%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET813+4 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 08:48:42 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET813+4 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 16:13:07 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.strict_order (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.on $$unsorted) % 0.37/0.57 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.set (-> $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.suc (-> $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.initial_segment (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.empty_set $$unsorted) % 0.37/0.57 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.least (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.strict_well_order (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.member_predicate $$unsorted) % 0.37/0.57 (define @t1 () (@var "B" $$unsorted)) % 0.37/0.57 (define @t2 () (@var "X" $$unsorted)) % 0.37/0.57 (define @t3 () (tptp.member @t2 @t1)) % 0.37/0.57 (define @t4 () (@var "A" $$unsorted)) % 0.37/0.57 (define @t5 () (tptp.member @t2 @t4)) % 0.37/0.57 (define @t6 () (@list @t2)) % 0.37/0.57 (define @t7 () (tptp.subset @t4 @t1)) % 0.37/0.57 (define @t8 () (@list @t4 @t1)) % 0.37/0.57 (define @t9 () (tptp.subset @t2 @t4)) % 0.37/0.57 (define @t10 () (@list @t2 @t4)) % 0.37/0.57 (define @t11 () (@list @t2 @t4 @t1)) % 0.37/0.57 (define @t12 () (@var "E" $$unsorted)) % 0.37/0.57 (define @t13 () (= @t2 @t4)) % 0.37/0.57 (define @t14 () (tptp.singleton @t4)) % 0.37/0.57 (define @t15 () (tptp.member @t2 @t14)) % 0.37/0.57 (define @t16 () (= @t15 @t13)) % 0.37/0.57 (define @t17 () (forall @t10 @t16)) % 0.37/0.57 (define @t18 () (@var "Y" $$unsorted)) % 0.37/0.57 (define @t19 () (tptp.member @t2 @t18)) % 0.37/0.57 (define @t20 () (tptp.member @t18 @t4)) % 0.37/0.57 (define @t21 () (@list @t18)) % 0.37/0.57 (define @t22 () (tptp.member @t4 tptp.on)) % 0.37/0.57 (define @t23 () (@list @t4)) % 0.37/0.57 (define @t24 () (@var "R" $$unsorted)) % 0.37/0.57 (define @t25 () (tptp.strict_order @t24 @t12)) % 0.37/0.57 (define @t26 () (@list @t24 @t12)) % 0.37/0.57 (define @t27 () (@var "M" $$unsorted)) % 0.37/0.57 (define @t28 () (tptp.member @t2 @t12)) % 0.37/0.57 (define @t29 () (@list @t2 @t18)) % 0.37/0.57 (define @t30 () (@var "Z" $$unsorted)) % 0.37/0.57 (define @t31 () (tptp.apply @t24 @t2 @t18)) % 0.37/0.57 (define @t32 () (tptp.member @t18 @t12)) % 0.37/0.57 (define @t33 () (tptp.apply @t24 @t18 @t2)) % 0.37/0.57 (define @t34 () (tptp.suc @t4)) % 0.37/0.57 (define @t35 () (tptp.member @t4 @t34)) % 0.37/0.57 (define @t36 () (forall @t23 (=> @t22 @t35))) % 0.37/0.57 (define @t37 () (not @t36)) % 0.37/0.57 (define @t38 () (@quantifiers_skolemize (forall @t23 (or (not @t22) @t35)) 0)) % 0.37/0.57 (define @t39 () (tptp.singleton @t38)) % 0.37/0.57 (define @t40 () (@list @t38 @t38)) % 0.37/0.57 (define @t41 () (tptp.member @t38 (tptp.suc @t38))) % 0.37/0.57 (define @t42 () (or (not (tptp.member @t38 tptp.on)) @t41)) % 0.37/0.57 (define @t43 () (@list true)) % 0.37/0.57 (define @t44 () (tptp.member @t38 (tptp.union @t38 @t39))) % 0.37/0.57 (define @t45 () (= @t41 @t44)) % 0.37/0.57 (define @t46 () (not @t44)) % 0.37/0.57 (define @t47 () (@list true false)) % 0.37/0.57 (define @t48 () (tptp.member @t38 @t39)) % 0.37/0.57 (define @t49 () (or (tptp.member @t38 @t38) @t48)) % 0.37/0.57 (define @t50 () (= @t44 @t49)) % 0.37/0.57 (define @t51 () (not @t49)) % 0.37/0.57 (define @t52 () (= @t48 (= @t38 @t38))) % 0.37/0.57 (define @t53 () (forall @t10 (= @t15 (= @t4 @t2)))) % 0.37/0.57 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.37/0.57 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.37/0.57 (assume @p3 (forall @t10 (= (tptp.member @t2 (tptp.power_set @t4)) @t9))) % 0.37/0.57 (assume @p4 (forall @t11 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.37/0.57 (assume @p5 (forall @t11 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.37/0.57 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.37/0.57 (assume @p7 (forall (@list @t1 @t4 @t12) (= (tptp.member @t1 (tptp.difference @t12 @t4)) (and (tptp.member @t1 @t12) (not (tptp.member @t1 @t4)))))) % 0.37/0.57 (assume @p8 @t17) % 0.37/0.57 (assume @p9 (forall @t11 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t13 (= @t2 @t1))))) % 0.37/0.57 (assume @p10 (forall @t10 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t21 (and @t20 @t19))))) % 0.37/0.57 (assume @p11 (forall @t10 (= (tptp.member @t2 (tptp.product @t4)) (forall @t21 (=> @t20 @t19))))) % 0.37/0.57 (assume @p12 (forall @t23 (= @t22 (and (tptp.set @t4) (tptp.strict_well_order tptp.member_predicate @t4) (forall @t6 (=> @t5 @t9)))))) % 0.37/0.57 (assume @p13 (forall @t26 (= (tptp.strict_well_order @t24 @t12) (and @t25 (forall @t23 (=> (and (tptp.subset @t4 @t12) (exists @t6 @t5)) (exists @t21 (tptp.least @t18 @t24 @t4)))))))) % 0.37/0.57 (assume @p14 (forall (@list @t24 @t12 @t27) (= (tptp.least @t27 @t24 @t12) (and (tptp.member @t27 @t12) (forall @t6 (=> @t28 (or (= @t27 @t2) (tptp.apply @t24 @t27 @t2)))))))) % 0.37/0.57 (assume @p15 (forall @t29 (= (tptp.apply tptp.member_predicate @t2 @t18) @t19))) % 0.37/0.57 (assume @p16 (forall @t26 (= @t25 (and (forall @t29 (=> (and @t28 @t32) (not (and @t31 @t33)))) (forall (@list @t2 @t18 @t30) (=> (and @t28 @t32 (tptp.member @t30 @t12)) (=> (and @t31 (tptp.apply @t24 @t18 @t30)) (tptp.apply @t24 @t2 @t30)))))))) % 0.37/0.57 (assume @p17 (forall @t6 (=> (tptp.set @t2) (forall @t21 (=> (tptp.member @t18 @t2) (tptp.set @t18)))))) % 0.37/0.57 (assume @p18 (forall (@list @t2 @t24 @t4 @t18) (= (tptp.member @t18 (tptp.initial_segment @t2 @t24 @t4)) (and @t20 @t33)))) % 0.37/0.57 (assume @p19 (forall (@list @t4 @t2) (= (tptp.member @t2 @t34) (tptp.member @t2 (tptp.union @t4 @t14))))) % 0.37/0.57 (assume @p20 @t37) % 0.37/0.57 (assume @p21 true) % 0.37/0.57 (step @p22 :rule eq-symm :args (@t2 @t4)) % 0.37/0.57 (step @p23 :rule refl :args (@t15)) % 0.37/0.57 (step @p24 :rule cong :premises (@p23 @p22) :args (@t16)) % 0.37/0.57 (step @p25 :rule cong :premises (@p24) :args (@t17)) % 0.37/0.57 (step @p26 :rule eq_resolve :premises (@p8 @p25)) % 0.37/0.57 (step @p27 :rule instantiate :premises (@p5) :args ((@list @t38 @t38 @t39))) % 0.37/0.57 (step @p28 :rule instantiate :premises (@p19) :args (@t40)) % 0.37/0.57 (step @p29 :rule bool-impl-elim :args (@t22 @t35)) % 0.37/0.57 (step @p30 :rule cong :premises (@p29) :args (@t36)) % 0.37/0.57 (step @p31 :rule cong :premises (@p30) :args (@t37)) % 0.37/0.57 (step @p32 :rule eq_resolve :premises (@p20 @p31)) % 0.37/0.57 (step @p33 :rule skolemize :premises (@p32)) % 0.37/0.57 (step @p34 :rule cnf_or_neg :args (@t42 1)) % 0.37/0.57 (step @p35 :rule chain_m_resolution :premises (@p34 @p33) :args ((not @t41) @t43 (@list @t42))) % 0.37/0.57 (step @p36 :rule cnf_equiv_pos2 :args (@t45)) % 0.37/0.57 (step @p37 :rule reordering :premises (@p36) :args ((or @t41 @t46 (not @t45)))) % 0.37/0.57 (step @p38 :rule chain_m_resolution :premises (@p37 @p35 @p28) :args (@t46 @t47 (@list @t41 @t45))) % 0.37/0.57 (step @p39 :rule cnf_equiv_pos2 :args (@t50)) % 0.37/0.57 (step @p40 :rule reordering :premises (@p39) :args ((or @t44 @t51 (not @t50)))) % 0.37/0.57 (step @p41 :rule chain_m_resolution :premises (@p40 @p38 @p27) :args (@t51 @t47 (@list @t44 @t50))) % 0.37/0.57 (step @p42 :rule cnf_or_neg :args (@t49 1)) % 0.37/0.57 (step @p43 :rule chain_m_resolution :premises (@p42 @p41) :args ((not @t48) @t43 (@list @t49))) % 0.37/0.57 (step @p44 :rule bool-eq-true :args (@t48)) % 0.37/0.57 (step @p45 :rule eq-refl :args (@t38)) % 0.37/0.57 (step @p46 :rule refl :args (@t48)) % 0.37/0.57 (step @p47 :rule cong :premises (@p46 @p45) :args (@t52)) % 0.37/0.57 (step @p48 :rule trans :premises (@p47 @p44)) % 0.37/0.57 (step @p49 :rule refl :args (@t53)) % 0.37/0.57 (step @p50 :rule cong :premises (@p49 @p48) :args ((=> @t53 @t52))) % 0.37/0.57 (assume-push @p58 @t53) % 0.37/0.57 (step @p52 :rule instantiate :premises (@p26) :args (@t40)) % 0.37/0.57 (step-pop @p59 :rule scope :premises (@p52)) % 0.37/0.57 (step @p53 :rule process_scope :premises (@p59) :args (@t52)) % 0.37/0.57 (step @p55 :rule eq_resolve :premises (@p53 @p50)) % 0.37/0.57 (step @p56 :rule implies_elim :premises (@p55)) % 0.37/0.57 (step @p57 false :rule chain_m_resolution :premises (@p56 @p43 @p26) :args (false @t47 (@list @t48 @t53))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------