%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET720+4 : TPTP v9.2.1. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.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 08:48:30 AM UTC 2026 % Result : Theorem 0.42s 0.61s % Output : Proof 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET720+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n018.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 16:10:20 EDT 2026 % 0.19/0.35 % CPUTime : % 0.34/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.42/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.42/0.61 % SZS status Theorem % 0.42/0.61 % SZS output start Proof % 0.42/0.61 ( % 0.42/0.61 (declare-sort $$unsorted 0) % 0.42/0.61 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.empty_set $$unsorted) % 0.42/0.61 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.61 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.42/0.61 (define @t1 () (@var "B" $$unsorted)) % 0.42/0.61 (define @t2 () (@var "X" $$unsorted)) % 0.42/0.61 (define @t3 () (tptp.member @t2 @t1)) % 0.42/0.61 (define @t4 () (@var "A" $$unsorted)) % 0.42/0.61 (define @t5 () (tptp.member @t2 @t4)) % 0.42/0.61 (define @t6 () (@list @t2)) % 0.42/0.61 (define @t7 () (tptp.subset @t4 @t1)) % 0.42/0.61 (define @t8 () (@list @t4 @t1)) % 0.42/0.61 (define @t9 () (@list @t2 @t4)) % 0.42/0.61 (define @t10 () (@list @t2 @t4 @t1)) % 0.42/0.61 (define @t11 () (@var "E" $$unsorted)) % 0.42/0.61 (define @t12 () (= @t2 @t4)) % 0.42/0.61 (define @t13 () (@var "Y" $$unsorted)) % 0.42/0.61 (define @t14 () (tptp.member @t2 @t13)) % 0.42/0.61 (define @t15 () (tptp.member @t13 @t4)) % 0.42/0.61 (define @t16 () (@list @t13)) % 0.42/0.61 (define @t17 () (@var "Y2" $$unsorted)) % 0.42/0.61 (define @t18 () (@var "Y1" $$unsorted)) % 0.42/0.61 (define @t19 () (= @t18 @t17)) % 0.42/0.61 (define @t20 () (@var "F" $$unsorted)) % 0.42/0.61 (define @t21 () (tptp.apply @t20 @t2 @t17)) % 0.42/0.61 (define @t22 () (tptp.apply @t20 @t2 @t18)) % 0.42/0.61 (define @t23 () (and @t22 @t21)) % 0.42/0.61 (define @t24 () (=> @t23 @t19)) % 0.42/0.61 (define @t25 () (tptp.member @t17 @t1)) % 0.42/0.61 (define @t26 () (tptp.member @t18 @t1)) % 0.42/0.61 (define @t27 () (and @t5 @t26 @t25)) % 0.42/0.61 (define @t28 () (@list @t2 @t18 @t17)) % 0.42/0.61 (define @t29 () (forall @t28 (=> @t27 @t24))) % 0.42/0.61 (define @t30 () (tptp.apply @t20 @t2 @t13)) % 0.42/0.61 (define @t31 () (tptp.member @t13 @t1)) % 0.42/0.61 (define @t32 () (and @t31 @t30)) % 0.42/0.61 (define @t33 () (exists @t16 @t32)) % 0.42/0.61 (define @t34 () (=> @t5 @t33)) % 0.42/0.61 (define @t35 () (forall @t6 @t34)) % 0.42/0.61 (define @t36 () (and @t35 @t29)) % 0.42/0.61 (define @t37 () (tptp.maps @t20 @t4 @t1)) % 0.42/0.61 (define @t38 () (= @t37 @t36)) % 0.42/0.61 (define @t39 () (@list @t20 @t4 @t1)) % 0.42/0.61 (define @t40 () (forall @t39 @t38)) % 0.42/0.61 (define @t41 () (@var "Z" $$unsorted)) % 0.42/0.61 (define @t42 () (@var "G" $$unsorted)) % 0.42/0.61 (define @t43 () (exists @t16 (and @t31 @t30 (tptp.apply @t42 @t13 @t41)))) % 0.42/0.61 (define @t44 () (@var "H" $$unsorted)) % 0.42/0.61 (define @t45 () (@var "C" $$unsorted)) % 0.42/0.61 (define @t46 () (and @t5 (tptp.member @t41 @t45))) % 0.42/0.61 (define @t47 () (tptp.apply @t42 @t2 @t17)) % 0.42/0.61 (define @t48 () (and @t22 @t47)) % 0.42/0.61 (define @t49 () (=> @t48 @t19)) % 0.42/0.61 (define @t50 () (forall @t28 (=> @t27 @t49))) % 0.42/0.61 (define @t51 () (tptp.equal_maps @t20 @t42 @t4 @t1)) % 0.42/0.61 (define @t52 () (= @t51 @t50)) % 0.42/0.61 (define @t53 () (forall (@list @t20 @t42 @t4 @t1) @t52)) % 0.42/0.61 (define @t54 () (@var "X2" $$unsorted)) % 0.42/0.61 (define @t55 () (@var "X1" $$unsorted)) % 0.42/0.61 (define @t56 () (tptp.member @t54 @t4)) % 0.42/0.61 (define @t57 () (tptp.member @t55 @t4)) % 0.42/0.61 (define @t58 () (tptp.injective @t20 @t4 @t1)) % 0.42/0.61 (define @t59 () (tptp.surjective @t20 @t4 @t1)) % 0.42/0.61 (define @t60 () (tptp.one_to_one @t20 @t4 @t1)) % 0.42/0.61 (define @t61 () (and @t5 @t31)) % 0.42/0.61 (define @t62 () (tptp.inverse_function @t20 @t4 @t1)) % 0.42/0.61 (define @t63 () (= @t30 (tptp.apply @t62 @t13 @t2))) % 0.42/0.61 (define @t64 () (@list @t20 @t4 @t1 @t2 @t13)) % 0.42/0.61 (define @t65 () (forall @t64 (=> @t61 @t63))) % 0.42/0.61 (define @t66 () (exists @t6 (and @t5 @t30))) % 0.42/0.61 (define @t67 () (@var "S" $$unsorted)) % 0.42/0.61 (define @t68 () (tptp.apply @t67 @t18 @t17)) % 0.42/0.61 (define @t69 () (tptp.apply @t20 @t54 @t17)) % 0.42/0.61 (define @t70 () (tptp.apply @t20 @t55 @t18)) % 0.42/0.61 (define @t71 () (@var "R" $$unsorted)) % 0.42/0.61 (define @t72 () (tptp.apply @t71 @t55 @t54)) % 0.42/0.61 (define @t73 () (and @t57 @t26 @t56 @t25 @t72 @t70 @t69)) % 0.42/0.61 (define @t74 () (@list @t55 @t18 @t54 @t17)) % 0.42/0.61 (define @t75 () (@list @t20 @t4 @t71 @t1 @t67)) % 0.42/0.61 (define @t76 () (tptp.equal_maps (tptp.inverse_function @t62 @t1 @t4) @t20 @t4 @t1)) % 0.42/0.61 (define @t77 () (and @t37 @t60)) % 0.42/0.61 (define @t78 () (forall @t39 (=> @t77 @t76))) % 0.42/0.61 (define @t79 () (not @t78)) % 0.42/0.61 (define @t80 () (not @t47)) % 0.42/0.61 (define @t81 () (not @t22)) % 0.42/0.61 (define @t82 () (not @t25)) % 0.42/0.61 (define @t83 () (not @t26)) % 0.42/0.61 (define @t84 () (not @t5)) % 0.42/0.61 (define @t85 () (or @t81 @t80 @t19)) % 0.42/0.61 (define @t86 () (or @t84 @t83 @t82)) % 0.42/0.61 (define @t87 () (not @t27)) % 0.42/0.61 (define @t88 () (not @t60)) % 0.42/0.61 (define @t89 () (not @t37)) % 0.42/0.61 (define @t90 () (or @t89 @t88 @t76)) % 0.42/0.61 (define @t91 () (forall @t39 @t90)) % 0.42/0.61 (define @t92 () (@quantifiers_skolemize @t91 2)) % 0.42/0.61 (define @t93 () (@quantifiers_skolemize @t91 1)) % 0.42/0.61 (define @t94 () (@quantifiers_skolemize @t91 0)) % 0.42/0.61 (define @t95 () (tptp.inverse_function @t94 @t93 @t92)) % 0.42/0.61 (define @t96 () (tptp.inverse_function @t95 @t92 @t93)) % 0.42/0.61 (define @t97 () (tptp.equal_maps @t96 @t94 @t93 @t92)) % 0.42/0.61 (define @t98 () (tptp.maps @t94 @t93 @t92)) % 0.42/0.61 (define @t99 () (not @t98)) % 0.42/0.61 (define @t100 () (or @t99 (not (tptp.one_to_one @t94 @t93 @t92)) @t97)) % 0.42/0.61 (define @t101 () (@list true)) % 0.42/0.61 (define @t102 () (@list @t100)) % 0.42/0.61 (define @t103 () (not (tptp.apply @t94 @t2 @t17))) % 0.42/0.61 (define @t104 () (not (tptp.member @t17 @t92))) % 0.42/0.61 (define @t105 () (not (tptp.member @t18 @t92))) % 0.42/0.61 (define @t106 () (not (tptp.member @t2 @t93))) % 0.42/0.61 (define @t107 () (forall @t28 (or @t106 @t105 @t104 (not (tptp.apply @t96 @t2 @t18)) @t103 @t19))) % 0.42/0.61 (define @t108 () (= @t97 @t107)) % 0.42/0.61 (define @t109 () (not @t107)) % 0.42/0.61 (define @t110 () (@list true false)) % 0.42/0.61 (define @t111 () (@quantifiers_skolemize @t107 0)) % 0.42/0.61 (define @t112 () (tptp.member @t111 @t93)) % 0.42/0.61 (define @t113 () (@quantifiers_skolemize @t107 2)) % 0.42/0.61 (define @t114 () (@quantifiers_skolemize @t107 1)) % 0.42/0.61 (define @t115 () (= @t114 @t113)) % 0.42/0.61 (define @t116 () (tptp.apply @t94 @t111 @t113)) % 0.42/0.61 (define @t117 () (not @t116)) % 0.42/0.61 (define @t118 () (tptp.apply @t96 @t111 @t114)) % 0.42/0.61 (define @t119 () (not @t118)) % 0.42/0.61 (define @t120 () (tptp.member @t113 @t92)) % 0.42/0.61 (define @t121 () (not @t120)) % 0.42/0.61 (define @t122 () (tptp.member @t114 @t92)) % 0.42/0.61 (define @t123 () (not @t122)) % 0.42/0.61 (define @t124 () (not @t112)) % 0.42/0.61 (define @t125 () (or @t124 @t123 @t121 @t119 @t117 @t115)) % 0.42/0.61 (define @t126 () (@list @t125)) % 0.42/0.61 (define @t127 () (not @t31)) % 0.42/0.61 (define @t128 () (or @t84 @t127 @t63)) % 0.42/0.61 (define @t129 () (tptp.apply @t95 @t114 @t111)) % 0.42/0.61 (define @t130 () (or @t123 @t124 (= @t129 @t118))) % 0.42/0.61 (define @t131 () (forall @t64 @t128)) % 0.42/0.61 (define @t132 () (= @t118 @t129)) % 0.42/0.61 (define @t133 () (or @t123 @t124 @t132)) % 0.42/0.61 (define @t134 () (@list false)) % 0.42/0.61 (define @t135 () (@list @t131)) % 0.42/0.61 (define @t136 () (@list false false)) % 0.42/0.61 (define @t137 () (not @t21)) % 0.42/0.61 (define @t138 () (or @t81 @t137 @t19)) % 0.42/0.61 (define @t139 () (not (forall @t16 (or @t127 (not @t30))))) % 0.42/0.61 (define @t140 () (forall @t16 (not @t32))) % 0.42/0.61 (define @t141 () (not @t140)) % 0.42/0.61 (define @t142 () (forall @t28 (or @t106 @t105 @t104 (not (tptp.apply @t94 @t2 @t18)) @t103 @t19))) % 0.42/0.61 (define @t143 () (and (forall @t6 (or @t106 (not (forall @t16 (or (not (tptp.member @t13 @t92)) (not (tptp.apply @t94 @t2 @t13))))))) @t142)) % 0.42/0.61 (define @t144 () (= @t98 @t143)) % 0.42/0.61 (define @t145 () (tptp.apply @t94 @t111 @t114)) % 0.42/0.61 (define @t146 () (not @t145)) % 0.42/0.61 (define @t147 () (or @t124 @t123 @t121 @t146 @t117 @t115)) % 0.42/0.61 (define @t148 () (= @t129 @t145)) % 0.42/0.61 (define @t149 () (not @t148)) % 0.42/0.61 (define @t150 () (or @t124 @t123 (= @t145 @t129))) % 0.42/0.61 (define @t151 () (or @t124 @t123 @t148)) % 0.42/0.61 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.42/0.61 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.42/0.61 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.42/0.61 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.42/0.61 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.42/0.61 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.42/0.61 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.42/0.61 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.42/0.61 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.42/0.61 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.42/0.61 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.42/0.61 (assume @p12 @t40) % 0.42/0.61 (assume @p13 (forall (@list @t44 @t42 @t20 @t4 @t1 @t45) (= (tptp.compose_predicate @t44 @t42 @t20 @t4 @t1 @t45) (forall (@list @t2 @t41) (=> @t46 (= (tptp.apply @t44 @t2 @t41) @t43)))))) % 0.42/0.61 (assume @p14 (forall (@list @t42 @t20 @t4 @t1 @t45 @t2 @t41) (=> @t46 (= (tptp.apply (tptp.compose_function @t42 @t20 @t4 @t1 @t45) @t2 @t41) @t43)))) % 0.42/0.61 (assume @p15 @t53) % 0.42/0.61 (assume @p16 (forall (@list @t20 @t4) (= (tptp.identity @t20 @t4) (forall @t6 (=> @t5 (tptp.apply @t20 @t2 @t2)))))) % 0.42/0.61 (assume @p17 (forall @t39 (= @t58 (forall (@list @t55 @t54 @t13) (=> (and @t57 @t56 @t31) (=> (and (tptp.apply @t20 @t55 @t13) (tptp.apply @t20 @t54 @t13)) (= @t55 @t54))))))) % 0.42/0.61 (assume @p18 (forall @t39 (= @t59 (forall @t16 (=> @t31 (exists (@list @t11) (and (tptp.member @t11 @t4) (tptp.apply @t20 @t11 @t13)))))))) % 0.42/0.61 (assume @p19 (forall @t39 (= @t60 (and @t58 @t59)))) % 0.42/0.61 (assume @p20 (forall (@list @t42 @t20 @t4 @t1) (= (tptp.inverse_predicate @t42 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t61 (= @t30 (tptp.apply @t42 @t13 @t2))))))) % 0.42/0.61 (assume @p21 @t65) % 0.42/0.61 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t66))) % 0.42/0.61 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t31 @t66)))) % 0.42/0.61 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t33))) % 0.42/0.61 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t33)))) % 0.42/0.61 (assume @p26 (forall @t75 (= (tptp.increasing @t20 @t4 @t71 @t1 @t67) (forall @t74 (=> @t73 @t68))))) % 0.42/0.61 (assume @p27 (forall @t75 (= (tptp.decreasing @t20 @t4 @t71 @t1 @t67) (forall @t74 (=> @t73 (tptp.apply @t67 @t17 @t18)))))) % 0.42/0.61 (assume @p28 (forall @t75 (= (tptp.isomorphism @t20 @t4 @t71 @t1 @t67) (and @t37 @t60 (forall @t74 (=> (and @t57 @t26 @t56 @t25 @t70 @t69) (= @t72 @t68))))))) % 0.42/0.61 (assume @p29 @t79) % 0.42/0.61 (assume @p30 true) % 0.42/0.61 (step @p31 :rule aci_norm :args ((= (or @t86 @t85) (or @t84 @t83 @t82 @t81 @t80 @t19)))) % 0.42/0.61 (step @p32 :rule aci_norm :args ((= (or (or @t81 @t80) @t19) @t85))) % 0.42/0.61 (step @p33 :rule refl :args (@t19)) % 0.42/0.61 (step @p34 :rule bool-and-de-morgan :args (@t22 @t47 true)) % 0.42/0.61 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or (not @t48) @t19))) % 0.42/0.61 (step @p36 :rule trans :premises (@p35 @p32)) % 0.42/0.61 (step @p37 :rule bool-impl-elim :args (@t48 @t19)) % 0.42/0.61 (step @p38 :rule trans :premises (@p37 @p36)) % 0.42/0.61 (step @p39 :rule aci_norm :args ((= (or @t84 (or @t83 @t82)) @t86))) % 0.42/0.61 (step @p40 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 0.42/0.61 (step @p41 :rule refl :args (@t84)) % 0.42/0.61 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or @t84 (not (and @t26 @t25))))) % 0.42/0.61 (step @p43 :rule bool-and-de-morgan :args (@t5 @t26 (and @t25))) % 0.42/0.61 (step @p44 :rule trans :premises (@p43 @p42)) % 0.42/0.61 (step @p45 :rule trans :premises (@p44 @p39)) % 0.42/0.61 (step @p46 :rule nary_cong :premises (@p45 @p38) :args ((or @t87 @t49))) % 0.42/0.61 (step @p47 :rule trans :premises (@p46 @p31)) % 0.42/0.61 (step @p48 :rule bool-impl-elim :args (@t27 @t49)) % 0.42/0.61 (step @p49 :rule trans :premises (@p48 @p47)) % 0.42/0.61 (step @p50 :rule cong :premises (@p49) :args (@t50)) % 0.42/0.61 (step @p51 :rule refl :args (@t51)) % 0.42/0.61 (step @p52 :rule cong :premises (@p51 @p50) :args (@t52)) % 0.42/0.61 (step @p53 :rule cong :premises (@p52) :args (@t53)) % 0.42/0.61 (step @p54 :rule eq_resolve :premises (@p15 @p53)) % 0.42/0.61 (step @p55 :rule instantiate :premises (@p54) :args ((@list @t96 @t94 @t93 @t92))) % 0.42/0.61 (step @p56 :rule aci_norm :args ((= (or (or @t89 @t88) @t76) @t90))) % 0.42/0.61 (step @p57 :rule refl :args (@t76)) % 0.42/0.61 (step @p58 :rule bool-and-de-morgan :args (@t37 @t60 true)) % 0.42/0.61 (step @p59 :rule nary_cong :premises (@p58 @p57) :args ((or (not @t77) @t76))) % 0.42/0.61 (step @p60 :rule trans :premises (@p59 @p56)) % 0.42/0.61 (step @p61 :rule bool-impl-elim :args (@t77 @t76)) % 0.42/0.61 (step @p62 :rule trans :premises (@p61 @p60)) % 0.42/0.61 (step @p63 :rule cong :premises (@p62) :args (@t78)) % 0.42/0.61 (step @p64 :rule cong :premises (@p63) :args (@t79)) % 0.42/0.61 (step @p65 :rule eq_resolve :premises (@p29 @p64)) % 0.42/0.61 (step @p66 :rule skolemize :premises (@p65)) % 0.42/0.61 (step @p67 :rule cnf_or_neg :args (@t100 2)) % 0.42/0.61 (step @p68 :rule chain_m_resolution :premises (@p67 @p66) :args ((not @t97) @t101 @t102)) % 0.42/0.61 (step @p69 :rule cnf_equiv_pos2 :args (@t108)) % 0.42/0.61 (step @p70 :rule reordering :premises (@p69) :args ((or @t97 @t109 (not @t108)))) % 0.42/0.61 (step @p71 :rule chain_m_resolution :premises (@p70 @p68 @p55) :args (@t109 @t110 (@list @t97 @t108))) % 0.42/0.61 (step @p72 :rule skolemize :premises (@p71)) % 0.42/0.61 (step @p73 :rule bool-double-not-elim :args (@t112)) % 0.42/0.61 (step @p74 :rule refl :args (@t125)) % 0.42/0.61 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t125 (not @t124)))) % 0.42/0.61 (step @p76 :rule cnf_or_neg :args (@t125 0)) % 0.42/0.61 (step @p77 :rule eq_resolve :premises (@p76 @p75)) % 0.42/0.61 (step @p78 :rule reordering :premises (@p77) :args ((or @t112 @t125))) % 0.42/0.61 (step @p79 :rule chain_m_resolution :premises (@p78 @p72) :args (@t112 @t101 @t126)) % 0.42/0.61 (step @p80 :rule bool-double-not-elim :args (@t122)) % 0.42/0.61 (step @p81 :rule nary_cong :premises (@p74 @p80) :args ((or @t125 (not @t123)))) % 0.42/0.61 (step @p82 :rule cnf_or_neg :args (@t125 1)) % 0.42/0.61 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.42/0.61 (step @p84 :rule reordering :premises (@p83) :args ((or @t122 @t125))) % 0.42/0.61 (step @p85 :rule chain_m_resolution :premises (@p84 @p72) :args (@t122 @t101 @t126)) % 0.42/0.61 (step @p86 :rule aci_norm :args ((= (or (or @t84 @t127) @t63) @t128))) % 0.42/0.61 (step @p87 :rule refl :args (@t63)) % 0.42/0.61 (step @p88 :rule bool-and-de-morgan :args (@t5 @t31 true)) % 0.42/0.61 (step @p89 :rule nary_cong :premises (@p88 @p87) :args ((or (not @t61) @t63))) % 0.42/0.61 (step @p90 :rule trans :premises (@p89 @p86)) % 0.42/0.61 (step @p91 :rule bool-impl-elim :args (@t61 @t63)) % 0.42/0.61 (step @p92 :rule trans :premises (@p91 @p90)) % 0.42/0.61 (step @p93 :rule cong :premises (@p92) :args (@t65)) % 0.42/0.61 (step @p94 :rule eq_resolve :premises (@p21 @p93)) % 0.42/0.61 (step @p95 :rule eq-symm :args (@t129 @t118)) % 0.42/0.61 (step @p96 :rule refl :args (@t124)) % 0.42/0.61 (step @p97 :rule refl :args (@t123)) % 0.42/0.61 (step @p98 :rule nary_cong :premises (@p97 @p96 @p95) :args (@t130)) % 0.42/0.61 (step @p99 :rule refl :args (@t131)) % 0.42/0.61 (step @p100 :rule cong :premises (@p99 @p98) :args ((=> @t131 @t130))) % 0.42/0.61 (assume-push @p196 @t131) % 0.42/0.61 (step @p102 :rule instantiate :premises (@p94) :args ((@list @t95 @t92 @t93 @t114 @t111))) % 0.42/0.61 (step-pop @p197 :rule scope :premises (@p102)) % 0.42/0.61 (step @p103 :rule process_scope :premises (@p197) :args (@t130)) % 0.42/0.61 (step @p105 :rule eq_resolve :premises (@p103 @p100)) % 0.42/0.61 (step @p106 :rule implies_elim :premises (@p105)) % 0.42/0.61 (step @p107 :rule chain_m_resolution :premises (@p106 @p94) :args (@t133 @t134 @t135)) % 0.42/0.61 (step @p108 :rule cnf_or_pos :args (@t133)) % 0.42/0.61 (step @p109 :rule reordering :premises (@p108) :args ((or @t124 @t123 @t132 (not @t133)))) % 0.42/0.61 (step @p110 :rule chain_m_resolution :premises (@p109 @p79 @p85 @p107) :args (@t132 (@list false false false) (@list @t112 @t122 @t133))) % 0.42/0.61 (step @p111 :rule bool-double-not-elim :args (@t118)) % 0.42/0.61 (step @p112 :rule nary_cong :premises (@p74 @p111) :args ((or @t125 (not @t119)))) % 0.42/0.61 (step @p113 :rule cnf_or_neg :args (@t125 3)) % 0.42/0.61 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 0.42/0.61 (step @p115 :rule reordering :premises (@p114) :args ((or @t118 @t125))) % 0.42/0.61 (step @p116 :rule chain_m_resolution :premises (@p115 @p72) :args (@t118 @t101 @t126)) % 0.42/0.61 (step @p117 :rule cnf_equiv_pos1 :args (@t132)) % 0.42/0.61 (step @p118 :rule reordering :premises (@p117) :args ((or @t119 @t129 (not @t132)))) % 0.42/0.61 (step @p119 :rule chain_m_resolution :premises (@p118 @p116 @p110) :args (@t129 @t136 (@list @t118 @t132))) % 0.42/0.61 (step @p120 :rule aci_norm :args ((= (or @t86 @t138) (or @t84 @t83 @t82 @t81 @t137 @t19)))) % 0.42/0.61 (step @p121 :rule aci_norm :args ((= (or (or @t81 @t137) @t19) @t138))) % 0.42/0.61 (step @p122 :rule bool-and-de-morgan :args (@t22 @t21 true)) % 0.42/0.61 (step @p123 :rule nary_cong :premises (@p122 @p33) :args ((or (not @t23) @t19))) % 0.42/0.61 (step @p124 :rule trans :premises (@p123 @p121)) % 0.42/0.61 (step @p125 :rule bool-impl-elim :args (@t23 @t19)) % 0.42/0.61 (step @p126 :rule trans :premises (@p125 @p124)) % 0.42/0.61 (step @p127 :rule nary_cong :premises (@p45 @p126) :args ((or @t87 @t24))) % 0.42/0.61 (step @p128 :rule trans :premises (@p127 @p120)) % 0.42/0.61 (step @p129 :rule bool-impl-elim :args (@t27 @t24)) % 0.42/0.61 (step @p130 :rule trans :premises (@p129 @p128)) % 0.42/0.61 (step @p131 :rule cong :premises (@p130) :args (@t29)) % 0.42/0.61 (step @p132 :rule bool-impl-elim :args (@t5 @t139)) % 0.42/0.61 (step @p133 :rule cong :premises (@p132) :args ((forall @t6 (=> @t5 @t139)))) % 0.42/0.61 (step @p134 :rule bool-and-de-morgan :args (@t31 @t30 true)) % 0.42/0.61 (step @p135 :rule cong :premises (@p134) :args (@t140)) % 0.42/0.61 (step @p136 :rule cong :premises (@p135) :args (@t141)) % 0.42/0.61 (step @p137 :rule exists-elim :args ((= @t33 @t141))) % 0.42/0.61 (step @p138 :rule trans :premises (@p137 @p136)) % 0.42/0.61 (step @p139 :rule refl :args (@t5)) % 0.42/0.61 (step @p140 :rule cong :premises (@p139 @p138) :args (@t34)) % 0.42/0.61 (step @p141 :rule cong :premises (@p140) :args (@t35)) % 0.42/0.61 (step @p142 :rule trans :premises (@p141 @p133)) % 0.42/0.61 (step @p143 :rule nary_cong :premises (@p142 @p131) :args (@t36)) % 0.42/0.61 (step @p144 :rule refl :args (@t37)) % 0.42/0.61 (step @p145 :rule cong :premises (@p144 @p143) :args (@t38)) % 0.42/0.61 (step @p146 :rule cong :premises (@p145) :args (@t40)) % 0.42/0.61 (step @p147 :rule eq_resolve :premises (@p12 @p146)) % 0.42/0.61 (step @p148 :rule instantiate :premises (@p147) :args ((@list @t94 @t93 @t92))) % 0.42/0.61 (step @p149 :rule bool-double-not-elim :args (@t98)) % 0.42/0.61 (step @p150 :rule refl :args (@t100)) % 0.42/0.61 (step @p151 :rule nary_cong :premises (@p150 @p149) :args ((or @t100 (not @t99)))) % 0.42/0.61 (step @p152 :rule cnf_or_neg :args (@t100 0)) % 0.42/0.61 (step @p153 :rule eq_resolve :premises (@p152 @p151)) % 0.42/0.61 (step @p154 :rule reordering :premises (@p153) :args ((or @t98 @t100))) % 0.42/0.61 (step @p155 :rule chain_m_resolution :premises (@p154 @p66) :args (@t98 @t101 @t102)) % 0.42/0.61 (step @p156 :rule cnf_equiv_pos1 :args (@t144)) % 0.42/0.61 (step @p157 :rule reordering :premises (@p156) :args ((or @t99 @t143 (not @t144)))) % 0.42/0.61 (step @p158 :rule chain_m_resolution :premises (@p157 @p155 @p148) :args (@t143 @t136 (@list @t98 @t144))) % 0.42/0.61 (step @p159 :rule cnf_and_pos :args (@t143 1)) % 0.42/0.61 (step @p160 :rule reordering :premises (@p159) :args ((or @t142 (not @t143)))) % 0.42/0.61 (step @p161 :rule chain_m_resolution :premises (@p160 @p158) :args (@t142 @t134 (@list @t143))) % 0.42/0.61 (step @p162 :rule instantiate :premises (@p161) :args ((@list @t111 @t114 @t113))) % 0.42/0.61 (step @p163 :rule cnf_or_neg :args (@t125 5)) % 0.42/0.61 (step @p164 :rule chain_m_resolution :premises (@p163 @p72) :args ((not @t115) @t101 @t126)) % 0.42/0.61 (step @p165 :rule bool-double-not-elim :args (@t116)) % 0.42/0.61 (step @p166 :rule nary_cong :premises (@p74 @p165) :args ((or @t125 (not @t117)))) % 0.42/0.61 (step @p167 :rule cnf_or_neg :args (@t125 4)) % 0.42/0.61 (step @p168 :rule eq_resolve :premises (@p167 @p166)) % 0.42/0.61 (step @p169 :rule reordering :premises (@p168) :args ((or @t116 @t125))) % 0.42/0.61 (step @p170 :rule chain_m_resolution :premises (@p169 @p72) :args (@t116 @t101 @t126)) % 0.42/0.61 (step @p171 :rule bool-double-not-elim :args (@t120)) % 0.42/0.61 (step @p172 :rule nary_cong :premises (@p74 @p171) :args ((or @t125 (not @t121)))) % 0.42/0.61 (step @p173 :rule cnf_or_neg :args (@t125 2)) % 0.42/0.61 (step @p174 :rule eq_resolve :premises (@p173 @p172)) % 0.42/0.61 (step @p175 :rule reordering :premises (@p174) :args ((or @t120 @t125))) % 0.42/0.61 (step @p176 :rule chain_m_resolution :premises (@p175 @p72) :args (@t120 @t101 @t126)) % 0.42/0.61 (step @p177 :rule cnf_or_pos :args (@t147)) % 0.42/0.61 (step @p178 :rule reordering :premises (@p177) :args ((or @t124 @t123 @t121 @t117 @t115 @t146 (not @t147)))) % 0.42/0.61 (step @p179 :rule chain_m_resolution :premises (@p178 @p79 @p85 @p176 @p170 @p164 @p162) :args (@t146 (@list false false false false true false) (@list @t112 @t122 @t120 @t116 @t115 @t147))) % 0.42/0.61 (step @p180 :rule cnf_equiv_pos1 :args (@t148)) % 0.42/0.61 (step @p181 :rule reordering :premises (@p180) :args ((or @t145 (not @t129) @t149))) % 0.42/0.61 (step @p182 :rule chain_m_resolution :premises (@p181 @p179 @p119) :args (@t149 @t110 (@list @t145 @t129))) % 0.42/0.61 (step @p183 :rule eq-symm :args (@t145 @t129)) % 0.42/0.61 (step @p184 :rule nary_cong :premises (@p96 @p97 @p183) :args (@t150)) % 0.42/0.61 (step @p185 :rule cong :premises (@p99 @p184) :args ((=> @t131 @t150))) % 0.42/0.61 (assume-push @p198 @t131) % 0.42/0.61 (step @p187 :rule instantiate :premises (@p94) :args ((@list @t94 @t93 @t92 @t111 @t114))) % 0.42/0.61 (step-pop @p199 :rule scope :premises (@p187)) % 0.42/0.61 (step @p188 :rule process_scope :premises (@p199) :args (@t150)) % 0.42/0.61 (step @p190 :rule eq_resolve :premises (@p188 @p185)) % 0.42/0.61 (step @p191 :rule implies_elim :premises (@p190)) % 0.42/0.61 (step @p192 :rule chain_m_resolution :premises (@p191 @p94) :args (@t151 @t134 @t135)) % 0.42/0.61 (step @p193 :rule cnf_or_pos :args (@t151)) % 0.42/0.61 (step @p194 :rule reordering :premises (@p193) :args ((or @t124 @t123 @t148 (not @t151)))) % 0.42/0.61 (step @p195 false :rule chain_m_resolution :premises (@p194 @p192 @p182 @p85 @p79) :args (false (@list false true false false) (@list @t151 @t148 @t122 @t112))) % 0.42/0.61 ) % 0.42/0.61 % SZS output end Proof % 0.42/0.62 % cvc5 exiting %------------------------------------------------------------------------------