%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET071+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 : n001.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 0.45s 0.64s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET071+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 : n001.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 14:51:35 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.64 % SZS status Theorem % 0.45/0.64 % SZS output start Proof % 0.45/0.64 ( % 0.45/0.64 (declare-sort $$unsorted 0) % 0.45/0.64 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.45/0.64 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.element_relation $$unsorted) % 0.45/0.64 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.universal_class $$unsorted) % 0.45/0.64 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.45/0.64 (declare-const tptp.function (-> $$unsorted Bool)) % 0.45/0.64 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.45/0.64 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.45/0.64 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.null_class $$unsorted) % 0.45/0.64 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.successor_relation $$unsorted) % 0.45/0.64 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.identity_relation $$unsorted) % 0.45/0.64 (define @t1 () (@var "Y" $$unsorted)) % 0.45/0.64 (define @t2 () (@var "U" $$unsorted)) % 0.45/0.64 (define @t3 () (tptp.member @t2 @t1)) % 0.45/0.64 (define @t4 () (@var "X" $$unsorted)) % 0.45/0.64 (define @t5 () (tptp.member @t2 @t4)) % 0.45/0.64 (define @t6 () (@list @t2)) % 0.45/0.64 (define @t7 () (tptp.subclass @t4 @t1)) % 0.45/0.64 (define @t8 () (@list @t4 @t1)) % 0.45/0.64 (define @t9 () (@list @t4)) % 0.45/0.64 (define @t10 () (or (= @t2 @t4) (= @t2 @t1))) % 0.45/0.64 (define @t11 () (tptp.member @t2 tptp.universal_class)) % 0.45/0.64 (define @t12 () (and @t11 @t10)) % 0.45/0.64 (define @t13 () (tptp.unordered_pair @t4 @t1)) % 0.45/0.64 (define @t14 () (tptp.member @t2 @t13)) % 0.45/0.64 (define @t15 () (= @t14 @t12)) % 0.45/0.64 (define @t16 () (forall (@list @t2 @t4 @t1) @t15)) % 0.45/0.64 (define @t17 () (tptp.singleton @t4)) % 0.45/0.64 (define @t18 () (tptp.singleton @t1)) % 0.45/0.64 (define @t19 () (tptp.ordered_pair @t4 @t1)) % 0.45/0.64 (define @t20 () (@var "V" $$unsorted)) % 0.45/0.64 (define @t21 () (tptp.cross_product @t4 @t1)) % 0.45/0.64 (define @t22 () (tptp.ordered_pair @t2 @t20)) % 0.45/0.64 (define @t23 () (tptp.member @t1 tptp.universal_class)) % 0.45/0.64 (define @t24 () (tptp.member @t4 tptp.universal_class)) % 0.45/0.64 (define @t25 () (@var "Z" $$unsorted)) % 0.45/0.64 (define @t26 () (@list @t4 @t1 @t25)) % 0.45/0.64 (define @t27 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.45/0.64 (define @t28 () (tptp.member @t25 @t1)) % 0.45/0.64 (define @t29 () (tptp.member @t25 @t4)) % 0.45/0.64 (define @t30 () (tptp.member @t25 tptp.universal_class)) % 0.45/0.64 (define @t31 () (@list @t4 @t25)) % 0.45/0.64 (define @t32 () (@var "XR" $$unsorted)) % 0.45/0.64 (define @t33 () (@var "W" $$unsorted)) % 0.45/0.64 (define @t34 () (tptp.cross_product @t27 tptp.universal_class)) % 0.45/0.64 (define @t35 () (tptp.ordered_pair @t22 @t33)) % 0.45/0.64 (define @t36 () (tptp.member @t35 @t34)) % 0.45/0.64 (define @t37 () (tptp.rotate @t4)) % 0.45/0.64 (define @t38 () (tptp.flip @t4)) % 0.45/0.64 (define @t39 () (tptp.successor @t4)) % 0.45/0.64 (define @t40 () (@list @t1)) % 0.45/0.64 (define @t41 () (@list @t25)) % 0.45/0.64 (define @t42 () (tptp.inductive @t4)) % 0.45/0.64 (define @t43 () (tptp.sum_class @t4)) % 0.45/0.64 (define @t44 () (@list @t2 @t4)) % 0.45/0.64 (define @t45 () (@var "YR" $$unsorted)) % 0.45/0.64 (define @t46 () (tptp.compose @t45 @t32)) % 0.45/0.64 (define @t47 () (@var "XF" $$unsorted)) % 0.45/0.64 (define @t48 () (tptp.function @t47)) % 0.45/0.64 (define @t49 () (@list @t47)) % 0.45/0.64 (define @t50 () (tptp.apply @t47 @t1)) % 0.45/0.64 (define @t51 () (tptp.member @t50 @t1)) % 0.45/0.64 (define @t52 () (= @t1 tptp.null_class)) % 0.45/0.64 (define @t53 () (or @t52 @t51)) % 0.45/0.64 (define @t54 () (forall @t40 (=> @t23 @t53))) % 0.45/0.64 (define @t55 () (and @t48 @t54)) % 0.45/0.64 (define @t56 () (exists @t49 @t55)) % 0.45/0.64 (define @t57 () (= @t13 tptp.null_class)) % 0.45/0.64 (define @t58 () (not @t23)) % 0.45/0.64 (define @t59 () (not @t24)) % 0.45/0.64 (define @t60 () (and @t59 @t58)) % 0.45/0.64 (define @t61 () (forall @t8 (=> @t60 @t57))) % 0.45/0.64 (define @t62 () (not @t61)) % 0.45/0.64 (define @t63 () (or @t24 @t23 @t57)) % 0.45/0.64 (define @t64 () (forall @t8 @t63)) % 0.45/0.64 (define @t65 () (@quantifiers_skolemize @t64 1)) % 0.45/0.64 (define @t66 () (@quantifiers_skolemize @t64 0)) % 0.45/0.64 (define @t67 () (tptp.unordered_pair @t66 @t65)) % 0.45/0.64 (define @t68 () (= tptp.null_class @t67)) % 0.45/0.64 (define @t69 () (tptp.member @t65 tptp.universal_class)) % 0.45/0.64 (define @t70 () (tptp.member @t66 tptp.universal_class)) % 0.45/0.64 (define @t71 () (or @t70 @t69 @t68)) % 0.45/0.64 (define @t72 () (not @t71)) % 0.45/0.64 (define @t73 () (not @t64)) % 0.45/0.64 (define @t74 () (= @t67 tptp.null_class)) % 0.45/0.64 (define @t75 () (or @t70 @t69 @t74)) % 0.45/0.64 (define @t76 () (not @t75)) % 0.45/0.64 (define @t77 () (@list true)) % 0.45/0.64 (define @t78 () (not @t69)) % 0.45/0.64 (define @t79 () (@list @t71)) % 0.45/0.64 (define @t80 () (or @t58 @t52 @t51)) % 0.45/0.64 (define @t81 () (forall @t40 @t80)) % 0.45/0.64 (define @t82 () (@quantifiers_skolemize (forall @t49 (or (not @t48) (not @t81))) 0)) % 0.45/0.64 (define @t83 () (tptp.apply @t82 @t67)) % 0.45/0.64 (define @t84 () (and @t48 @t81)) % 0.45/0.64 (define @t85 () (forall @t49 (not @t84))) % 0.45/0.64 (define @t86 () (not @t85)) % 0.45/0.64 (define @t87 () (forall @t40 (or @t58 @t52 (tptp.member (tptp.apply @t82 @t1) @t1)))) % 0.45/0.64 (define @t88 () (not @t87)) % 0.45/0.64 (define @t89 () (or (not (tptp.function @t82)) @t88)) % 0.45/0.64 (define @t90 () (tptp.member @t83 @t67)) % 0.45/0.64 (define @t91 () (tptp.member @t67 tptp.universal_class)) % 0.45/0.64 (define @t92 () (not @t91)) % 0.45/0.64 (define @t93 () (or @t92 @t74 @t90)) % 0.45/0.64 (define @t94 () (or @t92 @t68 @t90)) % 0.45/0.64 (define @t95 () (@list false)) % 0.45/0.64 (define @t96 () (= @t65 @t83)) % 0.45/0.64 (define @t97 () (= @t66 @t83)) % 0.45/0.64 (define @t98 () (or @t97 @t96)) % 0.45/0.64 (define @t99 () (tptp.member @t83 tptp.universal_class)) % 0.45/0.64 (define @t100 () (and @t99 @t98)) % 0.45/0.64 (define @t101 () (= @t90 @t100)) % 0.45/0.64 (define @t102 () (not @t100)) % 0.45/0.64 (define @t103 () (@list @t100)) % 0.45/0.64 (define @t104 () (not @t70)) % 0.45/0.64 (define @t105 () (not @t97)) % 0.45/0.64 (define @t106 () (not @t99)) % 0.45/0.64 (define @t107 () (= false true)) % 0.45/0.64 (define @t108 () (and @t99 @t97 @t104)) % 0.45/0.64 (define @t109 () (@list true false)) % 0.45/0.64 (define @t110 () (not @t96)) % 0.45/0.64 (define @t111 () (and @t99 @t96 @t78)) % 0.45/0.64 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.45/0.64 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 0.45/0.64 (assume @p3 (forall @t8 (= (= @t4 @t1) (and @t7 (tptp.subclass @t1 @t4))))) % 0.45/0.64 (assume @p4 @t16) % 0.45/0.64 (assume @p5 (forall @t8 (tptp.member @t13 tptp.universal_class))) % 0.45/0.64 (assume @p6 (forall @t9 (= @t17 (tptp.unordered_pair @t4 @t4)))) % 0.45/0.64 (assume @p7 (forall @t8 (= @t19 (tptp.unordered_pair @t17 (tptp.unordered_pair @t4 @t18))))) % 0.45/0.64 (assume @p8 (forall (@list @t2 @t20 @t4 @t1) (= (tptp.member @t22 @t21) (and @t5 (tptp.member @t20 @t1))))) % 0.45/0.64 (assume @p9 (forall @t8 (=> (and @t24 @t23) (and (= (tptp.first @t19) @t4) (= (tptp.second @t19) @t1))))) % 0.45/0.64 (assume @p10 (forall @t26 (=> (tptp.member @t25 @t21) (= @t25 (tptp.ordered_pair (tptp.first @t25) (tptp.second @t25)))))) % 0.45/0.64 (assume @p11 (forall @t8 (= (tptp.member @t19 tptp.element_relation) (and @t23 (tptp.member @t4 @t1))))) % 0.45/0.64 (assume @p12 (tptp.subclass tptp.element_relation @t27)) % 0.45/0.64 (assume @p13 (forall @t26 (= (tptp.member @t25 (tptp.intersection @t4 @t1)) (and @t29 @t28)))) % 0.45/0.64 (assume @p14 (forall @t31 (= (tptp.member @t25 (tptp.complement @t4)) (and @t30 (not @t29))))) % 0.45/0.64 (assume @p15 (forall (@list @t4 @t32 @t1) (= (tptp.restrict @t32 @t4 @t1) (tptp.intersection @t32 @t21)))) % 0.45/0.64 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 0.45/0.64 (assume @p17 (forall @t31 (= (tptp.member @t25 (tptp.domain_of @t4)) (and @t30 (not (= (tptp.restrict @t4 (tptp.singleton @t25) tptp.universal_class) tptp.null_class)))))) % 0.45/0.64 (assume @p18 (forall (@list @t4 @t2 @t20 @t33) (= (tptp.member @t35 @t37) (and @t36 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t20 @t33) @t2) @t4))))) % 0.45/0.64 (assume @p19 (forall @t9 (tptp.subclass @t37 @t34))) % 0.45/0.64 (assume @p20 (forall (@list @t2 @t20 @t33 @t4) (= (tptp.member @t35 @t38) (and @t36 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t20 @t2) @t33) @t4))))) % 0.45/0.64 (assume @p21 (forall @t9 (tptp.subclass @t38 @t34))) % 0.45/0.64 (assume @p22 (forall @t26 (= (tptp.member @t25 (tptp.union @t4 @t1)) (or @t29 @t28)))) % 0.45/0.64 (assume @p23 (forall @t9 (= @t39 (tptp.union @t4 @t17)))) % 0.45/0.64 (assume @p24 (tptp.subclass tptp.successor_relation @t27)) % 0.45/0.64 (assume @p25 (forall @t8 (= (tptp.member @t19 tptp.successor_relation) (and @t24 @t23 (= @t39 @t1))))) % 0.45/0.64 (assume @p26 (forall @t40 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 0.45/0.64 (assume @p27 (forall @t41 (= (tptp.range_of @t25) (tptp.domain_of (tptp.inverse @t25))))) % 0.45/0.64 (assume @p28 (forall (@list @t4 @t32) (= (tptp.image @t32 @t4) (tptp.range_of (tptp.restrict @t32 @t4 tptp.universal_class))))) % 0.45/0.64 (assume @p29 (forall @t9 (= @t42 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 0.45/0.64 (assume @p30 (exists @t9 (and @t24 @t42 (forall @t40 (=> (tptp.inductive @t1) @t7))))) % 0.45/0.64 (assume @p31 (forall @t44 (= (tptp.member @t2 @t43) (exists @t40 (and @t3 (tptp.member @t1 @t4)))))) % 0.45/0.64 (assume @p32 (forall @t9 (=> @t24 (tptp.member @t43 tptp.universal_class)))) % 0.45/0.64 (assume @p33 (forall @t44 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t11 (tptp.subclass @t2 @t4))))) % 0.45/0.64 (assume @p34 (forall @t6 (=> @t11 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.45/0.64 (assume @p35 (forall (@list @t32 @t45) (tptp.subclass @t46 @t27))) % 0.45/0.64 (assume @p36 (forall (@list @t32 @t45 @t2 @t20) (= (tptp.member @t22 @t46) (and @t11 (tptp.member @t20 (tptp.image @t45 (tptp.image @t32 (tptp.singleton @t2)))))))) % 0.45/0.64 (assume @p37 (forall @t41 (= (tptp.member @t25 tptp.identity_relation) (exists @t9 (and @t24 (= @t25 (tptp.ordered_pair @t4 @t4))))))) % 0.45/0.64 (assume @p38 (forall @t49 (= @t48 (and (tptp.subclass @t47 @t27) (tptp.subclass (tptp.compose @t47 (tptp.inverse @t47)) tptp.identity_relation))))) % 0.45/0.64 (assume @p39 (forall (@list @t4 @t47) (=> (and @t24 @t48) (tptp.member (tptp.image @t47 @t4) tptp.universal_class)))) % 0.45/0.64 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 0.45/0.64 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t11 @t5 (tptp.disjoint @t2 @t4)))))) % 0.45/0.64 (assume @p42 (forall (@list @t47 @t1) (= @t50 (tptp.sum_class (tptp.image @t47 @t18))))) % 0.45/0.64 (assume @p43 @t56) % 0.45/0.64 (assume @p44 @t62) % 0.45/0.64 (assume @p45 true) % 0.45/0.64 (step @p46 :rule aci_norm :args ((= (or (or @t24 @t23) @t57) @t63))) % 0.45/0.64 (step @p47 :rule refl :args (@t57)) % 0.45/0.64 (step @p48 :rule bool-double-not-elim :args (@t23)) % 0.45/0.64 (step @p49 :rule bool-double-not-elim :args (@t24)) % 0.45/0.64 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((or (not @t59) (not @t58)))) % 0.45/0.64 (step @p51 :rule bool-and-de-morgan :args (@t59 @t58 true)) % 0.45/0.64 (step @p52 :rule trans :premises (@p51 @p50)) % 0.45/0.64 (step @p53 :rule nary_cong :premises (@p52 @p47) :args ((or (not @t60) @t57))) % 0.45/0.64 (step @p54 :rule trans :premises (@p53 @p46)) % 0.45/0.64 (step @p55 :rule bool-impl-elim :args (@t60 @t57)) % 0.45/0.64 (step @p56 :rule trans :premises (@p55 @p54)) % 0.45/0.64 (step @p57 :rule cong :premises (@p56) :args (@t61)) % 0.45/0.64 (step @p58 :rule cong :premises (@p57) :args (@t62)) % 0.45/0.64 (step @p59 :rule eq_resolve :premises (@p44 @p58)) % 0.45/0.64 (step @p60 :rule refl :args (@t72)) % 0.45/0.64 (step @p61 :rule bool-double-not-elim :args (@t64)) % 0.45/0.64 (step @p62 :rule nary_cong :premises (@p61 @p60) :args ((or (not @t73) @t72))) % 0.45/0.64 (step @p63 :rule eq-symm :args (@t67 tptp.null_class)) % 0.45/0.64 (step @p64 :rule refl :args (@t69)) % 0.45/0.64 (step @p65 :rule refl :args (@t70)) % 0.45/0.64 (step @p66 :rule nary_cong :premises (@p65 @p64 @p63) :args (@t75)) % 0.45/0.64 (step @p67 :rule cong :premises (@p66) :args (@t76)) % 0.45/0.64 (step @p68 :rule refl :args (@t73)) % 0.45/0.64 (step @p69 :rule cong :premises (@p68 @p67) :args ((=> @t73 @t76))) % 0.45/0.64 (assume-push @p204 @t73) % 0.45/0.64 (step @p71 :rule skolemize :premises (@p59)) % 0.45/0.64 (step-pop @p205 :rule scope :premises (@p71)) % 0.45/0.64 (step @p72 :rule process_scope :premises (@p205) :args (@t76)) % 0.45/0.64 (step @p74 :rule eq_resolve :premises (@p72 @p69)) % 0.45/0.64 (step @p75 :rule implies_elim :premises (@p74)) % 0.45/0.64 (step @p76 :rule eq_resolve :premises (@p75 @p62)) % 0.45/0.64 (step @p77 :rule chain_m_resolution :premises (@p76 @p59) :args (@t72 @t77 (@list @t64))) % 0.45/0.64 (step @p78 :rule cnf_or_neg :args (@t71 1)) % 0.45/0.64 (step @p79 :rule chain_m_resolution :premises (@p78 @p77) :args (@t78 @t77 @t79)) % 0.45/0.64 (step @p80 :rule eq-symm :args (@t2 @t1)) % 0.45/0.64 (step @p81 :rule eq-symm :args (@t2 @t4)) % 0.45/0.64 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t10)) % 0.45/0.64 (step @p83 :rule refl :args (@t11)) % 0.45/0.64 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t12)) % 0.45/0.64 (step @p85 :rule refl :args (@t14)) % 0.45/0.64 (step @p86 :rule cong :premises (@p85 @p84) :args (@t15)) % 0.45/0.64 (step @p87 :rule cong :premises (@p86) :args (@t16)) % 0.45/0.64 (step @p88 :rule eq_resolve :premises (@p4 @p87)) % 0.45/0.64 (step @p89 :rule instantiate :premises (@p88) :args ((@list @t83 @t66 @t65))) % 0.45/0.64 (step @p90 :rule bool-and-de-morgan :args (@t48 @t81 true)) % 0.45/0.64 (step @p91 :rule cong :premises (@p90) :args (@t85)) % 0.45/0.64 (step @p92 :rule cong :premises (@p91) :args (@t86)) % 0.45/0.64 (step @p93 :rule exists-elim :args ((= (exists @t49 @t84) @t86))) % 0.45/0.64 (step @p94 :rule trans :premises (@p93 @p92)) % 0.45/0.64 (step @p95 :rule aci_norm :args ((= (or @t58 @t53) @t80))) % 0.45/0.64 (step @p96 :rule bool-impl-elim :args (@t23 @t53)) % 0.45/0.64 (step @p97 :rule trans :premises (@p96 @p95)) % 0.45/0.64 (step @p98 :rule cong :premises (@p97) :args (@t54)) % 0.45/0.64 (step @p99 :rule refl :args (@t48)) % 0.45/0.64 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t55)) % 0.45/0.64 (step @p101 :rule cong :premises (@p100) :args (@t56)) % 0.45/0.64 (step @p102 :rule trans :premises (@p101 @p94)) % 0.45/0.64 (step @p103 :rule eq_resolve :premises (@p43 @p102)) % 0.45/0.64 (step @p104 :rule skolemize :premises (@p103)) % 0.45/0.64 (step @p105 :rule bool-double-not-elim :args (@t87)) % 0.45/0.64 (step @p106 :rule refl :args (@t89)) % 0.45/0.64 (step @p107 :rule nary_cong :premises (@p106 @p105) :args ((or @t89 (not @t88)))) % 0.45/0.64 (step @p108 :rule cnf_or_neg :args (@t89 1)) % 0.45/0.64 (step @p109 :rule eq_resolve :premises (@p108 @p107)) % 0.45/0.64 (step @p110 :rule reordering :premises (@p109) :args ((or @t87 @t89))) % 0.45/0.64 (step @p111 :rule chain_m_resolution :premises (@p110 @p104) :args (@t87 @t77 (@list @t89))) % 0.45/0.64 (step @p112 :rule refl :args (@t90)) % 0.45/0.64 (step @p113 :rule refl :args (@t92)) % 0.45/0.64 (step @p114 :rule nary_cong :premises (@p113 @p63 @p112) :args (@t93)) % 0.45/0.64 (step @p115 :rule refl :args (@t87)) % 0.45/0.64 (step @p116 :rule cong :premises (@p115 @p114) :args ((=> @t87 @t93))) % 0.45/0.64 (assume-push @p206 @t87) % 0.45/0.64 (step @p118 :rule instantiate :premises (@p111) :args ((@list @t67))) % 0.45/0.64 (step-pop @p207 :rule scope :premises (@p118)) % 0.45/0.64 (step @p119 :rule process_scope :premises (@p207) :args (@t93)) % 0.45/0.64 (step @p121 :rule eq_resolve :premises (@p119 @p116)) % 0.45/0.64 (step @p122 :rule implies_elim :premises (@p121)) % 0.45/0.64 (step @p123 :rule chain_m_resolution :premises (@p122 @p111) :args (@t94 @t95 (@list @t87))) % 0.45/0.64 (step @p124 :rule instantiate :premises (@p5) :args ((@list @t66 @t65))) % 0.45/0.64 (step @p125 :rule cnf_or_neg :args (@t71 2)) % 0.45/0.64 (step @p126 :rule chain_m_resolution :premises (@p125 @p77) :args ((not @t68) @t77 @t79)) % 0.45/0.64 (step @p127 :rule cnf_or_pos :args (@t94)) % 0.45/0.64 (step @p128 :rule reordering :premises (@p127) :args ((or @t68 @t92 @t90 (not @t94)))) % 0.45/0.64 (step @p129 :rule chain_m_resolution :premises (@p128 @p126 @p124 @p123) :args (@t90 (@list true false false) (@list @t68 @t91 @t94))) % 0.45/0.64 (step @p130 :rule cnf_equiv_pos1 :args (@t101)) % 0.45/0.64 (step @p131 :rule reordering :premises (@p130) :args ((or (not @t90) @t100 (not @t101)))) % 0.45/0.64 (step @p132 :rule chain_m_resolution :premises (@p131 @p129 @p89) :args (@t100 (@list false false) (@list @t90 @t101))) % 0.45/0.64 (step @p133 :rule cnf_and_pos :args (@t100 0)) % 0.45/0.64 (step @p134 :rule reordering :premises (@p133) :args ((or @t99 @t102))) % 0.45/0.64 (step @p135 :rule chain_m_resolution :premises (@p134 @p132) :args (@t99 @t95 @t103)) % 0.45/0.64 (step @p136 :rule cnf_and_pos :args (@t100 1)) % 0.45/0.64 (step @p137 :rule reordering :premises (@p136) :args ((or @t98 @t102))) % 0.45/0.64 (step @p138 :rule chain_m_resolution :premises (@p137 @p132) :args (@t98 @t95 @t103)) % 0.45/0.64 (step @p139 :rule cnf_or_neg :args (@t71 0)) % 0.45/0.64 (step @p140 :rule chain_m_resolution :premises (@p139 @p77) :args (@t104 @t77 @t79)) % 0.45/0.64 (step @p141 :rule refl :args (@t105)) % 0.45/0.64 (step @p142 :rule refl :args (@t106)) % 0.45/0.64 (step @p143 :rule bool-double-not-elim :args (@t70)) % 0.45/0.64 (step @p144 :rule nary_cong :premises (@p143 @p142 @p141) :args ((or (not @t104) @t106 @t105))) % 0.45/0.64 (assume-push @p208 @t99) % 0.45/0.64 (assume-push @p209 @t97) % 0.45/0.64 (assume-push @p210 @t104) % 0.45/0.64 (step @p148 :rule evaluate :args (@t107)) % 0.45/0.64 (step @p149 :rule true_intro :premises (@p135)) % 0.45/0.64 (step @p150 :rule refl :args (tptp.universal_class)) % 0.45/0.64 (step @p151 :rule cong :premises (@p209 @p150) :args (@t70)) % 0.45/0.64 (step @p152 :rule false_intro :premises (@p140)) % 0.45/0.64 (step @p153 :rule symm :premises (@p152)) % 0.45/0.64 (step @p154 :rule trans :premises (@p153 @p151 @p149)) % 0.45/0.64 (step @p155 false :rule eq_resolve :premises (@p154 @p148)) % 0.45/0.64 (step-pop @p211 :rule scope :premises (@p155)) % 0.45/0.64 (step-pop @p212 :rule scope :premises (@p211)) % 0.45/0.64 (step-pop @p213 :rule scope :premises (@p212)) % 0.45/0.64 (step @p156 :rule process_scope :premises (@p213) :args (false)) % 0.45/0.64 (assume-push @p214 @t104) % 0.45/0.64 (assume-push @p215 @t99) % 0.45/0.64 (assume-push @p216 @t97) % 0.45/0.64 (step @p163 :rule and_intro :premises (@p135 @p216 @p140)) % 0.45/0.64 (step-pop @p217 :rule scope :premises (@p163)) % 0.45/0.64 (step-pop @p218 :rule scope :premises (@p217)) % 0.45/0.64 (step-pop @p219 :rule scope :premises (@p218)) % 0.45/0.64 (step @p164 :rule process_scope :premises (@p219) :args (@t108)) % 0.45/0.64 (step @p168 :rule implies_elim :premises (@p164)) % 0.45/0.64 (step @p169 :rule resolution :premises (@p168 @p156) :args (true @t108)) % 0.45/0.64 (step @p170 :rule not_and :premises (@p169)) % 0.45/0.64 (step @p171 :rule eq_resolve :premises (@p170 @p144)) % 0.45/0.64 (step @p172 :rule chain_m_resolution :premises (@p171 @p140 @p135) :args (@t105 @t109 (@list @t70 @t99))) % 0.45/0.64 (step @p173 :rule cnf_or_pos :args (@t98)) % 0.45/0.64 (step @p174 :rule reordering :premises (@p173) :args ((or @t97 @t96 (not @t98)))) % 0.45/0.64 (step @p175 :rule chain_m_resolution :premises (@p174 @p172 @p138) :args (@t96 @t109 (@list @t97 @t98))) % 0.45/0.64 (step @p176 :rule refl :args (@t110)) % 0.45/0.64 (step @p177 :rule bool-double-not-elim :args (@t69)) % 0.45/0.64 (step @p178 :rule nary_cong :premises (@p177 @p142 @p176) :args ((or (not @t78) @t106 @t110))) % 0.45/0.64 (assume-push @p220 @t99) % 0.45/0.64 (assume-push @p221 @t96) % 0.45/0.64 (assume-push @p222 @t78) % 0.45/0.64 (step @p148 :rule evaluate :args (@t107)) % 0.45/0.64 (step @p149 :rule true_intro :premises (@p135)) % 0.45/0.64 (step @p150 :rule refl :args (tptp.universal_class)) % 0.45/0.64 (step @p182 :rule cong :premises (@p221 @p150) :args (@t69)) % 0.45/0.64 (step @p183 :rule false_intro :premises (@p79)) % 0.45/0.64 (step @p184 :rule symm :premises (@p183)) % 0.45/0.64 (step @p185 :rule trans :premises (@p184 @p182 @p149)) % 0.45/0.64 (step @p186 false :rule eq_resolve :premises (@p185 @p148)) % 0.45/0.64 (step-pop @p223 :rule scope :premises (@p186)) % 0.45/0.64 (step-pop @p224 :rule scope :premises (@p223)) % 0.45/0.64 (step-pop @p225 :rule scope :premises (@p224)) % 0.45/0.64 (step @p187 :rule process_scope :premises (@p225) :args (false)) % 0.45/0.64 (assume-push @p226 @t78) % 0.45/0.64 (assume-push @p227 @t99) % 0.45/0.64 (assume-push @p228 @t96) % 0.45/0.64 (step @p194 :rule and_intro :premises (@p135 @p228 @p79)) % 0.45/0.64 (step-pop @p229 :rule scope :premises (@p194)) % 0.45/0.64 (step-pop @p230 :rule scope :premises (@p229)) % 0.45/0.64 (step-pop @p231 :rule scope :premises (@p230)) % 0.45/0.64 (step @p195 :rule process_scope :premises (@p231) :args (@t111)) % 0.45/0.64 (step @p199 :rule implies_elim :premises (@p195)) % 0.45/0.64 (step @p200 :rule resolution :premises (@p199 @p187) :args (true @t111)) % 0.45/0.64 (step @p201 :rule not_and :premises (@p200)) % 0.45/0.64 (step @p202 :rule eq_resolve :premises (@p201 @p178)) % 0.45/0.64 (step @p203 false :rule chain_m_resolution :premises (@p202 @p175 @p135 @p79) :args (false (@list false false true) (@list @t96 @t99 @t69))) % 0.45/0.64 ) % 0.45/0.64 % SZS output end Proof % 0.45/0.65 % cvc5 exiting %------------------------------------------------------------------------------