%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU178+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 : n022.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 08:50:51 AM UTC 2026 % Result : Theorem 0.45s 0.68s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU178+2 : TPTP v9.2.1. Released v3.3.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.32 % Computer : n022.cluster.edu % 0.17/0.32 % Model : x86_64 x86_64 % 0.17/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.32 % Memory : 8042.1875MB % 0.17/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.33 % CPULimit : 300 % 0.17/0.33 % WCLimit : 300 % 0.17/0.33 % DateTime : Tue Jun 2 16:33:53 EDT 2026 % 0.17/0.33 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.68 % SZS status Theorem % 0.45/0.68 % SZS output start Proof % 0.45/0.68 ( % 0.45/0.68 (declare-sort $$unsorted 0) % 0.45/0.68 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 0.45/0.68 (declare-const tptp.subset_difference (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.meet_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.cast_to_subset (-> $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.45/0.68 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.45/0.68 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.45/0.68 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.45/0.68 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.45/0.68 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.45/0.68 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.empty_set $$unsorted) % 0.45/0.68 (declare-const tptp.set_meet (-> $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.complements_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.45/0.68 (define @t1 () (@var "A" $$unsorted)) % 0.45/0.68 (define @t2 () (@var "B" $$unsorted)) % 0.45/0.68 (define @t3 () (tptp.in @t2 @t1)) % 0.45/0.68 (define @t4 () (not @t3)) % 0.45/0.68 (define @t5 () (tptp.in @t1 @t2)) % 0.45/0.68 (define @t6 () (@list @t1 @t2)) % 0.45/0.68 (define @t7 () (tptp.proper_subset @t2 @t1)) % 0.45/0.68 (define @t8 () (tptp.proper_subset @t1 @t2)) % 0.45/0.68 (define @t9 () (tptp.unordered_pair @t1 @t2)) % 0.45/0.68 (define @t10 () (tptp.set_union2 @t2 @t1)) % 0.45/0.68 (define @t11 () (tptp.set_union2 @t1 @t2)) % 0.45/0.68 (define @t12 () (tptp.set_intersection2 @t1 @t2)) % 0.45/0.68 (define @t13 () (tptp.subset @t1 @t2)) % 0.45/0.68 (define @t14 () (= @t1 @t2)) % 0.45/0.68 (define @t15 () (@var "D" $$unsorted)) % 0.45/0.68 (define @t16 () (@var "C" $$unsorted)) % 0.45/0.68 (define @t17 () (tptp.ordered_pair @t16 @t15)) % 0.45/0.68 (define @t18 () (@list @t16 @t15)) % 0.45/0.68 (define @t19 () (forall @t18 (not (= @t2 @t17)))) % 0.45/0.68 (define @t20 () (@list @t2)) % 0.45/0.68 (define @t21 () (forall @t20 (not (and @t3 @t19)))) % 0.45/0.68 (define @t22 () (tptp.relation @t1)) % 0.45/0.68 (define @t23 () (= @t22 @t21)) % 0.45/0.68 (define @t24 () (@list @t1)) % 0.45/0.68 (define @t25 () (forall @t24 @t23)) % 0.45/0.68 (define @t26 () (= @t2 tptp.empty_set)) % 0.45/0.68 (define @t27 () (= @t2 (tptp.set_meet @t1))) % 0.45/0.68 (define @t28 () (= @t1 tptp.empty_set)) % 0.45/0.68 (define @t29 () (tptp.in @t16 @t15)) % 0.45/0.68 (define @t30 () (tptp.in @t15 @t1)) % 0.45/0.68 (define @t31 () (@list @t15)) % 0.45/0.68 (define @t32 () (tptp.in @t16 @t2)) % 0.45/0.68 (define @t33 () (@list @t16)) % 0.45/0.68 (define @t34 () (not @t28)) % 0.45/0.68 (define @t35 () (tptp.singleton @t1)) % 0.45/0.68 (define @t36 () (tptp.powerset @t1)) % 0.45/0.68 (define @t37 () (tptp.empty @t2)) % 0.45/0.68 (define @t38 () (tptp.element @t2 @t1)) % 0.45/0.68 (define @t39 () (tptp.empty @t1)) % 0.45/0.68 (define @t40 () (not @t39)) % 0.45/0.68 (define @t41 () (tptp.in @t15 @t16)) % 0.45/0.68 (define @t42 () (@list @t1 @t2 @t16)) % 0.45/0.68 (define @t43 () (tptp.in @t15 @t2)) % 0.45/0.68 (define @t44 () (@var "F" $$unsorted)) % 0.45/0.68 (define @t45 () (@var "E" $$unsorted)) % 0.45/0.68 (define @t46 () (tptp.cartesian_product2 @t1 @t2)) % 0.45/0.68 (define @t47 () (tptp.in @t16 @t1)) % 0.45/0.68 (define @t48 () (forall @t33 (=> @t47 @t32))) % 0.45/0.68 (define @t49 () (= @t13 @t48)) % 0.45/0.68 (define @t50 () (forall @t6 @t49)) % 0.45/0.68 (define @t51 () (tptp.relation_dom @t1)) % 0.45/0.68 (define @t52 () (tptp.cast_to_subset @t1)) % 0.45/0.68 (define @t53 () (tptp.set_difference @t1 @t2)) % 0.45/0.68 (define @t54 () (tptp.relation_rng @t1)) % 0.45/0.68 (define @t55 () (tptp.subset_complement @t1 @t2)) % 0.45/0.68 (define @t56 () (tptp.element @t2 @t36)) % 0.45/0.68 (define @t57 () (tptp.ordered_pair @t1 @t2)) % 0.45/0.68 (define @t58 () (tptp.disjoint @t1 @t2)) % 0.45/0.68 (define @t59 () (tptp.complements_of_subsets @t1 @t2)) % 0.45/0.68 (define @t60 () (tptp.powerset @t36)) % 0.45/0.68 (define @t61 () (tptp.element @t2 @t60)) % 0.45/0.68 (define @t62 () (not @t14)) % 0.45/0.68 (define @t63 () (tptp.union_of_subsets @t1 @t2)) % 0.45/0.68 (define @t64 () (tptp.meet_of_subsets @t1 @t2)) % 0.45/0.68 (define @t65 () (tptp.subset_difference @t1 @t2 @t16)) % 0.45/0.68 (define @t66 () (tptp.element @t16 @t36)) % 0.45/0.68 (define @t67 () (and @t56 @t66)) % 0.45/0.68 (define @t68 () (not @t37)) % 0.45/0.68 (define @t69 () (tptp.disjoint @t35 @t2)) % 0.45/0.68 (define @t70 () (tptp.singleton @t2)) % 0.45/0.68 (define @t71 () (tptp.union @t2)) % 0.45/0.68 (define @t72 () (tptp.in @t1 @t16)) % 0.45/0.68 (define @t73 () (@list @t1 @t2 @t16 @t15)) % 0.45/0.68 (define @t74 () (tptp.element @t1 (tptp.powerset @t2))) % 0.45/0.68 (define @t75 () (tptp.set_difference @t2 @t16)) % 0.45/0.68 (define @t76 () (= @t1 @t16)) % 0.45/0.68 (define @t77 () (tptp.cartesian_product2 @t1 @t16)) % 0.45/0.68 (define @t78 () (not @t32)) % 0.45/0.68 (define @t79 () (tptp.subset @t16 @t2)) % 0.45/0.68 (define @t80 () (forall @t33 (not (and @t79 (not (tptp.are_equipotent @t16 @t2)) @t78)))) % 0.45/0.68 (define @t81 () (tptp.powerset @t16)) % 0.45/0.68 (define @t82 () (forall @t18 (=> (and @t32 (tptp.subset @t15 @t16)) @t43))) % 0.45/0.68 (define @t83 () (tptp.set_intersection2 @t2 @t16)) % 0.45/0.68 (define @t84 () (tptp.subset @t1 @t16)) % 0.45/0.68 (define @t85 () (tptp.element @t1 @t2)) % 0.45/0.68 (define @t86 () (and (tptp.in @t1 (tptp.relation_dom @t16)) (tptp.in @t2 (tptp.relation_rng @t16)))) % 0.45/0.68 (define @t87 () (tptp.in @t57 @t16)) % 0.45/0.68 (define @t88 () (=> @t87 @t86)) % 0.45/0.68 (define @t89 () (tptp.relation @t16)) % 0.45/0.68 (define @t90 () (forall @t42 (=> @t89 @t88))) % 0.45/0.68 (define @t91 () (tptp.subset @t1 (tptp.cartesian_product2 @t51 @t54))) % 0.45/0.68 (define @t92 () (forall @t24 (=> @t22 @t91))) % 0.45/0.68 (define @t93 () (not @t92)) % 0.45/0.68 (define @t94 () (tptp.in @t2 @t16)) % 0.45/0.68 (define @t95 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.45/0.68 (define @t96 () (and @t47 @t32)) % 0.45/0.68 (define @t97 () (not @t58)) % 0.45/0.68 (define @t98 () (tptp.subset_complement @t1 @t16)) % 0.45/0.68 (define @t99 () (tptp.disjoint @t2 @t16)) % 0.45/0.68 (define @t100 () (not @t26)) % 0.45/0.68 (define @t101 () (tptp.element @t2 @t81)) % 0.45/0.68 (define @t102 () (tptp.in @t16 @t12)) % 0.45/0.68 (define @t103 () (= @t35 (tptp.unordered_pair @t2 @t16))) % 0.45/0.68 (define @t104 () (@quantifiers_skolemize (forall @t24 (or (not @t22) @t91)) 0)) % 0.45/0.68 (define @t105 () (tptp.relation_rng @t104)) % 0.45/0.68 (define @t106 () (tptp.relation_dom @t104)) % 0.45/0.68 (define @t107 () (tptp.cartesian_product2 @t106 @t105)) % 0.45/0.68 (define @t108 () (forall @t33 (or (not (tptp.in @t16 @t104)) (tptp.in @t16 @t107)))) % 0.45/0.68 (define @t109 () (@quantifiers_skolemize @t108 0)) % 0.45/0.68 (define @t110 () (forall @t18 (not (= @t17 @t109)))) % 0.45/0.68 (define @t111 () (@quantifiers_skolemize @t110 1)) % 0.45/0.68 (define @t112 () (@quantifiers_skolemize @t110 0)) % 0.45/0.68 (define @t113 () (tptp.subset @t104 @t107)) % 0.45/0.68 (define @t114 () (tptp.relation @t104)) % 0.45/0.68 (define @t115 () (not @t114)) % 0.45/0.68 (define @t116 () (or @t115 @t113)) % 0.45/0.68 (define @t117 () (@list true)) % 0.45/0.68 (define @t118 () (@list @t116)) % 0.45/0.68 (define @t119 () (= @t113 @t108)) % 0.45/0.68 (define @t120 () (not @t108)) % 0.45/0.68 (define @t121 () (tptp.in @t109 @t107)) % 0.45/0.68 (define @t122 () (tptp.in @t109 @t104)) % 0.45/0.68 (define @t123 () (not @t122)) % 0.45/0.68 (define @t124 () (or @t123 @t121)) % 0.45/0.68 (define @t125 () (@list @t124)) % 0.45/0.68 (define @t126 () (forall @t20 (or (not (tptp.in @t2 @t104)) (not @t19)))) % 0.45/0.68 (define @t127 () (= @t114 @t126)) % 0.45/0.68 (define @t128 () (@list false false)) % 0.45/0.68 (define @t129 () (not (= @t109 @t17))) % 0.45/0.68 (define @t130 () (forall @t18 @t129)) % 0.45/0.68 (define @t131 () (not @t130)) % 0.45/0.68 (define @t132 () (or @t123 @t131)) % 0.45/0.68 (define @t133 () (not @t110)) % 0.45/0.68 (define @t134 () (or @t123 @t133)) % 0.45/0.68 (define @t135 () (tptp.ordered_pair @t112 @t111)) % 0.45/0.68 (define @t136 () (= @t109 @t135)) % 0.45/0.68 (define @t137 () (= @t135 @t109)) % 0.45/0.68 (define @t138 () (not (not @t137))) % 0.45/0.68 (define @t139 () (tptp.in @t135 @t107)) % 0.45/0.68 (define @t140 () (not @t87)) % 0.45/0.68 (define @t141 () (not @t89)) % 0.45/0.68 (define @t142 () (tptp.in @t135 @t104)) % 0.45/0.68 (define @t143 () (and (tptp.in @t112 @t106) (tptp.in @t111 @t105))) % 0.45/0.68 (define @t144 () (not @t142)) % 0.45/0.68 (define @t145 () (or @t115 @t144 @t143)) % 0.45/0.68 (define @t146 () (= @t139 @t143)) % 0.45/0.68 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.45/0.68 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 0.45/0.68 (assume @p3 (forall @t6 (= @t9 (tptp.unordered_pair @t2 @t1)))) % 0.45/0.68 (assume @p4 (forall @t6 (= @t11 @t10))) % 0.45/0.68 (assume @p5 (forall @t6 (= @t12 (tptp.set_intersection2 @t2 @t1)))) % 0.45/0.68 (assume @p6 (forall @t6 (= @t14 (and @t13 (tptp.subset @t2 @t1))))) % 0.45/0.68 (assume @p7 @t25) % 0.45/0.68 (assume @p8 (forall @t6 (and (=> @t34 (= @t27 (forall @t33 (= @t32 (forall @t31 (=> @t30 @t29)))))) (=> @t28 (= @t27 @t26))))) % 0.45/0.68 (assume @p9 (forall @t6 (= (= @t2 @t35) (forall @t33 (= @t32 (= @t16 @t1)))))) % 0.45/0.68 (assume @p10 (forall @t24 (= @t28 (forall @t20 @t4)))) % 0.45/0.68 (assume @p11 (forall @t6 (= (= @t2 @t36) (forall @t33 (= @t32 (tptp.subset @t16 @t1)))))) % 0.45/0.68 (assume @p12 (forall @t6 (and (=> @t40 (= @t38 @t3)) (=> @t39 (= @t38 @t37))))) % 0.45/0.68 (assume @p13 (forall @t42 (= (= @t16 @t9) (forall @t31 (= @t41 (or (= @t15 @t1) (= @t15 @t2))))))) % 0.45/0.68 (assume @p14 (forall @t42 (= (= @t16 @t11) (forall @t31 (= @t41 (or @t30 @t43)))))) % 0.45/0.68 (assume @p15 (forall @t42 (= (= @t16 @t46) (forall @t31 (= @t41 (exists (@list @t45 @t44) (and (tptp.in @t45 @t1) (tptp.in @t44 @t2) (= @t15 (tptp.ordered_pair @t45 @t44))))))))) % 0.45/0.68 (assume @p16 @t50) % 0.45/0.68 (assume @p17 (forall @t42 (= (= @t16 @t12) (forall @t31 (= @t41 (and @t30 @t43)))))) % 0.45/0.68 (assume @p18 (forall @t24 (=> @t22 (forall @t20 (= (= @t2 @t51) (forall @t33 (= @t32 (exists @t31 (tptp.in @t17 @t1))))))))) % 0.45/0.68 (assume @p19 (forall @t24 (= @t52 @t1))) % 0.45/0.68 (assume @p20 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t33 (= @t32 (exists @t31 (and @t29 @t30))))))) % 0.45/0.68 (assume @p21 (forall @t42 (= (= @t16 @t53) (forall @t31 (= @t41 (and @t30 (not @t43))))))) % 0.45/0.68 (assume @p22 (forall @t24 (=> @t22 (forall @t20 (= (= @t2 @t54) (forall @t33 (= @t32 (exists @t31 (tptp.in (tptp.ordered_pair @t15 @t16) @t1))))))))) % 0.45/0.68 (assume @p23 (forall @t6 (=> @t56 (= @t55 @t53)))) % 0.45/0.68 (assume @p24 (forall @t6 (= @t57 (tptp.unordered_pair @t9 @t35)))) % 0.45/0.68 (assume @p25 (forall @t6 (= @t58 (= @t12 tptp.empty_set)))) % 0.45/0.68 (assume @p26 (forall @t6 (=> @t61 (forall @t33 (=> (tptp.element @t16 @t60) (= (= @t16 @t59) (forall @t31 (=> (tptp.element @t15 @t36) (= @t41 (tptp.in (tptp.subset_complement @t1 @t15) @t2)))))))))) % 0.45/0.68 (assume @p27 (forall @t6 (= @t8 (and @t13 @t62)))) % 0.45/0.68 (assume @p28 true) % 0.45/0.68 (assume @p29 (forall @t24 (tptp.element @t52 @t36))) % 0.45/0.68 (assume @p30 (forall @t6 (=> @t56 (tptp.element @t55 @t36)))) % 0.45/0.68 (assume @p31 (forall @t6 (=> @t61 (tptp.element @t63 @t36)))) % 0.45/0.68 (assume @p32 (forall @t6 (=> @t61 (tptp.element @t64 @t36)))) % 0.45/0.68 (assume @p33 (forall @t42 (=> @t67 (tptp.element @t65 @t36)))) % 0.45/0.68 (assume @p34 (forall @t6 (=> @t61 (tptp.element @t59 @t60)))) % 0.45/0.68 (assume @p35 (forall @t24 (exists @t20 @t38))) % 0.45/0.68 (assume @p36 (forall @t24 (not (tptp.empty @t36)))) % 0.45/0.68 (assume @p37 (tptp.empty tptp.empty_set)) % 0.45/0.68 (assume @p38 (forall @t6 (not (tptp.empty @t57)))) % 0.45/0.68 (assume @p39 (forall @t24 (not (tptp.empty @t35)))) % 0.45/0.68 (assume @p40 (forall @t6 (=> @t40 (not (tptp.empty @t11))))) % 0.45/0.68 (assume @p41 (forall @t6 (not (tptp.empty @t9)))) % 0.45/0.68 (assume @p42 (forall @t6 (=> @t40 (not (tptp.empty @t10))))) % 0.45/0.68 (assume @p43 (forall @t6 (=> (and @t40 @t68) (not (tptp.empty @t46))))) % 0.45/0.68 (assume @p44 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.45/0.68 (assume @p45 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.45/0.68 (assume @p46 (forall @t6 (=> @t56 (= (tptp.subset_complement @t1 @t55) @t2)))) % 0.45/0.68 (assume @p47 (forall @t6 (=> @t61 (= (tptp.complements_of_subsets @t1 @t59) @t2)))) % 0.45/0.68 (assume @p48 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 0.45/0.68 (assume @p49 (forall @t24 (not (= @t35 tptp.empty_set)))) % 0.45/0.68 (assume @p50 (forall @t6 (=> @t5 (= (tptp.set_union2 @t35 @t2) @t2)))) % 0.45/0.68 (assume @p51 (forall @t6 (not (and @t69 @t5)))) % 0.45/0.68 (assume @p52 (forall @t6 (=> (not @t5) @t69))) % 0.45/0.68 (assume @p53 (forall @t6 (= (tptp.subset @t35 @t2) @t5))) % 0.45/0.68 (assume @p54 (forall @t6 (= (= @t53 tptp.empty_set) @t13))) % 0.45/0.68 (assume @p55 (forall @t6 (=> @t56 (forall @t33 (=> @t32 @t47))))) % 0.45/0.68 (assume @p56 (forall @t42 (=> @t13 (or @t47 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t16))))))) % 0.45/0.68 (assume @p57 (forall @t6 (= (tptp.subset @t1 @t70) (or @t28 (= @t1 @t70))))) % 0.45/0.68 (assume @p58 (forall @t6 (=> @t5 (tptp.subset @t1 @t71)))) % 0.45/0.68 (assume @p59 (forall @t73 (= (tptp.in @t57 (tptp.cartesian_product2 @t16 @t15)) (and @t72 (tptp.in @t2 @t15))))) % 0.45/0.68 (assume @p60 (forall @t6 (=> @t48 @t74))) % 0.45/0.68 (assume @p61 (exists @t24 (and @t39 @t22))) % 0.45/0.68 (assume @p62 (forall @t24 (=> @t40 (exists @t20 (and @t56 @t68))))) % 0.45/0.68 (assume @p63 (exists @t24 @t39)) % 0.45/0.68 (assume @p64 (forall @t24 (exists @t20 (and @t56 @t37)))) % 0.45/0.68 (assume @p65 (exists @t24 @t40)) % 0.45/0.68 (assume @p66 (forall @t6 (=> @t61 (= @t63 @t71)))) % 0.45/0.68 (assume @p67 (forall @t6 (=> @t61 (= @t64 (tptp.set_meet @t2))))) % 0.45/0.68 (assume @p68 (forall @t42 (=> @t67 (= @t65 @t75)))) % 0.45/0.68 (assume @p69 (forall @t6 (tptp.subset @t1 @t1))) % 0.45/0.68 (assume @p70 (forall @t6 (=> @t58 (tptp.disjoint @t2 @t1)))) % 0.45/0.68 (assume @p71 (forall @t73 (not (and (= @t9 (tptp.unordered_pair @t16 @t15)) (not @t76) (not (= @t1 @t15)))))) % 0.45/0.68 (assume @p72 (forall @t42 (=> @t13 (and (tptp.subset @t77 (tptp.cartesian_product2 @t2 @t16)) (tptp.subset (tptp.cartesian_product2 @t16 @t1) (tptp.cartesian_product2 @t16 @t2)))))) % 0.45/0.68 (assume @p73 (forall @t73 (=> (and @t13 (tptp.subset @t16 @t15)) (tptp.subset @t77 (tptp.cartesian_product2 @t2 @t15))))) % 0.45/0.68 (assume @p74 (forall @t6 (=> @t13 (= @t11 @t2)))) % 0.45/0.68 (assume @p75 (forall @t24 (exists @t20 (and @t5 @t82 (forall @t33 (=> @t32 (tptp.in @t81 @t2))) @t80)))) % 0.45/0.68 (assume @p76 (forall @t6 (tptp.subset @t12 @t1))) % 0.45/0.68 (assume @p77 (forall @t42 (=> (and @t13 @t84) (tptp.subset @t1 @t83)))) % 0.45/0.68 (assume @p78 (forall @t24 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.45/0.68 (assume @p79 (forall @t6 (=> @t5 @t85))) % 0.45/0.68 (assume @p80 (forall @t42 (=> (and @t13 (tptp.subset @t2 @t16)) @t84))) % 0.45/0.68 (assume @p81 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.45/0.68 (assume @p82 @t90) % 0.45/0.68 (assume @p83 @t93) % 0.45/0.68 (assume @p84 (forall @t42 (=> @t13 (tptp.subset (tptp.set_intersection2 @t1 @t16) @t83)))) % 0.45/0.68 (assume @p85 (forall @t6 (=> @t13 (= @t12 @t1)))) % 0.45/0.68 (assume @p86 (forall @t24 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.45/0.68 (assume @p87 (forall @t6 (=> @t85 (or @t37 @t5)))) % 0.45/0.68 (assume @p88 (forall @t6 (=> (forall @t33 (= @t47 @t32)) @t14))) % 0.45/0.68 (assume @p89 (forall @t24 (tptp.subset tptp.empty_set @t1))) % 0.45/0.68 (assume @p90 (forall @t42 (=> @t13 (tptp.subset (tptp.set_difference @t1 @t16) @t75)))) % 0.45/0.68 (assume @p91 (forall @t73 (=> (= @t57 @t17) (and @t76 (= @t2 @t15))))) % 0.45/0.68 (assume @p92 (forall @t6 (tptp.subset @t53 @t1))) % 0.45/0.68 (assume @p93 (forall @t42 (= (tptp.subset @t9 @t16) (and @t72 @t94)))) % 0.45/0.68 (assume @p94 (forall @t6 (= @t95 @t11))) % 0.45/0.68 (assume @p95 (forall @t24 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.45/0.68 (assume @p96 (forall @t6 (= @t74 @t13))) % 0.45/0.68 (assume @p97 (forall @t6 (and (not (and @t97 (forall @t33 (not @t96)))) (not (and (exists @t33 @t96) @t58))))) % 0.45/0.68 (assume @p98 (forall @t24 (=> (tptp.subset @t1 tptp.empty_set) @t28))) % 0.45/0.68 (assume @p99 (forall @t6 (= (tptp.set_difference @t11 @t2) @t53))) % 0.45/0.68 (assume @p100 (forall @t6 (=> @t56 (forall @t33 (=> @t66 (= @t99 (tptp.subset @t2 @t98))))))) % 0.45/0.68 (assume @p101 (forall @t6 (=> @t13 (= @t2 @t95)))) % 0.45/0.68 (assume @p102 (forall @t6 (=> @t61 (not (and @t100 (= @t59 tptp.empty_set)))))) % 0.45/0.68 (assume @p103 (forall @t6 (=> @t61 (=> @t100 (= (tptp.subset_difference @t1 @t52 @t63) (tptp.meet_of_subsets @t1 @t59)))))) % 0.45/0.68 (assume @p104 (forall @t6 (=> @t61 (=> @t100 (= (tptp.union_of_subsets @t1 @t59) (tptp.subset_difference @t1 @t52 @t64)))))) % 0.45/0.68 (assume @p105 (forall @t6 (= (tptp.set_difference @t1 @t53) @t12))) % 0.45/0.68 (assume @p106 (forall @t24 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.45/0.68 (assume @p107 (forall @t42 (=> (and @t5 @t101) (tptp.element @t1 @t16)))) % 0.45/0.68 (assume @p108 (forall @t6 (and (not (and @t97 (forall @t33 (not @t102)))) (not (and (exists @t33 @t102) @t58))))) % 0.45/0.68 (assume @p109 (forall @t24 (=> @t34 (forall @t20 (=> @t56 (forall @t33 (=> (tptp.element @t16 @t1) (=> @t78 (tptp.in @t16 @t55))))))))) % 0.45/0.68 (assume @p110 (forall @t42 (=> @t66 (not (and (tptp.in @t2 @t98) @t94))))) % 0.45/0.68 (assume @p111 (forall @t42 (not (and @t5 @t101 (tptp.empty @t16))))) % 0.45/0.68 (assume @p112 (forall @t6 (not (and @t13 @t7)))) % 0.45/0.68 (assume @p113 (forall @t42 (=> (and @t13 @t99) (tptp.disjoint @t1 @t16)))) % 0.45/0.68 (assume @p114 (forall @t6 (= (= (tptp.set_difference @t1 @t70) @t1) @t4))) % 0.45/0.68 (assume @p115 (forall @t24 (= (tptp.unordered_pair @t1 @t1) @t35))) % 0.45/0.68 (assume @p116 (forall @t24 (=> @t39 @t28))) % 0.45/0.68 (assume @p117 (forall @t6 (=> (tptp.subset @t35 @t70) @t14))) % 0.45/0.68 (assume @p118 (forall @t6 (not (and @t5 @t37)))) % 0.45/0.68 (assume @p119 (forall @t6 (tptp.subset @t1 @t11))) % 0.45/0.68 (assume @p120 (forall @t6 (= @t58 (= @t53 @t1)))) % 0.45/0.68 (assume @p121 (forall @t6 (not (and @t39 @t62 @t37)))) % 0.45/0.68 (assume @p122 (forall @t42 (=> (and @t13 @t79) (tptp.subset (tptp.set_union2 @t1 @t16) @t2)))) % 0.45/0.68 (assume @p123 (forall @t42 (=> @t103 @t14))) % 0.45/0.68 (assume @p124 (forall @t24 (= (tptp.union @t36) @t1))) % 0.45/0.68 (assume @p125 (forall @t24 (exists @t20 (and @t5 @t82 (forall @t33 (not (and @t32 (forall @t31 (not (and @t43 (forall (@list @t45) (=> (tptp.subset @t45 @t16) (tptp.in @t45 @t15))))))))) @t80)))) % 0.45/0.68 (assume @p126 (forall @t42 (=> @t103 (= @t2 @t16)))) % 0.45/0.68 (step @p127 :rule instantiate :premises (@p59) :args ((@list @t112 @t111 @t106 @t105))) % 0.45/0.68 (step @p128 :rule bool-impl-elim :args (@t47 @t32)) % 0.45/0.68 (step @p129 :rule cong :premises (@p128) :args (@t48)) % 0.45/0.68 (step @p130 :rule refl :args (@t13)) % 0.45/0.68 (step @p131 :rule cong :premises (@p130 @p129) :args (@t49)) % 0.45/0.68 (step @p132 :rule cong :premises (@p131) :args (@t50)) % 0.45/0.68 (step @p133 :rule eq_resolve :premises (@p16 @p132)) % 0.45/0.68 (step @p134 :rule instantiate :premises (@p133) :args ((@list @t104 @t107))) % 0.45/0.68 (step @p135 :rule bool-impl-elim :args (@t22 @t91)) % 0.45/0.68 (step @p136 :rule cong :premises (@p135) :args (@t92)) % 0.45/0.68 (step @p137 :rule cong :premises (@p136) :args (@t93)) % 0.45/0.68 (step @p138 :rule eq_resolve :premises (@p83 @p137)) % 0.45/0.68 (step @p139 :rule skolemize :premises (@p138)) % 0.45/0.68 (step @p140 :rule cnf_or_neg :args (@t116 1)) % 0.45/0.68 (step @p141 :rule chain_m_resolution :premises (@p140 @p139) :args ((not @t113) @t117 @t118)) % 0.45/0.68 (step @p142 :rule cnf_equiv_pos2 :args (@t119)) % 0.45/0.68 (step @p143 :rule reordering :premises (@p142) :args ((or @t113 @t120 (not @t119)))) % 0.45/0.68 (step @p144 :rule chain_m_resolution :premises (@p143 @p141 @p134) :args (@t120 (@list true false) (@list @t113 @t119))) % 0.45/0.68 (step @p145 :rule skolemize :premises (@p144)) % 0.45/0.68 (step @p146 :rule cnf_or_neg :args (@t124 1)) % 0.45/0.68 (step @p147 :rule chain_m_resolution :premises (@p146 @p145) :args ((not @t121) @t117 @t125)) % 0.45/0.68 (step @p148 :rule false_intro :premises (@p147)) % 0.45/0.68 (step @p149 :rule refl :args (@t107)) % 0.45/0.68 (step @p150 :rule bool-and-de-morgan :args (@t3 @t19 true)) % 0.45/0.68 (step @p151 :rule cong :premises (@p150) :args (@t21)) % 0.45/0.68 (step @p152 :rule refl :args (@t22)) % 0.45/0.68 (step @p153 :rule cong :premises (@p152 @p151) :args (@t23)) % 0.45/0.68 (step @p154 :rule cong :premises (@p153) :args (@t25)) % 0.45/0.68 (step @p155 :rule eq_resolve :premises (@p7 @p154)) % 0.45/0.68 (step @p156 :rule instantiate :premises (@p155) :args ((@list @t104))) % 0.45/0.68 (step @p157 :rule bool-double-not-elim :args (@t114)) % 0.45/0.68 (step @p158 :rule refl :args (@t116)) % 0.45/0.68 (step @p159 :rule nary_cong :premises (@p158 @p157) :args ((or @t116 (not @t115)))) % 0.45/0.68 (step @p160 :rule cnf_or_neg :args (@t116 0)) % 0.45/0.68 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 0.45/0.68 (step @p162 :rule reordering :premises (@p161) :args ((or @t114 @t116))) % 0.45/0.68 (step @p163 :rule chain_m_resolution :premises (@p162 @p139) :args (@t114 @t117 @t118)) % 0.45/0.68 (step @p164 :rule cnf_equiv_pos1 :args (@t127)) % 0.45/0.68 (step @p165 :rule reordering :premises (@p164) :args ((or @t115 @t126 (not @t127)))) % 0.45/0.68 (step @p166 :rule chain_m_resolution :premises (@p165 @p163 @p156) :args (@t126 @t128 (@list @t114 @t127))) % 0.45/0.68 (step @p167 :rule eq-symm :args (@t109 @t17)) % 0.45/0.68 (step @p168 :rule cong :premises (@p167) :args (@t129)) % 0.45/0.68 (step @p169 :rule cong :premises (@p168) :args (@t130)) % 0.45/0.68 (step @p170 :rule cong :premises (@p169) :args (@t131)) % 0.45/0.68 (step @p171 :rule refl :args (@t123)) % 0.45/0.68 (step @p172 :rule nary_cong :premises (@p171 @p170) :args (@t132)) % 0.45/0.68 (step @p173 :rule refl :args (@t126)) % 0.45/0.68 (step @p174 :rule cong :premises (@p173 @p172) :args ((=> @t126 @t132))) % 0.45/0.68 (assume-push @p233 @t126) % 0.45/0.68 (step @p176 :rule instantiate :premises (@p166) :args ((@list @t109))) % 0.45/0.68 (step-pop @p234 :rule scope :premises (@p176)) % 0.45/0.68 (step @p177 :rule process_scope :premises (@p234) :args (@t132)) % 0.45/0.68 (step @p179 :rule eq_resolve :premises (@p177 @p174)) % 0.45/0.68 (step @p180 :rule implies_elim :premises (@p179)) % 0.45/0.68 (step @p181 :rule chain_m_resolution :premises (@p180 @p166) :args (@t134 (@list false) (@list @t126))) % 0.45/0.68 (step @p182 :rule bool-double-not-elim :args (@t122)) % 0.45/0.68 (step @p183 :rule refl :args (@t124)) % 0.45/0.68 (step @p184 :rule nary_cong :premises (@p183 @p182) :args ((or @t124 (not @t123)))) % 0.45/0.68 (step @p185 :rule cnf_or_neg :args (@t124 0)) % 0.45/0.68 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.45/0.68 (step @p187 :rule reordering :premises (@p186) :args ((or @t122 @t124))) % 0.45/0.68 (step @p188 :rule chain_m_resolution :premises (@p187 @p145) :args (@t122 @t117 @t125)) % 0.45/0.68 (step @p189 :rule cnf_or_pos :args (@t134)) % 0.45/0.68 (step @p190 :rule reordering :premises (@p189) :args ((or @t123 @t133 (not @t134)))) % 0.45/0.68 (step @p191 :rule chain_m_resolution :premises (@p190 @p188 @p181) :args (@t133 @t128 (@list @t122 @t134))) % 0.45/0.68 (step @p192 :rule refl :args (@t136)) % 0.45/0.68 (step @p193 :rule bool-double-not-elim :args (@t110)) % 0.45/0.68 (step @p194 :rule nary_cong :premises (@p193 @p192) :args ((or (not @t133) @t136))) % 0.45/0.68 (step @p195 :rule eq-symm :args (@t135 @t109)) % 0.45/0.68 (step @p196 :rule bool-double-not-elim :args (@t137)) % 0.45/0.68 (step @p197 :rule trans :premises (@p196 @p195)) % 0.45/0.68 (step @p198 :rule refl :args (@t133)) % 0.45/0.68 (step @p199 :rule cong :premises (@p198 @p197) :args ((=> @t133 @t138))) % 0.45/0.68 (assume-push @p235 @t133) % 0.45/0.68 (step @p201 :rule skolemize :premises (@p191)) % 0.45/0.68 (step-pop @p236 :rule scope :premises (@p201)) % 0.45/0.68 (step @p202 :rule process_scope :premises (@p236) :args (@t138)) % 0.45/0.68 (step @p204 :rule eq_resolve :premises (@p202 @p199)) % 0.45/0.68 (step @p205 :rule implies_elim :premises (@p204)) % 0.45/0.68 (step @p206 :rule eq_resolve :premises (@p205 @p194)) % 0.45/0.68 (step @p207 :rule chain_m_resolution :premises (@p206 @p191) :args (@t136 @t117 (@list @t110))) % 0.45/0.68 (step @p208 :rule symm :premises (@p207)) % 0.45/0.68 (step @p209 :rule cong :premises (@p208 @p149) :args (@t139)) % 0.45/0.68 (step @p210 :rule trans :premises (@p209 @p148)) % 0.45/0.68 (step @p211 :rule false_elim :premises (@p210)) % 0.45/0.68 (step @p212 :rule aci_norm :args ((= (or @t141 (or @t140 @t86)) (or @t141 @t140 @t86)))) % 0.45/0.68 (step @p213 :rule bool-impl-elim :args (@t87 @t86)) % 0.45/0.68 (step @p214 :rule refl :args (@t141)) % 0.45/0.68 (step @p215 :rule nary_cong :premises (@p214 @p213) :args ((or @t141 @t88))) % 0.45/0.68 (step @p216 :rule trans :premises (@p215 @p212)) % 0.45/0.68 (step @p217 :rule bool-impl-elim :args (@t89 @t88)) % 0.45/0.68 (step @p218 :rule trans :premises (@p217 @p216)) % 0.45/0.68 (step @p219 :rule cong :premises (@p218) :args (@t90)) % 0.45/0.68 (step @p220 :rule eq_resolve :premises (@p82 @p219)) % 0.45/0.68 (step @p221 :rule instantiate :premises (@p220) :args ((@list @t112 @t111 @t104))) % 0.45/0.68 (step @p222 :rule true_intro :premises (@p188)) % 0.45/0.68 (step @p223 :rule refl :args (@t104)) % 0.45/0.68 (step @p224 :rule cong :premises (@p208 @p223) :args (@t142)) % 0.45/0.68 (step @p225 :rule trans :premises (@p224 @p222)) % 0.45/0.68 (step @p226 :rule true_elim :premises (@p225)) % 0.45/0.68 (step @p227 :rule cnf_or_pos :args (@t145)) % 0.45/0.68 (step @p228 :rule reordering :premises (@p227) :args ((or @t115 @t143 @t144 (not @t145)))) % 0.45/0.68 (step @p229 :rule chain_m_resolution :premises (@p228 @p163 @p226 @p221) :args (@t143 (@list false false false) (@list @t114 @t142 @t145))) % 0.45/0.68 (step @p230 :rule cnf_equiv_pos2 :args (@t146)) % 0.45/0.68 (step @p231 :rule reordering :premises (@p230) :args ((or @t139 (not @t143) (not @t146)))) % 0.45/0.68 (step @p232 false :rule chain_m_resolution :premises (@p231 @p229 @p211 @p127) :args (false (@list false true false) (@list @t143 @t139 @t146))) % 0.45/0.68 ) % 0.45/0.68 % SZS output end Proof % 0.45/0.68 % cvc5 exiting %------------------------------------------------------------------------------