%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU196+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:50:55 AM UTC 2026 % Result : Theorem 0.38s 0.69s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU196+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n003.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:37:14 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.69 % SZS status Theorem % 0.38/0.69 % SZS output start Proof % 0.38/0.69 ( % 0.38/0.69 (declare-sort $$unsorted 0) % 0.38/0.69 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 0.38/0.69 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.38/0.69 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.38/0.69 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.69 (declare-const tptp.empty_set $$unsorted) % 0.38/0.69 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.38/0.69 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.relation_inverse (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.38/0.69 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.69 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.69 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.69 (define @t1 () (@var "A" $$unsorted)) % 0.38/0.69 (define @t2 () (@var "B" $$unsorted)) % 0.38/0.69 (define @t3 () (tptp.in @t2 @t1)) % 0.38/0.69 (define @t4 () (not @t3)) % 0.38/0.69 (define @t5 () (tptp.in @t1 @t2)) % 0.38/0.69 (define @t6 () (@list @t1 @t2)) % 0.38/0.69 (define @t7 () (tptp.proper_subset @t2 @t1)) % 0.38/0.69 (define @t8 () (tptp.proper_subset @t1 @t2)) % 0.38/0.69 (define @t9 () (tptp.relation @t1)) % 0.38/0.69 (define @t10 () (tptp.empty @t1)) % 0.38/0.69 (define @t11 () (@list @t1)) % 0.38/0.69 (define @t12 () (tptp.unordered_pair @t1 @t2)) % 0.38/0.69 (define @t13 () (tptp.set_union2 @t2 @t1)) % 0.38/0.69 (define @t14 () (tptp.set_union2 @t1 @t2)) % 0.38/0.69 (define @t15 () (tptp.set_intersection2 @t1 @t2)) % 0.38/0.69 (define @t16 () (@var "D" $$unsorted)) % 0.38/0.69 (define @t17 () (@var "C" $$unsorted)) % 0.38/0.69 (define @t18 () (tptp.in @t17 @t1)) % 0.38/0.69 (define @t19 () (tptp.ordered_pair @t17 @t16)) % 0.38/0.69 (define @t20 () (tptp.in @t19 @t2)) % 0.38/0.69 (define @t21 () (@list @t17 @t16)) % 0.38/0.69 (define @t22 () (tptp.identity_relation @t1)) % 0.38/0.69 (define @t23 () (tptp.relation @t2)) % 0.38/0.69 (define @t24 () (tptp.subset @t1 @t2)) % 0.38/0.69 (define @t25 () (= @t1 @t2)) % 0.38/0.69 (define @t26 () (@var "E" $$unsorted)) % 0.38/0.69 (define @t27 () (tptp.ordered_pair @t16 @t26)) % 0.38/0.69 (define @t28 () (tptp.in @t16 @t2)) % 0.38/0.69 (define @t29 () (tptp.in @t27 @t17)) % 0.38/0.69 (define @t30 () (@list @t16 @t26)) % 0.38/0.69 (define @t31 () (tptp.relation_dom_restriction @t1 @t2)) % 0.38/0.69 (define @t32 () (tptp.relation @t17)) % 0.38/0.69 (define @t33 () (@list @t2 @t17)) % 0.38/0.69 (define @t34 () (@list @t2)) % 0.38/0.69 (define @t35 () (= @t2 tptp.empty_set)) % 0.38/0.69 (define @t36 () (= @t2 (tptp.set_meet @t1))) % 0.38/0.69 (define @t37 () (= @t1 tptp.empty_set)) % 0.38/0.69 (define @t38 () (tptp.in @t17 @t16)) % 0.38/0.69 (define @t39 () (tptp.in @t16 @t1)) % 0.38/0.69 (define @t40 () (@list @t16)) % 0.38/0.69 (define @t41 () (tptp.in @t17 @t2)) % 0.38/0.69 (define @t42 () (@list @t17)) % 0.38/0.69 (define @t43 () (not @t37)) % 0.38/0.69 (define @t44 () (tptp.singleton @t1)) % 0.38/0.69 (define @t45 () (tptp.powerset @t1)) % 0.38/0.69 (define @t46 () (tptp.in @t19 @t1)) % 0.38/0.69 (define @t47 () (tptp.empty @t2)) % 0.38/0.69 (define @t48 () (tptp.element @t2 @t1)) % 0.38/0.69 (define @t49 () (not @t10)) % 0.38/0.69 (define @t50 () (tptp.in @t16 @t17)) % 0.38/0.69 (define @t51 () (@list @t1 @t2 @t17)) % 0.38/0.69 (define @t52 () (@var "F" $$unsorted)) % 0.38/0.69 (define @t53 () (tptp.cartesian_product2 @t1 @t2)) % 0.38/0.69 (define @t54 () (forall @t42 (=> @t18 @t41))) % 0.38/0.69 (define @t55 () (tptp.relation_dom @t1)) % 0.38/0.69 (define @t56 () (tptp.cast_to_subset @t1)) % 0.38/0.69 (define @t57 () (tptp.set_difference @t1 @t2)) % 0.38/0.69 (define @t58 () (tptp.in (tptp.ordered_pair @t16 @t17) @t1)) % 0.38/0.69 (define @t59 () (tptp.relation_rng @t1)) % 0.38/0.69 (define @t60 () (tptp.subset_complement @t1 @t2)) % 0.38/0.69 (define @t61 () (tptp.element @t2 @t45)) % 0.38/0.69 (define @t62 () (tptp.ordered_pair @t1 @t2)) % 0.38/0.69 (define @t63 () (tptp.relation_inverse @t1)) % 0.38/0.69 (define @t64 () (tptp.disjoint @t1 @t2)) % 0.38/0.69 (define @t65 () (tptp.relation_composition @t1 @t2)) % 0.38/0.69 (define @t66 () (tptp.complements_of_subsets @t1 @t2)) % 0.38/0.69 (define @t67 () (tptp.powerset @t45)) % 0.38/0.69 (define @t68 () (tptp.element @t2 @t67)) % 0.38/0.69 (define @t69 () (not @t25)) % 0.38/0.69 (define @t70 () (tptp.relation @t65)) % 0.38/0.69 (define @t71 () (and @t9 @t23)) % 0.38/0.69 (define @t72 () (tptp.union_of_subsets @t1 @t2)) % 0.38/0.69 (define @t73 () (tptp.meet_of_subsets @t1 @t2)) % 0.38/0.69 (define @t74 () (tptp.subset_difference @t1 @t2 @t17)) % 0.38/0.69 (define @t75 () (tptp.element @t17 @t45)) % 0.38/0.69 (define @t76 () (and @t61 @t75)) % 0.38/0.69 (define @t77 () (tptp.relation @t31)) % 0.38/0.69 (define @t78 () (forall @t6 (=> @t9 @t77))) % 0.38/0.69 (define @t79 () (tptp.relation_composition @t2 @t1)) % 0.38/0.69 (define @t80 () (and @t10 @t23)) % 0.38/0.69 (define @t81 () (tptp.empty tptp.empty_set)) % 0.38/0.69 (define @t82 () (not @t47)) % 0.38/0.69 (define @t83 () (tptp.empty @t55)) % 0.38/0.69 (define @t84 () (and @t49 @t9)) % 0.38/0.69 (define @t85 () (tptp.empty @t59)) % 0.38/0.69 (define @t86 () (tptp.disjoint @t44 @t2)) % 0.38/0.69 (define @t87 () (tptp.singleton @t2)) % 0.38/0.69 (define @t88 () (tptp.union @t2)) % 0.38/0.69 (define @t89 () (tptp.in @t1 @t17)) % 0.38/0.69 (define @t90 () (@list @t1 @t2 @t17 @t16)) % 0.38/0.69 (define @t91 () (tptp.element @t1 (tptp.powerset @t2))) % 0.38/0.69 (define @t92 () (tptp.set_difference @t2 @t17)) % 0.38/0.69 (define @t93 () (= @t1 @t17)) % 0.38/0.69 (define @t94 () (tptp.cartesian_product2 @t1 @t17)) % 0.38/0.69 (define @t95 () (not @t41)) % 0.38/0.69 (define @t96 () (tptp.subset @t17 @t2)) % 0.38/0.69 (define @t97 () (forall @t42 (not (and @t96 (not (tptp.are_equipotent @t17 @t2)) @t95)))) % 0.38/0.69 (define @t98 () (tptp.powerset @t17)) % 0.38/0.69 (define @t99 () (forall @t21 (=> (and @t41 (tptp.subset @t16 @t17)) @t28))) % 0.38/0.69 (define @t100 () (tptp.set_intersection2 @t2 @t17)) % 0.38/0.69 (define @t101 () (tptp.subset @t1 @t17)) % 0.38/0.69 (define @t102 () (tptp.element @t1 @t2)) % 0.38/0.69 (define @t103 () (tptp.in @t1 (tptp.relation_dom @t17))) % 0.38/0.69 (define @t104 () (tptp.in @t62 @t17)) % 0.38/0.69 (define @t105 () (tptp.relation_rng @t2)) % 0.38/0.69 (define @t106 () (tptp.relation_dom @t2)) % 0.38/0.69 (define @t107 () (and (tptp.subset @t55 @t106) (tptp.subset @t59 @t105))) % 0.38/0.69 (define @t108 () (=> @t24 @t107)) % 0.38/0.69 (define @t109 () (forall @t34 (=> @t23 @t108))) % 0.38/0.69 (define @t110 () (=> @t9 @t109)) % 0.38/0.69 (define @t111 () (forall @t11 @t110)) % 0.38/0.69 (define @t112 () (tptp.relation_field @t17)) % 0.38/0.69 (define @t113 () (tptp.in @t2 @t17)) % 0.38/0.69 (define @t114 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.38/0.69 (define @t115 () (and @t18 @t41)) % 0.38/0.69 (define @t116 () (not @t64)) % 0.38/0.69 (define @t117 () (tptp.subset_complement @t1 @t17)) % 0.38/0.69 (define @t118 () (tptp.disjoint @t2 @t17)) % 0.38/0.69 (define @t119 () (tptp.relation_dom @t65)) % 0.38/0.69 (define @t120 () (not @t35)) % 0.38/0.69 (define @t121 () (tptp.element @t2 @t98)) % 0.38/0.69 (define @t122 () (tptp.in @t17 @t15)) % 0.38/0.69 (define @t123 () (= @t59 tptp.empty_set)) % 0.38/0.69 (define @t124 () (= @t55 tptp.empty_set)) % 0.38/0.69 (define @t125 () (tptp.relation_dom_restriction @t2 @t1)) % 0.38/0.69 (define @t126 () (tptp.subset @t125 @t2)) % 0.38/0.69 (define @t127 () (forall @t6 (=> @t23 @t126))) % 0.38/0.69 (define @t128 () (= @t44 (tptp.unordered_pair @t2 @t17))) % 0.38/0.69 (define @t129 () (tptp.subset (tptp.relation_rng @t125) @t105)) % 0.38/0.69 (define @t130 () (forall @t6 (=> @t23 @t129))) % 0.38/0.69 (define @t131 () (not @t130)) % 0.38/0.69 (define @t132 () (not @t23)) % 0.38/0.69 (define @t133 () (forall @t6 (or @t132 @t129))) % 0.38/0.69 (define @t134 () (@quantifiers_skolemize @t133 1)) % 0.38/0.69 (define @t135 () (tptp.relation @t134)) % 0.38/0.69 (define @t136 () (@quantifiers_skolemize @t133 0)) % 0.38/0.69 (define @t137 () (tptp.relation_dom_restriction @t134 @t136)) % 0.38/0.69 (define @t138 () (tptp.subset (tptp.relation_rng @t137) (tptp.relation_rng @t134))) % 0.38/0.69 (define @t139 () (not @t135)) % 0.38/0.69 (define @t140 () (or @t139 @t138)) % 0.38/0.69 (define @t141 () (@list true)) % 0.38/0.69 (define @t142 () (@list @t140)) % 0.38/0.69 (define @t143 () (@var "BOUND_VARIABLE_9062" $$unsorted)) % 0.38/0.69 (define @t144 () (and (tptp.subset @t55 (tptp.relation_dom @t143)) (tptp.subset @t59 (tptp.relation_rng @t143)))) % 0.38/0.69 (define @t145 () (not (tptp.subset @t1 @t143))) % 0.38/0.69 (define @t146 () (not (tptp.relation @t143))) % 0.38/0.69 (define @t147 () (not @t9)) % 0.38/0.69 (define @t148 () (or @t146 @t145 @t144)) % 0.38/0.69 (define @t149 () (or @t147 @t148)) % 0.38/0.69 (define @t150 () (forall (@list @t1 @t143) @t149)) % 0.38/0.69 (define @t151 () (@list @t143)) % 0.38/0.69 (define @t152 () (forall @t151 @t149)) % 0.38/0.69 (define @t153 () (forall @t151 @t148)) % 0.38/0.69 (define @t154 () (or @t147 @t153)) % 0.38/0.69 (define @t155 () (not @t24)) % 0.38/0.69 (define @t156 () (or @t132 @t155 @t107)) % 0.38/0.69 (define @t157 () (forall @t34 @t156)) % 0.38/0.69 (define @t158 () (and (tptp.subset (tptp.relation_dom @t137) (tptp.relation_dom @t134)) @t138)) % 0.38/0.69 (define @t159 () (not @t158)) % 0.38/0.69 (define @t160 () (tptp.relation @t137)) % 0.38/0.69 (define @t161 () (or @t139 @t160)) % 0.38/0.69 (define @t162 () (@list false false)) % 0.38/0.69 (define @t163 () (tptp.subset @t137 @t134)) % 0.38/0.69 (define @t164 () (or @t139 @t163)) % 0.38/0.69 (define @t165 () (not @t163)) % 0.38/0.69 (define @t166 () (not @t160)) % 0.38/0.69 (define @t167 () (or @t166 @t139 @t165 @t158)) % 0.38/0.69 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.38/0.69 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 0.38/0.69 (assume @p3 (forall @t11 (=> @t10 @t9))) % 0.38/0.69 (assume @p4 (forall @t6 (= @t12 (tptp.unordered_pair @t2 @t1)))) % 0.38/0.69 (assume @p5 (forall @t6 (= @t14 @t13))) % 0.38/0.69 (assume @p6 (forall @t6 (= @t15 (tptp.set_intersection2 @t2 @t1)))) % 0.38/0.69 (assume @p7 (forall @t6 (=> @t23 (= (= @t2 @t22) (forall @t21 (= @t20 (and @t18 (= @t17 @t16)))))))) % 0.38/0.69 (assume @p8 (forall @t6 (= @t25 (and @t24 (tptp.subset @t2 @t1))))) % 0.38/0.69 (assume @p9 (forall @t11 (=> @t9 (forall @t33 (=> @t32 (= (= @t17 @t31) (forall @t30 (= @t29 (and @t28 (tptp.in @t27 @t1)))))))))) % 0.38/0.69 (assume @p10 (forall @t11 (= @t9 (forall @t34 (not (and @t3 (forall @t21 (not (= @t2 @t19))))))))) % 0.38/0.69 (assume @p11 (forall @t6 (and (=> @t43 (= @t36 (forall @t42 (= @t41 (forall @t40 (=> @t39 @t38)))))) (=> @t37 (= @t36 @t35))))) % 0.38/0.69 (assume @p12 (forall @t6 (= (= @t2 @t44) (forall @t42 (= @t41 (= @t17 @t1)))))) % 0.38/0.69 (assume @p13 (forall @t11 (= @t37 (forall @t34 @t4)))) % 0.38/0.69 (assume @p14 (forall @t6 (= (= @t2 @t45) (forall @t42 (= @t41 (tptp.subset @t17 @t1)))))) % 0.38/0.69 (assume @p15 (forall @t11 (=> @t9 (forall @t34 (=> @t23 (= @t25 (forall @t21 (= @t46 @t20)))))))) % 0.38/0.69 (assume @p16 (forall @t6 (and (=> @t49 (= @t48 @t3)) (=> @t10 (= @t48 @t47))))) % 0.38/0.69 (assume @p17 (forall @t51 (= (= @t17 @t12) (forall @t40 (= @t50 (or (= @t16 @t1) (= @t16 @t2))))))) % 0.38/0.69 (assume @p18 (forall @t51 (= (= @t17 @t14) (forall @t40 (= @t50 (or @t39 @t28)))))) % 0.38/0.69 (assume @p19 (forall @t51 (= (= @t17 @t53) (forall @t40 (= @t50 (exists (@list @t26 @t52) (and (tptp.in @t26 @t1) (tptp.in @t52 @t2) (= @t16 (tptp.ordered_pair @t26 @t52))))))))) % 0.38/0.69 (assume @p20 (forall @t11 (=> @t9 (forall @t34 (=> @t23 (= @t24 (forall @t21 (=> @t46 @t20)))))))) % 0.38/0.69 (assume @p21 (forall @t6 (= @t24 @t54))) % 0.38/0.69 (assume @p22 (forall @t51 (= (= @t17 @t15) (forall @t40 (= @t50 (and @t39 @t28)))))) % 0.38/0.69 (assume @p23 (forall @t11 (=> @t9 (forall @t34 (= (= @t2 @t55) (forall @t42 (= @t41 (exists @t40 @t46)))))))) % 0.38/0.69 (assume @p24 (forall @t11 (= @t56 @t1))) % 0.38/0.69 (assume @p25 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t42 (= @t41 (exists @t40 (and @t38 @t39))))))) % 0.38/0.69 (assume @p26 (forall @t51 (= (= @t17 @t57) (forall @t40 (= @t50 (and @t39 (not @t28))))))) % 0.38/0.69 (assume @p27 (forall @t11 (=> @t9 (forall @t34 (= (= @t2 @t59) (forall @t42 (= @t41 (exists @t40 @t58)))))))) % 0.38/0.69 (assume @p28 (forall @t6 (=> @t61 (= @t60 @t57)))) % 0.38/0.69 (assume @p29 (forall @t6 (= @t62 (tptp.unordered_pair @t12 @t44)))) % 0.38/0.69 (assume @p30 (forall @t11 (=> @t9 (= (tptp.relation_field @t1) (tptp.set_union2 @t55 @t59))))) % 0.38/0.69 (assume @p31 (forall @t11 (=> @t9 (forall @t34 (=> @t23 (= (= @t2 @t63) (forall @t21 (= @t20 @t58)))))))) % 0.38/0.69 (assume @p32 (forall @t6 (= @t64 (= @t15 tptp.empty_set)))) % 0.38/0.69 (assume @p33 (forall @t11 (=> @t9 (forall @t34 (=> @t23 (forall @t42 (=> @t32 (= (= @t17 @t65) (forall @t30 (= @t29 (exists (@list @t52) (and (tptp.in (tptp.ordered_pair @t16 @t52) @t1) (tptp.in (tptp.ordered_pair @t52 @t26) @t2))))))))))))) % 0.38/0.69 (assume @p34 (forall @t6 (=> @t68 (forall @t42 (=> (tptp.element @t17 @t67) (= (= @t17 @t66) (forall @t40 (=> (tptp.element @t16 @t45) (= @t50 (tptp.in (tptp.subset_complement @t1 @t16) @t2)))))))))) % 0.38/0.69 (assume @p35 (forall @t6 (= @t8 (and @t24 @t69)))) % 0.38/0.69 (assume @p36 true) % 0.38/0.69 (assume @p37 (forall @t11 (tptp.element @t56 @t45))) % 0.38/0.69 (assume @p38 (forall @t6 (=> @t61 (tptp.element @t60 @t45)))) % 0.38/0.69 (assume @p39 (forall @t11 (=> @t9 (tptp.relation @t63)))) % 0.38/0.69 (assume @p40 (forall @t6 (=> @t71 @t70))) % 0.38/0.69 (assume @p41 (forall @t6 (=> @t68 (tptp.element @t72 @t45)))) % 0.38/0.69 (assume @p42 (forall @t11 (tptp.relation @t22))) % 0.38/0.69 (assume @p43 (forall @t6 (=> @t68 (tptp.element @t73 @t45)))) % 0.38/0.69 (assume @p44 (forall @t51 (=> @t76 (tptp.element @t74 @t45)))) % 0.38/0.69 (assume @p45 @t78) % 0.38/0.69 (assume @p46 (forall @t6 (=> @t68 (tptp.element @t66 @t67)))) % 0.38/0.69 (assume @p47 (forall @t11 (exists @t34 @t48))) % 0.38/0.69 (assume @p48 (forall @t6 (=> @t80 (and (tptp.empty @t79) (tptp.relation @t79))))) % 0.38/0.69 (assume @p49 (forall @t6 (=> @t71 (tptp.relation @t15)))) % 0.38/0.69 (assume @p50 (forall @t11 (not (tptp.empty @t45)))) % 0.38/0.69 (assume @p51 @t81) % 0.38/0.69 (assume @p52 (forall @t6 (not (tptp.empty @t62)))) % 0.38/0.69 (assume @p53 (forall @t6 (=> @t71 (tptp.relation @t14)))) % 0.38/0.69 (assume @p54 (forall @t11 (not (tptp.empty @t44)))) % 0.38/0.69 (assume @p55 (forall @t6 (=> @t49 (not (tptp.empty @t14))))) % 0.38/0.69 (assume @p56 (forall @t6 (not (tptp.empty @t12)))) % 0.38/0.69 (assume @p57 (forall @t6 (=> @t49 (not (tptp.empty @t13))))) % 0.38/0.69 (assume @p58 (and @t81 (tptp.relation tptp.empty_set))) % 0.38/0.69 (assume @p59 (forall @t6 (=> (and @t49 @t82) (not (tptp.empty @t53))))) % 0.38/0.69 (assume @p60 (forall @t11 (=> @t84 (not @t83)))) % 0.38/0.69 (assume @p61 (forall @t11 (=> @t84 (not @t85)))) % 0.38/0.69 (assume @p62 (forall @t11 (=> @t10 (and @t83 (tptp.relation @t55))))) % 0.38/0.69 (assume @p63 (forall @t11 (=> @t10 (and @t85 (tptp.relation @t59))))) % 0.38/0.69 (assume @p64 (forall @t6 (=> @t80 (and (tptp.empty @t65) @t70)))) % 0.38/0.69 (assume @p65 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.38/0.69 (assume @p66 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.38/0.69 (assume @p67 (forall @t6 (=> @t61 (= (tptp.subset_complement @t1 @t60) @t2)))) % 0.38/0.69 (assume @p68 (forall @t11 (=> @t9 (= (tptp.relation_inverse @t63) @t1)))) % 0.38/0.69 (assume @p69 (forall @t6 (=> @t68 (= (tptp.complements_of_subsets @t1 @t66) @t2)))) % 0.38/0.69 (assume @p70 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 0.38/0.69 (assume @p71 (forall @t11 (not (= @t44 tptp.empty_set)))) % 0.38/0.69 (assume @p72 (forall @t6 (=> @t5 (= (tptp.set_union2 @t44 @t2) @t2)))) % 0.38/0.69 (assume @p73 (forall @t6 (not (and @t86 @t5)))) % 0.38/0.69 (assume @p74 (forall @t6 (=> (not @t5) @t86))) % 0.38/0.69 (assume @p75 (forall @t6 (= (tptp.subset @t44 @t2) @t5))) % 0.38/0.69 (assume @p76 (forall @t6 (= (= @t57 tptp.empty_set) @t24))) % 0.38/0.69 (assume @p77 (forall @t6 (=> @t61 (forall @t42 (=> @t41 @t18))))) % 0.38/0.69 (assume @p78 (forall @t51 (=> @t24 (or @t18 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t17))))))) % 0.38/0.69 (assume @p79 (forall @t6 (= (tptp.subset @t1 @t87) (or @t37 (= @t1 @t87))))) % 0.38/0.69 (assume @p80 (forall @t6 (=> @t5 (tptp.subset @t1 @t88)))) % 0.38/0.69 (assume @p81 (forall @t90 (= (tptp.in @t62 (tptp.cartesian_product2 @t17 @t16)) (and @t89 (tptp.in @t2 @t16))))) % 0.38/0.69 (assume @p82 (forall @t6 (=> @t54 @t91))) % 0.38/0.69 (assume @p83 (exists @t11 (and @t10 @t9))) % 0.38/0.69 (assume @p84 (forall @t11 (=> @t49 (exists @t34 (and @t61 @t82))))) % 0.38/0.69 (assume @p85 (exists @t11 @t10)) % 0.38/0.69 (assume @p86 (exists @t11 @t84)) % 0.38/0.69 (assume @p87 (forall @t11 (exists @t34 (and @t61 @t47)))) % 0.38/0.69 (assume @p88 (exists @t11 @t49)) % 0.38/0.69 (assume @p89 (forall @t6 (=> @t68 (= @t72 @t88)))) % 0.38/0.69 (assume @p90 (forall @t6 (=> @t68 (= @t73 (tptp.set_meet @t2))))) % 0.38/0.69 (assume @p91 (forall @t51 (=> @t76 (= @t74 @t92)))) % 0.38/0.69 (assume @p92 (forall @t6 (tptp.subset @t1 @t1))) % 0.38/0.69 (assume @p93 (forall @t6 (=> @t64 (tptp.disjoint @t2 @t1)))) % 0.38/0.69 (assume @p94 (forall @t90 (not (and (= @t12 (tptp.unordered_pair @t17 @t16)) (not @t93) (not (= @t1 @t16)))))) % 0.38/0.69 (assume @p95 (forall @t51 (=> @t24 (and (tptp.subset @t94 (tptp.cartesian_product2 @t2 @t17)) (tptp.subset (tptp.cartesian_product2 @t17 @t1) (tptp.cartesian_product2 @t17 @t2)))))) % 0.38/0.69 (assume @p96 (forall @t90 (=> (and @t24 (tptp.subset @t17 @t16)) (tptp.subset @t94 (tptp.cartesian_product2 @t2 @t16))))) % 0.38/0.69 (assume @p97 (forall @t6 (=> @t24 (= @t14 @t2)))) % 0.38/0.69 (assume @p98 (forall @t11 (exists @t34 (and @t5 @t99 (forall @t42 (=> @t41 (tptp.in @t98 @t2))) @t97)))) % 0.38/0.69 (assume @p99 (forall @t6 (tptp.subset @t15 @t1))) % 0.38/0.69 (assume @p100 (forall @t51 (=> (and @t24 @t101) (tptp.subset @t1 @t100)))) % 0.38/0.69 (assume @p101 (forall @t11 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.38/0.69 (assume @p102 (forall @t6 (=> @t5 @t102))) % 0.38/0.69 (assume @p103 (forall @t51 (=> (and @t24 (tptp.subset @t2 @t17)) @t101))) % 0.38/0.69 (assume @p104 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.38/0.69 (assume @p105 (forall @t51 (=> @t32 (=> @t104 (and @t103 (tptp.in @t2 (tptp.relation_rng @t17))))))) % 0.38/0.69 (assume @p106 (forall @t11 (=> @t9 (tptp.subset @t1 (tptp.cartesian_product2 @t55 @t59))))) % 0.38/0.69 (assume @p107 @t111) % 0.38/0.69 (assume @p108 (forall @t51 (=> @t24 (tptp.subset (tptp.set_intersection2 @t1 @t17) @t100)))) % 0.38/0.69 (assume @p109 (forall @t6 (=> @t24 (= @t15 @t1)))) % 0.38/0.69 (assume @p110 (forall @t11 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.38/0.69 (assume @p111 (forall @t6 (=> @t102 (or @t47 @t5)))) % 0.38/0.69 (assume @p112 (forall @t6 (=> (forall @t42 (= @t18 @t41)) @t25))) % 0.38/0.69 (assume @p113 (forall @t11 (tptp.subset tptp.empty_set @t1))) % 0.38/0.69 (assume @p114 (forall @t51 (=> @t32 (=> @t104 (and (tptp.in @t1 @t112) (tptp.in @t2 @t112)))))) % 0.38/0.69 (assume @p115 (forall @t51 (=> @t24 (tptp.subset (tptp.set_difference @t1 @t17) @t92)))) % 0.38/0.69 (assume @p116 (forall @t90 (=> (= @t62 @t19) (and @t93 (= @t2 @t16))))) % 0.38/0.69 (assume @p117 (forall @t6 (tptp.subset @t57 @t1))) % 0.38/0.69 (assume @p118 (forall @t11 (=> @t9 (and (= @t59 (tptp.relation_dom @t63)) (= @t55 (tptp.relation_rng @t63)))))) % 0.38/0.69 (assume @p119 (forall @t51 (= (tptp.subset @t12 @t17) (and @t89 @t113)))) % 0.38/0.69 (assume @p120 (forall @t6 (= @t114 @t14))) % 0.38/0.69 (assume @p121 (forall @t11 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.38/0.69 (assume @p122 (forall @t6 (= @t91 @t24))) % 0.38/0.69 (assume @p123 (forall @t6 (and (not (and @t116 (forall @t42 (not @t115)))) (not (and (exists @t42 @t115) @t64))))) % 0.38/0.69 (assume @p124 (forall @t11 (=> (tptp.subset @t1 tptp.empty_set) @t37))) % 0.38/0.69 (assume @p125 (forall @t6 (= (tptp.set_difference @t14 @t2) @t57))) % 0.38/0.69 (assume @p126 (forall @t6 (=> @t61 (forall @t42 (=> @t75 (= @t118 (tptp.subset @t2 @t117))))))) % 0.38/0.69 (assume @p127 (forall @t11 (=> @t9 (forall @t34 (=> @t23 (tptp.subset @t119 @t55)))))) % 0.38/0.69 (assume @p128 (forall @t11 (=> @t9 (forall @t34 (=> @t23 (tptp.subset (tptp.relation_rng @t65) @t105)))))) % 0.38/0.69 (assume @p129 (forall @t6 (=> @t24 (= @t2 @t114)))) % 0.38/0.69 (assume @p130 (forall @t11 (=> @t9 (forall @t34 (=> @t23 (=> (tptp.subset @t59 @t106) (= @t119 @t55))))))) % 0.38/0.69 (assume @p131 (forall @t6 (=> @t68 (not (and @t120 (= @t66 tptp.empty_set)))))) % 0.38/0.69 (assume @p132 (forall @t11 (=> @t9 (forall @t34 (=> @t23 (=> (tptp.subset @t55 @t105) (= (tptp.relation_rng @t79) @t59))))))) % 0.38/0.69 (assume @p133 (forall @t6 (=> @t68 (=> @t120 (= (tptp.subset_difference @t1 @t56 @t72) (tptp.meet_of_subsets @t1 @t66)))))) % 0.38/0.69 (assume @p134 (forall @t6 (=> @t68 (=> @t120 (= (tptp.union_of_subsets @t1 @t66) (tptp.subset_difference @t1 @t56 @t73)))))) % 0.38/0.69 (assume @p135 (forall @t6 (= (tptp.set_difference @t1 @t57) @t15))) % 0.38/0.69 (assume @p136 (forall @t11 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.38/0.69 (assume @p137 (forall @t51 (=> (and @t5 @t121) (tptp.element @t1 @t17)))) % 0.38/0.69 (assume @p138 (forall @t6 (and (not (and @t116 (forall @t42 (not @t122)))) (not (and (exists @t42 @t122) @t64))))) % 0.38/0.69 (assume @p139 (forall @t11 (=> @t43 (forall @t34 (=> @t61 (forall @t42 (=> (tptp.element @t17 @t1) (=> @t95 (tptp.in @t17 @t60))))))))) % 0.38/0.69 (assume @p140 (forall @t51 (=> @t75 (not (and (tptp.in @t2 @t117) @t113))))) % 0.38/0.69 (assume @p141 (forall @t11 (=> @t9 (=> (forall @t33 (not (tptp.in (tptp.ordered_pair @t2 @t17) @t1))) @t37)))) % 0.38/0.69 (assume @p142 (forall @t51 (not (and @t5 @t121 (tptp.empty @t17))))) % 0.38/0.69 (assume @p143 (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set))) % 0.38/0.69 (assume @p144 (forall @t6 (not (and @t24 @t7)))) % 0.38/0.69 (assume @p145 (forall @t51 (=> (and @t24 @t118) (tptp.disjoint @t1 @t17)))) % 0.38/0.69 (assume @p146 (forall @t11 (=> @t9 (=> (or @t124 @t123) @t37)))) % 0.38/0.69 (assume @p147 (forall @t11 (=> @t9 (= @t124 @t123)))) % 0.38/0.69 (assume @p148 (forall @t6 (= (= (tptp.set_difference @t1 @t87) @t1) @t4))) % 0.38/0.69 (assume @p149 (forall @t11 (= (tptp.unordered_pair @t1 @t1) @t44))) % 0.38/0.69 (assume @p150 (forall @t11 (=> @t10 @t37))) % 0.38/0.69 (assume @p151 (forall @t6 (=> (tptp.subset @t44 @t87) @t25))) % 0.38/0.69 (assume @p152 (forall @t11 (and (= (tptp.relation_dom @t22) @t1) (= (tptp.relation_rng @t22) @t1)))) % 0.38/0.69 (assume @p153 (forall @t90 (=> (tptp.relation @t16) (= (tptp.in @t62 (tptp.relation_composition (tptp.identity_relation @t17) @t16)) (and @t89 (tptp.in @t62 @t16)))))) % 0.38/0.69 (assume @p154 (forall @t6 (not (and @t5 @t47)))) % 0.38/0.69 (assume @p155 (forall @t6 (tptp.subset @t1 @t14))) % 0.38/0.69 (assume @p156 (forall @t6 (= @t64 (= @t57 @t1)))) % 0.38/0.69 (assume @p157 (forall @t51 (=> @t32 (= (tptp.in @t1 (tptp.relation_dom (tptp.relation_dom_restriction @t17 @t2))) (and @t5 @t103))))) % 0.38/0.69 (assume @p158 @t127) % 0.38/0.69 (assume @p159 (forall @t6 (not (and @t10 @t69 @t47)))) % 0.38/0.69 (assume @p160 (forall @t51 (=> (and @t24 @t96) (tptp.subset (tptp.set_union2 @t1 @t17) @t2)))) % 0.38/0.69 (assume @p161 (forall @t51 (=> @t128 @t25))) % 0.38/0.69 (assume @p162 (forall @t6 (=> @t23 (= (tptp.relation_dom @t125) (tptp.set_intersection2 @t106 @t1))))) % 0.38/0.69 (assume @p163 (forall @t6 (=> @t23 (= @t125 (tptp.relation_composition @t22 @t2))))) % 0.38/0.69 (assume @p164 @t131) % 0.38/0.69 (assume @p165 (forall @t11 (= (tptp.union @t45) @t1))) % 0.38/0.69 (assume @p166 (forall @t11 (exists @t34 (and @t5 @t99 (forall @t42 (not (and @t41 (forall @t40 (not (and @t28 (forall (@list @t26) (=> (tptp.subset @t26 @t17) (tptp.in @t26 @t16))))))))) @t97)))) % 0.38/0.69 (assume @p167 (forall @t51 (=> @t128 (= @t2 @t17)))) % 0.38/0.69 (step @p168 :rule bool-impl-elim :args (@t23 @t129)) % 0.38/0.69 (step @p169 :rule cong :premises (@p168) :args (@t130)) % 0.38/0.69 (step @p170 :rule cong :premises (@p169) :args (@t131)) % 0.38/0.69 (step @p171 :rule eq_resolve :premises (@p164 @p170)) % 0.38/0.69 (step @p172 :rule skolemize :premises (@p171)) % 0.38/0.69 (step @p173 :rule bool-double-not-elim :args (@t135)) % 0.38/0.69 (step @p174 :rule refl :args (@t140)) % 0.38/0.69 (step @p175 :rule nary_cong :premises (@p174 @p173) :args ((or @t140 (not @t139)))) % 0.38/0.69 (step @p176 :rule cnf_or_neg :args (@t140 0)) % 0.38/0.69 (step @p177 :rule eq_resolve :premises (@p176 @p175)) % 0.38/0.69 (step @p178 :rule reordering :premises (@p177) :args ((or @t135 @t140))) % 0.38/0.69 (step @p179 :rule chain_m_resolution :premises (@p178 @p172) :args (@t135 @t141 @t142)) % 0.38/0.69 (step @p180 :rule aci_norm :args ((= @t149 (or @t147 @t146 @t145 @t144)))) % 0.38/0.69 (step @p181 :rule cong :premises (@p180) :args (@t150)) % 0.38/0.69 (step @p182 :rule quant-merge-prenex :args ((= (forall @t11 @t152) @t150))) % 0.38/0.69 (step @p183 :rule alpha_equiv :args (@t153 (@list @t143) (@list @t2))) % 0.38/0.69 (step @p184 :rule refl :args (@t147)) % 0.38/0.69 (step @p185 :rule nary_cong :premises (@p184 @p183) :args (@t154)) % 0.38/0.69 (step @p186 :rule quant-miniscope-or :args ((= @t152 @t154))) % 0.38/0.69 (step @p187 :rule trans :premises (@p186 @p185)) % 0.38/0.69 (step @p188 :rule symm :premises (@p187)) % 0.38/0.69 (step @p189 :rule cong :premises (@p188) :args ((forall @t11 (or @t147 @t157)))) % 0.38/0.69 (step @p190 :rule trans :premises (@p189 @p182)) % 0.38/0.69 (step @p191 :rule trans :premises (@p190 @p181)) % 0.38/0.69 (step @p192 :rule bool-impl-elim :args (@t9 @t157)) % 0.38/0.69 (step @p193 :rule cong :premises (@p192) :args ((forall @t11 (=> @t9 @t157)))) % 0.38/0.69 (step @p194 :rule trans :premises (@p193 @p191)) % 0.38/0.69 (step @p195 :rule aci_norm :args ((= (or @t132 (or @t155 @t107)) @t156))) % 0.38/0.69 (step @p196 :rule bool-impl-elim :args (@t24 @t107)) % 0.38/0.69 (step @p197 :rule refl :args (@t132)) % 0.38/0.69 (step @p198 :rule nary_cong :premises (@p197 @p196) :args ((or @t132 @t108))) % 0.38/0.69 (step @p199 :rule trans :premises (@p198 @p195)) % 0.38/0.69 (step @p200 :rule bool-impl-elim :args (@t23 @t108)) % 0.38/0.69 (step @p201 :rule trans :premises (@p200 @p199)) % 0.38/0.69 (step @p202 :rule cong :premises (@p201) :args (@t109)) % 0.38/0.69 (step @p203 :rule refl :args (@t9)) % 0.38/0.69 (step @p204 :rule cong :premises (@p203 @p202) :args (@t110)) % 0.38/0.69 (step @p205 :rule cong :premises (@p204) :args (@t111)) % 0.38/0.69 (step @p206 :rule trans :premises (@p205 @p194)) % 0.38/0.69 (step @p207 :rule eq_resolve :premises (@p107 @p206)) % 0.38/0.69 (step @p208 :rule instantiate :premises (@p207) :args ((@list @t137 @t134))) % 0.38/0.69 (step @p209 :rule cnf_or_neg :args (@t140 1)) % 0.38/0.69 (step @p210 :rule chain_m_resolution :premises (@p209 @p172) :args ((not @t138) @t141 @t142)) % 0.38/0.69 (step @p211 :rule cnf_and_pos :args (@t158 1)) % 0.38/0.69 (step @p212 :rule reordering :premises (@p211) :args ((or @t138 @t159))) % 0.38/0.69 (step @p213 :rule chain_m_resolution :premises (@p212 @p210) :args (@t159 @t141 (@list @t138))) % 0.38/0.69 (step @p214 :rule bool-impl-elim :args (@t9 @t77)) % 0.38/0.69 (step @p215 :rule cong :premises (@p214) :args (@t78)) % 0.38/0.69 (step @p216 :rule eq_resolve :premises (@p45 @p215)) % 0.38/0.69 (step @p217 :rule instantiate :premises (@p216) :args ((@list @t134 @t136))) % 0.38/0.69 (step @p218 :rule cnf_or_pos :args (@t161)) % 0.38/0.69 (step @p219 :rule reordering :premises (@p218) :args ((or @t139 @t160 (not @t161)))) % 0.38/0.69 (step @p220 :rule chain_m_resolution :premises (@p219 @p179 @p217) :args (@t160 @t162 (@list @t135 @t161))) % 0.38/0.69 (step @p221 :rule bool-impl-elim :args (@t23 @t126)) % 0.38/0.69 (step @p222 :rule cong :premises (@p221) :args (@t127)) % 0.38/0.69 (step @p223 :rule eq_resolve :premises (@p158 @p222)) % 0.38/0.69 (step @p224 :rule instantiate :premises (@p223) :args ((@list @t136 @t134))) % 0.38/0.69 (step @p225 :rule cnf_or_pos :args (@t164)) % 0.38/0.69 (step @p226 :rule reordering :premises (@p225) :args ((or @t139 @t163 (not @t164)))) % 0.38/0.69 (step @p227 :rule chain_m_resolution :premises (@p226 @p179 @p224) :args (@t163 @t162 (@list @t135 @t164))) % 0.38/0.69 (step @p228 :rule cnf_or_pos :args (@t167)) % 0.38/0.69 (step @p229 :rule reordering :premises (@p228) :args ((or @t139 @t166 @t165 @t158 (not @t167)))) % 0.38/0.69 (step @p230 false :rule chain_m_resolution :premises (@p229 @p227 @p220 @p213 @p208 @p179) :args (false (@list false false true false false) (@list @t163 @t160 @t158 @t167 @t135))) % 0.38/0.69 ) % 0.38/0.69 % SZS output end Proof % 0.38/0.70 % cvc5 exiting %------------------------------------------------------------------------------