%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM533+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n012.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 08:39:44 AM UTC 2026 % Result : Theorem 0.16s 0.37s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM533+1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.08/0.25 % Computer : n012.cluster.edu % 0.08/0.25 % Model : x86_64 x86_64 % 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.25 % Memory : 8042.1875MB % 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.25 % CPULimit : 300 % 0.08/0.25 % WCLimit : 300 % 0.08/0.25 % DateTime : Tue Jun 2 11:27:48 EDT 2026 % 0.08/0.25 % CPUTime : % 0.16/0.33 %----Proving TF0_NAR, FOF, or CNF % 0.16/0.37 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.16/0.37 % SZS status Theorem % 0.16/0.37 % SZS output start Proof % 0.16/0.37 ( % 0.16/0.37 (declare-sort $$unsorted 0) % 0.16/0.37 (declare-const tptp.xC $$unsorted) % 0.16/0.37 (declare-const tptp.xB $$unsorted) % 0.16/0.37 (declare-const tptp.slcrc0 $$unsorted) % 0.16/0.37 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.xA $$unsorted) % 0.16/0.37 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.16/0.37 (define @t1 () (@var "W0" $$unsorted)) % 0.16/0.37 (define @t2 () (tptp.aSet0 @t1)) % 0.16/0.37 (define @t3 () (@list @t1)) % 0.16/0.37 (define @t4 () (@var "W1" $$unsorted)) % 0.16/0.37 (define @t5 () (tptp.aElementOf0 @t4 @t1)) % 0.16/0.37 (define @t6 () (@list @t4)) % 0.16/0.37 (define @t7 () (tptp.isFinite0 @t1)) % 0.16/0.37 (define @t8 () (= @t1 tptp.slcrc0)) % 0.16/0.37 (define @t9 () (tptp.isCountable0 @t1)) % 0.16/0.37 (define @t10 () (and @t2 @t9)) % 0.16/0.37 (define @t11 () (@var "W2" $$unsorted)) % 0.16/0.37 (define @t12 () (tptp.aElementOf0 @t11 @t1)) % 0.16/0.37 (define @t13 () (tptp.aElementOf0 @t11 @t4)) % 0.16/0.37 (define @t14 () (@list @t11)) % 0.16/0.37 (define @t15 () (forall @t14 (=> @t13 @t12))) % 0.16/0.37 (define @t16 () (tptp.aSet0 @t4)) % 0.16/0.37 (define @t17 () (and @t16 @t15)) % 0.16/0.37 (define @t18 () (tptp.aSubsetOf0 @t4 @t1)) % 0.16/0.37 (define @t19 () (= @t18 @t17)) % 0.16/0.37 (define @t20 () (forall @t6 @t19)) % 0.16/0.37 (define @t21 () (=> @t2 @t20)) % 0.16/0.37 (define @t22 () (forall @t3 @t21)) % 0.16/0.37 (define @t23 () (tptp.aSet0 tptp.xC)) % 0.16/0.37 (define @t24 () (tptp.aSet0 tptp.xB)) % 0.16/0.37 (define @t25 () (tptp.aSet0 tptp.xA)) % 0.16/0.37 (define @t26 () (tptp.aSubsetOf0 tptp.xA tptp.xC)) % 0.16/0.37 (define @t27 () (tptp.aSubsetOf0 tptp.xB tptp.xC)) % 0.16/0.37 (define @t28 () (tptp.aSubsetOf0 tptp.xA tptp.xB)) % 0.16/0.37 (define @t29 () (@var "BOUND_VARIABLE_7557" $$unsorted)) % 0.16/0.37 (define @t30 () (= (tptp.aSubsetOf0 @t29 @t1) (and (tptp.aSet0 @t29) (forall @t14 (or (not (tptp.aElementOf0 @t11 @t29)) @t12))))) % 0.16/0.37 (define @t31 () (not @t2)) % 0.16/0.37 (define @t32 () (or @t31 @t30)) % 0.16/0.37 (define @t33 () (@list @t29)) % 0.16/0.37 (define @t34 () (forall @t33 @t32)) % 0.16/0.37 (define @t35 () (forall @t33 @t30)) % 0.16/0.37 (define @t36 () (or @t31 @t35)) % 0.16/0.37 (define @t37 () (forall @t6 (= @t18 (and @t16 (forall @t14 (or (not @t13) @t12)))))) % 0.16/0.37 (define @t38 () (tptp.aElementOf0 @t11 tptp.xC)) % 0.16/0.37 (define @t39 () (not (tptp.aElementOf0 @t11 tptp.xA))) % 0.16/0.37 (define @t40 () (forall @t14 (or @t39 @t38))) % 0.16/0.37 (define @t41 () (and @t25 @t40)) % 0.16/0.37 (define @t42 () (= @t26 @t41)) % 0.16/0.37 (define @t43 () (not @t23)) % 0.16/0.37 (define @t44 () (or @t43 @t42)) % 0.16/0.37 (define @t45 () (@list false false)) % 0.16/0.37 (define @t46 () (not @t41)) % 0.16/0.37 (define @t47 () (not @t40)) % 0.16/0.37 (define @t48 () (@quantifiers_skolemize @t40 0)) % 0.16/0.37 (define @t49 () (tptp.aElementOf0 @t48 tptp.xC)) % 0.16/0.37 (define @t50 () (tptp.aElementOf0 @t48 tptp.xA)) % 0.16/0.37 (define @t51 () (not @t50)) % 0.16/0.37 (define @t52 () (or @t51 @t49)) % 0.16/0.37 (define @t53 () (@list true)) % 0.16/0.37 (define @t54 () (@list @t52)) % 0.16/0.37 (define @t55 () (tptp.aElementOf0 @t11 tptp.xB)) % 0.16/0.37 (define @t56 () (forall @t14 (or (not @t55) @t38))) % 0.16/0.37 (define @t57 () (and @t24 @t56)) % 0.16/0.37 (define @t58 () (= @t27 @t57)) % 0.16/0.37 (define @t59 () (or @t43 @t58)) % 0.16/0.37 (define @t60 () (@list false)) % 0.16/0.37 (define @t61 () (@list @t48)) % 0.16/0.37 (define @t62 () (forall @t14 (or @t39 @t55))) % 0.16/0.37 (define @t63 () (and @t25 @t62)) % 0.16/0.37 (define @t64 () (= @t28 @t63)) % 0.16/0.37 (define @t65 () (not @t24)) % 0.16/0.37 (define @t66 () (or @t65 @t64)) % 0.16/0.37 (define @t67 () (tptp.aElementOf0 @t48 tptp.xB)) % 0.16/0.37 (define @t68 () (or @t51 @t67)) % 0.16/0.37 (define @t69 () (not @t67)) % 0.16/0.37 (define @t70 () (or @t69 @t49)) % 0.16/0.37 (assume @p1 (forall @t3 (=> @t2 true))) % 0.16/0.37 (assume @p2 (forall @t3 (=> (tptp.aElement0 @t1) true))) % 0.16/0.37 (assume @p3 (forall @t3 (=> @t2 (forall @t6 (=> @t5 (tptp.aElement0 @t4)))))) % 0.16/0.37 (assume @p4 (forall @t3 (=> @t2 (=> @t7 true)))) % 0.16/0.37 (assume @p5 (forall @t3 (= @t8 (and @t2 (not (exists @t6 @t5)))))) % 0.16/0.37 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.16/0.37 (assume @p7 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.16/0.37 (assume @p8 (forall @t3 (=> @t10 (not @t7)))) % 0.16/0.37 (assume @p9 (forall @t3 (=> @t10 (not @t8)))) % 0.16/0.37 (assume @p10 @t22) % 0.16/0.37 (assume @p11 (forall @t3 (=> (and @t2 @t7) (forall @t6 (=> @t18 (tptp.isFinite0 @t4)))))) % 0.16/0.37 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.16/0.37 (assume @p13 (forall (@list @t1 @t4) (=> (and @t2 @t16) (=> (and (tptp.aSubsetOf0 @t1 @t4) @t18) (= @t1 @t4))))) % 0.16/0.37 (assume @p14 (and @t25 @t24 @t23)) % 0.16/0.37 (assume @p15 (not (=> (and @t28 @t27) @t26))) % 0.16/0.37 (assume @p16 true) % 0.16/0.37 (step @p17 :rule quant-merge-prenex :args ((= (forall @t3 @t34) (forall (@list @t1 @t29) @t32)))) % 0.16/0.37 (step @p18 :rule alpha_equiv :args (@t35 (@list @t29) (@list @t4))) % 0.16/0.37 (step @p19 :rule refl :args (@t31)) % 0.16/0.37 (step @p20 :rule nary_cong :premises (@p19 @p18) :args (@t36)) % 0.16/0.37 (step @p21 :rule quant-miniscope-or :args ((= @t34 @t36))) % 0.16/0.37 (step @p22 :rule trans :premises (@p21 @p20)) % 0.16/0.37 (step @p23 :rule symm :premises (@p22)) % 0.16/0.37 (step @p24 :rule cong :premises (@p23) :args ((forall @t3 (or @t31 @t37)))) % 0.16/0.37 (step @p25 :rule trans :premises (@p24 @p17)) % 0.16/0.37 (step @p26 :rule bool-impl-elim :args (@t2 @t37)) % 0.16/0.37 (step @p27 :rule cong :premises (@p26) :args ((forall @t3 (=> @t2 @t37)))) % 0.16/0.37 (step @p28 :rule trans :premises (@p27 @p25)) % 0.16/0.37 (step @p29 :rule bool-impl-elim :args (@t13 @t12)) % 0.16/0.37 (step @p30 :rule cong :premises (@p29) :args (@t15)) % 0.16/0.37 (step @p31 :rule refl :args (@t16)) % 0.16/0.37 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t17)) % 0.16/0.37 (step @p33 :rule refl :args (@t18)) % 0.16/0.37 (step @p34 :rule cong :premises (@p33 @p32) :args (@t19)) % 0.16/0.37 (step @p35 :rule cong :premises (@p34) :args (@t20)) % 0.16/0.37 (step @p36 :rule refl :args (@t2)) % 0.16/0.37 (step @p37 :rule cong :premises (@p36 @p35) :args (@t21)) % 0.16/0.37 (step @p38 :rule cong :premises (@p37) :args (@t22)) % 0.16/0.37 (step @p39 :rule trans :premises (@p38 @p28)) % 0.16/0.37 (step @p40 :rule eq_resolve :premises (@p10 @p39)) % 0.16/0.37 (step @p41 :rule instantiate :premises (@p40) :args ((@list tptp.xC tptp.xA))) % 0.16/0.37 (step @p42 :rule and_elim :premises (@p14) :args (2)) % 0.16/0.37 (step @p43 :rule cnf_or_pos :args (@t44)) % 0.16/0.37 (step @p44 :rule reordering :premises (@p43) :args ((or @t43 @t42 (not @t44)))) % 0.16/0.37 (step @p45 :rule chain_m_resolution :premises (@p44 @p42 @p41) :args (@t42 @t45 (@list @t23 @t44))) % 0.16/0.37 (step @p46 :rule not_implies_elim2 :premises (@p15)) % 0.16/0.37 (step @p47 :rule cnf_equiv_pos2 :args (@t42)) % 0.16/0.37 (step @p48 :rule reordering :premises (@p47) :args ((or @t26 @t46 (not @t42)))) % 0.16/0.37 (step @p49 :rule chain_m_resolution :premises (@p48 @p46 @p45) :args (@t46 (@list true false) (@list @t26 @t42))) % 0.16/0.37 (step @p50 :rule and_elim :premises (@p14) :args (0)) % 0.16/0.37 (step @p51 :rule cnf_and_neg :args (@t41)) % 0.16/0.37 (step @p52 :rule reordering :premises (@p51) :args ((or (not @t25) @t41 @t47))) % 0.16/0.37 (step @p53 :rule chain_m_resolution :premises (@p52 @p50 @p49) :args (@t47 (@list false true) (@list @t25 @t41))) % 0.16/0.37 (step @p54 :rule skolemize :premises (@p53)) % 0.16/0.37 (step @p55 :rule cnf_or_neg :args (@t52 1)) % 0.16/0.37 (step @p56 :rule chain_m_resolution :premises (@p55 @p54) :args ((not @t49) @t53 @t54)) % 0.16/0.37 (step @p57 :rule instantiate :premises (@p40) :args ((@list tptp.xC tptp.xB))) % 0.16/0.37 (step @p58 :rule cnf_or_pos :args (@t59)) % 0.16/0.37 (step @p59 :rule reordering :premises (@p58) :args ((or @t43 @t58 (not @t59)))) % 0.16/0.37 (step @p60 :rule chain_m_resolution :premises (@p59 @p42 @p57) :args (@t58 @t45 (@list @t23 @t59))) % 0.16/0.37 (step @p61 :rule not_implies_elim1 :premises (@p15)) % 0.16/0.37 (step @p62 :rule and_elim :premises (@p61) :args (1)) % 0.16/0.37 (step @p63 :rule cnf_equiv_pos1 :args (@t58)) % 0.16/0.37 (step @p64 :rule reordering :premises (@p63) :args ((or (not @t27) @t57 (not @t58)))) % 0.16/0.37 (step @p65 :rule chain_m_resolution :premises (@p64 @p62 @p60) :args (@t57 @t45 (@list @t27 @t58))) % 0.16/0.37 (step @p66 :rule cnf_and_pos :args (@t57 1)) % 0.16/0.37 (step @p67 :rule reordering :premises (@p66) :args ((or @t56 (not @t57)))) % 0.16/0.37 (step @p68 :rule chain_m_resolution :premises (@p67 @p65) :args (@t56 @t60 (@list @t57))) % 0.16/0.37 (step @p69 :rule instantiate :premises (@p68) :args (@t61)) % 0.16/0.37 (step @p70 :rule instantiate :premises (@p40) :args ((@list tptp.xB tptp.xA))) % 0.16/0.37 (step @p71 :rule and_elim :premises (@p14) :args (1)) % 0.16/0.37 (step @p72 :rule cnf_or_pos :args (@t66)) % 0.16/0.37 (step @p73 :rule reordering :premises (@p72) :args ((or @t65 @t64 (not @t66)))) % 0.16/0.37 (step @p74 :rule chain_m_resolution :premises (@p73 @p71 @p70) :args (@t64 @t45 (@list @t24 @t66))) % 0.16/0.37 (step @p75 :rule and_elim :premises (@p61) :args (0)) % 0.16/0.37 (step @p76 :rule cnf_equiv_pos1 :args (@t64)) % 0.16/0.37 (step @p77 :rule reordering :premises (@p76) :args ((or (not @t28) @t63 (not @t64)))) % 0.16/0.37 (step @p78 :rule chain_m_resolution :premises (@p77 @p75 @p74) :args (@t63 @t45 (@list @t28 @t64))) % 0.16/0.37 (step @p79 :rule cnf_and_pos :args (@t63 1)) % 0.16/0.37 (step @p80 :rule reordering :premises (@p79) :args ((or @t62 (not @t63)))) % 0.16/0.37 (step @p81 :rule chain_m_resolution :premises (@p80 @p78) :args (@t62 @t60 (@list @t63))) % 0.16/0.37 (step @p82 :rule instantiate :premises (@p81) :args (@t61)) % 0.16/0.37 (step @p83 :rule bool-double-not-elim :args (@t50)) % 0.16/0.37 (step @p84 :rule refl :args (@t52)) % 0.16/0.37 (step @p85 :rule nary_cong :premises (@p84 @p83) :args ((or @t52 (not @t51)))) % 0.16/0.37 (step @p86 :rule cnf_or_neg :args (@t52 0)) % 0.16/0.37 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 0.16/0.37 (step @p88 :rule reordering :premises (@p87) :args ((or @t50 @t52))) % 0.16/0.37 (step @p89 :rule chain_m_resolution :premises (@p88 @p54) :args (@t50 @t53 @t54)) % 0.16/0.37 (step @p90 :rule cnf_or_pos :args (@t68)) % 0.16/0.37 (step @p91 :rule reordering :premises (@p90) :args ((or @t51 @t67 (not @t68)))) % 0.16/0.37 (step @p92 :rule chain_m_resolution :premises (@p91 @p89 @p82) :args (@t67 @t45 (@list @t50 @t68))) % 0.16/0.37 (step @p93 :rule cnf_or_pos :args (@t70)) % 0.16/0.37 (step @p94 :rule reordering :premises (@p93) :args ((or @t49 @t69 (not @t70)))) % 0.16/0.37 (step @p95 false :rule chain_m_resolution :premises (@p94 @p92 @p69 @p56) :args (false (@list false false true) (@list @t67 @t70 @t49))) % 0.16/0.37 ) % 0.16/0.37 % SZS output end Proof % 0.16/0.37 % cvc5 exiting %------------------------------------------------------------------------------