refl :args (@t187)) % 33.86/34.06 (step @p359 :rule bool-double-not-elim :args (@t161)) % 33.86/34.06 (step @p360 :rule nary_cong :premises (@p359 @p332 @p358) :args ((or (not @t185) @t183 @t187))) % 33.86/34.06 (assume-push @p503 @t185) % 33.86/34.06 (assume-push @p504 @t178) % 33.86/34.06 (assume-push @p505 @t185) % 33.86/34.06 (assume-push @p506 @t178) % 33.86/34.06 (step @p365 :rule false_intro :premises (@p503)) % 33.86/34.06 (step @p340 :rule refl :args (@t160)) % 33.86/34.06 (step @p366 :rule cong :premises (@p340 @p504) :args (@t186)) % 33.86/34.06 (step @p367 :rule trans :premises (@p366 @p365)) % 33.86/34.06 (step @p368 :rule false_elim :premises (@p367)) % 33.86/34.06 (step-pop @p507 :rule scope :premises (@p368)) % 33.86/34.06 (step-pop @p508 :rule scope :premises (@p507)) % 33.86/34.06 (step @p369 :rule process_scope :premises (@p508) :args (@t187)) % 33.86/34.06 (step @p372 :rule and_intro :premises (@p503 @p504)) % 33.86/34.06 (step @p373 :rule modus_ponens :premises (@p372 @p369)) % 33.86/34.06 (step-pop @p509 :rule scope :premises (@p373)) % 33.86/34.06 (step-pop @p510 :rule scope :premises (@p509)) % 33.86/34.06 (step @p374 :rule process_scope :premises (@p510) :args (@t187)) % 33.86/34.06 (step @p377 :rule implies_elim :premises (@p374)) % 33.86/34.06 (step @p378 :rule cnf_and_neg :args (@t188)) % 33.86/34.06 (step @p379 :rule resolution :premises (@p378 @p377) :args (true @t188)) % 33.86/34.06 (step @p380 :rule eq_resolve :premises (@p379 @p360)) % 33.86/34.06 (step @p381 :rule reordering :premises (@p380) :args ((or @t161 @t187 @t183))) % 33.86/34.06 (step @p382 :rule eq-symm :args (@t160 @t75)) % 33.86/34.06 (step @p383 :rule refl :args (@t189)) % 33.86/34.06 (step @p384 :rule cong :premises (@p383 @p382) :args (@t190)) % 33.86/34.06 (step @p385 :rule cong :premises (@p229 @p384) :args ((=> @t136 @t190))) % 33.86/34.06 (assume-push @p511 @t136) % 33.86/34.06 (step @p387 :rule instantiate :premises (@p225) :args (@t191)) % 33.86/34.06 (step-pop @p512 :rule scope :premises (@p387)) % 33.86/34.06 (step @p388 :rule process_scope :premises (@p512) :args (@t190)) % 33.86/34.06 (step @p390 :rule eq_resolve :premises (@p388 @p385)) % 33.86/34.06 (step @p391 :rule implies_elim :premises (@p390)) % 33.86/34.06 (step @p392 :rule chain_m_resolution :premises (@p391 @p225) :args (@t192 @t96 @t144)) % 33.86/34.06 (step @p393 :rule cnf_equiv_pos1 :args (@t192)) % 33.86/34.06 (step @p394 :rule reordering :premises (@p393) :args ((or (not @t189) @t181 (not @t192)))) % 33.86/34.06 (step @p395 :rule instantiate :premises (@p125) :args (@t191)) % 33.86/34.06 (step @p396 :rule bool-double-not-elim :args (@t164)) % 33.86/34.06 (step @p397 :rule nary_cong :premises (@p309 @p396) :args ((or @t168 (not @t165)))) % 33.86/34.06 (step @p398 :rule cnf_or_neg :args (@t168 1)) % 33.86/34.06 (step @p399 :rule eq_resolve :premises (@p398 @p397)) % 33.86/34.06 (step @p400 :rule reordering :premises (@p399) :args ((or @t164 @t168))) % 33.86/34.06 (step @p401 :rule chain_m_resolution :premises (@p400 @p304) :args (@t164 @t122 @t171)) % 33.86/34.06 (step @p402 :rule cnf_equiv_pos1 :args (@t194)) % 33.86/34.06 (step @p403 :rule reordering :premises (@p402) :args ((or @t165 @t193 (not @t194)))) % 33.86/34.06 (step @p404 :rule chain_m_resolution :premises (@p403 @p401 @p395) :args (@t193 @t99 (@list @t164 @t194))) % 33.86/34.06 (step @p405 :rule cnf_or_pos :args (@t193)) % 33.86/34.06 (step @p406 :rule reordering :premises (@p405) :args ((or @t186 @t189 (not @t193)))) % 33.86/34.06 (step @p407 :rule chain_m_resolution :premises (@p406 @p404 @p394 @p392 @p381 @p357 @p355 @p330) :args (@t183 (@list false true false true true true true) (@list @t193 @t189 @t192 @t186 @t161 @t181 @t162))) % 33.86/34.06 (step @p408 :rule cnf_equiv_pos1 :args (@t179)) % 33.86/34.06 (step @p409 :rule reordering :premises (@p408) :args ((or @t195 @t178 (not @t179)))) % 33.86/34.06 (step @p410 :rule chain_m_resolution :premises (@p409 @p407 @p328) :args (@t195 @t158 (@list @t178 @t179))) % 33.86/34.06 (step @p411 :rule cnf_or_pos :args (@t175)) % 33.86/34.06 (step @p412 :rule reordering :premises (@p411) :args ((or @t174 @t173 (not @t175)))) % 33.86/34.06 (step @p413 :rule chain_m_resolution :premises (@p412 @p410 @p317) :args (@t174 @t158 (@list @t173 @t175))) % 33.86/34.06 (step @p414 :rule instantiate :premises (@p75) :args (@t97)) % 33.86/34.06 (step @p415 :rule cnf_and_pos :args (@t126 1)) % 33.86/34.06 (step @p416 :rule reordering :premises (@p415) :args ((or @t124 @t128))) % 33.86/34.06 (step @p417 :rule chain_m_resolution :premises (@p416 @p187) :args (@t124 @t96 @t129)) % 33.86/34.06 (step @p418 :rule cnf_equiv_pos1 :args (@t197)) % 33.86/34.06 (step @p419 :rule reordering :premises (@p418) :args ((or (not @t124) @t196 (not @t197)))) % 33.86/34.06 (step @p420 :rule chain_m_resolution :premises (@p419 @p417 @p414) :args (@t196 @t99 (@list @t124 @t197))) % 33.86/34.06 (step @p421 :rule instantiate :premises (@p420) :args ((@list @t159 @t160))) % 33.86/34.06 (step @p422 :rule cnf_or_pos :args (@t199)) % 33.86/34.06 (step @p423 :rule reordering :premises (@p422) :args ((or @t163 @t162 @t161 @t198 @t187 (not @t199)))) % 33.86/34.06 (step @p424 :rule chain_m_resolution :premises (@p423 @p306 @p330 @p357 @p413 @p421) :args (@t187 (@list true true true false false) (@list @t163 @t162 @t161 @t174 @t199))) % 33.86/34.06 (step @p425 :rule chain_m_resolution :premises (@p406 @p424 @p404) :args (@t189 @t158 (@list @t186 @t193))) % 33.86/34.06 (step @p426 :rule chain_m_resolution :premises (@p394 @p425 @p392) :args (@t181 @t99 (@list @t189 @t192))) % 33.86/34.06 (step @p427 :rule refl :args (@t198)) % 33.86/34.06 (step @p428 :rule bool-double-not-elim :args (@t163)) % 33.86/34.06 (step @p429 :rule nary_cong :premises (@p428 @p427 @p331) :args ((or (not @t170) @t198 @t182))) % 33.86/34.06 (assume-push @p513 @t174) % 33.86/34.06 (assume-push @p514 @t181) % 33.86/34.06 (assume-push @p515 @t170) % 33.86/34.06 (step @p433 :rule evaluate :args ((= false true))) % 33.86/34.06 (step @p434 :rule true_intro :premises (@p513)) % 33.86/34.06 (step @p435 :rule symm :premises (@p514)) % 33.86/34.06 (step @p436 :rule refl :args (@t159)) % 33.86/34.06 (step @p437 :rule cong :premises (@p436 @p435) :args (@t163)) % 33.86/34.06 (step @p438 :rule false_intro :premises (@p515)) % 33.86/34.06 (step @p439 :rule symm :premises (@p438)) % 33.86/34.06 (step @p440 :rule trans :premises (@p439 @p437 @p434)) % 33.86/34.06 (step @p441 false :rule eq_resolve :premises (@p440 @p433)) % 33.86/34.06 (step-pop @p516 :rule scope :premises (@p441)) % 33.86/34.06 (step-pop @p517 :rule scope :premises (@p516)) % 33.86/34.06 (step-pop @p518 :rule scope :premises (@p517)) % 33.86/34.06 (step @p442 :rule process_scope :premises (@p518) :args (false)) % 33.86/34.06 (assume-push @p519 @t170) % 33.86/34.06 (assume-push @p520 @t174) % 33.86/34.06 (assume-push @p521 @t181) % 33.86/34.06 (step @p449 :rule and_intro :premises (@p520 @p521 @p519)) % 33.86/34.06 (step-pop @p522 :rule scope :premises (@p449)) % 33.86/34.06 (step-pop @p523 :rule scope :premises (@p522)) % 33.86/34.06 (step-pop @p524 :rule scope :premises (@p523)) % 33.86/34.06 (step @p450 :rule process_scope :premises (@p524) :args (@t200)) % 33.86/34.06 (step @p454 :rule implies_elim :premises (@p450)) % 33.86/34.06 (step @p455 :rule resolution :premises (@p454 @p442) :args (true @t200)) % 33.86/34.06 (step @p456 :rule not_and :premises (@p455)) % 33.86/34.06 (step @p457 :rule eq_resolve :premises (@p456 @p429)) % 33.86/34.06 (step @p458 false :rule chain_m_resolution :premises (@p457 @p426 @p413 @p306) :args (false (@list false false true) (@list @t181 @t174 @t163))) % 33.86/34.06 ) % 33.86/34.06 % SZS output end Proof % 33.86/34.06 % cvc5 exiting %------------------------------------------------------------------------------