%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET722+4 : TPTP v9.2.1. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n013.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 0.38s 0.65s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET722+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n013.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:10:00 EDT 2026 % 0.18/0.35 % CPUTime : % 0.32/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.65 % SZS status Theorem % 0.38/0.65 % SZS output start Proof % 0.38/0.65 ( % 0.38/0.65 (declare-sort $$unsorted 0) % 0.38/0.65 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.empty_set $$unsorted) % 0.38/0.65 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.65 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.65 (define @t1 () (@var "B" $$unsorted)) % 0.38/0.65 (define @t2 () (@var "X" $$unsorted)) % 0.38/0.65 (define @t3 () (tptp.member @t2 @t1)) % 0.38/0.65 (define @t4 () (@var "A" $$unsorted)) % 0.38/0.65 (define @t5 () (tptp.member @t2 @t4)) % 0.38/0.65 (define @t6 () (@list @t2)) % 0.38/0.65 (define @t7 () (tptp.subset @t4 @t1)) % 0.38/0.65 (define @t8 () (@list @t4 @t1)) % 0.38/0.65 (define @t9 () (@list @t2 @t4)) % 0.38/0.65 (define @t10 () (@list @t2 @t4 @t1)) % 0.38/0.65 (define @t11 () (@var "E" $$unsorted)) % 0.38/0.65 (define @t12 () (= @t2 @t4)) % 0.38/0.65 (define @t13 () (@var "Y" $$unsorted)) % 0.38/0.65 (define @t14 () (tptp.member @t2 @t13)) % 0.38/0.65 (define @t15 () (tptp.member @t13 @t4)) % 0.38/0.65 (define @t16 () (@list @t13)) % 0.38/0.65 (define @t17 () (@var "Y2" $$unsorted)) % 0.38/0.65 (define @t18 () (@var "Y1" $$unsorted)) % 0.38/0.65 (define @t19 () (= @t18 @t17)) % 0.38/0.65 (define @t20 () (@var "F" $$unsorted)) % 0.38/0.65 (define @t21 () (tptp.apply @t20 @t2 @t18)) % 0.38/0.65 (define @t22 () (tptp.member @t17 @t1)) % 0.38/0.65 (define @t23 () (tptp.member @t18 @t1)) % 0.38/0.65 (define @t24 () (and @t5 @t23 @t22)) % 0.38/0.65 (define @t25 () (@list @t2 @t18 @t17)) % 0.38/0.65 (define @t26 () (tptp.apply @t20 @t2 @t13)) % 0.38/0.65 (define @t27 () (tptp.member @t13 @t1)) % 0.38/0.65 (define @t28 () (exists @t16 (and @t27 @t26))) % 0.38/0.65 (define @t29 () (tptp.maps @t20 @t4 @t1)) % 0.38/0.65 (define @t30 () (@list @t20 @t4 @t1)) % 0.38/0.65 (define @t31 () (@var "Z" $$unsorted)) % 0.38/0.65 (define @t32 () (@var "G" $$unsorted)) % 0.38/0.65 (define @t33 () (tptp.apply @t32 @t13 @t31)) % 0.38/0.65 (define @t34 () (and @t27 @t26 @t33)) % 0.38/0.65 (define @t35 () (exists @t16 @t34)) % 0.38/0.65 (define @t36 () (@var "H" $$unsorted)) % 0.38/0.65 (define @t37 () (@var "C" $$unsorted)) % 0.38/0.65 (define @t38 () (tptp.member @t31 @t37)) % 0.38/0.65 (define @t39 () (and @t5 @t38)) % 0.38/0.65 (define @t40 () (tptp.compose_function @t32 @t20 @t4 @t1 @t37)) % 0.38/0.65 (define @t41 () (tptp.apply @t40 @t2 @t31)) % 0.38/0.65 (define @t42 () (=> @t39 (= @t41 @t35))) % 0.38/0.65 (define @t43 () (@list @t32 @t20 @t4 @t1 @t37 @t2 @t31)) % 0.38/0.65 (define @t44 () (forall @t43 @t42)) % 0.38/0.65 (define @t45 () (@var "X2" $$unsorted)) % 0.38/0.65 (define @t46 () (@var "X1" $$unsorted)) % 0.38/0.65 (define @t47 () (tptp.member @t45 @t4)) % 0.38/0.65 (define @t48 () (tptp.member @t46 @t4)) % 0.38/0.65 (define @t49 () (tptp.injective @t20 @t4 @t1)) % 0.38/0.65 (define @t50 () (tptp.apply @t20 @t11 @t13)) % 0.38/0.65 (define @t51 () (tptp.member @t11 @t4)) % 0.38/0.65 (define @t52 () (and @t51 @t50)) % 0.38/0.65 (define @t53 () (@list @t11)) % 0.38/0.65 (define @t54 () (exists @t53 @t52)) % 0.38/0.65 (define @t55 () (=> @t27 @t54)) % 0.38/0.65 (define @t56 () (forall @t16 @t55)) % 0.38/0.65 (define @t57 () (tptp.surjective @t20 @t4 @t1)) % 0.38/0.65 (define @t58 () (= @t57 @t56)) % 0.38/0.65 (define @t59 () (forall @t30 @t58)) % 0.38/0.65 (define @t60 () (tptp.one_to_one @t20 @t4 @t1)) % 0.38/0.65 (define @t61 () (and @t5 @t27)) % 0.38/0.65 (define @t62 () (exists @t6 (and @t5 @t26))) % 0.38/0.65 (define @t63 () (@var "S" $$unsorted)) % 0.38/0.65 (define @t64 () (tptp.apply @t63 @t18 @t17)) % 0.38/0.65 (define @t65 () (tptp.apply @t20 @t45 @t17)) % 0.38/0.65 (define @t66 () (tptp.apply @t20 @t46 @t18)) % 0.38/0.65 (define @t67 () (@var "R" $$unsorted)) % 0.38/0.65 (define @t68 () (tptp.apply @t67 @t46 @t45)) % 0.38/0.65 (define @t69 () (and @t48 @t23 @t47 @t22 @t68 @t66 @t65)) % 0.38/0.65 (define @t70 () (@list @t46 @t18 @t45 @t17)) % 0.38/0.65 (define @t71 () (@list @t20 @t4 @t67 @t1 @t63)) % 0.38/0.65 (define @t72 () (tptp.surjective @t32 @t1 @t37)) % 0.38/0.65 (define @t73 () (tptp.surjective @t40 @t4 @t37)) % 0.38/0.65 (define @t74 () (tptp.maps @t32 @t1 @t37)) % 0.38/0.65 (define @t75 () (and @t29 @t74 @t73)) % 0.38/0.65 (define @t76 () (@list @t20 @t32 @t4 @t1 @t37)) % 0.38/0.65 (define @t77 () (forall @t76 (=> @t75 @t72))) % 0.38/0.65 (define @t78 () (not @t77)) % 0.38/0.65 (define @t79 () (not (forall @t53 (or (not @t51) (not @t50))))) % 0.38/0.65 (define @t80 () (forall @t53 (not @t52))) % 0.38/0.65 (define @t81 () (not @t80)) % 0.38/0.65 (define @t82 () (not @t73)) % 0.38/0.65 (define @t83 () (not @t74)) % 0.38/0.65 (define @t84 () (not @t29)) % 0.38/0.65 (define @t85 () (or @t84 @t83 @t82 @t72)) % 0.38/0.65 (define @t86 () (forall @t76 @t85)) % 0.38/0.65 (define @t87 () (@quantifiers_skolemize @t86 4)) % 0.38/0.65 (define @t88 () (@quantifiers_skolemize @t86 3)) % 0.38/0.65 (define @t89 () (@quantifiers_skolemize @t86 1)) % 0.38/0.65 (define @t90 () (or @t84 @t83 @t82)) % 0.38/0.65 (define @t91 () (tptp.surjective @t89 @t88 @t87)) % 0.38/0.65 (define @t92 () (@quantifiers_skolemize @t86 2)) % 0.38/0.65 (define @t93 () (@quantifiers_skolemize @t86 0)) % 0.38/0.65 (define @t94 () (tptp.compose_function @t89 @t93 @t92 @t88 @t87)) % 0.38/0.65 (define @t95 () (tptp.surjective @t94 @t92 @t87)) % 0.38/0.65 (define @t96 () (not @t95)) % 0.38/0.65 (define @t97 () (or (not (tptp.maps @t93 @t92 @t88)) (not (tptp.maps @t89 @t88 @t87)) @t96 @t91)) % 0.38/0.65 (define @t98 () (@list true)) % 0.38/0.65 (define @t99 () (@list @t97)) % 0.38/0.65 (define @t100 () (not (tptp.member @t11 @t88))) % 0.38/0.65 (define @t101 () (not (tptp.member @t13 @t87))) % 0.38/0.65 (define @t102 () (forall @t16 (or @t101 (not (forall @t53 (or @t100 (not (tptp.apply @t89 @t11 @t13)))))))) % 0.38/0.65 (define @t103 () (= @t91 @t102)) % 0.38/0.65 (define @t104 () (not @t102)) % 0.38/0.65 (define @t105 () (@list true false)) % 0.38/0.65 (define @t106 () (@quantifiers_skolemize @t102 0)) % 0.38/0.65 (define @t107 () (forall @t53 (or @t100 (not (tptp.apply @t89 @t11 @t106))))) % 0.38/0.65 (define @t108 () (not @t107)) % 0.38/0.65 (define @t109 () (tptp.member @t106 @t87)) % 0.38/0.65 (define @t110 () (not @t109)) % 0.38/0.65 (define @t111 () (or @t110 @t108)) % 0.38/0.65 (define @t112 () (@list @t111)) % 0.38/0.65 (define @t113 () (not @t33)) % 0.38/0.65 (define @t114 () (not @t26)) % 0.38/0.65 (define @t115 () (not @t27)) % 0.38/0.65 (define @t116 () (or @t115 @t114 @t113)) % 0.38/0.65 (define @t117 () (not (forall @t16 @t116))) % 0.38/0.65 (define @t118 () (= @t41 @t117)) % 0.38/0.65 (define @t119 () (not @t38)) % 0.38/0.65 (define @t120 () (not @t5)) % 0.38/0.65 (define @t121 () (forall @t16 (not @t34))) % 0.38/0.65 (define @t122 () (not @t121)) % 0.38/0.65 (define @t123 () (not (tptp.member @t11 @t92))) % 0.38/0.65 (define @t124 () (forall @t53 (or @t123 (not (tptp.apply @t94 @t11 @t106))))) % 0.38/0.65 (define @t125 () (@quantifiers_skolemize @t124 0)) % 0.38/0.65 (define @t126 () (forall @t16 (or @t101 (not (forall @t53 (or @t123 (not (tptp.apply @t94 @t11 @t13)))))))) % 0.38/0.65 (define @t127 () (= @t95 @t126)) % 0.38/0.65 (define @t128 () (@list false false)) % 0.38/0.65 (define @t129 () (not @t124)) % 0.38/0.65 (define @t130 () (or @t110 @t129)) % 0.38/0.65 (define @t131 () (tptp.member @t125 @t92)) % 0.38/0.65 (define @t132 () (tptp.apply @t94 @t125 @t106)) % 0.38/0.65 (define @t133 () (not @t132)) % 0.38/0.65 (define @t134 () (not @t131)) % 0.38/0.65 (define @t135 () (or @t134 @t133)) % 0.38/0.65 (define @t136 () (@list @t135)) % 0.38/0.65 (define @t137 () (forall @t16 (or (not (tptp.member @t13 @t88)) (not (tptp.apply @t93 @t125 @t13)) (not (tptp.apply @t89 @t13 @t106))))) % 0.38/0.65 (define @t138 () (not @t137)) % 0.38/0.65 (define @t139 () (= @t132 @t138)) % 0.38/0.65 (define @t140 () (or @t134 @t110 @t139)) % 0.38/0.65 (define @t141 () (@quantifiers_skolemize @t137 0)) % 0.38/0.65 (define @t142 () (tptp.apply @t89 @t141 @t106)) % 0.38/0.65 (define @t143 () (not @t142)) % 0.38/0.65 (define @t144 () (tptp.member @t141 @t88)) % 0.38/0.65 (define @t145 () (not @t144)) % 0.38/0.65 (define @t146 () (or @t145 (not (tptp.apply @t93 @t125 @t141)) @t143)) % 0.38/0.65 (define @t147 () (@list @t146)) % 0.38/0.65 (define @t148 () (or @t145 @t143)) % 0.38/0.65 (define @t149 () (not @t148)) % 0.38/0.65 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.38/0.65 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.38/0.65 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.38/0.65 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.38/0.65 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.38/0.65 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.38/0.65 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.38/0.65 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.38/0.65 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.38/0.65 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.38/0.65 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.38/0.65 (assume @p12 (forall @t30 (= @t29 (and (forall @t6 (=> @t5 @t28)) (forall @t25 (=> @t24 (=> (and @t21 (tptp.apply @t20 @t2 @t17)) @t19))))))) % 0.38/0.65 (assume @p13 (forall (@list @t36 @t32 @t20 @t4 @t1 @t37) (= (tptp.compose_predicate @t36 @t32 @t20 @t4 @t1 @t37) (forall (@list @t2 @t31) (=> @t39 (= (tptp.apply @t36 @t2 @t31) @t35)))))) % 0.38/0.65 (assume @p14 @t44) % 0.38/0.65 (assume @p15 (forall (@list @t20 @t32 @t4 @t1) (= (tptp.equal_maps @t20 @t32 @t4 @t1) (forall @t25 (=> @t24 (=> (and @t21 (tptp.apply @t32 @t2 @t17)) @t19)))))) % 0.38/0.65 (assume @p16 (forall (@list @t20 @t4) (= (tptp.identity @t20 @t4) (forall @t6 (=> @t5 (tptp.apply @t20 @t2 @t2)))))) % 0.38/0.65 (assume @p17 (forall @t30 (= @t49 (forall (@list @t46 @t45 @t13) (=> (and @t48 @t47 @t27) (=> (and (tptp.apply @t20 @t46 @t13) (tptp.apply @t20 @t45 @t13)) (= @t46 @t45))))))) % 0.38/0.65 (assume @p18 @t59) % 0.38/0.65 (assume @p19 (forall @t30 (= @t60 (and @t49 @t57)))) % 0.38/0.65 (assume @p20 (forall (@list @t32 @t20 @t4 @t1) (= (tptp.inverse_predicate @t32 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t61 (= @t26 (tptp.apply @t32 @t13 @t2))))))) % 0.38/0.65 (assume @p21 (forall (@list @t20 @t4 @t1 @t2 @t13) (=> @t61 (= @t26 (tptp.apply (tptp.inverse_function @t20 @t4 @t1) @t13 @t2))))) % 0.38/0.65 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t62))) % 0.38/0.65 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t27 @t62)))) % 0.38/0.65 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t28))) % 0.38/0.65 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t28)))) % 0.38/0.65 (assume @p26 (forall @t71 (= (tptp.increasing @t20 @t4 @t67 @t1 @t63) (forall @t70 (=> @t69 @t64))))) % 0.38/0.65 (assume @p27 (forall @t71 (= (tptp.decreasing @t20 @t4 @t67 @t1 @t63) (forall @t70 (=> @t69 (tptp.apply @t63 @t17 @t18)))))) % 0.38/0.65 (assume @p28 (forall @t71 (= (tptp.isomorphism @t20 @t4 @t67 @t1 @t63) (and @t29 @t60 (forall @t70 (=> (and @t48 @t23 @t47 @t22 @t66 @t65) (= @t68 @t64))))))) % 0.38/0.65 (assume @p29 @t78) % 0.38/0.65 (assume @p30 true) % 0.38/0.65 (step @p31 :rule bool-impl-elim :args (@t27 @t79)) % 0.38/0.65 (step @p32 :rule cong :premises (@p31) :args ((forall @t16 (=> @t27 @t79)))) % 0.38/0.65 (step @p33 :rule bool-and-de-morgan :args (@t51 @t50 true)) % 0.38/0.65 (step @p34 :rule cong :premises (@p33) :args (@t80)) % 0.38/0.65 (step @p35 :rule cong :premises (@p34) :args (@t81)) % 0.38/0.65 (step @p36 :rule exists-elim :args ((= @t54 @t81))) % 0.38/0.65 (step @p37 :rule trans :premises (@p36 @p35)) % 0.38/0.65 (step @p38 :rule refl :args (@t27)) % 0.38/0.65 (step @p39 :rule cong :premises (@p38 @p37) :args (@t55)) % 0.38/0.65 (step @p40 :rule cong :premises (@p39) :args (@t56)) % 0.38/0.65 (step @p41 :rule trans :premises (@p40 @p32)) % 0.38/0.65 (step @p42 :rule refl :args (@t57)) % 0.38/0.65 (step @p43 :rule cong :premises (@p42 @p41) :args (@t58)) % 0.38/0.65 (step @p44 :rule cong :premises (@p43) :args (@t59)) % 0.38/0.65 (step @p45 :rule eq_resolve :premises (@p18 @p44)) % 0.38/0.65 (step @p46 :rule instantiate :premises (@p45) :args ((@list @t89 @t88 @t87))) % 0.38/0.65 (step @p47 :rule aci_norm :args ((= (or @t90 @t72) @t85))) % 0.38/0.65 (step @p48 :rule refl :args (@t72)) % 0.38/0.65 (step @p49 :rule aci_norm :args ((= (or @t84 (or @t83 @t82)) @t90))) % 0.38/0.65 (step @p50 :rule bool-and-de-morgan :args (@t74 @t73 true)) % 0.38/0.65 (step @p51 :rule refl :args (@t84)) % 0.38/0.65 (step @p52 :rule nary_cong :premises (@p51 @p50) :args ((or @t84 (not (and @t74 @t73))))) % 0.38/0.65 (step @p53 :rule bool-and-de-morgan :args (@t29 @t74 (and @t73))) % 0.38/0.65 (step @p54 :rule trans :premises (@p53 @p52)) % 0.38/0.65 (step @p55 :rule trans :premises (@p54 @p49)) % 0.38/0.65 (step @p56 :rule nary_cong :premises (@p55 @p48) :args ((or (not @t75) @t72))) % 0.38/0.65 (step @p57 :rule trans :premises (@p56 @p47)) % 0.38/0.65 (step @p58 :rule bool-impl-elim :args (@t75 @t72)) % 0.38/0.65 (step @p59 :rule trans :premises (@p58 @p57)) % 0.38/0.65 (step @p60 :rule cong :premises (@p59) :args (@t77)) % 0.38/0.65 (step @p61 :rule cong :premises (@p60) :args (@t78)) % 0.38/0.65 (step @p62 :rule eq_resolve :premises (@p29 @p61)) % 0.38/0.65 (step @p63 :rule skolemize :premises (@p62)) % 0.38/0.65 (step @p64 :rule cnf_or_neg :args (@t97 3)) % 0.38/0.65 (step @p65 :rule chain_m_resolution :premises (@p64 @p63) :args ((not @t91) @t98 @t99)) % 0.38/0.65 (step @p66 :rule cnf_equiv_pos2 :args (@t103)) % 0.38/0.65 (step @p67 :rule reordering :premises (@p66) :args ((or @t91 @t104 (not @t103)))) % 0.38/0.65 (step @p68 :rule chain_m_resolution :premises (@p67 @p65 @p46) :args (@t104 @t105 (@list @t91 @t103))) % 0.38/0.65 (step @p69 :rule skolemize :premises (@p68)) % 0.38/0.65 (step @p70 :rule bool-double-not-elim :args (@t107)) % 0.38/0.65 (step @p71 :rule refl :args (@t111)) % 0.38/0.65 (step @p72 :rule nary_cong :premises (@p71 @p70) :args ((or @t111 (not @t108)))) % 0.38/0.65 (step @p73 :rule cnf_or_neg :args (@t111 1)) % 0.38/0.65 (step @p74 :rule eq_resolve :premises (@p73 @p72)) % 0.38/0.65 (step @p75 :rule reordering :premises (@p74) :args ((or @t107 @t111))) % 0.38/0.65 (step @p76 :rule chain_m_resolution :premises (@p75 @p69) :args (@t107 @t98 @t112)) % 0.38/0.65 (step @p77 :rule aci_norm :args ((= (or (or @t120 @t119) @t118) (or @t120 @t119 @t118)))) % 0.38/0.65 (step @p78 :rule refl :args (@t118)) % 0.38/0.65 (step @p79 :rule bool-and-de-morgan :args (@t5 @t38 true)) % 0.38/0.65 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or (not @t39) @t118))) % 0.38/0.65 (step @p81 :rule trans :premises (@p80 @p77)) % 0.38/0.65 (step @p82 :rule bool-impl-elim :args (@t39 @t118)) % 0.38/0.65 (step @p83 :rule trans :premises (@p82 @p81)) % 0.38/0.65 (step @p84 :rule cong :premises (@p83) :args ((forall @t43 (=> @t39 @t118)))) % 0.38/0.65 (step @p85 :rule eq-symm :args (@t117 @t41)) % 0.38/0.65 (step @p86 :rule refl :args (@t41)) % 0.38/0.65 (step @p87 :rule aci_norm :args ((= (or @t115 (or @t114 @t113)) @t116))) % 0.38/0.65 (step @p88 :rule bool-and-de-morgan :args (@t26 @t33 true)) % 0.38/0.65 (step @p89 :rule refl :args (@t115)) % 0.38/0.65 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or @t115 (not (and @t26 @t33))))) % 0.38/0.65 (step @p91 :rule bool-and-de-morgan :args (@t27 @t26 (and @t33))) % 0.38/0.65 (step @p92 :rule trans :premises (@p91 @p90)) % 0.38/0.65 (step @p93 :rule trans :premises (@p92 @p87)) % 0.38/0.65 (step @p94 :rule cong :premises (@p93) :args (@t121)) % 0.38/0.65 (step @p95 :rule cong :premises (@p94) :args (@t122)) % 0.38/0.65 (step @p96 :rule exists-elim :args ((= @t35 @t122))) % 0.38/0.65 (step @p97 :rule trans :premises (@p96 @p95)) % 0.38/0.65 (step @p98 :rule cong :premises (@p97 @p86) :args ((= @t35 @t41))) % 0.38/0.65 (step @p99 :rule trans :premises (@p98 @p85)) % 0.38/0.65 (step @p100 :rule eq-symm :args (@t41 @t35)) % 0.38/0.65 (step @p101 :rule trans :premises (@p100 @p99)) % 0.38/0.65 (step @p102 :rule refl :args (@t39)) % 0.38/0.65 (step @p103 :rule cong :premises (@p102 @p101) :args (@t42)) % 0.38/0.65 (step @p104 :rule cong :premises (@p103) :args (@t44)) % 0.38/0.65 (step @p105 :rule trans :premises (@p104 @p84)) % 0.38/0.65 (step @p106 :rule eq_resolve :premises (@p14 @p105)) % 0.38/0.65 (step @p107 :rule instantiate :premises (@p106) :args ((@list @t89 @t93 @t92 @t88 @t87 @t125 @t106))) % 0.38/0.65 (step @p108 :rule instantiate :premises (@p45) :args ((@list @t94 @t92 @t87))) % 0.38/0.65 (step @p109 :rule bool-double-not-elim :args (@t95)) % 0.38/0.65 (step @p110 :rule refl :args (@t97)) % 0.38/0.65 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or @t97 (not @t96)))) % 0.38/0.65 (step @p112 :rule cnf_or_neg :args (@t97 2)) % 0.38/0.65 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 0.38/0.66 (step @p114 :rule reordering :premises (@p113) :args ((or @t95 @t97))) % 0.38/0.66 (step @p115 :rule chain_m_resolution :premises (@p114 @p63) :args (@t95 @t98 @t99)) % 0.38/0.66 (step @p116 :rule cnf_equiv_pos1 :args (@t127)) % 0.38/0.66 (step @p117 :rule reordering :premises (@p116) :args ((or @t96 @t126 (not @t127)))) % 0.38/0.66 (step @p118 :rule chain_m_resolution :premises (@p117 @p115 @p108) :args (@t126 @t128 (@list @t95 @t127))) % 0.38/0.66 (step @p119 :rule instantiate :premises (@p118) :args ((@list @t106))) % 0.38/0.66 (step @p120 :rule bool-double-not-elim :args (@t109)) % 0.38/0.66 (step @p121 :rule nary_cong :premises (@p71 @p120) :args ((or @t111 (not @t110)))) % 0.38/0.66 (step @p122 :rule cnf_or_neg :args (@t111 0)) % 0.38/0.66 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.38/0.66 (step @p124 :rule reordering :premises (@p123) :args ((or @t109 @t111))) % 0.38/0.66 (step @p125 :rule chain_m_resolution :premises (@p124 @p69) :args (@t109 @t98 @t112)) % 0.38/0.66 (step @p126 :rule cnf_or_pos :args (@t130)) % 0.38/0.66 (step @p127 :rule reordering :premises (@p126) :args ((or @t110 @t129 (not @t130)))) % 0.38/0.66 (step @p128 :rule chain_m_resolution :premises (@p127 @p125 @p119) :args (@t129 @t128 (@list @t109 @t130))) % 0.38/0.66 (step @p129 :rule skolemize :premises (@p128)) % 0.38/0.66 (step @p130 :rule bool-double-not-elim :args (@t131)) % 0.38/0.66 (step @p131 :rule refl :args (@t135)) % 0.38/0.66 (step @p132 :rule nary_cong :premises (@p131 @p130) :args ((or @t135 (not @t134)))) % 0.38/0.66 (step @p133 :rule cnf_or_neg :args (@t135 0)) % 0.38/0.66 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.38/0.66 (step @p135 :rule reordering :premises (@p134) :args ((or @t131 @t135))) % 0.38/0.66 (step @p136 :rule chain_m_resolution :premises (@p135 @p129) :args (@t131 @t98 @t136)) % 0.38/0.66 (step @p137 :rule cnf_or_pos :args (@t140)) % 0.38/0.66 (step @p138 :rule reordering :premises (@p137) :args ((or @t110 @t134 @t139 (not @t140)))) % 0.38/0.66 (step @p139 :rule chain_m_resolution :premises (@p138 @p125 @p136 @p107) :args (@t139 (@list false false false) (@list @t109 @t131 @t140))) % 0.38/0.66 (step @p140 :rule bool-double-not-elim :args (@t132)) % 0.38/0.66 (step @p141 :rule nary_cong :premises (@p131 @p140) :args ((or @t135 (not @t133)))) % 0.38/0.66 (step @p142 :rule cnf_or_neg :args (@t135 1)) % 0.38/0.66 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 0.38/0.66 (step @p144 :rule reordering :premises (@p143) :args ((or @t132 @t135))) % 0.38/0.66 (step @p145 :rule chain_m_resolution :premises (@p144 @p129) :args (@t132 @t98 @t136)) % 0.38/0.66 (step @p146 :rule cnf_equiv_pos1 :args (@t139)) % 0.38/0.66 (step @p147 :rule reordering :premises (@p146) :args ((or @t133 @t138 (not @t139)))) % 0.38/0.66 (step @p148 :rule chain_m_resolution :premises (@p147 @p145 @p139) :args (@t138 @t128 (@list @t132 @t139))) % 0.38/0.66 (step @p149 :rule skolemize :premises (@p148)) % 0.38/0.66 (step @p150 :rule bool-double-not-elim :args (@t142)) % 0.38/0.66 (step @p151 :rule refl :args (@t146)) % 0.38/0.66 (step @p152 :rule nary_cong :premises (@p151 @p150) :args ((or @t146 (not @t143)))) % 0.38/0.66 (step @p153 :rule cnf_or_neg :args (@t146 2)) % 0.38/0.66 (step @p154 :rule eq_resolve :premises (@p153 @p152)) % 0.38/0.66 (step @p155 :rule reordering :premises (@p154) :args ((or @t142 @t146))) % 0.38/0.66 (step @p156 :rule chain_m_resolution :premises (@p155 @p149) :args (@t142 @t98 @t147)) % 0.38/0.66 (step @p157 :rule bool-double-not-elim :args (@t144)) % 0.38/0.66 (step @p158 :rule nary_cong :premises (@p151 @p157) :args ((or @t146 (not @t145)))) % 0.38/0.66 (step @p159 :rule cnf_or_neg :args (@t146 0)) % 0.38/0.66 (step @p160 :rule eq_resolve :premises (@p159 @p158)) % 0.38/0.66 (step @p161 :rule reordering :premises (@p160) :args ((or @t144 @t146))) % 0.38/0.66 (step @p162 :rule chain_m_resolution :premises (@p161 @p149) :args (@t144 @t98 @t147)) % 0.38/0.66 (step @p163 :rule cnf_or_pos :args (@t148)) % 0.38/0.66 (step @p164 :rule reordering :premises (@p163) :args ((or @t145 @t143 @t149))) % 0.38/0.66 (step @p165 :rule chain_m_resolution :premises (@p164 @p162 @p156) :args (@t149 @t128 (@list @t144 @t142))) % 0.38/0.66 (assume-push @p172 @t107) % 0.38/0.66 (step @p167 :rule instantiate :premises (@p76) :args ((@list @t141))) % 0.38/0.66 (step-pop @p173 :rule scope :premises (@p167)) % 0.38/0.66 (step @p168 :rule process_scope :premises (@p173) :args (@t148)) % 0.38/0.66 (step @p170 :rule implies_elim :premises (@p168)) % 0.38/0.66 (step @p171 false :rule chain_m_resolution :premises (@p170 @p165 @p76) :args (false @t105 (@list @t148 @t107))) % 0.38/0.66 ) % 0.38/0.66 % SZS output end Proof % 0.38/0.66 % cvc5 exiting %------------------------------------------------------------------------------