%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET002+4 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:46:52 AM UTC 2026 % Result : Theorem 0.38s 0.56s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET002+4 : TPTP v9.2.1. Released v2.2.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 14:41:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.56 % SZS status Theorem % 0.38/0.56 % SZS output start Proof % 0.38/0.56 ( % 0.38/0.56 (declare-sort $$unsorted 0) % 0.38/0.56 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.empty_set $$unsorted) % 0.38/0.56 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.38/0.56 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.56 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.56 (define @t1 () (@var "B" $$unsorted)) % 0.38/0.56 (define @t2 () (@var "X" $$unsorted)) % 0.38/0.56 (define @t3 () (tptp.member @t2 @t1)) % 0.38/0.56 (define @t4 () (@var "A" $$unsorted)) % 0.38/0.56 (define @t5 () (tptp.member @t2 @t4)) % 0.38/0.56 (define @t6 () (@list @t2)) % 0.38/0.56 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.38/0.56 (define @t8 () (tptp.subset @t4 @t1)) % 0.38/0.56 (define @t9 () (= @t8 @t7)) % 0.38/0.56 (define @t10 () (@list @t4 @t1)) % 0.38/0.56 (define @t11 () (forall @t10 @t9)) % 0.38/0.56 (define @t12 () (@list @t2 @t4)) % 0.38/0.56 (define @t13 () (@list @t2 @t4 @t1)) % 0.38/0.56 (define @t14 () (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.38/0.56 (define @t15 () (@var "E" $$unsorted)) % 0.38/0.56 (define @t16 () (= @t2 @t4)) % 0.38/0.56 (define @t17 () (@var "Y" $$unsorted)) % 0.38/0.56 (define @t18 () (tptp.member @t2 @t17)) % 0.38/0.56 (define @t19 () (tptp.member @t17 @t4)) % 0.38/0.56 (define @t20 () (@list @t17)) % 0.38/0.56 (define @t21 () (forall (@list @t4) (tptp.equal_set (tptp.union @t4 @t4) @t4))) % 0.38/0.56 (define @t22 () (@quantifiers_skolemize @t21 0)) % 0.38/0.56 (define @t23 () (tptp.union @t22 @t22)) % 0.38/0.56 (define @t24 () (tptp.member @t2 @t23)) % 0.38/0.56 (define @t25 () (tptp.member @t2 @t22)) % 0.38/0.56 (define @t26 () (forall @t6 (or (not @t25) @t24))) % 0.38/0.56 (define @t27 () (@quantifiers_skolemize @t26 0)) % 0.38/0.56 (define @t28 () (tptp.member @t27 @t23)) % 0.38/0.56 (define @t29 () (tptp.member @t27 @t22)) % 0.38/0.56 (define @t30 () (or @t29 @t29)) % 0.38/0.56 (define @t31 () (= @t28 @t30)) % 0.38/0.56 (define @t32 () (= @t29 @t28)) % 0.38/0.56 (define @t33 () (@list false)) % 0.38/0.56 (define @t34 () (@list @t14)) % 0.38/0.56 (define @t35 () (@list @t23 @t22)) % 0.38/0.56 (define @t36 () (forall @t6 (or (not @t24) @t25))) % 0.38/0.56 (define @t37 () (@quantifiers_skolemize @t36 0)) % 0.38/0.56 (define @t38 () (tptp.member @t37 @t23)) % 0.38/0.56 (define @t39 () (tptp.member @t37 @t22)) % 0.38/0.56 (define @t40 () (not @t38)) % 0.38/0.56 (define @t41 () (or @t40 @t39)) % 0.38/0.56 (define @t42 () (or @t39 @t39)) % 0.38/0.56 (define @t43 () (= @t38 @t42)) % 0.38/0.56 (define @t44 () (= @t38 @t39)) % 0.38/0.56 (define @t45 () (not @t41)) % 0.38/0.56 (define @t46 () (not @t36)) % 0.38/0.56 (define @t47 () (tptp.subset @t23 @t22)) % 0.38/0.56 (define @t48 () (= @t47 @t36)) % 0.38/0.56 (define @t49 () (tptp.subset @t22 @t23)) % 0.38/0.56 (define @t50 () (and @t47 @t49)) % 0.38/0.56 (define @t51 () (tptp.equal_set @t23 @t22)) % 0.38/0.56 (define @t52 () (= @t51 @t50)) % 0.38/0.56 (define @t53 () (not @t50)) % 0.38/0.56 (define @t54 () (@list true false)) % 0.38/0.56 (define @t55 () (= @t49 @t26)) % 0.38/0.56 (define @t56 () (not @t26)) % 0.38/0.56 (define @t57 () (not @t29)) % 0.38/0.56 (define @t58 () (or @t57 @t28)) % 0.38/0.56 (define @t59 () (not @t58)) % 0.38/0.56 (define @t60 () (@list true)) % 0.38/0.56 (define @t61 () (@list @t58)) % 0.38/0.56 (assume @p1 @t11) % 0.38/0.56 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.38/0.56 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.38/0.56 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.38/0.56 (assume @p5 @t14) % 0.38/0.56 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.38/0.56 (assume @p7 (forall (@list @t1 @t4 @t15) (= (tptp.member @t1 (tptp.difference @t15 @t4)) (and (tptp.member @t1 @t15) (not (tptp.member @t1 @t4)))))) % 0.38/0.56 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t16))) % 0.38/0.56 (assume @p9 (forall @t13 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t16 (= @t2 @t1))))) % 0.38/0.56 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t20 (and @t19 @t18))))) % 0.38/0.56 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t20 (=> @t19 @t18))))) % 0.38/0.56 (assume @p12 (not @t21)) % 0.38/0.56 (assume @p13 true) % 0.38/0.56 (step @p14 :rule eq-symm :args (@t28 @t29)) % 0.38/0.56 (step @p15 :rule aci_norm :args ((= @t30 @t29))) % 0.38/0.56 (step @p16 :rule refl :args (@t28)) % 0.38/0.56 (step @p17 :rule cong :premises (@p16 @p15) :args (@t31)) % 0.38/0.56 (step @p18 :rule trans :premises (@p17 @p14)) % 0.38/0.56 (step @p19 :rule refl :args (@t14)) % 0.38/0.56 (step @p20 :rule cong :premises (@p19 @p18) :args ((=> @t14 @t31))) % 0.38/0.56 (assume-push @p102 @t14) % 0.38/0.56 (step @p22 :rule instantiate :premises (@p5) :args ((@list @t27 @t22 @t22))) % 0.38/0.56 (step-pop @p103 :rule scope :premises (@p22)) % 0.38/0.56 (step @p23 :rule process_scope :premises (@p103) :args (@t31)) % 0.38/0.56 (step @p25 :rule eq_resolve :premises (@p23 @p20)) % 0.38/0.56 (step @p26 :rule implies_elim :premises (@p25)) % 0.38/0.56 (step @p27 :rule chain_m_resolution :premises (@p26 @p5) :args (@t32 @t33 @t34)) % 0.38/0.56 (step @p28 :rule bool-impl-elim :args (@t5 @t3)) % 0.38/0.56 (step @p29 :rule cong :premises (@p28) :args (@t7)) % 0.38/0.56 (step @p30 :rule refl :args (@t8)) % 0.38/0.56 (step @p31 :rule cong :premises (@p30 @p29) :args (@t9)) % 0.38/0.56 (step @p32 :rule cong :premises (@p31) :args (@t11)) % 0.38/0.56 (step @p33 :rule eq_resolve :premises (@p1 @p32)) % 0.38/0.56 (step @p34 :rule instantiate :premises (@p33) :args ((@list @t22 @t23))) % 0.38/0.56 (step @p35 :rule instantiate :premises (@p33) :args (@t35)) % 0.38/0.56 (step @p36 :rule bool-double-not-elim :args (@t38)) % 0.38/0.56 (step @p37 :rule refl :args (@t41)) % 0.38/0.56 (step @p38 :rule nary_cong :premises (@p37 @p36) :args ((or @t41 (not @t40)))) % 0.38/0.56 (step @p39 :rule cnf_or_neg :args (@t41 0)) % 0.38/0.56 (step @p40 :rule eq_resolve :premises (@p39 @p38)) % 0.38/0.56 (step @p41 :rule reordering :premises (@p40) :args ((or @t38 @t41))) % 0.38/0.56 (step @p42 :rule cnf_or_neg :args (@t41 1)) % 0.38/0.56 (step @p43 :rule aci_norm :args ((= @t42 @t39))) % 0.38/0.56 (step @p44 :rule refl :args (@t38)) % 0.38/0.56 (step @p45 :rule cong :premises (@p44 @p43) :args (@t43)) % 0.38/0.56 (step @p46 :rule cong :premises (@p19 @p45) :args ((=> @t14 @t43))) % 0.38/0.56 (assume-push @p104 @t14) % 0.38/0.56 (step @p48 :rule instantiate :premises (@p5) :args ((@list @t37 @t22 @t22))) % 0.38/0.56 (step-pop @p105 :rule scope :premises (@p48)) % 0.38/0.56 (step @p49 :rule process_scope :premises (@p105) :args (@t43)) % 0.38/0.56 (step @p51 :rule eq_resolve :premises (@p49 @p46)) % 0.38/0.56 (step @p52 :rule implies_elim :premises (@p51)) % 0.38/0.56 (step @p53 :rule chain_m_resolution :premises (@p52 @p5) :args (@t44 @t33 @t34)) % 0.38/0.56 (step @p54 :rule cnf_equiv_pos1 :args (@t44)) % 0.38/0.56 (step @p55 :rule reordering :premises (@p54) :args ((or @t40 @t39 (not @t44)))) % 0.38/0.56 (step @p56 :rule chain_m_resolution :premises (@p55 @p53 @p42 @p41) :args (@t41 (@list false true false) (@list @t44 @t39 @t38))) % 0.38/0.56 (step @p57 :rule refl :args (@t45)) % 0.38/0.56 (step @p58 :rule bool-double-not-elim :args (@t36)) % 0.38/0.56 (step @p59 :rule nary_cong :premises (@p58 @p57) :args ((or (not @t46) @t45))) % 0.38/0.56 (assume-push @p106 @t46) % 0.38/0.56 (step @p61 :rule skolemize :premises (@p106)) % 0.38/0.56 (step-pop @p107 :rule scope :premises (@p61)) % 0.38/0.56 (step @p62 :rule process_scope :premises (@p107) :args (@t45)) % 0.38/0.56 (step @p64 :rule implies_elim :premises (@p62)) % 0.38/0.56 (step @p65 :rule eq_resolve :premises (@p64 @p59)) % 0.38/0.56 (step @p66 :rule chain_m_resolution :premises (@p65 @p56) :args (@t36 @t33 (@list @t41))) % 0.38/0.56 (step @p67 :rule cnf_equiv_pos2 :args (@t48)) % 0.38/0.56 (step @p68 :rule reordering :premises (@p67) :args ((or @t47 @t46 (not @t48)))) % 0.38/0.56 (step @p69 :rule chain_m_resolution :premises (@p68 @p66 @p35) :args (@t47 (@list false false) (@list @t36 @t48))) % 0.38/0.56 (step @p70 :rule instantiate :premises (@p2) :args (@t35)) % 0.38/0.56 (step @p71 :rule skolemize :premises (@p12)) % 0.38/0.56 (step @p72 :rule cnf_equiv_pos2 :args (@t52)) % 0.38/0.56 (step @p73 :rule reordering :premises (@p72) :args ((or @t51 @t53 (not @t52)))) % 0.38/0.56 (step @p74 :rule chain_m_resolution :premises (@p73 @p71 @p70) :args (@t53 @t54 (@list @t51 @t52))) % 0.38/0.56 (step @p75 :rule cnf_and_neg :args (@t50)) % 0.38/0.56 (step @p76 :rule chain_m_resolution :premises (@p75 @p74 @p69) :args ((not @t49) @t54 (@list @t50 @t47))) % 0.38/0.56 (step @p77 :rule cnf_equiv_pos2 :args (@t55)) % 0.38/0.56 (step @p78 :rule reordering :premises (@p77) :args ((or @t49 @t56 (not @t55)))) % 0.38/0.56 (step @p79 :rule chain_m_resolution :premises (@p78 @p76 @p34) :args (@t56 @t54 (@list @t49 @t55))) % 0.38/0.56 (step @p80 :rule refl :args (@t59)) % 0.38/0.56 (step @p81 :rule bool-double-not-elim :args (@t26)) % 0.38/0.56 (step @p82 :rule nary_cong :premises (@p81 @p80) :args ((or (not @t56) @t59))) % 0.38/0.56 (assume-push @p108 @t56) % 0.38/0.56 (step @p84 :rule skolemize :premises (@p108)) % 0.38/0.56 (step-pop @p109 :rule scope :premises (@p84)) % 0.38/0.56 (step @p85 :rule process_scope :premises (@p109) :args (@t59)) % 0.38/0.56 (step @p87 :rule implies_elim :premises (@p85)) % 0.38/0.56 (step @p88 :rule eq_resolve :premises (@p87 @p82)) % 0.38/0.56 (step @p89 :rule chain_m_resolution :premises (@p88 @p79) :args (@t59 @t60 (@list @t26))) % 0.38/0.56 (step @p90 :rule bool-double-not-elim :args (@t29)) % 0.38/0.56 (step @p91 :rule refl :args (@t58)) % 0.38/0.56 (step @p92 :rule nary_cong :premises (@p91 @p90) :args ((or @t58 (not @t57)))) % 0.38/0.56 (step @p93 :rule cnf_or_neg :args (@t58 0)) % 0.38/0.56 (step @p94 :rule eq_resolve :premises (@p93 @p92)) % 0.38/0.56 (step @p95 :rule reordering :premises (@p94) :args ((or @t29 @t58))) % 0.38/0.56 (step @p96 :rule chain_m_resolution :premises (@p95 @p89) :args (@t29 @t60 @t61)) % 0.38/0.56 (step @p97 :rule cnf_or_neg :args (@t58 1)) % 0.38/0.56 (step @p98 :rule chain_m_resolution :premises (@p97 @p89) :args ((not @t28) @t60 @t61)) % 0.38/0.56 (step @p99 :rule cnf_equiv_pos1 :args (@t32)) % 0.38/0.56 (step @p100 :rule reordering :premises (@p99) :args ((or @t57 @t28 (not @t32)))) % 0.38/0.56 (step @p101 false :rule chain_m_resolution :premises (@p100 @p98 @p96 @p27) :args (false (@list true false false) (@list @t28 @t29 @t32))) % 0.38/0.56 ) % 0.38/0.56 % SZS output end Proof % 0.38/0.56 % cvc5 exiting %------------------------------------------------------------------------------