%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET102+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 : n004.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 08:47:24 AM UTC 2026 % Result : Theorem 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET102+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.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 14:55:37 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (declare-sort $$unsorted 0) % 0.38/0.60 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.element_relation $$unsorted) % 0.38/0.60 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.universal_class $$unsorted) % 0.38/0.60 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.function (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.null_class $$unsorted) % 0.38/0.60 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.successor_relation $$unsorted) % 0.38/0.60 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.identity_relation $$unsorted) % 0.38/0.60 (define @t1 () (@var "Y" $$unsorted)) % 0.38/0.60 (define @t2 () (@var "U" $$unsorted)) % 0.38/0.60 (define @t3 () (tptp.member @t2 @t1)) % 0.38/0.60 (define @t4 () (@var "X" $$unsorted)) % 0.38/0.60 (define @t5 () (tptp.member @t2 @t4)) % 0.38/0.60 (define @t6 () (@list @t2)) % 0.38/0.60 (define @t7 () (tptp.subclass @t4 @t1)) % 0.38/0.60 (define @t8 () (@list @t4 @t1)) % 0.38/0.60 (define @t9 () (@list @t4)) % 0.38/0.60 (define @t10 () (or (= @t2 @t4) (= @t2 @t1))) % 0.38/0.60 (define @t11 () (tptp.member @t2 tptp.universal_class)) % 0.38/0.60 (define @t12 () (and @t11 @t10)) % 0.38/0.60 (define @t13 () (tptp.unordered_pair @t4 @t1)) % 0.38/0.60 (define @t14 () (tptp.member @t2 @t13)) % 0.38/0.60 (define @t15 () (= @t14 @t12)) % 0.38/0.60 (define @t16 () (@list @t2 @t4 @t1)) % 0.38/0.60 (define @t17 () (forall @t16 @t15)) % 0.38/0.60 (define @t18 () (tptp.singleton @t4)) % 0.38/0.60 (define @t19 () (tptp.singleton @t1)) % 0.38/0.60 (define @t20 () (tptp.unordered_pair @t4 @t19)) % 0.38/0.60 (define @t21 () (tptp.ordered_pair @t4 @t1)) % 0.38/0.60 (define @t22 () (@var "V" $$unsorted)) % 0.38/0.60 (define @t23 () (tptp.cross_product @t4 @t1)) % 0.38/0.60 (define @t24 () (tptp.ordered_pair @t2 @t22)) % 0.38/0.60 (define @t25 () (tptp.member @t1 tptp.universal_class)) % 0.38/0.60 (define @t26 () (tptp.member @t4 tptp.universal_class)) % 0.38/0.60 (define @t27 () (@var "Z" $$unsorted)) % 0.38/0.60 (define @t28 () (@list @t4 @t1 @t27)) % 0.38/0.60 (define @t29 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.38/0.60 (define @t30 () (tptp.member @t27 @t1)) % 0.38/0.60 (define @t31 () (tptp.member @t27 @t4)) % 0.38/0.60 (define @t32 () (tptp.member @t27 tptp.universal_class)) % 0.38/0.60 (define @t33 () (@list @t4 @t27)) % 0.38/0.60 (define @t34 () (@var "XR" $$unsorted)) % 0.38/0.60 (define @t35 () (@var "W" $$unsorted)) % 0.38/0.60 (define @t36 () (tptp.cross_product @t29 tptp.universal_class)) % 0.38/0.60 (define @t37 () (tptp.ordered_pair @t24 @t35)) % 0.38/0.60 (define @t38 () (tptp.member @t37 @t36)) % 0.38/0.60 (define @t39 () (tptp.rotate @t4)) % 0.38/0.60 (define @t40 () (tptp.flip @t4)) % 0.38/0.60 (define @t41 () (tptp.successor @t4)) % 0.38/0.60 (define @t42 () (@list @t1)) % 0.38/0.60 (define @t43 () (@list @t27)) % 0.38/0.60 (define @t44 () (tptp.inductive @t4)) % 0.38/0.60 (define @t45 () (tptp.sum_class @t4)) % 0.38/0.60 (define @t46 () (@list @t2 @t4)) % 0.38/0.60 (define @t47 () (@var "YR" $$unsorted)) % 0.38/0.60 (define @t48 () (tptp.compose @t47 @t34)) % 0.38/0.60 (define @t49 () (@var "XF" $$unsorted)) % 0.38/0.60 (define @t50 () (tptp.function @t49)) % 0.38/0.60 (define @t51 () (@list @t49)) % 0.38/0.60 (define @t52 () (tptp.apply @t49 @t1)) % 0.38/0.60 (define @t53 () (forall @t8 (tptp.member @t20 @t21))) % 0.38/0.60 (define @t54 () (@quantifiers_skolemize @t53 1)) % 0.38/0.60 (define @t55 () (tptp.singleton @t54)) % 0.38/0.60 (define @t56 () (@quantifiers_skolemize @t53 0)) % 0.38/0.60 (define @t57 () (tptp.unordered_pair @t56 @t55)) % 0.38/0.60 (define @t58 () (tptp.singleton @t56)) % 0.38/0.60 (define @t59 () (tptp.member @t57 (tptp.unordered_pair @t58 @t57))) % 0.38/0.60 (define @t60 () (tptp.member @t57 tptp.universal_class)) % 0.38/0.60 (define @t61 () (or (= @t58 @t57) (= @t57 @t57))) % 0.38/0.60 (define @t62 () (and @t60 @t61)) % 0.38/0.60 (define @t63 () (= @t59 @t62)) % 0.38/0.60 (define @t64 () (forall @t16 (= @t14 (and @t11 (or (= @t4 @t2) (= @t1 @t2)))))) % 0.38/0.60 (define @t65 () (= @t60 @t59)) % 0.38/0.60 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.38/0.60 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 0.38/0.60 (assume @p3 (forall @t8 (= (= @t4 @t1) (and @t7 (tptp.subclass @t1 @t4))))) % 0.38/0.60 (assume @p4 @t17) % 0.38/0.60 (assume @p5 (forall @t8 (tptp.member @t13 tptp.universal_class))) % 0.38/0.60 (assume @p6 (forall @t9 (= @t18 (tptp.unordered_pair @t4 @t4)))) % 0.38/0.60 (assume @p7 (forall @t8 (= @t21 (tptp.unordered_pair @t18 @t20)))) % 0.38/0.60 (assume @p8 (forall (@list @t2 @t22 @t4 @t1) (= (tptp.member @t24 @t23) (and @t5 (tptp.member @t22 @t1))))) % 0.38/0.60 (assume @p9 (forall @t8 (=> (and @t26 @t25) (and (= (tptp.first @t21) @t4) (= (tptp.second @t21) @t1))))) % 0.38/0.60 (assume @p10 (forall @t28 (=> (tptp.member @t27 @t23) (= @t27 (tptp.ordered_pair (tptp.first @t27) (tptp.second @t27)))))) % 0.38/0.60 (assume @p11 (forall @t8 (= (tptp.member @t21 tptp.element_relation) (and @t25 (tptp.member @t4 @t1))))) % 0.38/0.60 (assume @p12 (tptp.subclass tptp.element_relation @t29)) % 0.38/0.60 (assume @p13 (forall @t28 (= (tptp.member @t27 (tptp.intersection @t4 @t1)) (and @t31 @t30)))) % 0.38/0.60 (assume @p14 (forall @t33 (= (tptp.member @t27 (tptp.complement @t4)) (and @t32 (not @t31))))) % 0.38/0.60 (assume @p15 (forall (@list @t4 @t34 @t1) (= (tptp.restrict @t34 @t4 @t1) (tptp.intersection @t34 @t23)))) % 0.38/0.60 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 0.38/0.60 (assume @p17 (forall @t33 (= (tptp.member @t27 (tptp.domain_of @t4)) (and @t32 (not (= (tptp.restrict @t4 (tptp.singleton @t27) tptp.universal_class) tptp.null_class)))))) % 0.38/0.60 (assume @p18 (forall (@list @t4 @t2 @t22 @t35) (= (tptp.member @t37 @t39) (and @t38 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t35) @t2) @t4))))) % 0.38/0.60 (assume @p19 (forall @t9 (tptp.subclass @t39 @t36))) % 0.38/0.60 (assume @p20 (forall (@list @t2 @t22 @t35 @t4) (= (tptp.member @t37 @t40) (and @t38 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t22 @t2) @t35) @t4))))) % 0.38/0.60 (assume @p21 (forall @t9 (tptp.subclass @t40 @t36))) % 0.38/0.60 (assume @p22 (forall @t28 (= (tptp.member @t27 (tptp.union @t4 @t1)) (or @t31 @t30)))) % 0.38/0.60 (assume @p23 (forall @t9 (= @t41 (tptp.union @t4 @t18)))) % 0.38/0.60 (assume @p24 (tptp.subclass tptp.successor_relation @t29)) % 0.38/0.60 (assume @p25 (forall @t8 (= (tptp.member @t21 tptp.successor_relation) (and @t26 @t25 (= @t41 @t1))))) % 0.38/0.60 (assume @p26 (forall @t42 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 0.38/0.60 (assume @p27 (forall @t43 (= (tptp.range_of @t27) (tptp.domain_of (tptp.inverse @t27))))) % 0.38/0.60 (assume @p28 (forall (@list @t4 @t34) (= (tptp.image @t34 @t4) (tptp.range_of (tptp.restrict @t34 @t4 tptp.universal_class))))) % 0.38/0.60 (assume @p29 (forall @t9 (= @t44 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 0.38/0.60 (assume @p30 (exists @t9 (and @t26 @t44 (forall @t42 (=> (tptp.inductive @t1) @t7))))) % 0.38/0.60 (assume @p31 (forall @t46 (= (tptp.member @t2 @t45) (exists @t42 (and @t3 (tptp.member @t1 @t4)))))) % 0.38/0.60 (assume @p32 (forall @t9 (=> @t26 (tptp.member @t45 tptp.universal_class)))) % 0.38/0.60 (assume @p33 (forall @t46 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t11 (tptp.subclass @t2 @t4))))) % 0.38/0.60 (assume @p34 (forall @t6 (=> @t11 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.38/0.60 (assume @p35 (forall (@list @t34 @t47) (tptp.subclass @t48 @t29))) % 0.38/0.60 (assume @p36 (forall (@list @t34 @t47 @t2 @t22) (= (tptp.member @t24 @t48) (and @t11 (tptp.member @t22 (tptp.image @t47 (tptp.image @t34 (tptp.singleton @t2)))))))) % 0.38/0.60 (assume @p37 (forall @t43 (= (tptp.member @t27 tptp.identity_relation) (exists @t9 (and @t26 (= @t27 (tptp.ordered_pair @t4 @t4))))))) % 0.38/0.60 (assume @p38 (forall @t51 (= @t50 (and (tptp.subclass @t49 @t29) (tptp.subclass (tptp.compose @t49 (tptp.inverse @t49)) tptp.identity_relation))))) % 0.38/0.60 (assume @p39 (forall (@list @t4 @t49) (=> (and @t26 @t50) (tptp.member (tptp.image @t49 @t4) tptp.universal_class)))) % 0.38/0.60 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 0.38/0.60 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t11 @t5 (tptp.disjoint @t2 @t4)))))) % 0.38/0.60 (assume @p42 (forall (@list @t49 @t1) (= @t52 (tptp.sum_class (tptp.image @t49 @t19))))) % 0.38/0.60 (assume @p43 (exists @t51 (and @t50 (forall @t42 (=> @t25 (or (= @t1 tptp.null_class) (tptp.member @t52 @t1))))))) % 0.38/0.60 (assume @p44 (not @t53)) % 0.38/0.60 (assume @p45 true) % 0.38/0.60 (step @p46 :rule evaluate :args ((= false true))) % 0.38/0.60 (step @p47 :rule eq-symm :args (@t2 @t1)) % 0.38/0.60 (step @p48 :rule eq-symm :args (@t2 @t4)) % 0.38/0.60 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t10)) % 0.38/0.60 (step @p50 :rule refl :args (@t11)) % 0.38/0.60 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t12)) % 0.38/0.60 (step @p52 :rule refl :args (@t14)) % 0.38/0.60 (step @p53 :rule cong :premises (@p52 @p51) :args (@t15)) % 0.38/0.60 (step @p54 :rule cong :premises (@p53) :args (@t17)) % 0.38/0.60 (step @p55 :rule eq_resolve :premises (@p4 @p54)) % 0.38/0.60 (step @p56 :rule eq-symm :args (@t59 @t60)) % 0.38/0.60 (step @p57 :rule aci_norm :args ((= (and @t60 true) @t60))) % 0.38/0.60 (step @p58 :rule absorb :args ((= (or (= @t57 @t58) true) true))) % 0.38/0.60 (step @p59 :rule eq-refl :args (@t57)) % 0.38/0.60 (step @p60 :rule eq-symm :args (@t58 @t57)) % 0.38/0.60 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t61)) % 0.38/0.60 (step @p62 :rule trans :premises (@p61 @p58)) % 0.38/0.60 (step @p63 :rule refl :args (@t60)) % 0.38/0.60 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t62)) % 0.38/0.60 (step @p65 :rule trans :premises (@p64 @p57)) % 0.38/0.60 (step @p66 :rule refl :args (@t59)) % 0.38/0.60 (step @p67 :rule cong :premises (@p66 @p65) :args (@t63)) % 0.38/0.60 (step @p68 :rule trans :premises (@p67 @p56)) % 0.38/0.60 (step @p69 :rule refl :args (@t64)) % 0.38/0.60 (step @p70 :rule cong :premises (@p69 @p68) :args ((=> @t64 @t63))) % 0.38/0.60 (assume-push @p91 @t64) % 0.38/0.60 (step @p72 :rule instantiate :premises (@p55) :args ((@list @t57 @t58 @t57))) % 0.38/0.60 (step-pop @p92 :rule scope :premises (@p72)) % 0.38/0.60 (step @p73 :rule process_scope :premises (@p92) :args (@t63)) % 0.38/0.60 (step @p75 :rule eq_resolve :premises (@p73 @p70)) % 0.38/0.60 (step @p76 :rule implies_elim :premises (@p75)) % 0.38/0.60 (step @p77 :rule chain_m_resolution :premises (@p76 @p55) :args (@t65 (@list false) (@list @t64))) % 0.38/0.60 (step @p78 :rule instantiate :premises (@p5) :args ((@list @t56 @t55))) % 0.38/0.60 (step @p79 :rule cnf_equiv_pos1 :args (@t65)) % 0.38/0.60 (step @p80 :rule reordering :premises (@p79) :args ((or (not @t60) @t59 (not @t65)))) % 0.38/0.60 (step @p81 :rule chain_m_resolution :premises (@p80 @p78 @p77) :args (@t59 (@list false false) (@list @t60 @t65))) % 0.38/0.60 (step @p82 :rule true_intro :premises (@p81)) % 0.38/0.60 (step @p83 :rule instantiate :premises (@p7) :args ((@list @t56 @t54))) % 0.38/0.60 (step @p84 :rule refl :args (@t57)) % 0.38/0.60 (step @p85 :rule cong :premises (@p84 @p83) :args ((tptp.member @t57 (tptp.ordered_pair @t56 @t54)))) % 0.38/0.60 (step @p86 :rule skolemize :premises (@p44)) % 0.38/0.60 (step @p87 :rule false_intro :premises (@p86)) % 0.38/0.60 (step @p88 :rule symm :premises (@p87)) % 0.38/0.60 (step @p89 :rule trans :premises (@p88 @p85 @p82)) % 0.38/0.60 (step @p90 false :rule eq_resolve :premises (@p89 @p46)) % 0.38/0.60 ) % 0.38/0.60 % SZS output end Proof % 0.38/0.60 % cvc5 exiting %------------------------------------------------------------------------------