%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET799+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 : n015.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 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET799+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 % 0.18/0.33 % Computer : n015.cluster.edu % 0.18/0.33 % Model : x86_64 x86_64 % 0.18/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.33 % Memory : 8042.1875MB % 0.18/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.33 % CPULimit : 300 % 0.18/0.33 % WCLimit : 300 % 0.18/0.33 % DateTime : Tue Jun 2 16:12:49 EDT 2026 % 0.18/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.59 % SZS status Theorem % 0.37/0.59 % SZS output start Proof % 0.37/0.59 ( % 0.37/0.59 (declare-sort $$unsorted 0) % 0.37/0.59 (declare-const tptp.min (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.max (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.lower_bound (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.order (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.least (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.greatest_lower_bound (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.least_upper_bound (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.greatest (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.upper_bound (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.empty_set $$unsorted) % 0.37/0.59 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.total_order (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (define @t1 () (@var "B" $$unsorted)) % 0.37/0.59 (define @t2 () (@var "X" $$unsorted)) % 0.37/0.59 (define @t3 () (tptp.member @t2 @t1)) % 0.37/0.59 (define @t4 () (@var "A" $$unsorted)) % 0.37/0.59 (define @t5 () (tptp.member @t2 @t4)) % 0.37/0.59 (define @t6 () (@list @t2)) % 0.37/0.59 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.37/0.59 (define @t8 () (tptp.subset @t4 @t1)) % 0.37/0.59 (define @t9 () (= @t8 @t7)) % 0.37/0.59 (define @t10 () (@list @t4 @t1)) % 0.37/0.59 (define @t11 () (forall @t10 @t9)) % 0.37/0.59 (define @t12 () (@list @t2 @t4)) % 0.37/0.59 (define @t13 () (@list @t2 @t4 @t1)) % 0.37/0.59 (define @t14 () (@var "E" $$unsorted)) % 0.37/0.59 (define @t15 () (= @t2 @t4)) % 0.37/0.59 (define @t16 () (@var "Y" $$unsorted)) % 0.37/0.59 (define @t17 () (tptp.member @t2 @t16)) % 0.37/0.59 (define @t18 () (tptp.member @t16 @t4)) % 0.37/0.59 (define @t19 () (@list @t16)) % 0.37/0.59 (define @t20 () (@var "Z" $$unsorted)) % 0.37/0.59 (define @t21 () (@var "R" $$unsorted)) % 0.37/0.59 (define @t22 () (tptp.apply @t21 @t2 @t16)) % 0.37/0.59 (define @t23 () (tptp.member @t16 @t14)) % 0.37/0.59 (define @t24 () (tptp.member @t2 @t14)) % 0.37/0.59 (define @t25 () (tptp.apply @t21 @t16 @t2)) % 0.37/0.59 (define @t26 () (and @t24 @t23)) % 0.37/0.59 (define @t27 () (@list @t2 @t16)) % 0.37/0.59 (define @t28 () (tptp.order @t21 @t14)) % 0.37/0.59 (define @t29 () (@list @t21 @t14)) % 0.37/0.59 (define @t30 () (@var "M" $$unsorted)) % 0.37/0.59 (define @t31 () (tptp.apply @t21 @t2 @t30)) % 0.37/0.59 (define @t32 () (forall @t6 (=> @t24 @t31))) % 0.37/0.59 (define @t33 () (tptp.upper_bound @t30 @t21 @t14)) % 0.37/0.59 (define @t34 () (= @t33 @t32)) % 0.37/0.59 (define @t35 () (@list @t21 @t14 @t30)) % 0.37/0.59 (define @t36 () (forall @t35 @t34)) % 0.37/0.59 (define @t37 () (tptp.apply @t21 @t30 @t2)) % 0.37/0.59 (define @t38 () (forall @t6 (=> @t24 @t37))) % 0.37/0.59 (define @t39 () (tptp.member @t30 @t14)) % 0.37/0.59 (define @t40 () (= @t30 @t2)) % 0.37/0.59 (define @t41 () (tptp.apply @t21 @t4 @t30)) % 0.37/0.59 (define @t42 () (tptp.upper_bound @t30 @t21 @t2)) % 0.37/0.59 (define @t43 () (and @t39 @t42)) % 0.37/0.59 (define @t44 () (@list @t30)) % 0.37/0.59 (define @t45 () (forall @t44 (=> @t43 @t41))) % 0.37/0.59 (define @t46 () (tptp.upper_bound @t4 @t21 @t2)) % 0.37/0.59 (define @t47 () (tptp.member @t4 @t2)) % 0.37/0.59 (define @t48 () (and @t47 @t46 @t45)) % 0.37/0.59 (define @t49 () (tptp.least_upper_bound @t4 @t2 @t21 @t14)) % 0.37/0.59 (define @t50 () (= @t49 @t48)) % 0.37/0.59 (define @t51 () (@list @t4 @t2 @t21 @t14)) % 0.37/0.59 (define @t52 () (forall @t51 @t50)) % 0.37/0.59 (define @t53 () (@var "M2" $$unsorted)) % 0.37/0.59 (define @t54 () (@var "M1" $$unsorted)) % 0.37/0.59 (define @t55 () (tptp.apply @t21 @t54 @t53)) % 0.37/0.59 (define @t56 () (@var "X2" $$unsorted)) % 0.37/0.59 (define @t57 () (tptp.least_upper_bound @t53 @t56 @t21 @t14)) % 0.37/0.59 (define @t58 () (@var "X1" $$unsorted)) % 0.37/0.59 (define @t59 () (tptp.least_upper_bound @t54 @t58 @t21 @t14)) % 0.37/0.59 (define @t60 () (and @t59 @t57)) % 0.37/0.59 (define @t61 () (@list @t54 @t53)) % 0.37/0.59 (define @t62 () (forall @t61 (=> @t60 @t55))) % 0.37/0.59 (define @t63 () (tptp.subset @t58 @t56)) % 0.37/0.59 (define @t64 () (tptp.subset @t56 @t14)) % 0.37/0.59 (define @t65 () (tptp.subset @t58 @t14)) % 0.37/0.59 (define @t66 () (and @t65 @t64 @t63)) % 0.37/0.59 (define @t67 () (=> @t66 @t62)) % 0.37/0.59 (define @t68 () (@list @t58 @t56)) % 0.37/0.59 (define @t69 () (forall @t68 @t67)) % 0.37/0.59 (define @t70 () (=> @t28 @t69)) % 0.37/0.59 (define @t71 () (forall @t29 @t70)) % 0.37/0.59 (define @t72 () (not @t71)) % 0.37/0.59 (define @t73 () (@var "BOUND_VARIABLE_7792" $$unsorted)) % 0.37/0.59 (define @t74 () (@var "BOUND_VARIABLE_7790" $$unsorted)) % 0.37/0.59 (define @t75 () (tptp.apply @t21 @t74 @t73)) % 0.37/0.59 (define @t76 () (@var "BOUND_VARIABLE_7788" $$unsorted)) % 0.37/0.59 (define @t77 () (not (tptp.least_upper_bound @t73 @t76 @t21 @t14))) % 0.37/0.59 (define @t78 () (@var "BOUND_VARIABLE_7786" $$unsorted)) % 0.37/0.59 (define @t79 () (not (tptp.least_upper_bound @t74 @t78 @t21 @t14))) % 0.37/0.59 (define @t80 () (not (tptp.subset @t78 @t76))) % 0.37/0.59 (define @t81 () (not (tptp.subset @t76 @t14))) % 0.37/0.59 (define @t82 () (not (tptp.subset @t78 @t14))) % 0.37/0.59 (define @t83 () (not @t28)) % 0.37/0.59 (define @t84 () (or @t83 @t82 @t81 @t80 @t79 @t77 @t75)) % 0.37/0.59 (define @t85 () (@list @t21 @t14 @t78 @t76 @t74 @t73)) % 0.37/0.59 (define @t86 () (forall @t85 @t84)) % 0.37/0.59 (define @t87 () (@quantifiers_skolemize @t86 5)) % 0.37/0.59 (define @t88 () (@quantifiers_skolemize @t86 3)) % 0.37/0.59 (define @t89 () (@quantifiers_skolemize @t86 0)) % 0.37/0.59 (define @t90 () (not @t42)) % 0.37/0.59 (define @t91 () (not @t39)) % 0.37/0.59 (define @t92 () (@quantifiers_skolemize @t86 1)) % 0.37/0.59 (define @t93 () (or @t82 @t81 @t80 @t79 @t77 @t75)) % 0.37/0.59 (define @t94 () (or @t83 @t93)) % 0.37/0.59 (define @t95 () (forall @t85 @t94)) % 0.37/0.59 (define @t96 () (@list @t78 @t76 @t74 @t73)) % 0.37/0.59 (define @t97 () (forall @t96 @t94)) % 0.37/0.59 (define @t98 () (forall @t96 @t93)) % 0.37/0.59 (define @t99 () (@var "BOUND_VARIABLE_7768" $$unsorted)) % 0.37/0.59 (define @t100 () (@var "BOUND_VARIABLE_7766" $$unsorted)) % 0.37/0.59 (define @t101 () (or @t83 @t98)) % 0.37/0.59 (define @t102 () (tptp.apply @t21 @t100 @t99)) % 0.37/0.59 (define @t103 () (not (tptp.least_upper_bound @t99 @t56 @t21 @t14))) % 0.37/0.59 (define @t104 () (not (tptp.least_upper_bound @t100 @t58 @t21 @t14))) % 0.37/0.59 (define @t105 () (not @t63)) % 0.37/0.59 (define @t106 () (not @t64)) % 0.37/0.59 (define @t107 () (not @t65)) % 0.37/0.59 (define @t108 () (or @t107 @t106 @t105 @t104 @t103 @t102)) % 0.37/0.59 (define @t109 () (@list @t58 @t56 @t100 @t99)) % 0.37/0.59 (define @t110 () (forall @t109 @t108)) % 0.37/0.59 (define @t111 () (or @t104 @t103 @t102)) % 0.37/0.59 (define @t112 () (or @t107 @t106 @t105 @t111)) % 0.37/0.59 (define @t113 () (forall @t109 @t112)) % 0.37/0.59 (define @t114 () (@list @t100 @t99)) % 0.37/0.59 (define @t115 () (forall @t114 @t112)) % 0.37/0.59 (define @t116 () (forall @t114 @t111)) % 0.37/0.59 (define @t117 () (or @t107 @t106 @t105 @t116)) % 0.37/0.59 (define @t118 () (not @t57)) % 0.37/0.59 (define @t119 () (not @t59)) % 0.37/0.59 (define @t120 () (or @t119 @t118 @t55)) % 0.37/0.59 (define @t121 () (forall @t61 @t120)) % 0.37/0.59 (define @t122 () (or @t107 @t106 @t105 @t121)) % 0.37/0.59 (define @t123 () (or @t107 @t106 @t105)) % 0.37/0.59 (define @t124 () (tptp.least_upper_bound @t87 @t88 @t89 @t92)) % 0.37/0.59 (define @t125 () (@quantifiers_skolemize @t86 4)) % 0.37/0.59 (define @t126 () (tptp.apply @t89 @t125 @t87)) % 0.37/0.59 (define @t127 () (not @t124)) % 0.37/0.59 (define @t128 () (@quantifiers_skolemize @t86 2)) % 0.37/0.59 (define @t129 () (tptp.least_upper_bound @t125 @t128 @t89 @t92)) % 0.37/0.59 (define @t130 () (not @t129)) % 0.37/0.59 (define @t131 () (tptp.subset @t128 @t88)) % 0.37/0.59 (define @t132 () (not @t131)) % 0.37/0.59 (define @t133 () (or (not (tptp.order @t89 @t92)) (not (tptp.subset @t128 @t92)) (not (tptp.subset @t88 @t92)) @t132 @t130 @t127 @t126)) % 0.37/0.59 (define @t134 () (@list true)) % 0.37/0.59 (define @t135 () (@list @t133)) % 0.37/0.59 (define @t136 () (not (tptp.member @t30 @t92))) % 0.37/0.59 (define @t137 () (tptp.upper_bound @t87 @t89 @t88)) % 0.37/0.59 (define @t138 () (and (tptp.member @t87 @t88) @t137 (forall @t44 (or @t136 (not (tptp.upper_bound @t30 @t89 @t88)) (tptp.apply @t89 @t87 @t30))))) % 0.37/0.59 (define @t139 () (= @t124 @t138)) % 0.37/0.59 (define @t140 () (@list false false)) % 0.37/0.59 (define @t141 () (@list false)) % 0.37/0.59 (define @t142 () (tptp.member @t2 @t88)) % 0.37/0.59 (define @t143 () (forall @t6 (or (not @t142) (tptp.apply @t89 @t2 @t87)))) % 0.37/0.59 (define @t144 () (= @t137 @t143)) % 0.37/0.59 (define @t145 () (forall @t6 (or (not (tptp.member @t2 @t128)) @t142))) % 0.37/0.59 (define @t146 () (= @t131 @t145)) % 0.37/0.59 (define @t147 () (@list @t125)) % 0.37/0.59 (define @t148 () (tptp.member @t125 @t128)) % 0.37/0.59 (define @t149 () (and @t148 (tptp.upper_bound @t125 @t89 @t128) (forall @t44 (or @t136 (not (tptp.upper_bound @t30 @t89 @t128)) (tptp.apply @t89 @t125 @t30))))) % 0.37/0.59 (define @t150 () (= @t129 @t149)) % 0.37/0.59 (define @t151 () (tptp.member @t125 @t88)) % 0.37/0.59 (define @t152 () (not @t148)) % 0.37/0.59 (define @t153 () (or @t152 @t151)) % 0.37/0.59 (define @t154 () (not @t151)) % 0.37/0.59 (define @t155 () (or @t154 @t126)) % 0.37/0.59 (define @t156 () (not @t155)) % 0.37/0.59 (define @t157 () (@list true false)) % 0.37/0.59 (assume @p1 @t11) % 0.37/0.59 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.37/0.59 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.37/0.59 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.37/0.59 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.37/0.59 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.37/0.59 (assume @p7 (forall (@list @t1 @t4 @t14) (= (tptp.member @t1 (tptp.difference @t14 @t4)) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.37/0.59 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t15))) % 0.37/0.59 (assume @p9 (forall @t13 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t15 (= @t2 @t1))))) % 0.37/0.59 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t19 (and @t18 @t17))))) % 0.37/0.59 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t19 (=> @t18 @t17))))) % 0.37/0.59 (assume @p12 (forall @t29 (= @t28 (and (forall @t6 (=> @t24 (tptp.apply @t21 @t2 @t2))) (forall @t27 (=> @t26 (=> (and @t22 @t25) (= @t2 @t16)))) (forall (@list @t2 @t16 @t20) (=> (and @t24 @t23 (tptp.member @t20 @t14)) (=> (and @t22 (tptp.apply @t21 @t16 @t20)) (tptp.apply @t21 @t2 @t20)))))))) % 0.37/0.59 (assume @p13 (forall @t29 (= (tptp.total_order @t21 @t14) (and @t28 (forall @t27 (=> @t26 (or @t22 @t25))))))) % 0.37/0.59 (assume @p14 @t36) % 0.37/0.59 (assume @p15 (forall @t35 (= (tptp.lower_bound @t30 @t21 @t14) @t38))) % 0.37/0.59 (assume @p16 (forall @t35 (= (tptp.greatest @t30 @t21 @t14) (and @t39 @t32)))) % 0.37/0.59 (assume @p17 (forall @t35 (= (tptp.least @t30 @t21 @t14) (and @t39 @t38)))) % 0.37/0.59 (assume @p18 (forall @t35 (= (tptp.max @t30 @t21 @t14) (and @t39 (forall @t6 (=> (and @t24 @t37) @t40)))))) % 0.37/0.59 (assume @p19 (forall @t35 (= (tptp.min @t30 @t21 @t14) (and @t39 (forall @t6 (=> (and @t24 @t31) @t40)))))) % 0.37/0.59 (assume @p20 @t52) % 0.37/0.59 (assume @p21 (forall @t51 (= (tptp.greatest_lower_bound @t4 @t2 @t21 @t14) (and @t47 (tptp.lower_bound @t4 @t21 @t2) (forall @t44 (=> (and @t39 (tptp.lower_bound @t30 @t21 @t2)) (tptp.apply @t21 @t30 @t4))))))) % 0.37/0.59 (assume @p22 @t72) % 0.37/0.59 (assume @p23 true) % 0.37/0.59 (step @p24 :rule bool-impl-elim :args (@t24 @t31)) % 0.37/0.59 (step @p25 :rule cong :premises (@p24) :args (@t32)) % 0.37/0.59 (step @p26 :rule refl :args (@t33)) % 0.37/0.59 (step @p27 :rule cong :premises (@p26 @p25) :args (@t34)) % 0.37/0.59 (step @p28 :rule cong :premises (@p27) :args (@t36)) % 0.37/0.59 (step @p29 :rule eq_resolve :premises (@p14 @p28)) % 0.37/0.59 (step @p30 :rule instantiate :premises (@p29) :args ((@list @t89 @t88 @t87))) % 0.37/0.59 (step @p31 :rule aci_norm :args ((= (or (or @t91 @t90) @t41) (or @t91 @t90 @t41)))) % 0.37/0.59 (step @p32 :rule refl :args (@t41)) % 0.37/0.59 (step @p33 :rule bool-and-de-morgan :args (@t39 @t42 true)) % 0.37/0.59 (step @p34 :rule nary_cong :premises (@p33 @p32) :args ((or (not @t43) @t41))) % 0.37/0.59 (step @p35 :rule trans :premises (@p34 @p31)) % 0.37/0.59 (step @p36 :rule bool-impl-elim :args (@t43 @t41)) % 0.37/0.59 (step @p37 :rule trans :premises (@p36 @p35)) % 0.37/0.59 (step @p38 :rule cong :premises (@p37) :args (@t45)) % 0.37/0.59 (step @p39 :rule refl :args (@t46)) % 0.37/0.59 (step @p40 :rule refl :args (@t47)) % 0.37/0.59 (step @p41 :rule nary_cong :premises (@p40 @p39 @p38) :args (@t48)) % 0.37/0.59 (step @p42 :rule refl :args (@t49)) % 0.37/0.59 (step @p43 :rule cong :premises (@p42 @p41) :args (@t50)) % 0.37/0.59 (step @p44 :rule cong :premises (@p43) :args (@t52)) % 0.37/0.59 (step @p45 :rule eq_resolve :premises (@p20 @p44)) % 0.37/0.59 (step @p46 :rule instantiate :premises (@p45) :args ((@list @t87 @t88 @t89 @t92))) % 0.37/0.59 (step @p47 :rule aci_norm :args ((= @t94 @t84))) % 0.37/0.59 (step @p48 :rule cong :premises (@p47) :args (@t95)) % 0.37/0.59 (step @p49 :rule quant-merge-prenex :args ((= (forall @t29 @t97) @t95))) % 0.37/0.59 (step @p50 :rule alpha_equiv :args (@t98 (@list @t78 @t76 @t74 @t73) (@list @t58 @t56 @t100 @t99))) % 0.37/0.59 (step @p51 :rule refl :args (@t83)) % 0.37/0.59 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t101)) % 0.37/0.59 (step @p53 :rule quant-miniscope-or :args ((= @t97 @t101))) % 0.37/0.59 (step @p54 :rule trans :premises (@p53 @p52)) % 0.37/0.59 (step @p55 :rule symm :premises (@p54)) % 0.37/0.59 (step @p56 :rule cong :premises (@p55) :args ((forall @t29 (or @t83 @t110)))) % 0.37/0.59 (step @p57 :rule trans :premises (@p56 @p49)) % 0.37/0.59 (step @p58 :rule trans :premises (@p57 @p48)) % 0.37/0.59 (step @p59 :rule bool-impl-elim :args (@t28 @t110)) % 0.37/0.59 (step @p60 :rule cong :premises (@p59) :args ((forall @t29 (=> @t28 @t110)))) % 0.37/0.59 (step @p61 :rule trans :premises (@p60 @p58)) % 0.37/0.59 (step @p62 :rule aci_norm :args ((= @t112 @t108))) % 0.37/0.59 (step @p63 :rule cong :premises (@p62) :args (@t113)) % 0.37/0.59 (step @p64 :rule quant-merge-prenex :args ((= (forall @t68 @t115) @t113))) % 0.37/0.59 (step @p65 :rule alpha_equiv :args (@t116 (@list @t100 @t99) (@list @t54 @t53))) % 0.37/0.59 (step @p66 :rule refl :args (@t105)) % 0.37/0.59 (step @p67 :rule refl :args (@t106)) % 0.37/0.59 (step @p68 :rule refl :args (@t107)) % 0.37/0.59 (step @p69 :rule nary_cong :premises (@p68 @p67 @p66 @p65) :args (@t117)) % 0.37/0.59 (step @p70 :rule quant-miniscope-or :args ((= @t115 @t117))) % 0.37/0.59 (step @p71 :rule trans :premises (@p70 @p69)) % 0.37/0.59 (step @p72 :rule symm :premises (@p71)) % 0.37/0.59 (step @p73 :rule cong :premises (@p72) :args ((forall @t68 @t122))) % 0.37/0.59 (step @p74 :rule trans :premises (@p73 @p64)) % 0.37/0.59 (step @p75 :rule trans :premises (@p74 @p63)) % 0.37/0.59 (step @p76 :rule aci_norm :args ((= (or @t123 @t121) @t122))) % 0.37/0.59 (step @p77 :rule refl :args (@t121)) % 0.37/0.59 (step @p78 :rule aci_norm :args ((= (or @t107 (or @t106 @t105)) @t123))) % 0.37/0.59 (step @p79 :rule bool-and-de-morgan :args (@t64 @t63 true)) % 0.37/0.59 (step @p80 :rule nary_cong :premises (@p68 @p79) :args ((or @t107 (not (and @t64 @t63))))) % 0.37/0.59 (step @p81 :rule bool-and-de-morgan :args (@t65 @t64 (and @t63))) % 0.37/0.59 (step @p82 :rule trans :premises (@p81 @p80)) % 0.37/0.59 (step @p83 :rule trans :premises (@p82 @p78)) % 0.37/0.59 (step @p84 :rule nary_cong :premises (@p83 @p77) :args ((or (not @t66) @t121))) % 0.37/0.59 (step @p85 :rule trans :premises (@p84 @p76)) % 0.37/0.59 (step @p86 :rule bool-impl-elim :args (@t66 @t121)) % 0.37/0.59 (step @p87 :rule trans :premises (@p86 @p85)) % 0.37/0.59 (step @p88 :rule cong :premises (@p87) :args ((forall @t68 (=> @t66 @t121)))) % 0.37/0.59 (step @p89 :rule trans :premises (@p88 @p75)) % 0.37/0.59 (step @p90 :rule aci_norm :args ((= (or (or @t119 @t118) @t55) @t120))) % 0.37/0.59 (step @p91 :rule refl :args (@t55)) % 0.37/0.59 (step @p92 :rule bool-and-de-morgan :args (@t59 @t57 true)) % 0.37/0.59 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or (not @t60) @t55))) % 0.37/0.59 (step @p94 :rule trans :premises (@p93 @p90)) % 0.37/0.59 (step @p95 :rule bool-impl-elim :args (@t60 @t55)) % 0.37/0.59 (step @p96 :rule trans :premises (@p95 @p94)) % 0.37/0.59 (step @p97 :rule cong :premises (@p96) :args (@t62)) % 0.37/0.59 (step @p98 :rule refl :args (@t66)) % 0.37/0.59 (step @p99 :rule cong :premises (@p98 @p97) :args (@t67)) % 0.37/0.59 (step @p100 :rule cong :premises (@p99) :args (@t69)) % 0.37/0.59 (step @p101 :rule trans :premises (@p100 @p89)) % 0.37/0.59 (step @p102 :rule refl :args (@t28)) % 0.37/0.59 (step @p103 :rule cong :premises (@p102 @p101) :args (@t70)) % 0.37/0.59 (step @p104 :rule cong :premises (@p103) :args (@t71)) % 0.37/0.59 (step @p105 :rule trans :premises (@p104 @p61)) % 0.37/0.59 (step @p106 :rule cong :premises (@p105) :args (@t72)) % 0.37/0.59 (step @p107 :rule eq_resolve :premises (@p22 @p106)) % 0.37/0.59 (step @p108 :rule skolemize :premises (@p107)) % 0.37/0.59 (step @p109 :rule bool-double-not-elim :args (@t124)) % 0.37/0.59 (step @p110 :rule refl :args (@t133)) % 0.37/0.59 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or @t133 (not @t127)))) % 0.37/0.59 (step @p112 :rule cnf_or_neg :args (@t133 5)) % 0.37/0.59 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 0.37/0.59 (step @p114 :rule reordering :premises (@p113) :args ((or @t124 @t133))) % 0.37/0.59 (step @p115 :rule chain_m_resolution :premises (@p114 @p108) :args (@t124 @t134 @t135)) % 0.37/0.59 (step @p116 :rule cnf_equiv_pos1 :args (@t139)) % 0.37/0.59 (step @p117 :rule reordering :premises (@p116) :args ((or @t127 @t138 (not @t139)))) % 0.37/0.59 (step @p118 :rule chain_m_resolution :premises (@p117 @p115 @p46) :args (@t138 @t140 (@list @t124 @t139))) % 0.37/0.59 (step @p119 :rule cnf_and_pos :args (@t138 1)) % 0.37/0.59 (step @p120 :rule reordering :premises (@p119) :args ((or @t137 (not @t138)))) % 0.37/0.59 (step @p121 :rule chain_m_resolution :premises (@p120 @p118) :args (@t137 @t141 (@list @t138))) % 0.37/0.59 (step @p122 :rule cnf_equiv_pos1 :args (@t144)) % 0.37/0.59 (step @p123 :rule reordering :premises (@p122) :args ((or (not @t137) @t143 (not @t144)))) % 0.37/0.60 (step @p124 :rule chain_m_resolution :premises (@p123 @p121 @p30) :args (@t143 @t140 (@list @t137 @t144))) % 0.37/0.60 (step @p125 :rule bool-impl-elim :args (@t5 @t3)) % 0.37/0.60 (step @p126 :rule cong :premises (@p125) :args (@t7)) % 0.37/0.60 (step @p127 :rule refl :args (@t8)) % 0.37/0.60 (step @p128 :rule cong :premises (@p127 @p126) :args (@t9)) % 0.37/0.60 (step @p129 :rule cong :premises (@p128) :args (@t11)) % 0.37/0.60 (step @p130 :rule eq_resolve :premises (@p1 @p129)) % 0.37/0.60 (step @p131 :rule instantiate :premises (@p130) :args ((@list @t128 @t88))) % 0.37/0.60 (step @p132 :rule bool-double-not-elim :args (@t131)) % 0.37/0.60 (step @p133 :rule nary_cong :premises (@p110 @p132) :args ((or @t133 (not @t132)))) % 0.37/0.60 (step @p134 :rule cnf_or_neg :args (@t133 3)) % 0.37/0.60 (step @p135 :rule eq_resolve :premises (@p134 @p133)) % 0.37/0.60 (step @p136 :rule reordering :premises (@p135) :args ((or @t131 @t133))) % 0.37/0.60 (step @p137 :rule chain_m_resolution :premises (@p136 @p108) :args (@t131 @t134 @t135)) % 0.37/0.60 (step @p138 :rule cnf_equiv_pos1 :args (@t146)) % 0.37/0.60 (step @p139 :rule reordering :premises (@p138) :args ((or @t132 @t145 (not @t146)))) % 0.37/0.60 (step @p140 :rule chain_m_resolution :premises (@p139 @p137 @p131) :args (@t145 @t140 (@list @t131 @t146))) % 0.37/0.60 (step @p141 :rule instantiate :premises (@p140) :args (@t147)) % 0.37/0.60 (step @p142 :rule instantiate :premises (@p45) :args ((@list @t125 @t128 @t89 @t92))) % 0.37/0.60 (step @p143 :rule bool-double-not-elim :args (@t129)) % 0.37/0.60 (step @p144 :rule nary_cong :premises (@p110 @p143) :args ((or @t133 (not @t130)))) % 0.37/0.60 (step @p145 :rule cnf_or_neg :args (@t133 4)) % 0.37/0.60 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 0.37/0.60 (step @p147 :rule reordering :premises (@p146) :args ((or @t129 @t133))) % 0.37/0.60 (step @p148 :rule chain_m_resolution :premises (@p147 @p108) :args (@t129 @t134 @t135)) % 0.37/0.60 (step @p149 :rule cnf_equiv_pos1 :args (@t150)) % 0.37/0.60 (step @p150 :rule reordering :premises (@p149) :args ((or @t130 @t149 (not @t150)))) % 0.37/0.60 (step @p151 :rule chain_m_resolution :premises (@p150 @p148 @p142) :args (@t149 @t140 (@list @t129 @t150))) % 0.37/0.60 (step @p152 :rule cnf_and_pos :args (@t149 0)) % 0.37/0.60 (step @p153 :rule reordering :premises (@p152) :args ((or @t148 (not @t149)))) % 0.37/0.60 (step @p154 :rule chain_m_resolution :premises (@p153 @p151) :args (@t148 @t141 (@list @t149))) % 0.37/0.60 (step @p155 :rule cnf_or_pos :args (@t153)) % 0.37/0.60 (step @p156 :rule reordering :premises (@p155) :args ((or @t152 @t151 (not @t153)))) % 0.37/0.60 (step @p157 :rule chain_m_resolution :premises (@p156 @p154 @p141) :args (@t151 @t140 (@list @t148 @t153))) % 0.37/0.60 (step @p158 :rule cnf_or_neg :args (@t133 6)) % 0.37/0.60 (step @p159 :rule chain_m_resolution :premises (@p158 @p108) :args ((not @t126) @t134 @t135)) % 0.37/0.60 (step @p160 :rule cnf_or_pos :args (@t155)) % 0.37/0.60 (step @p161 :rule reordering :premises (@p160) :args ((or @t126 @t154 @t156))) % 0.37/0.60 (step @p162 :rule chain_m_resolution :premises (@p161 @p159 @p157) :args (@t156 @t157 (@list @t126 @t151))) % 0.37/0.60 (assume-push @p169 @t143) % 0.37/0.60 (step @p164 :rule instantiate :premises (@p124) :args (@t147)) % 0.37/0.60 (step-pop @p170 :rule scope :premises (@p164)) % 0.37/0.60 (step @p165 :rule process_scope :premises (@p170) :args (@t155)) % 0.37/0.60 (step @p167 :rule implies_elim :premises (@p165)) % 0.37/0.60 (step @p168 false :rule chain_m_resolution :premises (@p167 @p162 @p124) :args (false @t157 (@list @t155 @t143))) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------