%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU180+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 : n017.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 08:50:52 AM UTC 2026 % Result : Theorem 0.93s 1.15s % Output : Proof 0.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU180+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 % 0.18/0.34 % Computer : n017.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 16:32:31 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.93/1.15 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.93/1.15 % SZS status Theorem % 0.93/1.15 % SZS output start Proof % 0.93/1.15 ( % 0.93/1.15 (declare-sort $$unsorted 0) % 0.93/1.15 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 0.93/1.15 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.93/1.15 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.93/1.15 (declare-const tptp.relation_field (-> $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.93/1.15 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.93/1.15 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.93/1.15 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.93/1.15 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.empty_set $$unsorted) % 0.93/1.15 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.93/1.15 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.93/1.15 (define @t1 () (@var "A" $$unsorted)) % 0.93/1.15 (define @t2 () (@var "B" $$unsorted)) % 0.93/1.15 (define @t3 () (tptp.in @t2 @t1)) % 0.93/1.15 (define @t4 () (not @t3)) % 0.93/1.15 (define @t5 () (tptp.in @t1 @t2)) % 0.93/1.15 (define @t6 () (@list @t1 @t2)) % 0.93/1.15 (define @t7 () (tptp.proper_subset @t2 @t1)) % 0.93/1.15 (define @t8 () (tptp.proper_subset @t1 @t2)) % 0.93/1.15 (define @t9 () (tptp.unordered_pair @t1 @t2)) % 0.93/1.15 (define @t10 () (tptp.set_union2 @t2 @t1)) % 0.93/1.15 (define @t11 () (tptp.set_union2 @t1 @t2)) % 0.93/1.15 (define @t12 () (tptp.set_intersection2 @t1 @t2)) % 0.93/1.15 (define @t13 () (tptp.subset @t1 @t2)) % 0.93/1.15 (define @t14 () (= @t1 @t2)) % 0.93/1.15 (define @t15 () (@var "D" $$unsorted)) % 0.93/1.15 (define @t16 () (@var "C" $$unsorted)) % 0.93/1.15 (define @t17 () (tptp.ordered_pair @t16 @t15)) % 0.93/1.15 (define @t18 () (@list @t16 @t15)) % 0.93/1.15 (define @t19 () (@list @t2)) % 0.93/1.15 (define @t20 () (tptp.relation @t1)) % 0.93/1.15 (define @t21 () (@list @t1)) % 0.93/1.15 (define @t22 () (= @t2 tptp.empty_set)) % 0.93/1.15 (define @t23 () (= @t2 (tptp.set_meet @t1))) % 0.93/1.15 (define @t24 () (= @t1 tptp.empty_set)) % 0.93/1.15 (define @t25 () (tptp.in @t16 @t15)) % 0.93/1.15 (define @t26 () (tptp.in @t15 @t1)) % 0.93/1.15 (define @t27 () (@list @t15)) % 0.93/1.15 (define @t28 () (tptp.in @t16 @t2)) % 0.93/1.15 (define @t29 () (@list @t16)) % 0.93/1.15 (define @t30 () (not @t24)) % 0.93/1.15 (define @t31 () (tptp.singleton @t1)) % 0.93/1.15 (define @t32 () (tptp.powerset @t1)) % 0.93/1.15 (define @t33 () (tptp.empty @t2)) % 0.93/1.15 (define @t34 () (tptp.element @t2 @t1)) % 0.93/1.15 (define @t35 () (tptp.empty @t1)) % 0.93/1.15 (define @t36 () (not @t35)) % 0.93/1.15 (define @t37 () (tptp.in @t15 @t16)) % 0.93/1.15 (define @t38 () (@list @t1 @t2 @t16)) % 0.93/1.15 (define @t39 () (tptp.in @t15 @t2)) % 0.93/1.15 (define @t40 () (@var "F" $$unsorted)) % 0.93/1.15 (define @t41 () (@var "E" $$unsorted)) % 0.93/1.15 (define @t42 () (tptp.cartesian_product2 @t1 @t2)) % 0.93/1.15 (define @t43 () (tptp.in @t16 @t1)) % 0.93/1.15 (define @t44 () (forall @t29 (=> @t43 @t28))) % 0.93/1.15 (define @t45 () (tptp.relation_dom @t1)) % 0.93/1.15 (define @t46 () (tptp.cast_to_subset @t1)) % 0.93/1.15 (define @t47 () (tptp.set_difference @t1 @t2)) % 0.93/1.15 (define @t48 () (tptp.relation_rng @t1)) % 0.93/1.15 (define @t49 () (tptp.subset_complement @t1 @t2)) % 0.93/1.15 (define @t50 () (tptp.element @t2 @t32)) % 0.93/1.15 (define @t51 () (tptp.ordered_pair @t1 @t2)) % 0.93/1.15 (define @t52 () (= (tptp.relation_field @t1) (tptp.set_union2 @t45 @t48))) % 0.93/1.15 (define @t53 () (forall @t21 (=> @t20 @t52))) % 0.93/1.15 (define @t54 () (tptp.disjoint @t1 @t2)) % 0.93/1.15 (define @t55 () (tptp.complements_of_subsets @t1 @t2)) % 0.93/1.15 (define @t56 () (tptp.powerset @t32)) % 0.93/1.15 (define @t57 () (tptp.element @t2 @t56)) % 0.93/1.15 (define @t58 () (not @t14)) % 0.93/1.15 (define @t59 () (tptp.union_of_subsets @t1 @t2)) % 0.93/1.15 (define @t60 () (tptp.meet_of_subsets @t1 @t2)) % 0.93/1.15 (define @t61 () (tptp.subset_difference @t1 @t2 @t16)) % 0.93/1.15 (define @t62 () (tptp.element @t16 @t32)) % 0.93/1.15 (define @t63 () (and @t50 @t62)) % 0.93/1.15 (define @t64 () (tptp.relation @t2)) % 0.93/1.15 (define @t65 () (not @t33)) % 0.93/1.15 (define @t66 () (tptp.disjoint @t31 @t2)) % 0.93/1.15 (define @t67 () (tptp.subset @t31 @t2)) % 0.93/1.15 (define @t68 () (forall @t6 (= @t67 @t5))) % 0.93/1.15 (define @t69 () (tptp.singleton @t2)) % 0.93/1.15 (define @t70 () (tptp.union @t2)) % 0.93/1.15 (define @t71 () (tptp.in @t1 @t16)) % 0.93/1.15 (define @t72 () (@list @t1 @t2 @t16 @t15)) % 0.93/1.15 (define @t73 () (tptp.element @t1 (tptp.powerset @t2))) % 0.93/1.15 (define @t74 () (tptp.set_difference @t2 @t16)) % 0.93/1.15 (define @t75 () (= @t1 @t16)) % 0.93/1.15 (define @t76 () (tptp.cartesian_product2 @t1 @t16)) % 0.93/1.15 (define @t77 () (not @t28)) % 0.93/1.15 (define @t78 () (tptp.subset @t16 @t2)) % 0.93/1.15 (define @t79 () (forall @t29 (not (and @t78 (not (tptp.are_equipotent @t16 @t2)) @t77)))) % 0.93/1.15 (define @t80 () (tptp.powerset @t16)) % 0.93/1.15 (define @t81 () (forall @t18 (=> (and @t28 (tptp.subset @t15 @t16)) @t39))) % 0.93/1.15 (define @t82 () (tptp.set_intersection2 @t2 @t16)) % 0.93/1.15 (define @t83 () (tptp.subset @t1 @t16)) % 0.93/1.15 (define @t84 () (tptp.element @t1 @t2)) % 0.93/1.15 (define @t85 () (tptp.subset @t2 @t16)) % 0.93/1.15 (define @t86 () (and @t13 @t85)) % 0.93/1.15 (define @t87 () (forall @t38 (=> @t86 @t83))) % 0.93/1.15 (define @t88 () (and (tptp.in @t1 (tptp.relation_dom @t16)) (tptp.in @t2 (tptp.relation_rng @t16)))) % 0.93/1.15 (define @t89 () (tptp.in @t51 @t16)) % 0.93/1.15 (define @t90 () (=> @t89 @t88)) % 0.93/1.15 (define @t91 () (tptp.relation @t16)) % 0.93/1.15 (define @t92 () (forall @t38 (=> @t91 @t90))) % 0.93/1.15 (define @t93 () (tptp.relation_field @t16)) % 0.93/1.15 (define @t94 () (and (tptp.in @t1 @t93) (tptp.in @t2 @t93))) % 0.93/1.15 (define @t95 () (=> @t89 @t94)) % 0.93/1.15 (define @t96 () (forall @t38 (=> @t91 @t95))) % 0.93/1.15 (define @t97 () (not @t96)) % 0.93/1.15 (define @t98 () (tptp.in @t2 @t16)) % 0.93/1.15 (define @t99 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.93/1.15 (define @t100 () (and @t43 @t28)) % 0.93/1.15 (define @t101 () (not @t54)) % 0.93/1.15 (define @t102 () (tptp.subset_complement @t1 @t16)) % 0.93/1.15 (define @t103 () (tptp.disjoint @t2 @t16)) % 0.93/1.15 (define @t104 () (not @t22)) % 0.93/1.15 (define @t105 () (tptp.element @t2 @t80)) % 0.93/1.15 (define @t106 () (tptp.in @t16 @t12)) % 0.93/1.15 (define @t107 () (= @t31 (tptp.unordered_pair @t2 @t16))) % 0.93/1.15 (define @t108 () (not @t85)) % 0.93/1.15 (define @t109 () (not @t13)) % 0.93/1.15 (define @t110 () (not @t89)) % 0.93/1.15 (define @t111 () (not @t91)) % 0.93/1.15 (define @t112 () (or @t111 @t110 @t94)) % 0.93/1.15 (define @t113 () (forall @t38 @t112)) % 0.93/1.15 (define @t114 () (@quantifiers_skolemize @t113 2)) % 0.93/1.15 (define @t115 () (tptp.relation_field @t114)) % 0.93/1.15 (define @t116 () (tptp.relation_rng @t114)) % 0.93/1.15 (define @t117 () (@quantifiers_skolemize @t113 1)) % 0.93/1.15 (define @t118 () (tptp.singleton @t117)) % 0.93/1.15 (define @t119 () (@quantifiers_skolemize @t113 0)) % 0.93/1.15 (define @t120 () (tptp.in (tptp.ordered_pair @t119 @t117) @t114)) % 0.93/1.15 (define @t121 () (tptp.in @t117 @t115)) % 0.93/1.15 (define @t122 () (tptp.in @t119 @t115)) % 0.93/1.15 (define @t123 () (and @t122 @t121)) % 0.93/1.15 (define @t124 () (not @t120)) % 0.93/1.15 (define @t125 () (tptp.relation @t114)) % 0.93/1.15 (define @t126 () (not @t125)) % 0.93/1.15 (define @t127 () (or @t126 @t124 @t123)) % 0.93/1.15 (define @t128 () (@list true)) % 0.93/1.15 (define @t129 () (@list @t127)) % 0.93/1.15 (define @t130 () (tptp.in @t117 @t116)) % 0.93/1.15 (define @t131 () (tptp.relation_dom @t114)) % 0.93/1.15 (define @t132 () (tptp.in @t119 @t131)) % 0.93/1.15 (define @t133 () (and @t132 @t130)) % 0.93/1.15 (define @t134 () (or @t126 @t124 @t133)) % 0.93/1.15 (define @t135 () (@list false false false)) % 0.93/1.15 (define @t136 () (not @t133)) % 0.93/1.15 (define @t137 () (@list false)) % 0.93/1.15 (define @t138 () (@list @t133)) % 0.93/1.15 (define @t139 () (tptp.subset @t118 @t116)) % 0.93/1.15 (define @t140 () (= @t130 @t139)) % 0.93/1.15 (define @t141 () (@list false false)) % 0.93/1.15 (define @t142 () (tptp.set_union2 @t131 @t116)) % 0.93/1.15 (define @t143 () (tptp.singleton @t119)) % 0.93/1.15 (define @t144 () (@list @t131 @t116)) % 0.93/1.15 (define @t145 () (tptp.subset @t143 @t131)) % 0.93/1.15 (define @t146 () (= @t132 @t145)) % 0.93/1.15 (define @t147 () (tptp.subset @t143 @t142)) % 0.93/1.15 (define @t148 () (tptp.subset @t131 @t142)) % 0.93/1.15 (define @t149 () (not @t148)) % 0.93/1.15 (define @t150 () (not @t145)) % 0.93/1.15 (define @t151 () (or @t150 @t149 @t147)) % 0.93/1.15 (define @t152 () (= @t115 @t142)) % 0.93/1.15 (define @t153 () (or @t126 @t152)) % 0.93/1.15 (define @t154 () (tptp.subset @t143 @t115)) % 0.93/1.15 (define @t155 () (= @t122 @t154)) % 0.93/1.15 (define @t156 () (@list true false)) % 0.93/1.15 (define @t157 () (tptp.subset @t118 @t115)) % 0.93/1.15 (define @t158 () (= @t121 @t157)) % 0.93/1.15 (define @t159 () (not @t157)) % 0.93/1.15 (define @t160 () (not (tptp.subset @t116 @t115))) % 0.93/1.15 (define @t161 () (not @t139)) % 0.93/1.15 (define @t162 () (or @t161 @t160 @t157)) % 0.93/1.15 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.93/1.15 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 0.93/1.15 (assume @p3 (forall @t6 (= @t9 (tptp.unordered_pair @t2 @t1)))) % 0.93/1.15 (assume @p4 (forall @t6 (= @t11 @t10))) % 0.93/1.15 (assume @p5 (forall @t6 (= @t12 (tptp.set_intersection2 @t2 @t1)))) % 0.93/1.15 (assume @p6 (forall @t6 (= @t14 (and @t13 (tptp.subset @t2 @t1))))) % 0.93/1.15 (assume @p7 (forall @t21 (= @t20 (forall @t19 (not (and @t3 (forall @t18 (not (= @t2 @t17))))))))) % 0.93/1.15 (assume @p8 (forall @t6 (and (=> @t30 (= @t23 (forall @t29 (= @t28 (forall @t27 (=> @t26 @t25)))))) (=> @t24 (= @t23 @t22))))) % 0.93/1.15 (assume @p9 (forall @t6 (= (= @t2 @t31) (forall @t29 (= @t28 (= @t16 @t1)))))) % 0.93/1.15 (assume @p10 (forall @t21 (= @t24 (forall @t19 @t4)))) % 0.93/1.15 (assume @p11 (forall @t6 (= (= @t2 @t32) (forall @t29 (= @t28 (tptp.subset @t16 @t1)))))) % 0.93/1.15 (assume @p12 (forall @t6 (and (=> @t36 (= @t34 @t3)) (=> @t35 (= @t34 @t33))))) % 0.93/1.15 (assume @p13 (forall @t38 (= (= @t16 @t9) (forall @t27 (= @t37 (or (= @t15 @t1) (= @t15 @t2))))))) % 0.93/1.15 (assume @p14 (forall @t38 (= (= @t16 @t11) (forall @t27 (= @t37 (or @t26 @t39)))))) % 0.93/1.15 (assume @p15 (forall @t38 (= (= @t16 @t42) (forall @t27 (= @t37 (exists (@list @t41 @t40) (and (tptp.in @t41 @t1) (tptp.in @t40 @t2) (= @t15 (tptp.ordered_pair @t41 @t40))))))))) % 0.93/1.15 (assume @p16 (forall @t6 (= @t13 @t44))) % 0.93/1.15 (assume @p17 (forall @t38 (= (= @t16 @t12) (forall @t27 (= @t37 (and @t26 @t39)))))) % 0.93/1.15 (assume @p18 (forall @t21 (=> @t20 (forall @t19 (= (= @t2 @t45) (forall @t29 (= @t28 (exists @t27 (tptp.in @t17 @t1))))))))) % 0.93/1.15 (assume @p19 (forall @t21 (= @t46 @t1))) % 0.93/1.15 (assume @p20 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t29 (= @t28 (exists @t27 (and @t25 @t26))))))) % 0.93/1.15 (assume @p21 (forall @t38 (= (= @t16 @t47) (forall @t27 (= @t37 (and @t26 (not @t39))))))) % 0.93/1.15 (assume @p22 (forall @t21 (=> @t20 (forall @t19 (= (= @t2 @t48) (forall @t29 (= @t28 (exists @t27 (tptp.in (tptp.ordered_pair @t15 @t16) @t1))))))))) % 0.93/1.15 (assume @p23 (forall @t6 (=> @t50 (= @t49 @t47)))) % 0.93/1.15 (assume @p24 (forall @t6 (= @t51 (tptp.unordered_pair @t9 @t31)))) % 0.93/1.15 (assume @p25 @t53) % 0.93/1.15 (assume @p26 (forall @t6 (= @t54 (= @t12 tptp.empty_set)))) % 0.93/1.15 (assume @p27 (forall @t6 (=> @t57 (forall @t29 (=> (tptp.element @t16 @t56) (= (= @t16 @t55) (forall @t27 (=> (tptp.element @t15 @t32) (= @t37 (tptp.in (tptp.subset_complement @t1 @t15) @t2)))))))))) % 0.93/1.15 (assume @p28 (forall @t6 (= @t8 (and @t13 @t58)))) % 0.93/1.15 (assume @p29 true) % 0.93/1.15 (assume @p30 (forall @t21 (tptp.element @t46 @t32))) % 0.93/1.15 (assume @p31 (forall @t6 (=> @t50 (tptp.element @t49 @t32)))) % 0.93/1.15 (assume @p32 (forall @t6 (=> @t57 (tptp.element @t59 @t32)))) % 0.93/1.15 (assume @p33 (forall @t6 (=> @t57 (tptp.element @t60 @t32)))) % 0.93/1.15 (assume @p34 (forall @t38 (=> @t63 (tptp.element @t61 @t32)))) % 0.93/1.15 (assume @p35 (forall @t6 (=> @t57 (tptp.element @t55 @t56)))) % 0.93/1.15 (assume @p36 (forall @t21 (exists @t19 @t34))) % 0.93/1.15 (assume @p37 (forall @t21 (not (tptp.empty @t32)))) % 0.93/1.15 (assume @p38 (tptp.empty tptp.empty_set)) % 0.93/1.15 (assume @p39 (forall @t6 (not (tptp.empty @t51)))) % 0.93/1.15 (assume @p40 (forall @t6 (=> (and @t20 @t64) (tptp.relation @t11)))) % 0.93/1.15 (assume @p41 (forall @t21 (not (tptp.empty @t31)))) % 0.93/1.15 (assume @p42 (forall @t6 (=> @t36 (not (tptp.empty @t11))))) % 0.93/1.15 (assume @p43 (forall @t6 (not (tptp.empty @t9)))) % 0.93/1.15 (assume @p44 (forall @t6 (=> @t36 (not (tptp.empty @t10))))) % 0.93/1.15 (assume @p45 (forall @t6 (=> (and @t36 @t65) (not (tptp.empty @t42))))) % 0.93/1.15 (assume @p46 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.93/1.15 (assume @p47 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.93/1.15 (assume @p48 (forall @t6 (=> @t50 (= (tptp.subset_complement @t1 @t49) @t2)))) % 0.93/1.15 (assume @p49 (forall @t6 (=> @t57 (= (tptp.complements_of_subsets @t1 @t55) @t2)))) % 0.93/1.15 (assume @p50 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 0.93/1.15 (assume @p51 (forall @t21 (not (= @t31 tptp.empty_set)))) % 0.93/1.15 (assume @p52 (forall @t6 (=> @t5 (= (tptp.set_union2 @t31 @t2) @t2)))) % 0.93/1.15 (assume @p53 (forall @t6 (not (and @t66 @t5)))) % 0.93/1.15 (assume @p54 (forall @t6 (=> (not @t5) @t66))) % 0.93/1.15 (assume @p55 @t68) % 0.93/1.15 (assume @p56 (forall @t6 (= (= @t47 tptp.empty_set) @t13))) % 0.93/1.15 (assume @p57 (forall @t6 (=> @t50 (forall @t29 (=> @t28 @t43))))) % 0.93/1.15 (assume @p58 (forall @t38 (=> @t13 (or @t43 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t16))))))) % 0.93/1.15 (assume @p59 (forall @t6 (= (tptp.subset @t1 @t69) (or @t24 (= @t1 @t69))))) % 0.93/1.15 (assume @p60 (forall @t6 (=> @t5 (tptp.subset @t1 @t70)))) % 0.93/1.15 (assume @p61 (forall @t72 (= (tptp.in @t51 (tptp.cartesian_product2 @t16 @t15)) (and @t71 (tptp.in @t2 @t15))))) % 0.93/1.15 (assume @p62 (forall @t6 (=> @t44 @t73))) % 0.93/1.15 (assume @p63 (exists @t21 (and @t35 @t20))) % 0.93/1.15 (assume @p64 (forall @t21 (=> @t36 (exists @t19 (and @t50 @t65))))) % 0.93/1.15 (assume @p65 (exists @t21 @t35)) % 0.93/1.15 (assume @p66 (forall @t21 (exists @t19 (and @t50 @t33)))) % 0.93/1.15 (assume @p67 (exists @t21 @t36)) % 0.93/1.15 (assume @p68 (forall @t6 (=> @t57 (= @t59 @t70)))) % 0.93/1.15 (assume @p69 (forall @t6 (=> @t57 (= @t60 (tptp.set_meet @t2))))) % 0.93/1.15 (assume @p70 (forall @t38 (=> @t63 (= @t61 @t74)))) % 0.93/1.15 (assume @p71 (forall @t6 (tptp.subset @t1 @t1))) % 0.93/1.15 (assume @p72 (forall @t6 (=> @t54 (tptp.disjoint @t2 @t1)))) % 0.93/1.15 (assume @p73 (forall @t72 (not (and (= @t9 (tptp.unordered_pair @t16 @t15)) (not @t75) (not (= @t1 @t15)))))) % 0.93/1.15 (assume @p74 (forall @t38 (=> @t13 (and (tptp.subset @t76 (tptp.cartesian_product2 @t2 @t16)) (tptp.subset (tptp.cartesian_product2 @t16 @t1) (tptp.cartesian_product2 @t16 @t2)))))) % 0.93/1.15 (assume @p75 (forall @t72 (=> (and @t13 (tptp.subset @t16 @t15)) (tptp.subset @t76 (tptp.cartesian_product2 @t2 @t15))))) % 0.93/1.15 (assume @p76 (forall @t6 (=> @t13 (= @t11 @t2)))) % 0.93/1.15 (assume @p77 (forall @t21 (exists @t19 (and @t5 @t81 (forall @t29 (=> @t28 (tptp.in @t80 @t2))) @t79)))) % 0.93/1.15 (assume @p78 (forall @t6 (tptp.subset @t12 @t1))) % 0.93/1.15 (assume @p79 (forall @t38 (=> (and @t13 @t83) (tptp.subset @t1 @t82)))) % 0.93/1.15 (assume @p80 (forall @t21 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.93/1.15 (assume @p81 (forall @t6 (=> @t5 @t84))) % 0.93/1.15 (assume @p82 @t87) % 0.93/1.15 (assume @p83 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.93/1.15 (assume @p84 @t92) % 0.93/1.15 (assume @p85 (forall @t21 (=> @t20 (tptp.subset @t1 (tptp.cartesian_product2 @t45 @t48))))) % 0.93/1.15 (assume @p86 (forall @t21 (=> @t20 (forall @t19 (=> @t64 (=> @t13 (and (tptp.subset @t45 (tptp.relation_dom @t2)) (tptp.subset @t48 (tptp.relation_rng @t2))))))))) % 0.93/1.15 (assume @p87 (forall @t38 (=> @t13 (tptp.subset (tptp.set_intersection2 @t1 @t16) @t82)))) % 0.93/1.15 (assume @p88 (forall @t6 (=> @t13 (= @t12 @t1)))) % 0.93/1.15 (assume @p89 (forall @t21 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.93/1.15 (assume @p90 (forall @t6 (=> @t84 (or @t33 @t5)))) % 0.93/1.15 (assume @p91 (forall @t6 (=> (forall @t29 (= @t43 @t28)) @t14))) % 0.93/1.15 (assume @p92 (forall @t21 (tptp.subset tptp.empty_set @t1))) % 0.93/1.15 (assume @p93 @t97) % 0.93/1.15 (assume @p94 (forall @t38 (=> @t13 (tptp.subset (tptp.set_difference @t1 @t16) @t74)))) % 0.93/1.15 (assume @p95 (forall @t72 (=> (= @t51 @t17) (and @t75 (= @t2 @t15))))) % 0.93/1.15 (assume @p96 (forall @t6 (tptp.subset @t47 @t1))) % 0.93/1.15 (assume @p97 (forall @t38 (= (tptp.subset @t9 @t16) (and @t71 @t98)))) % 0.93/1.15 (assume @p98 (forall @t6 (= @t99 @t11))) % 0.93/1.15 (assume @p99 (forall @t21 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.93/1.15 (assume @p100 (forall @t6 (= @t73 @t13))) % 0.93/1.15 (assume @p101 (forall @t6 (and (not (and @t101 (forall @t29 (not @t100)))) (not (and (exists @t29 @t100) @t54))))) % 0.93/1.15 (assume @p102 (forall @t21 (=> (tptp.subset @t1 tptp.empty_set) @t24))) % 0.93/1.15 (assume @p103 (forall @t6 (= (tptp.set_difference @t11 @t2) @t47))) % 0.93/1.15 (assume @p104 (forall @t6 (=> @t50 (forall @t29 (=> @t62 (= @t103 (tptp.subset @t2 @t102))))))) % 0.93/1.15 (assume @p105 (forall @t6 (=> @t13 (= @t2 @t99)))) % 0.93/1.15 (assume @p106 (forall @t6 (=> @t57 (not (and @t104 (= @t55 tptp.empty_set)))))) % 0.93/1.15 (assume @p107 (forall @t6 (=> @t57 (=> @t104 (= (tptp.subset_difference @t1 @t46 @t59) (tptp.meet_of_subsets @t1 @t55)))))) % 0.93/1.15 (assume @p108 (forall @t6 (=> @t57 (=> @t104 (= (tptp.union_of_subsets @t1 @t55) (tptp.subset_difference @t1 @t46 @t60)))))) % 0.93/1.15 (assume @p109 (forall @t6 (= (tptp.set_difference @t1 @t47) @t12))) % 0.93/1.15 (assume @p110 (forall @t21 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.93/1.15 (assume @p111 (forall @t38 (=> (and @t5 @t105) (tptp.element @t1 @t16)))) % 0.93/1.15 (assume @p112 (forall @t6 (and (not (and @t101 (forall @t29 (not @t106)))) (not (and (exists @t29 @t106) @t54))))) % 0.93/1.15 (assume @p113 (forall @t21 (=> @t30 (forall @t19 (=> @t50 (forall @t29 (=> (tptp.element @t16 @t1) (=> @t77 (tptp.in @t16 @t49))))))))) % 0.93/1.15 (assume @p114 (forall @t38 (=> @t62 (not (and (tptp.in @t2 @t102) @t98))))) % 0.93/1.15 (assume @p115 (forall @t38 (not (and @t5 @t105 (tptp.empty @t16))))) % 0.93/1.15 (assume @p116 (forall @t6 (not (and @t13 @t7)))) % 0.93/1.15 (assume @p117 (forall @t38 (=> (and @t13 @t103) (tptp.disjoint @t1 @t16)))) % 0.93/1.15 (assume @p118 (forall @t6 (= (= (tptp.set_difference @t1 @t69) @t1) @t4))) % 0.93/1.15 (assume @p119 (forall @t21 (= (tptp.unordered_pair @t1 @t1) @t31))) % 0.93/1.15 (assume @p120 (forall @t21 (=> @t35 @t24))) % 0.93/1.15 (assume @p121 (forall @t6 (=> (tptp.subset @t31 @t69) @t14))) % 0.93/1.15 (assume @p122 (forall @t6 (not (and @t5 @t33)))) % 0.93/1.15 (assume @p123 (forall @t6 (tptp.subset @t1 @t11))) % 0.93/1.15 (assume @p124 (forall @t6 (= @t54 (= @t47 @t1)))) % 0.93/1.15 (assume @p125 (forall @t6 (not (and @t35 @t58 @t33)))) % 0.93/1.15 (assume @p126 (forall @t38 (=> (and @t13 @t78) (tptp.subset (tptp.set_union2 @t1 @t16) @t2)))) % 0.93/1.15 (assume @p127 (forall @t38 (=> @t107 @t14))) % 0.93/1.15 (assume @p128 (forall @t21 (= (tptp.union @t32) @t1))) % 0.93/1.15 (assume @p129 (forall @t21 (exists @t19 (and @t5 @t81 (forall @t29 (not (and @t28 (forall @t27 (not (and @t39 (forall (@list @t41) (=> (tptp.subset @t41 @t16) (tptp.in @t41 @t15))))))))) @t79)))) % 0.93/1.15 (assume @p130 (forall @t38 (=> @t107 (= @t2 @t16)))) % 0.93/1.15 (step @p131 :rule evaluate :args ((= true false))) % 0.93/1.15 (step @p132 :rule aci_norm :args ((= (or (or @t109 @t108) @t83) (or @t109 @t108 @t83)))) % 0.93/1.15 (step @p133 :rule refl :args (@t83)) % 0.93/1.15 (step @p134 :rule bool-and-de-morgan :args (@t13 @t85 true)) % 0.93/1.15 (step @p135 :rule nary_cong :premises (@p134 @p133) :args ((or (not @t86) @t83))) % 0.93/1.15 (step @p136 :rule trans :premises (@p135 @p132)) % 0.93/1.15 (step @p137 :rule bool-impl-elim :args (@t86 @t83)) % 0.93/1.15 (step @p138 :rule trans :premises (@p137 @p136)) % 0.93/1.15 (step @p139 :rule cong :premises (@p138) :args (@t87)) % 0.93/1.15 (step @p140 :rule eq_resolve :premises (@p82 @p139)) % 0.93/1.15 (step @p141 :rule instantiate :premises (@p140) :args ((@list @t118 @t116 @t115))) % 0.93/1.15 (step @p142 :rule eq-symm :args (@t67 @t5)) % 0.93/1.15 (step @p143 :rule cong :premises (@p142) :args (@t68)) % 0.93/1.15 (step @p144 :rule eq_resolve :premises (@p55 @p143)) % 0.93/1.15 (step @p145 :rule instantiate :premises (@p144) :args ((@list @t117 @t116))) % 0.93/1.15 (step @p146 :rule aci_norm :args ((= (or @t111 (or @t110 @t88)) (or @t111 @t110 @t88)))) % 0.93/1.15 (step @p147 :rule bool-impl-elim :args (@t89 @t88)) % 0.93/1.15 (step @p148 :rule refl :args (@t111)) % 0.93/1.15 (step @p149 :rule nary_cong :premises (@p148 @p147) :args ((or @t111 @t90))) % 0.93/1.15 (step @p150 :rule trans :premises (@p149 @p146)) % 0.93/1.15 (step @p151 :rule bool-impl-elim :args (@t91 @t90)) % 0.93/1.15 (step @p152 :rule trans :premises (@p151 @p150)) % 0.93/1.15 (step @p153 :rule cong :premises (@p152) :args (@t92)) % 0.93/1.15 (step @p154 :rule eq_resolve :premises (@p84 @p153)) % 0.93/1.15 (step @p155 :rule instantiate :premises (@p154) :args ((@list @t119 @t117 @t114))) % 0.93/1.15 (step @p156 :rule aci_norm :args ((= (or @t111 (or @t110 @t94)) @t112))) % 0.93/1.15 (step @p157 :rule bool-impl-elim :args (@t89 @t94)) % 0.93/1.15 (step @p158 :rule nary_cong :premises (@p148 @p157) :args ((or @t111 @t95))) % 0.93/1.15 (step @p159 :rule trans :premises (@p158 @p156)) % 0.93/1.15 (step @p160 :rule bool-impl-elim :args (@t91 @t95)) % 0.93/1.15 (step @p161 :rule trans :premises (@p160 @p159)) % 0.93/1.15 (step @p162 :rule cong :premises (@p161) :args (@t96)) % 0.93/1.15 (step @p163 :rule cong :premises (@p162) :args (@t97)) % 0.93/1.15 (step @p164 :rule eq_resolve :premises (@p93 @p163)) % 0.93/1.15 (step @p165 :rule skolemize :premises (@p164)) % 0.93/1.15 (step @p166 :rule bool-double-not-elim :args (@t120)) % 0.93/1.15 (step @p167 :rule refl :args (@t127)) % 0.93/1.15 (step @p168 :rule nary_cong :premises (@p167 @p166) :args ((or @t127 (not @t124)))) % 0.93/1.15 (step @p169 :rule cnf_or_neg :args (@t127 1)) % 0.93/1.15 (step @p170 :rule eq_resolve :premises (@p169 @p168)) % 0.93/1.15 (step @p171 :rule reordering :premises (@p170) :args ((or @t120 @t127))) % 0.93/1.15 (step @p172 :rule chain_m_resolution :premises (@p171 @p165) :args (@t120 @t128 @t129)) % 0.93/1.15 (step @p173 :rule bool-double-not-elim :args (@t125)) % 0.93/1.15 (step @p174 :rule nary_cong :premises (@p167 @p173) :args ((or @t127 (not @t126)))) % 0.93/1.15 (step @p175 :rule cnf_or_neg :args (@t127 0)) % 0.93/1.15 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 0.93/1.15 (step @p177 :rule reordering :premises (@p176) :args ((or @t125 @t127))) % 0.93/1.15 (step @p178 :rule chain_m_resolution :premises (@p177 @p165) :args (@t125 @t128 @t129)) % 0.93/1.15 (step @p179 :rule cnf_or_pos :args (@t134)) % 0.93/1.15 (step @p180 :rule reordering :premises (@p179) :args ((or @t126 @t124 @t133 (not @t134)))) % 0.93/1.15 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p172 @p155) :args (@t133 @t135 (@list @t125 @t120 @t134))) % 0.93/1.15 (step @p182 :rule cnf_and_pos :args (@t133 1)) % 0.93/1.15 (step @p183 :rule reordering :premises (@p182) :args ((or @t130 @t136))) % 0.93/1.15 (step @p184 :rule chain_m_resolution :premises (@p183 @p181) :args (@t130 @t137 @t138)) % 0.93/1.15 (step @p185 :rule cnf_equiv_pos1 :args (@t140)) % 0.93/1.15 (step @p186 :rule reordering :premises (@p185) :args ((or (not @t130) @t139 (not @t140)))) % 0.93/1.15 (step @p187 :rule chain_m_resolution :premises (@p186 @p184 @p145) :args (@t139 @t141 (@list @t130 @t140))) % 0.93/1.15 (step @p188 :rule instantiate :premises (@p144) :args ((@list @t117 @t115))) % 0.93/1.15 (step @p189 :rule instantiate :premises (@p144) :args ((@list @t119 @t115))) % 0.93/1.15 (step @p190 :rule instantiate :premises (@p140) :args ((@list @t143 @t131 @t142))) % 0.93/1.15 (step @p191 :rule instantiate :premises (@p123) :args (@t144)) % 0.93/1.15 (step @p192 :rule instantiate :premises (@p144) :args ((@list @t119 @t131))) % 0.93/1.15 (step @p193 :rule cnf_and_pos :args (@t133 0)) % 0.93/1.15 (step @p194 :rule reordering :premises (@p193) :args ((or @t132 @t136))) % 0.93/1.15 (step @p195 :rule chain_m_resolution :premises (@p194 @p181) :args (@t132 @t137 @t138)) % 0.93/1.15 (step @p196 :rule cnf_equiv_pos1 :args (@t146)) % 0.93/1.15 (step @p197 :rule reordering :premises (@p196) :args ((or (not @t132) @t145 (not @t146)))) % 0.93/1.15 (step @p198 :rule chain_m_resolution :premises (@p197 @p195 @p192) :args (@t145 @t141 (@list @t132 @t146))) % 0.93/1.15 (step @p199 :rule cnf_or_pos :args (@t151)) % 0.93/1.15 (step @p200 :rule reordering :premises (@p199) :args ((or @t150 @t149 @t147 (not @t151)))) % 0.93/1.15 (step @p201 :rule chain_m_resolution :premises (@p200 @p198 @p191 @p190) :args (@t147 @t135 (@list @t145 @t148 @t151))) % 0.93/1.15 (step @p202 :rule true_intro :premises (@p201)) % 0.93/1.15 (step @p203 :rule bool-impl-elim :args (@t20 @t52)) % 0.93/1.15 (step @p204 :rule cong :premises (@p203) :args (@t53)) % 0.93/1.15 (step @p205 :rule eq_resolve :premises (@p25 @p204)) % 0.93/1.15 (step @p206 :rule instantiate :premises (@p205) :args ((@list @t114))) % 0.93/1.15 (step @p207 :rule cnf_or_pos :args (@t153)) % 0.93/1.15 (step @p208 :rule reordering :premises (@p207) :args ((or @t126 @t152 (not @t153)))) % 0.93/1.15 (step @p209 :rule chain_m_resolution :premises (@p208 @p178 @p206) :args (@t152 @t141 (@list @t125 @t153))) % 0.93/1.15 (step @p210 :rule refl :args (@t143)) % 0.93/1.15 (step @p211 :rule cong :premises (@p210 @p209) :args (@t154)) % 0.93/1.15 (step @p212 :rule trans :premises (@p211 @p202)) % 0.93/1.15 (step @p213 :rule true_elim :premises (@p212)) % 0.93/1.15 (step @p214 :rule cnf_equiv_pos2 :args (@t155)) % 0.93/1.15 (step @p215 :rule reordering :premises (@p214) :args ((or @t122 (not @t154) (not @t155)))) % 0.93/1.15 (step @p216 :rule chain_m_resolution :premises (@p215 @p213 @p189) :args (@t122 @t141 (@list @t154 @t155))) % 0.93/1.15 (step @p217 :rule cnf_or_neg :args (@t127 2)) % 0.93/1.15 (step @p218 :rule chain_m_resolution :premises (@p217 @p165) :args ((not @t123) @t128 @t129)) % 0.93/1.15 (step @p219 :rule cnf_and_neg :args (@t123)) % 0.93/1.15 (step @p220 :rule chain_m_resolution :premises (@p219 @p218 @p216) :args ((not @t121) @t156 (@list @t123 @t122))) % 0.93/1.15 (step @p221 :rule cnf_equiv_pos2 :args (@t158)) % 0.93/1.15 (step @p222 :rule reordering :premises (@p221) :args ((or @t121 @t159 (not @t158)))) % 0.93/1.15 (step @p223 :rule chain_m_resolution :premises (@p222 @p220 @p188) :args (@t159 @t156 (@list @t121 @t158))) % 0.93/1.15 (step @p224 :rule cnf_or_pos :args (@t162)) % 0.93/1.15 (step @p225 :rule reordering :premises (@p224) :args ((or @t157 @t161 @t160 (not @t162)))) % 0.93/1.15 (step @p226 :rule chain_m_resolution :premises (@p225 @p223 @p187 @p141) :args (@t160 (@list true false false) (@list @t157 @t139 @t162))) % 0.93/1.15 (step @p227 :rule false_intro :premises (@p226)) % 0.93/1.15 (step @p228 :rule symm :premises (@p209)) % 0.93/1.15 (step @p229 :rule refl :args (@t116)) % 0.93/1.15 (step @p230 :rule cong :premises (@p229 @p228) :args ((tptp.subset @t116 @t142))) % 0.93/1.15 (step @p231 :rule instantiate :premises (@p4) :args (@t144)) % 0.93/1.15 (step @p232 :rule symm :premises (@p231)) % 0.93/1.15 (step @p233 :rule cong :premises (@p229 @p232) :args ((tptp.subset @t116 (tptp.set_union2 @t116 @t131)))) % 0.93/1.15 (step @p234 :rule instantiate :premises (@p123) :args ((@list @t116 @t131))) % 0.93/1.15 (step @p235 :rule true_intro :premises (@p234)) % 0.93/1.15 (step @p236 :rule symm :premises (@p235)) % 0.93/1.15 (step @p237 :rule trans :premises (@p236 @p233 @p230 @p227)) % 0.93/1.15 (step @p238 false :rule eq_resolve :premises (@p237 @p131)) % 0.93/1.15 ) % 0.93/1.15 % SZS output end Proof % 0.93/1.15 % cvc5 exiting %------------------------------------------------------------------------------