%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET796+4 : TPTP v9.2.1. Bugfixed 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 : n026.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 08:48:40 AM UTC 2026 % Result : Theorem 0.43s 0.60s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET796+4 : TPTP v9.2.1. Bugfixed v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n026.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:12:55 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.43/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.43/0.60 % SZS status Theorem % 0.43/0.60 % SZS output start Proof % 0.43/0.60 ( % 0.43/0.60 (declare-sort $$unsorted 0) % 0.43/0.60 (declare-const tptp.min (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.max (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.lower_bound (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.order (-> $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.least (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.43/0.60 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.43/0.60 (declare-const tptp.greatest_lower_bound (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.43/0.60 (declare-const tptp.least_upper_bound (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.greatest (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.60 (declare-const tptp.upper_bound (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.empty_set $$unsorted) % 0.43/0.60 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.43/0.60 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.60 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.60 (declare-const tptp.total_order (-> $$unsorted $$unsorted Bool)) % 0.43/0.60 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.60 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.60 (define @t1 () (@var "B" $$unsorted)) % 0.43/0.60 (define @t2 () (@var "X" $$unsorted)) % 0.43/0.60 (define @t3 () (tptp.member @t2 @t1)) % 0.43/0.60 (define @t4 () (@var "A" $$unsorted)) % 0.43/0.60 (define @t5 () (tptp.member @t2 @t4)) % 0.43/0.60 (define @t6 () (@list @t2)) % 0.43/0.60 (define @t7 () (tptp.subset @t4 @t1)) % 0.43/0.60 (define @t8 () (@list @t4 @t1)) % 0.43/0.60 (define @t9 () (@list @t2 @t4)) % 0.43/0.60 (define @t10 () (@list @t2 @t4 @t1)) % 0.43/0.60 (define @t11 () (@var "E" $$unsorted)) % 0.43/0.60 (define @t12 () (tptp.member @t1 @t11)) % 0.43/0.60 (define @t13 () (= @t2 @t4)) % 0.43/0.60 (define @t14 () (or @t13 (= @t2 @t1))) % 0.43/0.60 (define @t15 () (tptp.unordered_pair @t4 @t1)) % 0.43/0.60 (define @t16 () (tptp.member @t2 @t15)) % 0.43/0.60 (define @t17 () (= @t16 @t14)) % 0.43/0.60 (define @t18 () (forall @t10 @t17)) % 0.43/0.60 (define @t19 () (@var "Y" $$unsorted)) % 0.43/0.60 (define @t20 () (tptp.member @t2 @t19)) % 0.43/0.60 (define @t21 () (tptp.member @t19 @t4)) % 0.43/0.60 (define @t22 () (@list @t19)) % 0.43/0.60 (define @t23 () (@var "Z" $$unsorted)) % 0.43/0.60 (define @t24 () (@var "R" $$unsorted)) % 0.43/0.60 (define @t25 () (tptp.apply @t24 @t2 @t23)) % 0.43/0.60 (define @t26 () (tptp.apply @t24 @t19 @t23)) % 0.43/0.60 (define @t27 () (tptp.apply @t24 @t2 @t19)) % 0.43/0.60 (define @t28 () (and @t27 @t26)) % 0.43/0.60 (define @t29 () (=> @t28 @t25)) % 0.43/0.60 (define @t30 () (tptp.member @t23 @t11)) % 0.43/0.60 (define @t31 () (tptp.member @t19 @t11)) % 0.43/0.60 (define @t32 () (tptp.member @t2 @t11)) % 0.43/0.60 (define @t33 () (and @t32 @t31 @t30)) % 0.43/0.60 (define @t34 () (@list @t2 @t19 @t23)) % 0.43/0.60 (define @t35 () (forall @t34 (=> @t33 @t29))) % 0.43/0.60 (define @t36 () (= @t2 @t19)) % 0.43/0.60 (define @t37 () (tptp.apply @t24 @t19 @t2)) % 0.43/0.60 (define @t38 () (and @t27 @t37)) % 0.43/0.60 (define @t39 () (=> @t38 @t36)) % 0.43/0.60 (define @t40 () (and @t32 @t31)) % 0.43/0.60 (define @t41 () (@list @t2 @t19)) % 0.43/0.60 (define @t42 () (forall @t41 (=> @t40 @t39))) % 0.43/0.60 (define @t43 () (tptp.apply @t24 @t2 @t2)) % 0.43/0.60 (define @t44 () (forall @t6 (=> @t32 @t43))) % 0.43/0.60 (define @t45 () (and @t44 @t42 @t35)) % 0.43/0.60 (define @t46 () (tptp.order @t24 @t11)) % 0.43/0.60 (define @t47 () (= @t46 @t45)) % 0.43/0.60 (define @t48 () (@list @t24 @t11)) % 0.43/0.60 (define @t49 () (forall @t48 @t47)) % 0.43/0.60 (define @t50 () (@var "M" $$unsorted)) % 0.43/0.60 (define @t51 () (tptp.apply @t24 @t2 @t50)) % 0.43/0.60 (define @t52 () (forall @t6 (=> @t32 @t51))) % 0.43/0.60 (define @t53 () (@list @t24 @t11 @t50)) % 0.43/0.60 (define @t54 () (tptp.apply @t24 @t50 @t2)) % 0.43/0.60 (define @t55 () (forall @t6 (=> @t32 @t54))) % 0.43/0.60 (define @t56 () (tptp.lower_bound @t50 @t24 @t11)) % 0.43/0.60 (define @t57 () (= @t56 @t55)) % 0.43/0.60 (define @t58 () (forall @t53 @t57)) % 0.43/0.60 (define @t59 () (tptp.member @t50 @t11)) % 0.43/0.60 (define @t60 () (= @t50 @t2)) % 0.43/0.60 (define @t61 () (@list @t50)) % 0.43/0.60 (define @t62 () (tptp.member @t4 @t2)) % 0.43/0.60 (define @t63 () (@list @t4 @t2 @t24 @t11)) % 0.43/0.60 (define @t64 () (tptp.apply @t24 @t50 @t4)) % 0.43/0.60 (define @t65 () (tptp.lower_bound @t50 @t24 @t2)) % 0.43/0.60 (define @t66 () (and @t59 @t65)) % 0.43/0.60 (define @t67 () (forall @t61 (=> @t66 @t64))) % 0.43/0.60 (define @t68 () (tptp.lower_bound @t4 @t24 @t2)) % 0.43/0.60 (define @t69 () (and @t62 @t68 @t67)) % 0.43/0.60 (define @t70 () (tptp.greatest_lower_bound @t4 @t2 @t24 @t11)) % 0.43/0.60 (define @t71 () (= @t70 @t69)) % 0.43/0.60 (define @t72 () (forall @t63 @t71)) % 0.43/0.60 (define @t73 () (tptp.greatest_lower_bound @t4 @t15 @t24 @t11)) % 0.43/0.60 (define @t74 () (tptp.apply @t24 @t4 @t1)) % 0.43/0.60 (define @t75 () (tptp.member @t4 @t11)) % 0.43/0.60 (define @t76 () (and @t46 @t75 @t12 @t74)) % 0.43/0.60 (define @t77 () (@list @t24 @t11 @t4 @t1)) % 0.43/0.60 (define @t78 () (forall @t77 (=> @t76 @t73))) % 0.43/0.60 (define @t79 () (not @t78)) % 0.43/0.60 (define @t80 () (not @t26)) % 0.43/0.60 (define @t81 () (not @t27)) % 0.43/0.60 (define @t82 () (not @t30)) % 0.43/0.60 (define @t83 () (not @t31)) % 0.43/0.60 (define @t84 () (not @t32)) % 0.43/0.60 (define @t85 () (or @t81 @t80 @t25)) % 0.43/0.60 (define @t86 () (or @t84 @t83 @t82)) % 0.43/0.60 (define @t87 () (not @t37)) % 0.43/0.60 (define @t88 () (or @t81 @t87 @t36)) % 0.43/0.60 (define @t89 () (not @t74)) % 0.43/0.60 (define @t90 () (not @t12)) % 0.43/0.60 (define @t91 () (not @t75)) % 0.43/0.60 (define @t92 () (not @t46)) % 0.43/0.60 (define @t93 () (or @t92 @t91 @t90 @t89 @t73)) % 0.43/0.60 (define @t94 () (forall @t77 @t93)) % 0.43/0.60 (define @t95 () (@quantifiers_skolemize @t94 1)) % 0.43/0.60 (define @t96 () (@quantifiers_skolemize @t94 0)) % 0.43/0.60 (define @t97 () (or @t92 @t91 @t90 @t89)) % 0.43/0.60 (define @t98 () (tptp.order @t96 @t95)) % 0.43/0.60 (define @t99 () (@quantifiers_skolemize @t94 3)) % 0.43/0.60 (define @t100 () (@quantifiers_skolemize @t94 2)) % 0.43/0.60 (define @t101 () (tptp.unordered_pair @t100 @t99)) % 0.43/0.60 (define @t102 () (tptp.greatest_lower_bound @t100 @t101 @t96 @t95)) % 0.43/0.60 (define @t103 () (tptp.apply @t96 @t100 @t99)) % 0.43/0.60 (define @t104 () (not @t103)) % 0.43/0.60 (define @t105 () (tptp.member @t100 @t95)) % 0.43/0.60 (define @t106 () (not @t105)) % 0.43/0.60 (define @t107 () (not @t98)) % 0.43/0.60 (define @t108 () (or @t107 @t106 (not (tptp.member @t99 @t95)) @t104 @t102)) % 0.43/0.60 (define @t109 () (@list true)) % 0.43/0.60 (define @t110 () (@list @t108)) % 0.43/0.60 (define @t111 () (not (tptp.apply @t96 @t2 @t19))) % 0.43/0.60 (define @t112 () (not (tptp.member @t19 @t95))) % 0.43/0.60 (define @t113 () (not (tptp.member @t2 @t95))) % 0.43/0.60 (define @t114 () (forall @t6 (or @t113 (tptp.apply @t96 @t2 @t2)))) % 0.43/0.60 (define @t115 () (and @t114 (forall @t41 (or @t113 @t112 @t111 (not (tptp.apply @t96 @t19 @t2)) @t36)) (forall @t34 (or @t113 @t112 (not (tptp.member @t23 @t95)) @t111 (not (tptp.apply @t96 @t19 @t23)) (tptp.apply @t96 @t2 @t23))))) % 0.43/0.60 (define @t116 () (= @t98 @t115)) % 0.43/0.60 (define @t117 () (@list false false)) % 0.43/0.60 (define @t118 () (@list false)) % 0.43/0.60 (define @t119 () (@list @t100)) % 0.43/0.60 (define @t120 () (tptp.apply @t96 @t100 @t100)) % 0.43/0.60 (define @t121 () (or @t106 @t120)) % 0.43/0.60 (define @t122 () (forall @t61 (or (not (tptp.member @t50 @t95)) (not (tptp.lower_bound @t50 @t96 @t101)) (tptp.apply @t96 @t50 @t100)))) % 0.43/0.60 (define @t123 () (@quantifiers_skolemize @t122 0)) % 0.43/0.60 (define @t124 () (tptp.lower_bound @t123 @t96 @t101)) % 0.43/0.60 (define @t125 () (tptp.apply @t96 @t123 @t100)) % 0.43/0.60 (define @t126 () (not @t124)) % 0.43/0.60 (define @t127 () (or (not (tptp.member @t123 @t95)) @t126 @t125)) % 0.43/0.60 (define @t128 () (not (tptp.member @t2 @t101))) % 0.43/0.60 (define @t129 () (forall @t6 (or @t128 (tptp.apply @t96 @t123 @t2)))) % 0.43/0.60 (define @t130 () (= @t124 @t129)) % 0.43/0.60 (define @t131 () (tptp.member @t100 @t101)) % 0.43/0.60 (define @t132 () (or (= @t100 @t100) (= @t99 @t100))) % 0.43/0.60 (define @t133 () (= @t131 @t132)) % 0.43/0.60 (define @t134 () (forall @t10 (= @t16 (or (= @t4 @t2) (= @t1 @t2))))) % 0.43/0.60 (define @t135 () (not @t131)) % 0.43/0.60 (define @t136 () (or @t135 @t125)) % 0.43/0.60 (define @t137 () (not @t127)) % 0.43/0.60 (define @t138 () (not @t122)) % 0.43/0.60 (define @t139 () (not @t65)) % 0.43/0.60 (define @t140 () (not @t59)) % 0.43/0.60 (define @t141 () (tptp.lower_bound @t100 @t96 @t101)) % 0.43/0.60 (define @t142 () (and @t131 @t141 @t122)) % 0.43/0.60 (define @t143 () (= @t102 @t142)) % 0.43/0.60 (define @t144 () (not @t142)) % 0.43/0.60 (define @t145 () (@list true false)) % 0.43/0.60 (define @t146 () (forall @t6 (or @t128 (tptp.apply @t96 @t100 @t2)))) % 0.43/0.60 (define @t147 () (= @t141 @t146)) % 0.43/0.60 (define @t148 () (not @t146)) % 0.43/0.60 (define @t149 () (@quantifiers_skolemize @t146 0)) % 0.43/0.60 (define @t150 () (tptp.apply @t96 @t100 @t149)) % 0.43/0.60 (define @t151 () (tptp.member @t149 @t101)) % 0.43/0.60 (define @t152 () (not @t151)) % 0.43/0.60 (define @t153 () (or @t152 @t150)) % 0.43/0.60 (define @t154 () (not @t153)) % 0.43/0.60 (define @t155 () (not @t150)) % 0.43/0.60 (define @t156 () (@list @t153)) % 0.43/0.60 (define @t157 () (= @t99 @t149)) % 0.43/0.60 (define @t158 () (= @t100 @t149)) % 0.43/0.60 (define @t159 () (or @t158 @t157)) % 0.43/0.60 (define @t160 () (= @t151 @t159)) % 0.43/0.60 (define @t161 () (not @t157)) % 0.43/0.60 (define @t162 () (not @t155)) % 0.43/0.60 (define @t163 () (= false true)) % 0.43/0.60 (define @t164 () (and @t103 @t157 @t155)) % 0.43/0.60 (define @t165 () (not @t158)) % 0.43/0.60 (define @t166 () (not @t120)) % 0.43/0.60 (define @t167 () (and @t120 @t158 @t155)) % 0.43/0.60 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.43/0.60 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.43/0.60 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.43/0.60 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.43/0.60 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.43/0.60 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.43/0.60 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and @t12 (not (tptp.member @t1 @t4)))))) % 0.43/0.60 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t13))) % 0.43/0.60 (assume @p9 @t18) % 0.43/0.60 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t22 (and @t21 @t20))))) % 0.43/0.60 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t22 (=> @t21 @t20))))) % 0.43/0.60 (assume @p12 @t49) % 0.43/0.60 (assume @p13 (forall @t48 (= (tptp.total_order @t24 @t11) (and @t46 (forall @t41 (=> @t40 (or @t27 @t37))))))) % 0.43/0.60 (assume @p14 (forall @t53 (= (tptp.upper_bound @t50 @t24 @t11) @t52))) % 0.43/0.60 (assume @p15 @t58) % 0.43/0.60 (assume @p16 (forall @t53 (= (tptp.greatest @t50 @t24 @t11) (and @t59 @t52)))) % 0.43/0.60 (assume @p17 (forall @t53 (= (tptp.least @t50 @t24 @t11) (and @t59 @t55)))) % 0.43/0.60 (assume @p18 (forall @t53 (= (tptp.max @t50 @t24 @t11) (and @t59 (forall @t6 (=> (and @t32 @t54) @t60)))))) % 0.43/0.60 (assume @p19 (forall @t53 (= (tptp.min @t50 @t24 @t11) (and @t59 (forall @t6 (=> (and @t32 @t51) @t60)))))) % 0.43/0.60 (assume @p20 (forall @t63 (= (tptp.least_upper_bound @t4 @t2 @t24 @t11) (and @t62 (tptp.upper_bound @t4 @t24 @t2) (forall @t61 (=> (and @t59 (tptp.upper_bound @t50 @t24 @t2)) (tptp.apply @t24 @t4 @t50))))))) % 0.43/0.60 (assume @p21 @t72) % 0.43/0.60 (assume @p22 @t79) % 0.43/0.60 (assume @p23 true) % 0.43/0.60 (step @p24 :rule aci_norm :args ((= (or @t86 @t85) (or @t84 @t83 @t82 @t81 @t80 @t25)))) % 0.43/0.60 (step @p25 :rule aci_norm :args ((= (or (or @t81 @t80) @t25) @t85))) % 0.43/0.60 (step @p26 :rule refl :args (@t25)) % 0.43/0.60 (step @p27 :rule bool-and-de-morgan :args (@t27 @t26 true)) % 0.43/0.60 (step @p28 :rule nary_cong :premises (@p27 @p26) :args ((or (not @t28) @t25))) % 0.43/0.60 (step @p29 :rule trans :premises (@p28 @p25)) % 0.43/0.60 (step @p30 :rule bool-impl-elim :args (@t28 @t25)) % 0.43/0.60 (step @p31 :rule trans :premises (@p30 @p29)) % 0.43/0.60 (step @p32 :rule aci_norm :args ((= (or @t84 (or @t83 @t82)) @t86))) % 0.43/0.60 (step @p33 :rule bool-and-de-morgan :args (@t31 @t30 true)) % 0.43/0.60 (step @p34 :rule refl :args (@t84)) % 0.43/0.60 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or @t84 (not (and @t31 @t30))))) % 0.43/0.60 (step @p36 :rule bool-and-de-morgan :args (@t32 @t31 (and @t30))) % 0.43/0.60 (step @p37 :rule trans :premises (@p36 @p35)) % 0.43/0.60 (step @p38 :rule trans :premises (@p37 @p32)) % 0.43/0.60 (step @p39 :rule nary_cong :premises (@p38 @p31) :args ((or (not @t33) @t29))) % 0.43/0.60 (step @p40 :rule trans :premises (@p39 @p24)) % 0.43/0.60 (step @p41 :rule bool-impl-elim :args (@t33 @t29)) % 0.43/0.60 (step @p42 :rule trans :premises (@p41 @p40)) % 0.43/0.60 (step @p43 :rule cong :premises (@p42) :args (@t35)) % 0.43/0.60 (step @p44 :rule aci_norm :args ((= (or (or @t84 @t83) @t88) (or @t84 @t83 @t81 @t87 @t36)))) % 0.43/0.60 (step @p45 :rule aci_norm :args ((= (or (or @t81 @t87) @t36) @t88))) % 0.43/0.60 (step @p46 :rule refl :args (@t36)) % 0.43/0.60 (step @p47 :rule bool-and-de-morgan :args (@t27 @t37 true)) % 0.43/0.60 (step @p48 :rule nary_cong :premises (@p47 @p46) :args ((or (not @t38) @t36))) % 0.43/0.60 (step @p49 :rule trans :premises (@p48 @p45)) % 0.43/0.60 (step @p50 :rule bool-impl-elim :args (@t38 @t36)) % 0.43/0.60 (step @p51 :rule trans :premises (@p50 @p49)) % 0.43/0.60 (step @p52 :rule bool-and-de-morgan :args (@t32 @t31 true)) % 0.43/0.60 (step @p53 :rule nary_cong :premises (@p52 @p51) :args ((or (not @t40) @t39))) % 0.43/0.60 (step @p54 :rule trans :premises (@p53 @p44)) % 0.43/0.60 (step @p55 :rule bool-impl-elim :args (@t40 @t39)) % 0.43/0.60 (step @p56 :rule trans :premises (@p55 @p54)) % 0.43/0.60 (step @p57 :rule cong :premises (@p56) :args (@t42)) % 0.43/0.60 (step @p58 :rule bool-impl-elim :args (@t32 @t43)) % 0.43/0.60 (step @p59 :rule cong :premises (@p58) :args (@t44)) % 0.43/0.60 (step @p60 :rule nary_cong :premises (@p59 @p57 @p43) :args (@t45)) % 0.43/0.60 (step @p61 :rule refl :args (@t46)) % 0.43/0.60 (step @p62 :rule cong :premises (@p61 @p60) :args (@t47)) % 0.43/0.60 (step @p63 :rule cong :premises (@p62) :args (@t49)) % 0.43/0.60 (step @p64 :rule eq_resolve :premises (@p12 @p63)) % 0.43/0.60 (step @p65 :rule instantiate :premises (@p64) :args ((@list @t96 @t95))) % 0.43/0.60 (step @p66 :rule aci_norm :args ((= (or @t97 @t73) @t93))) % 0.43/0.60 (step @p67 :rule refl :args (@t73)) % 0.43/0.60 (step @p68 :rule aci_norm :args ((= (or @t92 (or @t91 (or @t90 @t89))) @t97))) % 0.43/0.60 (step @p69 :rule bool-and-de-morgan :args (@t12 @t74 true)) % 0.43/0.60 (step @p70 :rule refl :args (@t91)) % 0.43/0.60 (step @p71 :rule nary_cong :premises (@p70 @p69) :args ((or @t91 (not (and @t12 @t74))))) % 0.43/0.60 (step @p72 :rule bool-and-de-morgan :args (@t75 @t12 (and @t74))) % 0.43/0.60 (step @p73 :rule trans :premises (@p72 @p71)) % 0.43/0.60 (step @p74 :rule refl :args (@t92)) % 0.43/0.60 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t92 (not (and @t75 @t12 @t74))))) % 0.43/0.60 (step @p76 :rule bool-and-de-morgan :args (@t46 @t75 (and @t12 @t74))) % 0.43/0.60 (step @p77 :rule trans :premises (@p76 @p75)) % 0.43/0.60 (step @p78 :rule trans :premises (@p77 @p68)) % 0.43/0.60 (step @p79 :rule nary_cong :premises (@p78 @p67) :args ((or (not @t76) @t73))) % 0.43/0.60 (step @p80 :rule trans :premises (@p79 @p66)) % 0.43/0.60 (step @p81 :rule bool-impl-elim :args (@t76 @t73)) % 0.43/0.60 (step @p82 :rule trans :premises (@p81 @p80)) % 0.43/0.60 (step @p83 :rule cong :premises (@p82) :args (@t78)) % 0.43/0.60 (step @p84 :rule cong :premises (@p83) :args (@t79)) % 0.43/0.60 (step @p85 :rule eq_resolve :premises (@p22 @p84)) % 0.43/0.60 (step @p86 :rule skolemize :premises (@p85)) % 0.43/0.60 (step @p87 :rule bool-double-not-elim :args (@t98)) % 0.43/0.60 (step @p88 :rule refl :args (@t108)) % 0.43/0.60 (step @p89 :rule nary_cong :premises (@p88 @p87) :args ((or @t108 (not @t107)))) % 0.43/0.60 (step @p90 :rule cnf_or_neg :args (@t108 0)) % 0.43/0.60 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.43/0.60 (step @p92 :rule reordering :premises (@p91) :args ((or @t98 @t108))) % 0.43/0.60 (step @p93 :rule chain_m_resolution :premises (@p92 @p86) :args (@t98 @t109 @t110)) % 0.43/0.60 (step @p94 :rule cnf_equiv_pos1 :args (@t116)) % 0.43/0.60 (step @p95 :rule reordering :premises (@p94) :args ((or @t107 @t115 (not @t116)))) % 0.43/0.60 (step @p96 :rule chain_m_resolution :premises (@p95 @p93 @p65) :args (@t115 @t117 (@list @t98 @t116))) % 0.43/0.60 (step @p97 :rule cnf_and_pos :args (@t115 0)) % 0.43/0.60 (step @p98 :rule reordering :premises (@p97) :args ((or @t114 (not @t115)))) % 0.43/0.60 (step @p99 :rule chain_m_resolution :premises (@p98 @p96) :args (@t114 @t118 (@list @t115))) % 0.43/0.60 (step @p100 :rule instantiate :premises (@p99) :args (@t119)) % 0.43/0.60 (step @p101 :rule bool-double-not-elim :args (@t105)) % 0.43/0.60 (step @p102 :rule nary_cong :premises (@p88 @p101) :args ((or @t108 (not @t106)))) % 0.43/0.60 (step @p103 :rule cnf_or_neg :args (@t108 1)) % 0.43/0.60 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.43/0.60 (step @p105 :rule reordering :premises (@p104) :args ((or @t105 @t108))) % 0.43/0.60 (step @p106 :rule chain_m_resolution :premises (@p105 @p86) :args (@t105 @t109 @t110)) % 0.43/0.60 (step @p107 :rule cnf_or_pos :args (@t121)) % 0.43/0.60 (step @p108 :rule reordering :premises (@p107) :args ((or @t106 @t120 (not @t121)))) % 0.43/0.60 (step @p109 :rule chain_m_resolution :premises (@p108 @p106 @p100) :args (@t120 @t117 (@list @t105 @t121))) % 0.43/0.60 (step @p110 :rule bool-impl-elim :args (@t32 @t54)) % 0.43/0.60 (step @p111 :rule cong :premises (@p110) :args (@t55)) % 0.43/0.60 (step @p112 :rule refl :args (@t56)) % 0.43/0.60 (step @p113 :rule cong :premises (@p112 @p111) :args (@t57)) % 0.43/0.60 (step @p114 :rule cong :premises (@p113) :args (@t58)) % 0.43/0.60 (step @p115 :rule eq_resolve :premises (@p15 @p114)) % 0.43/0.60 (step @p116 :rule instantiate :premises (@p115) :args ((@list @t96 @t101 @t100))) % 0.43/0.60 (step @p117 :rule bool-double-not-elim :args (@t124)) % 0.43/0.60 (step @p118 :rule refl :args (@t127)) % 0.43/0.60 (step @p119 :rule nary_cong :premises (@p118 @p117) :args ((or @t127 (not @t126)))) % 0.43/0.60 (step @p120 :rule cnf_or_neg :args (@t127 1)) % 0.43/0.60 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.43/0.60 (step @p122 :rule reordering :premises (@p121) :args ((or @t124 @t127))) % 0.43/0.60 (step @p123 :rule cnf_or_neg :args (@t127 2)) % 0.43/0.60 (step @p124 :rule instantiate :premises (@p115) :args ((@list @t96 @t101 @t123))) % 0.43/0.60 (step @p125 :rule cnf_equiv_pos1 :args (@t130)) % 0.43/0.60 (step @p126 :rule reordering :premises (@p125) :args ((or @t126 @t129 (not @t130)))) % 0.43/0.60 (step @p127 :rule eq-symm :args (@t2 @t1)) % 0.43/0.60 (step @p128 :rule eq-symm :args (@t2 @t4)) % 0.43/0.60 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t14)) % 0.43/0.60 (step @p130 :rule refl :args (@t16)) % 0.43/0.60 (step @p131 :rule cong :premises (@p130 @p129) :args (@t17)) % 0.43/0.60 (step @p132 :rule cong :premises (@p131) :args (@t18)) % 0.43/0.60 (step @p133 :rule eq_resolve :premises (@p9 @p132)) % 0.43/0.60 (step @p134 :rule bool-eq-true :args (@t131)) % 0.43/0.60 (step @p135 :rule absorb :args ((= (or true (= @t100 @t99)) true))) % 0.43/0.60 (step @p136 :rule eq-symm :args (@t99 @t100)) % 0.43/0.60 (step @p137 :rule eq-refl :args (@t100)) % 0.43/0.60 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t132)) % 0.43/0.60 (step @p139 :rule trans :premises (@p138 @p135)) % 0.43/0.60 (step @p140 :rule refl :args (@t131)) % 0.43/0.60 (step @p141 :rule cong :premises (@p140 @p139) :args (@t133)) % 0.43/0.60 (step @p142 :rule trans :premises (@p141 @p134)) % 0.43/0.60 (step @p143 :rule refl :args (@t134)) % 0.43/0.60 (step @p144 :rule cong :premises (@p143 @p142) :args ((=> @t134 @t133))) % 0.43/0.60 (assume-push @p290 @t134) % 0.43/0.60 (step @p146 :rule instantiate :premises (@p133) :args ((@list @t100 @t100 @t99))) % 0.43/0.60 (step-pop @p291 :rule scope :premises (@p146)) % 0.43/0.60 (step @p147 :rule process_scope :premises (@p291) :args (@t133)) % 0.43/0.60 (step @p149 :rule eq_resolve :premises (@p147 @p144)) % 0.43/0.60 (step @p150 :rule implies_elim :premises (@p149)) % 0.43/0.60 (step @p151 :rule chain_m_resolution :premises (@p150 @p133) :args (@t131 @t118 (@list @t134))) % 0.43/0.60 (step @p152 :rule cnf_or_pos :args (@t136)) % 0.43/0.60 (step @p153 :rule reordering :premises (@p152) :args ((or @t135 @t125 (not @t136)))) % 0.43/0.60 (assume-push @p292 @t129) % 0.43/0.60 (step @p155 :rule instantiate :premises (@p292) :args (@t119)) % 0.43/0.60 (step-pop @p293 :rule scope :premises (@p155)) % 0.43/0.60 (step @p156 :rule process_scope :premises (@p293) :args (@t136)) % 0.43/0.60 (step @p158 :rule implies_elim :premises (@p156)) % 0.43/0.60 (step @p159 :rule chain_m_resolution :premises (@p158 @p153 @p151 @p126 @p124 @p123 @p122) :args (@t127 (@list true false false false true false) (@list @t136 @t131 @t129 @t130 @t125 @t124))) % 0.43/0.60 (step @p160 :rule refl :args (@t137)) % 0.43/0.60 (step @p161 :rule bool-double-not-elim :args (@t122)) % 0.43/0.60 (step @p162 :rule nary_cong :premises (@p161 @p160) :args ((or (not @t138) @t137))) % 0.43/0.60 (assume-push @p294 @t138) % 0.43/0.60 (step @p164 :rule skolemize :premises (@p294)) % 0.43/0.60 (step-pop @p295 :rule scope :premises (@p164)) % 0.43/0.60 (step @p165 :rule process_scope :premises (@p295) :args (@t137)) % 0.43/0.60 (step @p167 :rule implies_elim :premises (@p165)) % 0.43/0.60 (step @p168 :rule eq_resolve :premises (@p167 @p162)) % 0.43/0.60 (step @p169 :rule chain_m_resolution :premises (@p168 @p159) :args (@t122 @t118 (@list @t127))) % 0.43/0.60 (step @p170 :rule aci_norm :args ((= (or (or @t140 @t139) @t64) (or @t140 @t139 @t64)))) % 0.43/0.60 (step @p171 :rule refl :args (@t64)) % 0.43/0.60 (step @p172 :rule bool-and-de-morgan :args (@t59 @t65 true)) % 0.43/0.60 (step @p173 :rule nary_cong :premises (@p172 @p171) :args ((or (not @t66) @t64))) % 0.43/0.60 (step @p174 :rule trans :premises (@p173 @p170)) % 0.43/0.60 (step @p175 :rule bool-impl-elim :args (@t66 @t64)) % 0.43/0.60 (step @p176 :rule trans :premises (@p175 @p174)) % 0.43/0.60 (step @p177 :rule cong :premises (@p176) :args (@t67)) % 0.43/0.60 (step @p178 :rule refl :args (@t68)) % 0.43/0.60 (step @p179 :rule refl :args (@t62)) % 0.43/0.60 (step @p180 :rule nary_cong :premises (@p179 @p178 @p177) :args (@t69)) % 0.43/0.60 (step @p181 :rule refl :args (@t70)) % 0.43/0.60 (step @p182 :rule cong :premises (@p181 @p180) :args (@t71)) % 0.43/0.60 (step @p183 :rule cong :premises (@p182) :args (@t72)) % 0.43/0.60 (step @p184 :rule eq_resolve :premises (@p21 @p183)) % 0.43/0.60 (step @p185 :rule instantiate :premises (@p184) :args ((@list @t100 @t101 @t96 @t95))) % 0.43/0.60 (step @p186 :rule cnf_or_neg :args (@t108 4)) % 0.43/0.60 (step @p187 :rule chain_m_resolution :premises (@p186 @p86) :args ((not @t102) @t109 @t110)) % 0.43/0.60 (step @p188 :rule cnf_equiv_pos2 :args (@t143)) % 0.43/0.60 (step @p189 :rule reordering :premises (@p188) :args ((or @t102 @t144 (not @t143)))) % 0.43/0.60 (step @p190 :rule chain_m_resolution :premises (@p189 @p187 @p185) :args (@t144 @t145 (@list @t102 @t143))) % 0.43/0.60 (step @p191 :rule cnf_and_neg :args (@t142)) % 0.43/0.60 (step @p192 :rule chain_m_resolution :premises (@p191 @p190 @p151 @p169) :args ((not @t141) (@list true false false) (@list @t142 @t131 @t122))) % 0.43/0.60 (step @p193 :rule cnf_equiv_pos2 :args (@t147)) % 0.43/0.60 (step @p194 :rule reordering :premises (@p193) :args ((or @t141 @t148 (not @t147)))) % 0.43/0.60 (step @p195 :rule chain_m_resolution :premises (@p194 @p192 @p116) :args (@t148 @t145 (@list @t141 @t147))) % 0.43/0.60 (step @p196 :rule refl :args (@t154)) % 0.43/0.60 (step @p197 :rule bool-double-not-elim :args (@t146)) % 0.43/0.60 (step @p198 :rule nary_cong :premises (@p197 @p196) :args ((or (not @t148) @t154))) % 0.43/0.60 (assume-push @p296 @t148) % 0.43/0.60 (step @p200 :rule skolemize :premises (@p296)) % 0.43/0.60 (step-pop @p297 :rule scope :premises (@p200)) % 0.43/0.60 (step @p201 :rule process_scope :premises (@p297) :args (@t154)) % 0.43/0.60 (step @p203 :rule implies_elim :premises (@p201)) % 0.43/0.60 (step @p204 :rule eq_resolve :premises (@p203 @p198)) % 0.43/0.60 (step @p205 :rule chain_m_resolution :premises (@p204 @p195) :args (@t154 @t109 (@list @t146))) % 0.43/0.60 (step @p206 :rule cnf_or_neg :args (@t153 1)) % 0.43/0.60 (step @p207 :rule chain_m_resolution :premises (@p206 @p205) :args (@t155 @t109 @t156)) % 0.43/0.60 (step @p208 :rule bool-double-not-elim :args (@t151)) % 0.43/0.60 (step @p209 :rule refl :args (@t153)) % 0.43/0.60 (step @p210 :rule nary_cong :premises (@p209 @p208) :args ((or @t153 (not @t152)))) % 0.43/0.60 (step @p211 :rule cnf_or_neg :args (@t153 0)) % 0.43/0.60 (step @p212 :rule eq_resolve :premises (@p211 @p210)) % 0.43/0.60 (step @p213 :rule reordering :premises (@p212) :args ((or @t151 @t153))) % 0.43/0.60 (step @p214 :rule instantiate :premises (@p133) :args ((@list @t149 @t100 @t99))) % 0.43/0.60 (step @p215 :rule cnf_equiv_pos1 :args (@t160)) % 0.43/0.60 (step @p216 :rule reordering :premises (@p215) :args ((or @t152 @t159 (not @t160)))) % 0.43/0.60 (step @p217 :rule cnf_or_pos :args (@t159)) % 0.43/0.60 (step @p218 :rule reordering :premises (@p217) :args ((or @t158 @t157 (not @t159)))) % 0.43/0.60 (step @p219 :rule bool-double-not-elim :args (@t103)) % 0.43/0.60 (step @p220 :rule nary_cong :premises (@p88 @p219) :args ((or @t108 (not @t104)))) % 0.43/0.60 (step @p221 :rule cnf_or_neg :args (@t108 3)) % 0.43/0.60 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 0.43/0.60 (step @p223 :rule reordering :premises (@p222) :args ((or @t103 @t108))) % 0.43/0.60 (step @p224 :rule chain_m_resolution :premises (@p223 @p86) :args (@t103 @t109 @t110)) % 0.43/0.60 (step @p225 :rule refl :args (@t161)) % 0.43/0.60 (step @p226 :rule bool-double-not-elim :args (@t150)) % 0.43/0.60 (step @p227 :rule refl :args (@t104)) % 0.43/0.60 (step @p228 :rule nary_cong :premises (@p227 @p226 @p225) :args ((or @t104 @t162 @t161))) % 0.43/0.60 (assume-push @p298 @t103) % 0.43/0.60 (assume-push @p299 @t157) % 0.43/0.60 (assume-push @p300 @t155) % 0.43/0.60 (step @p232 :rule evaluate :args (@t163)) % 0.43/0.60 (step @p233 :rule true_intro :premises (@p224)) % 0.43/0.60 (step @p234 :rule symm :premises (@p299)) % 0.43/0.60 (step @p235 :rule refl :args (@t100)) % 0.43/0.60 (step @p236 :rule refl :args (@t96)) % 0.43/0.60 (step @p237 :rule cong :premises (@p236 @p235 @p234) :args (@t150)) % 0.43/0.60 (step @p238 :rule false_intro :premises (@p300)) % 0.43/0.60 (step @p239 :rule symm :premises (@p238)) % 0.43/0.60 (step @p240 :rule trans :premises (@p239 @p237 @p233)) % 0.43/0.60 (step @p241 false :rule eq_resolve :premises (@p240 @p232)) % 0.43/0.60 (step-pop @p301 :rule scope :premises (@p241)) % 0.43/0.60 (step-pop @p302 :rule scope :premises (@p301)) % 0.43/0.60 (step-pop @p303 :rule scope :premises (@p302)) % 0.43/0.60 (step @p242 :rule process_scope :premises (@p303) :args (false)) % 0.43/0.60 (assume-push @p304 @t103) % 0.43/0.60 (assume-push @p305 @t155) % 0.43/0.60 (assume-push @p306 @t157) % 0.43/0.60 (step @p249 :rule and_intro :premises (@p224 @p306 @p305)) % 0.43/0.60 (step-pop @p307 :rule scope :premises (@p249)) % 0.43/0.60 (step-pop @p308 :rule scope :premises (@p307)) % 0.43/0.60 (step-pop @p309 :rule scope :premises (@p308)) % 0.43/0.60 (step @p250 :rule process_scope :premises (@p309) :args (@t164)) % 0.43/0.60 (step @p254 :rule implies_elim :premises (@p250)) % 0.43/0.60 (step @p255 :rule resolution :premises (@p254 @p242) :args (true @t164)) % 0.43/0.60 (step @p256 :rule not_and :premises (@p255)) % 0.43/0.60 (step @p257 :rule eq_resolve :premises (@p256 @p228)) % 0.43/0.60 (step @p258 :rule chain_m_resolution :premises (@p257 @p224 @p218 @p216 @p214 @p206 @p213) :args ((or @t153 @t158) (@list false false false false true false) (@list @t103 @t157 @t159 @t160 @t150 @t151))) % 0.43/0.60 (step @p259 :rule chain_m_resolution :premises (@p258 @p205) :args (@t158 @t109 @t156)) % 0.43/0.60 (step @p260 :rule refl :args (@t165)) % 0.43/0.60 (step @p261 :rule refl :args (@t166)) % 0.43/0.60 (step @p262 :rule nary_cong :premises (@p261 @p226 @p260) :args ((or @t166 @t162 @t165))) % 0.43/0.60 (assume-push @p310 @t120) % 0.43/0.61 (assume-push @p311 @t158) % 0.43/0.61 (assume-push @p312 @t155) % 0.43/0.61 (step @p232 :rule evaluate :args (@t163)) % 0.43/0.61 (step @p266 :rule true_intro :premises (@p109)) % 0.43/0.61 (step @p267 :rule symm :premises (@p311)) % 0.43/0.61 (step @p235 :rule refl :args (@t100)) % 0.43/0.61 (step @p236 :rule refl :args (@t96)) % 0.43/0.61 (step @p268 :rule cong :premises (@p236 @p235 @p267) :args (@t150)) % 0.43/0.61 (step @p269 :rule false_intro :premises (@p312)) % 0.43/0.61 (step @p270 :rule symm :premises (@p269)) % 0.43/0.61 (step @p271 :rule trans :premises (@p270 @p268 @p266)) % 0.43/0.61 (step @p272 false :rule eq_resolve :premises (@p271 @p232)) % 0.43/0.61 (step-pop @p313 :rule scope :premises (@p272)) % 0.43/0.61 (step-pop @p314 :rule scope :premises (@p313)) % 0.43/0.61 (step-pop @p315 :rule scope :premises (@p314)) % 0.43/0.61 (step @p273 :rule process_scope :premises (@p315) :args (false)) % 0.43/0.61 (assume-push @p316 @t120) % 0.43/0.61 (assume-push @p317 @t155) % 0.43/0.61 (assume-push @p318 @t158) % 0.43/0.61 (step @p280 :rule and_intro :premises (@p109 @p318 @p317)) % 0.43/0.61 (step-pop @p319 :rule scope :premises (@p280)) % 0.43/0.61 (step-pop @p320 :rule scope :premises (@p319)) % 0.43/0.61 (step-pop @p321 :rule scope :premises (@p320)) % 0.43/0.61 (step @p281 :rule process_scope :premises (@p321) :args (@t167)) % 0.43/0.61 (step @p285 :rule implies_elim :premises (@p281)) % 0.43/0.61 (step @p286 :rule resolution :premises (@p285 @p273) :args (true @t167)) % 0.43/0.61 (step @p287 :rule not_and :premises (@p286)) % 0.43/0.61 (step @p288 :rule eq_resolve :premises (@p287 @p262)) % 0.43/0.61 (step @p289 false :rule chain_m_resolution :premises (@p288 @p259 @p207 @p109) :args (false (@list false true false) (@list @t158 @t150 @t120))) % 0.43/0.61 ) % 0.43/0.61 % SZS output end Proof % 0.43/0.61 % cvc5 exiting %------------------------------------------------------------------------------