%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET013+4 : 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 : n009.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 08:46:55 AM UTC 2026 % Result : Theorem 0.40s 0.57s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET013+4 : TPTP v9.2.1. Released v2.2.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n009.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 14:40:14 EDT 2026 % 0.16/0.35 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.57 % SZS status Theorem % 0.40/0.57 % SZS output start Proof % 0.40/0.57 ( % 0.40/0.57 (declare-sort $$unsorted 0) % 0.40/0.57 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.57 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.57 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.57 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.40/0.57 (declare-const tptp.empty_set $$unsorted) % 0.40/0.57 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.57 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.40/0.57 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.40/0.57 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.40/0.57 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.40/0.57 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.57 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.40/0.57 (define @t1 () (@var "B" $$unsorted)) % 0.40/0.57 (define @t2 () (@var "X" $$unsorted)) % 0.40/0.57 (define @t3 () (tptp.member @t2 @t1)) % 0.40/0.57 (define @t4 () (@var "A" $$unsorted)) % 0.40/0.57 (define @t5 () (tptp.member @t2 @t4)) % 0.40/0.57 (define @t6 () (@list @t2)) % 0.40/0.57 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.40/0.57 (define @t8 () (tptp.subset @t4 @t1)) % 0.40/0.57 (define @t9 () (= @t8 @t7)) % 0.40/0.57 (define @t10 () (@list @t4 @t1)) % 0.40/0.57 (define @t11 () (forall @t10 @t9)) % 0.40/0.57 (define @t12 () (@list @t2 @t4)) % 0.40/0.57 (define @t13 () (tptp.intersection @t4 @t1)) % 0.40/0.57 (define @t14 () (@list @t2 @t4 @t1)) % 0.40/0.57 (define @t15 () (@var "E" $$unsorted)) % 0.40/0.57 (define @t16 () (= @t2 @t4)) % 0.40/0.57 (define @t17 () (@var "Y" $$unsorted)) % 0.40/0.57 (define @t18 () (tptp.member @t2 @t17)) % 0.40/0.57 (define @t19 () (tptp.member @t17 @t4)) % 0.40/0.57 (define @t20 () (@list @t17)) % 0.40/0.57 (define @t21 () (forall @t10 (tptp.equal_set @t13 (tptp.intersection @t1 @t4)))) % 0.40/0.57 (define @t22 () (@quantifiers_skolemize @t21 1)) % 0.40/0.57 (define @t23 () (@quantifiers_skolemize @t21 0)) % 0.40/0.57 (define @t24 () (tptp.intersection @t23 @t22)) % 0.40/0.57 (define @t25 () (tptp.member @t2 @t24)) % 0.40/0.57 (define @t26 () (tptp.intersection @t22 @t23)) % 0.40/0.57 (define @t27 () (tptp.member @t2 @t26)) % 0.40/0.57 (define @t28 () (forall @t6 (or (not @t27) @t25))) % 0.40/0.57 (define @t29 () (@quantifiers_skolemize @t28 0)) % 0.40/0.57 (define @t30 () (@list @t24 @t26)) % 0.40/0.57 (define @t31 () (forall @t6 (or (not @t25) @t27))) % 0.40/0.57 (define @t32 () (@quantifiers_skolemize @t31 0)) % 0.40/0.57 (define @t33 () (tptp.member @t32 @t24)) % 0.40/0.57 (define @t34 () (tptp.member @t32 @t26)) % 0.40/0.57 (define @t35 () (not @t33)) % 0.40/0.57 (define @t36 () (or @t35 @t34)) % 0.40/0.57 (define @t37 () (tptp.member @t32 @t22)) % 0.40/0.57 (define @t38 () (tptp.member @t32 @t23)) % 0.40/0.57 (define @t39 () (and @t38 @t37)) % 0.40/0.57 (define @t40 () (= @t33 @t39)) % 0.40/0.57 (define @t41 () (and @t37 @t38)) % 0.40/0.57 (define @t42 () (= @t34 @t41)) % 0.40/0.57 (define @t43 () (not @t39)) % 0.40/0.57 (define @t44 () (not @t36)) % 0.40/0.57 (define @t45 () (not @t31)) % 0.40/0.57 (define @t46 () (@list false)) % 0.40/0.57 (define @t47 () (tptp.subset @t24 @t26)) % 0.40/0.57 (define @t48 () (= @t47 @t31)) % 0.40/0.57 (define @t49 () (@list false false)) % 0.40/0.57 (define @t50 () (tptp.subset @t26 @t24)) % 0.40/0.57 (define @t51 () (and @t47 @t50)) % 0.40/0.57 (define @t52 () (tptp.equal_set @t24 @t26)) % 0.40/0.57 (define @t53 () (= @t52 @t51)) % 0.40/0.57 (define @t54 () (not @t51)) % 0.40/0.57 (define @t55 () (@list true false)) % 0.40/0.57 (define @t56 () (= @t50 @t28)) % 0.40/0.57 (define @t57 () (not @t28)) % 0.40/0.57 (define @t58 () (tptp.member @t29 @t24)) % 0.40/0.57 (define @t59 () (tptp.member @t29 @t26)) % 0.40/0.57 (define @t60 () (not @t59)) % 0.40/0.57 (define @t61 () (or @t60 @t58)) % 0.40/0.57 (define @t62 () (not @t61)) % 0.40/0.57 (define @t63 () (@list true)) % 0.40/0.57 (define @t64 () (@list @t61)) % 0.40/0.57 (define @t65 () (tptp.member @t29 @t22)) % 0.40/0.57 (define @t66 () (tptp.member @t29 @t23)) % 0.40/0.57 (define @t67 () (and @t66 @t65)) % 0.40/0.57 (define @t68 () (= @t58 @t67)) % 0.40/0.57 (define @t69 () (not @t67)) % 0.40/0.57 (define @t70 () (and @t65 @t66)) % 0.40/0.57 (define @t71 () (= @t59 @t70)) % 0.40/0.57 (define @t72 () (not @t70)) % 0.40/0.57 (define @t73 () (@list @t70)) % 0.40/0.57 (assume @p1 @t11) % 0.40/0.57 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.40/0.57 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.40/0.57 (assume @p4 (forall @t14 (= (tptp.member @t2 @t13) (and @t5 @t3)))) % 0.40/0.57 (assume @p5 (forall @t14 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.40/0.57 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.40/0.57 (assume @p7 (forall (@list @t1 @t4 @t15) (= (tptp.member @t1 (tptp.difference @t15 @t4)) (and (tptp.member @t1 @t15) (not (tptp.member @t1 @t4)))))) % 0.40/0.57 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t16))) % 0.40/0.57 (assume @p9 (forall @t14 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t16 (= @t2 @t1))))) % 0.40/0.57 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t20 (and @t19 @t18))))) % 0.40/0.57 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t20 (=> @t19 @t18))))) % 0.40/0.57 (assume @p12 (not @t21)) % 0.40/0.57 (assume @p13 true) % 0.40/0.57 (step @p14 :rule instantiate :premises (@p4) :args ((@list @t29 @t23 @t22))) % 0.40/0.57 (step @p15 :rule bool-impl-elim :args (@t5 @t3)) % 0.40/0.57 (step @p16 :rule cong :premises (@p15) :args (@t7)) % 0.40/0.57 (step @p17 :rule refl :args (@t8)) % 0.40/0.57 (step @p18 :rule cong :premises (@p17 @p16) :args (@t9)) % 0.40/0.57 (step @p19 :rule cong :premises (@p18) :args (@t11)) % 0.40/0.57 (step @p20 :rule eq_resolve :premises (@p1 @p19)) % 0.40/0.57 (step @p21 :rule instantiate :premises (@p20) :args ((@list @t26 @t24))) % 0.40/0.57 (step @p22 :rule instantiate :premises (@p20) :args (@t30)) % 0.40/0.57 (step @p23 :rule bool-double-not-elim :args (@t33)) % 0.40/0.57 (step @p24 :rule refl :args (@t36)) % 0.40/0.57 (step @p25 :rule nary_cong :premises (@p24 @p23) :args ((or @t36 (not @t35)))) % 0.40/0.57 (step @p26 :rule cnf_or_neg :args (@t36 0)) % 0.40/0.57 (step @p27 :rule eq_resolve :premises (@p26 @p25)) % 0.40/0.57 (step @p28 :rule reordering :premises (@p27) :args ((or @t33 @t36))) % 0.40/0.57 (step @p29 :rule cnf_or_neg :args (@t36 1)) % 0.40/0.57 (step @p30 :rule instantiate :premises (@p4) :args ((@list @t32 @t23 @t22))) % 0.40/0.57 (step @p31 :rule cnf_equiv_pos1 :args (@t40)) % 0.40/0.57 (step @p32 :rule reordering :premises (@p31) :args ((or @t35 @t39 (not @t40)))) % 0.40/0.57 (step @p33 :rule instantiate :premises (@p4) :args ((@list @t32 @t22 @t23))) % 0.40/0.57 (step @p34 :rule cnf_equiv_pos2 :args (@t42)) % 0.40/0.57 (step @p35 :rule reordering :premises (@p34) :args ((or @t34 (not @t41) (not @t42)))) % 0.40/0.57 (step @p36 :rule cnf_and_pos :args (@t39 0)) % 0.40/0.57 (step @p37 :rule reordering :premises (@p36) :args ((or @t38 @t43))) % 0.40/0.57 (step @p38 :rule cnf_and_pos :args (@t39 1)) % 0.40/0.57 (step @p39 :rule reordering :premises (@p38) :args ((or @t37 @t43))) % 0.40/0.57 (step @p40 :rule cnf_and_neg :args (@t41)) % 0.40/0.57 (step @p41 :rule reordering :premises (@p40) :args ((or @t41 (not @t38) (not @t37)))) % 0.40/0.57 (step @p42 :rule chain_m_resolution :premises (@p41 @p39 @p37 @p35 @p33 @p32 @p30 @p29 @p28) :args (@t36 (@list false false true false false false true false) (@list @t37 @t38 @t41 @t42 @t39 @t40 @t34 @t33))) % 0.40/0.57 (step @p43 :rule refl :args (@t44)) % 0.40/0.57 (step @p44 :rule bool-double-not-elim :args (@t31)) % 0.40/0.57 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((or (not @t45) @t44))) % 0.40/0.57 (assume-push @p101 @t45) % 0.40/0.57 (step @p47 :rule skolemize :premises (@p101)) % 0.40/0.57 (step-pop @p102 :rule scope :premises (@p47)) % 0.40/0.57 (step @p48 :rule process_scope :premises (@p102) :args (@t44)) % 0.40/0.57 (step @p50 :rule implies_elim :premises (@p48)) % 0.40/0.57 (step @p51 :rule eq_resolve :premises (@p50 @p45)) % 0.40/0.57 (step @p52 :rule chain_m_resolution :premises (@p51 @p42) :args (@t31 @t46 (@list @t36))) % 0.40/0.57 (step @p53 :rule cnf_equiv_pos2 :args (@t48)) % 0.40/0.57 (step @p54 :rule reordering :premises (@p53) :args ((or @t47 @t45 (not @t48)))) % 0.40/0.57 (step @p55 :rule chain_m_resolution :premises (@p54 @p52 @p22) :args (@t47 @t49 (@list @t31 @t48))) % 0.40/0.57 (step @p56 :rule instantiate :premises (@p2) :args (@t30)) % 0.40/0.57 (step @p57 :rule skolemize :premises (@p12)) % 0.40/0.57 (step @p58 :rule cnf_equiv_pos2 :args (@t53)) % 0.40/0.57 (step @p59 :rule reordering :premises (@p58) :args ((or @t52 @t54 (not @t53)))) % 0.40/0.57 (step @p60 :rule chain_m_resolution :premises (@p59 @p57 @p56) :args (@t54 @t55 (@list @t52 @t53))) % 0.40/0.57 (step @p61 :rule cnf_and_neg :args (@t51)) % 0.40/0.57 (step @p62 :rule chain_m_resolution :premises (@p61 @p60 @p55) :args ((not @t50) @t55 (@list @t51 @t47))) % 0.40/0.57 (step @p63 :rule cnf_equiv_pos2 :args (@t56)) % 0.40/0.57 (step @p64 :rule reordering :premises (@p63) :args ((or @t50 @t57 (not @t56)))) % 0.40/0.57 (step @p65 :rule chain_m_resolution :premises (@p64 @p62 @p21) :args (@t57 @t55 (@list @t50 @t56))) % 0.40/0.57 (step @p66 :rule refl :args (@t62)) % 0.40/0.57 (step @p67 :rule bool-double-not-elim :args (@t28)) % 0.40/0.57 (step @p68 :rule nary_cong :premises (@p67 @p66) :args ((or (not @t57) @t62))) % 0.40/0.57 (assume-push @p103 @t57) % 0.40/0.57 (step @p70 :rule skolemize :premises (@p103)) % 0.40/0.57 (step-pop @p104 :rule scope :premises (@p70)) % 0.40/0.57 (step @p71 :rule process_scope :premises (@p104) :args (@t62)) % 0.40/0.57 (step @p73 :rule implies_elim :premises (@p71)) % 0.40/0.57 (step @p74 :rule eq_resolve :premises (@p73 @p68)) % 0.40/0.57 (step @p75 :rule chain_m_resolution :premises (@p74 @p65) :args (@t62 @t63 (@list @t28))) % 0.40/0.57 (step @p76 :rule cnf_or_neg :args (@t61 1)) % 0.40/0.57 (step @p77 :rule chain_m_resolution :premises (@p76 @p75) :args ((not @t58) @t63 @t64)) % 0.40/0.57 (step @p78 :rule cnf_equiv_pos2 :args (@t68)) % 0.40/0.57 (step @p79 :rule reordering :premises (@p78) :args ((or @t58 @t69 (not @t68)))) % 0.40/0.57 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p14) :args (@t69 @t55 (@list @t58 @t68))) % 0.40/0.57 (step @p81 :rule instantiate :premises (@p4) :args ((@list @t29 @t22 @t23))) % 0.40/0.57 (step @p82 :rule bool-double-not-elim :args (@t59)) % 0.40/0.57 (step @p83 :rule refl :args (@t61)) % 0.40/0.57 (step @p84 :rule nary_cong :premises (@p83 @p82) :args ((or @t61 (not @t60)))) % 0.40/0.57 (step @p85 :rule cnf_or_neg :args (@t61 0)) % 0.40/0.57 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.40/0.57 (step @p87 :rule reordering :premises (@p86) :args ((or @t59 @t61))) % 0.40/0.57 (step @p88 :rule chain_m_resolution :premises (@p87 @p75) :args (@t59 @t63 @t64)) % 0.40/0.57 (step @p89 :rule cnf_equiv_pos1 :args (@t71)) % 0.40/0.57 (step @p90 :rule reordering :premises (@p89) :args ((or @t60 @t70 (not @t71)))) % 0.40/0.57 (step @p91 :rule chain_m_resolution :premises (@p90 @p88 @p81) :args (@t70 @t49 (@list @t59 @t71))) % 0.40/0.57 (step @p92 :rule cnf_and_pos :args (@t70 0)) % 0.40/0.57 (step @p93 :rule reordering :premises (@p92) :args ((or @t65 @t72))) % 0.40/0.57 (step @p94 :rule chain_m_resolution :premises (@p93 @p91) :args (@t65 @t46 @t73)) % 0.40/0.57 (step @p95 :rule cnf_and_pos :args (@t70 1)) % 0.40/0.57 (step @p96 :rule reordering :premises (@p95) :args ((or @t66 @t72))) % 0.40/0.57 (step @p97 :rule chain_m_resolution :premises (@p96 @p91) :args (@t66 @t46 @t73)) % 0.40/0.57 (step @p98 :rule cnf_and_neg :args (@t67)) % 0.40/0.57 (step @p99 :rule reordering :premises (@p98) :args ((or @t67 (not @t65) (not @t66)))) % 0.40/0.57 (step @p100 false :rule chain_m_resolution :premises (@p99 @p97 @p94 @p80) :args (false (@list false false true) (@list @t66 @t65 @t67))) % 0.40/0.57 ) % 0.40/0.57 % SZS output end Proof % 0.40/0.57 % cvc5 exiting %------------------------------------------------------------------------------