%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU354+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:51:29 AM UTC 2026 % Result : Theorem 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU354+1 : TPTP v9.2.1. Released v3.3.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n003.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 17:00:29 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.59 % SZS status Theorem % 0.37/0.59 % SZS output start Proof % 0.37/0.59 ( % 0.37/0.59 (declare-sort $$unsorted 0) % 0.37/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.empty_set $$unsorted) % 0.37/0.59 (declare-const tptp.k1_pcomps_1 (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.proper_element (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.v3_membered (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.natural (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.v1_membered (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.v1_xreal_0 (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.v5_membered (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.v2_membered (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.union_of_subsets (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.v1_rat_1 (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.v1_xcmplx_0 (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.v1_int_1 (-> $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.v4_membered (-> $$unsorted Bool)) % 0.37/0.59 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.59 (define @t2 () (@var "B" $$unsorted)) % 0.37/0.59 (define @t3 () (tptp.in @t1 @t2)) % 0.37/0.59 (define @t4 () (@list @t1 @t2)) % 0.37/0.59 (define @t5 () (tptp.v1_xcmplx_0 @t2)) % 0.37/0.59 (define @t6 () (tptp.element @t2 @t1)) % 0.37/0.59 (define @t7 () (@list @t2)) % 0.37/0.59 (define @t8 () (tptp.v1_membered @t1)) % 0.37/0.59 (define @t9 () (@list @t1)) % 0.37/0.59 (define @t10 () (tptp.v1_xreal_0 @t2)) % 0.37/0.59 (define @t11 () (tptp.v2_membered @t1)) % 0.37/0.59 (define @t12 () (tptp.v1_rat_1 @t2)) % 0.37/0.59 (define @t13 () (tptp.v3_membered @t1)) % 0.37/0.59 (define @t14 () (tptp.v1_int_1 @t2)) % 0.37/0.59 (define @t15 () (tptp.v4_membered @t1)) % 0.37/0.59 (define @t16 () (tptp.v5_membered @t1)) % 0.37/0.59 (define @t17 () (tptp.empty @t1)) % 0.37/0.59 (define @t18 () (tptp.v1_membered @t2)) % 0.37/0.59 (define @t19 () (tptp.powerset @t1)) % 0.37/0.59 (define @t20 () (tptp.element @t2 @t19)) % 0.37/0.59 (define @t21 () (tptp.v2_membered @t2)) % 0.37/0.59 (define @t22 () (tptp.v3_membered @t2)) % 0.37/0.59 (define @t23 () (tptp.v4_membered @t2)) % 0.37/0.59 (define @t24 () (= (tptp.proper_element @t2 @t1) (not (= @t2 (tptp.union @t1))))) % 0.37/0.59 (define @t25 () (forall @t4 (=> @t6 @t24))) % 0.37/0.59 (define @t26 () (tptp.powerset @t19)) % 0.37/0.59 (define @t27 () (tptp.k1_pcomps_1 @t1)) % 0.37/0.59 (define @t28 () (tptp.union_of_subsets @t1 @t2)) % 0.37/0.59 (define @t29 () (tptp.element @t2 @t26)) % 0.37/0.59 (define @t30 () (not @t17)) % 0.37/0.59 (define @t31 () (tptp.empty @t2)) % 0.37/0.59 (define @t32 () (tptp.proper_element @t2 @t19)) % 0.37/0.59 (define @t33 () (tptp.element @t1 @t2)) % 0.37/0.59 (define @t34 () (@var "C" $$unsorted)) % 0.37/0.59 (define @t35 () (tptp.element @t2 (tptp.powerset @t34))) % 0.37/0.59 (define @t36 () (@list @t1 @t2 @t34)) % 0.37/0.59 (define @t37 () (not (= @t2 @t1))) % 0.37/0.59 (define @t38 () (= @t32 @t37)) % 0.37/0.59 (define @t39 () (=> @t20 @t38)) % 0.37/0.59 (define @t40 () (forall @t4 @t39)) % 0.37/0.59 (define @t41 () (not @t40)) % 0.37/0.59 (define @t42 () (not (= @t1 @t2))) % 0.37/0.59 (define @t43 () (tptp.union @t19)) % 0.37/0.59 (define @t44 () (forall @t9 (= @t43 @t1))) % 0.37/0.59 (define @t45 () (= @t32 @t42)) % 0.37/0.59 (define @t46 () (forall @t4 (or (not @t20) @t45))) % 0.37/0.59 (define @t47 () (@quantifiers_skolemize @t46 0)) % 0.37/0.59 (define @t48 () (@quantifiers_skolemize @t46 1)) % 0.37/0.59 (define @t49 () (= @t47 @t48)) % 0.37/0.59 (define @t50 () (not @t49)) % 0.37/0.59 (define @t51 () (tptp.powerset @t47)) % 0.37/0.59 (define @t52 () (tptp.proper_element @t48 @t51)) % 0.37/0.59 (define @t53 () (= @t52 @t50)) % 0.37/0.59 (define @t54 () (tptp.element @t48 @t51)) % 0.37/0.59 (define @t55 () (not @t54)) % 0.37/0.59 (define @t56 () (or @t55 @t53)) % 0.37/0.59 (define @t57 () (@list true)) % 0.37/0.59 (define @t58 () (@list @t56)) % 0.37/0.59 (define @t59 () (tptp.union @t51)) % 0.37/0.59 (define @t60 () (= @t48 @t59)) % 0.37/0.59 (define @t61 () (not @t60)) % 0.37/0.59 (define @t62 () (= @t52 @t61)) % 0.37/0.59 (define @t63 () (or @t55 @t62)) % 0.37/0.59 (define @t64 () (@list false false)) % 0.37/0.59 (define @t65 () (not @t62)) % 0.37/0.59 (define @t66 () (= @t47 @t59)) % 0.37/0.59 (define @t67 () (not @t66)) % 0.37/0.59 (define @t68 () (not @t50)) % 0.37/0.59 (define @t69 () (and @t66 @t60 @t50)) % 0.37/0.59 (define @t70 () (not @t52)) % 0.37/0.59 (define @t71 () (and @t49 @t66)) % 0.37/0.59 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.37/0.59 (assume @p2 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.37/0.59 (assume @p3 (forall @t9 (=> @t11 (forall @t7 (=> @t6 (and @t5 @t10)))))) % 0.37/0.59 (assume @p4 (forall @t9 (=> @t13 (forall @t7 (=> @t6 (and @t5 @t10 @t12)))))) % 0.37/0.59 (assume @p5 (forall @t9 (=> @t15 (forall @t7 (=> @t6 (and @t5 @t10 @t14 @t12)))))) % 0.37/0.59 (assume @p6 (forall @t9 (=> @t16 (forall @t7 (=> @t6 (and @t5 (tptp.natural @t2) @t10 @t14 @t12)))))) % 0.37/0.59 (assume @p7 (forall @t9 (=> @t17 (and @t8 @t11 @t13 @t15 @t16)))) % 0.37/0.59 (assume @p8 (forall @t9 (=> @t8 (forall @t7 (=> @t20 @t18))))) % 0.37/0.59 (assume @p9 (forall @t9 (=> @t11 (forall @t7 (=> @t20 (and @t18 @t21)))))) % 0.37/0.59 (assume @p10 (forall @t9 (=> @t13 (forall @t7 (=> @t20 (and @t18 @t21 @t22)))))) % 0.37/0.59 (assume @p11 (forall @t9 (=> @t15 (forall @t7 (=> @t20 (and @t18 @t21 @t22 @t23)))))) % 0.37/0.59 (assume @p12 (forall @t9 (=> @t16 @t15))) % 0.37/0.59 (assume @p13 (forall @t9 (=> @t16 (forall @t7 (=> @t20 (and @t18 @t21 @t22 @t23 (tptp.v5_membered @t2))))))) % 0.37/0.59 (assume @p14 (forall @t9 (=> @t15 @t13))) % 0.37/0.59 (assume @p15 (forall @t9 (=> @t13 @t11))) % 0.37/0.59 (assume @p16 (forall @t9 (=> @t11 @t8))) % 0.37/0.59 (assume @p17 @t25) % 0.37/0.59 (assume @p18 (forall @t9 (tptp.element @t27 @t26))) % 0.37/0.59 (assume @p19 true) % 0.37/0.59 (assume @p20 (forall @t4 (=> @t29 (tptp.element @t28 @t19)))) % 0.37/0.59 (assume @p21 (forall @t9 (exists @t7 @t6))) % 0.37/0.59 (assume @p22 (forall @t9 (not (tptp.empty @t19)))) % 0.37/0.59 (assume @p23 (and (tptp.empty tptp.empty_set) (tptp.v1_membered tptp.empty_set) (tptp.v2_membered tptp.empty_set) (tptp.v3_membered tptp.empty_set) (tptp.v4_membered tptp.empty_set) (tptp.v5_membered tptp.empty_set))) % 0.37/0.59 (assume @p24 (exists @t9 (and @t30 @t8 @t11 @t13 @t15 @t16))) % 0.37/0.59 (assume @p25 (forall @t9 (=> @t30 (exists @t7 (and @t20 (not @t31)))))) % 0.37/0.59 (assume @p26 (forall @t9 (exists @t7 (and @t20 @t31)))) % 0.37/0.59 (assume @p27 (forall @t9 (exists @t7 (and @t20 (not @t32))))) % 0.37/0.59 (assume @p28 (forall @t9 (= @t27 @t19))) % 0.37/0.59 (assume @p29 (forall @t4 (=> @t29 (= @t28 (tptp.union @t2))))) % 0.37/0.59 (assume @p30 (forall @t4 (tptp.subset @t1 @t1))) % 0.37/0.59 (assume @p31 (forall @t4 (=> @t3 @t33))) % 0.37/0.59 (assume @p32 (forall @t4 (=> @t33 (or @t31 @t3)))) % 0.37/0.59 (assume @p33 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 0.37/0.59 (assume @p34 (forall @t36 (=> (and @t3 @t35) (tptp.element @t1 @t34)))) % 0.37/0.59 (assume @p35 (forall @t36 (not (and @t3 @t35 (tptp.empty @t34))))) % 0.37/0.59 (assume @p36 @t41) % 0.37/0.59 (assume @p37 (forall @t9 (=> @t17 (= @t1 tptp.empty_set)))) % 0.37/0.59 (assume @p38 (forall @t4 (not (and @t3 @t31)))) % 0.37/0.59 (assume @p39 (forall @t4 (not (and @t17 @t42 @t31)))) % 0.37/0.59 (assume @p40 @t44) % 0.37/0.59 (step @p41 :rule eq-symm :args (@t43 @t1)) % 0.37/0.59 (step @p42 :rule cong :premises (@p41) :args (@t44)) % 0.37/0.59 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 0.37/0.59 (step @p44 :rule instantiate :premises (@p43) :args ((@list @t47))) % 0.37/0.59 (step @p45 :rule bool-impl-elim :args (@t20 @t45)) % 0.37/0.59 (step @p46 :rule cong :premises (@p45) :args ((forall @t4 (=> @t20 @t45)))) % 0.37/0.59 (step @p47 :rule eq-symm :args (@t2 @t1)) % 0.37/0.59 (step @p48 :rule cong :premises (@p47) :args (@t37)) % 0.37/0.59 (step @p49 :rule refl :args (@t32)) % 0.37/0.59 (step @p50 :rule cong :premises (@p49 @p48) :args (@t38)) % 0.37/0.59 (step @p51 :rule refl :args (@t20)) % 0.37/0.59 (step @p52 :rule cong :premises (@p51 @p50) :args (@t39)) % 0.37/0.59 (step @p53 :rule cong :premises (@p52) :args (@t40)) % 0.37/0.59 (step @p54 :rule trans :premises (@p53 @p46)) % 0.37/0.59 (step @p55 :rule cong :premises (@p54) :args (@t41)) % 0.37/0.59 (step @p56 :rule eq_resolve :premises (@p36 @p55)) % 0.37/0.59 (step @p57 :rule skolemize :premises (@p56)) % 0.37/0.59 (step @p58 :rule cnf_or_neg :args (@t56 1)) % 0.37/0.59 (step @p59 :rule chain_m_resolution :premises (@p58 @p57) :args ((not @t53) @t57 @t58)) % 0.37/0.59 (step @p60 :rule cnf_equiv_neg1 :args (@t53)) % 0.37/0.59 (step @p61 :rule reordering :premises (@p60) :args ((or @t52 @t50 @t53))) % 0.37/0.59 (step @p62 :rule bool-impl-elim :args (@t6 @t24)) % 0.37/0.59 (step @p63 :rule cong :premises (@p62) :args (@t25)) % 0.37/0.59 (step @p64 :rule eq_resolve :premises (@p17 @p63)) % 0.37/0.59 (step @p65 :rule instantiate :premises (@p64) :args ((@list @t51 @t48))) % 0.37/0.59 (step @p66 :rule bool-double-not-elim :args (@t54)) % 0.37/0.59 (step @p67 :rule refl :args (@t56)) % 0.37/0.59 (step @p68 :rule nary_cong :premises (@p67 @p66) :args ((or @t56 (not @t55)))) % 0.37/0.59 (step @p69 :rule cnf_or_neg :args (@t56 0)) % 0.37/0.59 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 0.37/0.59 (step @p71 :rule reordering :premises (@p70) :args ((or @t54 @t56))) % 0.37/0.59 (step @p72 :rule chain_m_resolution :premises (@p71 @p57) :args (@t54 @t57 @t58)) % 0.37/0.60 (step @p73 :rule cnf_or_pos :args (@t63)) % 0.37/0.60 (step @p74 :rule reordering :premises (@p73) :args ((or @t55 @t62 (not @t63)))) % 0.37/0.60 (step @p75 :rule chain_m_resolution :premises (@p74 @p72 @p65) :args (@t62 @t64 (@list @t54 @t63))) % 0.37/0.60 (step @p76 :rule bool-double-not-elim :args (@t60)) % 0.37/0.60 (step @p77 :rule refl :args (@t52)) % 0.37/0.60 (step @p78 :rule refl :args (@t65)) % 0.37/0.60 (step @p79 :rule nary_cong :premises (@p78 @p77 @p76) :args ((or @t65 @t52 (not @t61)))) % 0.37/0.60 (step @p80 :rule cnf_equiv_pos2 :args (@t62)) % 0.37/0.60 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 0.37/0.60 (step @p82 :rule reordering :premises (@p81) :args ((or @t52 @t60 @t65))) % 0.37/0.60 (step @p83 :rule refl :args (@t67)) % 0.37/0.60 (step @p84 :rule refl :args (@t61)) % 0.37/0.60 (step @p85 :rule bool-double-not-elim :args (@t49)) % 0.37/0.60 (step @p86 :rule nary_cong :premises (@p85 @p84 @p83) :args ((or @t68 @t61 @t67))) % 0.37/0.60 (assume-push @p144 @t66) % 0.37/0.60 (assume-push @p145 @t60) % 0.37/0.60 (assume-push @p146 @t50) % 0.37/0.60 (step @p90 :rule evaluate :args ((= false true))) % 0.37/0.60 (step @p91 :rule symm :premises (@p145)) % 0.37/0.60 (step @p92 :rule trans :premises (@p44 @p91)) % 0.37/0.60 (step @p93 :rule true_intro :premises (@p92)) % 0.37/0.60 (step @p94 :rule false_intro :premises (@p146)) % 0.37/0.60 (step @p95 :rule symm :premises (@p94)) % 0.37/0.60 (step @p96 :rule trans :premises (@p95 @p93)) % 0.37/0.60 (step @p97 false :rule eq_resolve :premises (@p96 @p90)) % 0.37/0.60 (step-pop @p147 :rule scope :premises (@p97)) % 0.37/0.60 (step-pop @p148 :rule scope :premises (@p147)) % 0.37/0.60 (step-pop @p149 :rule scope :premises (@p148)) % 0.37/0.60 (step @p98 :rule process_scope :premises (@p149) :args (false)) % 0.37/0.60 (assume-push @p150 @t50) % 0.37/0.60 (assume-push @p151 @t60) % 0.37/0.60 (assume-push @p152 @t66) % 0.37/0.60 (step @p105 :rule and_intro :premises (@p44 @p151 @p150)) % 0.37/0.60 (step-pop @p153 :rule scope :premises (@p105)) % 0.37/0.60 (step-pop @p154 :rule scope :premises (@p153)) % 0.37/0.60 (step-pop @p155 :rule scope :premises (@p154)) % 0.37/0.60 (step @p106 :rule process_scope :premises (@p155) :args (@t69)) % 0.37/0.60 (step @p110 :rule implies_elim :premises (@p106)) % 0.37/0.60 (step @p111 :rule resolution :premises (@p110 @p98) :args (true @t69)) % 0.37/0.60 (step @p112 :rule not_and :premises (@p111)) % 0.37/0.60 (step @p113 :rule eq_resolve :premises (@p112 @p86)) % 0.37/0.60 (step @p114 :rule chain_m_resolution :premises (@p113 @p44 @p82 @p75 @p61 @p59) :args (@t52 (@list false false false true true) (@list @t66 @t60 @t62 @t49 @t53))) % 0.37/0.60 (step @p115 :rule refl :args (@t70)) % 0.37/0.60 (step @p116 :rule refl :args (@t53)) % 0.37/0.60 (step @p117 :rule nary_cong :premises (@p116 @p115 @p85) :args ((or @t53 @t70 @t68))) % 0.37/0.60 (step @p118 :rule cnf_equiv_neg2 :args (@t53)) % 0.37/0.60 (step @p119 :rule eq_resolve :premises (@p118 @p117)) % 0.37/0.60 (step @p120 :rule reordering :premises (@p119) :args ((or @t49 @t53 @t70))) % 0.37/0.60 (step @p121 :rule chain_m_resolution :premises (@p120 @p59 @p114) :args (@t49 (@list true false) (@list @t53 @t52))) % 0.37/0.60 (step @p122 :rule cnf_equiv_pos1 :args (@t62)) % 0.37/0.60 (step @p123 :rule reordering :premises (@p122) :args ((or @t70 @t61 @t65))) % 0.37/0.60 (step @p124 :rule chain_m_resolution :premises (@p123 @p114 @p75) :args (@t61 @t64 (@list @t52 @t62))) % 0.37/0.60 (assume-push @p156 @t49) % 0.37/0.60 (assume-push @p157 @t66) % 0.37/0.60 (assume-push @p158 @t66) % 0.37/0.60 (assume-push @p159 @t49) % 0.37/0.60 (step @p129 :rule symm :premises (@p156)) % 0.37/0.60 (step @p130 :rule trans :premises (@p129 @p44)) % 0.37/0.60 (step-pop @p160 :rule scope :premises (@p130)) % 0.37/0.60 (step-pop @p161 :rule scope :premises (@p160)) % 0.37/0.60 (step @p131 :rule process_scope :premises (@p161) :args (@t60)) % 0.37/0.60 (step @p134 :rule and_intro :premises (@p44 @p156)) % 0.37/0.60 (step @p135 :rule modus_ponens :premises (@p134 @p131)) % 0.37/0.60 (step-pop @p162 :rule scope :premises (@p135)) % 0.37/0.60 (step-pop @p163 :rule scope :premises (@p162)) % 0.37/0.60 (step @p136 :rule process_scope :premises (@p163) :args (@t60)) % 0.37/0.60 (step @p139 :rule implies_elim :premises (@p136)) % 0.37/0.60 (step @p140 :rule cnf_and_neg :args (@t71)) % 0.37/0.60 (step @p141 :rule resolution :premises (@p140 @p139) :args (true @t71)) % 0.37/0.60 (step @p142 :rule reordering :premises (@p141) :args ((or @t50 @t60 @t67))) % 0.37/0.60 (step @p143 false :rule chain_m_resolution :premises (@p142 @p124 @p121 @p44) :args (false (@list true false false) (@list @t60 @t49 @t66))) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------