%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET054+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 : n013.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 08:47:08 AM UTC 2026 % Result : Theorem 0.35s 0.59s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET054+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 % 0.16/0.33 % Computer : n013.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % 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 14:48:30 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.59 % SZS status Theorem % 0.35/0.59 % SZS output start Proof % 0.35/0.59 ( % 0.35/0.59 (declare-sort $$unsorted 0) % 0.35/0.59 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.element_relation $$unsorted) % 0.35/0.59 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.universal_class $$unsorted) % 0.35/0.59 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.function (-> $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.null_class $$unsorted) % 0.35/0.59 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.successor_relation $$unsorted) % 0.35/0.59 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.identity_relation $$unsorted) % 0.35/0.59 (define @t1 () (@var "Y" $$unsorted)) % 0.35/0.59 (define @t2 () (@var "U" $$unsorted)) % 0.35/0.59 (define @t3 () (tptp.member @t2 @t1)) % 0.35/0.59 (define @t4 () (@var "X" $$unsorted)) % 0.35/0.59 (define @t5 () (tptp.member @t2 @t4)) % 0.35/0.59 (define @t6 () (@list @t2)) % 0.35/0.59 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.35/0.59 (define @t8 () (tptp.subclass @t4 @t1)) % 0.35/0.59 (define @t9 () (= @t8 @t7)) % 0.35/0.59 (define @t10 () (@list @t4 @t1)) % 0.35/0.59 (define @t11 () (forall @t10 @t9)) % 0.35/0.59 (define @t12 () (@list @t4)) % 0.35/0.59 (define @t13 () (tptp.member @t2 tptp.universal_class)) % 0.35/0.59 (define @t14 () (tptp.unordered_pair @t4 @t1)) % 0.35/0.59 (define @t15 () (tptp.singleton @t4)) % 0.35/0.59 (define @t16 () (tptp.singleton @t1)) % 0.35/0.59 (define @t17 () (tptp.ordered_pair @t4 @t1)) % 0.35/0.59 (define @t18 () (@var "V" $$unsorted)) % 0.35/0.59 (define @t19 () (tptp.cross_product @t4 @t1)) % 0.35/0.59 (define @t20 () (tptp.ordered_pair @t2 @t18)) % 0.35/0.59 (define @t21 () (tptp.member @t1 tptp.universal_class)) % 0.35/0.59 (define @t22 () (tptp.member @t4 tptp.universal_class)) % 0.35/0.59 (define @t23 () (@var "Z" $$unsorted)) % 0.35/0.59 (define @t24 () (@list @t4 @t1 @t23)) % 0.35/0.59 (define @t25 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.35/0.59 (define @t26 () (tptp.member @t23 @t1)) % 0.35/0.59 (define @t27 () (tptp.member @t23 @t4)) % 0.35/0.59 (define @t28 () (tptp.member @t23 tptp.universal_class)) % 0.35/0.59 (define @t29 () (@list @t4 @t23)) % 0.35/0.59 (define @t30 () (@var "XR" $$unsorted)) % 0.35/0.59 (define @t31 () (@var "W" $$unsorted)) % 0.35/0.59 (define @t32 () (tptp.cross_product @t25 tptp.universal_class)) % 0.35/0.59 (define @t33 () (tptp.ordered_pair @t20 @t31)) % 0.35/0.59 (define @t34 () (tptp.member @t33 @t32)) % 0.35/0.59 (define @t35 () (tptp.rotate @t4)) % 0.35/0.59 (define @t36 () (tptp.flip @t4)) % 0.35/0.59 (define @t37 () (tptp.successor @t4)) % 0.35/0.59 (define @t38 () (@list @t1)) % 0.35/0.59 (define @t39 () (@list @t23)) % 0.35/0.59 (define @t40 () (tptp.inductive @t4)) % 0.35/0.59 (define @t41 () (tptp.sum_class @t4)) % 0.35/0.59 (define @t42 () (@list @t2 @t4)) % 0.35/0.59 (define @t43 () (@var "YR" $$unsorted)) % 0.35/0.59 (define @t44 () (tptp.compose @t43 @t30)) % 0.35/0.59 (define @t45 () (@var "XF" $$unsorted)) % 0.35/0.59 (define @t46 () (tptp.function @t45)) % 0.35/0.59 (define @t47 () (@list @t45)) % 0.35/0.59 (define @t48 () (tptp.apply @t45 @t1)) % 0.35/0.59 (define @t49 () (forall @t12 (tptp.subclass @t4 @t4))) % 0.35/0.59 (define @t50 () (@quantifiers_skolemize @t49 0)) % 0.35/0.59 (define @t51 () (tptp.subclass @t50 @t50)) % 0.35/0.59 (define @t52 () (tptp.member @t2 @t50)) % 0.35/0.59 (define @t53 () (forall @t6 (or (not @t52) @t52))) % 0.35/0.59 (define @t54 () (= @t51 @t53)) % 0.35/0.59 (define @t55 () (forall @t10 (= @t8 (forall @t6 (or (not @t5) @t3))))) % 0.35/0.59 (assume @p1 @t11) % 0.35/0.59 (assume @p2 (forall @t12 (tptp.subclass @t4 tptp.universal_class))) % 0.35/0.59 (assume @p3 (forall @t10 (= (= @t4 @t1) (and @t8 (tptp.subclass @t1 @t4))))) % 0.35/0.59 (assume @p4 (forall (@list @t2 @t4 @t1) (= (tptp.member @t2 @t14) (and @t13 (or (= @t2 @t4) (= @t2 @t1)))))) % 0.35/0.59 (assume @p5 (forall @t10 (tptp.member @t14 tptp.universal_class))) % 0.35/0.59 (assume @p6 (forall @t12 (= @t15 (tptp.unordered_pair @t4 @t4)))) % 0.35/0.59 (assume @p7 (forall @t10 (= @t17 (tptp.unordered_pair @t15 (tptp.unordered_pair @t4 @t16))))) % 0.35/0.59 (assume @p8 (forall (@list @t2 @t18 @t4 @t1) (= (tptp.member @t20 @t19) (and @t5 (tptp.member @t18 @t1))))) % 0.35/0.59 (assume @p9 (forall @t10 (=> (and @t22 @t21) (and (= (tptp.first @t17) @t4) (= (tptp.second @t17) @t1))))) % 0.35/0.59 (assume @p10 (forall @t24 (=> (tptp.member @t23 @t19) (= @t23 (tptp.ordered_pair (tptp.first @t23) (tptp.second @t23)))))) % 0.35/0.59 (assume @p11 (forall @t10 (= (tptp.member @t17 tptp.element_relation) (and @t21 (tptp.member @t4 @t1))))) % 0.35/0.59 (assume @p12 (tptp.subclass tptp.element_relation @t25)) % 0.35/0.59 (assume @p13 (forall @t24 (= (tptp.member @t23 (tptp.intersection @t4 @t1)) (and @t27 @t26)))) % 0.35/0.59 (assume @p14 (forall @t29 (= (tptp.member @t23 (tptp.complement @t4)) (and @t28 (not @t27))))) % 0.35/0.59 (assume @p15 (forall (@list @t4 @t30 @t1) (= (tptp.restrict @t30 @t4 @t1) (tptp.intersection @t30 @t19)))) % 0.35/0.59 (assume @p16 (forall @t12 (not (tptp.member @t4 tptp.null_class)))) % 0.35/0.59 (assume @p17 (forall @t29 (= (tptp.member @t23 (tptp.domain_of @t4)) (and @t28 (not (= (tptp.restrict @t4 (tptp.singleton @t23) tptp.universal_class) tptp.null_class)))))) % 0.35/0.59 (assume @p18 (forall (@list @t4 @t2 @t18 @t31) (= (tptp.member @t33 @t35) (and @t34 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t18 @t31) @t2) @t4))))) % 0.35/0.59 (assume @p19 (forall @t12 (tptp.subclass @t35 @t32))) % 0.35/0.59 (assume @p20 (forall (@list @t2 @t18 @t31 @t4) (= (tptp.member @t33 @t36) (and @t34 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t18 @t2) @t31) @t4))))) % 0.35/0.59 (assume @p21 (forall @t12 (tptp.subclass @t36 @t32))) % 0.35/0.59 (assume @p22 (forall @t24 (= (tptp.member @t23 (tptp.union @t4 @t1)) (or @t27 @t26)))) % 0.35/0.59 (assume @p23 (forall @t12 (= @t37 (tptp.union @t4 @t15)))) % 0.35/0.59 (assume @p24 (tptp.subclass tptp.successor_relation @t25)) % 0.35/0.59 (assume @p25 (forall @t10 (= (tptp.member @t17 tptp.successor_relation) (and @t22 @t21 (= @t37 @t1))))) % 0.35/0.59 (assume @p26 (forall @t38 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 0.35/0.59 (assume @p27 (forall @t39 (= (tptp.range_of @t23) (tptp.domain_of (tptp.inverse @t23))))) % 0.35/0.59 (assume @p28 (forall (@list @t4 @t30) (= (tptp.image @t30 @t4) (tptp.range_of (tptp.restrict @t30 @t4 tptp.universal_class))))) % 0.35/0.59 (assume @p29 (forall @t12 (= @t40 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 0.35/0.59 (assume @p30 (exists @t12 (and @t22 @t40 (forall @t38 (=> (tptp.inductive @t1) @t8))))) % 0.35/0.59 (assume @p31 (forall @t42 (= (tptp.member @t2 @t41) (exists @t38 (and @t3 (tptp.member @t1 @t4)))))) % 0.35/0.59 (assume @p32 (forall @t12 (=> @t22 (tptp.member @t41 tptp.universal_class)))) % 0.35/0.59 (assume @p33 (forall @t42 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t13 (tptp.subclass @t2 @t4))))) % 0.35/0.59 (assume @p34 (forall @t6 (=> @t13 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.35/0.59 (assume @p35 (forall (@list @t30 @t43) (tptp.subclass @t44 @t25))) % 0.35/0.59 (assume @p36 (forall (@list @t30 @t43 @t2 @t18) (= (tptp.member @t20 @t44) (and @t13 (tptp.member @t18 (tptp.image @t43 (tptp.image @t30 (tptp.singleton @t2)))))))) % 0.35/0.59 (assume @p37 (forall @t39 (= (tptp.member @t23 tptp.identity_relation) (exists @t12 (and @t22 (= @t23 (tptp.ordered_pair @t4 @t4))))))) % 0.35/0.59 (assume @p38 (forall @t47 (= @t46 (and (tptp.subclass @t45 @t25) (tptp.subclass (tptp.compose @t45 (tptp.inverse @t45)) tptp.identity_relation))))) % 0.35/0.59 (assume @p39 (forall (@list @t4 @t45) (=> (and @t22 @t46) (tptp.member (tptp.image @t45 @t4) tptp.universal_class)))) % 0.35/0.59 (assume @p40 (forall @t10 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 0.35/0.59 (assume @p41 (forall @t12 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t13 @t5 (tptp.disjoint @t2 @t4)))))) % 0.35/0.59 (assume @p42 (forall (@list @t45 @t1) (= @t48 (tptp.sum_class (tptp.image @t45 @t16))))) % 0.35/0.59 (assume @p43 (exists @t47 (and @t46 (forall @t38 (=> @t21 (or (= @t1 tptp.null_class) (tptp.member @t48 @t1))))))) % 0.35/0.59 (assume @p44 (not @t49)) % 0.35/0.59 (assume @p45 true) % 0.35/0.59 (step @p46 :rule bool-impl-elim :args (@t5 @t3)) % 0.35/0.59 (step @p47 :rule cong :premises (@p46) :args (@t7)) % 0.35/0.59 (step @p48 :rule refl :args (@t8)) % 0.35/0.59 (step @p49 :rule cong :premises (@p48 @p47) :args (@t9)) % 0.35/0.59 (step @p50 :rule cong :premises (@p49) :args (@t11)) % 0.35/0.59 (step @p51 :rule eq_resolve :premises (@p1 @p50)) % 0.35/0.59 (step @p52 :rule skolemize :premises (@p44)) % 0.35/0.59 (step @p53 :rule bool-eq-true :args (@t51)) % 0.35/0.59 (step @p54 :rule quant-unused-vars :args ((= (forall @t6 true) true))) % 0.35/0.59 (step @p55 :rule bool-or-taut2 :args (false @t52 false false)) % 0.35/0.59 (step @p56 :rule cong :premises (@p55) :args (@t53)) % 0.35/0.59 (step @p57 :rule trans :premises (@p56 @p54)) % 0.35/0.59 (step @p58 :rule refl :args (@t51)) % 0.35/0.59 (step @p59 :rule cong :premises (@p58 @p57) :args (@t54)) % 0.35/0.59 (step @p60 :rule trans :premises (@p59 @p53)) % 0.35/0.59 (step @p61 :rule refl :args (@t55)) % 0.35/0.59 (step @p62 :rule cong :premises (@p61 @p60) :args ((=> @t55 @t54))) % 0.35/0.59 (assume-push @p70 @t55) % 0.35/0.59 (step @p64 :rule instantiate :premises (@p51) :args ((@list @t50 @t50))) % 0.35/0.59 (step-pop @p71 :rule scope :premises (@p64)) % 0.35/0.59 (step @p65 :rule process_scope :premises (@p71) :args (@t54)) % 0.35/0.59 (step @p67 :rule eq_resolve :premises (@p65 @p62)) % 0.35/0.59 (step @p68 :rule implies_elim :premises (@p67)) % 0.35/0.59 (step @p69 false :rule chain_m_resolution :premises (@p68 @p52 @p51) :args (false (@list true false) (@list @t51 @t55))) % 0.35/0.59 ) % 0.35/0.59 % SZS output end Proof % 0.35/0.60 % cvc5 exiting %------------------------------------------------------------------------------