%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET688+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 : n023.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 0.40s 0.58s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET688+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 % 0.17/0.35 % Computer : n023.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:07:58 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.58 % SZS status Theorem % 0.40/0.58 % SZS output start Proof % 0.40/0.58 ( % 0.40/0.58 (declare-sort $$unsorted 0) % 0.40/0.58 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.empty_set $$unsorted) % 0.40/0.58 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.40/0.58 (define @t1 () (@var "B" $$unsorted)) % 0.40/0.58 (define @t2 () (@var "X" $$unsorted)) % 0.40/0.58 (define @t3 () (tptp.member @t2 @t1)) % 0.40/0.58 (define @t4 () (@var "A" $$unsorted)) % 0.40/0.58 (define @t5 () (tptp.member @t2 @t4)) % 0.40/0.58 (define @t6 () (@list @t2)) % 0.40/0.58 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.40/0.58 (define @t8 () (tptp.subset @t4 @t1)) % 0.40/0.58 (define @t9 () (= @t8 @t7)) % 0.40/0.58 (define @t10 () (@list @t4 @t1)) % 0.40/0.58 (define @t11 () (forall @t10 @t9)) % 0.40/0.58 (define @t12 () (tptp.equal_set @t4 @t1)) % 0.40/0.58 (define @t13 () (@list @t2 @t4)) % 0.40/0.58 (define @t14 () (@list @t2 @t4 @t1)) % 0.40/0.58 (define @t15 () (@var "E" $$unsorted)) % 0.40/0.58 (define @t16 () (= @t2 @t4)) % 0.40/0.58 (define @t17 () (@var "Y" $$unsorted)) % 0.40/0.58 (define @t18 () (tptp.member @t2 @t17)) % 0.40/0.58 (define @t19 () (tptp.member @t17 @t4)) % 0.40/0.58 (define @t20 () (@list @t17)) % 0.40/0.58 (define @t21 () (@var "C" $$unsorted)) % 0.40/0.58 (define @t22 () (not (tptp.equal_set @t4 @t21))) % 0.40/0.58 (define @t23 () (tptp.equal_set @t1 @t21)) % 0.40/0.58 (define @t24 () (not @t23)) % 0.40/0.58 (define @t25 () (tptp.subset @t1 @t21)) % 0.40/0.58 (define @t26 () (not @t12)) % 0.40/0.58 (define @t27 () (and @t8 @t26 @t25 @t24)) % 0.40/0.58 (define @t28 () (@list @t4 @t1 @t21)) % 0.40/0.58 (define @t29 () (forall @t28 (=> @t27 @t22))) % 0.40/0.58 (define @t30 () (not @t29)) % 0.40/0.58 (define @t31 () (not @t25)) % 0.40/0.58 (define @t32 () (not @t8)) % 0.40/0.58 (define @t33 () (or @t32 @t12 @t31 @t23 @t22)) % 0.40/0.58 (define @t34 () (forall @t28 @t33)) % 0.40/0.58 (define @t35 () (@quantifiers_skolemize @t34 1)) % 0.40/0.58 (define @t36 () (@quantifiers_skolemize @t34 2)) % 0.40/0.58 (define @t37 () (not @t24)) % 0.40/0.58 (define @t38 () (not @t26)) % 0.40/0.58 (define @t39 () (or @t32 @t38 @t31 @t37)) % 0.40/0.58 (define @t40 () (@quantifiers_skolemize @t34 0)) % 0.40/0.58 (define @t41 () (tptp.equal_set @t40 @t36)) % 0.40/0.58 (define @t42 () (not @t41)) % 0.40/0.58 (define @t43 () (tptp.equal_set @t35 @t36)) % 0.40/0.58 (define @t44 () (tptp.subset @t35 @t36)) % 0.40/0.58 (define @t45 () (not @t44)) % 0.40/0.58 (define @t46 () (tptp.subset @t40 @t35)) % 0.40/0.58 (define @t47 () (not @t46)) % 0.40/0.58 (define @t48 () (or @t47 (tptp.equal_set @t40 @t35) @t45 @t43 @t42)) % 0.40/0.58 (define @t49 () (@list true)) % 0.40/0.58 (define @t50 () (@list @t48)) % 0.40/0.58 (define @t51 () (tptp.subset @t36 @t35)) % 0.40/0.58 (define @t52 () (and @t44 @t51)) % 0.40/0.58 (define @t53 () (= @t43 @t52)) % 0.40/0.58 (define @t54 () (not @t52)) % 0.40/0.58 (define @t55 () (@list true false)) % 0.40/0.58 (define @t56 () (not @t51)) % 0.40/0.58 (define @t57 () (tptp.member @t2 @t35)) % 0.40/0.58 (define @t58 () (not (tptp.member @t2 @t36))) % 0.40/0.58 (define @t59 () (forall @t6 (or @t58 @t57))) % 0.40/0.58 (define @t60 () (= @t51 @t59)) % 0.40/0.58 (define @t61 () (not @t59)) % 0.40/0.58 (define @t62 () (@quantifiers_skolemize @t59 0)) % 0.40/0.58 (define @t63 () (tptp.member @t62 @t36)) % 0.40/0.58 (define @t64 () (tptp.member @t62 @t35)) % 0.40/0.58 (define @t65 () (not @t63)) % 0.40/0.58 (define @t66 () (or @t65 @t64)) % 0.40/0.58 (define @t67 () (@list @t66)) % 0.40/0.58 (define @t68 () (tptp.subset @t36 @t40)) % 0.40/0.58 (define @t69 () (and (tptp.subset @t40 @t36) @t68)) % 0.40/0.58 (define @t70 () (= @t41 @t69)) % 0.40/0.58 (define @t71 () (@list false false)) % 0.40/0.58 (define @t72 () (tptp.member @t2 @t40)) % 0.40/0.58 (define @t73 () (forall @t6 (or @t58 @t72))) % 0.40/0.58 (define @t74 () (= @t68 @t73)) % 0.40/0.58 (define @t75 () (@list @t62)) % 0.40/0.58 (define @t76 () (forall @t6 (or (not @t72) @t57))) % 0.40/0.58 (define @t77 () (= @t46 @t76)) % 0.40/0.58 (define @t78 () (tptp.member @t62 @t40)) % 0.40/0.58 (define @t79 () (not @t78)) % 0.40/0.58 (define @t80 () (or @t79 @t64)) % 0.40/0.58 (define @t81 () (or @t65 @t78)) % 0.40/0.58 (assume @p1 @t11) % 0.40/0.58 (assume @p2 (forall @t10 (= @t12 (and @t8 (tptp.subset @t1 @t4))))) % 0.40/0.58 (assume @p3 (forall @t13 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.40/0.58 (assume @p4 (forall @t14 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.40/0.58 (assume @p5 (forall @t14 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.40/0.58 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.40/0.58 (assume @p7 (forall (@list @t1 @t4 @t15) (= (tptp.member @t1 (tptp.difference @t15 @t4)) (and (tptp.member @t1 @t15) (not (tptp.member @t1 @t4)))))) % 0.40/0.58 (assume @p8 (forall @t13 (= (tptp.member @t2 (tptp.singleton @t4)) @t16))) % 0.40/0.58 (assume @p9 (forall @t14 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t16 (= @t2 @t1))))) % 0.40/0.58 (assume @p10 (forall @t13 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t20 (and @t19 @t18))))) % 0.40/0.58 (assume @p11 (forall @t13 (= (tptp.member @t2 (tptp.product @t4)) (forall @t20 (=> @t19 @t18))))) % 0.40/0.58 (assume @p12 @t30) % 0.40/0.58 (assume @p13 true) % 0.40/0.58 (step @p14 :rule bool-impl-elim :args (@t5 @t3)) % 0.40/0.58 (step @p15 :rule cong :premises (@p14) :args (@t7)) % 0.40/0.58 (step @p16 :rule refl :args (@t8)) % 0.40/0.58 (step @p17 :rule cong :premises (@p16 @p15) :args (@t9)) % 0.40/0.58 (step @p18 :rule cong :premises (@p17) :args (@t11)) % 0.40/0.58 (step @p19 :rule eq_resolve :premises (@p1 @p18)) % 0.40/0.58 (step @p20 :rule instantiate :premises (@p19) :args ((@list @t36 @t35))) % 0.40/0.58 (step @p21 :rule instantiate :premises (@p2) :args ((@list @t35 @t36))) % 0.40/0.58 (step @p22 :rule aci_norm :args ((= (or (or @t32 @t12 @t31 @t23) @t22) @t33))) % 0.40/0.58 (step @p23 :rule refl :args (@t22)) % 0.40/0.58 (step @p24 :rule bool-double-not-elim :args (@t23)) % 0.40/0.58 (step @p25 :rule refl :args (@t31)) % 0.40/0.58 (step @p26 :rule bool-double-not-elim :args (@t12)) % 0.40/0.58 (step @p27 :rule refl :args (@t32)) % 0.40/0.58 (step @p28 :rule nary_cong :premises (@p27 @p26 @p25 @p24) :args (@t39)) % 0.40/0.58 (step @p29 :rule aci_norm :args ((= (or @t32 (or @t38 (or @t31 @t37))) @t39))) % 0.40/0.58 (step @p30 :rule trans :premises (@p29 @p28)) % 0.40/0.58 (step @p31 :rule bool-and-de-morgan :args (@t25 @t24 true)) % 0.40/0.58 (step @p32 :rule refl :args (@t38)) % 0.40/0.58 (step @p33 :rule nary_cong :premises (@p32 @p31) :args ((or @t38 (not (and @t25 @t24))))) % 0.40/0.58 (step @p34 :rule bool-and-de-morgan :args (@t26 @t25 (and @t24))) % 0.40/0.58 (step @p35 :rule trans :premises (@p34 @p33)) % 0.40/0.58 (step @p36 :rule nary_cong :premises (@p27 @p35) :args ((or @t32 (not (and @t26 @t25 @t24))))) % 0.40/0.58 (step @p37 :rule bool-and-de-morgan :args (@t8 @t26 (and @t25 @t24))) % 0.40/0.58 (step @p38 :rule trans :premises (@p37 @p36)) % 0.40/0.58 (step @p39 :rule trans :premises (@p38 @p30)) % 0.40/0.58 (step @p40 :rule nary_cong :premises (@p39 @p23) :args ((or (not @t27) @t22))) % 0.40/0.58 (step @p41 :rule trans :premises (@p40 @p22)) % 0.40/0.58 (step @p42 :rule bool-impl-elim :args (@t27 @t22)) % 0.40/0.58 (step @p43 :rule trans :premises (@p42 @p41)) % 0.40/0.58 (step @p44 :rule cong :premises (@p43) :args (@t29)) % 0.40/0.58 (step @p45 :rule cong :premises (@p44) :args (@t30)) % 0.40/0.58 (step @p46 :rule eq_resolve :premises (@p12 @p45)) % 0.40/0.58 (step @p47 :rule skolemize :premises (@p46)) % 0.40/0.58 (step @p48 :rule cnf_or_neg :args (@t48 3)) % 0.40/0.58 (step @p49 :rule chain_m_resolution :premises (@p48 @p47) :args ((not @t43) @t49 @t50)) % 0.40/0.58 (step @p50 :rule cnf_equiv_pos2 :args (@t53)) % 0.40/0.58 (step @p51 :rule reordering :premises (@p50) :args ((or @t43 @t54 (not @t53)))) % 0.40/0.58 (step @p52 :rule chain_m_resolution :premises (@p51 @p49 @p21) :args (@t54 @t55 (@list @t43 @t53))) % 0.40/0.58 (step @p53 :rule bool-double-not-elim :args (@t44)) % 0.40/0.58 (step @p54 :rule refl :args (@t48)) % 0.40/0.58 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t48 (not @t45)))) % 0.40/0.58 (step @p56 :rule cnf_or_neg :args (@t48 2)) % 0.40/0.58 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 0.40/0.58 (step @p58 :rule reordering :premises (@p57) :args ((or @t44 @t48))) % 0.40/0.58 (step @p59 :rule chain_m_resolution :premises (@p58 @p47) :args (@t44 @t49 @t50)) % 0.40/0.58 (step @p60 :rule cnf_and_neg :args (@t52)) % 0.40/0.58 (step @p61 :rule reordering :premises (@p60) :args ((or @t45 @t52 @t56))) % 0.40/0.58 (step @p62 :rule chain_m_resolution :premises (@p61 @p59 @p52) :args (@t56 (@list false true) (@list @t44 @t52))) % 0.40/0.58 (step @p63 :rule cnf_equiv_pos2 :args (@t60)) % 0.40/0.58 (step @p64 :rule reordering :premises (@p63) :args ((or @t51 @t61 (not @t60)))) % 0.40/0.58 (step @p65 :rule chain_m_resolution :premises (@p64 @p62 @p20) :args (@t61 @t55 (@list @t51 @t60))) % 0.40/0.58 (step @p66 :rule skolemize :premises (@p65)) % 0.40/0.58 (step @p67 :rule bool-double-not-elim :args (@t63)) % 0.40/0.58 (step @p68 :rule refl :args (@t66)) % 0.40/0.58 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or @t66 (not @t65)))) % 0.40/0.58 (step @p70 :rule cnf_or_neg :args (@t66 0)) % 0.40/0.58 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 0.40/0.58 (step @p72 :rule reordering :premises (@p71) :args ((or @t63 @t66))) % 0.40/0.58 (step @p73 :rule chain_m_resolution :premises (@p72 @p66) :args (@t63 @t49 @t67)) % 0.40/0.58 (step @p74 :rule instantiate :premises (@p19) :args ((@list @t36 @t40))) % 0.40/0.58 (step @p75 :rule instantiate :premises (@p2) :args ((@list @t40 @t36))) % 0.40/0.58 (step @p76 :rule bool-double-not-elim :args (@t41)) % 0.40/0.58 (step @p77 :rule nary_cong :premises (@p54 @p76) :args ((or @t48 (not @t42)))) % 0.40/0.58 (step @p78 :rule cnf_or_neg :args (@t48 4)) % 0.40/0.58 (step @p79 :rule eq_resolve :premises (@p78 @p77)) % 0.40/0.58 (step @p80 :rule reordering :premises (@p79) :args ((or @t41 @t48))) % 0.40/0.58 (step @p81 :rule chain_m_resolution :premises (@p80 @p47) :args (@t41 @t49 @t50)) % 0.40/0.58 (step @p82 :rule cnf_equiv_pos1 :args (@t70)) % 0.40/0.58 (step @p83 :rule reordering :premises (@p82) :args ((or @t42 @t69 (not @t70)))) % 0.40/0.58 (step @p84 :rule chain_m_resolution :premises (@p83 @p81 @p75) :args (@t69 @t71 (@list @t41 @t70))) % 0.40/0.58 (step @p85 :rule cnf_and_pos :args (@t69 1)) % 0.40/0.58 (step @p86 :rule reordering :premises (@p85) :args ((or @t68 (not @t69)))) % 0.40/0.58 (step @p87 :rule chain_m_resolution :premises (@p86 @p84) :args (@t68 (@list false) (@list @t69))) % 0.40/0.58 (step @p88 :rule cnf_equiv_pos1 :args (@t74)) % 0.40/0.58 (step @p89 :rule reordering :premises (@p88) :args ((or (not @t68) @t73 (not @t74)))) % 0.40/0.58 (step @p90 :rule chain_m_resolution :premises (@p89 @p87 @p74) :args (@t73 @t71 (@list @t68 @t74))) % 0.40/0.58 (step @p91 :rule instantiate :premises (@p90) :args (@t75)) % 0.40/0.58 (step @p92 :rule instantiate :premises (@p19) :args ((@list @t40 @t35))) % 0.40/0.58 (step @p93 :rule bool-double-not-elim :args (@t46)) % 0.40/0.58 (step @p94 :rule nary_cong :premises (@p54 @p93) :args ((or @t48 (not @t47)))) % 0.40/0.58 (step @p95 :rule cnf_or_neg :args (@t48 0)) % 0.40/0.58 (step @p96 :rule eq_resolve :premises (@p95 @p94)) % 0.40/0.58 (step @p97 :rule reordering :premises (@p96) :args ((or @t46 @t48))) % 0.40/0.58 (step @p98 :rule chain_m_resolution :premises (@p97 @p47) :args (@t46 @t49 @t50)) % 0.40/0.58 (step @p99 :rule cnf_equiv_pos1 :args (@t77)) % 0.40/0.58 (step @p100 :rule reordering :premises (@p99) :args ((or @t47 @t76 (not @t77)))) % 0.40/0.58 (step @p101 :rule chain_m_resolution :premises (@p100 @p98 @p92) :args (@t76 @t71 (@list @t46 @t77))) % 0.40/0.58 (step @p102 :rule instantiate :premises (@p101) :args (@t75)) % 0.40/0.58 (step @p103 :rule cnf_or_neg :args (@t66 1)) % 0.40/0.58 (step @p104 :rule chain_m_resolution :premises (@p103 @p66) :args ((not @t64) @t49 @t67)) % 0.40/0.58 (step @p105 :rule cnf_or_pos :args (@t80)) % 0.40/0.58 (step @p106 :rule reordering :premises (@p105) :args ((or @t64 @t79 (not @t80)))) % 0.40/0.58 (step @p107 :rule chain_m_resolution :premises (@p106 @p104 @p102) :args (@t79 @t55 (@list @t64 @t80))) % 0.40/0.58 (step @p108 :rule cnf_or_pos :args (@t81)) % 0.40/0.58 (step @p109 :rule reordering :premises (@p108) :args ((or @t65 @t78 (not @t81)))) % 0.40/0.58 (step @p110 false :rule chain_m_resolution :premises (@p109 @p107 @p91 @p73) :args (false (@list true false false) (@list @t78 @t81 @t63))) % 0.40/0.58 ) % 0.40/0.58 % SZS output end Proof % 0.40/0.58 % cvc5 exiting %------------------------------------------------------------------------------