%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU172+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 : n009.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 08:50:50 AM UTC 2026 % Result : Theorem 1.23s 1.43s % Output : Proof 1.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU172+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 % 0.17/0.35 % Computer : n009.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:33:14 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 1.23/1.43 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.23/1.43 % SZS status Theorem % 1.23/1.43 % SZS output start Proof % 1.23/1.43 ( % 1.23/1.43 (declare-sort $$unsorted 0) % 1.23/1.43 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 1.23/1.43 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 1.23/1.43 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 1.23/1.43 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 1.23/1.43 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 1.23/1.43 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.23/1.43 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 1.23/1.43 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 1.23/1.43 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 1.23/1.43 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 1.23/1.43 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 1.23/1.43 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 1.23/1.43 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 1.23/1.43 (declare-const tptp.empty_set $$unsorted) % 1.23/1.43 (declare-const tptp.empty (-> $$unsorted Bool)) % 1.23/1.43 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 1.23/1.43 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 1.23/1.43 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 1.23/1.43 (define @t1 () (@var "A" $$unsorted)) % 1.23/1.43 (define @t2 () (@var "B" $$unsorted)) % 1.23/1.43 (define @t3 () (tptp.in @t2 @t1)) % 1.23/1.43 (define @t4 () (not @t3)) % 1.23/1.43 (define @t5 () (tptp.in @t1 @t2)) % 1.23/1.43 (define @t6 () (@list @t1 @t2)) % 1.23/1.43 (define @t7 () (tptp.proper_subset @t2 @t1)) % 1.23/1.43 (define @t8 () (tptp.proper_subset @t1 @t2)) % 1.23/1.43 (define @t9 () (tptp.unordered_pair @t1 @t2)) % 1.23/1.43 (define @t10 () (tptp.set_union2 @t2 @t1)) % 1.23/1.43 (define @t11 () (tptp.set_union2 @t1 @t2)) % 1.23/1.43 (define @t12 () (tptp.set_intersection2 @t1 @t2)) % 1.23/1.43 (define @t13 () (tptp.subset @t1 @t2)) % 1.23/1.43 (define @t14 () (= @t1 @t2)) % 1.23/1.43 (define @t15 () (@var "C" $$unsorted)) % 1.23/1.43 (define @t16 () (tptp.in @t15 @t2)) % 1.23/1.43 (define @t17 () (@list @t15)) % 1.23/1.43 (define @t18 () (tptp.singleton @t1)) % 1.23/1.43 (define @t19 () (@list @t2)) % 1.23/1.43 (define @t20 () (= @t1 tptp.empty_set)) % 1.23/1.43 (define @t21 () (@list @t1)) % 1.23/1.43 (define @t22 () (tptp.powerset @t1)) % 1.23/1.43 (define @t23 () (tptp.empty @t2)) % 1.23/1.43 (define @t24 () (tptp.element @t2 @t1)) % 1.23/1.43 (define @t25 () (tptp.empty @t1)) % 1.23/1.43 (define @t26 () (not @t25)) % 1.23/1.43 (define @t27 () (@var "D" $$unsorted)) % 1.23/1.43 (define @t28 () (tptp.in @t27 @t15)) % 1.23/1.43 (define @t29 () (@list @t27)) % 1.23/1.43 (define @t30 () (@list @t1 @t2 @t15)) % 1.23/1.43 (define @t31 () (tptp.in @t27 @t2)) % 1.23/1.43 (define @t32 () (tptp.in @t27 @t1)) % 1.23/1.43 (define @t33 () (@var "F" $$unsorted)) % 1.23/1.43 (define @t34 () (@var "E" $$unsorted)) % 1.23/1.43 (define @t35 () (tptp.in @t15 @t1)) % 1.23/1.43 (define @t36 () (tptp.set_difference @t1 @t2)) % 1.23/1.43 (define @t37 () (tptp.subset_complement @t1 @t2)) % 1.23/1.43 (define @t38 () (tptp.element @t2 @t22)) % 1.23/1.43 (define @t39 () (tptp.ordered_pair @t1 @t2)) % 1.23/1.43 (define @t40 () (tptp.disjoint @t1 @t2)) % 1.23/1.43 (define @t41 () (not @t14)) % 1.23/1.43 (define @t42 () (tptp.element @t37 @t22)) % 1.23/1.43 (define @t43 () (forall @t6 (=> @t38 @t42))) % 1.23/1.43 (define @t44 () (tptp.set_union2 @t18 @t2)) % 1.23/1.43 (define @t45 () (=> @t5 (= @t44 @t2))) % 1.23/1.43 (define @t46 () (forall @t6 @t45)) % 1.23/1.43 (define @t47 () (tptp.disjoint @t18 @t2)) % 1.23/1.43 (define @t48 () (tptp.singleton @t2)) % 1.23/1.43 (define @t49 () (tptp.in @t1 @t15)) % 1.23/1.43 (define @t50 () (@list @t1 @t2 @t15 @t27)) % 1.23/1.43 (define @t51 () (= @t1 @t15)) % 1.23/1.43 (define @t52 () (tptp.cartesian_product2 @t1 @t15)) % 1.23/1.43 (define @t53 () (not @t16)) % 1.23/1.43 (define @t54 () (tptp.subset @t15 @t2)) % 1.23/1.43 (define @t55 () (forall @t17 (not (and @t54 (not (tptp.are_equipotent @t15 @t2)) @t53)))) % 1.23/1.43 (define @t56 () (forall (@list @t15 @t27) (=> (and @t16 (tptp.subset @t27 @t15)) @t31))) % 1.23/1.43 (define @t57 () (tptp.set_intersection2 @t2 @t15)) % 1.23/1.43 (define @t58 () (tptp.subset @t1 @t15)) % 1.23/1.43 (define @t59 () (tptp.in @t2 @t15)) % 1.23/1.43 (define @t60 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 1.23/1.43 (define @t61 () (and @t35 @t16)) % 1.23/1.43 (define @t62 () (exists @t17 @t61)) % 1.23/1.43 (define @t63 () (and @t62 @t40)) % 1.23/1.43 (define @t64 () (not @t63)) % 1.23/1.43 (define @t65 () (forall @t17 (not @t61))) % 1.23/1.43 (define @t66 () (not @t40)) % 1.23/1.43 (define @t67 () (and @t66 @t65)) % 1.23/1.43 (define @t68 () (not @t67)) % 1.23/1.43 (define @t69 () (and @t68 @t64)) % 1.23/1.43 (define @t70 () (forall @t6 @t69)) % 1.23/1.43 (define @t71 () (tptp.subset_complement @t1 @t15)) % 1.23/1.43 (define @t72 () (tptp.disjoint @t2 @t15)) % 1.23/1.43 (define @t73 () (= @t72 (tptp.subset @t2 @t71))) % 1.23/1.43 (define @t74 () (tptp.element @t15 @t22)) % 1.23/1.43 (define @t75 () (forall @t17 (=> @t74 @t73))) % 1.23/1.43 (define @t76 () (=> @t38 @t75)) % 1.23/1.43 (define @t77 () (forall @t6 @t76)) % 1.23/1.43 (define @t78 () (tptp.in @t15 @t12)) % 1.23/1.43 (define @t79 () (tptp.in @t2 @t71)) % 1.23/1.43 (define @t80 () (not (and @t79 @t59))) % 1.23/1.43 (define @t81 () (forall @t30 (=> @t74 @t80))) % 1.23/1.43 (define @t82 () (not @t81)) % 1.23/1.43 (define @t83 () (= @t18 (tptp.unordered_pair @t2 @t15))) % 1.23/1.43 (define @t84 () (@var "BOUND_VARIABLE_8226" $$unsorted)) % 1.23/1.43 (define @t85 () (@var "BOUND_VARIABLE_8240" $$unsorted)) % 1.23/1.43 (define @t86 () (not (tptp.in @t85 @t84))) % 1.23/1.43 (define @t87 () (@var "BOUND_VARIABLE_8224" $$unsorted)) % 1.23/1.43 (define @t88 () (not (tptp.in @t85 @t87))) % 1.23/1.43 (define @t89 () (not (tptp.disjoint @t87 @t84))) % 1.23/1.43 (define @t90 () (or @t89 @t88 @t86)) % 1.23/1.43 (define @t91 () (or @t88 @t86)) % 1.23/1.43 (define @t92 () (or @t91 @t89)) % 1.23/1.43 (define @t93 () (@list @t87 @t84 @t85)) % 1.23/1.43 (define @t94 () (forall @t93 @t92)) % 1.23/1.43 (define @t95 () (@list @t85)) % 1.23/1.43 (define @t96 () (forall @t95 @t92)) % 1.23/1.43 (define @t97 () (@list @t87 @t84)) % 1.23/1.43 (define @t98 () (forall @t95 @t91)) % 1.23/1.43 (define @t99 () (@list @t15)) % 1.23/1.43 (define @t100 () (or @t98 @t89)) % 1.23/1.43 (define @t101 () (forall @t97 (or (forall @t17 (or (not (tptp.in @t15 @t87)) (not (tptp.in @t15 @t84)))) @t89))) % 1.23/1.43 (define @t102 () (@var "BOUND_VARIABLE_8211" $$unsorted)) % 1.23/1.43 (define @t103 () (@var "BOUND_VARIABLE_8209" $$unsorted)) % 1.23/1.43 (define @t104 () (forall (@list @t103 @t102) (or (tptp.disjoint @t103 @t102) (not (forall @t17 (or (not (tptp.in @t15 @t103)) (not (tptp.in @t15 @t102)))))))) % 1.23/1.43 (define @t105 () (forall @t17 (or (not @t35) @t53))) % 1.23/1.43 (define @t106 () (or @t105 @t66)) % 1.23/1.43 (define @t107 () (forall @t6 @t106)) % 1.23/1.43 (define @t108 () (@list @t1 @t2)) % 1.23/1.43 (define @t109 () (not @t105)) % 1.23/1.43 (define @t110 () (or @t40 @t109)) % 1.23/1.43 (define @t111 () (forall @t6 @t110)) % 1.23/1.43 (define @t112 () (and @t111 @t107)) % 1.23/1.43 (define @t113 () (and (not (and @t66 @t105)) (not (and @t109 @t40)))) % 1.23/1.43 (define @t114 () (not @t65)) % 1.23/1.43 (define @t115 () (@var "BOUND_VARIABLE_8268" $$unsorted)) % 1.23/1.43 (define @t116 () (= (tptp.disjoint @t2 @t115) (tptp.subset @t2 (tptp.subset_complement @t1 @t115)))) % 1.23/1.43 (define @t117 () (not (tptp.element @t115 @t22))) % 1.23/1.43 (define @t118 () (not @t38)) % 1.23/1.43 (define @t119 () (or @t118 @t117 @t116)) % 1.23/1.43 (define @t120 () (or @t117 @t116)) % 1.23/1.43 (define @t121 () (or @t118 @t120)) % 1.23/1.43 (define @t122 () (@list @t1 @t2 @t115)) % 1.23/1.43 (define @t123 () (forall @t122 @t121)) % 1.23/1.43 (define @t124 () (@list @t115)) % 1.23/1.43 (define @t125 () (forall @t124 @t121)) % 1.23/1.43 (define @t126 () (forall @t124 @t120)) % 1.23/1.43 (define @t127 () (or @t118 @t126)) % 1.23/1.43 (define @t128 () (not @t74)) % 1.23/1.43 (define @t129 () (forall @t17 (or @t128 @t73))) % 1.23/1.43 (define @t130 () (not @t59)) % 1.23/1.43 (define @t131 () (not @t79)) % 1.23/1.43 (define @t132 () (or @t128 @t131 @t130)) % 1.23/1.43 (define @t133 () (forall @t30 @t132)) % 1.23/1.43 (define @t134 () (@quantifiers_skolemize @t133 2)) % 1.23/1.43 (define @t135 () (@quantifiers_skolemize @t133 0)) % 1.23/1.43 (define @t136 () (tptp.subset_complement @t135 @t134)) % 1.23/1.43 (define @t137 () (tptp.disjoint @t136 @t134)) % 1.23/1.43 (define @t138 () (tptp.subset @t136 @t136)) % 1.23/1.43 (define @t139 () (tptp.powerset @t135)) % 1.23/1.43 (define @t140 () (tptp.element @t134 @t139)) % 1.23/1.43 (define @t141 () (not @t140)) % 1.23/1.43 (define @t142 () (tptp.element @t136 @t139)) % 1.23/1.43 (define @t143 () (not @t142)) % 1.23/1.43 (define @t144 () (or @t143 @t141 (= @t137 @t138))) % 1.23/1.43 (define @t145 () (forall @t122 @t119)) % 1.23/1.43 (define @t146 () (= @t138 @t137)) % 1.23/1.43 (define @t147 () (or @t143 @t141 @t146)) % 1.23/1.43 (define @t148 () (@quantifiers_skolemize @t133 1)) % 1.23/1.43 (define @t149 () (tptp.in @t148 @t134)) % 1.23/1.43 (define @t150 () (not @t149)) % 1.23/1.43 (define @t151 () (tptp.in @t148 @t136)) % 1.23/1.43 (define @t152 () (not @t151)) % 1.23/1.43 (define @t153 () (or @t141 @t152 @t150)) % 1.23/1.43 (define @t154 () (@list true)) % 1.23/1.43 (define @t155 () (@list @t153)) % 1.23/1.43 (define @t156 () (or @t141 @t142)) % 1.23/1.43 (define @t157 () (@list false false)) % 1.23/1.43 (define @t158 () (@list false false false)) % 1.23/1.43 (define @t159 () (tptp.singleton @t148)) % 1.23/1.43 (define @t160 () (= @t2 @t44)) % 1.23/1.43 (define @t161 () (= @t136 (tptp.set_union2 @t159 @t136))) % 1.23/1.43 (define @t162 () (or @t152 @t161)) % 1.23/1.43 (define @t163 () (not @t137)) % 1.23/1.43 (define @t164 () (or @t163 @t152 @t150)) % 1.23/1.43 (define @t165 () (not @t164)) % 1.23/1.43 (define @t166 () (forall @t93 @t90)) % 1.23/1.43 (assume @p1 (forall @t6 (=> @t5 @t4))) % 1.23/1.43 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 1.23/1.43 (assume @p3 (forall @t6 (= @t9 (tptp.unordered_pair @t2 @t1)))) % 1.23/1.43 (assume @p4 (forall @t6 (= @t11 @t10))) % 1.23/1.43 (assume @p5 (forall @t6 (= @t12 (tptp.set_intersection2 @t2 @t1)))) % 1.23/1.43 (assume @p6 (forall @t6 (= @t14 (and @t13 (tptp.subset @t2 @t1))))) % 1.23/1.43 (assume @p7 (forall @t6 (= (= @t2 @t18) (forall @t17 (= @t16 (= @t15 @t1)))))) % 1.23/1.43 (assume @p8 (forall @t21 (= @t20 (forall @t19 @t4)))) % 1.23/1.43 (assume @p9 (forall @t6 (= (= @t2 @t22) (forall @t17 (= @t16 (tptp.subset @t15 @t1)))))) % 1.23/1.43 (assume @p10 (forall @t6 (and (=> @t26 (= @t24 @t3)) (=> @t25 (= @t24 @t23))))) % 1.23/1.43 (assume @p11 (forall @t30 (= (= @t15 @t9) (forall @t29 (= @t28 (or (= @t27 @t1) (= @t27 @t2))))))) % 1.23/1.43 (assume @p12 (forall @t30 (= (= @t15 @t11) (forall @t29 (= @t28 (or @t32 @t31)))))) % 1.23/1.43 (assume @p13 (forall @t30 (= (= @t15 (tptp.cartesian_product2 @t1 @t2)) (forall @t29 (= @t28 (exists (@list @t34 @t33) (and (tptp.in @t34 @t1) (tptp.in @t33 @t2) (= @t27 (tptp.ordered_pair @t34 @t33))))))))) % 1.23/1.43 (assume @p14 (forall @t6 (= @t13 (forall @t17 (=> @t35 @t16))))) % 1.23/1.43 (assume @p15 (forall @t30 (= (= @t15 @t12) (forall @t29 (= @t28 (and @t32 @t31)))))) % 1.23/1.43 (assume @p16 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t17 (= @t16 (exists @t29 (and (tptp.in @t15 @t27) @t32))))))) % 1.23/1.43 (assume @p17 (forall @t30 (= (= @t15 @t36) (forall @t29 (= @t28 (and @t32 (not @t31))))))) % 1.23/1.43 (assume @p18 (forall @t6 (=> @t38 (= @t37 @t36)))) % 1.23/1.43 (assume @p19 (forall @t6 (= @t39 (tptp.unordered_pair @t9 @t18)))) % 1.23/1.43 (assume @p20 (forall @t6 (= @t40 (= @t12 tptp.empty_set)))) % 1.23/1.43 (assume @p21 (forall @t6 (= @t8 (and @t13 @t41)))) % 1.23/1.43 (assume @p22 true) % 1.23/1.43 (assume @p23 @t43) % 1.23/1.43 (assume @p24 (forall @t21 (exists @t19 @t24))) % 1.23/1.43 (assume @p25 (forall @t21 (not (tptp.empty @t22)))) % 1.23/1.43 (assume @p26 (tptp.empty tptp.empty_set)) % 1.23/1.43 (assume @p27 (forall @t6 (not (tptp.empty @t39)))) % 1.23/1.43 (assume @p28 (forall @t6 (=> @t26 (not (tptp.empty @t11))))) % 1.23/1.43 (assume @p29 (forall @t6 (=> @t26 (not (tptp.empty @t10))))) % 1.23/1.43 (assume @p30 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 1.23/1.43 (assume @p31 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 1.23/1.43 (assume @p32 (forall @t6 (=> @t38 (= (tptp.subset_complement @t1 @t37) @t2)))) % 1.23/1.43 (assume @p33 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 1.23/1.43 (assume @p34 (forall @t21 (not (= @t18 tptp.empty_set)))) % 1.23/1.43 (assume @p35 @t46) % 1.23/1.43 (assume @p36 (forall @t6 (not (and @t47 @t5)))) % 1.23/1.43 (assume @p37 (forall @t6 (=> (not @t5) @t47))) % 1.23/1.43 (assume @p38 (forall @t6 (= (tptp.subset @t18 @t2) @t5))) % 1.23/1.43 (assume @p39 (forall @t6 (= (= @t36 tptp.empty_set) @t13))) % 1.23/1.43 (assume @p40 (forall @t6 (=> @t38 (forall @t17 (=> @t16 @t35))))) % 1.23/1.43 (assume @p41 (forall @t30 (=> @t13 (or @t35 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t15))))))) % 1.23/1.43 (assume @p42 (forall @t6 (= (tptp.subset @t1 @t48) (or @t20 (= @t1 @t48))))) % 1.23/1.43 (assume @p43 (forall @t6 (=> @t5 (tptp.subset @t1 (tptp.union @t2))))) % 1.23/1.43 (assume @p44 (forall @t50 (= (tptp.in @t39 (tptp.cartesian_product2 @t15 @t27)) (and @t49 (tptp.in @t2 @t27))))) % 1.23/1.43 (assume @p45 (forall @t21 (=> @t26 (exists @t19 (and @t38 (not @t23)))))) % 1.23/1.43 (assume @p46 (exists @t21 @t25)) % 1.23/1.43 (assume @p47 (forall @t21 (exists @t19 (and @t38 @t23)))) % 1.23/1.43 (assume @p48 (exists @t21 @t26)) % 1.23/1.43 (assume @p49 (forall @t6 (tptp.subset @t1 @t1))) % 1.23/1.43 (assume @p50 (forall @t6 (=> @t40 (tptp.disjoint @t2 @t1)))) % 1.23/1.43 (assume @p51 (forall @t50 (not (and (= @t9 (tptp.unordered_pair @t15 @t27)) (not @t51) (not (= @t1 @t27)))))) % 1.23/1.43 (assume @p52 (forall @t30 (=> @t13 (and (tptp.subset @t52 (tptp.cartesian_product2 @t2 @t15)) (tptp.subset (tptp.cartesian_product2 @t15 @t1) (tptp.cartesian_product2 @t15 @t2)))))) % 1.23/1.43 (assume @p53 (forall @t50 (=> (and @t13 (tptp.subset @t15 @t27)) (tptp.subset @t52 (tptp.cartesian_product2 @t2 @t27))))) % 1.23/1.43 (assume @p54 (forall @t6 (=> @t13 (= @t11 @t2)))) % 1.23/1.43 (assume @p55 (forall @t21 (exists @t19 (and @t5 @t56 (forall @t17 (=> @t16 (tptp.in (tptp.powerset @t15) @t2))) @t55)))) % 1.23/1.43 (assume @p56 (forall @t6 (tptp.subset @t12 @t1))) % 1.23/1.43 (assume @p57 (forall @t30 (=> (and @t13 @t58) (tptp.subset @t1 @t57)))) % 1.23/1.43 (assume @p58 (forall @t21 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 1.23/1.43 (assume @p59 (forall @t30 (=> (and @t13 (tptp.subset @t2 @t15)) @t58))) % 1.23/1.43 (assume @p60 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 1.23/1.43 (assume @p61 (forall @t30 (=> @t13 (tptp.subset (tptp.set_intersection2 @t1 @t15) @t57)))) % 1.23/1.43 (assume @p62 (forall @t6 (=> @t13 (= @t12 @t1)))) % 1.23/1.43 (assume @p63 (forall @t21 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 1.23/1.43 (assume @p64 (forall @t6 (=> (forall @t17 (= @t35 @t16)) @t14))) % 1.23/1.43 (assume @p65 (forall @t21 (tptp.subset tptp.empty_set @t1))) % 1.23/1.43 (assume @p66 (forall @t30 (=> @t13 (tptp.subset (tptp.set_difference @t1 @t15) (tptp.set_difference @t2 @t15))))) % 1.23/1.43 (assume @p67 (forall @t50 (=> (= @t39 (tptp.ordered_pair @t15 @t27)) (and @t51 (= @t2 @t27))))) % 1.23/1.43 (assume @p68 (forall @t6 (tptp.subset @t36 @t1))) % 1.23/1.43 (assume @p69 (forall @t30 (= (tptp.subset @t9 @t15) (and @t49 @t59)))) % 1.23/1.43 (assume @p70 (forall @t6 (= @t60 @t11))) % 1.23/1.43 (assume @p71 (forall @t21 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 1.23/1.43 (assume @p72 @t70) % 1.23/1.43 (assume @p73 (forall @t21 (=> (tptp.subset @t1 tptp.empty_set) @t20))) % 1.23/1.43 (assume @p74 (forall @t6 (= (tptp.set_difference @t11 @t2) @t36))) % 1.23/1.43 (assume @p75 @t77) % 1.23/1.43 (assume @p76 (forall @t6 (=> @t13 (= @t2 @t60)))) % 1.23/1.43 (assume @p77 (forall @t6 (= (tptp.set_difference @t1 @t36) @t12))) % 1.23/1.43 (assume @p78 (forall @t21 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 1.23/1.43 (assume @p79 (forall @t6 (and (not (and @t66 (forall @t17 (not @t78)))) (not (and (exists @t17 @t78) @t40))))) % 1.23/1.43 (assume @p80 (forall @t21 (=> (not @t20) (forall @t19 (=> @t38 (forall @t17 (=> (tptp.element @t15 @t1) (=> @t53 (tptp.in @t15 @t37))))))))) % 1.23/1.43 (assume @p81 @t82) % 1.23/1.43 (assume @p82 (forall @t6 (not (and @t13 @t7)))) % 1.23/1.43 (assume @p83 (forall @t30 (=> (and @t13 @t72) (tptp.disjoint @t1 @t15)))) % 1.23/1.43 (assume @p84 (forall @t6 (= (= (tptp.set_difference @t1 @t48) @t1) @t4))) % 1.23/1.43 (assume @p85 (forall @t21 (= (tptp.unordered_pair @t1 @t1) @t18))) % 1.23/1.43 (assume @p86 (forall @t21 (=> @t25 @t20))) % 1.23/1.43 (assume @p87 (forall @t6 (=> (tptp.subset @t18 @t48) @t14))) % 1.23/1.43 (assume @p88 (forall @t6 (not (and @t5 @t23)))) % 1.23/1.43 (assume @p89 (forall @t6 (tptp.subset @t1 @t11))) % 1.23/1.43 (assume @p90 (forall @t6 (= @t40 (= @t36 @t1)))) % 1.23/1.43 (assume @p91 (forall @t6 (not (and @t25 @t41 @t23)))) % 1.23/1.43 (assume @p92 (forall @t30 (=> (and @t13 @t54) (tptp.subset (tptp.set_union2 @t1 @t15) @t2)))) % 1.23/1.43 (assume @p93 (forall @t30 (=> @t83 @t14))) % 1.23/1.43 (assume @p94 (forall @t21 (= (tptp.union @t22) @t1))) % 1.23/1.43 (assume @p95 (forall @t21 (exists @t19 (and @t5 @t56 (forall @t17 (not (and @t16 (forall @t29 (not (and @t31 (forall (@list @t34) (=> (tptp.subset @t34 @t15) (tptp.in @t34 @t27))))))))) @t55)))) % 1.23/1.43 (assume @p96 (forall @t30 (=> @t83 (= @t2 @t15)))) % 1.23/1.43 (step @p97 :rule aci_norm :args ((= @t92 @t90))) % 1.23/1.43 (step @p98 :rule cong :premises (@p97) :args (@t94)) % 1.23/1.43 (step @p99 :rule quant-merge-prenex :args ((= (forall @t97 @t96) @t94))) % 1.23/1.43 (step @p100 :rule refl :args (@t89)) % 1.23/1.43 (step @p101 :rule alpha_equiv :args (@t98 (@list @t85) @t99)) % 1.23/1.43 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t100)) % 1.23/1.43 (step @p103 :rule quant-miniscope-or :args ((= @t96 @t100))) % 1.23/1.43 (step @p104 :rule trans :premises (@p103 @p102)) % 1.23/1.43 (step @p105 :rule symm :premises (@p104)) % 1.23/1.43 (step @p106 :rule cong :premises (@p105) :args (@t101)) % 1.23/1.43 (step @p107 :rule trans :premises (@p106 @p99)) % 1.23/1.43 (step @p108 :rule trans :premises (@p107 @p98)) % 1.23/1.43 (step @p109 :rule refl :args (@t104)) % 1.23/1.43 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((and @t104 @t101))) % 1.23/1.43 (step @p111 :rule alpha_equiv :args (@t107 @t108 (@list @t87 @t84))) % 1.23/1.43 (step @p112 :rule alpha_equiv :args (@t111 @t108 (@list @t103 @t102))) % 1.23/1.43 (step @p113 :rule nary_cong :premises (@p112 @p111) :args (@t112)) % 1.23/1.43 (step @p114 :rule quant-miniscope-and :args ((= (forall @t6 (and @t110 @t106)) @t112))) % 1.23/1.43 (step @p115 :rule trans :premises (@p114 @p113)) % 1.23/1.43 (step @p116 :rule trans :premises (@p115 @p110)) % 1.23/1.43 (step @p117 :rule refl :args (@t66)) % 1.23/1.43 (step @p118 :rule bool-double-not-elim :args (@t105)) % 1.23/1.43 (step @p119 :rule nary_cong :premises (@p118 @p117) :args ((or (not @t109) @t66))) % 1.23/1.43 (step @p120 :rule bool-and-de-morgan :args (@t109 @t40 true)) % 1.23/1.43 (step @p121 :rule trans :premises (@p120 @p119)) % 1.23/1.43 (step @p122 :rule refl :args (@t109)) % 1.23/1.43 (step @p123 :rule bool-double-not-elim :args (@t40)) % 1.23/1.43 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((or (not @t66) @t109))) % 1.23/1.43 (step @p125 :rule bool-and-de-morgan :args (@t66 @t105 true)) % 1.23/1.43 (step @p126 :rule trans :premises (@p125 @p124)) % 1.23/1.43 (step @p127 :rule nary_cong :premises (@p126 @p121) :args (@t113)) % 1.23/1.43 (step @p128 :rule cong :premises (@p127) :args ((forall @t6 @t113))) % 1.23/1.43 (step @p129 :rule trans :premises (@p128 @p116)) % 1.23/1.43 (step @p130 :rule refl :args (@t40)) % 1.23/1.43 (step @p131 :rule bool-and-de-morgan :args (@t35 @t16 true)) % 1.23/1.43 (step @p132 :rule cong :premises (@p131) :args (@t65)) % 1.23/1.43 (step @p133 :rule cong :premises (@p132) :args (@t114)) % 1.23/1.43 (step @p134 :rule exists-elim :args ((= @t62 @t114))) % 1.23/1.43 (step @p135 :rule trans :premises (@p134 @p133)) % 1.23/1.43 (step @p136 :rule nary_cong :premises (@p135 @p130) :args (@t63)) % 1.23/1.43 (step @p137 :rule cong :premises (@p136) :args (@t64)) % 1.23/1.43 (step @p138 :rule refl :args (@t66)) % 1.23/1.43 (step @p139 :rule nary_cong :premises (@p138 @p132) :args (@t67)) % 1.23/1.43 (step @p140 :rule cong :premises (@p139) :args (@t68)) % 1.23/1.43 (step @p141 :rule nary_cong :premises (@p140 @p137) :args (@t69)) % 1.23/1.43 (step @p142 :rule cong :premises (@p141) :args (@t70)) % 1.23/1.43 (step @p143 :rule trans :premises (@p142 @p129)) % 1.23/1.43 (step @p144 :rule eq_resolve :premises (@p72 @p143)) % 1.23/1.43 (step @p145 :rule and_elim :premises (@p144) :args (1)) % 1.23/1.43 (step @p146 :rule aci_norm :args ((= @t121 @t119))) % 1.23/1.43 (step @p147 :rule cong :premises (@p146) :args (@t123)) % 1.23/1.43 (step @p148 :rule quant-merge-prenex :args ((= (forall @t6 @t125) @t123))) % 1.23/1.43 (step @p149 :rule alpha_equiv :args (@t126 (@list @t115) @t99)) % 1.23/1.43 (step @p150 :rule refl :args (@t118)) % 1.23/1.43 (step @p151 :rule nary_cong :premises (@p150 @p149) :args (@t127)) % 1.23/1.43 (step @p152 :rule quant-miniscope-or :args ((= @t125 @t127))) % 1.23/1.43 (step @p153 :rule trans :premises (@p152 @p151)) % 1.23/1.43 (step @p154 :rule symm :premises (@p153)) % 1.23/1.43 (step @p155 :rule cong :premises (@p154) :args ((forall @t6 (or @t118 @t129)))) % 1.23/1.43 (step @p156 :rule trans :premises (@p155 @p148)) % 1.23/1.43 (step @p157 :rule trans :premises (@p156 @p147)) % 1.23/1.43 (step @p158 :rule bool-impl-elim :args (@t38 @t129)) % 1.23/1.43 (step @p159 :rule cong :premises (@p158) :args ((forall @t6 (=> @t38 @t129)))) % 1.23/1.43 (step @p160 :rule trans :premises (@p159 @p157)) % 1.23/1.43 (step @p161 :rule bool-impl-elim :args (@t74 @t73)) % 1.23/1.43 (step @p162 :rule cong :premises (@p161) :args (@t75)) % 1.23/1.43 (step @p163 :rule refl :args (@t38)) % 1.23/1.43 (step @p164 :rule cong :premises (@p163 @p162) :args (@t76)) % 1.23/1.43 (step @p165 :rule cong :premises (@p164) :args (@t77)) % 1.23/1.43 (step @p166 :rule trans :premises (@p165 @p160)) % 1.23/1.43 (step @p167 :rule eq_resolve :premises (@p75 @p166)) % 1.23/1.43 (step @p168 :rule eq-symm :args (@t137 @t138)) % 1.23/1.43 (step @p169 :rule refl :args (@t141)) % 1.23/1.43 (step @p170 :rule refl :args (@t143)) % 1.23/1.43 (step @p171 :rule nary_cong :premises (@p170 @p169 @p168) :args (@t144)) % 1.23/1.43 (step @p172 :rule refl :args (@t145)) % 1.23/1.43 (step @p173 :rule cong :premises (@p172 @p171) :args ((=> @t145 @t144))) % 1.23/1.43 (assume-push @p253 @t145) % 1.23/1.43 (step @p175 :rule instantiate :premises (@p167) :args ((@list @t135 @t136 @t134))) % 1.23/1.43 (step-pop @p254 :rule scope :premises (@p175)) % 1.23/1.43 (step @p176 :rule process_scope :premises (@p254) :args (@t144)) % 1.23/1.43 (step @p178 :rule eq_resolve :premises (@p176 @p173)) % 1.23/1.44 (step @p179 :rule implies_elim :premises (@p178)) % 1.23/1.44 (step @p180 :rule chain_m_resolution :premises (@p179 @p167) :args (@t147 (@list false) (@list @t145))) % 1.23/1.44 (step @p181 :rule bool-impl-elim :args (@t38 @t42)) % 1.23/1.44 (step @p182 :rule cong :premises (@p181) :args (@t43)) % 1.23/1.44 (step @p183 :rule eq_resolve :premises (@p23 @p182)) % 1.23/1.44 (step @p184 :rule instantiate :premises (@p183) :args ((@list @t135 @t134))) % 1.23/1.44 (step @p185 :rule aci_norm :args ((= (or @t128 (or @t131 @t130)) @t132))) % 1.23/1.44 (step @p186 :rule bool-and-de-morgan :args (@t79 @t59 true)) % 1.23/1.44 (step @p187 :rule refl :args (@t128)) % 1.23/1.44 (step @p188 :rule nary_cong :premises (@p187 @p186) :args ((or @t128 @t80))) % 1.23/1.44 (step @p189 :rule trans :premises (@p188 @p185)) % 1.23/1.44 (step @p190 :rule bool-impl-elim :args (@t74 @t80)) % 1.23/1.44 (step @p191 :rule trans :premises (@p190 @p189)) % 1.23/1.44 (step @p192 :rule cong :premises (@p191) :args (@t81)) % 1.23/1.44 (step @p193 :rule cong :premises (@p192) :args (@t82)) % 1.23/1.44 (step @p194 :rule eq_resolve :premises (@p81 @p193)) % 1.23/1.44 (step @p195 :rule skolemize :premises (@p194)) % 1.23/1.44 (step @p196 :rule bool-double-not-elim :args (@t140)) % 1.23/1.44 (step @p197 :rule refl :args (@t153)) % 1.23/1.44 (step @p198 :rule nary_cong :premises (@p197 @p196) :args ((or @t153 (not @t141)))) % 1.23/1.44 (step @p199 :rule cnf_or_neg :args (@t153 0)) % 1.23/1.44 (step @p200 :rule eq_resolve :premises (@p199 @p198)) % 1.23/1.44 (step @p201 :rule reordering :premises (@p200) :args ((or @t140 @t153))) % 1.23/1.44 (step @p202 :rule chain_m_resolution :premises (@p201 @p195) :args (@t140 @t154 @t155)) % 1.23/1.44 (step @p203 :rule cnf_or_pos :args (@t156)) % 1.23/1.44 (step @p204 :rule reordering :premises (@p203) :args ((or @t141 @t142 (not @t156)))) % 1.23/1.44 (step @p205 :rule chain_m_resolution :premises (@p204 @p202 @p184) :args (@t142 @t157 (@list @t140 @t156))) % 1.23/1.44 (step @p206 :rule cnf_or_pos :args (@t147)) % 1.23/1.44 (step @p207 :rule reordering :premises (@p206) :args ((or @t141 @t143 @t146 (not @t147)))) % 1.23/1.44 (step @p208 :rule chain_m_resolution :premises (@p207 @p202 @p205 @p180) :args (@t146 @t158 (@list @t140 @t142 @t147))) % 1.23/1.44 (step @p209 :rule instantiate :premises (@p89) :args ((@list @t136 @t159))) % 1.23/1.44 (step @p210 :rule true_intro :premises (@p209)) % 1.23/1.44 (step @p211 :rule instantiate :premises (@p4) :args ((@list @t159 @t136))) % 1.23/1.44 (step @p212 :rule bool-impl-elim :args (@t5 @t160)) % 1.23/1.44 (step @p213 :rule cong :premises (@p212) :args ((forall @t6 (=> @t5 @t160)))) % 1.23/1.44 (step @p214 :rule eq-symm :args (@t44 @t2)) % 1.23/1.44 (step @p215 :rule refl :args (@t5)) % 1.23/1.44 (step @p216 :rule cong :premises (@p215 @p214) :args (@t45)) % 1.23/1.44 (step @p217 :rule cong :premises (@p216) :args (@t46)) % 1.23/1.44 (step @p218 :rule trans :premises (@p217 @p213)) % 1.23/1.44 (step @p219 :rule eq_resolve :premises (@p35 @p218)) % 1.23/1.44 (step @p220 :rule instantiate :premises (@p219) :args ((@list @t148 @t136))) % 1.23/1.44 (step @p221 :rule bool-double-not-elim :args (@t151)) % 1.23/1.44 (step @p222 :rule nary_cong :premises (@p197 @p221) :args ((or @t153 (not @t152)))) % 1.23/1.44 (step @p223 :rule cnf_or_neg :args (@t153 1)) % 1.23/1.44 (step @p224 :rule eq_resolve :premises (@p223 @p222)) % 1.23/1.44 (step @p225 :rule reordering :premises (@p224) :args ((or @t151 @t153))) % 1.23/1.44 (step @p226 :rule chain_m_resolution :premises (@p225 @p195) :args (@t151 @t154 @t155)) % 1.23/1.44 (step @p227 :rule cnf_or_pos :args (@t162)) % 1.23/1.44 (step @p228 :rule reordering :premises (@p227) :args ((or @t152 @t161 (not @t162)))) % 1.23/1.44 (step @p229 :rule chain_m_resolution :premises (@p228 @p226 @p220) :args (@t161 @t157 (@list @t151 @t162))) % 1.23/1.44 (step @p230 :rule trans :premises (@p229 @p211)) % 1.23/1.44 (step @p231 :rule refl :args (@t136)) % 1.23/1.44 (step @p232 :rule cong :premises (@p231 @p230) :args (@t138)) % 1.23/1.44 (step @p233 :rule trans :premises (@p232 @p210)) % 1.23/1.44 (step @p234 :rule true_elim :premises (@p233)) % 1.23/1.44 (step @p235 :rule cnf_equiv_pos1 :args (@t146)) % 1.23/1.44 (step @p236 :rule reordering :premises (@p235) :args ((or (not @t138) @t137 (not @t146)))) % 1.23/1.44 (step @p237 :rule chain_m_resolution :premises (@p236 @p234 @p208) :args (@t137 @t157 (@list @t138 @t146))) % 1.23/1.44 (step @p238 :rule bool-double-not-elim :args (@t149)) % 1.23/1.44 (step @p239 :rule nary_cong :premises (@p197 @p238) :args ((or @t153 (not @t150)))) % 1.23/1.44 (step @p240 :rule cnf_or_neg :args (@t153 2)) % 1.23/1.44 (step @p241 :rule eq_resolve :premises (@p240 @p239)) % 1.23/1.44 (step @p242 :rule reordering :premises (@p241) :args ((or @t149 @t153))) % 1.23/1.44 (step @p243 :rule chain_m_resolution :premises (@p242 @p195) :args (@t149 @t154 @t155)) % 1.23/1.44 (step @p244 :rule cnf_or_pos :args (@t164)) % 1.23/1.44 (step @p245 :rule reordering :premises (@p244) :args ((or @t152 @t150 @t163 @t165))) % 1.23/1.44 (step @p246 :rule chain_m_resolution :premises (@p245 @p226 @p243 @p237) :args (@t165 @t158 (@list @t151 @t149 @t137))) % 1.23/1.44 (assume-push @p255 @t166) % 1.23/1.44 (step @p248 :rule instantiate :premises (@p145) :args ((@list @t136 @t134 @t148))) % 1.23/1.44 (step-pop @p256 :rule scope :premises (@p248)) % 1.23/1.44 (step @p249 :rule process_scope :premises (@p256) :args (@t164)) % 1.23/1.44 (step @p251 :rule implies_elim :premises (@p249)) % 1.23/1.44 (step @p252 false :rule chain_m_resolution :premises (@p251 @p246 @p145) :args (false (@list true false) (@list @t164 @t166))) % 1.23/1.44 ) % 1.23/1.44 % SZS output end Proof % 1.23/1.44 % cvc5 exiting %------------------------------------------------------------------------------