%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET086+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n016.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 08:47:20 AM UTC 2026 % Result : Theorem 0.38s 0.59s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET086+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n016.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:52:09 EDT 2026 % 0.16/0.34 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.59 % SZS status Theorem % 0.38/0.59 % SZS output start Proof % 0.38/0.59 ( % 0.38/0.59 (declare-sort $$unsorted 0) % 0.38/0.59 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.element_relation $$unsorted) % 0.38/0.59 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.universal_class $$unsorted) % 0.38/0.59 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.function (-> $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.null_class $$unsorted) % 0.38/0.59 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.successor_relation $$unsorted) % 0.38/0.59 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.identity_relation $$unsorted) % 0.38/0.59 (define @t1 () (@var "Y" $$unsorted)) % 0.38/0.59 (define @t2 () (@var "U" $$unsorted)) % 0.38/0.59 (define @t3 () (tptp.member @t2 @t1)) % 0.38/0.59 (define @t4 () (@var "X" $$unsorted)) % 0.38/0.59 (define @t5 () (tptp.member @t2 @t4)) % 0.38/0.59 (define @t6 () (@list @t2)) % 0.38/0.59 (define @t7 () (tptp.subclass @t4 @t1)) % 0.38/0.59 (define @t8 () (@list @t4 @t1)) % 0.38/0.59 (define @t9 () (@list @t4)) % 0.38/0.59 (define @t10 () (= @t2 @t4)) % 0.38/0.59 (define @t11 () (tptp.member @t2 tptp.universal_class)) % 0.38/0.59 (define @t12 () (tptp.unordered_pair @t4 @t1)) % 0.38/0.59 (define @t13 () (tptp.singleton @t4)) % 0.38/0.59 (define @t14 () (tptp.singleton @t1)) % 0.38/0.59 (define @t15 () (tptp.ordered_pair @t4 @t1)) % 0.38/0.59 (define @t16 () (@var "V" $$unsorted)) % 0.38/0.59 (define @t17 () (tptp.cross_product @t4 @t1)) % 0.38/0.59 (define @t18 () (tptp.ordered_pair @t2 @t16)) % 0.38/0.59 (define @t19 () (tptp.member @t1 tptp.universal_class)) % 0.38/0.59 (define @t20 () (tptp.member @t4 tptp.universal_class)) % 0.38/0.59 (define @t21 () (@var "Z" $$unsorted)) % 0.38/0.59 (define @t22 () (@list @t4 @t1 @t21)) % 0.38/0.59 (define @t23 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.38/0.59 (define @t24 () (tptp.member @t21 @t1)) % 0.38/0.59 (define @t25 () (tptp.member @t21 @t4)) % 0.38/0.59 (define @t26 () (tptp.member @t21 tptp.universal_class)) % 0.38/0.59 (define @t27 () (@list @t4 @t21)) % 0.38/0.59 (define @t28 () (@var "XR" $$unsorted)) % 0.38/0.59 (define @t29 () (@var "W" $$unsorted)) % 0.38/0.59 (define @t30 () (tptp.cross_product @t23 tptp.universal_class)) % 0.38/0.59 (define @t31 () (tptp.ordered_pair @t18 @t29)) % 0.38/0.59 (define @t32 () (tptp.member @t31 @t30)) % 0.38/0.59 (define @t33 () (tptp.rotate @t4)) % 0.38/0.59 (define @t34 () (tptp.flip @t4)) % 0.38/0.59 (define @t35 () (tptp.successor @t4)) % 0.38/0.59 (define @t36 () (@list @t1)) % 0.38/0.59 (define @t37 () (@list @t21)) % 0.38/0.59 (define @t38 () (tptp.inductive @t4)) % 0.38/0.59 (define @t39 () (tptp.sum_class @t4)) % 0.38/0.59 (define @t40 () (@list @t2 @t4)) % 0.38/0.59 (define @t41 () (@var "YR" $$unsorted)) % 0.38/0.59 (define @t42 () (tptp.compose @t41 @t28)) % 0.38/0.59 (define @t43 () (tptp.singleton @t2)) % 0.38/0.59 (define @t44 () (@var "XF" $$unsorted)) % 0.38/0.59 (define @t45 () (tptp.function @t44)) % 0.38/0.59 (define @t46 () (@list @t44)) % 0.38/0.59 (define @t47 () (tptp.apply @t44 @t1)) % 0.38/0.59 (define @t48 () (= @t4 @t14)) % 0.38/0.59 (define @t49 () (and @t19 @t48)) % 0.38/0.59 (define @t50 () (exists @t36 @t49)) % 0.38/0.59 (define @t51 () (not @t50)) % 0.38/0.59 (define @t52 () (and @t51 @t10)) % 0.38/0.59 (define @t53 () (= @t4 @t43)) % 0.38/0.59 (define @t54 () (and @t11 @t53)) % 0.38/0.59 (define @t55 () (or @t54 @t52)) % 0.38/0.59 (define @t56 () (exists @t6 @t55)) % 0.38/0.59 (define @t57 () (forall @t9 @t56)) % 0.38/0.59 (define @t58 () (not @t57)) % 0.38/0.59 (define @t59 () (@var "BOUND_VARIABLE_7888" $$unsorted)) % 0.38/0.59 (define @t60 () (not (tptp.member @t59 tptp.universal_class))) % 0.38/0.59 (define @t61 () (tptp.singleton @t59)) % 0.38/0.59 (define @t62 () (@var "BOUND_VARIABLE_7859" $$unsorted)) % 0.38/0.59 (define @t63 () (tptp.singleton @t62)) % 0.38/0.59 (define @t64 () (not (tptp.member @t62 tptp.universal_class))) % 0.38/0.59 (define @t65 () (@list @t62)) % 0.38/0.59 (define @t66 () (not (forall @t65 (or @t64 (not (= @t63 @t61)))))) % 0.38/0.59 (define @t67 () (or @t66 @t60)) % 0.38/0.59 (define @t68 () (not (= @t61 @t61))) % 0.38/0.59 (define @t69 () (not (= @t61 @t63))) % 0.38/0.59 (define @t70 () (or @t64 @t69)) % 0.38/0.59 (define @t71 () (forall @t65 @t70)) % 0.38/0.59 (define @t72 () (not @t71)) % 0.38/0.59 (define @t73 () (or @t72 @t60 @t68)) % 0.38/0.59 (define @t74 () (@list @t59)) % 0.38/0.59 (define @t75 () (not (= @t4 @t61))) % 0.38/0.59 (define @t76 () (forall @t65 (or @t64 (not (= @t4 @t63))))) % 0.38/0.59 (define @t77 () (not @t76)) % 0.38/0.59 (define @t78 () (or @t75 @t77 @t60 @t75)) % 0.38/0.59 (define @t79 () (or @t77 @t60 @t75)) % 0.38/0.59 (define @t80 () (forall @t9 @t79)) % 0.38/0.59 (define @t81 () (forall @t74 @t80)) % 0.38/0.59 (define @t82 () (forall (@list @t59 @t4) @t79)) % 0.38/0.59 (define @t83 () (@list @t4 @t59)) % 0.38/0.59 (define @t84 () (or @t60 @t75)) % 0.38/0.59 (define @t85 () (or @t77 @t84)) % 0.38/0.59 (define @t86 () (forall @t83 @t85)) % 0.38/0.59 (define @t87 () (forall @t74 @t85)) % 0.38/0.59 (define @t88 () (forall @t74 @t84)) % 0.38/0.59 (define @t89 () (or @t77 @t88)) % 0.38/0.59 (define @t90 () (forall @t36 (or (not @t19) (not @t48)))) % 0.38/0.59 (define @t91 () (not @t90)) % 0.38/0.59 (define @t92 () (not (= @t4 @t4))) % 0.38/0.59 (define @t93 () (@var "BOUND_VARIABLE_7869" $$unsorted)) % 0.38/0.59 (define @t94 () (not (= @t4 @t93))) % 0.38/0.59 (define @t95 () (@list @t93)) % 0.38/0.59 (define @t96 () (or @t94 @t94)) % 0.38/0.59 (define @t97 () (forall @t95 @t94)) % 0.38/0.59 (define @t98 () (or @t91 @t97)) % 0.38/0.59 (define @t99 () (forall @t95 (or @t91 @t94))) % 0.38/0.59 (define @t100 () (= @t4 @t2)) % 0.38/0.59 (define @t101 () (or @t91 (not @t100))) % 0.38/0.59 (define @t102 () (forall @t6 @t101)) % 0.38/0.59 (define @t103 () (@list @t2)) % 0.38/0.59 (define @t104 () (or (not @t11) (not @t53))) % 0.38/0.59 (define @t105 () (forall @t6 @t104)) % 0.38/0.59 (define @t106 () (and @t105 @t102)) % 0.38/0.59 (define @t107 () (and @t90 @t100)) % 0.38/0.59 (define @t108 () (or @t54 @t107)) % 0.38/0.59 (define @t109 () (forall @t6 (not @t108))) % 0.38/0.59 (define @t110 () (not @t109)) % 0.38/0.59 (define @t111 () (forall @t36 (not @t49))) % 0.38/0.59 (define @t112 () (not @t111)) % 0.38/0.59 (define @t113 () (@quantifiers_skolemize (forall @t74 @t67) 0)) % 0.38/0.59 (define @t114 () (tptp.singleton @t113)) % 0.38/0.59 (define @t115 () (forall @t65 (or @t64 (not (= @t63 @t114))))) % 0.38/0.59 (define @t116 () (tptp.member @t113 tptp.universal_class)) % 0.38/0.59 (define @t117 () (not @t116)) % 0.38/0.59 (define @t118 () (not @t115)) % 0.38/0.59 (define @t119 () (or @t118 @t117)) % 0.38/0.59 (define @t120 () (@list true)) % 0.38/0.59 (define @t121 () (@list @t119)) % 0.38/0.59 (define @t122 () (not (= @t114 @t114))) % 0.38/0.59 (define @t123 () (or @t117 @t122)) % 0.38/0.59 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.38/0.59 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 0.38/0.59 (assume @p3 (forall @t8 (= (= @t4 @t1) (and @t7 (tptp.subclass @t1 @t4))))) % 0.38/0.59 (assume @p4 (forall (@list @t2 @t4 @t1) (= (tptp.member @t2 @t12) (and @t11 (or @t10 (= @t2 @t1)))))) % 0.38/0.59 (assume @p5 (forall @t8 (tptp.member @t12 tptp.universal_class))) % 0.38/0.59 (assume @p6 (forall @t9 (= @t13 (tptp.unordered_pair @t4 @t4)))) % 0.38/0.59 (assume @p7 (forall @t8 (= @t15 (tptp.unordered_pair @t13 (tptp.unordered_pair @t4 @t14))))) % 0.38/0.59 (assume @p8 (forall (@list @t2 @t16 @t4 @t1) (= (tptp.member @t18 @t17) (and @t5 (tptp.member @t16 @t1))))) % 0.38/0.59 (assume @p9 (forall @t8 (=> (and @t20 @t19) (and (= (tptp.first @t15) @t4) (= (tptp.second @t15) @t1))))) % 0.38/0.59 (assume @p10 (forall @t22 (=> (tptp.member @t21 @t17) (= @t21 (tptp.ordered_pair (tptp.first @t21) (tptp.second @t21)))))) % 0.38/0.59 (assume @p11 (forall @t8 (= (tptp.member @t15 tptp.element_relation) (and @t19 (tptp.member @t4 @t1))))) % 0.38/0.59 (assume @p12 (tptp.subclass tptp.element_relation @t23)) % 0.38/0.59 (assume @p13 (forall @t22 (= (tptp.member @t21 (tptp.intersection @t4 @t1)) (and @t25 @t24)))) % 0.38/0.59 (assume @p14 (forall @t27 (= (tptp.member @t21 (tptp.complement @t4)) (and @t26 (not @t25))))) % 0.38/0.59 (assume @p15 (forall (@list @t4 @t28 @t1) (= (tptp.restrict @t28 @t4 @t1) (tptp.intersection @t28 @t17)))) % 0.38/0.59 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 0.38/0.59 (assume @p17 (forall @t27 (= (tptp.member @t21 (tptp.domain_of @t4)) (and @t26 (not (= (tptp.restrict @t4 (tptp.singleton @t21) tptp.universal_class) tptp.null_class)))))) % 0.38/0.59 (assume @p18 (forall (@list @t4 @t2 @t16 @t29) (= (tptp.member @t31 @t33) (and @t32 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t16 @t29) @t2) @t4))))) % 0.38/0.59 (assume @p19 (forall @t9 (tptp.subclass @t33 @t30))) % 0.38/0.59 (assume @p20 (forall (@list @t2 @t16 @t29 @t4) (= (tptp.member @t31 @t34) (and @t32 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t16 @t2) @t29) @t4))))) % 0.38/0.59 (assume @p21 (forall @t9 (tptp.subclass @t34 @t30))) % 0.38/0.59 (assume @p22 (forall @t22 (= (tptp.member @t21 (tptp.union @t4 @t1)) (or @t25 @t24)))) % 0.38/0.59 (assume @p23 (forall @t9 (= @t35 (tptp.union @t4 @t13)))) % 0.38/0.59 (assume @p24 (tptp.subclass tptp.successor_relation @t23)) % 0.38/0.59 (assume @p25 (forall @t8 (= (tptp.member @t15 tptp.successor_relation) (and @t20 @t19 (= @t35 @t1))))) % 0.38/0.59 (assume @p26 (forall @t36 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 0.38/0.59 (assume @p27 (forall @t37 (= (tptp.range_of @t21) (tptp.domain_of (tptp.inverse @t21))))) % 0.38/0.59 (assume @p28 (forall (@list @t4 @t28) (= (tptp.image @t28 @t4) (tptp.range_of (tptp.restrict @t28 @t4 tptp.universal_class))))) % 0.38/0.59 (assume @p29 (forall @t9 (= @t38 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 0.38/0.59 (assume @p30 (exists @t9 (and @t20 @t38 (forall @t36 (=> (tptp.inductive @t1) @t7))))) % 0.38/0.59 (assume @p31 (forall @t40 (= (tptp.member @t2 @t39) (exists @t36 (and @t3 (tptp.member @t1 @t4)))))) % 0.38/0.59 (assume @p32 (forall @t9 (=> @t20 (tptp.member @t39 tptp.universal_class)))) % 0.38/0.59 (assume @p33 (forall @t40 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t11 (tptp.subclass @t2 @t4))))) % 0.38/0.59 (assume @p34 (forall @t6 (=> @t11 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.38/0.59 (assume @p35 (forall (@list @t28 @t41) (tptp.subclass @t42 @t23))) % 0.38/0.59 (assume @p36 (forall (@list @t28 @t41 @t2 @t16) (= (tptp.member @t18 @t42) (and @t11 (tptp.member @t16 (tptp.image @t41 (tptp.image @t28 @t43))))))) % 0.38/0.59 (assume @p37 (forall @t37 (= (tptp.member @t21 tptp.identity_relation) (exists @t9 (and @t20 (= @t21 (tptp.ordered_pair @t4 @t4))))))) % 0.38/0.59 (assume @p38 (forall @t46 (= @t45 (and (tptp.subclass @t44 @t23) (tptp.subclass (tptp.compose @t44 (tptp.inverse @t44)) tptp.identity_relation))))) % 0.38/0.59 (assume @p39 (forall (@list @t4 @t44) (=> (and @t20 @t45) (tptp.member (tptp.image @t44 @t4) tptp.universal_class)))) % 0.38/0.59 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 0.38/0.59 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t11 @t5 (tptp.disjoint @t2 @t4)))))) % 0.38/0.59 (assume @p42 (forall (@list @t44 @t1) (= @t47 (tptp.sum_class (tptp.image @t44 @t14))))) % 0.38/0.59 (assume @p43 (exists @t46 (and @t45 (forall @t36 (=> @t19 (or (= @t1 tptp.null_class) (tptp.member @t47 @t1))))))) % 0.38/0.59 (assume @p44 @t58) % 0.38/0.59 (assume @p45 true) % 0.38/0.59 (step @p46 :rule aci_norm :args ((= (or @t66 @t60 false) @t67))) % 0.38/0.59 (step @p47 :rule evaluate :args ((not true))) % 0.38/0.59 (step @p48 :rule eq-refl :args (@t61)) % 0.38/0.59 (step @p49 :rule cong :premises (@p48) :args (@t68)) % 0.38/0.59 (step @p50 :rule trans :premises (@p49 @p47)) % 0.38/0.59 (step @p51 :rule refl :args (@t60)) % 0.38/0.59 (step @p52 :rule eq-symm :args (@t61 @t63)) % 0.38/0.59 (step @p53 :rule cong :premises (@p52) :args (@t69)) % 0.38/0.59 (step @p54 :rule refl :args (@t64)) % 0.38/0.59 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t70)) % 0.38/0.59 (step @p56 :rule cong :premises (@p55) :args (@t71)) % 0.38/0.59 (step @p57 :rule cong :premises (@p56) :args (@t72)) % 0.38/0.59 (step @p58 :rule nary_cong :premises (@p57 @p51 @p50) :args (@t73)) % 0.38/0.59 (step @p59 :rule trans :premises (@p58 @p46)) % 0.38/0.59 (step @p60 :rule cong :premises (@p59) :args ((forall @t74 @t73))) % 0.38/0.59 (step @p61 :rule quant-var-elim-eq :args ((= (forall @t9 @t78) @t73))) % 0.38/0.59 (step @p62 :rule aci_norm :args ((= @t79 @t78))) % 0.38/0.59 (step @p63 :rule cong :premises (@p62) :args (@t80)) % 0.38/0.59 (step @p64 :rule trans :premises (@p63 @p61)) % 0.38/0.59 (step @p65 :rule cong :premises (@p64) :args (@t81)) % 0.38/0.59 (step @p66 :rule quant-merge-prenex :args ((= @t81 @t82))) % 0.38/0.59 (step @p67 :rule symm :premises (@p66)) % 0.38/0.59 (step @p68 :rule quant_var_reordering :args ((= (forall @t83 @t79) @t82))) % 0.38/0.59 (step @p69 :rule trans :premises (@p68 @p67 @p65)) % 0.38/0.59 (step @p70 :rule trans :premises (@p69 @p60)) % 0.38/0.59 (step @p71 :rule aci_norm :args ((= @t85 @t79))) % 0.38/0.59 (step @p72 :rule cong :premises (@p71) :args (@t86)) % 0.38/0.59 (step @p73 :rule trans :premises (@p72 @p70)) % 0.38/0.59 (step @p74 :rule quant-merge-prenex :args ((= (forall @t9 @t87) @t86))) % 0.38/0.59 (step @p75 :rule alpha_equiv :args (@t88 (@list @t59) (@list @t1))) % 0.38/0.59 (step @p76 :rule refl :args (@t77)) % 0.38/0.59 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t89)) % 0.38/0.59 (step @p78 :rule quant-miniscope-or :args ((= @t87 @t89))) % 0.38/0.59 (step @p79 :rule trans :premises (@p78 @p77)) % 0.38/0.59 (step @p80 :rule symm :premises (@p79)) % 0.38/0.59 (step @p81 :rule cong :premises (@p80) :args ((forall @t9 (or @t77 @t90)))) % 0.38/0.59 (step @p82 :rule trans :premises (@p81 @p74)) % 0.38/0.59 (step @p83 :rule trans :premises (@p82 @p73)) % 0.38/0.59 (step @p84 :rule bool-double-not-elim :args (@t90)) % 0.38/0.59 (step @p85 :rule nary_cong :premises (@p76 @p84) :args ((or @t77 (not @t91)))) % 0.38/0.59 (step @p86 :rule bool-and-de-morgan :args (@t76 @t91 true)) % 0.38/0.59 (step @p87 :rule trans :premises (@p86 @p85)) % 0.38/0.59 (step @p88 :rule cong :premises (@p87) :args ((forall @t9 (not (and @t76 @t91))))) % 0.38/0.59 (step @p89 :rule trans :premises (@p88 @p83)) % 0.38/0.59 (step @p90 :rule aci_norm :args ((= (or @t91 false) @t91))) % 0.38/0.59 (step @p91 :rule eq-refl :args (@t4)) % 0.38/0.59 (step @p92 :rule cong :premises (@p91) :args (@t92)) % 0.38/0.59 (step @p93 :rule trans :premises (@p92 @p47)) % 0.38/0.59 (step @p94 :rule quant-var-elim-eq :args ((= (forall @t95 (or (not (= @t93 @t4)) @t94)) @t92))) % 0.38/0.59 (step @p95 :rule refl :args (@t94)) % 0.38/0.59 (step @p96 :rule eq-symm :args (@t4 @t93)) % 0.38/0.59 (step @p97 :rule cong :premises (@p96) :args (@t94)) % 0.38/0.59 (step @p98 :rule nary_cong :premises (@p97 @p95) :args (@t96)) % 0.38/0.59 (step @p99 :rule aci_norm :args ((= @t94 @t96))) % 0.38/0.59 (step @p100 :rule trans :premises (@p99 @p98)) % 0.38/0.59 (step @p101 :rule cong :premises (@p100) :args (@t97)) % 0.38/0.59 (step @p102 :rule trans :premises (@p101 @p94)) % 0.38/0.59 (step @p103 :rule trans :premises (@p102 @p93)) % 0.38/0.59 (step @p104 :rule refl :args (@t91)) % 0.38/0.59 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t98)) % 0.38/0.59 (step @p106 :rule trans :premises (@p105 @p90)) % 0.38/0.59 (step @p107 :rule quant-miniscope-or :args ((= @t99 @t98))) % 0.38/0.59 (step @p108 :rule trans :premises (@p107 @p106)) % 0.38/0.59 (step @p109 :rule refl :args (@t76)) % 0.38/0.59 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((and @t76 @t99))) % 0.38/0.59 (step @p111 :rule alpha_equiv :args (@t102 @t103 (@list @t93))) % 0.38/0.59 (step @p112 :rule alpha_equiv :args (@t105 @t103 (@list @t62))) % 0.38/0.59 (step @p113 :rule nary_cong :premises (@p112 @p111) :args (@t106)) % 0.38/0.59 (step @p114 :rule quant-miniscope-and :args ((= (forall @t6 (and @t104 @t101)) @t106))) % 0.38/0.59 (step @p115 :rule trans :premises (@p114 @p113)) % 0.38/0.59 (step @p116 :rule trans :premises (@p115 @p110)) % 0.38/0.59 (step @p117 :rule bool-and-de-morgan :args (@t90 @t100 true)) % 0.38/0.59 (step @p118 :rule bool-and-de-morgan :args (@t11 @t53 true)) % 0.38/0.59 (step @p119 :rule nary_cong :premises (@p118 @p117) :args ((and (not @t54) (not @t107)))) % 0.38/0.59 (step @p120 :rule bool-or-de-morgan :args (@t54 @t107 false)) % 0.38/0.59 (step @p121 :rule trans :premises (@p120 @p119)) % 0.38/0.59 (step @p122 :rule cong :premises (@p121) :args (@t109)) % 0.38/0.59 (step @p123 :rule trans :premises (@p122 @p116)) % 0.38/0.59 (step @p124 :rule cong :premises (@p123) :args (@t110)) % 0.38/0.59 (step @p125 :rule exists-elim :args ((= (exists @t6 @t108) @t110))) % 0.38/0.59 (step @p126 :rule trans :premises (@p125 @p124)) % 0.38/0.59 (step @p127 :rule eq-symm :args (@t2 @t4)) % 0.38/0.59 (step @p128 :rule bool-and-de-morgan :args (@t19 @t48 true)) % 0.38/0.59 (step @p129 :rule cong :premises (@p128) :args (@t111)) % 0.38/0.59 (step @p130 :rule cong :premises (@p129) :args (@t112)) % 0.38/0.59 (step @p131 :rule exists-elim :args ((= @t50 @t112))) % 0.38/0.59 (step @p132 :rule trans :premises (@p131 @p130)) % 0.38/0.59 (step @p133 :rule cong :premises (@p132) :args (@t51)) % 0.38/0.59 (step @p134 :rule trans :premises (@p133 @p84)) % 0.38/0.59 (step @p135 :rule nary_cong :premises (@p134 @p127) :args (@t52)) % 0.38/0.59 (step @p136 :rule refl :args (@t54)) % 0.38/0.59 (step @p137 :rule nary_cong :premises (@p136 @p135) :args (@t55)) % 0.38/0.59 (step @p138 :rule cong :premises (@p137) :args (@t56)) % 0.38/0.59 (step @p139 :rule trans :premises (@p138 @p126)) % 0.38/0.59 (step @p140 :rule cong :premises (@p139) :args (@t57)) % 0.38/0.60 (step @p141 :rule trans :premises (@p140 @p89)) % 0.38/0.60 (step @p142 :rule cong :premises (@p141) :args (@t58)) % 0.38/0.60 (step @p143 :rule eq_resolve :premises (@p44 @p142)) % 0.38/0.60 (step @p144 :rule skolemize :premises (@p143)) % 0.38/0.60 (step @p145 :rule bool-double-not-elim :args (@t115)) % 0.38/0.60 (step @p146 :rule refl :args (@t119)) % 0.38/0.60 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or @t119 (not @t118)))) % 0.38/0.60 (step @p148 :rule cnf_or_neg :args (@t119 0)) % 0.38/0.60 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.38/0.60 (step @p150 :rule reordering :premises (@p149) :args ((or @t115 @t119))) % 0.38/0.60 (step @p151 :rule chain_m_resolution :premises (@p150 @p144) :args (@t115 @t120 @t121)) % 0.38/0.60 (step @p152 :rule bool-double-not-elim :args (@t116)) % 0.38/0.60 (step @p153 :rule nary_cong :premises (@p146 @p152) :args ((or @t119 (not @t117)))) % 0.38/0.60 (step @p154 :rule cnf_or_neg :args (@t119 1)) % 0.38/0.60 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 0.38/0.60 (step @p156 :rule reordering :premises (@p155) :args ((or @t116 @t119))) % 0.38/0.60 (step @p157 :rule chain_m_resolution :premises (@p156 @p144) :args (@t116 @t120 @t121)) % 0.38/0.60 (step @p158 :rule aci_norm :args ((= (or @t117 false) @t117))) % 0.38/0.60 (step @p159 :rule eq-refl :args (@t114)) % 0.38/0.60 (step @p160 :rule cong :premises (@p159) :args (@t122)) % 0.38/0.60 (step @p161 :rule trans :premises (@p160 @p47)) % 0.38/0.60 (step @p162 :rule refl :args (@t117)) % 0.38/0.60 (step @p163 :rule nary_cong :premises (@p162 @p161) :args (@t123)) % 0.38/0.60 (step @p164 :rule trans :premises (@p163 @p158)) % 0.38/0.60 (step @p165 :rule refl :args (@t115)) % 0.38/0.60 (step @p166 :rule cong :premises (@p165 @p164) :args ((=> @t115 @t123))) % 0.38/0.60 (assume-push @p174 @t115) % 0.38/0.60 (step @p168 :rule instantiate :premises (@p151) :args ((@list @t113))) % 0.38/0.60 (step-pop @p175 :rule scope :premises (@p168)) % 0.38/0.60 (step @p169 :rule process_scope :premises (@p175) :args (@t123)) % 0.38/0.60 (step @p171 :rule eq_resolve :premises (@p169 @p166)) % 0.38/0.60 (step @p172 :rule implies_elim :premises (@p171)) % 0.38/0.60 (step @p173 false :rule chain_m_resolution :premises (@p172 @p157 @p151) :args (false (@list false false) (@list @t116 @t115))) % 0.38/0.60 ) % 0.38/0.60 % SZS output end Proof % 0.38/0.60 % cvc5 exiting %------------------------------------------------------------------------------