%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET715+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 : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:29 AM UTC 2026 % Result : Theorem 0.42s 0.59s % Output : Proof 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET715+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % 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 16:11:05 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.42/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.42/0.59 % SZS status Theorem % 0.42/0.59 % SZS output start Proof % 0.42/0.59 ( % 0.42/0.59 (declare-sort $$unsorted 0) % 0.42/0.59 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.empty_set $$unsorted) % 0.42/0.59 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.42/0.59 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.42/0.59 (define @t1 () (@var "B" $$unsorted)) % 0.42/0.59 (define @t2 () (@var "X" $$unsorted)) % 0.42/0.59 (define @t3 () (tptp.member @t2 @t1)) % 0.42/0.59 (define @t4 () (@var "A" $$unsorted)) % 0.42/0.59 (define @t5 () (tptp.member @t2 @t4)) % 0.42/0.59 (define @t6 () (@list @t2)) % 0.42/0.59 (define @t7 () (tptp.subset @t4 @t1)) % 0.42/0.59 (define @t8 () (@list @t4 @t1)) % 0.42/0.59 (define @t9 () (@list @t2 @t4)) % 0.42/0.59 (define @t10 () (@list @t2 @t4 @t1)) % 0.42/0.59 (define @t11 () (@var "E" $$unsorted)) % 0.42/0.59 (define @t12 () (= @t2 @t4)) % 0.42/0.59 (define @t13 () (@var "Y" $$unsorted)) % 0.42/0.59 (define @t14 () (tptp.member @t2 @t13)) % 0.42/0.59 (define @t15 () (tptp.member @t13 @t4)) % 0.42/0.59 (define @t16 () (@list @t13)) % 0.42/0.59 (define @t17 () (@var "Y2" $$unsorted)) % 0.42/0.59 (define @t18 () (@var "Y1" $$unsorted)) % 0.42/0.59 (define @t19 () (= @t18 @t17)) % 0.42/0.59 (define @t20 () (@var "F" $$unsorted)) % 0.42/0.59 (define @t21 () (tptp.apply @t20 @t2 @t18)) % 0.42/0.59 (define @t22 () (tptp.member @t17 @t1)) % 0.42/0.59 (define @t23 () (tptp.member @t18 @t1)) % 0.42/0.59 (define @t24 () (and @t5 @t23 @t22)) % 0.42/0.59 (define @t25 () (@list @t2 @t18 @t17)) % 0.42/0.59 (define @t26 () (tptp.apply @t20 @t2 @t13)) % 0.42/0.59 (define @t27 () (tptp.member @t13 @t1)) % 0.42/0.59 (define @t28 () (exists @t16 (and @t27 @t26))) % 0.42/0.59 (define @t29 () (tptp.maps @t20 @t4 @t1)) % 0.42/0.59 (define @t30 () (@list @t20 @t4 @t1)) % 0.42/0.59 (define @t31 () (@var "Z" $$unsorted)) % 0.42/0.59 (define @t32 () (@var "G" $$unsorted)) % 0.42/0.59 (define @t33 () (tptp.apply @t32 @t13 @t31)) % 0.42/0.59 (define @t34 () (and @t27 @t26 @t33)) % 0.42/0.59 (define @t35 () (exists @t16 @t34)) % 0.42/0.59 (define @t36 () (@var "H" $$unsorted)) % 0.42/0.59 (define @t37 () (@var "C" $$unsorted)) % 0.42/0.59 (define @t38 () (tptp.member @t31 @t37)) % 0.42/0.59 (define @t39 () (and @t5 @t38)) % 0.42/0.59 (define @t40 () (tptp.apply (tptp.compose_function @t32 @t20 @t4 @t1 @t37) @t2 @t31)) % 0.42/0.59 (define @t41 () (=> @t39 (= @t40 @t35))) % 0.42/0.59 (define @t42 () (@list @t32 @t20 @t4 @t1 @t37 @t2 @t31)) % 0.42/0.59 (define @t43 () (forall @t42 @t41)) % 0.42/0.59 (define @t44 () (tptp.apply @t20 @t2 @t2)) % 0.42/0.59 (define @t45 () (forall @t6 (=> @t5 @t44))) % 0.42/0.59 (define @t46 () (tptp.identity @t20 @t4)) % 0.42/0.59 (define @t47 () (= @t46 @t45)) % 0.42/0.59 (define @t48 () (forall (@list @t20 @t4) @t47)) % 0.42/0.59 (define @t49 () (@var "X2" $$unsorted)) % 0.42/0.59 (define @t50 () (@var "X1" $$unsorted)) % 0.42/0.59 (define @t51 () (tptp.member @t49 @t4)) % 0.42/0.59 (define @t52 () (tptp.member @t50 @t4)) % 0.42/0.59 (define @t53 () (tptp.injective @t20 @t4 @t1)) % 0.42/0.59 (define @t54 () (tptp.apply @t20 @t11 @t13)) % 0.42/0.59 (define @t55 () (tptp.member @t11 @t4)) % 0.42/0.59 (define @t56 () (and @t55 @t54)) % 0.42/0.59 (define @t57 () (@list @t11)) % 0.42/0.59 (define @t58 () (exists @t57 @t56)) % 0.42/0.59 (define @t59 () (=> @t27 @t58)) % 0.42/0.59 (define @t60 () (forall @t16 @t59)) % 0.42/0.59 (define @t61 () (tptp.surjective @t20 @t4 @t1)) % 0.42/0.59 (define @t62 () (= @t61 @t60)) % 0.42/0.59 (define @t63 () (forall @t30 @t62)) % 0.42/0.59 (define @t64 () (tptp.one_to_one @t20 @t4 @t1)) % 0.42/0.59 (define @t65 () (and @t5 @t27)) % 0.42/0.59 (define @t66 () (tptp.inverse_function @t20 @t4 @t1)) % 0.42/0.59 (define @t67 () (= @t26 (tptp.apply @t66 @t13 @t2))) % 0.42/0.59 (define @t68 () (forall (@list @t20 @t4 @t1 @t2 @t13) (=> @t65 @t67))) % 0.42/0.59 (define @t69 () (exists @t6 (and @t5 @t26))) % 0.42/0.59 (define @t70 () (@var "S" $$unsorted)) % 0.42/0.59 (define @t71 () (tptp.apply @t70 @t18 @t17)) % 0.42/0.59 (define @t72 () (tptp.apply @t20 @t49 @t17)) % 0.42/0.59 (define @t73 () (tptp.apply @t20 @t50 @t18)) % 0.42/0.59 (define @t74 () (@var "R" $$unsorted)) % 0.42/0.59 (define @t75 () (tptp.apply @t74 @t50 @t49)) % 0.42/0.59 (define @t76 () (and @t52 @t23 @t51 @t22 @t75 @t73 @t72)) % 0.42/0.59 (define @t77 () (@list @t50 @t18 @t49 @t17)) % 0.42/0.59 (define @t78 () (@list @t20 @t4 @t74 @t1 @t70)) % 0.42/0.59 (define @t79 () (tptp.identity (tptp.compose_function @t20 @t66 @t1 @t4 @t1) @t1)) % 0.42/0.59 (define @t80 () (and @t29 @t64)) % 0.42/0.59 (define @t81 () (forall @t30 (=> @t80 @t79))) % 0.42/0.59 (define @t82 () (not @t81)) % 0.42/0.59 (define @t83 () (not (forall @t57 (or (not @t55) (not @t54))))) % 0.42/0.59 (define @t84 () (forall @t57 (not @t56))) % 0.42/0.59 (define @t85 () (not @t84)) % 0.42/0.59 (define @t86 () (not @t64)) % 0.42/0.59 (define @t87 () (not @t29)) % 0.42/0.59 (define @t88 () (or @t87 @t86 @t79)) % 0.42/0.59 (define @t89 () (forall @t30 @t88)) % 0.42/0.59 (define @t90 () (@quantifiers_skolemize @t89 2)) % 0.42/0.59 (define @t91 () (@quantifiers_skolemize @t89 1)) % 0.42/0.59 (define @t92 () (@quantifiers_skolemize @t89 0)) % 0.42/0.59 (define @t93 () (@list @t92 @t91 @t90)) % 0.42/0.59 (define @t94 () (tptp.one_to_one @t92 @t91 @t90)) % 0.42/0.59 (define @t95 () (tptp.inverse_function @t92 @t91 @t90)) % 0.42/0.59 (define @t96 () (tptp.compose_function @t92 @t95 @t90 @t91 @t90)) % 0.42/0.59 (define @t97 () (tptp.identity @t96 @t90)) % 0.42/0.59 (define @t98 () (not @t94)) % 0.42/0.59 (define @t99 () (or (not (tptp.maps @t92 @t91 @t90)) @t98 @t97)) % 0.42/0.59 (define @t100 () (@list true)) % 0.42/0.59 (define @t101 () (@list @t99)) % 0.42/0.59 (define @t102 () (tptp.surjective @t92 @t91 @t90)) % 0.42/0.59 (define @t103 () (and (tptp.injective @t92 @t91 @t90) @t102)) % 0.42/0.59 (define @t104 () (= @t94 @t103)) % 0.42/0.59 (define @t105 () (@list false false)) % 0.42/0.59 (define @t106 () (not (tptp.member @t11 @t91))) % 0.42/0.59 (define @t107 () (forall @t16 (or (not (tptp.member @t13 @t90)) (not (forall @t57 (or @t106 (not (tptp.apply @t92 @t11 @t13)))))))) % 0.42/0.59 (define @t108 () (= @t102 @t107)) % 0.42/0.59 (define @t109 () (forall @t6 (or (not (tptp.member @t2 @t90)) (tptp.apply @t96 @t2 @t2)))) % 0.42/0.59 (define @t110 () (@quantifiers_skolemize @t109 0)) % 0.42/0.59 (define @t111 () (= @t97 @t109)) % 0.42/0.59 (define @t112 () (not @t109)) % 0.42/0.59 (define @t113 () (@list true false)) % 0.42/0.59 (define @t114 () (tptp.member @t110 @t90)) % 0.42/0.59 (define @t115 () (tptp.apply @t96 @t110 @t110)) % 0.42/0.59 (define @t116 () (not @t114)) % 0.42/0.59 (define @t117 () (or @t116 @t115)) % 0.42/0.59 (define @t118 () (@list @t117)) % 0.42/0.59 (define @t119 () (forall @t57 (or @t106 (not (tptp.apply @t92 @t11 @t110))))) % 0.42/0.59 (define @t120 () (not @t119)) % 0.42/0.59 (define @t121 () (or @t116 @t120)) % 0.42/0.59 (define @t122 () (@quantifiers_skolemize @t119 0)) % 0.42/0.59 (define @t123 () (tptp.apply @t92 @t122 @t110)) % 0.42/0.59 (define @t124 () (not @t123)) % 0.42/0.59 (define @t125 () (tptp.member @t122 @t91)) % 0.42/0.59 (define @t126 () (not @t125)) % 0.42/0.59 (define @t127 () (or @t126 @t124)) % 0.42/0.59 (define @t128 () (@list @t127)) % 0.42/0.59 (define @t129 () (not @t27)) % 0.42/0.59 (define @t130 () (not @t5)) % 0.42/0.59 (define @t131 () (tptp.apply @t95 @t110 @t122)) % 0.42/0.59 (define @t132 () (= @t123 @t131)) % 0.42/0.59 (define @t133 () (or @t126 @t116 @t132)) % 0.42/0.59 (define @t134 () (@list false false false)) % 0.42/0.59 (define @t135 () (not @t33)) % 0.42/0.59 (define @t136 () (not @t26)) % 0.42/0.59 (define @t137 () (or @t129 @t136 @t135)) % 0.42/0.59 (define @t138 () (not (forall @t16 @t137))) % 0.42/0.59 (define @t139 () (= @t40 @t138)) % 0.42/0.59 (define @t140 () (not @t38)) % 0.42/0.59 (define @t141 () (forall @t16 (not @t34))) % 0.42/0.59 (define @t142 () (not @t141)) % 0.42/0.59 (define @t143 () (forall @t16 (or (not (tptp.member @t13 @t91)) (not (tptp.apply @t95 @t110 @t13)) (not (tptp.apply @t92 @t13 @t110))))) % 0.42/0.59 (define @t144 () (not @t143)) % 0.42/0.59 (define @t145 () (= @t115 @t144)) % 0.42/0.59 (define @t146 () (or @t116 @t116 @t145)) % 0.42/0.59 (define @t147 () (not @t145)) % 0.42/0.59 (define @t148 () (not @t131)) % 0.42/0.59 (define @t149 () (or @t126 @t148 @t124)) % 0.42/0.59 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.42/0.59 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.42/0.59 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.42/0.59 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.42/0.59 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.42/0.59 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.42/0.59 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.42/0.59 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.42/0.59 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.42/0.59 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.42/0.59 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.42/0.59 (assume @p12 (forall @t30 (= @t29 (and (forall @t6 (=> @t5 @t28)) (forall @t25 (=> @t24 (=> (and @t21 (tptp.apply @t20 @t2 @t17)) @t19))))))) % 0.42/0.59 (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)))))) % 0.42/0.59 (assume @p14 @t43) % 0.42/0.59 (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)))))) % 0.42/0.59 (assume @p16 @t48) % 0.42/0.59 (assume @p17 (forall @t30 (= @t53 (forall (@list @t50 @t49 @t13) (=> (and @t52 @t51 @t27) (=> (and (tptp.apply @t20 @t50 @t13) (tptp.apply @t20 @t49 @t13)) (= @t50 @t49))))))) % 0.42/0.59 (assume @p18 @t63) % 0.42/0.59 (assume @p19 (forall @t30 (= @t64 (and @t53 @t61)))) % 0.42/0.59 (assume @p20 (forall (@list @t32 @t20 @t4 @t1) (= (tptp.inverse_predicate @t32 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t65 (= @t26 (tptp.apply @t32 @t13 @t2))))))) % 0.42/0.59 (assume @p21 @t68) % 0.42/0.59 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t69))) % 0.42/0.59 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t27 @t69)))) % 0.42/0.59 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t28))) % 0.42/0.59 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t28)))) % 0.42/0.59 (assume @p26 (forall @t78 (= (tptp.increasing @t20 @t4 @t74 @t1 @t70) (forall @t77 (=> @t76 @t71))))) % 0.42/0.59 (assume @p27 (forall @t78 (= (tptp.decreasing @t20 @t4 @t74 @t1 @t70) (forall @t77 (=> @t76 (tptp.apply @t70 @t17 @t18)))))) % 0.42/0.59 (assume @p28 (forall @t78 (= (tptp.isomorphism @t20 @t4 @t74 @t1 @t70) (and @t29 @t64 (forall @t77 (=> (and @t52 @t23 @t51 @t22 @t73 @t72) (= @t75 @t71))))))) % 0.42/0.59 (assume @p29 @t82) % 0.42/0.59 (assume @p30 true) % 0.42/0.59 (step @p31 :rule bool-impl-elim :args (@t27 @t83)) % 0.42/0.59 (step @p32 :rule cong :premises (@p31) :args ((forall @t16 (=> @t27 @t83)))) % 0.42/0.59 (step @p33 :rule bool-and-de-morgan :args (@t55 @t54 true)) % 0.42/0.59 (step @p34 :rule cong :premises (@p33) :args (@t84)) % 0.42/0.59 (step @p35 :rule cong :premises (@p34) :args (@t85)) % 0.42/0.59 (step @p36 :rule exists-elim :args ((= @t58 @t85))) % 0.42/0.59 (step @p37 :rule trans :premises (@p36 @p35)) % 0.42/0.59 (step @p38 :rule refl :args (@t27)) % 0.42/0.59 (step @p39 :rule cong :premises (@p38 @p37) :args (@t59)) % 0.42/0.59 (step @p40 :rule cong :premises (@p39) :args (@t60)) % 0.42/0.59 (step @p41 :rule trans :premises (@p40 @p32)) % 0.42/0.59 (step @p42 :rule refl :args (@t61)) % 0.42/0.59 (step @p43 :rule cong :premises (@p42 @p41) :args (@t62)) % 0.42/0.59 (step @p44 :rule cong :premises (@p43) :args (@t63)) % 0.42/0.59 (step @p45 :rule eq_resolve :premises (@p18 @p44)) % 0.42/0.59 (step @p46 :rule instantiate :premises (@p45) :args (@t93)) % 0.42/0.59 (step @p47 :rule instantiate :premises (@p19) :args (@t93)) % 0.42/0.59 (step @p48 :rule aci_norm :args ((= (or (or @t87 @t86) @t79) @t88))) % 0.42/0.59 (step @p49 :rule refl :args (@t79)) % 0.42/0.59 (step @p50 :rule bool-and-de-morgan :args (@t29 @t64 true)) % 0.42/0.59 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or (not @t80) @t79))) % 0.42/0.59 (step @p52 :rule trans :premises (@p51 @p48)) % 0.42/0.59 (step @p53 :rule bool-impl-elim :args (@t80 @t79)) % 0.42/0.59 (step @p54 :rule trans :premises (@p53 @p52)) % 0.42/0.59 (step @p55 :rule cong :premises (@p54) :args (@t81)) % 0.42/0.59 (step @p56 :rule cong :premises (@p55) :args (@t82)) % 0.42/0.59 (step @p57 :rule eq_resolve :premises (@p29 @p56)) % 0.42/0.59 (step @p58 :rule skolemize :premises (@p57)) % 0.42/0.59 (step @p59 :rule bool-double-not-elim :args (@t94)) % 0.42/0.59 (step @p60 :rule refl :args (@t99)) % 0.42/0.59 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or @t99 (not @t98)))) % 0.42/0.59 (step @p62 :rule cnf_or_neg :args (@t99 1)) % 0.42/0.59 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 0.42/0.59 (step @p64 :rule reordering :premises (@p63) :args ((or @t94 @t99))) % 0.42/0.59 (step @p65 :rule chain_m_resolution :premises (@p64 @p58) :args (@t94 @t100 @t101)) % 0.42/0.59 (step @p66 :rule cnf_equiv_pos1 :args (@t104)) % 0.42/0.59 (step @p67 :rule reordering :premises (@p66) :args ((or @t98 @t103 (not @t104)))) % 0.42/0.59 (step @p68 :rule chain_m_resolution :premises (@p67 @p65 @p47) :args (@t103 @t105 (@list @t94 @t104))) % 0.42/0.59 (step @p69 :rule cnf_and_pos :args (@t103 1)) % 0.42/0.59 (step @p70 :rule reordering :premises (@p69) :args ((or @t102 (not @t103)))) % 0.42/0.59 (step @p71 :rule chain_m_resolution :premises (@p70 @p68) :args (@t102 (@list false) (@list @t103))) % 0.42/0.59 (step @p72 :rule cnf_equiv_pos1 :args (@t108)) % 0.42/0.59 (step @p73 :rule reordering :premises (@p72) :args ((or (not @t102) @t107 (not @t108)))) % 0.42/0.59 (step @p74 :rule chain_m_resolution :premises (@p73 @p71 @p46) :args (@t107 @t105 (@list @t102 @t108))) % 0.42/0.59 (step @p75 :rule instantiate :premises (@p74) :args ((@list @t110))) % 0.42/0.59 (step @p76 :rule bool-impl-elim :args (@t5 @t44)) % 0.42/0.59 (step @p77 :rule cong :premises (@p76) :args (@t45)) % 0.42/0.59 (step @p78 :rule refl :args (@t46)) % 0.42/0.59 (step @p79 :rule cong :premises (@p78 @p77) :args (@t47)) % 0.42/0.59 (step @p80 :rule cong :premises (@p79) :args (@t48)) % 0.42/0.59 (step @p81 :rule eq_resolve :premises (@p16 @p80)) % 0.42/0.59 (step @p82 :rule instantiate :premises (@p81) :args ((@list @t96 @t90))) % 0.42/0.59 (step @p83 :rule cnf_or_neg :args (@t99 2)) % 0.42/0.59 (step @p84 :rule chain_m_resolution :premises (@p83 @p58) :args ((not @t97) @t100 @t101)) % 0.42/0.59 (step @p85 :rule cnf_equiv_pos2 :args (@t111)) % 0.42/0.59 (step @p86 :rule reordering :premises (@p85) :args ((or @t97 @t112 (not @t111)))) % 0.42/0.59 (step @p87 :rule chain_m_resolution :premises (@p86 @p84 @p82) :args (@t112 @t113 (@list @t97 @t111))) % 0.42/0.59 (step @p88 :rule skolemize :premises (@p87)) % 0.42/0.59 (step @p89 :rule bool-double-not-elim :args (@t114)) % 0.42/0.59 (step @p90 :rule refl :args (@t117)) % 0.42/0.59 (step @p91 :rule nary_cong :premises (@p90 @p89) :args ((or @t117 (not @t116)))) % 0.42/0.59 (step @p92 :rule cnf_or_neg :args (@t117 0)) % 0.42/0.59 (step @p93 :rule eq_resolve :premises (@p92 @p91)) % 0.42/0.59 (step @p94 :rule reordering :premises (@p93) :args ((or @t114 @t117))) % 0.42/0.59 (step @p95 :rule chain_m_resolution :premises (@p94 @p88) :args (@t114 @t100 @t118)) % 0.42/0.59 (step @p96 :rule cnf_or_pos :args (@t121)) % 0.42/0.59 (step @p97 :rule reordering :premises (@p96) :args ((or @t116 @t120 (not @t121)))) % 0.42/0.59 (step @p98 :rule chain_m_resolution :premises (@p97 @p95 @p75) :args (@t120 @t105 (@list @t114 @t121))) % 0.42/0.59 (step @p99 :rule skolemize :premises (@p98)) % 0.42/0.59 (step @p100 :rule bool-double-not-elim :args (@t123)) % 0.42/0.59 (step @p101 :rule refl :args (@t127)) % 0.42/0.59 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or @t127 (not @t124)))) % 0.42/0.59 (step @p103 :rule cnf_or_neg :args (@t127 1)) % 0.42/0.59 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.42/0.59 (step @p105 :rule reordering :premises (@p104) :args ((or @t123 @t127))) % 0.42/0.59 (step @p106 :rule chain_m_resolution :premises (@p105 @p99) :args (@t123 @t100 @t128)) % 0.42/0.59 (step @p107 :rule aci_norm :args ((= (or (or @t130 @t129) @t67) (or @t130 @t129 @t67)))) % 0.42/0.59 (step @p108 :rule refl :args (@t67)) % 0.42/0.59 (step @p109 :rule bool-and-de-morgan :args (@t5 @t27 true)) % 0.42/0.59 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or (not @t65) @t67))) % 0.42/0.59 (step @p111 :rule trans :premises (@p110 @p107)) % 0.42/0.59 (step @p112 :rule bool-impl-elim :args (@t65 @t67)) % 0.42/0.59 (step @p113 :rule trans :premises (@p112 @p111)) % 0.42/0.59 (step @p114 :rule cong :premises (@p113) :args (@t68)) % 0.42/0.59 (step @p115 :rule eq_resolve :premises (@p21 @p114)) % 0.42/0.59 (step @p116 :rule instantiate :premises (@p115) :args ((@list @t92 @t91 @t90 @t122 @t110))) % 0.42/0.59 (step @p117 :rule bool-double-not-elim :args (@t125)) % 0.42/0.59 (step @p118 :rule nary_cong :premises (@p101 @p117) :args ((or @t127 (not @t126)))) % 0.42/0.59 (step @p119 :rule cnf_or_neg :args (@t127 0)) % 0.42/0.59 (step @p120 :rule eq_resolve :premises (@p119 @p118)) % 0.42/0.59 (step @p121 :rule reordering :premises (@p120) :args ((or @t125 @t127))) % 0.42/0.59 (step @p122 :rule chain_m_resolution :premises (@p121 @p99) :args (@t125 @t100 @t128)) % 0.42/0.59 (step @p123 :rule cnf_or_pos :args (@t133)) % 0.42/0.59 (step @p124 :rule reordering :premises (@p123) :args ((or @t116 @t126 @t132 (not @t133)))) % 0.42/0.59 (step @p125 :rule chain_m_resolution :premises (@p124 @p95 @p122 @p116) :args (@t132 @t134 (@list @t114 @t125 @t133))) % 0.42/0.59 (step @p126 :rule aci_norm :args ((= (or (or @t130 @t140) @t139) (or @t130 @t140 @t139)))) % 0.42/0.59 (step @p127 :rule refl :args (@t139)) % 0.42/0.59 (step @p128 :rule bool-and-de-morgan :args (@t5 @t38 true)) % 0.42/0.59 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or (not @t39) @t139))) % 0.42/0.59 (step @p130 :rule trans :premises (@p129 @p126)) % 0.42/0.59 (step @p131 :rule bool-impl-elim :args (@t39 @t139)) % 0.42/0.59 (step @p132 :rule trans :premises (@p131 @p130)) % 0.42/0.59 (step @p133 :rule cong :premises (@p132) :args ((forall @t42 (=> @t39 @t139)))) % 0.42/0.59 (step @p134 :rule eq-symm :args (@t138 @t40)) % 0.42/0.59 (step @p135 :rule refl :args (@t40)) % 0.42/0.59 (step @p136 :rule aci_norm :args ((= (or @t129 (or @t136 @t135)) @t137))) % 0.42/0.59 (step @p137 :rule bool-and-de-morgan :args (@t26 @t33 true)) % 0.42/0.59 (step @p138 :rule refl :args (@t129)) % 0.42/0.59 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((or @t129 (not (and @t26 @t33))))) % 0.42/0.59 (step @p140 :rule bool-and-de-morgan :args (@t27 @t26 (and @t33))) % 0.42/0.59 (step @p141 :rule trans :premises (@p140 @p139)) % 0.42/0.59 (step @p142 :rule trans :premises (@p141 @p136)) % 0.42/0.59 (step @p143 :rule cong :premises (@p142) :args (@t141)) % 0.42/0.59 (step @p144 :rule cong :premises (@p143) :args (@t142)) % 0.42/0.59 (step @p145 :rule exists-elim :args ((= @t35 @t142))) % 0.42/0.59 (step @p146 :rule trans :premises (@p145 @p144)) % 0.42/0.59 (step @p147 :rule cong :premises (@p146 @p135) :args ((= @t35 @t40))) % 0.42/0.59 (step @p148 :rule trans :premises (@p147 @p134)) % 0.42/0.59 (step @p149 :rule eq-symm :args (@t40 @t35)) % 0.42/0.59 (step @p150 :rule trans :premises (@p149 @p148)) % 0.42/0.59 (step @p151 :rule refl :args (@t39)) % 0.42/0.59 (step @p152 :rule cong :premises (@p151 @p150) :args (@t41)) % 0.42/0.59 (step @p153 :rule cong :premises (@p152) :args (@t43)) % 0.42/0.59 (step @p154 :rule trans :premises (@p153 @p133)) % 0.42/0.59 (step @p155 :rule eq_resolve :premises (@p14 @p154)) % 0.42/0.59 (step @p156 :rule instantiate :premises (@p155) :args ((@list @t92 @t95 @t90 @t91 @t90 @t110 @t110))) % 0.42/0.59 (step @p157 :rule cnf_or_pos :args (@t146)) % 0.42/0.59 (step @p158 :rule factoring :premises (@p157)) % 0.42/0.59 (step @p159 :rule reordering :premises (@p158) :args ((or @t116 @t145 (not @t146)))) % 0.42/0.59 (step @p160 :rule chain_m_resolution :premises (@p159 @p95 @p156) :args (@t145 @t105 (@list @t114 @t146))) % 0.42/0.59 (step @p161 :rule cnf_or_neg :args (@t117 1)) % 0.42/0.59 (step @p162 :rule chain_m_resolution :premises (@p161 @p88) :args ((not @t115) @t100 @t118)) % 0.42/0.59 (step @p163 :rule bool-double-not-elim :args (@t143)) % 0.42/0.59 (step @p164 :rule refl :args (@t115)) % 0.42/0.59 (step @p165 :rule refl :args (@t147)) % 0.42/0.59 (step @p166 :rule nary_cong :premises (@p165 @p164 @p163) :args ((or @t147 @t115 (not @t144)))) % 0.42/0.59 (step @p167 :rule cnf_equiv_pos2 :args (@t145)) % 0.42/0.59 (step @p168 :rule eq_resolve :premises (@p167 @p166)) % 0.42/0.59 (step @p169 :rule reordering :premises (@p168) :args ((or @t115 @t143 @t147))) % 0.42/0.59 (step @p170 :rule chain_m_resolution :premises (@p169 @p162 @p160) :args (@t143 @t113 (@list @t115 @t145))) % 0.42/0.59 (step @p171 :rule instantiate :premises (@p170) :args ((@list @t122))) % 0.42/0.59 (step @p172 :rule cnf_or_pos :args (@t149)) % 0.42/0.59 (step @p173 :rule reordering :premises (@p172) :args ((or @t126 @t124 @t148 (not @t149)))) % 0.42/0.59 (step @p174 :rule chain_m_resolution :premises (@p173 @p122 @p106 @p171) :args (@t148 @t134 (@list @t125 @t123 @t149))) % 0.42/0.59 (step @p175 :rule cnf_equiv_pos1 :args (@t132)) % 0.42/0.60 (step @p176 :rule reordering :premises (@p175) :args ((or @t124 @t131 (not @t132)))) % 0.42/0.60 (step @p177 false :rule chain_m_resolution :premises (@p176 @p174 @p125 @p106) :args (false (@list true false false) (@list @t131 @t132 @t123))) % 0.42/0.60 ) % 0.42/0.60 % SZS output end Proof % 0.42/0.60 % cvc5 exiting %------------------------------------------------------------------------------