%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET011+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 : n014.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 08:46:54 AM UTC 2026 % Result : Theorem 0.44s 0.63s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET011+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 % 0.16/0.34 % Computer : n014.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:40:28 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.48 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.63 % SZS status Theorem % 0.44/0.63 % SZS output start Proof % 0.44/0.63 ( % 0.44/0.63 (declare-sort $$unsorted 0) % 0.44/0.63 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (define @t1 () (@var "C" $$unsorted)) % 0.44/0.63 (define @t2 () (@var "D" $$unsorted)) % 0.44/0.63 (define @t3 () (tptp.member @t2 @t1)) % 0.44/0.63 (define @t4 () (@var "B" $$unsorted)) % 0.44/0.63 (define @t5 () (tptp.member @t2 @t4)) % 0.44/0.63 (define @t6 () (tptp.intersection @t4 @t1)) % 0.44/0.63 (define @t7 () (@list @t4 @t1 @t2)) % 0.44/0.63 (define @t8 () (tptp.difference @t4 @t1)) % 0.44/0.63 (define @t9 () (tptp.subset @t4 @t1)) % 0.44/0.63 (define @t10 () (= @t4 @t1)) % 0.44/0.63 (define @t11 () (@list @t4 @t1)) % 0.44/0.63 (define @t12 () (@list @t2)) % 0.44/0.63 (define @t13 () (forall @t11 (= @t10 (forall @t12 (= @t5 @t3))))) % 0.44/0.63 (define @t14 () (tptp.difference @t4 @t8)) % 0.44/0.63 (define @t15 () (forall @t11 (= @t14 @t6))) % 0.44/0.63 (define @t16 () (not @t15)) % 0.44/0.63 (define @t17 () (forall @t11 (= @t6 @t14))) % 0.44/0.63 (define @t18 () (@quantifiers_skolemize @t17 1)) % 0.44/0.63 (define @t19 () (@quantifiers_skolemize @t17 0)) % 0.44/0.63 (define @t20 () (tptp.intersection @t19 @t18)) % 0.44/0.63 (define @t21 () (tptp.difference @t19 @t18)) % 0.44/0.63 (define @t22 () (tptp.difference @t19 @t21)) % 0.44/0.63 (define @t23 () (forall @t12 (= (tptp.member @t2 @t22) (tptp.member @t2 @t20)))) % 0.44/0.63 (define @t24 () (@quantifiers_skolemize @t23 0)) % 0.44/0.63 (define @t25 () (tptp.member @t24 @t19)) % 0.44/0.63 (define @t26 () (tptp.member @t24 @t18)) % 0.44/0.63 (define @t27 () (and @t26 @t25)) % 0.44/0.63 (define @t28 () (not @t27)) % 0.44/0.63 (define @t29 () (tptp.member @t24 @t21)) % 0.44/0.63 (define @t30 () (not @t29)) % 0.44/0.63 (define @t31 () (and @t25 @t30)) % 0.44/0.63 (define @t32 () (not @t31)) % 0.44/0.63 (define @t33 () (tptp.intersection @t18 @t19)) % 0.44/0.63 (define @t34 () (tptp.member @t24 @t33)) % 0.44/0.63 (define @t35 () (= @t34 @t27)) % 0.44/0.63 (define @t36 () (not @t35)) % 0.44/0.63 (define @t37 () (not @t34)) % 0.44/0.63 (define @t38 () (tptp.member @t24 @t22)) % 0.44/0.63 (define @t39 () (= @t38 @t31)) % 0.44/0.63 (define @t40 () (not @t39)) % 0.44/0.63 (define @t41 () (= (= @t22 @t20) @t23)) % 0.44/0.63 (define @t42 () (= @t20 @t22)) % 0.44/0.63 (define @t43 () (= @t42 @t23)) % 0.44/0.63 (define @t44 () (not @t23)) % 0.44/0.63 (define @t45 () (@list true false)) % 0.44/0.63 (define @t46 () (tptp.member @t24 @t20)) % 0.44/0.63 (define @t47 () (= @t38 @t46)) % 0.44/0.63 (define @t48 () (not @t46)) % 0.44/0.63 (define @t49 () (= @t20 @t33)) % 0.44/0.63 (define @t50 () (not @t49)) % 0.44/0.63 (define @t51 () (and @t49 @t37)) % 0.44/0.63 (define @t52 () (not @t26)) % 0.44/0.63 (define @t53 () (and @t25 @t52)) % 0.44/0.63 (define @t54 () (= @t29 @t53)) % 0.44/0.63 (define @t55 () (not @t54)) % 0.44/0.63 (define @t56 () (not @t53)) % 0.44/0.63 (define @t57 () (not @t25)) % 0.44/0.63 (define @t58 () (@list false false)) % 0.44/0.63 (define @t59 () (and @t49 @t48)) % 0.44/0.63 (assume @p1 (forall @t7 (= (tptp.member @t2 @t6) (and @t5 @t3)))) % 0.44/0.63 (assume @p2 (forall @t7 (= (tptp.member @t2 @t8) (and @t5 (not @t3))))) % 0.44/0.63 (assume @p3 (forall @t11 (= @t10 (and @t9 (tptp.subset @t1 @t4))))) % 0.44/0.63 (assume @p4 (forall @t11 (= @t6 (tptp.intersection @t1 @t4)))) % 0.44/0.63 (assume @p5 (forall @t11 (= @t9 (forall @t12 (=> @t5 @t3))))) % 0.44/0.63 (assume @p6 (forall (@list @t4) (tptp.subset @t4 @t4))) % 0.44/0.63 (assume @p7 @t13) % 0.44/0.63 (assume @p8 @t16) % 0.44/0.63 (assume @p9 true) % 0.44/0.63 (step @p10 :rule instantiate :premises (@p4) :args ((@list @t19 @t18))) % 0.44/0.63 (step @p11 :rule instantiate :premises (@p2) :args ((@list @t19 @t21 @t24))) % 0.44/0.63 (step @p12 :rule cnf_and_pos :args (@t27 1)) % 0.44/0.63 (step @p13 :rule reordering :premises (@p12) :args ((or @t25 @t28))) % 0.44/0.63 (step @p14 :rule cnf_and_pos :args (@t31 0)) % 0.44/0.63 (step @p15 :rule reordering :premises (@p14) :args ((or @t25 @t32))) % 0.44/0.63 (step @p16 :rule instantiate :premises (@p1) :args ((@list @t18 @t19 @t24))) % 0.44/0.63 (step @p17 :rule cnf_equiv_pos1 :args (@t35)) % 0.44/0.63 (step @p18 :rule reordering :premises (@p17) :args ((or @t27 @t37 @t36))) % 0.44/0.63 (step @p19 :rule cnf_equiv_pos1 :args (@t39)) % 0.44/0.63 (step @p20 :rule reordering :premises (@p19) :args ((or (not @t38) @t31 @t40))) % 0.44/0.63 (step @p21 :rule refl :args (@t23)) % 0.44/0.63 (step @p22 :rule eq-symm :args (@t22 @t20)) % 0.44/0.63 (step @p23 :rule cong :premises (@p22 @p21) :args (@t41)) % 0.44/0.63 (step @p24 :rule refl :args (@t13)) % 0.44/0.63 (step @p25 :rule cong :premises (@p24 @p23) :args ((=> @t13 @t41))) % 0.44/0.63 (assume-push @p134 @t13) % 0.44/0.63 (step @p27 :rule instantiate :premises (@p7) :args ((@list @t22 @t20))) % 0.44/0.63 (step-pop @p135 :rule scope :premises (@p27)) % 0.44/0.63 (step @p28 :rule process_scope :premises (@p135) :args (@t41)) % 0.44/0.63 (step @p30 :rule eq_resolve :premises (@p28 @p25)) % 0.44/0.63 (step @p31 :rule implies_elim :premises (@p30)) % 0.44/0.63 (step @p32 :rule chain_m_resolution :premises (@p31 @p7) :args (@t43 (@list false) (@list @t13))) % 0.44/0.63 (step @p33 :rule eq-symm :args (@t14 @t6)) % 0.44/0.63 (step @p34 :rule cong :premises (@p33) :args (@t15)) % 0.44/0.63 (step @p35 :rule cong :premises (@p34) :args (@t16)) % 0.44/0.63 (step @p36 :rule eq_resolve :premises (@p8 @p35)) % 0.44/0.63 (step @p37 :rule skolemize :premises (@p36)) % 0.44/0.63 (step @p38 :rule cnf_equiv_pos2 :args (@t43)) % 0.44/0.63 (step @p39 :rule reordering :premises (@p38) :args ((or @t42 @t44 (not @t43)))) % 0.44/0.63 (step @p40 :rule chain_m_resolution :premises (@p39 @p37 @p32) :args (@t44 @t45 (@list @t42 @t43))) % 0.44/0.63 (step @p41 :rule skolemize :premises (@p40)) % 0.44/0.63 (step @p42 :rule cnf_equiv_neg1 :args (@t47)) % 0.44/0.63 (step @p43 :rule reordering :premises (@p42) :args ((or @t38 @t46 @t47))) % 0.44/0.63 (step @p44 :rule refl :args (@t48)) % 0.44/0.63 (step @p45 :rule bool-double-not-elim :args (@t34)) % 0.44/0.63 (step @p46 :rule refl :args (@t50)) % 0.44/0.63 (step @p47 :rule nary_cong :premises (@p46 @p45 @p44) :args ((or @t50 (not @t37) @t48))) % 0.44/0.63 (assume-push @p136 @t49) % 0.44/0.63 (assume-push @p137 @t37) % 0.44/0.63 (assume-push @p138 @t37) % 0.44/0.63 (assume-push @p139 @t49) % 0.44/0.63 (step @p52 :rule false_intro :premises (@p137)) % 0.44/0.63 (step @p53 :rule refl :args (@t24)) % 0.44/0.63 (step @p54 :rule cong :premises (@p53 @p10) :args (@t46)) % 0.44/0.63 (step @p55 :rule trans :premises (@p54 @p52)) % 0.44/0.63 (step @p56 :rule false_elim :premises (@p55)) % 0.44/0.63 (step-pop @p140 :rule scope :premises (@p56)) % 0.44/0.63 (step-pop @p141 :rule scope :premises (@p140)) % 0.44/0.63 (step @p57 :rule process_scope :premises (@p141) :args (@t48)) % 0.44/0.63 (step @p60 :rule and_intro :premises (@p137 @p10)) % 0.44/0.63 (step @p61 :rule modus_ponens :premises (@p60 @p57)) % 0.44/0.63 (step-pop @p142 :rule scope :premises (@p61)) % 0.44/0.63 (step-pop @p143 :rule scope :premises (@p142)) % 0.44/0.63 (step @p62 :rule process_scope :premises (@p143) :args (@t48)) % 0.44/0.63 (step @p65 :rule implies_elim :premises (@p62)) % 0.44/0.63 (step @p66 :rule cnf_and_neg :args (@t51)) % 0.44/0.63 (step @p67 :rule resolution :premises (@p66 @p65) :args (true @t51)) % 0.44/0.63 (step @p68 :rule eq_resolve :premises (@p67 @p47)) % 0.44/0.63 (step @p69 :rule reordering :premises (@p68) :args ((or @t50 @t48 @t34))) % 0.44/0.63 (step @p70 :rule chain_m_resolution :premises (@p69 @p10 @p43 @p41 @p20 @p11 @p18 @p16 @p15 @p13) :args (@t25 (@list false false true true false true false true true) (@list @t49 @t46 @t47 @t38 @t39 @t34 @t35 @t31 @t27))) % 0.44/0.63 (step @p71 :rule cnf_and_pos :args (@t31 1)) % 0.44/0.63 (step @p72 :rule reordering :premises (@p71) :args ((or @t30 @t32))) % 0.44/0.63 (step @p73 :rule instantiate :premises (@p2) :args ((@list @t19 @t18 @t24))) % 0.44/0.63 (step @p74 :rule cnf_equiv_pos1 :args (@t54)) % 0.44/0.63 (step @p75 :rule reordering :premises (@p74) :args ((or @t30 @t53 @t55))) % 0.44/0.63 (step @p76 :rule cnf_and_pos :args (@t53 1)) % 0.44/0.63 (step @p77 :rule reordering :premises (@p76) :args ((or @t52 @t56))) % 0.44/0.63 (step @p78 :rule cnf_and_pos :args (@t27 0)) % 0.44/0.63 (step @p79 :rule reordering :premises (@p78) :args ((or @t26 @t28))) % 0.44/0.63 (step @p80 :rule chain_m_resolution :premises (@p18 @p16 @p69 @p10 @p79 @p43 @p41 @p77 @p20 @p11 @p75 @p73 @p72) :args (@t30 (@list false false false true false true true true false false false true) (@list @t35 @t34 @t49 @t27 @t46 @t47 @t26 @t38 @t39 @t53 @t54 @t31))) % 0.44/0.63 (step @p81 :rule bool-double-not-elim :args (@t29)) % 0.44/0.63 (step @p82 :rule refl :args (@t57)) % 0.44/0.63 (step @p83 :rule refl :args (@t31)) % 0.44/0.63 (step @p84 :rule nary_cong :premises (@p83 @p82 @p81) :args ((or @t31 @t57 (not @t30)))) % 0.44/0.63 (step @p85 :rule cnf_and_neg :args (@t31)) % 0.44/0.63 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.44/0.63 (step @p87 :rule reordering :premises (@p86) :args ((or @t29 @t31 @t57))) % 0.44/0.63 (step @p88 :rule chain_m_resolution :premises (@p87 @p80 @p70) :args (@t31 @t45 (@list @t29 @t25))) % 0.44/0.63 (step @p89 :rule cnf_equiv_pos2 :args (@t39)) % 0.44/0.63 (step @p90 :rule reordering :premises (@p89) :args ((or @t38 @t32 @t40))) % 0.44/0.63 (step @p91 :rule chain_m_resolution :premises (@p90 @p88 @p11) :args (@t38 @t58 (@list @t31 @t39))) % 0.44/0.63 (step @p92 :rule cnf_equiv_neg2 :args (@t47)) % 0.44/0.63 (step @p93 :rule chain_m_resolution :premises (@p92 @p41 @p91) :args (@t48 @t45 (@list @t47 @t38))) % 0.44/0.63 (step @p94 :rule cnf_equiv_pos2 :args (@t54)) % 0.44/0.64 (step @p95 :rule reordering :premises (@p94) :args ((or @t29 @t56 @t55))) % 0.44/0.64 (step @p96 :rule chain_m_resolution :premises (@p95 @p80 @p73) :args (@t56 @t45 (@list @t29 @t54))) % 0.44/0.64 (step @p97 :rule bool-double-not-elim :args (@t26)) % 0.44/0.64 (step @p98 :rule refl :args (@t53)) % 0.44/0.64 (step @p99 :rule nary_cong :premises (@p98 @p82 @p97) :args ((or @t53 @t57 (not @t52)))) % 0.44/0.64 (step @p100 :rule cnf_and_neg :args (@t53)) % 0.44/0.64 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.44/0.64 (step @p102 :rule reordering :premises (@p101) :args ((or @t26 @t57 @t53))) % 0.44/0.64 (step @p103 :rule chain_m_resolution :premises (@p102 @p70 @p96) :args (@t26 (@list false true) (@list @t25 @t53))) % 0.44/0.64 (step @p104 :rule cnf_and_neg :args (@t27)) % 0.44/0.64 (step @p105 :rule chain_m_resolution :premises (@p104 @p103 @p70) :args (@t27 @t58 (@list @t26 @t25))) % 0.44/0.64 (step @p106 :rule cnf_equiv_pos2 :args (@t35)) % 0.44/0.64 (step @p107 :rule reordering :premises (@p106) :args ((or @t34 @t28 @t36))) % 0.44/0.64 (step @p108 :rule chain_m_resolution :premises (@p107 @p105 @p16) :args (@t34 @t58 (@list @t27 @t35))) % 0.44/0.64 (step @p109 :rule refl :args (@t37)) % 0.44/0.64 (step @p110 :rule bool-double-not-elim :args (@t46)) % 0.44/0.64 (step @p111 :rule nary_cong :premises (@p46 @p110 @p109) :args ((or @t50 (not @t48) @t37))) % 0.44/0.64 (assume-push @p144 @t49) % 0.44/0.64 (assume-push @p145 @t48) % 0.44/0.64 (assume-push @p146 @t48) % 0.44/0.64 (assume-push @p147 @t49) % 0.44/0.64 (step @p116 :rule false_intro :premises (@p145)) % 0.44/0.64 (step @p117 :rule symm :premises (@p10)) % 0.44/0.64 (step @p53 :rule refl :args (@t24)) % 0.44/0.64 (step @p118 :rule cong :premises (@p53 @p117) :args (@t34)) % 0.44/0.64 (step @p119 :rule trans :premises (@p118 @p116)) % 0.44/0.64 (step @p120 :rule false_elim :premises (@p119)) % 0.44/0.64 (step-pop @p148 :rule scope :premises (@p120)) % 0.44/0.64 (step-pop @p149 :rule scope :premises (@p148)) % 0.44/0.64 (step @p121 :rule process_scope :premises (@p149) :args (@t37)) % 0.44/0.64 (step @p124 :rule and_intro :premises (@p145 @p10)) % 0.44/0.64 (step @p125 :rule modus_ponens :premises (@p124 @p121)) % 0.44/0.64 (step-pop @p150 :rule scope :premises (@p125)) % 0.44/0.64 (step-pop @p151 :rule scope :premises (@p150)) % 0.44/0.64 (step @p126 :rule process_scope :premises (@p151) :args (@t37)) % 0.44/0.64 (step @p129 :rule implies_elim :premises (@p126)) % 0.44/0.64 (step @p130 :rule cnf_and_neg :args (@t59)) % 0.44/0.64 (step @p131 :rule resolution :premises (@p130 @p129) :args (true @t59)) % 0.44/0.64 (step @p132 :rule eq_resolve :premises (@p131 @p111)) % 0.44/0.64 (step @p133 false :rule chain_m_resolution :premises (@p132 @p108 @p93 @p10) :args (false (@list false true false) (@list @t34 @t46 @t49))) % 0.44/0.64 ) % 0.44/0.64 % SZS output end Proof % 0.44/0.64 % cvc5 exiting %------------------------------------------------------------------------------