%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET766+4 : 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 : n029.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 08:48:36 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET766+4 : TPTP v9.2.1. Released v2.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n029.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 16:11:17 EDT 2026 % 0.16/0.34 % CPUTime : % 0.32/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (declare-const tptp.pre_order (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.equivalence (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.equivalence_class (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.empty_set $$unsorted) % 0.38/0.57 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.partition (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (define @t1 () (@var "B" $$unsorted)) % 0.38/0.57 (define @t2 () (@var "X" $$unsorted)) % 0.38/0.57 (define @t3 () (tptp.member @t2 @t1)) % 0.38/0.57 (define @t4 () (@var "A" $$unsorted)) % 0.38/0.57 (define @t5 () (tptp.member @t2 @t4)) % 0.38/0.57 (define @t6 () (@list @t2)) % 0.38/0.57 (define @t7 () (tptp.subset @t4 @t1)) % 0.38/0.57 (define @t8 () (@list @t4 @t1)) % 0.38/0.57 (define @t9 () (@list @t2 @t4)) % 0.38/0.57 (define @t10 () (and @t5 @t3)) % 0.38/0.57 (define @t11 () (@list @t2 @t4 @t1)) % 0.38/0.57 (define @t12 () (@var "E" $$unsorted)) % 0.38/0.57 (define @t13 () (= @t2 @t4)) % 0.38/0.57 (define @t14 () (@var "Y" $$unsorted)) % 0.38/0.57 (define @t15 () (tptp.member @t2 @t14)) % 0.38/0.57 (define @t16 () (tptp.member @t14 @t4)) % 0.38/0.57 (define @t17 () (@list @t14)) % 0.38/0.57 (define @t18 () (exists @t17 (and @t16 @t15))) % 0.38/0.57 (define @t19 () (@var "Z" $$unsorted)) % 0.38/0.57 (define @t20 () (and @t5 @t16)) % 0.38/0.57 (define @t21 () (@list @t2 @t14)) % 0.38/0.57 (define @t22 () (tptp.member @t2 @t12)) % 0.38/0.57 (define @t23 () (@var "R" $$unsorted)) % 0.38/0.57 (define @t24 () (tptp.apply @t23 @t2 @t19)) % 0.38/0.57 (define @t25 () (tptp.apply @t23 @t14 @t19)) % 0.38/0.57 (define @t26 () (tptp.apply @t23 @t2 @t14)) % 0.38/0.57 (define @t27 () (and @t26 @t25)) % 0.38/0.57 (define @t28 () (=> @t27 @t24)) % 0.38/0.57 (define @t29 () (tptp.member @t19 @t4)) % 0.38/0.57 (define @t30 () (and @t5 @t16 @t29)) % 0.38/0.57 (define @t31 () (@list @t2 @t14 @t19)) % 0.38/0.57 (define @t32 () (forall @t31 (=> @t30 @t28))) % 0.38/0.57 (define @t33 () (tptp.apply @t23 @t14 @t2)) % 0.38/0.57 (define @t34 () (=> @t26 @t33)) % 0.38/0.57 (define @t35 () (forall @t21 (=> @t20 @t34))) % 0.38/0.57 (define @t36 () (tptp.apply @t23 @t2 @t2)) % 0.38/0.57 (define @t37 () (forall @t6 (=> @t5 @t36))) % 0.38/0.57 (define @t38 () (and @t37 @t35 @t32)) % 0.38/0.57 (define @t39 () (tptp.equivalence @t23 @t4)) % 0.38/0.57 (define @t40 () (= @t39 @t38)) % 0.38/0.57 (define @t41 () (forall (@list @t4 @t23) @t40)) % 0.38/0.57 (define @t42 () (tptp.equivalence_class @t4 @t12 @t23)) % 0.38/0.57 (define @t43 () (tptp.member @t4 @t42)) % 0.38/0.57 (define @t44 () (tptp.member @t4 @t12)) % 0.38/0.57 (define @t45 () (tptp.equivalence @t23 @t12)) % 0.38/0.57 (define @t46 () (and @t45 @t44)) % 0.38/0.57 (define @t47 () (@list @t12 @t23 @t4)) % 0.38/0.57 (define @t48 () (forall @t47 (=> @t46 @t43))) % 0.38/0.57 (define @t49 () (not @t48)) % 0.38/0.57 (define @t50 () (not @t25)) % 0.38/0.57 (define @t51 () (not @t26)) % 0.38/0.57 (define @t52 () (not @t29)) % 0.38/0.57 (define @t53 () (not @t16)) % 0.38/0.57 (define @t54 () (not @t5)) % 0.38/0.57 (define @t55 () (or @t51 @t50 @t24)) % 0.38/0.57 (define @t56 () (or @t54 @t53 @t52)) % 0.38/0.57 (define @t57 () (not @t44)) % 0.38/0.57 (define @t58 () (not @t45)) % 0.38/0.57 (define @t59 () (or @t58 @t57 @t43)) % 0.38/0.57 (define @t60 () (forall @t47 @t59)) % 0.38/0.57 (define @t61 () (@quantifiers_skolemize @t60 1)) % 0.38/0.57 (define @t62 () (@quantifiers_skolemize @t60 0)) % 0.38/0.57 (define @t63 () (tptp.equivalence @t61 @t62)) % 0.38/0.57 (define @t64 () (@quantifiers_skolemize @t60 2)) % 0.38/0.57 (define @t65 () (tptp.member @t64 (tptp.equivalence_class @t64 @t62 @t61))) % 0.38/0.57 (define @t66 () (tptp.member @t64 @t62)) % 0.38/0.57 (define @t67 () (not @t66)) % 0.38/0.57 (define @t68 () (not @t63)) % 0.38/0.57 (define @t69 () (or @t68 @t67 @t65)) % 0.38/0.57 (define @t70 () (@list true)) % 0.38/0.57 (define @t71 () (@list @t69)) % 0.38/0.57 (define @t72 () (not (tptp.apply @t61 @t2 @t14))) % 0.38/0.57 (define @t73 () (not (tptp.member @t14 @t62))) % 0.38/0.57 (define @t74 () (not (tptp.member @t2 @t62))) % 0.38/0.57 (define @t75 () (forall @t6 (or @t74 (tptp.apply @t61 @t2 @t2)))) % 0.38/0.57 (define @t76 () (and @t75 (forall @t21 (or @t74 @t73 @t72 (tptp.apply @t61 @t14 @t2))) (forall @t31 (or @t74 @t73 (not (tptp.member @t19 @t62)) @t72 (not (tptp.apply @t61 @t14 @t19)) (tptp.apply @t61 @t2 @t19))))) % 0.38/0.57 (define @t77 () (= @t63 @t76)) % 0.38/0.57 (define @t78 () (tptp.apply @t61 @t64 @t64)) % 0.38/0.57 (define @t79 () (and @t66 @t78)) % 0.38/0.57 (define @t80 () (= @t65 @t79)) % 0.38/0.57 (define @t81 () (not @t79)) % 0.38/0.57 (define @t82 () (@list true false)) % 0.38/0.57 (define @t83 () (not @t78)) % 0.38/0.57 (define @t84 () (@list false true)) % 0.38/0.57 (define @t85 () (or @t67 @t78)) % 0.38/0.57 (define @t86 () (not @t85)) % 0.38/0.57 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.38/0.57 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.38/0.57 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.38/0.57 (assume @p4 (forall @t11 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) @t10))) % 0.38/0.57 (assume @p5 (forall @t11 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.38/0.57 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.38/0.57 (assume @p7 (forall (@list @t1 @t4 @t12) (= (tptp.member @t1 (tptp.difference @t12 @t4)) (and (tptp.member @t1 @t12) (not (tptp.member @t1 @t4)))))) % 0.38/0.57 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t13))) % 0.38/0.57 (assume @p9 (forall @t11 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t13 (= @t2 @t1))))) % 0.38/0.57 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) @t18))) % 0.38/0.57 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t17 (=> @t16 @t15))))) % 0.38/0.57 (assume @p12 (forall @t8 (= (tptp.disjoint @t4 @t1) (not (exists @t6 @t10))))) % 0.38/0.57 (assume @p13 (forall (@list @t4 @t12) (= (tptp.partition @t4 @t12) (and (forall @t6 (=> @t5 (tptp.subset @t2 @t12))) (forall @t6 (=> @t22 @t18)) (forall @t21 (=> @t20 (=> (exists (@list @t19) (and (tptp.member @t19 @t2) (tptp.member @t19 @t14))) (= @t2 @t14)))))))) % 0.38/0.57 (assume @p14 @t41) % 0.38/0.57 (assume @p15 (forall (@list @t23 @t12 @t4 @t2) (= (tptp.member @t2 @t42) (and @t22 (tptp.apply @t23 @t4 @t2))))) % 0.38/0.57 (assume @p16 (forall (@list @t23 @t12) (= (tptp.pre_order @t23 @t12) (and (forall @t6 (=> @t22 @t36)) (forall @t31 (=> (and @t22 (tptp.member @t14 @t12) (tptp.member @t19 @t12)) @t28)))))) % 0.38/0.57 (assume @p17 @t49) % 0.38/0.57 (assume @p18 true) % 0.38/0.57 (step @p19 :rule aci_norm :args ((= (or @t56 @t55) (or @t54 @t53 @t52 @t51 @t50 @t24)))) % 0.38/0.57 (step @p20 :rule aci_norm :args ((= (or (or @t51 @t50) @t24) @t55))) % 0.38/0.57 (step @p21 :rule refl :args (@t24)) % 0.38/0.57 (step @p22 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 0.38/0.57 (step @p23 :rule nary_cong :premises (@p22 @p21) :args ((or (not @t27) @t24))) % 0.38/0.57 (step @p24 :rule trans :premises (@p23 @p20)) % 0.38/0.57 (step @p25 :rule bool-impl-elim :args (@t27 @t24)) % 0.38/0.57 (step @p26 :rule trans :premises (@p25 @p24)) % 0.38/0.57 (step @p27 :rule aci_norm :args ((= (or @t54 (or @t53 @t52)) @t56))) % 0.38/0.57 (step @p28 :rule bool-and-de-morgan :args (@t16 @t29 true)) % 0.38/0.57 (step @p29 :rule refl :args (@t54)) % 0.38/0.57 (step @p30 :rule nary_cong :premises (@p29 @p28) :args ((or @t54 (not (and @t16 @t29))))) % 0.38/0.57 (step @p31 :rule bool-and-de-morgan :args (@t5 @t16 (and @t29))) % 0.38/0.57 (step @p32 :rule trans :premises (@p31 @p30)) % 0.38/0.57 (step @p33 :rule trans :premises (@p32 @p27)) % 0.38/0.57 (step @p34 :rule nary_cong :premises (@p33 @p26) :args ((or (not @t30) @t28))) % 0.38/0.57 (step @p35 :rule trans :premises (@p34 @p19)) % 0.38/0.57 (step @p36 :rule bool-impl-elim :args (@t30 @t28)) % 0.38/0.57 (step @p37 :rule trans :premises (@p36 @p35)) % 0.38/0.57 (step @p38 :rule cong :premises (@p37) :args (@t32)) % 0.38/0.57 (step @p39 :rule aci_norm :args ((= (or (or @t54 @t53) (or @t51 @t33)) (or @t54 @t53 @t51 @t33)))) % 0.38/0.57 (step @p40 :rule bool-impl-elim :args (@t26 @t33)) % 0.38/0.57 (step @p41 :rule bool-and-de-morgan :args (@t5 @t16 true)) % 0.38/0.57 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or (not @t20) @t34))) % 0.38/0.57 (step @p43 :rule trans :premises (@p42 @p39)) % 0.38/0.57 (step @p44 :rule bool-impl-elim :args (@t20 @t34)) % 0.38/0.57 (step @p45 :rule trans :premises (@p44 @p43)) % 0.38/0.57 (step @p46 :rule cong :premises (@p45) :args (@t35)) % 0.38/0.57 (step @p47 :rule bool-impl-elim :args (@t5 @t36)) % 0.38/0.57 (step @p48 :rule cong :premises (@p47) :args (@t37)) % 0.38/0.57 (step @p49 :rule nary_cong :premises (@p48 @p46 @p38) :args (@t38)) % 0.38/0.57 (step @p50 :rule refl :args (@t39)) % 0.38/0.57 (step @p51 :rule cong :premises (@p50 @p49) :args (@t40)) % 0.38/0.57 (step @p52 :rule cong :premises (@p51) :args (@t41)) % 0.38/0.57 (step @p53 :rule eq_resolve :premises (@p14 @p52)) % 0.38/0.57 (step @p54 :rule instantiate :premises (@p53) :args ((@list @t62 @t61))) % 0.38/0.57 (step @p55 :rule aci_norm :args ((= (or (or @t58 @t57) @t43) @t59))) % 0.38/0.57 (step @p56 :rule refl :args (@t43)) % 0.38/0.57 (step @p57 :rule bool-and-de-morgan :args (@t45 @t44 true)) % 0.38/0.57 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or (not @t46) @t43))) % 0.38/0.57 (step @p59 :rule trans :premises (@p58 @p55)) % 0.38/0.57 (step @p60 :rule bool-impl-elim :args (@t46 @t43)) % 0.38/0.57 (step @p61 :rule trans :premises (@p60 @p59)) % 0.38/0.57 (step @p62 :rule cong :premises (@p61) :args (@t48)) % 0.38/0.57 (step @p63 :rule cong :premises (@p62) :args (@t49)) % 0.38/0.57 (step @p64 :rule eq_resolve :premises (@p17 @p63)) % 0.38/0.57 (step @p65 :rule skolemize :premises (@p64)) % 0.38/0.57 (step @p66 :rule bool-double-not-elim :args (@t63)) % 0.38/0.57 (step @p67 :rule refl :args (@t69)) % 0.38/0.57 (step @p68 :rule nary_cong :premises (@p67 @p66) :args ((or @t69 (not @t68)))) % 0.38/0.57 (step @p69 :rule cnf_or_neg :args (@t69 0)) % 0.38/0.57 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 0.38/0.57 (step @p71 :rule reordering :premises (@p70) :args ((or @t63 @t69))) % 0.38/0.57 (step @p72 :rule chain_m_resolution :premises (@p71 @p65) :args (@t63 @t70 @t71)) % 0.38/0.57 (step @p73 :rule cnf_equiv_pos1 :args (@t77)) % 0.38/0.57 (step @p74 :rule reordering :premises (@p73) :args ((or @t68 @t76 (not @t77)))) % 0.38/0.57 (step @p75 :rule chain_m_resolution :premises (@p74 @p72 @p54) :args (@t76 (@list false false) (@list @t63 @t77))) % 0.38/0.57 (step @p76 :rule cnf_and_pos :args (@t76 0)) % 0.38/0.57 (step @p77 :rule reordering :premises (@p76) :args ((or @t75 (not @t76)))) % 0.38/0.57 (step @p78 :rule chain_m_resolution :premises (@p77 @p75) :args (@t75 (@list false) (@list @t76))) % 0.38/0.57 (step @p79 :rule instantiate :premises (@p15) :args ((@list @t61 @t62 @t64 @t64))) % 0.38/0.57 (step @p80 :rule cnf_or_neg :args (@t69 2)) % 0.38/0.57 (step @p81 :rule chain_m_resolution :premises (@p80 @p65) :args ((not @t65) @t70 @t71)) % 0.38/0.57 (step @p82 :rule cnf_equiv_pos2 :args (@t80)) % 0.38/0.57 (step @p83 :rule reordering :premises (@p82) :args ((or @t65 @t81 (not @t80)))) % 0.38/0.57 (step @p84 :rule chain_m_resolution :premises (@p83 @p81 @p79) :args (@t81 @t82 (@list @t65 @t80))) % 0.38/0.57 (step @p85 :rule bool-double-not-elim :args (@t66)) % 0.38/0.57 (step @p86 :rule nary_cong :premises (@p67 @p85) :args ((or @t69 (not @t67)))) % 0.38/0.57 (step @p87 :rule cnf_or_neg :args (@t69 1)) % 0.38/0.57 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 0.38/0.57 (step @p89 :rule reordering :premises (@p88) :args ((or @t66 @t69))) % 0.38/0.57 (step @p90 :rule chain_m_resolution :premises (@p89 @p65) :args (@t66 @t70 @t71)) % 0.38/0.57 (step @p91 :rule cnf_and_neg :args (@t79)) % 0.38/0.57 (step @p92 :rule reordering :premises (@p91) :args ((or @t67 @t79 @t83))) % 0.38/0.57 (step @p93 :rule chain_m_resolution :premises (@p92 @p90 @p84) :args (@t83 @t84 (@list @t66 @t79))) % 0.38/0.57 (step @p94 :rule cnf_or_pos :args (@t85)) % 0.38/0.57 (step @p95 :rule reordering :premises (@p94) :args ((or @t67 @t78 @t86))) % 0.38/0.57 (step @p96 :rule chain_m_resolution :premises (@p95 @p90 @p93) :args (@t86 @t84 (@list @t66 @t78))) % 0.38/0.57 (assume-push @p103 @t75) % 0.38/0.57 (step @p98 :rule instantiate :premises (@p78) :args ((@list @t64))) % 0.38/0.57 (step-pop @p104 :rule scope :premises (@p98)) % 0.38/0.57 (step @p99 :rule process_scope :premises (@p104) :args (@t85)) % 0.38/0.57 (step @p101 :rule implies_elim :premises (@p99)) % 0.38/0.57 (step @p102 false :rule chain_m_resolution :premises (@p101 @p96 @p78) :args (false @t82 (@list @t85 @t75))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------