%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET072+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:47:15 AM UTC 2026 % Result : Theorem 4.10s 4.39s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET072+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n002.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 14:50:48 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 4.10/4.39 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 4.10/4.39 % SZS status Theorem % 4.10/4.39 % SZS output start Proof % 4.10/4.39 ( % 4.10/4.39 (declare-sort $$unsorted 0) % 4.10/4.39 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 4.10/4.39 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.element_relation $$unsorted) % 4.10/4.39 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.universal_class $$unsorted) % 4.10/4.39 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.inductive (-> $$unsorted Bool)) % 4.10/4.39 (declare-const tptp.function (-> $$unsorted Bool)) % 4.10/4.39 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 4.10/4.39 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 4.10/4.39 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.null_class $$unsorted) % 4.10/4.39 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.successor_relation $$unsorted) % 4.10/4.39 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 4.10/4.39 (declare-const tptp.identity_relation $$unsorted) % 4.10/4.39 (define @t1 () (@var "Y" $$unsorted)) % 4.10/4.39 (define @t2 () (@var "U" $$unsorted)) % 4.10/4.39 (define @t3 () (tptp.member @t2 @t1)) % 4.10/4.39 (define @t4 () (@var "X" $$unsorted)) % 4.10/4.39 (define @t5 () (tptp.member @t2 @t4)) % 4.10/4.39 (define @t6 () (@list @t2)) % 4.10/4.39 (define @t7 () (tptp.subclass @t4 @t1)) % 4.10/4.39 (define @t8 () (@list @t4 @t1)) % 4.10/4.39 (define @t9 () (@list @t4)) % 4.10/4.39 (define @t10 () (= @t4 @t1)) % 4.10/4.39 (define @t11 () (or (= @t2 @t4) (= @t2 @t1))) % 4.10/4.39 (define @t12 () (tptp.member @t2 tptp.universal_class)) % 4.10/4.39 (define @t13 () (and @t12 @t11)) % 4.10/4.39 (define @t14 () (tptp.unordered_pair @t4 @t1)) % 4.10/4.39 (define @t15 () (tptp.member @t2 @t14)) % 4.10/4.39 (define @t16 () (= @t15 @t13)) % 4.10/4.39 (define @t17 () (@list @t2 @t4 @t1)) % 4.10/4.39 (define @t18 () (forall @t17 @t16)) % 4.10/4.39 (define @t19 () (tptp.singleton @t4)) % 4.10/4.39 (define @t20 () (tptp.singleton @t1)) % 4.10/4.39 (define @t21 () (tptp.ordered_pair @t4 @t1)) % 4.10/4.39 (define @t22 () (@var "V" $$unsorted)) % 4.10/4.39 (define @t23 () (tptp.cross_product @t4 @t1)) % 4.10/4.39 (define @t24 () (tptp.ordered_pair @t2 @t22)) % 4.10/4.39 (define @t25 () (tptp.second @t21)) % 4.10/4.39 (define @t26 () (tptp.first @t21)) % 4.10/4.39 (define @t27 () (and (= @t26 @t4) (= @t25 @t1))) % 4.10/4.39 (define @t28 () (tptp.member @t1 tptp.universal_class)) % 4.10/4.39 (define @t29 () (tptp.member @t4 tptp.universal_class)) % 4.10/4.39 (define @t30 () (and @t29 @t28)) % 4.10/4.39 (define @t31 () (=> @t30 @t27)) % 4.10/4.39 (define @t32 () (forall @t8 @t31)) % 4.10/4.39 (define @t33 () (@var "Z" $$unsorted)) % 4.10/4.39 (define @t34 () (@list @t4 @t1 @t33)) % 4.10/4.39 (define @t35 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 4.10/4.39 (define @t36 () (tptp.member @t33 @t1)) % 4.10/4.39 (define @t37 () (tptp.member @t33 @t4)) % 4.10/4.39 (define @t38 () (tptp.member @t33 tptp.universal_class)) % 4.10/4.39 (define @t39 () (@list @t4 @t33)) % 4.10/4.39 (define @t40 () (@var "XR" $$unsorted)) % 4.10/4.39 (define @t41 () (@var "W" $$unsorted)) % 4.10/4.39 (define @t42 () (tptp.cross_product @t35 tptp.universal_class)) % 4.10/4.39 (define @t43 () (tptp.ordered_pair @t24 @t41)) % 4.10/4.39 (define @t44 () (tptp.member @t43 @t42)) % 4.10/4.39 (define @t45 () (tptp.rotate @t4)) % 4.10/4.39 (define @t46 () (tptp.flip @t4)) % 4.10/4.39 (define @t47 () (tptp.successor @t4)) % 4.10/4.39 (define @t48 () (@list @t1)) % 4.10/4.39 (define @t49 () (@list @t33)) % 4.10/4.39 (define @t50 () (tptp.inductive @t4)) % 4.10/4.39 (define @t51 () (tptp.sum_class @t4)) % 4.10/4.39 (define @t52 () (@list @t2 @t4)) % 4.10/4.39 (define @t53 () (@var "YR" $$unsorted)) % 4.10/4.39 (define @t54 () (tptp.compose @t53 @t40)) % 4.10/4.39 (define @t55 () (@var "XF" $$unsorted)) % 4.10/4.39 (define @t56 () (tptp.function @t55)) % 4.10/4.39 (define @t57 () (@list @t55)) % 4.10/4.39 (define @t58 () (tptp.apply @t55 @t1)) % 4.10/4.39 (define @t59 () (= (tptp.unordered_pair @t4 @t33) (tptp.unordered_pair @t1 @t33))) % 4.10/4.39 (define @t60 () (and @t29 @t28 @t59)) % 4.10/4.39 (define @t61 () (forall @t34 (=> @t60 @t10))) % 4.10/4.39 (define @t62 () (not @t61)) % 4.10/4.39 (define @t63 () (and (= @t4 @t26) (= @t1 @t25))) % 4.10/4.39 (define @t64 () (not @t28)) % 4.10/4.39 (define @t65 () (not @t29)) % 4.10/4.39 (define @t66 () (not @t59)) % 4.10/4.39 (define @t67 () (or @t65 @t64 @t66 @t10)) % 4.10/4.39 (define @t68 () (forall @t34 @t67)) % 4.10/4.39 (define @t69 () (@quantifiers_skolemize @t68 0)) % 4.10/4.39 (define @t70 () (or @t65 @t64 @t66)) % 4.10/4.39 (define @t71 () (tptp.member @t69 tptp.universal_class)) % 4.10/4.39 (define @t72 () (@quantifiers_skolemize @t68 1)) % 4.10/4.39 (define @t73 () (= @t69 @t72)) % 4.10/4.39 (define @t74 () (@quantifiers_skolemize @t68 2)) % 4.10/4.39 (define @t75 () (tptp.unordered_pair @t72 @t74)) % 4.10/4.39 (define @t76 () (tptp.unordered_pair @t69 @t74)) % 4.10/4.39 (define @t77 () (= @t76 @t75)) % 4.10/4.39 (define @t78 () (not @t77)) % 4.10/4.39 (define @t79 () (tptp.member @t72 tptp.universal_class)) % 4.10/4.39 (define @t80 () (not @t79)) % 4.10/4.39 (define @t81 () (not @t71)) % 4.10/4.39 (define @t82 () (or @t81 @t80 @t78 @t73)) % 4.10/4.39 (define @t83 () (@list true)) % 4.10/4.39 (define @t84 () (@list @t82)) % 4.10/4.39 (define @t85 () (tptp.ordered_pair @t69 @t69)) % 4.10/4.39 (define @t86 () (= @t69 (tptp.first @t85))) % 4.10/4.39 (define @t87 () (and @t86 (= @t69 (tptp.second @t85)))) % 4.10/4.39 (define @t88 () (or @t81 @t81 @t87)) % 4.10/4.39 (define @t89 () (@list false false)) % 4.10/4.39 (define @t90 () (@list false)) % 4.10/4.39 (define @t91 () (= @t74 @t69)) % 4.10/4.39 (define @t92 () (or (= @t72 @t69) @t91)) % 4.10/4.39 (define @t93 () (and @t71 @t92)) % 4.10/4.39 (define @t94 () (tptp.member @t69 @t75)) % 4.10/4.39 (define @t95 () (= @t94 @t93)) % 4.10/4.39 (define @t96 () (forall @t17 (= @t15 (and @t12 (or (= @t4 @t2) (= @t1 @t2)))))) % 4.10/4.39 (define @t97 () (= @t69 @t74)) % 4.10/4.39 (define @t98 () (or @t73 @t97)) % 4.10/4.39 (define @t99 () (and @t71 @t98)) % 4.10/4.39 (define @t100 () (= @t94 @t99)) % 4.10/4.39 (define @t101 () (@list @t96)) % 4.10/4.39 (define @t102 () (tptp.member @t69 @t76)) % 4.10/4.39 (define @t103 () (or (= @t69 @t69) @t91)) % 4.10/4.39 (define @t104 () (and @t71 @t103)) % 4.10/4.39 (define @t105 () (= @t102 @t104)) % 4.10/4.39 (define @t106 () (= @t71 @t102)) % 4.10/4.39 (define @t107 () (@list true false)) % 4.10/4.39 (define @t108 () (= @t74 @t72)) % 4.10/4.39 (define @t109 () (or @t73 @t108)) % 4.10/4.39 (define @t110 () (and @t79 @t109)) % 4.10/4.39 (define @t111 () (tptp.member @t72 @t76)) % 4.10/4.39 (define @t112 () (= @t111 @t110)) % 4.10/4.39 (define @t113 () (= @t72 @t74)) % 4.10/4.39 (define @t114 () (or @t73 @t113)) % 4.10/4.39 (define @t115 () (and @t79 @t114)) % 4.10/4.39 (define @t116 () (= @t111 @t115)) % 4.10/4.39 (define @t117 () (tptp.member @t72 @t75)) % 4.10/4.39 (define @t118 () (or (= @t72 @t72) @t108)) % 4.10/4.39 (define @t119 () (and @t79 @t118)) % 4.10/4.39 (define @t120 () (= @t117 @t119)) % 4.10/4.39 (define @t121 () (= @t79 @t117)) % 4.10/4.39 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 4.10/4.39 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 4.10/4.39 (assume @p3 (forall @t8 (= @t10 (and @t7 (tptp.subclass @t1 @t4))))) % 4.10/4.39 (assume @p4 @t18) % 4.10/4.39 (assume @p5 (forall @t8 (tptp.member @t14 tptp.universal_class))) % 4.10/4.39 (assume @p6 (forall @t9 (= @t19 (tptp.unordered_pair @t4 @t4)))) % 4.10/4.39 (assume @p7 (forall @t8 (= @t21 (tptp.unordered_pair @t19 (tptp.unordered_pair @t4 @t20))))) % 4.10/4.39 (assume @p8 (forall (@list @t2 @t22 @t4 @t1) (= (tptp.member @t24 @t23) (and @t5 (tptp.member @t22 @t1))))) % 4.10/4.39 (assume @p9 @t32) % 4.10/4.39 (assume @p10 (forall @t34 (=> (tptp.member @t33 @t23) (= @t33 (tptp.ordered_pair (tptp.first @t33) (tptp.second @t33)))))) % 4.10/4.39 (assume @p11 (forall @t8 (= (tptp.member @t21 tptp.element_relation) (and @t28 (tptp.member @t4 @t1))))) % 4.10/4.39 (assume @p12 (tptp.subclass tptp.element_relation @t35)) % 4.10/4.39 (assume @p13 (forall @t34 (= (tptp.member @t33 (tptp.intersection @t4 @t1)) (and @t37 @t36)))) % 4.10/4.39 (assume @p14 (forall @t39 (= (tptp.member @t33 (tptp.complement @t4)) (and @t38 (not @t37))))) % 4.10/4.39 (assume @p15 (forall (@list @t4 @t40 @t1) (= (tptp.restrict @t40 @t4 @t1) (tptp.intersection @t40 @t23)))) % 4.10/4.39 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 4.10/4.39 (assume @p17 (forall @t39 (= (tptp.member @t33 (tptp.domain_of @t4)) (and @t38 (not (= (tptp.restrict @t4 (tptp.singleton @t33) tptp.universal_class) tptp.null_class)))))) % 4.10/4.39 (assume @p18 (forall (@list @t4 @t2 @t22 @t41) (= (tptp.member @t43 @t45) (and @t44 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t41) @t2) @t4))))) % 4.10/4.39 (assume @p19 (forall @t9 (tptp.subclass @t45 @t42))) % 4.10/4.39 (assume @p20 (forall (@list @t2 @t22 @t41 @t4) (= (tptp.member @t43 @t46) (and @t44 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t2) @t41) @t4))))) % 4.10/4.39 (assume @p21 (forall @t9 (tptp.subclass @t46 @t42))) % 4.10/4.39 (assume @p22 (forall @t34 (= (tptp.member @t33 (tptp.union @t4 @t1)) (or @t37 @t36)))) % 4.10/4.39 (assume @p23 (forall @t9 (= @t47 (tptp.union @t4 @t19)))) % 4.10/4.39 (assume @p24 (tptp.subclass tptp.successor_relation @t35)) % 4.10/4.39 (assume @p25 (forall @t8 (= (tptp.member @t21 tptp.successor_relation) (and @t29 @t28 (= @t47 @t1))))) % 4.10/4.39 (assume @p26 (forall @t48 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 4.10/4.39 (assume @p27 (forall @t49 (= (tptp.range_of @t33) (tptp.domain_of (tptp.inverse @t33))))) % 4.10/4.39 (assume @p28 (forall (@list @t4 @t40) (= (tptp.image @t40 @t4) (tptp.range_of (tptp.restrict @t40 @t4 tptp.universal_class))))) % 4.10/4.39 (assume @p29 (forall @t9 (= @t50 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 4.10/4.39 (assume @p30 (exists @t9 (and @t29 @t50 (forall @t48 (=> (tptp.inductive @t1) @t7))))) % 4.10/4.39 (assume @p31 (forall @t52 (= (tptp.member @t2 @t51) (exists @t48 (and @t3 (tptp.member @t1 @t4)))))) % 4.10/4.39 (assume @p32 (forall @t9 (=> @t29 (tptp.member @t51 tptp.universal_class)))) % 4.10/4.39 (assume @p33 (forall @t52 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t12 (tptp.subclass @t2 @t4))))) % 4.10/4.39 (assume @p34 (forall @t6 (=> @t12 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 4.10/4.39 (assume @p35 (forall (@list @t40 @t53) (tptp.subclass @t54 @t35))) % 4.10/4.39 (assume @p36 (forall (@list @t40 @t53 @t2 @t22) (= (tptp.member @t24 @t54) (and @t12 (tptp.member @t22 (tptp.image @t53 (tptp.image @t40 (tptp.singleton @t2)))))))) % 4.10/4.39 (assume @p37 (forall @t49 (= (tptp.member @t33 tptp.identity_relation) (exists @t9 (and @t29 (= @t33 (tptp.ordered_pair @t4 @t4))))))) % 4.10/4.39 (assume @p38 (forall @t57 (= @t56 (and (tptp.subclass @t55 @t35) (tptp.subclass (tptp.compose @t55 (tptp.inverse @t55)) tptp.identity_relation))))) % 4.10/4.39 (assume @p39 (forall (@list @t4 @t55) (=> (and @t29 @t56) (tptp.member (tptp.image @t55 @t4) tptp.universal_class)))) % 4.10/4.39 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 4.10/4.39 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t12 @t5 (tptp.disjoint @t2 @t4)))))) % 4.10/4.39 (assume @p42 (forall (@list @t55 @t1) (= @t58 (tptp.sum_class (tptp.image @t55 @t20))))) % 4.10/4.39 (assume @p43 (exists @t57 (and @t56 (forall @t48 (=> @t28 (or (= @t1 tptp.null_class) (tptp.member @t58 @t1))))))) % 4.10/4.39 (assume @p44 @t62) % 4.10/4.39 (assume @p45 true) % 4.10/4.39 (step @p46 :rule evaluate :args ((= false true))) % 4.10/4.39 (step @p47 :rule aci_norm :args ((= (or (or @t65 @t64) @t63) (or @t65 @t64 @t63)))) % 4.10/4.39 (step @p48 :rule refl :args (@t63)) % 4.10/4.39 (step @p49 :rule bool-and-de-morgan :args (@t29 @t28 true)) % 4.10/4.39 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((or (not @t30) @t63))) % 4.10/4.39 (step @p51 :rule trans :premises (@p50 @p47)) % 4.10/4.39 (step @p52 :rule bool-impl-elim :args (@t30 @t63)) % 4.10/4.39 (step @p53 :rule trans :premises (@p52 @p51)) % 4.10/4.39 (step @p54 :rule cong :premises (@p53) :args ((forall @t8 (=> @t30 @t63)))) % 4.10/4.39 (step @p55 :rule eq-symm :args (@t25 @t1)) % 4.10/4.39 (step @p56 :rule eq-symm :args (@t26 @t4)) % 4.10/4.39 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t27)) % 4.10/4.39 (step @p58 :rule refl :args (@t30)) % 4.10/4.39 (step @p59 :rule cong :premises (@p58 @p57) :args (@t31)) % 4.10/4.39 (step @p60 :rule cong :premises (@p59) :args (@t32)) % 4.10/4.39 (step @p61 :rule trans :premises (@p60 @p54)) % 4.10/4.39 (step @p62 :rule eq_resolve :premises (@p9 @p61)) % 4.10/4.39 (step @p63 :rule instantiate :premises (@p62) :args ((@list @t69 @t69))) % 4.10/4.39 (step @p64 :rule aci_norm :args ((= (or @t70 @t10) @t67))) % 4.10/4.39 (step @p65 :rule refl :args (@t10)) % 4.10/4.39 (step @p66 :rule aci_norm :args ((= (or @t65 (or @t64 @t66)) @t70))) % 4.10/4.39 (step @p67 :rule bool-and-de-morgan :args (@t28 @t59 true)) % 4.10/4.39 (step @p68 :rule refl :args (@t65)) % 4.10/4.39 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or @t65 (not (and @t28 @t59))))) % 4.10/4.39 (step @p70 :rule bool-and-de-morgan :args (@t29 @t28 (and @t59))) % 4.10/4.39 (step @p71 :rule trans :premises (@p70 @p69)) % 4.10/4.39 (step @p72 :rule trans :premises (@p71 @p66)) % 4.10/4.39 (step @p73 :rule nary_cong :premises (@p72 @p65) :args ((or (not @t60) @t10))) % 4.10/4.39 (step @p74 :rule trans :premises (@p73 @p64)) % 4.10/4.39 (step @p75 :rule bool-impl-elim :args (@t60 @t10)) % 4.10/4.39 (step @p76 :rule trans :premises (@p75 @p74)) % 4.10/4.39 (step @p77 :rule cong :premises (@p76) :args (@t61)) % 4.10/4.39 (step @p78 :rule cong :premises (@p77) :args (@t62)) % 4.10/4.39 (step @p79 :rule eq_resolve :premises (@p44 @p78)) % 4.10/4.39 (step @p80 :rule skolemize :premises (@p79)) % 4.10/4.39 (step @p81 :rule bool-double-not-elim :args (@t71)) % 4.10/4.39 (step @p82 :rule refl :args (@t82)) % 4.10/4.39 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t82 (not @t81)))) % 4.10/4.39 (step @p84 :rule cnf_or_neg :args (@t82 0)) % 4.10/4.39 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 4.10/4.39 (step @p86 :rule reordering :premises (@p85) :args ((or @t71 @t82))) % 4.10/4.39 (step @p87 :rule chain_m_resolution :premises (@p86 @p80) :args (@t71 @t83 @t84)) % 4.10/4.39 (step @p88 :rule cnf_or_pos :args (@t88)) % 4.10/4.39 (step @p89 :rule factoring :premises (@p88)) % 4.10/4.39 (step @p90 :rule reordering :premises (@p89) :args ((or @t81 @t87 (not @t88)))) % 4.10/4.39 (step @p91 :rule chain_m_resolution :premises (@p90 @p87 @p63) :args (@t87 @t89 (@list @t71 @t88))) % 4.10/4.39 (step @p92 :rule cnf_and_pos :args (@t87 0)) % 4.10/4.39 (step @p93 :rule reordering :premises (@p92) :args ((or @t86 (not @t87)))) % 4.10/4.39 (step @p94 :rule chain_m_resolution :premises (@p93 @p91) :args (@t86 @t90 (@list @t87))) % 4.10/4.39 (step @p95 :rule eq-symm :args (@t2 @t1)) % 4.10/4.39 (step @p96 :rule eq-symm :args (@t2 @t4)) % 4.10/4.39 (step @p97 :rule nary_cong :premises (@p96 @p95) :args (@t11)) % 4.10/4.39 (step @p98 :rule refl :args (@t12)) % 4.10/4.39 (step @p99 :rule nary_cong :premises (@p98 @p97) :args (@t13)) % 4.10/4.39 (step @p100 :rule refl :args (@t15)) % 4.10/4.39 (step @p101 :rule cong :premises (@p100 @p99) :args (@t16)) % 4.10/4.39 (step @p102 :rule cong :premises (@p101) :args (@t18)) % 4.10/4.39 (step @p103 :rule eq_resolve :premises (@p4 @p102)) % 4.10/4.39 (step @p104 :rule eq-symm :args (@t74 @t69)) % 4.10/4.39 (step @p105 :rule eq-symm :args (@t72 @t69)) % 4.10/4.39 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t92)) % 4.10/4.39 (step @p107 :rule refl :args (@t71)) % 4.10/4.39 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t93)) % 4.10/4.39 (step @p109 :rule refl :args (@t94)) % 4.10/4.39 (step @p110 :rule cong :premises (@p109 @p108) :args (@t95)) % 4.10/4.39 (step @p111 :rule refl :args (@t96)) % 4.10/4.39 (step @p112 :rule cong :premises (@p111 @p110) :args ((=> @t96 @t95))) % 4.10/4.39 (assume-push @p231 @t96) % 4.10/4.39 (step @p114 :rule instantiate :premises (@p103) :args ((@list @t69 @t72 @t74))) % 4.10/4.39 (step-pop @p232 :rule scope :premises (@p114)) % 4.10/4.39 (step @p115 :rule process_scope :premises (@p232) :args (@t95)) % 4.10/4.39 (step @p117 :rule eq_resolve :premises (@p115 @p112)) % 4.10/4.39 (step @p118 :rule implies_elim :premises (@p117)) % 4.10/4.39 (step @p119 :rule chain_m_resolution :premises (@p118 @p103) :args (@t100 @t90 @t101)) % 4.10/4.39 (step @p120 :rule eq-symm :args (@t102 @t71)) % 4.10/4.39 (step @p121 :rule aci_norm :args ((= (and @t71 true) @t71))) % 4.10/4.39 (step @p122 :rule absorb :args ((= (or true @t97) true))) % 4.10/4.39 (step @p123 :rule eq-refl :args (@t69)) % 4.10/4.39 (step @p124 :rule nary_cong :premises (@p123 @p104) :args (@t103)) % 4.10/4.39 (step @p125 :rule trans :premises (@p124 @p122)) % 4.10/4.39 (step @p126 :rule nary_cong :premises (@p107 @p125) :args (@t104)) % 4.10/4.39 (step @p127 :rule trans :premises (@p126 @p121)) % 4.10/4.39 (step @p128 :rule refl :args (@t102)) % 4.10/4.39 (step @p129 :rule cong :premises (@p128 @p127) :args (@t105)) % 4.10/4.39 (step @p130 :rule trans :premises (@p129 @p120)) % 4.10/4.39 (step @p131 :rule cong :premises (@p111 @p130) :args ((=> @t96 @t105))) % 4.10/4.39 (assume-push @p233 @t96) % 4.10/4.39 (step @p133 :rule instantiate :premises (@p103) :args ((@list @t69 @t69 @t74))) % 4.10/4.39 (step-pop @p234 :rule scope :premises (@p133)) % 4.10/4.39 (step @p134 :rule process_scope :premises (@p234) :args (@t105)) % 4.10/4.39 (step @p136 :rule eq_resolve :premises (@p134 @p131)) % 4.10/4.39 (step @p137 :rule implies_elim :premises (@p136)) % 4.10/4.39 (step @p138 :rule chain_m_resolution :premises (@p137 @p103) :args (@t106 @t90 @t101)) % 4.10/4.39 (step @p139 :rule cnf_equiv_pos1 :args (@t106)) % 4.10/4.39 (step @p140 :rule reordering :premises (@p139) :args ((or @t81 @t102 (not @t106)))) % 4.10/4.39 (step @p141 :rule chain_m_resolution :premises (@p140 @p87 @p138) :args (@t102 @t89 (@list @t71 @t106))) % 4.10/4.39 (step @p142 :rule true_intro :premises (@p141)) % 4.10/4.39 (step @p143 :rule bool-double-not-elim :args (@t77)) % 4.10/4.39 (step @p144 :rule nary_cong :premises (@p82 @p143) :args ((or @t82 (not @t78)))) % 4.10/4.39 (step @p145 :rule cnf_or_neg :args (@t82 2)) % 4.10/4.39 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 4.10/4.39 (step @p147 :rule reordering :premises (@p146) :args ((or @t77 @t82))) % 4.10/4.39 (step @p148 :rule chain_m_resolution :premises (@p147 @p80) :args (@t77 @t83 @t84)) % 4.10/4.39 (step @p149 :rule symm :premises (@p148)) % 4.10/4.39 (step @p150 :rule refl :args (@t69)) % 4.10/4.39 (step @p151 :rule cong :premises (@p150 @p149) :args (@t94)) % 4.10/4.39 (step @p152 :rule trans :premises (@p151 @p142)) % 4.10/4.39 (step @p153 :rule true_elim :premises (@p152)) % 4.10/4.39 (step @p154 :rule cnf_equiv_pos1 :args (@t100)) % 4.10/4.39 (step @p155 :rule reordering :premises (@p154) :args ((or @t99 (not @t94) (not @t100)))) % 4.10/4.39 (step @p156 :rule chain_m_resolution :premises (@p155 @p153 @p119) :args (@t99 @t89 (@list @t94 @t100))) % 4.10/4.39 (step @p157 :rule cnf_and_pos :args (@t99 1)) % 4.10/4.39 (step @p158 :rule reordering :premises (@p157) :args ((or @t98 (not @t99)))) % 4.10/4.39 (step @p159 :rule chain_m_resolution :premises (@p158 @p156) :args (@t98 @t90 (@list @t99))) % 4.10/4.39 (step @p160 :rule cnf_or_neg :args (@t82 3)) % 4.10/4.39 (step @p161 :rule chain_m_resolution :premises (@p160 @p80) :args ((not @t73) @t83 @t84)) % 4.10/4.39 (step @p162 :rule cnf_or_pos :args (@t98)) % 4.10/4.39 (step @p163 :rule reordering :premises (@p162) :args ((or @t73 @t97 (not @t98)))) % 4.10/4.39 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p159) :args (@t97 @t107 (@list @t73 @t98))) % 4.10/4.39 (step @p165 :rule symm :premises (@p164)) % 4.10/4.39 (step @p166 :rule eq-symm :args (@t74 @t72)) % 4.10/4.39 (step @p167 :rule refl :args (@t73)) % 4.10/4.39 (step @p168 :rule nary_cong :premises (@p167 @p166) :args (@t109)) % 4.10/4.39 (step @p169 :rule refl :args (@t79)) % 4.10/4.39 (step @p170 :rule nary_cong :premises (@p169 @p168) :args (@t110)) % 4.10/4.39 (step @p171 :rule refl :args (@t111)) % 4.10/4.39 (step @p172 :rule cong :premises (@p171 @p170) :args (@t112)) % 4.10/4.39 (step @p173 :rule cong :premises (@p111 @p172) :args ((=> @t96 @t112))) % 4.10/4.39 (assume-push @p235 @t96) % 4.10/4.39 (step @p175 :rule instantiate :premises (@p103) :args ((@list @t72 @t69 @t74))) % 4.10/4.39 (step-pop @p236 :rule scope :premises (@p175)) % 4.10/4.39 (step @p176 :rule process_scope :premises (@p236) :args (@t112)) % 4.10/4.39 (step @p178 :rule eq_resolve :premises (@p176 @p173)) % 4.10/4.39 (step @p179 :rule implies_elim :premises (@p178)) % 4.10/4.39 (step @p180 :rule chain_m_resolution :premises (@p179 @p103) :args (@t116 @t90 @t101)) % 4.10/4.39 (step @p181 :rule eq-symm :args (@t117 @t79)) % 4.10/4.39 (step @p182 :rule aci_norm :args ((= (and @t79 true) @t79))) % 4.10/4.39 (step @p183 :rule absorb :args ((= (or true @t113) true))) % 4.10/4.39 (step @p184 :rule eq-refl :args (@t72)) % 4.10/4.39 (step @p185 :rule nary_cong :premises (@p184 @p166) :args (@t118)) % 4.10/4.39 (step @p186 :rule trans :premises (@p185 @p183)) % 4.10/4.39 (step @p187 :rule nary_cong :premises (@p169 @p186) :args (@t119)) % 4.10/4.39 (step @p188 :rule trans :premises (@p187 @p182)) % 4.10/4.39 (step @p189 :rule refl :args (@t117)) % 4.10/4.39 (step @p190 :rule cong :premises (@p189 @p188) :args (@t120)) % 4.10/4.39 (step @p191 :rule trans :premises (@p190 @p181)) % 4.10/4.39 (step @p192 :rule cong :premises (@p111 @p191) :args ((=> @t96 @t120))) % 4.10/4.39 (assume-push @p237 @t96) % 4.10/4.39 (step @p194 :rule instantiate :premises (@p103) :args ((@list @t72 @t72 @t74))) % 4.10/4.39 (step-pop @p238 :rule scope :premises (@p194)) % 4.10/4.39 (step @p195 :rule process_scope :premises (@p238) :args (@t120)) % 4.10/4.39 (step @p197 :rule eq_resolve :premises (@p195 @p192)) % 4.10/4.39 (step @p198 :rule implies_elim :premises (@p197)) % 4.10/4.39 (step @p199 :rule chain_m_resolution :premises (@p198 @p103) :args (@t121 @t90 @t101)) % 4.10/4.39 (step @p200 :rule bool-double-not-elim :args (@t79)) % 4.10/4.39 (step @p201 :rule nary_cong :premises (@p82 @p200) :args ((or @t82 (not @t80)))) % 4.10/4.39 (step @p202 :rule cnf_or_neg :args (@t82 1)) % 4.10/4.39 (step @p203 :rule eq_resolve :premises (@p202 @p201)) % 4.10/4.39 (step @p204 :rule reordering :premises (@p203) :args ((or @t79 @t82))) % 4.10/4.39 (step @p205 :rule chain_m_resolution :premises (@p204 @p80) :args (@t79 @t83 @t84)) % 4.10/4.39 (step @p206 :rule cnf_equiv_pos1 :args (@t121)) % 4.10/4.39 (step @p207 :rule reordering :premises (@p206) :args ((or @t80 @t117 (not @t121)))) % 4.10/4.39 (step @p208 :rule chain_m_resolution :premises (@p207 @p205 @p199) :args (@t117 @t89 (@list @t79 @t121))) % 4.10/4.39 (step @p209 :rule true_intro :premises (@p208)) % 0.35/4.41 (step @p210 :rule refl :args (@t72)) % 0.35/4.41 (step @p211 :rule cong :premises (@p210 @p148) :args (@t111)) % 0.35/4.41 (step @p212 :rule trans :premises (@p211 @p209)) % 0.35/4.41 (step @p213 :rule true_elim :premises (@p212)) % 0.35/4.41 (step @p214 :rule cnf_equiv_pos1 :args (@t116)) % 0.35/4.41 (step @p215 :rule reordering :premises (@p214) :args ((or @t115 (not @t111) (not @t116)))) % 0.35/4.41 (step @p216 :rule chain_m_resolution :premises (@p215 @p213 @p180) :args (@t115 @t89 (@list @t111 @t116))) % 0.35/4.41 (step @p217 :rule cnf_and_pos :args (@t115 1)) % 0.35/4.41 (step @p218 :rule reordering :premises (@p217) :args ((or @t114 (not @t115)))) % 0.35/4.41 (step @p219 :rule chain_m_resolution :premises (@p218 @p216) :args (@t114 @t90 (@list @t115))) % 0.35/4.41 (step @p220 :rule cnf_or_pos :args (@t114)) % 0.35/4.41 (step @p221 :rule reordering :premises (@p220) :args ((or @t73 @t113 (not @t114)))) % 0.35/4.41 (step @p222 :rule chain_m_resolution :premises (@p221 @p161 @p219) :args (@t113 @t107 (@list @t73 @t114))) % 0.35/4.41 (step @p223 :rule trans :premises (@p222 @p165 @p94)) % 0.35/4.41 (step @p224 :rule symm :premises (@p223)) % 0.35/4.41 (step @p225 :rule trans :premises (@p94 @p224)) % 0.35/4.41 (step @p226 :rule true_intro :premises (@p225)) % 0.35/4.41 (step @p227 :rule false_intro :premises (@p161)) % 0.35/4.41 (step @p228 :rule symm :premises (@p227)) % 0.35/4.41 (step @p229 :rule trans :premises (@p228 @p226)) % 0.35/4.41 (step @p230 false :rule eq_resolve :premises (@p229 @p46)) % 0.35/4.41 ) % 0.35/4.41 % SZS output end Proof % 0.35/4.41 % cvc5 exiting %------------------------------------------------------------------------------