%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET347+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 : n022.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 08:47:49 AM UTC 2026 % Result : Theorem 0.36s 0.59s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : SET347+4 : TPTP v9.2.1. Released v2.2.0. % 0.09/0.15 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.36 % Computer : n022.cluster.edu % 0.17/0.36 % Model : x86_64 x86_64 % 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.36 % Memory : 8042.1875MB % 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.36 % CPULimit : 300 % 0.17/0.36 % WCLimit : 300 % 0.17/0.36 % DateTime : Tue Jun 2 15:29:08 EDT 2026 % 0.17/0.37 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.59 % SZS status Theorem % 0.36/0.59 % SZS output start Proof % 0.36/0.59 ( % 0.36/0.59 (declare-sort $$unsorted 0) % 0.36/0.59 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.empty_set $$unsorted) % 0.36/0.59 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (define @t1 () (@var "B" $$unsorted)) % 0.36/0.59 (define @t2 () (@var "X" $$unsorted)) % 0.36/0.59 (define @t3 () (tptp.member @t2 @t1)) % 0.36/0.59 (define @t4 () (@var "A" $$unsorted)) % 0.36/0.59 (define @t5 () (tptp.member @t2 @t4)) % 0.36/0.59 (define @t6 () (@list @t2)) % 0.36/0.59 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.36/0.59 (define @t8 () (tptp.subset @t4 @t1)) % 0.36/0.59 (define @t9 () (= @t8 @t7)) % 0.36/0.59 (define @t10 () (@list @t4 @t1)) % 0.36/0.59 (define @t11 () (forall @t10 @t9)) % 0.36/0.59 (define @t12 () (@list @t2 @t4)) % 0.36/0.59 (define @t13 () (@list @t2 @t4 @t1)) % 0.36/0.59 (define @t14 () (tptp.member @t2 tptp.empty_set)) % 0.36/0.59 (define @t15 () (not @t14)) % 0.36/0.59 (define @t16 () (forall @t6 @t15)) % 0.36/0.59 (define @t17 () (@var "E" $$unsorted)) % 0.36/0.59 (define @t18 () (= @t2 @t4)) % 0.36/0.59 (define @t19 () (@var "Y" $$unsorted)) % 0.36/0.59 (define @t20 () (tptp.member @t2 @t19)) % 0.36/0.59 (define @t21 () (tptp.member @t19 @t4)) % 0.36/0.59 (define @t22 () (and @t21 @t20)) % 0.36/0.59 (define @t23 () (@list @t19)) % 0.36/0.59 (define @t24 () (exists @t23 @t22)) % 0.36/0.59 (define @t25 () (tptp.member @t2 (tptp.sum @t4))) % 0.36/0.59 (define @t26 () (= @t25 @t24)) % 0.36/0.59 (define @t27 () (forall @t12 @t26)) % 0.36/0.59 (define @t28 () (tptp.sum tptp.empty_set)) % 0.36/0.59 (define @t29 () (tptp.equal_set @t28 tptp.empty_set)) % 0.36/0.59 (define @t30 () (forall @t23 (not @t22))) % 0.36/0.59 (define @t31 () (not @t30)) % 0.36/0.60 (define @t32 () (tptp.member @t2 @t28)) % 0.36/0.60 (define @t33 () (forall @t6 (or (not @t32) @t14))) % 0.36/0.60 (define @t34 () (@quantifiers_skolemize @t33 0)) % 0.36/0.60 (define @t35 () (@list @t28 tptp.empty_set)) % 0.36/0.60 (define @t36 () (forall @t6 (or @t15 @t32))) % 0.36/0.60 (define @t37 () (@quantifiers_skolemize @t36 0)) % 0.36/0.60 (define @t38 () (tptp.member @t37 tptp.empty_set)) % 0.36/0.60 (define @t39 () (not @t38)) % 0.36/0.60 (define @t40 () (or @t39 (tptp.member @t37 @t28))) % 0.36/0.60 (define @t41 () (@list true)) % 0.36/0.60 (define @t42 () (not @t40)) % 0.36/0.60 (define @t43 () (not @t36)) % 0.36/0.60 (define @t44 () (tptp.subset tptp.empty_set @t28)) % 0.36/0.60 (define @t45 () (= @t44 @t36)) % 0.36/0.60 (define @t46 () (@list false false)) % 0.36/0.60 (define @t47 () (tptp.subset @t28 tptp.empty_set)) % 0.36/0.60 (define @t48 () (and @t47 @t44)) % 0.36/0.60 (define @t49 () (= @t29 @t48)) % 0.36/0.60 (define @t50 () (not @t48)) % 0.36/0.60 (define @t51 () (@list true false)) % 0.36/0.60 (define @t52 () (= @t47 @t33)) % 0.36/0.60 (define @t53 () (not @t33)) % 0.36/0.60 (define @t54 () (tptp.member @t34 @t28)) % 0.36/0.60 (define @t55 () (not @t54)) % 0.36/0.60 (define @t56 () (or @t55 (tptp.member @t34 tptp.empty_set))) % 0.36/0.60 (define @t57 () (not @t56)) % 0.36/0.60 (define @t58 () (forall @t23 (or (not (tptp.member @t19 tptp.empty_set)) (not (tptp.member @t34 @t19))))) % 0.36/0.60 (define @t59 () (not @t58)) % 0.36/0.60 (define @t60 () (= @t54 @t59)) % 0.36/0.60 (define @t61 () (@quantifiers_skolemize @t58 0)) % 0.36/0.60 (define @t62 () (tptp.member @t61 tptp.empty_set)) % 0.36/0.60 (define @t63 () (not @t62)) % 0.36/0.60 (define @t64 () (or @t63 (not (tptp.member @t34 @t61)))) % 0.36/0.60 (define @t65 () (not @t64)) % 0.36/0.60 (assume @p1 @t11) % 0.36/0.60 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.36/0.60 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.36/0.60 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.36/0.60 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.36/0.60 (assume @p6 @t16) % 0.36/0.60 (assume @p7 (forall (@list @t1 @t4 @t17) (= (tptp.member @t1 (tptp.difference @t17 @t4)) (and (tptp.member @t1 @t17) (not (tptp.member @t1 @t4)))))) % 0.36/0.60 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t18))) % 0.36/0.60 (assume @p9 (forall @t13 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t18 (= @t2 @t1))))) % 0.36/0.60 (assume @p10 @t27) % 0.36/0.60 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t23 (=> @t21 @t20))))) % 0.36/0.60 (assume @p12 (not @t29)) % 0.36/0.60 (assume @p13 true) % 0.36/0.60 (step @p14 :rule bool-and-de-morgan :args (@t21 @t20 true)) % 0.36/0.60 (step @p15 :rule cong :premises (@p14) :args (@t30)) % 0.36/0.60 (step @p16 :rule cong :premises (@p15) :args (@t31)) % 0.36/0.60 (step @p17 :rule exists-elim :args ((= @t24 @t31))) % 0.36/0.60 (step @p18 :rule trans :premises (@p17 @p16)) % 0.36/0.60 (step @p19 :rule refl :args (@t25)) % 0.36/0.60 (step @p20 :rule cong :premises (@p19 @p18) :args (@t26)) % 0.36/0.60 (step @p21 :rule cong :premises (@p20) :args (@t27)) % 0.36/0.60 (step @p22 :rule eq_resolve :premises (@p10 @p21)) % 0.36/0.60 (step @p23 :rule instantiate :premises (@p22) :args ((@list @t34 tptp.empty_set))) % 0.36/0.60 (step @p24 :rule bool-impl-elim :args (@t5 @t3)) % 0.36/0.60 (step @p25 :rule cong :premises (@p24) :args (@t7)) % 0.36/0.60 (step @p26 :rule refl :args (@t8)) % 0.36/0.60 (step @p27 :rule cong :premises (@p26 @p25) :args (@t9)) % 0.36/0.60 (step @p28 :rule cong :premises (@p27) :args (@t11)) % 0.36/0.60 (step @p29 :rule eq_resolve :premises (@p1 @p28)) % 0.36/0.60 (step @p30 :rule instantiate :premises (@p29) :args (@t35)) % 0.36/0.60 (step @p31 :rule instantiate :premises (@p29) :args ((@list tptp.empty_set @t28))) % 0.36/0.60 (step @p32 :rule instantiate :premises (@p6) :args ((@list @t37))) % 0.36/0.60 (step @p33 :rule bool-double-not-elim :args (@t38)) % 0.36/0.60 (step @p34 :rule refl :args (@t40)) % 0.36/0.60 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or @t40 (not @t39)))) % 0.36/0.60 (step @p36 :rule cnf_or_neg :args (@t40 0)) % 0.36/0.60 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.36/0.60 (step @p38 :rule reordering :premises (@p37) :args ((or @t38 @t40))) % 0.36/0.60 (step @p39 :rule chain_m_resolution :premises (@p38 @p32) :args (@t40 @t41 (@list @t38))) % 0.36/0.60 (step @p40 :rule refl :args (@t42)) % 0.36/0.60 (step @p41 :rule bool-double-not-elim :args (@t36)) % 0.36/0.60 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or (not @t43) @t42))) % 0.36/0.60 (assume-push @p105 @t43) % 0.36/0.60 (step @p44 :rule skolemize :premises (@p105)) % 0.36/0.60 (step-pop @p106 :rule scope :premises (@p44)) % 0.36/0.60 (step @p45 :rule process_scope :premises (@p106) :args (@t42)) % 0.36/0.60 (step @p47 :rule implies_elim :premises (@p45)) % 0.36/0.60 (step @p48 :rule eq_resolve :premises (@p47 @p42)) % 0.36/0.60 (step @p49 :rule chain_m_resolution :premises (@p48 @p39) :args (@t36 (@list false) (@list @t40))) % 0.36/0.60 (step @p50 :rule cnf_equiv_pos2 :args (@t45)) % 0.36/0.60 (step @p51 :rule reordering :premises (@p50) :args ((or @t44 @t43 (not @t45)))) % 0.36/0.60 (step @p52 :rule chain_m_resolution :premises (@p51 @p49 @p31) :args (@t44 @t46 (@list @t36 @t45))) % 0.36/0.60 (step @p53 :rule instantiate :premises (@p2) :args (@t35)) % 0.36/0.60 (step @p54 :rule cnf_equiv_pos2 :args (@t49)) % 0.36/0.60 (step @p55 :rule reordering :premises (@p54) :args ((or @t29 @t50 (not @t49)))) % 0.36/0.60 (step @p56 :rule chain_m_resolution :premises (@p55 @p12 @p53) :args (@t50 @t51 (@list @t29 @t49))) % 0.36/0.60 (step @p57 :rule cnf_and_neg :args (@t48)) % 0.36/0.60 (step @p58 :rule chain_m_resolution :premises (@p57 @p56 @p52) :args ((not @t47) @t51 (@list @t48 @t44))) % 0.36/0.60 (step @p59 :rule cnf_equiv_pos2 :args (@t52)) % 0.36/0.60 (step @p60 :rule reordering :premises (@p59) :args ((or @t47 @t53 (not @t52)))) % 0.36/0.60 (step @p61 :rule chain_m_resolution :premises (@p60 @p58 @p30) :args (@t53 @t51 (@list @t47 @t52))) % 0.36/0.60 (step @p62 :rule refl :args (@t57)) % 0.36/0.60 (step @p63 :rule bool-double-not-elim :args (@t33)) % 0.36/0.60 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or (not @t53) @t57))) % 0.36/0.60 (assume-push @p107 @t53) % 0.36/0.60 (step @p66 :rule skolemize :premises (@p107)) % 0.36/0.60 (step-pop @p108 :rule scope :premises (@p66)) % 0.36/0.60 (step @p67 :rule process_scope :premises (@p108) :args (@t57)) % 0.36/0.60 (step @p69 :rule implies_elim :premises (@p67)) % 0.36/0.60 (step @p70 :rule eq_resolve :premises (@p69 @p64)) % 0.36/0.60 (step @p71 :rule chain_m_resolution :premises (@p70 @p61) :args (@t57 @t41 (@list @t33))) % 0.36/0.60 (step @p72 :rule bool-double-not-elim :args (@t54)) % 0.36/0.60 (step @p73 :rule refl :args (@t56)) % 0.36/0.60 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t56 (not @t55)))) % 0.36/0.60 (step @p75 :rule cnf_or_neg :args (@t56 0)) % 0.36/0.60 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.36/0.60 (step @p77 :rule reordering :premises (@p76) :args ((or @t54 @t56))) % 0.36/0.60 (step @p78 :rule chain_m_resolution :premises (@p77 @p71) :args (@t54 @t41 (@list @t56))) % 0.36/0.60 (step @p79 :rule cnf_equiv_pos1 :args (@t60)) % 0.36/0.60 (step @p80 :rule reordering :premises (@p79) :args ((or @t55 @t59 (not @t60)))) % 0.36/0.60 (step @p81 :rule chain_m_resolution :premises (@p80 @p78 @p23) :args (@t59 @t46 (@list @t54 @t60))) % 0.36/0.60 (step @p82 :rule refl :args (@t65)) % 0.36/0.60 (step @p83 :rule bool-double-not-elim :args (@t58)) % 0.36/0.60 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or (not @t59) @t65))) % 0.36/0.60 (assume-push @p109 @t59) % 0.36/0.60 (step @p86 :rule skolemize :premises (@p109)) % 0.36/0.60 (step-pop @p110 :rule scope :premises (@p86)) % 0.36/0.60 (step @p87 :rule process_scope :premises (@p110) :args (@t65)) % 0.36/0.60 (step @p89 :rule implies_elim :premises (@p87)) % 0.36/0.60 (step @p90 :rule eq_resolve :premises (@p89 @p84)) % 0.36/0.60 (step @p91 :rule chain_m_resolution :premises (@p90 @p81) :args (@t65 @t41 (@list @t58))) % 0.36/0.60 (step @p92 :rule bool-double-not-elim :args (@t62)) % 0.36/0.60 (step @p93 :rule refl :args (@t64)) % 0.36/0.60 (step @p94 :rule nary_cong :premises (@p93 @p92) :args ((or @t64 (not @t63)))) % 0.36/0.60 (step @p95 :rule cnf_or_neg :args (@t64 0)) % 0.36/0.60 (step @p96 :rule eq_resolve :premises (@p95 @p94)) % 0.36/0.60 (step @p97 :rule reordering :premises (@p96) :args ((or @t62 @t64))) % 0.36/0.60 (step @p98 :rule chain_m_resolution :premises (@p97 @p91) :args (@t62 @t41 (@list @t64))) % 0.36/0.60 (assume-push @p111 @t16) % 0.36/0.60 (step @p100 :rule instantiate :premises (@p6) :args ((@list @t61))) % 0.36/0.60 (step-pop @p112 :rule scope :premises (@p100)) % 0.36/0.60 (step @p101 :rule process_scope :premises (@p112) :args (@t63)) % 0.36/0.60 (step @p103 :rule implies_elim :premises (@p101)) % 0.36/0.60 (step @p104 false :rule chain_m_resolution :premises (@p103 @p98 @p6) :args (false @t46 (@list @t62 @t16))) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.60 % cvc5 exiting %------------------------------------------------------------------------------