%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET689+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 : n002.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 08:48:26 AM UTC 2026 % Result : Theorem 0.39s 0.57s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET689+4 : TPTP v9.2.1. Released v2.2.0. % 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 : n002.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 16:07:18 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.57 % SZS status Theorem % 0.39/0.57 % SZS output start Proof % 0.39/0.57 ( % 0.39/0.57 (declare-sort $$unsorted 0) % 0.39/0.57 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.empty_set $$unsorted) % 0.39/0.57 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.39/0.57 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.39/0.57 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.39/0.57 (define @t1 () (@var "B" $$unsorted)) % 0.39/0.57 (define @t2 () (@var "X" $$unsorted)) % 0.39/0.57 (define @t3 () (tptp.member @t2 @t1)) % 0.39/0.57 (define @t4 () (@var "A" $$unsorted)) % 0.39/0.57 (define @t5 () (tptp.member @t2 @t4)) % 0.39/0.57 (define @t6 () (@list @t2)) % 0.39/0.57 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.39/0.57 (define @t8 () (tptp.subset @t4 @t1)) % 0.39/0.57 (define @t9 () (= @t8 @t7)) % 0.39/0.57 (define @t10 () (@list @t4 @t1)) % 0.39/0.57 (define @t11 () (forall @t10 @t9)) % 0.39/0.57 (define @t12 () (@list @t2 @t4)) % 0.39/0.57 (define @t13 () (@list @t2 @t4 @t1)) % 0.39/0.57 (define @t14 () (@var "E" $$unsorted)) % 0.39/0.57 (define @t15 () (= @t2 @t4)) % 0.39/0.57 (define @t16 () (@var "Y" $$unsorted)) % 0.39/0.57 (define @t17 () (tptp.member @t2 @t16)) % 0.39/0.57 (define @t18 () (tptp.member @t16 @t4)) % 0.39/0.57 (define @t19 () (@list @t16)) % 0.39/0.57 (define @t20 () (@var "C" $$unsorted)) % 0.39/0.57 (define @t21 () (tptp.equal_set @t4 @t20)) % 0.39/0.57 (define @t22 () (tptp.subset @t20 @t4)) % 0.39/0.57 (define @t23 () (tptp.subset @t1 @t20)) % 0.39/0.57 (define @t24 () (and @t8 @t23 @t22)) % 0.39/0.57 (define @t25 () (@list @t4 @t1 @t20)) % 0.39/0.57 (define @t26 () (forall @t25 (=> @t24 @t21))) % 0.39/0.57 (define @t27 () (not @t26)) % 0.39/0.57 (define @t28 () (not @t22)) % 0.39/0.57 (define @t29 () (not @t23)) % 0.39/0.57 (define @t30 () (not @t8)) % 0.39/0.57 (define @t31 () (or @t30 @t29 @t28 @t21)) % 0.39/0.57 (define @t32 () (forall @t25 @t31)) % 0.39/0.57 (define @t33 () (@quantifiers_skolemize @t32 2)) % 0.39/0.57 (define @t34 () (@quantifiers_skolemize @t32 0)) % 0.39/0.57 (define @t35 () (@list @t34 @t33)) % 0.39/0.57 (define @t36 () (or @t30 @t29 @t28)) % 0.39/0.57 (define @t37 () (tptp.equal_set @t34 @t33)) % 0.39/0.57 (define @t38 () (tptp.subset @t33 @t34)) % 0.39/0.57 (define @t39 () (not @t38)) % 0.39/0.57 (define @t40 () (@quantifiers_skolemize @t32 1)) % 0.39/0.57 (define @t41 () (tptp.subset @t40 @t33)) % 0.39/0.57 (define @t42 () (not @t41)) % 0.39/0.57 (define @t43 () (tptp.subset @t34 @t40)) % 0.39/0.57 (define @t44 () (not @t43)) % 0.39/0.57 (define @t45 () (or @t44 @t42 @t39 @t37)) % 0.39/0.57 (define @t46 () (@list true)) % 0.39/0.57 (define @t47 () (@list @t45)) % 0.39/0.57 (define @t48 () (tptp.subset @t34 @t33)) % 0.39/0.57 (define @t49 () (and @t48 @t38)) % 0.39/0.57 (define @t50 () (= @t37 @t49)) % 0.39/0.57 (define @t51 () (not @t49)) % 0.39/0.57 (define @t52 () (@list true false)) % 0.39/0.57 (define @t53 () (not @t48)) % 0.39/0.57 (define @t54 () (tptp.member @t2 @t33)) % 0.39/0.57 (define @t55 () (not (tptp.member @t2 @t34))) % 0.39/0.57 (define @t56 () (forall @t6 (or @t55 @t54))) % 0.39/0.57 (define @t57 () (= @t48 @t56)) % 0.39/0.57 (define @t58 () (not @t56)) % 0.39/0.57 (define @t59 () (@quantifiers_skolemize @t56 0)) % 0.39/0.57 (define @t60 () (tptp.member @t59 @t33)) % 0.39/0.57 (define @t61 () (tptp.member @t59 @t34)) % 0.39/0.57 (define @t62 () (not @t61)) % 0.39/0.57 (define @t63 () (or @t62 @t60)) % 0.39/0.57 (define @t64 () (@list @t63)) % 0.39/0.57 (define @t65 () (tptp.member @t2 @t40)) % 0.39/0.57 (define @t66 () (forall @t6 (or (not @t65) @t54))) % 0.39/0.57 (define @t67 () (= @t41 @t66)) % 0.39/0.57 (define @t68 () (@list false false)) % 0.39/0.57 (define @t69 () (@list @t59)) % 0.39/0.57 (define @t70 () (forall @t6 (or @t55 @t65))) % 0.39/0.57 (define @t71 () (= @t43 @t70)) % 0.39/0.57 (define @t72 () (tptp.member @t59 @t40)) % 0.39/0.57 (define @t73 () (or @t62 @t72)) % 0.39/0.57 (define @t74 () (not @t72)) % 0.39/0.57 (define @t75 () (or @t74 @t60)) % 0.39/0.57 (assume @p1 @t11) % 0.39/0.57 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.39/0.57 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.39/0.57 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.39/0.57 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.39/0.57 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.39/0.57 (assume @p7 (forall (@list @t1 @t4 @t14) (= (tptp.member @t1 (tptp.difference @t14 @t4)) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.39/0.57 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t15))) % 0.39/0.57 (assume @p9 (forall @t13 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t15 (= @t2 @t1))))) % 0.39/0.57 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t19 (and @t18 @t17))))) % 0.39/0.57 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t19 (=> @t18 @t17))))) % 0.39/0.57 (assume @p12 @t27) % 0.39/0.57 (assume @p13 true) % 0.39/0.57 (step @p14 :rule bool-impl-elim :args (@t5 @t3)) % 0.39/0.57 (step @p15 :rule cong :premises (@p14) :args (@t7)) % 0.39/0.57 (step @p16 :rule refl :args (@t8)) % 0.39/0.57 (step @p17 :rule cong :premises (@p16 @p15) :args (@t9)) % 0.39/0.57 (step @p18 :rule cong :premises (@p17) :args (@t11)) % 0.39/0.57 (step @p19 :rule eq_resolve :premises (@p1 @p18)) % 0.39/0.57 (step @p20 :rule instantiate :premises (@p19) :args (@t35)) % 0.39/0.57 (step @p21 :rule instantiate :premises (@p2) :args (@t35)) % 0.39/0.57 (step @p22 :rule aci_norm :args ((= (or @t36 @t21) @t31))) % 0.39/0.57 (step @p23 :rule refl :args (@t21)) % 0.39/0.57 (step @p24 :rule aci_norm :args ((= (or @t30 (or @t29 @t28)) @t36))) % 0.39/0.57 (step @p25 :rule bool-and-de-morgan :args (@t23 @t22 true)) % 0.39/0.57 (step @p26 :rule refl :args (@t30)) % 0.39/0.57 (step @p27 :rule nary_cong :premises (@p26 @p25) :args ((or @t30 (not (and @t23 @t22))))) % 0.39/0.57 (step @p28 :rule bool-and-de-morgan :args (@t8 @t23 (and @t22))) % 0.39/0.57 (step @p29 :rule trans :premises (@p28 @p27)) % 0.39/0.57 (step @p30 :rule trans :premises (@p29 @p24)) % 0.39/0.57 (step @p31 :rule nary_cong :premises (@p30 @p23) :args ((or (not @t24) @t21))) % 0.39/0.57 (step @p32 :rule trans :premises (@p31 @p22)) % 0.39/0.57 (step @p33 :rule bool-impl-elim :args (@t24 @t21)) % 0.39/0.57 (step @p34 :rule trans :premises (@p33 @p32)) % 0.39/0.57 (step @p35 :rule cong :premises (@p34) :args (@t26)) % 0.39/0.57 (step @p36 :rule cong :premises (@p35) :args (@t27)) % 0.39/0.57 (step @p37 :rule eq_resolve :premises (@p12 @p36)) % 0.39/0.57 (step @p38 :rule skolemize :premises (@p37)) % 0.39/0.57 (step @p39 :rule cnf_or_neg :args (@t45 3)) % 0.39/0.57 (step @p40 :rule chain_m_resolution :premises (@p39 @p38) :args ((not @t37) @t46 @t47)) % 0.39/0.57 (step @p41 :rule cnf_equiv_pos2 :args (@t50)) % 0.39/0.57 (step @p42 :rule reordering :premises (@p41) :args ((or @t37 @t51 (not @t50)))) % 0.39/0.57 (step @p43 :rule chain_m_resolution :premises (@p42 @p40 @p21) :args (@t51 @t52 (@list @t37 @t50))) % 0.39/0.57 (step @p44 :rule bool-double-not-elim :args (@t38)) % 0.39/0.57 (step @p45 :rule refl :args (@t45)) % 0.39/0.57 (step @p46 :rule nary_cong :premises (@p45 @p44) :args ((or @t45 (not @t39)))) % 0.39/0.57 (step @p47 :rule cnf_or_neg :args (@t45 2)) % 0.39/0.57 (step @p48 :rule eq_resolve :premises (@p47 @p46)) % 0.39/0.57 (step @p49 :rule reordering :premises (@p48) :args ((or @t38 @t45))) % 0.39/0.57 (step @p50 :rule chain_m_resolution :premises (@p49 @p38) :args (@t38 @t46 @t47)) % 0.39/0.57 (step @p51 :rule cnf_and_neg :args (@t49)) % 0.39/0.57 (step @p52 :rule reordering :premises (@p51) :args ((or @t39 @t49 @t53))) % 0.39/0.57 (step @p53 :rule chain_m_resolution :premises (@p52 @p50 @p43) :args (@t53 (@list false true) (@list @t38 @t49))) % 0.39/0.57 (step @p54 :rule cnf_equiv_pos2 :args (@t57)) % 0.39/0.57 (step @p55 :rule reordering :premises (@p54) :args ((or @t48 @t58 (not @t57)))) % 0.39/0.57 (step @p56 :rule chain_m_resolution :premises (@p55 @p53 @p20) :args (@t58 @t52 (@list @t48 @t57))) % 0.39/0.57 (step @p57 :rule skolemize :premises (@p56)) % 0.39/0.57 (step @p58 :rule cnf_or_neg :args (@t63 1)) % 0.39/0.57 (step @p59 :rule chain_m_resolution :premises (@p58 @p57) :args ((not @t60) @t46 @t64)) % 0.39/0.57 (step @p60 :rule instantiate :premises (@p19) :args ((@list @t40 @t33))) % 0.39/0.57 (step @p61 :rule bool-double-not-elim :args (@t41)) % 0.39/0.57 (step @p62 :rule nary_cong :premises (@p45 @p61) :args ((or @t45 (not @t42)))) % 0.39/0.57 (step @p63 :rule cnf_or_neg :args (@t45 1)) % 0.39/0.57 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 0.39/0.57 (step @p65 :rule reordering :premises (@p64) :args ((or @t41 @t45))) % 0.39/0.57 (step @p66 :rule chain_m_resolution :premises (@p65 @p38) :args (@t41 @t46 @t47)) % 0.39/0.57 (step @p67 :rule cnf_equiv_pos1 :args (@t67)) % 0.39/0.57 (step @p68 :rule reordering :premises (@p67) :args ((or @t42 @t66 (not @t67)))) % 0.39/0.57 (step @p69 :rule chain_m_resolution :premises (@p68 @p66 @p60) :args (@t66 @t68 (@list @t41 @t67))) % 0.39/0.57 (step @p70 :rule instantiate :premises (@p69) :args (@t69)) % 0.39/0.57 (step @p71 :rule instantiate :premises (@p19) :args ((@list @t34 @t40))) % 0.39/0.57 (step @p72 :rule bool-double-not-elim :args (@t43)) % 0.39/0.57 (step @p73 :rule nary_cong :premises (@p45 @p72) :args ((or @t45 (not @t44)))) % 0.39/0.57 (step @p74 :rule cnf_or_neg :args (@t45 0)) % 0.39/0.57 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.39/0.57 (step @p76 :rule reordering :premises (@p75) :args ((or @t43 @t45))) % 0.39/0.57 (step @p77 :rule chain_m_resolution :premises (@p76 @p38) :args (@t43 @t46 @t47)) % 0.39/0.57 (step @p78 :rule cnf_equiv_pos1 :args (@t71)) % 0.39/0.57 (step @p79 :rule reordering :premises (@p78) :args ((or @t44 @t70 (not @t71)))) % 0.39/0.57 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p71) :args (@t70 @t68 (@list @t43 @t71))) % 0.39/0.57 (step @p81 :rule instantiate :premises (@p80) :args (@t69)) % 0.39/0.57 (step @p82 :rule bool-double-not-elim :args (@t61)) % 0.39/0.57 (step @p83 :rule refl :args (@t63)) % 0.39/0.57 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or @t63 (not @t62)))) % 0.39/0.57 (step @p85 :rule cnf_or_neg :args (@t63 0)) % 0.39/0.57 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.39/0.57 (step @p87 :rule reordering :premises (@p86) :args ((or @t61 @t63))) % 0.39/0.57 (step @p88 :rule chain_m_resolution :premises (@p87 @p57) :args (@t61 @t46 @t64)) % 0.39/0.57 (step @p89 :rule cnf_or_pos :args (@t73)) % 0.39/0.57 (step @p90 :rule reordering :premises (@p89) :args ((or @t62 @t72 (not @t73)))) % 0.39/0.57 (step @p91 :rule chain_m_resolution :premises (@p90 @p88 @p81) :args (@t72 @t68 (@list @t61 @t73))) % 0.39/0.57 (step @p92 :rule cnf_or_pos :args (@t75)) % 0.39/0.57 (step @p93 :rule reordering :premises (@p92) :args ((or @t60 @t74 (not @t75)))) % 0.39/0.57 (step @p94 false :rule chain_m_resolution :premises (@p93 @p91 @p70 @p59) :args (false (@list false false true) (@list @t72 @t75 @t60))) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------