%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET060+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 : n017.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 08:47:10 AM UTC 2026 % Result : Theorem 0.40s 0.61s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET060+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 % 0.18/0.35 % Computer : n017.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 14:48:16 EDT 2026 % 0.18/0.35 % CPUTime : % 0.32/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.61 % SZS status Theorem % 0.40/0.61 % SZS output start Proof % 0.40/0.61 ( % 0.40/0.61 (declare-sort $$unsorted 0) % 0.40/0.61 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.element_relation $$unsorted) % 0.40/0.61 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.universal_class $$unsorted) % 0.40/0.61 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.function (-> $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.null_class $$unsorted) % 0.40/0.61 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.successor_relation $$unsorted) % 0.40/0.61 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.61 (declare-const tptp.identity_relation $$unsorted) % 0.40/0.61 (define @t1 () (@var "Y" $$unsorted)) % 0.40/0.61 (define @t2 () (@var "U" $$unsorted)) % 0.40/0.61 (define @t3 () (tptp.member @t2 @t1)) % 0.40/0.61 (define @t4 () (@var "X" $$unsorted)) % 0.40/0.61 (define @t5 () (tptp.member @t2 @t4)) % 0.40/0.61 (define @t6 () (@list @t2)) % 0.40/0.61 (define @t7 () (tptp.subclass @t4 @t1)) % 0.40/0.61 (define @t8 () (@list @t4 @t1)) % 0.40/0.61 (define @t9 () (@list @t4)) % 0.40/0.61 (define @t10 () (tptp.member @t2 tptp.universal_class)) % 0.40/0.61 (define @t11 () (tptp.unordered_pair @t4 @t1)) % 0.40/0.61 (define @t12 () (tptp.singleton @t4)) % 0.40/0.61 (define @t13 () (tptp.singleton @t1)) % 0.40/0.61 (define @t14 () (tptp.ordered_pair @t4 @t1)) % 0.40/0.61 (define @t15 () (@var "V" $$unsorted)) % 0.40/0.61 (define @t16 () (tptp.cross_product @t4 @t1)) % 0.40/0.61 (define @t17 () (tptp.ordered_pair @t2 @t15)) % 0.40/0.61 (define @t18 () (tptp.member @t1 tptp.universal_class)) % 0.40/0.61 (define @t19 () (tptp.member @t4 tptp.universal_class)) % 0.40/0.61 (define @t20 () (@var "Z" $$unsorted)) % 0.40/0.61 (define @t21 () (@list @t4 @t1 @t20)) % 0.40/0.61 (define @t22 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.40/0.61 (define @t23 () (tptp.member @t20 @t1)) % 0.40/0.61 (define @t24 () (tptp.member @t20 @t4)) % 0.40/0.61 (define @t25 () (tptp.member @t20 tptp.universal_class)) % 0.40/0.61 (define @t26 () (tptp.complement @t4)) % 0.40/0.61 (define @t27 () (@list @t4 @t20)) % 0.40/0.61 (define @t28 () (@var "XR" $$unsorted)) % 0.40/0.61 (define @t29 () (@var "W" $$unsorted)) % 0.40/0.61 (define @t30 () (tptp.cross_product @t22 tptp.universal_class)) % 0.40/0.61 (define @t31 () (tptp.ordered_pair @t17 @t29)) % 0.40/0.61 (define @t32 () (tptp.member @t31 @t30)) % 0.40/0.61 (define @t33 () (tptp.rotate @t4)) % 0.40/0.61 (define @t34 () (tptp.flip @t4)) % 0.40/0.61 (define @t35 () (tptp.successor @t4)) % 0.40/0.61 (define @t36 () (@list @t1)) % 0.40/0.61 (define @t37 () (@list @t20)) % 0.40/0.61 (define @t38 () (tptp.inductive @t4)) % 0.40/0.61 (define @t39 () (tptp.sum_class @t4)) % 0.40/0.61 (define @t40 () (@list @t2 @t4)) % 0.40/0.61 (define @t41 () (@var "YR" $$unsorted)) % 0.40/0.61 (define @t42 () (tptp.compose @t41 @t28)) % 0.40/0.61 (define @t43 () (@var "XF" $$unsorted)) % 0.40/0.61 (define @t44 () (tptp.function @t43)) % 0.40/0.61 (define @t45 () (@list @t43)) % 0.40/0.61 (define @t46 () (tptp.apply @t43 @t1)) % 0.40/0.61 (define @t47 () (forall @t8 (not (tptp.member @t1 (tptp.intersection @t26 @t4))))) % 0.40/0.61 (define @t48 () (not @t47)) % 0.40/0.61 (define @t49 () (@quantifiers_skolemize @t47 1)) % 0.40/0.61 (define @t50 () (@quantifiers_skolemize @t47 0)) % 0.40/0.61 (define @t51 () (tptp.complement @t50)) % 0.40/0.61 (define @t52 () (tptp.member @t49 (tptp.intersection @t51 @t50))) % 0.40/0.61 (define @t53 () (not @t52)) % 0.40/0.61 (define @t54 () (not @t53)) % 0.40/0.61 (define @t55 () (tptp.member @t49 @t50)) % 0.40/0.61 (define @t56 () (tptp.member @t49 @t51)) % 0.40/0.61 (define @t57 () (and @t56 @t55)) % 0.40/0.61 (define @t58 () (= @t52 @t57)) % 0.40/0.61 (define @t59 () (not @t57)) % 0.40/0.61 (define @t60 () (@list false)) % 0.40/0.61 (define @t61 () (@list @t57)) % 0.40/0.61 (define @t62 () (not @t55)) % 0.40/0.61 (define @t63 () (and (tptp.member @t49 tptp.universal_class) @t62)) % 0.40/0.61 (define @t64 () (not @t63)) % 0.40/0.61 (define @t65 () (= @t56 @t63)) % 0.40/0.61 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.40/0.61 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 0.40/0.61 (assume @p3 (forall @t8 (= (= @t4 @t1) (and @t7 (tptp.subclass @t1 @t4))))) % 0.40/0.61 (assume @p4 (forall (@list @t2 @t4 @t1) (= (tptp.member @t2 @t11) (and @t10 (or (= @t2 @t4) (= @t2 @t1)))))) % 0.40/0.61 (assume @p5 (forall @t8 (tptp.member @t11 tptp.universal_class))) % 0.40/0.61 (assume @p6 (forall @t9 (= @t12 (tptp.unordered_pair @t4 @t4)))) % 0.40/0.61 (assume @p7 (forall @t8 (= @t14 (tptp.unordered_pair @t12 (tptp.unordered_pair @t4 @t13))))) % 0.40/0.61 (assume @p8 (forall (@list @t2 @t15 @t4 @t1) (= (tptp.member @t17 @t16) (and @t5 (tptp.member @t15 @t1))))) % 0.40/0.61 (assume @p9 (forall @t8 (=> (and @t19 @t18) (and (= (tptp.first @t14) @t4) (= (tptp.second @t14) @t1))))) % 0.40/0.61 (assume @p10 (forall @t21 (=> (tptp.member @t20 @t16) (= @t20 (tptp.ordered_pair (tptp.first @t20) (tptp.second @t20)))))) % 0.40/0.61 (assume @p11 (forall @t8 (= (tptp.member @t14 tptp.element_relation) (and @t18 (tptp.member @t4 @t1))))) % 0.40/0.61 (assume @p12 (tptp.subclass tptp.element_relation @t22)) % 0.40/0.61 (assume @p13 (forall @t21 (= (tptp.member @t20 (tptp.intersection @t4 @t1)) (and @t24 @t23)))) % 0.40/0.61 (assume @p14 (forall @t27 (= (tptp.member @t20 @t26) (and @t25 (not @t24))))) % 0.40/0.61 (assume @p15 (forall (@list @t4 @t28 @t1) (= (tptp.restrict @t28 @t4 @t1) (tptp.intersection @t28 @t16)))) % 0.40/0.61 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 0.40/0.61 (assume @p17 (forall @t27 (= (tptp.member @t20 (tptp.domain_of @t4)) (and @t25 (not (= (tptp.restrict @t4 (tptp.singleton @t20) tptp.universal_class) tptp.null_class)))))) % 0.40/0.61 (assume @p18 (forall (@list @t4 @t2 @t15 @t29) (= (tptp.member @t31 @t33) (and @t32 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t15 @t29) @t2) @t4))))) % 0.40/0.61 (assume @p19 (forall @t9 (tptp.subclass @t33 @t30))) % 0.40/0.61 (assume @p20 (forall (@list @t2 @t15 @t29 @t4) (= (tptp.member @t31 @t34) (and @t32 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t15 @t2) @t29) @t4))))) % 0.40/0.61 (assume @p21 (forall @t9 (tptp.subclass @t34 @t30))) % 0.40/0.61 (assume @p22 (forall @t21 (= (tptp.member @t20 (tptp.union @t4 @t1)) (or @t24 @t23)))) % 0.40/0.61 (assume @p23 (forall @t9 (= @t35 (tptp.union @t4 @t12)))) % 0.40/0.61 (assume @p24 (tptp.subclass tptp.successor_relation @t22)) % 0.40/0.61 (assume @p25 (forall @t8 (= (tptp.member @t14 tptp.successor_relation) (and @t19 @t18 (= @t35 @t1))))) % 0.40/0.61 (assume @p26 (forall @t36 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 0.40/0.61 (assume @p27 (forall @t37 (= (tptp.range_of @t20) (tptp.domain_of (tptp.inverse @t20))))) % 0.40/0.61 (assume @p28 (forall (@list @t4 @t28) (= (tptp.image @t28 @t4) (tptp.range_of (tptp.restrict @t28 @t4 tptp.universal_class))))) % 0.40/0.61 (assume @p29 (forall @t9 (= @t38 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 0.40/0.61 (assume @p30 (exists @t9 (and @t19 @t38 (forall @t36 (=> (tptp.inductive @t1) @t7))))) % 0.40/0.61 (assume @p31 (forall @t40 (= (tptp.member @t2 @t39) (exists @t36 (and @t3 (tptp.member @t1 @t4)))))) % 0.40/0.61 (assume @p32 (forall @t9 (=> @t19 (tptp.member @t39 tptp.universal_class)))) % 0.40/0.61 (assume @p33 (forall @t40 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t10 (tptp.subclass @t2 @t4))))) % 0.40/0.61 (assume @p34 (forall @t6 (=> @t10 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.40/0.61 (assume @p35 (forall (@list @t28 @t41) (tptp.subclass @t42 @t22))) % 0.40/0.61 (assume @p36 (forall (@list @t28 @t41 @t2 @t15) (= (tptp.member @t17 @t42) (and @t10 (tptp.member @t15 (tptp.image @t41 (tptp.image @t28 (tptp.singleton @t2)))))))) % 0.40/0.61 (assume @p37 (forall @t37 (= (tptp.member @t20 tptp.identity_relation) (exists @t9 (and @t19 (= @t20 (tptp.ordered_pair @t4 @t4))))))) % 0.40/0.61 (assume @p38 (forall @t45 (= @t44 (and (tptp.subclass @t43 @t22) (tptp.subclass (tptp.compose @t43 (tptp.inverse @t43)) tptp.identity_relation))))) % 0.40/0.61 (assume @p39 (forall (@list @t4 @t43) (=> (and @t19 @t44) (tptp.member (tptp.image @t43 @t4) tptp.universal_class)))) % 0.40/0.61 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 0.40/0.61 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t10 @t5 (tptp.disjoint @t2 @t4)))))) % 0.40/0.61 (assume @p42 (forall (@list @t43 @t1) (= @t46 (tptp.sum_class (tptp.image @t43 @t13))))) % 0.40/0.61 (assume @p43 (exists @t45 (and @t44 (forall @t36 (=> @t18 (or (= @t1 tptp.null_class) (tptp.member @t46 @t1))))))) % 0.40/0.61 (assume @p44 @t48) % 0.40/0.61 (assume @p45 true) % 0.40/0.61 (step @p46 :rule instantiate :premises (@p13) :args ((@list @t51 @t50 @t49))) % 0.40/0.61 (step @p47 :rule refl :args (@t52)) % 0.40/0.61 (step @p48 :rule bool-double-not-elim :args (@t47)) % 0.40/0.61 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or (not @t48) @t52))) % 0.40/0.61 (step @p50 :rule bool-double-not-elim :args (@t52)) % 0.40/0.61 (step @p51 :rule refl :args (@t48)) % 0.40/0.61 (step @p52 :rule cong :premises (@p51 @p50) :args ((=> @t48 @t54))) % 0.40/0.61 (assume-push @p77 @t48) % 0.40/0.61 (step @p54 :rule skolemize :premises (@p44)) % 0.40/0.61 (step-pop @p78 :rule scope :premises (@p54)) % 0.40/0.61 (step @p55 :rule process_scope :premises (@p78) :args (@t54)) % 0.40/0.61 (step @p57 :rule eq_resolve :premises (@p55 @p52)) % 0.40/0.61 (step @p58 :rule implies_elim :premises (@p57)) % 0.40/0.61 (step @p59 :rule eq_resolve :premises (@p58 @p49)) % 0.40/0.61 (step @p60 :rule chain_m_resolution :premises (@p59 @p44) :args (@t52 (@list true) (@list @t47))) % 0.40/0.61 (step @p61 :rule cnf_equiv_pos1 :args (@t58)) % 0.40/0.61 (step @p62 :rule reordering :premises (@p61) :args ((or @t53 @t57 (not @t58)))) % 0.40/0.61 (step @p63 :rule chain_m_resolution :premises (@p62 @p60 @p46) :args (@t57 (@list false false) (@list @t52 @t58))) % 0.40/0.61 (step @p64 :rule cnf_and_pos :args (@t57 0)) % 0.40/0.61 (step @p65 :rule reordering :premises (@p64) :args ((or @t56 @t59))) % 0.40/0.61 (step @p66 :rule chain_m_resolution :premises (@p65 @p63) :args (@t56 @t60 @t61)) % 0.40/0.62 (step @p67 :rule cnf_and_pos :args (@t57 1)) % 0.40/0.62 (step @p68 :rule reordering :premises (@p67) :args ((or @t55 @t59))) % 0.40/0.62 (step @p69 :rule chain_m_resolution :premises (@p68 @p63) :args (@t55 @t60 @t61)) % 0.40/0.62 (step @p70 :rule cnf_and_pos :args (@t63 1)) % 0.40/0.62 (step @p71 :rule reordering :premises (@p70) :args ((or @t62 @t64))) % 0.40/0.62 (step @p72 :rule chain_m_resolution :premises (@p71 @p69) :args (@t64 @t60 (@list @t55))) % 0.40/0.62 (step @p73 :rule instantiate :premises (@p14) :args ((@list @t50 @t49))) % 0.40/0.62 (step @p74 :rule cnf_equiv_pos1 :args (@t65)) % 0.40/0.62 (step @p75 :rule reordering :premises (@p74) :args ((or (not @t56) @t63 (not @t65)))) % 0.40/0.62 (step @p76 false :rule chain_m_resolution :premises (@p75 @p73 @p72 @p66) :args (false (@list false true false) (@list @t65 @t63 @t56))) % 0.40/0.62 ) % 0.40/0.62 % SZS output end Proof % 0.40/0.62 % cvc5 exiting %------------------------------------------------------------------------------