%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET024+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 : n005.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 08:47:01 AM UTC 2026 % Result : Theorem 0.39s 0.59s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET024+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n005.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 14:42:03 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.59 % SZS status Theorem % 0.39/0.59 % SZS output start Proof % 0.39/0.59 ( % 0.39/0.59 (declare-sort $$unsorted 0) % 0.39/0.59 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.element_relation $$unsorted) % 0.39/0.59 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.universal_class $$unsorted) % 0.39/0.59 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.function (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.null_class $$unsorted) % 0.39/0.59 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.successor_relation $$unsorted) % 0.39/0.59 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.identity_relation $$unsorted) % 0.39/0.59 (define @t1 () (@var "Y" $$unsorted)) % 0.39/0.59 (define @t2 () (@var "U" $$unsorted)) % 0.39/0.59 (define @t3 () (tptp.member @t2 @t1)) % 0.39/0.59 (define @t4 () (@var "X" $$unsorted)) % 0.39/0.59 (define @t5 () (tptp.member @t2 @t4)) % 0.39/0.59 (define @t6 () (@list @t2)) % 0.39/0.59 (define @t7 () (tptp.subclass @t4 @t1)) % 0.39/0.59 (define @t8 () (@list @t4 @t1)) % 0.39/0.59 (define @t9 () (@list @t4)) % 0.39/0.59 (define @t10 () (or (= @t2 @t4) (= @t2 @t1))) % 0.39/0.59 (define @t11 () (tptp.member @t2 tptp.universal_class)) % 0.39/0.59 (define @t12 () (and @t11 @t10)) % 0.39/0.59 (define @t13 () (tptp.unordered_pair @t4 @t1)) % 0.39/0.59 (define @t14 () (tptp.member @t2 @t13)) % 0.39/0.59 (define @t15 () (= @t14 @t12)) % 0.39/0.59 (define @t16 () (@list @t2 @t4 @t1)) % 0.39/0.59 (define @t17 () (forall @t16 @t15)) % 0.39/0.59 (define @t18 () (tptp.singleton @t4)) % 0.39/0.59 (define @t19 () (tptp.singleton @t1)) % 0.39/0.59 (define @t20 () (tptp.ordered_pair @t4 @t1)) % 0.39/0.59 (define @t21 () (@var "V" $$unsorted)) % 0.39/0.59 (define @t22 () (tptp.cross_product @t4 @t1)) % 0.39/0.59 (define @t23 () (tptp.ordered_pair @t2 @t21)) % 0.39/0.59 (define @t24 () (tptp.member @t1 tptp.universal_class)) % 0.39/0.59 (define @t25 () (tptp.member @t4 tptp.universal_class)) % 0.39/0.59 (define @t26 () (@var "Z" $$unsorted)) % 0.39/0.59 (define @t27 () (@list @t4 @t1 @t26)) % 0.39/0.59 (define @t28 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.39/0.59 (define @t29 () (tptp.member @t26 @t1)) % 0.39/0.59 (define @t30 () (tptp.member @t26 @t4)) % 0.39/0.59 (define @t31 () (tptp.member @t26 tptp.universal_class)) % 0.39/0.59 (define @t32 () (@list @t4 @t26)) % 0.39/0.59 (define @t33 () (@var "XR" $$unsorted)) % 0.39/0.59 (define @t34 () (@var "W" $$unsorted)) % 0.39/0.59 (define @t35 () (tptp.cross_product @t28 tptp.universal_class)) % 0.39/0.59 (define @t36 () (tptp.ordered_pair @t23 @t34)) % 0.39/0.59 (define @t37 () (tptp.member @t36 @t35)) % 0.39/0.59 (define @t38 () (tptp.rotate @t4)) % 0.39/0.59 (define @t39 () (tptp.flip @t4)) % 0.39/0.59 (define @t40 () (tptp.successor @t4)) % 0.39/0.59 (define @t41 () (@list @t1)) % 0.39/0.59 (define @t42 () (@list @t26)) % 0.39/0.59 (define @t43 () (tptp.inductive @t4)) % 0.39/0.59 (define @t44 () (tptp.sum_class @t4)) % 0.39/0.59 (define @t45 () (@list @t2 @t4)) % 0.39/0.59 (define @t46 () (@var "YR" $$unsorted)) % 0.39/0.59 (define @t47 () (tptp.compose @t46 @t33)) % 0.39/0.59 (define @t48 () (@var "XF" $$unsorted)) % 0.39/0.59 (define @t49 () (tptp.function @t48)) % 0.39/0.59 (define @t50 () (@list @t48)) % 0.39/0.59 (define @t51 () (tptp.apply @t48 @t1)) % 0.39/0.59 (define @t52 () (tptp.member @t4 @t18)) % 0.39/0.59 (define @t53 () (forall @t9 (=> @t25 @t52))) % 0.39/0.59 (define @t54 () (not @t53)) % 0.39/0.59 (define @t55 () (@quantifiers_skolemize (forall @t9 (or (not @t25) @t52)) 0)) % 0.39/0.59 (define @t56 () (tptp.member @t55 (tptp.unordered_pair @t55 @t55))) % 0.39/0.59 (define @t57 () (tptp.member @t55 tptp.universal_class)) % 0.39/0.59 (define @t58 () (= @t55 @t55)) % 0.39/0.59 (define @t59 () (or @t58 @t58)) % 0.39/0.59 (define @t60 () (and @t57 @t59)) % 0.39/0.59 (define @t61 () (= @t56 @t60)) % 0.39/0.59 (define @t62 () (forall @t16 (= @t14 (and @t11 (or (= @t4 @t2) (= @t1 @t2)))))) % 0.39/0.59 (define @t63 () (= @t57 @t56)) % 0.39/0.59 (define @t64 () (tptp.member @t55 (tptp.singleton @t55))) % 0.39/0.59 (define @t65 () (not @t57)) % 0.39/0.59 (define @t66 () (or @t65 @t64)) % 0.39/0.59 (define @t67 () (@list true)) % 0.39/0.59 (define @t68 () (@list @t66)) % 0.39/0.59 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.39/0.59 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 0.39/0.59 (assume @p3 (forall @t8 (= (= @t4 @t1) (and @t7 (tptp.subclass @t1 @t4))))) % 0.39/0.59 (assume @p4 @t17) % 0.39/0.59 (assume @p5 (forall @t8 (tptp.member @t13 tptp.universal_class))) % 0.39/0.59 (assume @p6 (forall @t9 (= @t18 (tptp.unordered_pair @t4 @t4)))) % 0.39/0.59 (assume @p7 (forall @t8 (= @t20 (tptp.unordered_pair @t18 (tptp.unordered_pair @t4 @t19))))) % 0.39/0.59 (assume @p8 (forall (@list @t2 @t21 @t4 @t1) (= (tptp.member @t23 @t22) (and @t5 (tptp.member @t21 @t1))))) % 0.39/0.59 (assume @p9 (forall @t8 (=> (and @t25 @t24) (and (= (tptp.first @t20) @t4) (= (tptp.second @t20) @t1))))) % 0.39/0.59 (assume @p10 (forall @t27 (=> (tptp.member @t26 @t22) (= @t26 (tptp.ordered_pair (tptp.first @t26) (tptp.second @t26)))))) % 0.39/0.59 (assume @p11 (forall @t8 (= (tptp.member @t20 tptp.element_relation) (and @t24 (tptp.member @t4 @t1))))) % 0.39/0.59 (assume @p12 (tptp.subclass tptp.element_relation @t28)) % 0.39/0.59 (assume @p13 (forall @t27 (= (tptp.member @t26 (tptp.intersection @t4 @t1)) (and @t30 @t29)))) % 0.39/0.59 (assume @p14 (forall @t32 (= (tptp.member @t26 (tptp.complement @t4)) (and @t31 (not @t30))))) % 0.39/0.59 (assume @p15 (forall (@list @t4 @t33 @t1) (= (tptp.restrict @t33 @t4 @t1) (tptp.intersection @t33 @t22)))) % 0.39/0.59 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 0.39/0.59 (assume @p17 (forall @t32 (= (tptp.member @t26 (tptp.domain_of @t4)) (and @t31 (not (= (tptp.restrict @t4 (tptp.singleton @t26) tptp.universal_class) tptp.null_class)))))) % 0.39/0.59 (assume @p18 (forall (@list @t4 @t2 @t21 @t34) (= (tptp.member @t36 @t38) (and @t37 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t34) @t2) @t4))))) % 0.39/0.59 (assume @p19 (forall @t9 (tptp.subclass @t38 @t35))) % 0.39/0.59 (assume @p20 (forall (@list @t2 @t21 @t34 @t4) (= (tptp.member @t36 @t39) (and @t37 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t21 @t2) @t34) @t4))))) % 0.39/0.59 (assume @p21 (forall @t9 (tptp.subclass @t39 @t35))) % 0.39/0.59 (assume @p22 (forall @t27 (= (tptp.member @t26 (tptp.union @t4 @t1)) (or @t30 @t29)))) % 0.39/0.59 (assume @p23 (forall @t9 (= @t40 (tptp.union @t4 @t18)))) % 0.39/0.59 (assume @p24 (tptp.subclass tptp.successor_relation @t28)) % 0.39/0.59 (assume @p25 (forall @t8 (= (tptp.member @t20 tptp.successor_relation) (and @t25 @t24 (= @t40 @t1))))) % 0.39/0.59 (assume @p26 (forall @t41 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 0.39/0.59 (assume @p27 (forall @t42 (= (tptp.range_of @t26) (tptp.domain_of (tptp.inverse @t26))))) % 0.39/0.59 (assume @p28 (forall (@list @t4 @t33) (= (tptp.image @t33 @t4) (tptp.range_of (tptp.restrict @t33 @t4 tptp.universal_class))))) % 0.39/0.59 (assume @p29 (forall @t9 (= @t43 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 0.39/0.59 (assume @p30 (exists @t9 (and @t25 @t43 (forall @t41 (=> (tptp.inductive @t1) @t7))))) % 0.39/0.59 (assume @p31 (forall @t45 (= (tptp.member @t2 @t44) (exists @t41 (and @t3 (tptp.member @t1 @t4)))))) % 0.39/0.59 (assume @p32 (forall @t9 (=> @t25 (tptp.member @t44 tptp.universal_class)))) % 0.39/0.59 (assume @p33 (forall @t45 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t11 (tptp.subclass @t2 @t4))))) % 0.39/0.59 (assume @p34 (forall @t6 (=> @t11 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.39/0.59 (assume @p35 (forall (@list @t33 @t46) (tptp.subclass @t47 @t28))) % 0.39/0.59 (assume @p36 (forall (@list @t33 @t46 @t2 @t21) (= (tptp.member @t23 @t47) (and @t11 (tptp.member @t21 (tptp.image @t46 (tptp.image @t33 (tptp.singleton @t2)))))))) % 0.39/0.59 (assume @p37 (forall @t42 (= (tptp.member @t26 tptp.identity_relation) (exists @t9 (and @t25 (= @t26 (tptp.ordered_pair @t4 @t4))))))) % 0.39/0.59 (assume @p38 (forall @t50 (= @t49 (and (tptp.subclass @t48 @t28) (tptp.subclass (tptp.compose @t48 (tptp.inverse @t48)) tptp.identity_relation))))) % 0.39/0.59 (assume @p39 (forall (@list @t4 @t48) (=> (and @t25 @t49) (tptp.member (tptp.image @t48 @t4) tptp.universal_class)))) % 0.39/0.59 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 0.39/0.59 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t11 @t5 (tptp.disjoint @t2 @t4)))))) % 0.39/0.59 (assume @p42 (forall (@list @t48 @t1) (= @t51 (tptp.sum_class (tptp.image @t48 @t19))))) % 0.39/0.59 (assume @p43 (exists @t50 (and @t49 (forall @t41 (=> @t24 (or (= @t1 tptp.null_class) (tptp.member @t51 @t1))))))) % 0.39/0.59 (assume @p44 @t54) % 0.39/0.59 (assume @p45 true) % 0.39/0.59 (step @p46 :rule evaluate :args ((= false true))) % 0.39/0.59 (step @p47 :rule eq-symm :args (@t2 @t1)) % 0.39/0.59 (step @p48 :rule eq-symm :args (@t2 @t4)) % 0.39/0.59 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t10)) % 0.39/0.59 (step @p50 :rule refl :args (@t11)) % 0.39/0.59 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t12)) % 0.39/0.59 (step @p52 :rule refl :args (@t14)) % 0.39/0.59 (step @p53 :rule cong :premises (@p52 @p51) :args (@t15)) % 0.39/0.59 (step @p54 :rule cong :premises (@p53) :args (@t17)) % 0.39/0.59 (step @p55 :rule eq_resolve :premises (@p4 @p54)) % 0.39/0.59 (step @p56 :rule eq-symm :args (@t56 @t57)) % 0.39/0.59 (step @p57 :rule aci_norm :args ((= (and @t57 true) @t57))) % 0.39/0.59 (step @p58 :rule eq-refl :args (@t55)) % 0.39/0.59 (step @p59 :rule aci_norm :args ((= @t59 @t58))) % 0.39/0.59 (step @p60 :rule trans :premises (@p59 @p58)) % 0.39/0.59 (step @p61 :rule refl :args (@t57)) % 0.39/0.59 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t60)) % 0.39/0.59 (step @p63 :rule trans :premises (@p62 @p57)) % 0.39/0.59 (step @p64 :rule refl :args (@t56)) % 0.39/0.59 (step @p65 :rule cong :premises (@p64 @p63) :args (@t61)) % 0.39/0.59 (step @p66 :rule trans :premises (@p65 @p56)) % 0.39/0.59 (step @p67 :rule refl :args (@t62)) % 0.39/0.59 (step @p68 :rule cong :premises (@p67 @p66) :args ((=> @t62 @t61))) % 0.39/0.59 (assume-push @p101 @t62) % 0.39/0.59 (step @p70 :rule instantiate :premises (@p55) :args ((@list @t55 @t55 @t55))) % 0.39/0.59 (step-pop @p102 :rule scope :premises (@p70)) % 0.39/0.59 (step @p71 :rule process_scope :premises (@p102) :args (@t61)) % 0.39/0.59 (step @p73 :rule eq_resolve :premises (@p71 @p68)) % 0.39/0.59 (step @p74 :rule implies_elim :premises (@p73)) % 0.39/0.59 (step @p75 :rule chain_m_resolution :premises (@p74 @p55) :args (@t63 (@list false) (@list @t62))) % 0.39/0.59 (step @p76 :rule bool-impl-elim :args (@t25 @t52)) % 0.39/0.59 (step @p77 :rule cong :premises (@p76) :args (@t53)) % 0.39/0.59 (step @p78 :rule cong :premises (@p77) :args (@t54)) % 0.39/0.59 (step @p79 :rule eq_resolve :premises (@p44 @p78)) % 0.39/0.59 (step @p80 :rule skolemize :premises (@p79)) % 0.39/0.59 (step @p81 :rule bool-double-not-elim :args (@t57)) % 0.39/0.59 (step @p82 :rule refl :args (@t66)) % 0.39/0.59 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t66 (not @t65)))) % 0.39/0.59 (step @p84 :rule cnf_or_neg :args (@t66 0)) % 0.39/0.59 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 0.39/0.59 (step @p86 :rule reordering :premises (@p85) :args ((or @t57 @t66))) % 0.39/0.59 (step @p87 :rule chain_m_resolution :premises (@p86 @p80) :args (@t57 @t67 @t68)) % 0.39/0.59 (step @p88 :rule cnf_equiv_pos1 :args (@t63)) % 0.39/0.59 (step @p89 :rule reordering :premises (@p88) :args ((or @t65 @t56 (not @t63)))) % 0.39/0.59 (step @p90 :rule chain_m_resolution :premises (@p89 @p87 @p75) :args (@t56 (@list false false) (@list @t57 @t63))) % 0.39/0.59 (step @p91 :rule true_intro :premises (@p90)) % 0.39/0.59 (step @p92 :rule instantiate :premises (@p6) :args ((@list @t55))) % 0.39/0.59 (step @p93 :rule refl :args (@t55)) % 0.39/0.59 (step @p94 :rule cong :premises (@p93 @p92) :args (@t64)) % 0.39/0.59 (step @p95 :rule cnf_or_neg :args (@t66 1)) % 0.39/0.59 (step @p96 :rule chain_m_resolution :premises (@p95 @p80) :args ((not @t64) @t67 @t68)) % 0.39/0.59 (step @p97 :rule false_intro :premises (@p96)) % 0.39/0.59 (step @p98 :rule symm :premises (@p97)) % 0.39/0.59 (step @p99 :rule trans :premises (@p98 @p94 @p91)) % 0.39/0.59 (step @p100 false :rule eq_resolve :premises (@p99 @p46)) % 0.39/0.59 ) % 0.39/0.59 % SZS output end Proof % 0.39/0.59 % cvc5 exiting %------------------------------------------------------------------------------