%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET591+3 : 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 : n022.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 08:48:08 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET591+3 : 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 % 0.16/0.33 % Computer : n022.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Jun 2 16:03:53 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.48 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.empty_set $$unsorted) % 0.37/0.58 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (define @t1 () (@var "C" $$unsorted)) % 0.37/0.58 (define @t2 () (@var "D" $$unsorted)) % 0.37/0.58 (define @t3 () (tptp.member @t2 @t1)) % 0.37/0.58 (define @t4 () (@var "B" $$unsorted)) % 0.37/0.58 (define @t5 () (tptp.member @t2 @t4)) % 0.37/0.58 (define @t6 () (@list @t2)) % 0.37/0.58 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.37/0.58 (define @t8 () (tptp.subset @t4 @t1)) % 0.37/0.58 (define @t9 () (= @t8 @t7)) % 0.37/0.58 (define @t10 () (@list @t4 @t1)) % 0.37/0.58 (define @t11 () (forall @t10 @t9)) % 0.37/0.58 (define @t12 () (@list @t4)) % 0.37/0.58 (define @t13 () (@list @t1)) % 0.37/0.58 (define @t14 () (= @t4 tptp.empty_set)) % 0.37/0.58 (define @t15 () (tptp.subset @t4 (tptp.difference @t1 @t4))) % 0.37/0.58 (define @t16 () (forall @t10 (=> @t15 @t14))) % 0.37/0.58 (define @t17 () (not @t16)) % 0.37/0.58 (define @t18 () (forall @t10 (or (not @t15) @t14))) % 0.37/0.58 (define @t19 () (@quantifiers_skolemize @t18 0)) % 0.37/0.58 (define @t20 () (forall @t13 (not (tptp.member @t1 @t19)))) % 0.37/0.58 (define @t21 () (@quantifiers_skolemize @t20 0)) % 0.37/0.58 (define @t22 () (@quantifiers_skolemize @t18 1)) % 0.37/0.58 (define @t23 () (@list tptp.empty_set @t19)) % 0.37/0.58 (define @t24 () (= tptp.empty_set @t19)) % 0.37/0.58 (define @t25 () (tptp.difference @t22 @t19)) % 0.37/0.58 (define @t26 () (tptp.subset @t19 @t25)) % 0.37/0.58 (define @t27 () (not @t26)) % 0.37/0.58 (define @t28 () (or @t27 @t24)) % 0.37/0.58 (define @t29 () (not @t28)) % 0.37/0.58 (define @t30 () (not @t18)) % 0.37/0.58 (define @t31 () (or @t27 (= @t19 tptp.empty_set))) % 0.37/0.58 (define @t32 () (not @t31)) % 0.37/0.58 (define @t33 () (@list true)) % 0.37/0.58 (define @t34 () (@list @t28)) % 0.37/0.58 (define @t35 () (tptp.subset @t19 tptp.empty_set)) % 0.37/0.58 (define @t36 () (tptp.subset tptp.empty_set @t19)) % 0.37/0.58 (define @t37 () (and @t36 @t35)) % 0.37/0.58 (define @t38 () (= @t24 @t37)) % 0.37/0.58 (define @t39 () (not @t37)) % 0.37/0.58 (define @t40 () (@list true false)) % 0.37/0.58 (define @t41 () (tptp.member @t2 @t19)) % 0.37/0.58 (define @t42 () (tptp.member @t2 tptp.empty_set)) % 0.37/0.58 (define @t43 () (forall @t6 (or (not @t42) @t41))) % 0.37/0.58 (define @t44 () (@quantifiers_skolemize @t43 0)) % 0.37/0.58 (define @t45 () (tptp.member @t44 tptp.empty_set)) % 0.37/0.58 (define @t46 () (not @t45)) % 0.37/0.58 (define @t47 () (or @t46 (tptp.member @t44 @t19))) % 0.37/0.58 (define @t48 () (not @t47)) % 0.37/0.58 (define @t49 () (not @t43)) % 0.37/0.58 (define @t50 () (@list false)) % 0.37/0.58 (define @t51 () (= @t36 @t43)) % 0.37/0.58 (define @t52 () (@list false false)) % 0.37/0.58 (define @t53 () (not @t35)) % 0.37/0.58 (define @t54 () (not @t41)) % 0.37/0.58 (define @t55 () (forall @t6 (or @t54 @t42))) % 0.37/0.58 (define @t56 () (= @t35 @t55)) % 0.37/0.58 (define @t57 () (not @t55)) % 0.37/0.58 (define @t58 () (@quantifiers_skolemize @t55 0)) % 0.37/0.58 (define @t59 () (tptp.member @t58 @t19)) % 0.37/0.58 (define @t60 () (not @t59)) % 0.37/0.58 (define @t61 () (or @t60 (tptp.member @t58 tptp.empty_set))) % 0.37/0.58 (define @t62 () (not @t61)) % 0.37/0.58 (define @t63 () (not @t20)) % 0.37/0.58 (define @t64 () (tptp.member @t21 @t19)) % 0.37/0.58 (define @t65 () (not @t64)) % 0.37/0.58 (define @t66 () (not @t65)) % 0.37/0.58 (define @t67 () (and (tptp.member @t21 @t22) @t65)) % 0.37/0.58 (define @t68 () (not @t67)) % 0.37/0.58 (define @t69 () (forall @t6 (or @t54 (tptp.member @t2 @t25)))) % 0.37/0.58 (define @t70 () (= @t26 @t69)) % 0.37/0.58 (define @t71 () (tptp.member @t21 @t25)) % 0.37/0.58 (define @t72 () (or @t65 @t71)) % 0.37/0.58 (define @t73 () (= @t71 @t67)) % 0.37/0.58 (assume @p1 @t11) % 0.37/0.58 (assume @p2 (forall (@list @t4 @t1 @t2) (= (tptp.member @t2 (tptp.difference @t4 @t1)) (and @t5 (not @t3))))) % 0.37/0.58 (assume @p3 (forall @t12 (not (tptp.member @t4 tptp.empty_set)))) % 0.37/0.58 (assume @p4 (forall @t10 (= (= @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.37/0.58 (assume @p5 (forall @t12 (tptp.subset @t4 @t4))) % 0.37/0.58 (assume @p6 (forall @t12 (= (tptp.empty @t4) (forall @t13 (not (tptp.member @t1 @t4)))))) % 0.37/0.58 (assume @p7 @t17) % 0.37/0.58 (assume @p8 true) % 0.37/0.58 (step @p9 :rule instantiate :premises (@p2) :args ((@list @t22 @t19 @t21))) % 0.37/0.58 (step @p10 :rule bool-impl-elim :args (@t5 @t3)) % 0.37/0.58 (step @p11 :rule cong :premises (@p10) :args (@t7)) % 0.37/0.58 (step @p12 :rule refl :args (@t8)) % 0.37/0.58 (step @p13 :rule cong :premises (@p12 @p11) :args (@t9)) % 0.37/0.58 (step @p14 :rule cong :premises (@p13) :args (@t11)) % 0.37/0.58 (step @p15 :rule eq_resolve :premises (@p1 @p14)) % 0.37/0.58 (step @p16 :rule instantiate :premises (@p15) :args ((@list @t19 tptp.empty_set))) % 0.37/0.58 (step @p17 :rule instantiate :premises (@p4) :args (@t23)) % 0.37/0.58 (step @p18 :rule bool-impl-elim :args (@t15 @t14)) % 0.37/0.58 (step @p19 :rule cong :premises (@p18) :args (@t16)) % 0.37/0.58 (step @p20 :rule cong :premises (@p19) :args (@t17)) % 0.37/0.58 (step @p21 :rule eq_resolve :premises (@p7 @p20)) % 0.37/0.58 (step @p22 :rule refl :args (@t29)) % 0.37/0.58 (step @p23 :rule bool-double-not-elim :args (@t18)) % 0.37/0.58 (step @p24 :rule nary_cong :premises (@p23 @p22) :args ((or (not @t30) @t29))) % 0.37/0.58 (step @p25 :rule eq-symm :args (@t19 tptp.empty_set)) % 0.37/0.58 (step @p26 :rule refl :args (@t27)) % 0.37/0.58 (step @p27 :rule nary_cong :premises (@p26 @p25) :args (@t31)) % 0.37/0.58 (step @p28 :rule cong :premises (@p27) :args (@t32)) % 0.37/0.58 (step @p29 :rule refl :args (@t30)) % 0.37/0.58 (step @p30 :rule cong :premises (@p29 @p28) :args ((=> @t30 @t32))) % 0.37/0.58 (assume-push @p130 @t30) % 0.37/0.58 (step @p32 :rule skolemize :premises (@p21)) % 0.37/0.58 (step-pop @p131 :rule scope :premises (@p32)) % 0.37/0.58 (step @p33 :rule process_scope :premises (@p131) :args (@t32)) % 0.37/0.58 (step @p35 :rule eq_resolve :premises (@p33 @p30)) % 0.37/0.58 (step @p36 :rule implies_elim :premises (@p35)) % 0.37/0.58 (step @p37 :rule eq_resolve :premises (@p36 @p24)) % 0.37/0.58 (step @p38 :rule chain_m_resolution :premises (@p37 @p21) :args (@t29 @t33 (@list @t18))) % 0.37/0.58 (step @p39 :rule cnf_or_neg :args (@t28 1)) % 0.37/0.58 (step @p40 :rule chain_m_resolution :premises (@p39 @p38) :args ((not @t24) @t33 @t34)) % 0.37/0.58 (step @p41 :rule cnf_equiv_pos2 :args (@t38)) % 0.37/0.58 (step @p42 :rule reordering :premises (@p41) :args ((or @t24 @t39 (not @t38)))) % 0.37/0.58 (step @p43 :rule chain_m_resolution :premises (@p42 @p40 @p17) :args (@t39 @t40 (@list @t24 @t38))) % 0.37/0.58 (step @p44 :rule instantiate :premises (@p15) :args (@t23)) % 0.37/0.58 (step @p45 :rule instantiate :premises (@p3) :args ((@list @t44))) % 0.37/0.58 (step @p46 :rule bool-double-not-elim :args (@t45)) % 0.37/0.58 (step @p47 :rule refl :args (@t47)) % 0.37/0.58 (step @p48 :rule nary_cong :premises (@p47 @p46) :args ((or @t47 (not @t46)))) % 0.37/0.58 (step @p49 :rule cnf_or_neg :args (@t47 0)) % 0.37/0.58 (step @p50 :rule eq_resolve :premises (@p49 @p48)) % 0.37/0.58 (step @p51 :rule reordering :premises (@p50) :args ((or @t45 @t47))) % 0.37/0.58 (step @p52 :rule chain_m_resolution :premises (@p51 @p45) :args (@t47 @t33 (@list @t45))) % 0.37/0.58 (step @p53 :rule refl :args (@t48)) % 0.37/0.58 (step @p54 :rule bool-double-not-elim :args (@t43)) % 0.37/0.58 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or (not @t49) @t48))) % 0.37/0.58 (assume-push @p132 @t49) % 0.37/0.58 (step @p57 :rule skolemize :premises (@p132)) % 0.37/0.58 (step-pop @p133 :rule scope :premises (@p57)) % 0.37/0.58 (step @p58 :rule process_scope :premises (@p133) :args (@t48)) % 0.37/0.58 (step @p60 :rule implies_elim :premises (@p58)) % 0.37/0.58 (step @p61 :rule eq_resolve :premises (@p60 @p55)) % 0.37/0.58 (step @p62 :rule chain_m_resolution :premises (@p61 @p52) :args (@t43 @t50 (@list @t47))) % 0.37/0.58 (step @p63 :rule cnf_equiv_pos2 :args (@t51)) % 0.37/0.58 (step @p64 :rule reordering :premises (@p63) :args ((or @t36 @t49 (not @t51)))) % 0.37/0.58 (step @p65 :rule chain_m_resolution :premises (@p64 @p62 @p44) :args (@t36 @t52 (@list @t43 @t51))) % 0.37/0.58 (step @p66 :rule cnf_and_neg :args (@t37)) % 0.37/0.58 (step @p67 :rule reordering :premises (@p66) :args ((or (not @t36) @t37 @t53))) % 0.37/0.58 (step @p68 :rule chain_m_resolution :premises (@p67 @p65 @p43) :args (@t53 (@list false true) (@list @t36 @t37))) % 0.37/0.58 (step @p69 :rule cnf_equiv_pos2 :args (@t56)) % 0.37/0.58 (step @p70 :rule reordering :premises (@p69) :args ((or @t35 @t57 (not @t56)))) % 0.37/0.58 (step @p71 :rule chain_m_resolution :premises (@p70 @p68 @p16) :args (@t57 @t40 (@list @t35 @t56))) % 0.37/0.58 (step @p72 :rule refl :args (@t62)) % 0.37/0.58 (step @p73 :rule bool-double-not-elim :args (@t55)) % 0.37/0.58 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or (not @t57) @t62))) % 0.37/0.58 (assume-push @p134 @t57) % 0.37/0.58 (step @p76 :rule skolemize :premises (@p134)) % 0.37/0.58 (step-pop @p135 :rule scope :premises (@p76)) % 0.37/0.58 (step @p77 :rule process_scope :premises (@p135) :args (@t62)) % 0.37/0.58 (step @p79 :rule implies_elim :premises (@p77)) % 0.37/0.58 (step @p80 :rule eq_resolve :premises (@p79 @p74)) % 0.37/0.58 (step @p81 :rule chain_m_resolution :premises (@p80 @p71) :args (@t62 @t33 (@list @t55))) % 0.37/0.58 (step @p82 :rule bool-double-not-elim :args (@t59)) % 0.37/0.58 (step @p83 :rule refl :args (@t61)) % 0.37/0.58 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or @t61 (not @t60)))) % 0.37/0.58 (step @p85 :rule cnf_or_neg :args (@t61 0)) % 0.37/0.58 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.37/0.58 (step @p87 :rule reordering :premises (@p86) :args ((or @t59 @t61))) % 0.37/0.58 (step @p88 :rule chain_m_resolution :premises (@p87 @p81) :args (@t59 @t33 (@list @t61))) % 0.37/0.58 (assume-push @p136 @t20) % 0.37/0.58 (step @p90 :rule instantiate :premises (@p136) :args ((@list @t58))) % 0.37/0.58 (step-pop @p137 :rule scope :premises (@p90)) % 0.37/0.58 (step @p91 :rule process_scope :premises (@p137) :args (@t60)) % 0.37/0.58 (step @p93 :rule implies_elim :premises (@p91)) % 0.37/0.58 (step @p94 :rule chain_m_resolution :premises (@p93 @p88) :args (@t63 @t50 (@list @t59))) % 0.37/0.58 (step @p95 :rule refl :args (@t64)) % 0.37/0.58 (step @p96 :rule bool-double-not-elim :args (@t20)) % 0.37/0.58 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or (not @t63) @t64))) % 0.37/0.58 (step @p98 :rule bool-double-not-elim :args (@t64)) % 0.37/0.58 (step @p99 :rule refl :args (@t63)) % 0.37/0.58 (step @p100 :rule cong :premises (@p99 @p98) :args ((=> @t63 @t66))) % 0.37/0.58 (assume-push @p138 @t63) % 0.37/0.58 (step @p102 :rule skolemize :premises (@p138)) % 0.37/0.58 (step-pop @p139 :rule scope :premises (@p102)) % 0.37/0.58 (step @p103 :rule process_scope :premises (@p139) :args (@t66)) % 0.37/0.59 (step @p105 :rule eq_resolve :premises (@p103 @p100)) % 0.37/0.59 (step @p106 :rule implies_elim :premises (@p105)) % 0.37/0.59 (step @p107 :rule eq_resolve :premises (@p106 @p97)) % 0.37/0.59 (step @p108 :rule chain_m_resolution :premises (@p107 @p94) :args (@t64 @t33 (@list @t20))) % 0.37/0.59 (step @p109 :rule cnf_and_pos :args (@t67 1)) % 0.37/0.59 (step @p110 :rule reordering :premises (@p109) :args ((or @t65 @t68))) % 0.37/0.59 (step @p111 :rule chain_m_resolution :premises (@p110 @p108) :args (@t68 @t50 (@list @t64))) % 0.37/0.59 (step @p112 :rule instantiate :premises (@p15) :args ((@list @t19 @t25))) % 0.37/0.59 (step @p113 :rule bool-double-not-elim :args (@t26)) % 0.37/0.59 (step @p114 :rule refl :args (@t28)) % 0.37/0.59 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or @t28 (not @t27)))) % 0.37/0.59 (step @p116 :rule cnf_or_neg :args (@t28 0)) % 0.37/0.59 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 0.37/0.59 (step @p118 :rule reordering :premises (@p117) :args ((or @t26 @t28))) % 0.37/0.59 (step @p119 :rule chain_m_resolution :premises (@p118 @p38) :args (@t26 @t33 @t34)) % 0.37/0.59 (step @p120 :rule cnf_equiv_pos1 :args (@t70)) % 0.37/0.59 (step @p121 :rule reordering :premises (@p120) :args ((or @t27 @t69 (not @t70)))) % 0.37/0.59 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p112) :args (@t69 @t52 (@list @t26 @t70))) % 0.37/0.59 (step @p123 :rule instantiate :premises (@p122) :args ((@list @t21))) % 0.37/0.59 (step @p124 :rule cnf_or_pos :args (@t72)) % 0.37/0.59 (step @p125 :rule reordering :premises (@p124) :args ((or @t65 @t71 (not @t72)))) % 0.37/0.59 (step @p126 :rule chain_m_resolution :premises (@p125 @p108 @p123) :args (@t71 @t52 (@list @t64 @t72))) % 0.37/0.59 (step @p127 :rule cnf_equiv_pos1 :args (@t73)) % 0.37/0.59 (step @p128 :rule reordering :premises (@p127) :args ((or @t67 (not @t71) (not @t73)))) % 0.37/0.59 (step @p129 false :rule chain_m_resolution :premises (@p128 @p126 @p111 @p9) :args (false (@list false true false) (@list @t71 @t67 @t73))) % 0.37/0.59 ) % 0.37/0.59 % SZS output end Proof % 0.37/0.59 % cvc5 exiting %------------------------------------------------------------------------------