%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET889+1 : TPTP v9.2.1. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n010.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 08:48:55 AM UTC 2026 % Result : Theorem 16.17s 16.42s % Output : Proof 16.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET889+1 : TPTP v9.2.1. Bugfixed v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n010.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 16:16:40 EDT 2026 % 0.15/0.34 % CPUTime : % 0.26/0.50 %----Proving TF0_NAR, FOF, or CNF % 16.17/16.42 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 16.17/16.42 --- Run --no-e-matching --full-saturate-quant at 6... % 16.17/16.42 % SZS status Theorem % 16.17/16.42 % SZS output start Proof % 16.17/16.42 ( % 16.17/16.42 (declare-sort $$unsorted 0) % 16.17/16.42 (declare-const tptp.empty_set $$unsorted) % 16.17/16.42 (declare-const tptp.empty (-> $$unsorted Bool)) % 16.17/16.42 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 16.17/16.42 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 16.17/16.42 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 16.17/16.42 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 16.17/16.42 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 16.17/16.42 (define @t1 () (@var "A" $$unsorted)) % 16.17/16.42 (define @t2 () (@var "B" $$unsorted)) % 16.17/16.42 (define @t3 () (@list @t1 @t2)) % 16.17/16.42 (define @t4 () (tptp.unordered_pair @t1 @t2)) % 16.17/16.42 (define @t5 () (@var "C" $$unsorted)) % 16.17/16.42 (define @t6 () (tptp.in @t5 @t2)) % 16.17/16.42 (define @t7 () (@list @t5)) % 16.17/16.42 (define @t8 () (forall @t3 (= (= @t2 (tptp.powerset @t1)) (forall @t7 (= @t6 (tptp.subset @t5 @t1)))))) % 16.17/16.42 (define @t9 () (@var "D" $$unsorted)) % 16.17/16.42 (define @t10 () (or (= @t9 @t1) (= @t9 @t2))) % 16.17/16.42 (define @t11 () (tptp.in @t9 @t5)) % 16.17/16.42 (define @t12 () (= @t11 @t10)) % 16.17/16.42 (define @t13 () (@list @t9)) % 16.17/16.42 (define @t14 () (forall @t13 @t12)) % 16.17/16.42 (define @t15 () (= (= @t5 @t4) @t14)) % 16.17/16.42 (define @t16 () (@list @t1 @t2 @t5)) % 16.17/16.42 (define @t17 () (forall @t16 @t15)) % 16.17/16.42 (define @t18 () (tptp.singleton @t2)) % 16.17/16.42 (define @t19 () (forall @t3 (= (tptp.subset @t1 @t18) (or (= @t1 tptp.empty_set) (= @t1 @t18))))) % 16.17/16.42 (define @t20 () (tptp.empty @t1)) % 16.17/16.42 (define @t21 () (@list @t1)) % 16.17/16.42 (define @t22 () (tptp.singleton @t1)) % 16.17/16.42 (define @t23 () (forall @t21 (= (tptp.powerset @t22) (tptp.unordered_pair tptp.empty_set @t22)))) % 16.17/16.42 (define @t24 () (@quantifiers_skolemize @t23 0)) % 16.17/16.42 (define @t25 () (tptp.singleton @t24)) % 16.17/16.42 (define @t26 () (tptp.unordered_pair tptp.empty_set @t25)) % 16.17/16.42 (define @t27 () (tptp.in @t9 @t26)) % 16.17/16.42 (define @t28 () (forall @t13 (= @t27 (or (= @t9 tptp.empty_set) (= @t9 @t25))))) % 16.17/16.42 (define @t29 () (or (= tptp.empty_set @t9) (= @t25 @t9))) % 16.17/16.42 (define @t30 () (= @t27 @t29)) % 16.17/16.42 (define @t31 () (forall @t13 @t30)) % 16.17/16.42 (define @t32 () (= (= @t26 @t26) @t31)) % 16.17/16.42 (define @t33 () (forall @t16 (= (= @t4 @t5) (forall @t13 (= @t11 (or (= @t1 @t9) (= @t2 @t9))))))) % 16.17/16.42 (define @t34 () (@list false)) % 16.17/16.42 (define @t35 () (tptp.in @t5 @t26)) % 16.17/16.42 (define @t36 () (tptp.subset @t5 @t25)) % 16.17/16.42 (define @t37 () (forall @t7 (= @t36 @t35))) % 16.17/16.42 (define @t38 () (@quantifiers_skolemize @t37 0)) % 16.17/16.42 (define @t39 () (or (= @t38 tptp.empty_set) (= @t38 @t25))) % 16.17/16.42 (define @t40 () (tptp.in @t38 @t26)) % 16.17/16.42 (define @t41 () (= @t40 @t39)) % 16.17/16.42 (define @t42 () (or (= tptp.empty_set @t38) (= @t25 @t38))) % 16.17/16.42 (define @t43 () (= @t40 @t42)) % 16.17/16.42 (define @t44 () (forall @t7 (= @t35 @t36))) % 16.17/16.42 (define @t45 () (tptp.powerset @t25)) % 16.17/16.42 (define @t46 () (= (= @t26 @t45) @t44)) % 16.17/16.42 (define @t47 () (= @t45 @t26)) % 16.17/16.42 (define @t48 () (= @t47 @t37)) % 16.17/16.42 (define @t49 () (not @t37)) % 16.17/16.42 (define @t50 () (@list true false)) % 16.17/16.42 (define @t51 () (tptp.subset @t38 @t25)) % 16.17/16.42 (define @t52 () (= @t51 @t40)) % 16.17/16.42 (define @t53 () (= @t51 @t39)) % 16.17/16.42 (define @t54 () (= @t51 @t42)) % 16.17/16.42 (define @t55 () (not @t54)) % 16.17/16.42 (define @t56 () (not @t42)) % 16.17/16.42 (define @t57 () (not @t43)) % 16.17/16.42 (define @t58 () (not @t40)) % 16.17/16.42 (assume @p1 (forall @t3 (=> (tptp.in @t1 @t2) (not (tptp.in @t2 @t1))))) % 16.17/16.42 (assume @p2 (forall @t3 (= @t4 (tptp.unordered_pair @t2 @t1)))) % 16.17/16.42 (assume @p3 @t8) % 16.17/16.42 (assume @p4 @t17) % 16.17/16.42 (assume @p5 (tptp.empty tptp.empty_set)) % 16.17/16.42 (assume @p6 @t19) % 16.17/16.42 (assume @p7 (exists @t21 @t20)) % 16.17/16.42 (assume @p8 (exists @t21 (not @t20))) % 16.17/16.42 (assume @p9 (forall @t3 (tptp.subset @t1 @t1))) % 16.17/16.42 (assume @p10 (forall @t3 (=> (forall @t7 (= (tptp.in @t5 @t1) @t6)) (= @t1 @t2)))) % 16.17/16.42 (assume @p11 (not @t23)) % 16.17/16.42 (assume @p12 true) % 16.17/16.42 (step @p13 :rule eq-symm :args (@t9 @t2)) % 16.17/16.42 (step @p14 :rule eq-symm :args (@t9 @t1)) % 16.17/16.42 (step @p15 :rule nary_cong :premises (@p14 @p13) :args (@t10)) % 16.17/16.42 (step @p16 :rule refl :args (@t11)) % 16.17/16.42 (step @p17 :rule cong :premises (@p16 @p15) :args (@t12)) % 16.17/16.42 (step @p18 :rule cong :premises (@p17) :args (@t14)) % 16.17/16.42 (step @p19 :rule eq-symm :args (@t5 @t4)) % 16.17/16.42 (step @p20 :rule cong :premises (@p19 @p18) :args (@t15)) % 16.17/16.42 (step @p21 :rule cong :premises (@p20) :args (@t17)) % 16.17/16.42 (step @p22 :rule eq_resolve :premises (@p4 @p21)) % 16.17/16.42 (step @p23 :rule bool-eq-true :args (@t28)) % 16.17/16.42 (step @p24 :rule eq-symm :args (true @t28)) % 16.17/16.42 (step @p25 :rule trans :premises (@p24 @p23)) % 16.17/16.42 (step @p26 :rule eq-symm :args (@t25 @t9)) % 16.17/16.42 (step @p27 :rule eq-symm :args (tptp.empty_set @t9)) % 16.17/16.42 (step @p28 :rule nary_cong :premises (@p27 @p26) :args (@t29)) % 16.17/16.42 (step @p29 :rule refl :args (@t27)) % 16.17/16.42 (step @p30 :rule cong :premises (@p29 @p28) :args (@t30)) % 16.17/16.42 (step @p31 :rule cong :premises (@p30) :args (@t31)) % 16.17/16.42 (step @p32 :rule eq-refl :args (@t26)) % 16.17/16.42 (step @p33 :rule cong :premises (@p32 @p31) :args (@t32)) % 16.17/16.42 (step @p34 :rule trans :premises (@p33 @p25)) % 16.17/16.42 (step @p35 :rule refl :args (@t33)) % 16.17/16.42 (step @p36 :rule cong :premises (@p35 @p34) :args ((=> @t33 @t32))) % 16.17/16.42 (assume-push @p102 @t33) % 16.17/16.42 (step @p38 :rule instantiate :premises (@p22) :args ((@list tptp.empty_set @t25 @t26))) % 16.17/16.42 (step-pop @p103 :rule scope :premises (@p38)) % 16.17/16.42 (step @p39 :rule process_scope :premises (@p103) :args (@t32)) % 16.17/16.42 (step @p41 :rule eq_resolve :premises (@p39 @p36)) % 16.17/16.42 (step @p42 :rule implies_elim :premises (@p41)) % 16.17/16.42 (step @p43 :rule chain_m_resolution :premises (@p42 @p22) :args (@t28 @t34 (@list @t33))) % 16.17/16.43 (step @p44 :rule eq-symm :args (@t38 @t25)) % 16.17/16.43 (step @p45 :rule eq-symm :args (@t38 tptp.empty_set)) % 16.17/16.43 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t39)) % 16.17/16.43 (step @p47 :rule refl :args (@t40)) % 16.17/16.43 (step @p48 :rule cong :premises (@p47 @p46) :args (@t41)) % 16.17/16.43 (step @p49 :rule refl :args (@t28)) % 16.17/16.43 (step @p50 :rule cong :premises (@p49 @p48) :args ((=> @t28 @t41))) % 16.17/16.43 (assume-push @p104 @t28) % 16.17/16.43 (step @p52 :rule instantiate :premises (@p43) :args ((@list @t38))) % 16.17/16.43 (step-pop @p105 :rule scope :premises (@p52)) % 16.17/16.43 (step @p53 :rule process_scope :premises (@p105) :args (@t41)) % 16.17/16.43 (step @p55 :rule eq_resolve :premises (@p53 @p50)) % 16.17/16.43 (step @p56 :rule implies_elim :premises (@p55)) % 16.17/16.43 (step @p57 :rule chain_m_resolution :premises (@p56 @p43) :args (@t43 @t34 (@list @t28))) % 16.17/16.43 (step @p58 :rule eq-symm :args (@t35 @t36)) % 16.17/16.43 (step @p59 :rule cong :premises (@p58) :args (@t44)) % 16.17/16.43 (step @p60 :rule eq-symm :args (@t26 @t45)) % 16.17/16.43 (step @p61 :rule cong :premises (@p60 @p59) :args (@t46)) % 16.17/16.43 (step @p62 :rule refl :args (@t8)) % 16.17/16.43 (step @p63 :rule cong :premises (@p62 @p61) :args ((=> @t8 @t46))) % 16.17/16.43 (assume-push @p106 @t8) % 16.17/16.43 (step @p65 :rule instantiate :premises (@p3) :args ((@list @t25 @t26))) % 16.17/16.43 (step-pop @p107 :rule scope :premises (@p65)) % 16.17/16.43 (step @p66 :rule process_scope :premises (@p107) :args (@t46)) % 16.17/16.43 (step @p68 :rule eq_resolve :premises (@p66 @p63)) % 16.17/16.43 (step @p69 :rule implies_elim :premises (@p68)) % 16.17/16.43 (step @p70 :rule chain_m_resolution :premises (@p69 @p3) :args (@t48 @t34 (@list @t8))) % 16.17/16.43 (step @p71 :rule skolemize :premises (@p11)) % 16.17/16.43 (step @p72 :rule cnf_equiv_pos2 :args (@t48)) % 16.17/16.43 (step @p73 :rule reordering :premises (@p72) :args ((or @t47 @t49 (not @t48)))) % 16.17/16.43 (step @p74 :rule chain_m_resolution :premises (@p73 @p71 @p70) :args (@t49 @t50 (@list @t47 @t48))) % 16.17/16.43 (step @p75 :rule skolemize :premises (@p74)) % 16.17/16.43 (step @p76 :rule cnf_equiv_neg1 :args (@t52)) % 16.17/16.43 (step @p77 :rule reordering :premises (@p76) :args ((or @t51 @t40 @t52))) % 16.17/16.43 (step @p78 :rule refl :args (@t51)) % 16.17/16.43 (step @p79 :rule cong :premises (@p78 @p46) :args (@t53)) % 16.17/16.43 (step @p80 :rule refl :args (@t19)) % 16.17/16.43 (step @p81 :rule cong :premises (@p80 @p79) :args ((=> @t19 @t53))) % 16.17/16.43 (assume-push @p108 @t19) % 16.17/16.43 (step @p83 :rule instantiate :premises (@p6) :args ((@list @t38 @t24))) % 16.17/16.43 (step-pop @p109 :rule scope :premises (@p83)) % 16.17/16.43 (step @p84 :rule process_scope :premises (@p109) :args (@t53)) % 16.17/16.43 (step @p86 :rule eq_resolve :premises (@p84 @p81)) % 16.17/16.43 (step @p87 :rule implies_elim :premises (@p86)) % 16.17/16.43 (step @p88 :rule chain_m_resolution :premises (@p87 @p6) :args (@t54 @t34 (@list @t19))) % 16.17/16.43 (step @p89 :rule cnf_equiv_pos2 :args (@t54)) % 16.17/16.43 (step @p90 :rule reordering :premises (@p89) :args ((or @t51 @t56 @t55))) % 16.17/16.43 (step @p91 :rule cnf_equiv_pos1 :args (@t43)) % 16.17/16.43 (step @p92 :rule reordering :premises (@p91) :args ((or @t58 @t42 @t57))) % 16.17/16.43 (step @p93 :rule chain_m_resolution :premises (@p92 @p57 @p90 @p88 @p77 @p75) :args (@t51 (@list false true false false true) (@list @t43 @t42 @t54 @t40 @t52))) % 16.17/16.43 (step @p94 :rule cnf_equiv_neg2 :args (@t52)) % 16.17/16.43 (step @p95 :rule chain_m_resolution :premises (@p94 @p75 @p93) :args (@t58 @t50 (@list @t52 @t51))) % 16.17/16.43 (step @p96 :rule cnf_equiv_pos1 :args (@t54)) % 16.17/16.43 (step @p97 :rule reordering :premises (@p96) :args ((or (not @t51) @t42 @t55))) % 16.17/16.43 (step @p98 :rule chain_m_resolution :premises (@p97 @p93 @p88) :args (@t42 (@list false false) (@list @t51 @t54))) % 16.17/16.43 (step @p99 :rule cnf_equiv_pos2 :args (@t43)) % 16.17/16.43 (step @p100 :rule reordering :premises (@p99) :args ((or @t40 @t56 @t57))) % 16.17/16.43 (step @p101 false :rule chain_m_resolution :premises (@p100 @p98 @p95 @p57) :args (false (@list false true false) (@list @t42 @t40 @t43))) % 16.17/16.43 ) % 16.17/16.43 % SZS output end Proof % 16.17/16.43 % cvc5 exiting %------------------------------------------------------------------------------