%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET731+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 : n008.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 08:48:32 AM UTC 2026 % Result : Theorem 0.38s 0.62s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET731+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.00/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n008.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:10:33 EDT 2026 % 0.16/0.35 % CPUTime : % 0.26/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.62 % SZS status Theorem % 0.38/0.62 % SZS output start Proof % 0.38/0.62 ( % 0.38/0.62 (declare-sort $$unsorted 0) % 0.38/0.62 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.empty_set $$unsorted) % 0.38/0.62 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (define @t1 () (@var "B" $$unsorted)) % 0.38/0.62 (define @t2 () (@var "X" $$unsorted)) % 0.38/0.62 (define @t3 () (tptp.member @t2 @t1)) % 0.38/0.62 (define @t4 () (@var "A" $$unsorted)) % 0.38/0.62 (define @t5 () (tptp.member @t2 @t4)) % 0.38/0.62 (define @t6 () (@list @t2)) % 0.38/0.62 (define @t7 () (tptp.subset @t4 @t1)) % 0.38/0.62 (define @t8 () (@list @t4 @t1)) % 0.38/0.62 (define @t9 () (@list @t2 @t4)) % 0.38/0.62 (define @t10 () (@list @t2 @t4 @t1)) % 0.38/0.62 (define @t11 () (@var "E" $$unsorted)) % 0.38/0.62 (define @t12 () (= @t2 @t4)) % 0.38/0.62 (define @t13 () (@var "Y" $$unsorted)) % 0.38/0.62 (define @t14 () (tptp.member @t2 @t13)) % 0.38/0.62 (define @t15 () (tptp.member @t13 @t4)) % 0.38/0.62 (define @t16 () (@list @t13)) % 0.38/0.62 (define @t17 () (@var "Y2" $$unsorted)) % 0.38/0.62 (define @t18 () (@var "Y1" $$unsorted)) % 0.38/0.62 (define @t19 () (= @t18 @t17)) % 0.38/0.62 (define @t20 () (@var "F" $$unsorted)) % 0.38/0.62 (define @t21 () (tptp.apply @t20 @t2 @t18)) % 0.38/0.62 (define @t22 () (tptp.member @t17 @t1)) % 0.38/0.62 (define @t23 () (tptp.member @t18 @t1)) % 0.38/0.62 (define @t24 () (and @t5 @t23 @t22)) % 0.38/0.62 (define @t25 () (@list @t2 @t18 @t17)) % 0.38/0.62 (define @t26 () (tptp.apply @t20 @t2 @t13)) % 0.38/0.62 (define @t27 () (tptp.member @t13 @t1)) % 0.38/0.62 (define @t28 () (exists @t16 (and @t27 @t26))) % 0.38/0.62 (define @t29 () (tptp.maps @t20 @t4 @t1)) % 0.38/0.62 (define @t30 () (@list @t20 @t4 @t1)) % 0.38/0.62 (define @t31 () (@var "Z" $$unsorted)) % 0.38/0.62 (define @t32 () (@var "G" $$unsorted)) % 0.38/0.62 (define @t33 () (exists @t16 (and @t27 @t26 (tptp.apply @t32 @t13 @t31)))) % 0.38/0.62 (define @t34 () (@var "H" $$unsorted)) % 0.38/0.62 (define @t35 () (@var "C" $$unsorted)) % 0.38/0.62 (define @t36 () (and @t5 (tptp.member @t31 @t35))) % 0.38/0.62 (define @t37 () (@list @t20 @t32 @t4 @t1)) % 0.38/0.62 (define @t38 () (@var "X2" $$unsorted)) % 0.38/0.62 (define @t39 () (@var "X1" $$unsorted)) % 0.38/0.62 (define @t40 () (tptp.member @t38 @t4)) % 0.38/0.62 (define @t41 () (tptp.member @t39 @t4)) % 0.38/0.62 (define @t42 () (tptp.injective @t20 @t4 @t1)) % 0.38/0.62 (define @t43 () (tptp.apply @t20 @t11 @t13)) % 0.38/0.62 (define @t44 () (tptp.member @t11 @t4)) % 0.38/0.62 (define @t45 () (and @t44 @t43)) % 0.38/0.62 (define @t46 () (@list @t11)) % 0.38/0.62 (define @t47 () (exists @t46 @t45)) % 0.38/0.62 (define @t48 () (=> @t27 @t47)) % 0.38/0.62 (define @t49 () (forall @t16 @t48)) % 0.38/0.62 (define @t50 () (tptp.surjective @t20 @t4 @t1)) % 0.38/0.62 (define @t51 () (= @t50 @t49)) % 0.38/0.62 (define @t52 () (forall @t30 @t51)) % 0.38/0.62 (define @t53 () (tptp.one_to_one @t20 @t4 @t1)) % 0.38/0.62 (define @t54 () (and @t5 @t27)) % 0.38/0.62 (define @t55 () (@list @t2 @t13)) % 0.38/0.62 (define @t56 () (and @t5 @t26)) % 0.38/0.62 (define @t57 () (exists @t6 @t56)) % 0.38/0.62 (define @t58 () (tptp.image2 @t20 @t4)) % 0.38/0.62 (define @t59 () (tptp.member @t13 @t58)) % 0.38/0.62 (define @t60 () (= @t59 @t57)) % 0.38/0.62 (define @t61 () (forall (@list @t20 @t4 @t13) @t60)) % 0.38/0.62 (define @t62 () (@var "S" $$unsorted)) % 0.38/0.62 (define @t63 () (tptp.apply @t62 @t18 @t17)) % 0.38/0.62 (define @t64 () (tptp.apply @t20 @t38 @t17)) % 0.38/0.62 (define @t65 () (tptp.apply @t20 @t39 @t18)) % 0.38/0.62 (define @t66 () (@var "R" $$unsorted)) % 0.38/0.62 (define @t67 () (tptp.apply @t66 @t39 @t38)) % 0.38/0.62 (define @t68 () (and @t41 @t23 @t40 @t22 @t67 @t65 @t64)) % 0.38/0.62 (define @t69 () (@list @t39 @t18 @t38 @t17)) % 0.38/0.62 (define @t70 () (@list @t20 @t4 @t66 @t1 @t62)) % 0.38/0.62 (define @t71 () (tptp.surjective @t32 @t4 @t35)) % 0.38/0.62 (define @t72 () (tptp.apply @t32 @t2 @t13)) % 0.38/0.62 (define @t73 () (tptp.member @t13 @t35)) % 0.38/0.62 (define @t74 () (and @t5 @t73)) % 0.38/0.62 (define @t75 () (=> @t74 (= @t72 @t26))) % 0.38/0.62 (define @t76 () (forall @t55 @t75)) % 0.38/0.62 (define @t77 () (tptp.subset @t35 @t1)) % 0.38/0.62 (define @t78 () (and @t29 @t77 (= @t58 @t35) @t76)) % 0.38/0.62 (define @t79 () (=> @t78 @t71)) % 0.38/0.62 (define @t80 () (@list @t20 @t32 @t4 @t1 @t35)) % 0.38/0.62 (define @t81 () (forall @t80 @t79)) % 0.38/0.62 (define @t82 () (not @t81)) % 0.38/0.62 (define @t83 () (forall @t6 (not @t56))) % 0.38/0.62 (define @t84 () (not @t83)) % 0.38/0.62 (define @t85 () (tptp.surjective @t32 @t4 @t58)) % 0.38/0.62 (define @t86 () (= @t26 @t72)) % 0.38/0.62 (define @t87 () (not @t5)) % 0.38/0.62 (define @t88 () (not (forall @t55 (or @t87 (not @t59) @t86)))) % 0.38/0.62 (define @t89 () (not (tptp.subset @t58 @t1))) % 0.38/0.62 (define @t90 () (not @t29)) % 0.38/0.62 (define @t91 () (or @t90 @t89 @t88 @t85)) % 0.38/0.62 (define @t92 () (forall @t37 @t91)) % 0.38/0.62 (define @t93 () (@quantifiers_skolemize @t92 1)) % 0.38/0.62 (define @t94 () (@quantifiers_skolemize @t92 2)) % 0.38/0.62 (define @t95 () (not (tptp.member @t11 @t94))) % 0.38/0.62 (define @t96 () (@quantifiers_skolemize @t92 0)) % 0.38/0.62 (define @t97 () (tptp.image2 @t96 @t94)) % 0.38/0.62 (define @t98 () (not (tptp.member @t13 @t97))) % 0.38/0.62 (define @t99 () (forall @t16 (or @t98 (not (forall @t46 (or @t95 (not (tptp.apply @t93 @t11 @t13)))))))) % 0.38/0.62 (define @t100 () (@quantifiers_skolemize @t99 0)) % 0.38/0.62 (define @t101 () (not (forall @t46 (or (not @t44) (not @t43))))) % 0.38/0.62 (define @t102 () (forall @t46 (not @t45))) % 0.38/0.62 (define @t103 () (not @t102)) % 0.38/0.62 (define @t104 () (not (= @t58 @t58))) % 0.38/0.62 (define @t105 () (or @t90 @t89 @t104 @t88 @t85)) % 0.38/0.62 (define @t106 () (not @t73)) % 0.38/0.62 (define @t107 () (or @t87 @t106 @t86)) % 0.38/0.62 (define @t108 () (forall @t55 @t107)) % 0.38/0.62 (define @t109 () (not @t108)) % 0.38/0.62 (define @t110 () (= @t35 @t58)) % 0.38/0.62 (define @t111 () (not @t110)) % 0.38/0.62 (define @t112 () (not @t77)) % 0.38/0.62 (define @t113 () (or @t111 @t90 @t112 @t111 @t109 @t71)) % 0.38/0.62 (define @t114 () (@list @t35)) % 0.38/0.62 (define @t115 () (or @t90 @t112 @t111 @t109 @t71)) % 0.38/0.62 (define @t116 () (forall @t114 @t115)) % 0.38/0.62 (define @t117 () (forall @t37 @t116)) % 0.38/0.62 (define @t118 () (or @t90 @t112 @t111 @t109)) % 0.38/0.62 (define @t119 () (and @t29 @t77 @t110 @t108)) % 0.38/0.62 (define @t120 () (tptp.surjective @t93 @t94 @t97)) % 0.38/0.62 (define @t121 () (not (tptp.member @t2 @t94))) % 0.38/0.62 (define @t122 () (forall @t55 (or @t121 @t98 (= (tptp.apply @t96 @t2 @t13) (tptp.apply @t93 @t2 @t13))))) % 0.38/0.62 (define @t123 () (not @t122)) % 0.38/0.62 (define @t124 () (@quantifiers_skolemize @t92 3)) % 0.38/0.62 (define @t125 () (or (not (tptp.maps @t96 @t94 @t124)) (not (tptp.subset @t97 @t124)) @t123 @t120)) % 0.38/0.62 (define @t126 () (@list true)) % 0.38/0.62 (define @t127 () (@list @t125)) % 0.38/0.62 (define @t128 () (= @t120 @t99)) % 0.38/0.62 (define @t129 () (not @t99)) % 0.38/0.62 (define @t130 () (tptp.member @t100 @t97)) % 0.38/0.62 (define @t131 () (forall @t46 (or @t95 (not (tptp.apply @t93 @t11 @t100))))) % 0.38/0.62 (define @t132 () (not @t131)) % 0.38/0.62 (define @t133 () (not @t130)) % 0.38/0.62 (define @t134 () (or @t133 @t132)) % 0.38/0.62 (define @t135 () (@list @t134)) % 0.38/0.62 (define @t136 () (forall @t6 (or @t121 (not (tptp.apply @t96 @t2 @t100))))) % 0.38/0.62 (define @t137 () (not @t136)) % 0.38/0.62 (define @t138 () (= @t130 @t137)) % 0.38/0.62 (define @t139 () (@list false false)) % 0.38/0.62 (define @t140 () (@quantifiers_skolemize @t136 0)) % 0.38/0.62 (define @t141 () (tptp.apply @t96 @t140 @t100)) % 0.38/0.62 (define @t142 () (not @t141)) % 0.38/0.62 (define @t143 () (tptp.member @t140 @t94)) % 0.38/0.62 (define @t144 () (not @t143)) % 0.38/0.62 (define @t145 () (or @t144 @t142)) % 0.38/0.62 (define @t146 () (@list @t145)) % 0.38/0.62 (define @t147 () (tptp.apply @t93 @t140 @t100)) % 0.38/0.62 (define @t148 () (= @t141 @t147)) % 0.38/0.62 (define @t149 () (or @t144 @t133 @t148)) % 0.38/0.62 (define @t150 () (not @t147)) % 0.38/0.62 (define @t151 () (or @t144 @t150)) % 0.38/0.62 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.38/0.62 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.38/0.62 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.38/0.62 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.38/0.62 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.38/0.62 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.38/0.62 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.38/0.62 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.38/0.62 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.38/0.62 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.38/0.62 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.38/0.62 (assume @p12 (forall @t30 (= @t29 (and (forall @t6 (=> @t5 @t28)) (forall @t25 (=> @t24 (=> (and @t21 (tptp.apply @t20 @t2 @t17)) @t19))))))) % 0.38/0.62 (assume @p13 (forall (@list @t34 @t32 @t20 @t4 @t1 @t35) (= (tptp.compose_predicate @t34 @t32 @t20 @t4 @t1 @t35) (forall (@list @t2 @t31) (=> @t36 (= (tptp.apply @t34 @t2 @t31) @t33)))))) % 0.38/0.62 (assume @p14 (forall (@list @t32 @t20 @t4 @t1 @t35 @t2 @t31) (=> @t36 (= (tptp.apply (tptp.compose_function @t32 @t20 @t4 @t1 @t35) @t2 @t31) @t33)))) % 0.38/0.62 (assume @p15 (forall @t37 (= (tptp.equal_maps @t20 @t32 @t4 @t1) (forall @t25 (=> @t24 (=> (and @t21 (tptp.apply @t32 @t2 @t17)) @t19)))))) % 0.38/0.62 (assume @p16 (forall (@list @t20 @t4) (= (tptp.identity @t20 @t4) (forall @t6 (=> @t5 (tptp.apply @t20 @t2 @t2)))))) % 0.38/0.62 (assume @p17 (forall @t30 (= @t42 (forall (@list @t39 @t38 @t13) (=> (and @t41 @t40 @t27) (=> (and (tptp.apply @t20 @t39 @t13) (tptp.apply @t20 @t38 @t13)) (= @t39 @t38))))))) % 0.38/0.62 (assume @p18 @t52) % 0.38/0.62 (assume @p19 (forall @t30 (= @t53 (and @t42 @t50)))) % 0.38/0.62 (assume @p20 (forall (@list @t32 @t20 @t4 @t1) (= (tptp.inverse_predicate @t32 @t20 @t4 @t1) (forall @t55 (=> @t54 (= @t26 (tptp.apply @t32 @t13 @t2))))))) % 0.38/0.62 (assume @p21 (forall (@list @t20 @t4 @t1 @t2 @t13) (=> @t54 (= @t26 (tptp.apply (tptp.inverse_function @t20 @t4 @t1) @t13 @t2))))) % 0.38/0.62 (assume @p22 @t61) % 0.38/0.62 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t27 @t57)))) % 0.38/0.62 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t28))) % 0.38/0.62 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t28)))) % 0.38/0.62 (assume @p26 (forall @t70 (= (tptp.increasing @t20 @t4 @t66 @t1 @t62) (forall @t69 (=> @t68 @t63))))) % 0.38/0.62 (assume @p27 (forall @t70 (= (tptp.decreasing @t20 @t4 @t66 @t1 @t62) (forall @t69 (=> @t68 (tptp.apply @t62 @t17 @t18)))))) % 0.38/0.62 (assume @p28 (forall @t70 (= (tptp.isomorphism @t20 @t4 @t66 @t1 @t62) (and @t29 @t53 (forall @t69 (=> (and @t41 @t23 @t40 @t22 @t65 @t64) (= @t67 @t63))))))) % 0.38/0.62 (assume @p29 @t82) % 0.38/0.62 (assume @p30 true) % 0.38/0.62 (step @p31 :rule bool-and-de-morgan :args (@t5 @t26 true)) % 0.38/0.62 (step @p32 :rule cong :premises (@p31) :args (@t83)) % 0.38/0.62 (step @p33 :rule cong :premises (@p32) :args (@t84)) % 0.38/0.62 (step @p34 :rule exists-elim :args ((= @t57 @t84))) % 0.38/0.62 (step @p35 :rule trans :premises (@p34 @p33)) % 0.38/0.62 (step @p36 :rule refl :args (@t59)) % 0.38/0.62 (step @p37 :rule cong :premises (@p36 @p35) :args (@t60)) % 0.38/0.62 (step @p38 :rule cong :premises (@p37) :args (@t61)) % 0.38/0.62 (step @p39 :rule eq_resolve :premises (@p22 @p38)) % 0.38/0.62 (step @p40 :rule instantiate :premises (@p39) :args ((@list @t96 @t94 @t100))) % 0.38/0.62 (step @p41 :rule bool-impl-elim :args (@t27 @t101)) % 0.38/0.62 (step @p42 :rule cong :premises (@p41) :args ((forall @t16 (=> @t27 @t101)))) % 0.38/0.62 (step @p43 :rule bool-and-de-morgan :args (@t44 @t43 true)) % 0.38/0.62 (step @p44 :rule cong :premises (@p43) :args (@t102)) % 0.38/0.62 (step @p45 :rule cong :premises (@p44) :args (@t103)) % 0.38/0.62 (step @p46 :rule exists-elim :args ((= @t47 @t103))) % 0.38/0.62 (step @p47 :rule trans :premises (@p46 @p45)) % 0.38/0.62 (step @p48 :rule refl :args (@t27)) % 0.38/0.62 (step @p49 :rule cong :premises (@p48 @p47) :args (@t48)) % 0.38/0.62 (step @p50 :rule cong :premises (@p49) :args (@t49)) % 0.38/0.62 (step @p51 :rule trans :premises (@p50 @p42)) % 0.38/0.62 (step @p52 :rule refl :args (@t50)) % 0.38/0.62 (step @p53 :rule cong :premises (@p52 @p51) :args (@t51)) % 0.38/0.62 (step @p54 :rule cong :premises (@p53) :args (@t52)) % 0.38/0.62 (step @p55 :rule eq_resolve :premises (@p18 @p54)) % 0.38/0.62 (step @p56 :rule instantiate :premises (@p55) :args ((@list @t93 @t94 @t97))) % 0.38/0.62 (step @p57 :rule aci_norm :args ((= (or @t90 @t89 false @t88 @t85) @t91))) % 0.38/0.62 (step @p58 :rule refl :args (@t85)) % 0.38/0.62 (step @p59 :rule refl :args (@t88)) % 0.38/0.62 (step @p60 :rule evaluate :args ((not true))) % 0.38/0.62 (step @p61 :rule eq-refl :args (@t58)) % 0.38/0.62 (step @p62 :rule cong :premises (@p61) :args (@t104)) % 0.38/0.62 (step @p63 :rule trans :premises (@p62 @p60)) % 0.38/0.62 (step @p64 :rule refl :args (@t89)) % 0.38/0.62 (step @p65 :rule refl :args (@t90)) % 0.38/0.62 (step @p66 :rule nary_cong :premises (@p65 @p64 @p63 @p59 @p58) :args (@t105)) % 0.38/0.62 (step @p67 :rule trans :premises (@p66 @p57)) % 0.38/0.62 (step @p68 :rule cong :premises (@p67) :args ((forall @t37 @t105))) % 0.38/0.62 (step @p69 :rule quant-var-elim-eq :args ((= (forall @t114 @t113) @t105))) % 0.38/0.62 (step @p70 :rule aci_norm :args ((= @t115 @t113))) % 0.38/0.62 (step @p71 :rule cong :premises (@p70) :args (@t116)) % 0.38/0.62 (step @p72 :rule trans :premises (@p71 @p69)) % 0.38/0.62 (step @p73 :rule cong :premises (@p72) :args (@t117)) % 0.38/0.62 (step @p74 :rule quant-merge-prenex :args ((= @t117 (forall @t80 @t115)))) % 0.38/0.62 (step @p75 :rule symm :premises (@p74)) % 0.38/0.62 (step @p76 :rule trans :premises (@p75 @p73)) % 0.38/0.62 (step @p77 :rule trans :premises (@p76 @p68)) % 0.38/0.62 (step @p78 :rule aci_norm :args ((= (or @t118 @t71) @t115))) % 0.38/0.62 (step @p79 :rule refl :args (@t71)) % 0.38/0.62 (step @p80 :rule aci_norm :args ((= (or @t90 (or @t112 (or @t111 @t109))) @t118))) % 0.38/0.62 (step @p81 :rule bool-and-de-morgan :args (@t110 @t108 true)) % 0.38/0.62 (step @p82 :rule refl :args (@t112)) % 0.38/0.62 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t112 (not (and @t110 @t108))))) % 0.38/0.62 (step @p84 :rule bool-and-de-morgan :args (@t77 @t110 (and @t108))) % 0.38/0.62 (step @p85 :rule trans :premises (@p84 @p83)) % 0.38/0.62 (step @p86 :rule refl :args (@t90)) % 0.38/0.62 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or @t90 (not (and @t77 @t110 @t108))))) % 0.38/0.62 (step @p88 :rule bool-and-de-morgan :args (@t29 @t77 (and @t110 @t108))) % 0.38/0.62 (step @p89 :rule trans :premises (@p88 @p87)) % 0.38/0.62 (step @p90 :rule trans :premises (@p89 @p80)) % 0.38/0.62 (step @p91 :rule nary_cong :premises (@p90 @p79) :args ((or (not @t119) @t71))) % 0.38/0.62 (step @p92 :rule trans :premises (@p91 @p78)) % 0.38/0.62 (step @p93 :rule bool-impl-elim :args (@t119 @t71)) % 0.38/0.62 (step @p94 :rule trans :premises (@p93 @p92)) % 0.38/0.62 (step @p95 :rule cong :premises (@p94) :args ((forall @t80 (=> @t119 @t71)))) % 0.38/0.62 (step @p96 :rule trans :premises (@p95 @p77)) % 0.38/0.62 (step @p97 :rule refl :args (@t71)) % 0.38/0.62 (step @p98 :rule aci_norm :args ((= (or (or @t87 @t106) @t86) @t107))) % 0.38/0.62 (step @p99 :rule refl :args (@t86)) % 0.38/0.62 (step @p100 :rule bool-and-de-morgan :args (@t5 @t73 true)) % 0.38/0.62 (step @p101 :rule nary_cong :premises (@p100 @p99) :args ((or (not @t74) @t86))) % 0.38/0.62 (step @p102 :rule trans :premises (@p101 @p98)) % 0.38/0.62 (step @p103 :rule bool-impl-elim :args (@t74 @t86)) % 0.38/0.62 (step @p104 :rule trans :premises (@p103 @p102)) % 0.38/0.62 (step @p105 :rule cong :premises (@p104) :args ((forall @t55 (=> @t74 @t86)))) % 0.38/0.62 (step @p106 :rule eq-symm :args (@t72 @t26)) % 0.38/0.62 (step @p107 :rule refl :args (@t74)) % 0.38/0.62 (step @p108 :rule cong :premises (@p107 @p106) :args (@t75)) % 0.38/0.62 (step @p109 :rule cong :premises (@p108) :args (@t76)) % 0.38/0.62 (step @p110 :rule trans :premises (@p109 @p105)) % 0.38/0.62 (step @p111 :rule eq-symm :args (@t58 @t35)) % 0.38/0.62 (step @p112 :rule refl :args (@t77)) % 0.38/0.62 (step @p113 :rule refl :args (@t29)) % 0.38/0.62 (step @p114 :rule nary_cong :premises (@p113 @p112 @p111 @p110) :args (@t78)) % 0.38/0.62 (step @p115 :rule cong :premises (@p114 @p97) :args (@t79)) % 0.38/0.62 (step @p116 :rule cong :premises (@p115) :args (@t81)) % 0.38/0.62 (step @p117 :rule trans :premises (@p116 @p96)) % 0.38/0.62 (step @p118 :rule cong :premises (@p117) :args (@t82)) % 0.38/0.62 (step @p119 :rule eq_resolve :premises (@p29 @p118)) % 0.38/0.62 (step @p120 :rule skolemize :premises (@p119)) % 0.38/0.62 (step @p121 :rule cnf_or_neg :args (@t125 3)) % 0.38/0.62 (step @p122 :rule chain_m_resolution :premises (@p121 @p120) :args ((not @t120) @t126 @t127)) % 0.38/0.62 (step @p123 :rule cnf_equiv_pos2 :args (@t128)) % 0.38/0.62 (step @p124 :rule reordering :premises (@p123) :args ((or @t120 @t129 (not @t128)))) % 0.38/0.62 (step @p125 :rule chain_m_resolution :premises (@p124 @p122 @p56) :args (@t129 (@list true false) (@list @t120 @t128))) % 0.38/0.62 (step @p126 :rule skolemize :premises (@p125)) % 0.38/0.62 (step @p127 :rule bool-double-not-elim :args (@t130)) % 0.38/0.62 (step @p128 :rule refl :args (@t134)) % 0.38/0.62 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or @t134 (not @t133)))) % 0.38/0.62 (step @p130 :rule cnf_or_neg :args (@t134 0)) % 0.38/0.62 (step @p131 :rule eq_resolve :premises (@p130 @p129)) % 0.38/0.62 (step @p132 :rule reordering :premises (@p131) :args ((or @t130 @t134))) % 0.38/0.62 (step @p133 :rule chain_m_resolution :premises (@p132 @p126) :args (@t130 @t126 @t135)) % 0.38/0.62 (step @p134 :rule cnf_equiv_pos1 :args (@t138)) % 0.38/0.62 (step @p135 :rule reordering :premises (@p134) :args ((or @t133 @t137 (not @t138)))) % 0.38/0.62 (step @p136 :rule chain_m_resolution :premises (@p135 @p133 @p40) :args (@t137 @t139 (@list @t130 @t138))) % 0.38/0.62 (step @p137 :rule skolemize :premises (@p136)) % 0.38/0.62 (step @p138 :rule bool-double-not-elim :args (@t141)) % 0.38/0.62 (step @p139 :rule refl :args (@t145)) % 0.38/0.62 (step @p140 :rule nary_cong :premises (@p139 @p138) :args ((or @t145 (not @t142)))) % 0.38/0.62 (step @p141 :rule cnf_or_neg :args (@t145 1)) % 0.38/0.62 (step @p142 :rule eq_resolve :premises (@p141 @p140)) % 0.38/0.62 (step @p143 :rule reordering :premises (@p142) :args ((or @t141 @t145))) % 0.38/0.62 (step @p144 :rule chain_m_resolution :premises (@p143 @p137) :args (@t141 @t126 @t146)) % 0.38/0.62 (step @p145 :rule bool-double-not-elim :args (@t122)) % 0.38/0.62 (step @p146 :rule refl :args (@t125)) % 0.38/0.62 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or @t125 (not @t123)))) % 0.38/0.62 (step @p148 :rule cnf_or_neg :args (@t125 2)) % 0.38/0.62 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.38/0.62 (step @p150 :rule reordering :premises (@p149) :args ((or @t122 @t125))) % 0.38/0.62 (step @p151 :rule chain_m_resolution :premises (@p150 @p120) :args (@t122 @t126 @t127)) % 0.38/0.62 (step @p152 :rule instantiate :premises (@p151) :args ((@list @t140 @t100))) % 0.38/0.62 (step @p153 :rule bool-double-not-elim :args (@t143)) % 0.38/0.62 (step @p154 :rule nary_cong :premises (@p139 @p153) :args ((or @t145 (not @t144)))) % 0.38/0.62 (step @p155 :rule cnf_or_neg :args (@t145 0)) % 0.38/0.62 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 0.38/0.62 (step @p157 :rule reordering :premises (@p156) :args ((or @t143 @t145))) % 0.38/0.62 (step @p158 :rule chain_m_resolution :premises (@p157 @p137) :args (@t143 @t126 @t146)) % 0.38/0.62 (step @p159 :rule cnf_or_pos :args (@t149)) % 0.38/0.62 (step @p160 :rule reordering :premises (@p159) :args ((or @t133 @t144 @t148 (not @t149)))) % 0.38/0.62 (step @p161 :rule chain_m_resolution :premises (@p160 @p133 @p158 @p152) :args (@t148 (@list false false false) (@list @t130 @t143 @t149))) % 0.38/0.62 (step @p162 :rule bool-double-not-elim :args (@t131)) % 0.38/0.62 (step @p163 :rule nary_cong :premises (@p128 @p162) :args ((or @t134 (not @t132)))) % 0.38/0.62 (step @p164 :rule cnf_or_neg :args (@t134 1)) % 0.38/0.62 (step @p165 :rule eq_resolve :premises (@p164 @p163)) % 0.38/0.62 (step @p166 :rule reordering :premises (@p165) :args ((or @t131 @t134))) % 0.38/0.62 (step @p167 :rule chain_m_resolution :premises (@p166 @p126) :args (@t131 @t126 @t135)) % 0.38/0.62 (step @p168 :rule instantiate :premises (@p167) :args ((@list @t140))) % 0.38/0.62 (step @p169 :rule cnf_or_pos :args (@t151)) % 0.38/0.62 (step @p170 :rule reordering :premises (@p169) :args ((or @t144 @t150 (not @t151)))) % 0.38/0.62 (step @p171 :rule chain_m_resolution :premises (@p170 @p158 @p168) :args (@t150 @t139 (@list @t143 @t151))) % 0.38/0.62 (step @p172 :rule cnf_equiv_pos1 :args (@t148)) % 0.38/0.62 (step @p173 :rule reordering :premises (@p172) :args ((or @t142 @t147 (not @t148)))) % 0.38/0.62 (step @p174 false :rule chain_m_resolution :premises (@p173 @p171 @p161 @p144) :args (false (@list true false false) (@list @t147 @t148 @t141))) % 0.38/0.62 ) % 0.38/0.62 % SZS output end Proof % 0.38/0.62 % cvc5 exiting %------------------------------------------------------------------------------