%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET580^3 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n015.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 08:48:05 AM UTC 2026 % Result : Theorem 0.39s 0.57s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET580^3 : TPTP v9.2.1. Released v3.6.0. % 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n015.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:03:19 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.39/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.57 % SZS status Theorem % 0.39/0.57 % SZS output start Proof % 0.39/0.57 ( % 0.39/0.57 (declare-sort $$unsorted 0) % 0.39/0.57 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.39/0.57 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.39/0.57 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.39/0.57 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.39/0.57 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.39/0.57 (define tptp.union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.57 (define tptp.excl_union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.39/0.57 (define tptp.intersection () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.57 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.39/0.57 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.39/0.57 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.39/0.57 (define tptp.subset () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.39/0.57 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.39/0.57 (define tptp.misses () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (not (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))))) % 0.39/0.57 (define @t1 () (@var "U" $$unsorted)) % 0.39/0.57 (define @t2 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.57 (define @t3 () (_ @t2 @t1)) % 0.39/0.57 (define @t4 () (not @t3)) % 0.39/0.57 (define @t5 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.57 (define @t6 () (_ @t5 @t1)) % 0.39/0.57 (define @t7 () (= @t6 @t4)) % 0.39/0.57 (define @t8 () (= (_ (_ (_ tptp.excl_union @t5) @t2) @t1) @t7)) % 0.39/0.57 (define @t9 () (@list @t5 @t2 @t1)) % 0.39/0.57 (define @t10 () (forall @t9 @t8)) % 0.39/0.57 (define @t11 () (not @t10)) % 0.39/0.57 (define @t12 () (@var "X" $$unsorted)) % 0.39/0.57 (define @t13 () (@var "M" (-> $$unsorted Bool))) % 0.39/0.57 (define @t14 () (lambda (@list @t12 @t13) (_ @t13 @t12))) % 0.39/0.57 (define @t15 () (lambda (@list @t12) false)) % 0.39/0.57 (define @t16 () (@var "Y" $$unsorted)) % 0.39/0.57 (define @t17 () (= @t1 @t12)) % 0.39/0.57 (define @t18 () (lambda (@list @t12 @t16 @t1) (or @t17 (= @t1 @t16)))) % 0.39/0.57 (define @t19 () (lambda (@list @t12 @t1) @t17)) % 0.39/0.57 (define @t20 () (lambda @t9 (or @t6 @t3))) % 0.39/0.57 (define @t21 () (not @t6)) % 0.39/0.57 (define @t22 () (and @t21 @t3)) % 0.39/0.57 (define @t23 () (and @t6 @t4)) % 0.39/0.57 (define @t24 () (or @t23 @t22)) % 0.39/0.57 (define @t25 () (lambda @t9 @t24)) % 0.39/0.57 (define @t26 () (and @t6 @t3)) % 0.39/0.57 (define @t27 () (lambda @t9 @t26)) % 0.39/0.57 (define @t28 () (lambda @t9 @t23)) % 0.39/0.57 (define @t29 () (lambda (@list @t5 @t1) @t21)) % 0.39/0.57 (define @t30 () (@list @t5 @t2)) % 0.39/0.57 (define @t31 () (lambda @t30 (= (_ (_ tptp.intersection @t5) @t2) tptp.emptyset))) % 0.39/0.57 (define @t32 () (@list @t1)) % 0.39/0.57 (define @t33 () (lambda @t30 (forall @t32 (=> @t6 @t3)))) % 0.39/0.57 (define @t34 () (exists @t32 @t26)) % 0.39/0.57 (define @t35 () (lambda @t30 @t34)) % 0.39/0.57 (define @t36 () (lambda @t30 (not @t34))) % 0.39/0.57 (define @t37 () (_ @t2 @t1)) % 0.39/0.57 (define @t38 () (_ @t5 @t1)) % 0.39/0.57 (define @t39 () (= @t24 @t7)) % 0.39/0.57 (define @t40 () (lambda @t32 @t24)) % 0.39/0.57 (define @t41 () (lambda (@list @t2 @t1) @t24)) % 0.39/0.57 (define @t42 () (_ @t25 @t5)) % 0.39/0.57 (define @t43 () (_ (_ @t42 @t2) @t1)) % 0.39/0.57 (define @t44 () (forall @t9 (= @t43 @t7))) % 0.39/0.57 (define @t45 () (not @t37)) % 0.39/0.57 (define @t46 () (forall @t9 (= (or (and @t38 @t45) (and (not @t38) @t37)) (= @t38 @t45)))) % 0.39/0.57 (define @t47 () (@quantifiers_skolemize @t46 2)) % 0.39/0.57 (define @t48 () (_ (@quantifiers_skolemize @t46 1) @t47)) % 0.39/0.57 (define @t49 () (_ (@quantifiers_skolemize @t46 0) @t47)) % 0.39/0.57 (define @t50 () (not @t49)) % 0.39/0.57 (define @t51 () (and @t50 @t48)) % 0.39/0.57 (define @t52 () (not @t51)) % 0.39/0.57 (define @t53 () (not @t48)) % 0.39/0.57 (define @t54 () (and @t49 @t53)) % 0.39/0.57 (define @t55 () (not @t53)) % 0.39/0.57 (define @t56 () (= @t49 @t53)) % 0.39/0.57 (define @t57 () (or @t54 @t51)) % 0.39/0.57 (define @t58 () (= @t57 @t56)) % 0.39/0.57 (define @t59 () (not @t54)) % 0.39/0.57 (define @t60 () (not @t56)) % 0.39/0.57 (define @t61 () (not @t57)) % 0.39/0.57 (define @t62 () (@list true true)) % 0.39/0.57 (define @t63 () (@list true)) % 0.39/0.57 (assume @p1 @t11) % 0.39/0.57 (assume @p2 true) % 0.39/0.57 (step @p3 (= tptp.in @t14) :rule refl :args (@t14)) % 0.39/0.57 (step @p4 (= tptp.is_a @t14) :rule refl :args (@t14)) % 0.39/0.57 (step @p5 (= tptp.emptyset @t15) :rule refl :args (@t15)) % 0.39/0.57 (step @p6 (= tptp.unord_pair @t18) :rule refl :args (@t18)) % 0.39/0.57 (step @p7 (= tptp.singleton @t19) :rule refl :args (@t19)) % 0.39/0.57 (step @p8 (= tptp.union @t20) :rule refl :args (@t20)) % 0.39/0.57 (step @p9 (= tptp.excl_union @t25) :rule refl :args (@t25)) % 0.39/0.57 (step @p10 (= tptp.intersection @t27) :rule refl :args (@t27)) % 0.39/0.57 (step @p11 (= tptp.setminus @t28) :rule refl :args (@t28)) % 0.39/0.57 (step @p12 (= tptp.complement @t29) :rule refl :args (@t29)) % 0.39/0.57 (step @p13 (= tptp.disjoint @t31) :rule refl :args (@t31)) % 0.39/0.57 (step @p14 (= tptp.subset @t33) :rule refl :args (@t33)) % 0.39/0.57 (step @p15 (= tptp.meets @t35) :rule refl :args (@t35)) % 0.39/0.57 (step @p16 (= tptp.misses @t36) :rule refl :args (@t36)) % 0.39/0.57 (step @p17 :rule refl :args (@t37)) % 0.39/0.57 (step @p18 :rule refl :args (@t3)) % 0.39/0.57 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t3 @t37))) % 0.39/0.57 (step @p20 :rule symm :premises (@p19)) % 0.39/0.57 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.39/0.57 (step @p22 :rule cong :premises (@p21) :args (@t4)) % 0.39/0.57 (step @p23 :rule refl :args (@t38)) % 0.39/0.57 (step @p24 :rule refl :args (@t6)) % 0.39/0.57 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t6 @t38))) % 0.39/0.57 (step @p26 :rule symm :premises (@p25)) % 0.39/0.57 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.39/0.57 (step @p28 :rule cong :premises (@p27 @p22) :args (@t7)) % 0.39/0.57 (step @p29 :rule cong :premises (@p27) :args (@t21)) % 0.39/0.57 (step @p30 :rule nary_cong :premises (@p29 @p21) :args (@t22)) % 0.39/0.57 (step @p31 :rule nary_cong :premises (@p27 @p22) :args (@t23)) % 0.39/0.57 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t24)) % 0.39/0.57 (step @p33 :rule cong :premises (@p32 @p28) :args (@t39)) % 0.39/0.57 (step @p34 :rule cong :premises (@p33) :args ((forall @t9 @t39))) % 0.39/0.57 (step @p35 :rule eq-symm :args (@t7 @t24)) % 0.39/0.57 (step @p36 :rule beta-reduce :args ((= (_ @t40 @t1) @t24))) % 0.39/0.57 (step @p37 :rule refl :args (@t1)) % 0.39/0.57 (step @p38 :rule beta-reduce :args ((= (_ @t41 @t2) @t40))) % 0.39/0.57 (step @p39 :rule refl :args (@t2)) % 0.39/0.57 (step @p40 :rule beta-reduce :args ((= @t42 @t41))) % 0.39/0.57 (step @p41 :rule ho_cong :premises (@p40 @p39)) % 0.39/0.57 (step @p42 :rule trans :premises (@p41 @p38)) % 0.39/0.57 (step @p43 :rule ho_cong :premises (@p42 @p37)) % 0.39/0.57 (step @p44 :rule trans :premises (@p43 @p36)) % 0.39/0.57 (step @p45 :rule refl :args (@t7)) % 0.39/0.57 (step @p46 :rule cong :premises (@p45 @p44) :args ((= @t7 @t43))) % 0.39/0.57 (step @p47 :rule trans :premises (@p46 @p35)) % 0.39/0.57 (step @p48 :rule eq-symm :args (@t43 @t7)) % 0.39/0.57 (step @p49 :rule trans :premises (@p48 @p47)) % 0.39/0.57 (step @p50 :rule cong :premises (@p49) :args (@t44)) % 0.39/0.57 (step @p51 :rule trans :premises (@p50 @p34)) % 0.39/0.57 (step @p52 :rule cong :premises (@p51) :args ((not @t44))) % 0.39/0.57 (step @p53 :rule refl :args (@t5)) % 0.39/0.57 (step @p54 :rule ho_cong :premises (@p9 @p53)) % 0.39/0.57 (step @p55 :rule ho_cong :premises (@p54 @p39)) % 0.39/0.57 (step @p56 :rule ho_cong :premises (@p55 @p37)) % 0.39/0.57 (step @p57 :rule cong :premises (@p56 @p45) :args (@t8)) % 0.39/0.57 (step @p58 :rule cong :premises (@p57) :args (@t10)) % 0.39/0.57 (step @p59 :rule cong :premises (@p58) :args (@t11)) % 0.39/0.57 (step @p60 :rule trans :premises (@p59 @p52)) % 0.39/0.57 (step @p61 :rule eq_resolve :premises (@p1 @p60)) % 0.39/0.57 (step @p62 :rule skolemize :premises (@p61)) % 0.39/0.57 (step @p63 :rule cnf_and_pos :args (@t51 0)) % 0.39/0.57 (step @p64 :rule reordering :premises (@p63) :args ((or @t50 @t52))) % 0.39/0.57 (step @p65 :rule bool-double-not-elim :args (@t48)) % 0.39/0.57 (step @p66 :rule refl :args (@t50)) % 0.39/0.57 (step @p67 :rule refl :args (@t54)) % 0.39/0.57 (step @p68 :rule nary_cong :premises (@p67 @p66 @p65) :args ((or @t54 @t50 @t55))) % 0.39/0.57 (step @p69 :rule cnf_and_neg :args (@t54)) % 0.39/0.57 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 0.39/0.57 (step @p71 :rule reordering :premises (@p70) :args ((or @t48 @t54 @t50))) % 0.39/0.57 (step @p72 :rule refl :args (@t56)) % 0.39/0.57 (step @p73 :rule nary_cong :premises (@p72 @p66 @p65) :args ((or @t56 @t50 @t55))) % 0.39/0.57 (step @p74 :rule cnf_equiv_neg2 :args (@t56)) % 0.39/0.57 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.39/0.57 (step @p76 :rule reordering :premises (@p75) :args ((or @t48 @t50 @t56))) % 0.39/0.57 (step @p77 :rule cnf_or_neg :args (@t57 0)) % 0.39/0.57 (step @p78 :rule cnf_equiv_neg2 :args (@t58)) % 0.39/0.57 (step @p79 :rule chain_m_resolution :premises (@p78 @p62 @p77 @p76 @p71) :args ((or @t48 @t50) (@list true false false false) (@list @t58 @t57 @t56 @t54))) % 0.39/0.57 (step @p80 :rule cnf_and_pos :args (@t54 1)) % 0.39/0.57 (step @p81 :rule reordering :premises (@p80) :args ((or @t53 @t59))) % 0.39/0.57 (step @p82 :rule cnf_equiv_pos1 :args (@t56)) % 0.39/0.57 (step @p83 :rule reordering :premises (@p82) :args ((or @t53 @t50 @t60))) % 0.39/0.57 (step @p84 :rule cnf_or_pos :args (@t57)) % 0.39/0.57 (step @p85 :rule reordering :premises (@p84) :args ((or @t54 @t51 @t61))) % 0.39/0.57 (step @p86 :rule cnf_equiv_neg1 :args (@t58)) % 0.39/0.57 (step @p87 :rule reordering :premises (@p86) :args ((or @t57 @t56 @t58))) % 0.39/0.57 (step @p88 :rule chain_m_resolution :premises (@p87 @p62 @p85 @p83 @p81 @p79 @p64) :args (@t50 (@list true true true true false true) (@list @t58 @t57 @t56 @t54 @t48 @t51))) % 0.39/0.57 (step @p89 :rule refl :args (@t53)) % 0.39/0.57 (step @p90 :rule bool-double-not-elim :args (@t49)) % 0.39/0.57 (step @p91 :rule refl :args (@t51)) % 0.39/0.57 (step @p92 :rule nary_cong :premises (@p91 @p90 @p89) :args ((or @t51 (not @t50) @t53))) % 0.39/0.57 (step @p93 :rule cnf_and_neg :args (@t51)) % 0.39/0.57 (step @p94 :rule eq_resolve :premises (@p93 @p92)) % 0.39/0.57 (step @p95 :rule reordering :premises (@p94) :args ((or @t49 @t53 @t51))) % 0.39/0.57 (step @p96 :rule cnf_equiv_neg1 :args (@t56)) % 0.39/0.57 (step @p97 :rule reordering :premises (@p96) :args ((or @t49 @t53 @t56))) % 0.39/0.57 (step @p98 :rule cnf_or_neg :args (@t57 1)) % 0.39/0.57 (step @p99 :rule chain_m_resolution :premises (@p78 @p62 @p98 @p97 @p88 @p95 @p88) :args (@t53 (@list true false false true false true) (@list @t58 @t57 @t56 @t49 @t51 @t49))) % 0.39/0.57 (step @p100 :rule refl :args (@t49)) % 0.39/0.57 (step @p101 :rule refl :args (@t60)) % 0.39/0.57 (step @p102 :rule nary_cong :premises (@p101 @p100 @p65) :args ((or @t60 @t49 @t55))) % 0.39/0.57 (step @p103 :rule cnf_equiv_pos2 :args (@t56)) % 0.39/0.57 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.39/0.57 (step @p105 :rule reordering :premises (@p104) :args ((or @t49 @t48 @t60))) % 0.39/0.57 (step @p106 :rule chain_m_resolution :premises (@p105 @p88 @p99) :args (@t60 @t62 (@list @t49 @t48))) % 0.39/0.57 (step @p107 :rule cnf_and_pos :args (@t51 1)) % 0.39/0.57 (step @p108 :rule reordering :premises (@p107) :args ((or @t48 @t52))) % 0.39/0.57 (step @p109 :rule chain_m_resolution :premises (@p108 @p99) :args (@t52 @t63 (@list @t48))) % 0.39/0.57 (step @p110 :rule cnf_and_pos :args (@t54 0)) % 0.39/0.57 (step @p111 :rule reordering :premises (@p110) :args ((or @t49 @t59))) % 0.39/0.57 (step @p112 :rule chain_m_resolution :premises (@p111 @p88) :args (@t59 @t63 (@list @t49))) % 0.39/0.57 (step @p113 :rule chain_m_resolution :premises (@p85 @p112 @p109) :args (@t61 @t62 (@list @t54 @t51))) % 0.39/0.57 (step @p114 false :rule chain_m_resolution :premises (@p87 @p113 @p106 @p62) :args (false (@list true true true) (@list @t57 @t56 @t58))) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------