%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET093+1 : TPTP v9.2.1. Bugfixed v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n028.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 08:47:21 AM UTC 2026 % Result : Theorem 0.37s 0.60s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET093+1 : TPTP v9.2.1. Bugfixed v7.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n028.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 14:52:35 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.60 % SZS status Theorem % 0.37/0.60 % SZS output start Proof % 0.37/0.60 ( % 0.37/0.60 (declare-sort $$unsorted 0) % 0.37/0.60 (declare-const tptp.member_of (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.element_relation $$unsorted) % 0.37/0.60 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.universal_class $$unsorted) % 0.37/0.60 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.function (-> $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.null_class $$unsorted) % 0.37/0.60 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.successor_relation $$unsorted) % 0.37/0.60 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.identity_relation $$unsorted) % 0.37/0.60 (define @t1 () (@var "Y" $$unsorted)) % 0.37/0.60 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.60 (define @t3 () (tptp.member @t2 @t1)) % 0.37/0.60 (define @t4 () (@var "X" $$unsorted)) % 0.37/0.60 (define @t5 () (tptp.member @t2 @t4)) % 0.37/0.60 (define @t6 () (@list @t2)) % 0.37/0.60 (define @t7 () (tptp.subclass @t4 @t1)) % 0.37/0.60 (define @t8 () (@list @t4 @t1)) % 0.37/0.60 (define @t9 () (@list @t4)) % 0.37/0.60 (define @t10 () (tptp.member @t2 tptp.universal_class)) % 0.37/0.60 (define @t11 () (tptp.unordered_pair @t4 @t1)) % 0.37/0.60 (define @t12 () (tptp.singleton @t4)) % 0.37/0.60 (define @t13 () (tptp.singleton @t1)) % 0.37/0.60 (define @t14 () (tptp.ordered_pair @t4 @t1)) % 0.37/0.60 (define @t15 () (@var "V" $$unsorted)) % 0.37/0.60 (define @t16 () (tptp.cross_product @t4 @t1)) % 0.37/0.60 (define @t17 () (tptp.ordered_pair @t2 @t15)) % 0.37/0.60 (define @t18 () (tptp.member @t1 tptp.universal_class)) % 0.37/0.60 (define @t19 () (tptp.member @t4 tptp.universal_class)) % 0.37/0.60 (define @t20 () (@var "Z" $$unsorted)) % 0.37/0.60 (define @t21 () (@list @t4 @t1 @t20)) % 0.37/0.60 (define @t22 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.37/0.60 (define @t23 () (tptp.member @t20 @t1)) % 0.37/0.60 (define @t24 () (tptp.member @t20 @t4)) % 0.37/0.60 (define @t25 () (tptp.member @t20 tptp.universal_class)) % 0.37/0.60 (define @t26 () (@list @t4 @t20)) % 0.37/0.60 (define @t27 () (@var "XR" $$unsorted)) % 0.37/0.60 (define @t28 () (@var "W" $$unsorted)) % 0.37/0.60 (define @t29 () (tptp.cross_product @t22 tptp.universal_class)) % 0.37/0.60 (define @t30 () (tptp.ordered_pair @t17 @t28)) % 0.37/0.60 (define @t31 () (tptp.member @t30 @t29)) % 0.37/0.60 (define @t32 () (tptp.rotate @t4)) % 0.37/0.60 (define @t33 () (tptp.flip @t4)) % 0.37/0.60 (define @t34 () (tptp.successor @t4)) % 0.37/0.60 (define @t35 () (@list @t1)) % 0.37/0.60 (define @t36 () (@list @t20)) % 0.37/0.60 (define @t37 () (tptp.inductive @t4)) % 0.37/0.60 (define @t38 () (tptp.sum_class @t4)) % 0.37/0.60 (define @t39 () (@list @t2 @t4)) % 0.37/0.60 (define @t40 () (@var "YR" $$unsorted)) % 0.37/0.60 (define @t41 () (tptp.compose @t40 @t27)) % 0.37/0.60 (define @t42 () (@var "XF" $$unsorted)) % 0.37/0.60 (define @t43 () (tptp.function @t42)) % 0.37/0.60 (define @t44 () (@list @t42)) % 0.37/0.60 (define @t45 () (tptp.apply @t42 @t1)) % 0.37/0.60 (define @t46 () (tptp.member_of @t13)) % 0.37/0.60 (define @t47 () (tptp.member_of @t4)) % 0.37/0.60 (define @t48 () (= @t47 @t4)) % 0.37/0.60 (define @t49 () (tptp.singleton @t47)) % 0.37/0.60 (define @t50 () (= @t49 @t4)) % 0.37/0.60 (define @t51 () (=> @t50 @t19)) % 0.37/0.60 (define @t52 () (forall @t9 @t51)) % 0.37/0.60 (define @t53 () (not @t52)) % 0.37/0.60 (define @t54 () (= @t4 @t49)) % 0.37/0.60 (define @t55 () (@quantifiers_skolemize (forall @t9 (or (not @t54) @t19)) 0)) % 0.37/0.60 (define @t56 () (tptp.member_of @t55)) % 0.37/0.60 (define @t57 () (= @t55 (tptp.singleton @t56))) % 0.37/0.60 (define @t58 () (tptp.member @t55 tptp.universal_class)) % 0.37/0.60 (define @t59 () (not @t57)) % 0.37/0.60 (define @t60 () (or @t59 @t58)) % 0.37/0.60 (define @t61 () (@list true)) % 0.37/0.60 (define @t62 () (@list @t60)) % 0.37/0.60 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.37/0.60 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 0.37/0.60 (assume @p3 (forall @t8 (= (= @t4 @t1) (and @t7 (tptp.subclass @t1 @t4))))) % 0.37/0.60 (assume @p4 (forall (@list @t2 @t4 @t1) (= (tptp.member @t2 @t11) (and @t10 (or (= @t2 @t4) (= @t2 @t1)))))) % 0.37/0.60 (assume @p5 (forall @t8 (tptp.member @t11 tptp.universal_class))) % 0.37/0.60 (assume @p6 (forall @t9 (= @t12 (tptp.unordered_pair @t4 @t4)))) % 0.37/0.60 (assume @p7 (forall @t8 (= @t14 (tptp.unordered_pair @t12 (tptp.unordered_pair @t4 @t13))))) % 0.37/0.60 (assume @p8 (forall (@list @t2 @t15 @t4 @t1) (= (tptp.member @t17 @t16) (and @t5 (tptp.member @t15 @t1))))) % 0.37/0.60 (assume @p9 (forall @t8 (=> (and @t19 @t18) (and (= (tptp.first @t14) @t4) (= (tptp.second @t14) @t1))))) % 0.37/0.60 (assume @p10 (forall @t21 (=> (tptp.member @t20 @t16) (= @t20 (tptp.ordered_pair (tptp.first @t20) (tptp.second @t20)))))) % 0.37/0.60 (assume @p11 (forall @t8 (= (tptp.member @t14 tptp.element_relation) (and @t18 (tptp.member @t4 @t1))))) % 0.37/0.60 (assume @p12 (tptp.subclass tptp.element_relation @t22)) % 0.37/0.60 (assume @p13 (forall @t21 (= (tptp.member @t20 (tptp.intersection @t4 @t1)) (and @t24 @t23)))) % 0.37/0.60 (assume @p14 (forall @t26 (= (tptp.member @t20 (tptp.complement @t4)) (and @t25 (not @t24))))) % 0.37/0.60 (assume @p15 (forall (@list @t4 @t27 @t1) (= (tptp.restrict @t27 @t4 @t1) (tptp.intersection @t27 @t16)))) % 0.37/0.60 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 0.37/0.60 (assume @p17 (forall @t26 (= (tptp.member @t20 (tptp.domain_of @t4)) (and @t25 (not (= (tptp.restrict @t4 (tptp.singleton @t20) tptp.universal_class) tptp.null_class)))))) % 0.37/0.60 (assume @p18 (forall (@list @t4 @t2 @t15 @t28) (= (tptp.member @t30 @t32) (and @t31 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t15 @t28) @t2) @t4))))) % 0.37/0.60 (assume @p19 (forall @t9 (tptp.subclass @t32 @t29))) % 0.37/0.60 (assume @p20 (forall (@list @t2 @t15 @t28 @t4) (= (tptp.member @t30 @t33) (and @t31 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t15 @t2) @t28) @t4))))) % 0.37/0.60 (assume @p21 (forall @t9 (tptp.subclass @t33 @t29))) % 0.37/0.60 (assume @p22 (forall @t21 (= (tptp.member @t20 (tptp.union @t4 @t1)) (or @t24 @t23)))) % 0.37/0.60 (assume @p23 (forall @t9 (= @t34 (tptp.union @t4 @t12)))) % 0.37/0.60 (assume @p24 (tptp.subclass tptp.successor_relation @t22)) % 0.37/0.60 (assume @p25 (forall @t8 (= (tptp.member @t14 tptp.successor_relation) (and @t19 @t18 (= @t34 @t1))))) % 0.37/0.60 (assume @p26 (forall @t35 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 0.37/0.60 (assume @p27 (forall @t36 (= (tptp.range_of @t20) (tptp.domain_of (tptp.inverse @t20))))) % 0.37/0.60 (assume @p28 (forall (@list @t4 @t27) (= (tptp.image @t27 @t4) (tptp.range_of (tptp.restrict @t27 @t4 tptp.universal_class))))) % 0.37/0.60 (assume @p29 (forall @t9 (= @t37 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 0.37/0.60 (assume @p30 (exists @t9 (and @t19 @t37 (forall @t35 (=> (tptp.inductive @t1) @t7))))) % 0.37/0.60 (assume @p31 (forall @t39 (= (tptp.member @t2 @t38) (exists @t35 (and @t3 (tptp.member @t1 @t4)))))) % 0.37/0.60 (assume @p32 (forall @t9 (=> @t19 (tptp.member @t38 tptp.universal_class)))) % 0.37/0.60 (assume @p33 (forall @t39 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t10 (tptp.subclass @t2 @t4))))) % 0.37/0.60 (assume @p34 (forall @t6 (=> @t10 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.37/0.60 (assume @p35 (forall (@list @t27 @t40) (tptp.subclass @t41 @t22))) % 0.37/0.60 (assume @p36 (forall (@list @t27 @t40 @t2 @t15) (= (tptp.member @t17 @t41) (and @t10 (tptp.member @t15 (tptp.image @t40 (tptp.image @t27 (tptp.singleton @t2)))))))) % 0.37/0.60 (assume @p37 (forall @t36 (= (tptp.member @t20 tptp.identity_relation) (exists @t9 (and @t19 (= @t20 (tptp.ordered_pair @t4 @t4))))))) % 0.37/0.60 (assume @p38 (forall @t44 (= @t43 (and (tptp.subclass @t42 @t22) (tptp.subclass (tptp.compose @t42 (tptp.inverse @t42)) tptp.identity_relation))))) % 0.37/0.60 (assume @p39 (forall (@list @t4 @t42) (=> (and @t19 @t43) (tptp.member (tptp.image @t42 @t4) tptp.universal_class)))) % 0.37/0.60 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 0.37/0.60 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t10 @t5 (tptp.disjoint @t2 @t4)))))) % 0.37/0.60 (assume @p42 (forall (@list @t42 @t1) (= @t45 (tptp.sum_class (tptp.image @t42 @t13))))) % 0.37/0.60 (assume @p43 (exists @t44 (and @t43 (forall @t35 (=> @t18 (or (= @t1 tptp.null_class) (tptp.member @t45 @t1))))))) % 0.37/0.60 (assume @p44 (forall @t35 (=> @t18 (tptp.member @t46 tptp.universal_class)))) % 0.37/0.60 (assume @p45 (forall @t35 (=> @t18 (= (tptp.singleton @t46) @t13)))) % 0.37/0.60 (assume @p46 (forall @t9 (or (tptp.member @t47 tptp.universal_class) @t48))) % 0.37/0.60 (assume @p47 (forall @t9 (or @t50 @t48))) % 0.37/0.60 (assume @p48 @t53) % 0.37/0.60 (assume @p49 true) % 0.37/0.60 (step @p50 :rule evaluate :args ((= false true))) % 0.37/0.60 (step @p51 :rule instantiate :premises (@p5) :args ((@list @t56 @t56))) % 0.37/0.60 (step @p52 :rule true_intro :premises (@p51)) % 0.37/0.60 (step @p53 :rule refl :args (tptp.universal_class)) % 0.37/0.60 (step @p54 :rule instantiate :premises (@p6) :args ((@list @t56))) % 0.37/0.60 (step @p55 :rule bool-impl-elim :args (@t54 @t19)) % 0.37/0.60 (step @p56 :rule cong :premises (@p55) :args ((forall @t9 (=> @t54 @t19)))) % 0.37/0.60 (step @p57 :rule refl :args (@t19)) % 0.37/0.60 (step @p58 :rule eq-symm :args (@t49 @t4)) % 0.37/0.60 (step @p59 :rule cong :premises (@p58 @p57) :args (@t51)) % 0.37/0.60 (step @p60 :rule cong :premises (@p59) :args (@t52)) % 0.37/0.60 (step @p61 :rule trans :premises (@p60 @p56)) % 0.37/0.60 (step @p62 :rule cong :premises (@p61) :args (@t53)) % 0.37/0.60 (step @p63 :rule eq_resolve :premises (@p48 @p62)) % 0.37/0.60 (step @p64 :rule skolemize :premises (@p63)) % 0.37/0.60 (step @p65 :rule bool-double-not-elim :args (@t57)) % 0.37/0.60 (step @p66 :rule refl :args (@t60)) % 0.37/0.60 (step @p67 :rule nary_cong :premises (@p66 @p65) :args ((or @t60 (not @t59)))) % 0.37/0.60 (step @p68 :rule cnf_or_neg :args (@t60 0)) % 0.37/0.60 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.37/0.60 (step @p70 :rule reordering :premises (@p69) :args ((or @t57 @t60))) % 0.37/0.60 (step @p71 :rule chain_m_resolution :premises (@p70 @p64) :args (@t57 @t61 @t62)) % 0.37/0.60 (step @p72 :rule trans :premises (@p71 @p54)) % 0.37/0.60 (step @p73 :rule cong :premises (@p72 @p53) :args (@t58)) % 0.37/0.60 (step @p74 :rule cnf_or_neg :args (@t60 1)) % 0.37/0.60 (step @p75 :rule chain_m_resolution :premises (@p74 @p64) :args ((not @t58) @t61 @t62)) % 0.37/0.60 (step @p76 :rule false_intro :premises (@p75)) % 0.37/0.60 (step @p77 :rule symm :premises (@p76)) % 0.37/0.60 (step @p78 :rule trans :premises (@p77 @p73 @p52)) % 0.37/0.60 (step @p79 false :rule eq_resolve :premises (@p78 @p50)) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------