%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET637+3 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.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 08:48:20 AM UTC 2026 % Result : Theorem 0.47s 0.64s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET637+3 : TPTP v9.2.1. Released v2.2.0. % 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n001.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:06:20 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.47/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.47/0.64 % SZS status Theorem % 0.47/0.64 % SZS output start Proof % 0.47/0.64 ( % 0.47/0.64 (declare-sort $$unsorted 0) % 0.47/0.64 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.47/0.64 (declare-const tptp.empty_set $$unsorted) % 0.47/0.64 (declare-const tptp.intersect (-> $$unsorted $$unsorted Bool)) % 0.47/0.64 (declare-const tptp.not_equal (-> $$unsorted $$unsorted Bool)) % 0.47/0.64 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.47/0.64 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.47/0.64 (define @t1 () (@var "C" $$unsorted)) % 0.47/0.64 (define @t2 () (@var "D" $$unsorted)) % 0.47/0.64 (define @t3 () (tptp.member @t2 @t1)) % 0.47/0.64 (define @t4 () (@var "B" $$unsorted)) % 0.47/0.64 (define @t5 () (tptp.member @t2 @t4)) % 0.47/0.64 (define @t6 () (and @t5 @t3)) % 0.47/0.64 (define @t7 () (tptp.intersection @t4 @t1)) % 0.47/0.64 (define @t8 () (@list @t2)) % 0.47/0.64 (define @t9 () (exists @t8 @t6)) % 0.47/0.64 (define @t10 () (tptp.intersect @t4 @t1)) % 0.47/0.64 (define @t11 () (= @t10 @t9)) % 0.47/0.64 (define @t12 () (@list @t4 @t1)) % 0.47/0.64 (define @t13 () (forall @t12 @t11)) % 0.47/0.64 (define @t14 () (@list @t4)) % 0.47/0.64 (define @t15 () (forall @t14 (not (tptp.member @t4 tptp.empty_set)))) % 0.47/0.64 (define @t16 () (= @t4 @t1)) % 0.47/0.64 (define @t17 () (forall @t12 (= (tptp.not_equal @t4 @t1) (not @t16)))) % 0.47/0.64 (define @t18 () (@list @t1)) % 0.47/0.64 (define @t19 () (forall @t12 (= @t10 (tptp.not_equal @t7 tptp.empty_set)))) % 0.47/0.64 (define @t20 () (forall @t18 (not (tptp.member @t1 tptp.empty_set)))) % 0.47/0.64 (define @t21 () (@list false)) % 0.47/0.64 (define @t22 () (tptp.empty tptp.empty_set)) % 0.47/0.64 (define @t23 () (= @t22 @t20)) % 0.47/0.64 (define @t24 () (@list false false)) % 0.47/0.64 (define @t25 () (@quantifiers_skolemize @t19 1)) % 0.47/0.64 (define @t26 () (@quantifiers_skolemize @t19 0)) % 0.47/0.64 (define @t27 () (tptp.intersection @t26 @t25)) % 0.47/0.64 (define @t28 () (not (= @t27 tptp.empty_set))) % 0.47/0.64 (define @t29 () (tptp.not_equal @t27 tptp.empty_set)) % 0.47/0.64 (define @t30 () (= @t29 @t28)) % 0.47/0.64 (define @t31 () (= tptp.empty_set @t27)) % 0.47/0.64 (define @t32 () (not @t31)) % 0.47/0.64 (define @t33 () (= @t29 @t32)) % 0.47/0.64 (define @t34 () (forall @t8 (not @t6))) % 0.47/0.64 (define @t35 () (not @t34)) % 0.47/0.64 (define @t36 () (forall @t8 (or (not (tptp.member @t2 @t26)) (not (tptp.member @t2 @t25))))) % 0.47/0.64 (define @t37 () (not @t36)) % 0.47/0.64 (define @t38 () (tptp.intersect @t26 @t25)) % 0.47/0.64 (define @t39 () (= @t38 @t37)) % 0.47/0.64 (define @t40 () (not @t39)) % 0.47/0.64 (define @t41 () (forall @t8 (= (tptp.member @t2 tptp.empty_set) (tptp.member @t2 @t27)))) % 0.47/0.64 (define @t42 () (@quantifiers_skolemize @t41 0)) % 0.47/0.64 (define @t43 () (@list @t42)) % 0.47/0.64 (define @t44 () (tptp.member @t42 @t25)) % 0.47/0.64 (define @t45 () (not @t44)) % 0.47/0.64 (define @t46 () (tptp.member @t42 @t26)) % 0.47/0.64 (define @t47 () (not @t46)) % 0.47/0.64 (define @t48 () (or @t47 @t45)) % 0.47/0.64 (define @t49 () (= @t38 @t29)) % 0.47/0.64 (define @t50 () (not @t33)) % 0.47/0.64 (define @t51 () (not @t29)) % 0.47/0.64 (define @t52 () (= @t31 @t41)) % 0.47/0.64 (define @t53 () (not @t41)) % 0.47/0.64 (define @t54 () (tptp.member @t42 @t27)) % 0.47/0.64 (define @t55 () (tptp.member @t42 tptp.empty_set)) % 0.47/0.64 (define @t56 () (= @t55 @t54)) % 0.47/0.64 (define @t57 () (not @t56)) % 0.47/0.64 (define @t58 () (and @t46 @t44)) % 0.47/0.64 (define @t59 () (= @t54 @t58)) % 0.47/0.64 (define @t60 () (not @t58)) % 0.47/0.64 (define @t61 () (not @t37)) % 0.47/0.64 (define @t62 () (@list true false)) % 0.47/0.64 (define @t63 () (@quantifiers_skolemize @t36 0)) % 0.47/0.64 (define @t64 () (tptp.member @t63 @t25)) % 0.47/0.64 (define @t65 () (not @t64)) % 0.47/0.64 (define @t66 () (tptp.member @t63 @t26)) % 0.47/0.64 (define @t67 () (not @t66)) % 0.47/0.64 (define @t68 () (or @t67 @t65)) % 0.47/0.64 (define @t69 () (not @t68)) % 0.47/0.64 (define @t70 () (@list true)) % 0.47/0.64 (define @t71 () (and @t66 @t64)) % 0.47/0.64 (define @t72 () (tptp.member @t63 @t27)) % 0.47/0.64 (define @t73 () (= @t72 @t71)) % 0.47/0.64 (define @t74 () (forall @t18 (not (tptp.member @t1 @t27)))) % 0.47/0.64 (define @t75 () (tptp.empty @t27)) % 0.47/0.64 (define @t76 () (= @t75 @t74)) % 0.47/0.64 (define @t77 () (not @t75)) % 0.47/0.64 (define @t78 () (and @t31 @t22)) % 0.47/0.64 (assume @p1 (forall (@list @t4 @t1 @t2) (= (tptp.member @t2 @t7) @t6))) % 0.47/0.64 (assume @p2 @t13) % 0.47/0.64 (assume @p3 @t15) % 0.47/0.64 (assume @p4 (forall @t12 (= @t16 (forall @t8 (= @t5 @t3))))) % 0.47/0.64 (assume @p5 @t17) % 0.47/0.64 (assume @p6 (forall @t12 (= @t7 (tptp.intersection @t1 @t4)))) % 0.47/0.64 (assume @p7 (forall @t12 (=> @t10 (tptp.intersect @t1 @t4)))) % 0.47/0.64 (assume @p8 (forall @t14 (= (tptp.empty @t4) (forall @t18 (not (tptp.member @t1 @t4)))))) % 0.47/0.64 (assume @p9 (not @t19)) % 0.47/0.64 (assume @p10 true) % 0.47/0.64 (step @p11 :rule instantiate :premises (@p8) :args ((@list tptp.empty_set))) % 0.47/0.64 (step @p12 :rule alpha_equiv :args (@t15 (@list @t4) (@list @t1))) % 0.47/0.64 (step @p13 :rule equiv_elim1 :premises (@p12)) % 0.47/0.64 (step @p14 :rule chain_m_resolution :premises (@p13 @p3) :args (@t20 @t21 (@list @t15))) % 0.47/0.64 (step @p15 :rule cnf_equiv_pos2 :args (@t23)) % 0.47/0.64 (step @p16 :rule reordering :premises (@p15) :args ((or @t22 (not @t20) (not @t23)))) % 0.47/0.64 (step @p17 :rule chain_m_resolution :premises (@p16 @p14 @p11) :args (@t22 @t24 (@list @t20 @t23))) % 0.47/0.64 (step @p18 :rule eq-symm :args (@t27 tptp.empty_set)) % 0.47/0.64 (step @p19 :rule cong :premises (@p18) :args (@t28)) % 0.47/0.64 (step @p20 :rule refl :args (@t29)) % 0.47/0.64 (step @p21 :rule cong :premises (@p20 @p19) :args (@t30)) % 0.47/0.64 (step @p22 :rule refl :args (@t17)) % 0.47/0.64 (step @p23 :rule cong :premises (@p22 @p21) :args ((=> @t17 @t30))) % 0.47/0.64 (assume-push @p154 @t17) % 0.47/0.64 (step @p25 :rule instantiate :premises (@p5) :args ((@list @t27 tptp.empty_set))) % 0.47/0.64 (step-pop @p155 :rule scope :premises (@p25)) % 0.47/0.64 (step @p26 :rule process_scope :premises (@p155) :args (@t30)) % 0.47/0.64 (step @p28 :rule eq_resolve :premises (@p26 @p23)) % 0.47/0.64 (step @p29 :rule implies_elim :premises (@p28)) % 0.47/0.64 (step @p30 :rule chain_m_resolution :premises (@p29 @p5) :args (@t33 @t21 (@list @t17))) % 0.47/0.64 (step @p31 :rule bool-and-de-morgan :args (@t5 @t3 true)) % 0.47/0.64 (step @p32 :rule cong :premises (@p31) :args (@t34)) % 0.47/0.64 (step @p33 :rule cong :premises (@p32) :args (@t35)) % 0.47/0.64 (step @p34 :rule exists-elim :args ((= @t9 @t35))) % 0.47/0.64 (step @p35 :rule trans :premises (@p34 @p33)) % 0.47/0.64 (step @p36 :rule refl :args (@t10)) % 0.47/0.64 (step @p37 :rule cong :premises (@p36 @p35) :args (@t11)) % 0.47/0.64 (step @p38 :rule cong :premises (@p37) :args (@t13)) % 0.47/0.64 (step @p39 :rule eq_resolve :premises (@p2 @p38)) % 0.47/0.64 (step @p40 :rule instantiate :premises (@p39) :args ((@list @t26 @t25))) % 0.47/0.64 (step @p41 :rule cnf_equiv_pos1 :args (@t39)) % 0.47/0.64 (step @p42 :rule reordering :premises (@p41) :args ((or (not @t38) @t37 @t40))) % 0.47/0.64 (assume-push @p156 @t36) % 0.47/0.64 (step @p44 :rule instantiate :premises (@p156) :args (@t43)) % 0.47/0.64 (step-pop @p157 :rule scope :premises (@p44)) % 0.47/0.64 (step @p45 :rule process_scope :premises (@p157) :args (@t48)) % 0.47/0.64 (step @p47 :rule implies_elim :premises (@p45)) % 0.47/0.64 (step @p48 :rule skolemize :premises (@p9)) % 0.47/0.64 (step @p49 :rule cnf_equiv_neg1 :args (@t49)) % 0.47/0.64 (step @p50 :rule reordering :premises (@p49) :args ((or @t38 @t29 @t49))) % 0.47/0.64 (step @p51 :rule cnf_equiv_pos1 :args (@t33)) % 0.47/0.64 (step @p52 :rule reordering :premises (@p51) :args ((or @t51 @t32 @t50))) % 0.47/0.64 (step @p53 :rule instantiate :premises (@p4) :args ((@list tptp.empty_set @t27))) % 0.47/0.64 (step @p54 :rule cnf_equiv_pos2 :args (@t52)) % 0.47/0.64 (step @p55 :rule reordering :premises (@p54) :args ((or @t31 @t53 (not @t52)))) % 0.47/0.64 (step @p56 :rule refl :args (@t57)) % 0.47/0.64 (step @p57 :rule bool-double-not-elim :args (@t41)) % 0.47/0.64 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or (not @t53) @t57))) % 0.47/0.64 (assume-push @p158 @t53) % 0.47/0.64 (step @p60 :rule skolemize :premises (@p158)) % 0.47/0.64 (step-pop @p159 :rule scope :premises (@p60)) % 0.47/0.64 (step @p61 :rule process_scope :premises (@p159) :args (@t57)) % 0.47/0.64 (step @p63 :rule implies_elim :premises (@p61)) % 0.47/0.64 (step @p64 :rule eq_resolve :premises (@p63 @p58)) % 0.47/0.64 (step @p65 :rule instantiate :premises (@p3) :args (@t43)) % 0.47/0.64 (step @p66 :rule cnf_equiv_neg1 :args (@t56)) % 0.47/0.64 (step @p67 :rule reordering :premises (@p66) :args ((or @t55 @t54 @t56))) % 0.47/0.64 (step @p68 :rule instantiate :premises (@p1) :args ((@list @t26 @t25 @t42))) % 0.47/0.64 (step @p69 :rule cnf_equiv_pos1 :args (@t59)) % 0.47/0.64 (step @p70 :rule reordering :premises (@p69) :args ((or (not @t54) @t58 (not @t59)))) % 0.47/0.64 (step @p71 :rule cnf_and_pos :args (@t58 0)) % 0.47/0.64 (step @p72 :rule reordering :premises (@p71) :args ((or @t46 @t60))) % 0.47/0.64 (step @p73 :rule cnf_and_pos :args (@t58 1)) % 0.47/0.64 (step @p74 :rule reordering :premises (@p73) :args ((or @t44 @t60))) % 0.47/0.64 (step @p75 :rule cnf_or_pos :args (@t48)) % 0.47/0.64 (step @p76 :rule reordering :premises (@p75) :args ((or @t45 @t47 (not @t48)))) % 0.47/0.64 (step @p77 :rule chain_m_resolution :premises (@p76 @p74 @p72 @p70 @p68 @p67 @p65 @p64 @p55 @p53 @p52 @p30 @p50 @p48 @p47 @p42 @p40) :args (@t37 (@list false false false false false true true true false true false false true false true false) (@list @t44 @t46 @t58 @t59 @t54 @t55 @t56 @t41 @t52 @t31 @t33 @t29 @t49 @t48 @t38 @t39))) % 0.47/0.64 (step @p78 :rule bool-double-not-elim :args (@t36)) % 0.47/0.64 (step @p79 :rule refl :args (@t38)) % 0.47/0.64 (step @p80 :rule refl :args (@t40)) % 0.47/0.64 (step @p81 :rule nary_cong :premises (@p80 @p79 @p78) :args ((or @t40 @t38 @t61))) % 0.47/0.64 (step @p82 :rule cnf_equiv_pos2 :args (@t39)) % 0.47/0.64 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.47/0.64 (step @p84 :rule reordering :premises (@p83) :args ((or @t38 @t36 @t40))) % 0.47/0.64 (step @p85 :rule chain_m_resolution :premises (@p84 @p77 @p40) :args (@t38 @t62 (@list @t36 @t39))) % 0.47/0.64 (step @p86 :rule cnf_equiv_neg2 :args (@t49)) % 0.47/0.64 (step @p87 :rule chain_m_resolution :premises (@p86 @p48 @p85) :args (@t51 @t62 (@list @t49 @t38))) % 0.47/0.64 (step @p88 :rule bool-double-not-elim :args (@t31)) % 0.47/0.64 (step @p89 :rule refl :args (@t50)) % 0.47/0.64 (step @p90 :rule nary_cong :premises (@p89 @p20 @p88) :args ((or @t50 @t29 (not @t32)))) % 0.47/0.64 (step @p91 :rule cnf_equiv_pos2 :args (@t33)) % 0.47/0.64 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 0.47/0.64 (step @p93 :rule reordering :premises (@p92) :args ((or @t29 @t31 @t50))) % 0.47/0.64 (step @p94 :rule chain_m_resolution :premises (@p93 @p87 @p30) :args (@t31 @t62 (@list @t29 @t33))) % 0.47/0.64 (step @p95 :rule instantiate :premises (@p8) :args ((@list @t27))) % 0.47/0.64 (step @p96 :rule instantiate :premises (@p1) :args ((@list @t26 @t25 @t63))) % 0.47/0.64 (step @p97 :rule refl :args (@t69)) % 0.47/0.64 (step @p98 :rule nary_cong :premises (@p78 @p97) :args ((or @t61 @t69))) % 0.47/0.64 (assume-push @p160 @t37) % 0.47/0.64 (step @p100 :rule skolemize :premises (@p160)) % 0.47/0.64 (step-pop @p161 :rule scope :premises (@p100)) % 0.47/0.64 (step @p101 :rule process_scope :premises (@p161) :args (@t69)) % 0.47/0.64 (step @p103 :rule implies_elim :premises (@p101)) % 0.47/0.64 (step @p104 :rule eq_resolve :premises (@p103 @p98)) % 0.47/0.64 (step @p105 :rule chain_m_resolution :premises (@p104 @p77) :args (@t69 @t70 (@list @t36))) % 0.47/0.64 (step @p106 :rule bool-double-not-elim :args (@t66)) % 0.47/0.64 (step @p107 :rule refl :args (@t68)) % 0.47/0.64 (step @p108 :rule nary_cong :premises (@p107 @p106) :args ((or @t68 (not @t67)))) % 0.47/0.64 (step @p109 :rule cnf_or_neg :args (@t68 0)) % 0.47/0.64 (step @p110 :rule eq_resolve :premises (@p109 @p108)) % 0.47/0.64 (step @p111 :rule reordering :premises (@p110) :args ((or @t66 @t68))) % 0.47/0.64 (step @p112 :rule bool-double-not-elim :args (@t64)) % 0.47/0.64 (step @p113 :rule nary_cong :premises (@p107 @p112) :args ((or @t68 (not @t65)))) % 0.47/0.64 (step @p114 :rule cnf_or_neg :args (@t68 1)) % 0.47/0.64 (step @p115 :rule eq_resolve :premises (@p114 @p113)) % 0.47/0.64 (step @p116 :rule reordering :premises (@p115) :args ((or @t64 @t68))) % 0.47/0.64 (step @p117 :rule cnf_and_neg :args (@t71)) % 0.47/0.64 (step @p118 :rule reordering :premises (@p117) :args ((or @t67 @t65 @t71))) % 0.47/0.64 (step @p119 :rule chain_m_resolution :premises (@p118 @p116 @p111) :args ((or @t68 @t71) @t24 (@list @t64 @t66))) % 0.47/0.64 (step @p120 :rule chain_m_resolution :premises (@p119 @p105) :args (@t71 @t70 (@list @t68))) % 0.47/0.64 (step @p121 :rule cnf_equiv_pos2 :args (@t73)) % 0.47/0.64 (step @p122 :rule reordering :premises (@p121) :args ((or @t72 (not @t71) (not @t73)))) % 0.47/0.64 (step @p123 :rule chain_m_resolution :premises (@p122 @p120 @p96) :args (@t72 @t24 (@list @t71 @t73))) % 0.47/0.64 (assume-push @p162 @t74) % 0.47/0.64 (step @p125 :rule instantiate :premises (@p162) :args ((@list @t63))) % 0.47/0.64 (step-pop @p163 :rule scope :premises (@p125)) % 0.47/0.64 (step @p126 :rule process_scope :premises (@p163) :args ((not @t72))) % 0.47/0.64 (step @p128 :rule implies_elim :premises (@p126)) % 0.47/0.64 (step @p129 :rule chain_m_resolution :premises (@p128 @p123) :args ((not @t74) @t21 (@list @t72))) % 0.47/0.64 (step @p130 :rule cnf_equiv_pos1 :args (@t76)) % 0.47/0.64 (step @p131 :rule reordering :premises (@p130) :args ((or @t74 @t77 (not @t76)))) % 0.47/0.64 (step @p132 :rule chain_m_resolution :premises (@p131 @p129 @p95) :args (@t77 @t62 (@list @t74 @t76))) % 0.47/0.64 (assume-push @p164 @t31) % 0.47/0.64 (assume-push @p165 @t22) % 0.47/0.64 (assume-push @p166 @t22) % 0.47/0.64 (assume-push @p167 @t31) % 0.47/0.64 (step @p137 :rule true_intro :premises (@p17)) % 0.47/0.64 (step @p138 :rule symm :premises (@p164)) % 0.47/0.64 (step @p139 :rule cong :premises (@p138) :args (@t75)) % 0.47/0.64 (step @p140 :rule trans :premises (@p139 @p137)) % 0.47/0.64 (step @p141 :rule true_elim :premises (@p140)) % 0.47/0.64 (step-pop @p168 :rule scope :premises (@p141)) % 0.47/0.64 (step-pop @p169 :rule scope :premises (@p168)) % 0.47/0.64 (step @p142 :rule process_scope :premises (@p169) :args (@t75)) % 0.47/0.64 (step @p145 :rule and_intro :premises (@p17 @p164)) % 0.47/0.64 (step @p146 :rule modus_ponens :premises (@p145 @p142)) % 0.47/0.64 (step-pop @p170 :rule scope :premises (@p146)) % 0.47/0.64 (step-pop @p171 :rule scope :premises (@p170)) % 0.47/0.64 (step @p147 :rule process_scope :premises (@p171) :args (@t75)) % 0.47/0.64 (step @p150 :rule implies_elim :premises (@p147)) % 0.47/0.64 (step @p151 :rule cnf_and_neg :args (@t78)) % 0.47/0.64 (step @p152 :rule resolution :premises (@p151 @p150) :args (true @t78)) % 0.47/0.64 (step @p153 false :rule chain_m_resolution :premises (@p152 @p132 @p94 @p17) :args (false (@list true false false) (@list @t75 @t31 @t22))) % 0.47/0.64 ) % 0.47/0.64 % SZS output end Proof % 0.47/0.64 % cvc5 exiting %------------------------------------------------------------------------------