%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU503^1 : TPTP v9.2.1. Released v3.7.0. % 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 08:51:58 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 : SEU503^1 : TPTP v9.2.1. Released v3.7.0. % 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 17:39:43 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.38/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (declare-const tptp.emptyset $$unsorted) % 0.38/0.57 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.38/0.57 (declare-const tptp.emptysetE Bool) % 0.38/0.57 (declare-const tptp.prop2setE Bool) % 0.38/0.57 (declare-const tptp.dsetconstrI Bool) % 0.38/0.57 (declare-const tptp.descrp Bool) % 0.38/0.57 (declare-const tptp.exuE1 Bool) % 0.38/0.57 (declare-const tptp.descr (-> (-> $$unsorted Bool) $$unsorted)) % 0.38/0.57 (declare-const tptp.emptysetimpfalse Bool) % 0.38/0.57 (declare-const tptp.wellorderingAx Bool) % 0.38/0.57 (declare-const tptp.replAx Bool) % 0.38/0.57 (declare-const tptp.dsetconstrEL Bool) % 0.38/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.setextAx Bool) % 0.38/0.57 (declare-const tptp.foundationAx Bool) % 0.38/0.57 (declare-const tptp.emptysetAx Bool) % 0.38/0.57 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.dsetconstrER Bool) % 0.38/0.57 (declare-const tptp.setadjoinAx Bool) % 0.38/0.57 (declare-const tptp.powersetAx Bool) % 0.38/0.57 (declare-const tptp.omegaSAx Bool) % 0.38/0.57 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.omega0Ax Bool) % 0.38/0.57 (declare-const tptp.setunionAx Bool) % 0.38/0.57 (declare-const tptp.omega $$unsorted) % 0.38/0.57 (declare-const tptp.omegaIndAx Bool) % 0.38/0.57 (define tptp.exu () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xphi" (-> $$unsorted Bool)))) (lambda (@list _let_3) (exists (@list _let_2) (and (_ _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (= _let_2 _let_1)))))))))) % 0.38/0.57 (define tptp.prop2set () (let ((_let_1 (@var "Xphi" Bool))) (lambda (@list _let_1) (_ (_ tptp.dsetconstr (_ tptp.powerset tptp.emptyset)) (lambda (@list (@var "Xx" $$unsorted)) _let_1))))) % 0.38/0.57 (define @t1 () (@var "B" $$unsorted)) % 0.38/0.57 (define @t2 () (@var "A" $$unsorted)) % 0.38/0.57 (define @t3 () (@var "Xx" $$unsorted)) % 0.38/0.57 (define @t4 () (_ tptp.in @t3)) % 0.38/0.57 (define @t5 () (_ @t4 @t1)) % 0.38/0.57 (define @t6 () (_ @t4 @t2)) % 0.38/0.57 (define @t7 () (@list @t3)) % 0.38/0.57 (define @t8 () (@list @t2 @t1)) % 0.38/0.57 (define @t9 () (_ @t4 tptp.emptyset)) % 0.38/0.57 (define @t10 () (not @t9)) % 0.38/0.57 (define @t11 () (forall @t7 @t10)) % 0.38/0.57 (define @t12 () (= tptp.emptysetAx @t11)) % 0.38/0.57 (define @t13 () (@var "Xy" $$unsorted)) % 0.38/0.57 (define @t14 () (_ tptp.in @t13)) % 0.38/0.57 (define @t15 () (_ @t14 @t2)) % 0.38/0.57 (define @t16 () (_ tptp.setadjoin @t3)) % 0.38/0.57 (define @t17 () (_ tptp.in @t1)) % 0.38/0.57 (define @t18 () (_ @t17 @t2)) % 0.38/0.57 (define @t19 () (@list @t1)) % 0.38/0.57 (define @t20 () (_ tptp.in tptp.emptyset)) % 0.38/0.57 (define @t21 () (_ tptp.in (_ @t16 @t3))) % 0.38/0.57 (define @t22 () (_ @t4 tptp.omega)) % 0.38/0.57 (define @t23 () (@list @t2)) % 0.38/0.57 (define @t24 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.38/0.57 (define @t25 () (@list @t13)) % 0.38/0.57 (define @t26 () (@var "E" $$unsorted)) % 0.38/0.57 (define @t27 () (@var "D" $$unsorted)) % 0.38/0.57 (define @t28 () (_ @t14 @t27)) % 0.38/0.57 (define @t29 () (@var "C" $$unsorted)) % 0.38/0.57 (define @t30 () (_ @t14 @t29)) % 0.38/0.57 (define @t31 () (_ @t4 @t29)) % 0.38/0.57 (define @t32 () (_ (_ tptp.in @t27) @t1)) % 0.38/0.57 (define @t33 () (forall @t7 (=> @t31 @t6))) % 0.38/0.57 (define @t34 () (@list @t29)) % 0.38/0.57 (define @t35 () (_ @t4 @t27)) % 0.38/0.57 (define @t36 () (_ (_ tptp.in @t29) @t1)) % 0.38/0.57 (define @t37 () (= @t3 @t13)) % 0.38/0.57 (define @t38 () (@var "Xphi" (-> $$unsorted Bool))) % 0.38/0.57 (define @t39 () (_ @t38 @t3)) % 0.38/0.57 (define @t40 () (lambda @t7 @t39)) % 0.38/0.57 (define @t41 () (_ tptp.exu @t40)) % 0.38/0.57 (define @t42 () (@list @t38)) % 0.38/0.57 (define @t43 () (_ @t38 @t13)) % 0.38/0.57 (define @t44 () (_ @t4 (_ (_ tptp.dsetconstr @t2) (lambda @t25 @t43)))) % 0.38/0.57 (define @t45 () (@list @t2 @t38 @t3)) % 0.38/0.57 (define @t46 () (exists @t7 (and @t39 (forall @t25 (=> @t43 @t37))))) % 0.38/0.57 (define @t47 () (@var "Xphi" Bool)) % 0.38/0.57 (define @t48 () (@list @t47)) % 0.38/0.57 (define @t49 () (=> tptp.emptysetimpfalse @t11)) % 0.38/0.57 (define @t50 () (=> tptp.emptysetE @t49)) % 0.38/0.57 (define @t51 () (=> tptp.prop2setE @t50)) % 0.38/0.57 (define @t52 () (=> tptp.exuE1 @t51)) % 0.38/0.57 (define @t53 () (=> tptp.dsetconstrER @t52)) % 0.38/0.57 (define @t54 () (=> tptp.dsetconstrEL @t53)) % 0.38/0.57 (define @t55 () (=> tptp.dsetconstrI @t54)) % 0.38/0.57 (define @t56 () (=> tptp.descrp @t55)) % 0.38/0.57 (define @t57 () (=> tptp.wellorderingAx @t56)) % 0.38/0.57 (define @t58 () (=> tptp.foundationAx @t57)) % 0.38/0.57 (define @t59 () (=> tptp.replAx @t58)) % 0.38/0.57 (define @t60 () (=> tptp.omegaIndAx @t59)) % 0.38/0.57 (define @t61 () (=> tptp.omegaSAx @t60)) % 0.38/0.57 (define @t62 () (=> tptp.omega0Ax @t61)) % 0.38/0.57 (define @t63 () (=> tptp.setunionAx @t62)) % 0.38/0.57 (define @t64 () (=> tptp.powersetAx @t63)) % 0.38/0.57 (define @t65 () (=> tptp.setadjoinAx @t64)) % 0.38/0.57 (define @t66 () (=> tptp.emptysetAx @t65)) % 0.38/0.57 (define @t67 () (=> tptp.setextAx @t66)) % 0.38/0.57 (define @t68 () (not @t67)) % 0.38/0.57 (define @t69 () (lambda @t42 @t46)) % 0.38/0.57 (define @t70 () (lambda @t48 (_ (_ tptp.dsetconstr (_ tptp.powerset tptp.emptyset)) (lambda @t7 @t47)))) % 0.38/0.57 (define @t71 () (tptp.in @t3 tptp.emptyset)) % 0.38/0.57 (define @t72 () (forall @t7 (not @t71))) % 0.38/0.57 (define @t73 () (=> tptp.emptysetimpfalse @t72)) % 0.38/0.57 (assume @p1 (= tptp.setextAx (forall @t8 (=> (forall @t7 (= @t6 @t5)) (= @t2 @t1))))) % 0.38/0.57 (assume @p2 @t12) % 0.38/0.57 (assume @p3 (= tptp.setadjoinAx (forall (@list @t3 @t2 @t13) (= (_ @t14 (_ @t16 @t2)) (or (= @t13 @t3) @t15))))) % 0.38/0.57 (assume @p4 (= tptp.powersetAx (forall @t8 (= (_ @t17 (_ tptp.powerset @t2)) (forall @t7 (=> @t5 @t6)))))) % 0.38/0.57 (assume @p5 (= tptp.setunionAx (forall (@list @t2 @t3) (= (_ @t4 (_ tptp.setunion @t2)) (exists @t19 (and @t5 @t18)))))) % 0.38/0.57 (assume @p6 (= tptp.omega0Ax (_ @t20 tptp.omega))) % 0.38/0.57 (assume @p7 (= tptp.omegaSAx (forall @t7 (=> @t22 (_ @t21 tptp.omega))))) % 0.38/0.57 (assume @p8 (= tptp.omegaIndAx (forall @t23 (=> (and (_ @t20 @t2) (forall @t7 (=> (and @t22 @t6) (_ @t21 @t2)))) (forall @t7 (=> @t22 @t6)))))) % 0.38/0.57 (assume @p9 (= tptp.replAx (forall (@list @t24 @t2) (=> (forall @t7 (=> @t6 (_ tptp.exu (lambda @t25 (_ (_ @t24 @t3) @t13))))) (exists @t19 (forall @t7 (= @t5 (exists @t25 (and @t15 (_ (_ @t24 @t13) @t3)))))))))) % 0.38/0.57 (assume @p10 (= tptp.foundationAx (forall @t23 (=> (exists @t7 @t6) (exists @t19 (and @t18 (not (exists @t7 (and @t5 @t6))))))))) % 0.38/0.57 (assume @p11 (= tptp.wellorderingAx (forall @t23 (exists @t19 (and (forall @t34 (=> @t36 @t33)) (forall (@list @t3 @t13) (=> (and @t6 @t15) (=> (forall @t34 (=> @t36 (= @t31 @t30))) @t37))) (forall (@list @t29 @t27) (=> (and @t36 @t32) (or (forall @t7 (=> @t31 @t35)) (forall @t7 (=> @t35 @t31))))) (forall @t34 (=> (and @t33 (exists @t7 @t31)) (exists (@list @t27 @t3) (and @t32 @t31 (not (exists @t25 (and @t28 @t30))) (forall (@list @t26) (=> (_ (_ tptp.in @t26) @t1) (or (forall @t25 (=> (_ @t14 @t26) @t28)) (_ @t4 @t26))))))))))))) % 0.38/0.57 (assume @p12 (= tptp.descrp (forall @t42 (=> @t41 (_ @t38 (_ tptp.descr @t40)))))) % 0.38/0.57 (assume @p13 (= tptp.dsetconstrI (forall @t45 (=> @t6 (=> @t39 @t44))))) % 0.38/0.57 (assume @p14 (= tptp.dsetconstrEL (forall @t45 (=> @t44 @t6)))) % 0.38/0.57 (assume @p15 (= tptp.dsetconstrER (forall @t45 (=> @t44 @t39)))) % 0.38/0.57 (assume @p16 (= tptp.exuE1 (forall @t42 (=> @t41 @t46)))) % 0.38/0.57 (assume @p17 (= tptp.prop2setE (forall (@list @t47 @t3) (=> (_ @t4 (_ tptp.prop2set @t47)) @t47)))) % 0.38/0.57 (assume @p18 (= tptp.emptysetE (forall @t7 (=> @t9 (forall @t48 @t47))))) % 0.38/0.57 (assume @p19 (= tptp.emptysetimpfalse (forall @t7 (=> @t9 false)))) % 0.38/0.57 (assume @p20 @t68) % 0.38/0.57 (assume @p21 true) % 0.38/0.57 (step @p22 (= tptp.exu @t69) :rule refl :args (@t69)) % 0.38/0.57 (step @p23 (= tptp.prop2set @t70) :rule refl :args (@t70)) % 0.38/0.57 (step @p24 :rule refl :args (@t71)) % 0.38/0.57 (step @p25 :rule refl :args (@t9)) % 0.38/0.57 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t9 @t71))) % 0.38/0.57 (step @p27 :rule symm :premises (@p26)) % 0.38/0.57 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.38/0.57 (step @p29 :rule cong :premises (@p28) :args (@t10)) % 0.38/0.57 (step @p30 :rule cong :premises (@p29) :args (@t11)) % 0.38/0.57 (step @p31 :rule refl :args (tptp.emptysetimpfalse)) % 0.38/0.57 (step @p32 :rule cong :premises (@p31 @p30) :args (@t49)) % 0.38/0.57 (step @p33 :rule refl :args (tptp.emptysetE)) % 0.38/0.57 (step @p34 :rule cong :premises (@p33 @p32) :args (@t50)) % 0.38/0.57 (step @p35 :rule refl :args (tptp.prop2setE)) % 0.38/0.57 (step @p36 :rule cong :premises (@p35 @p34) :args (@t51)) % 0.38/0.57 (step @p37 :rule refl :args (tptp.exuE1)) % 0.38/0.57 (step @p38 :rule cong :premises (@p37 @p36) :args (@t52)) % 0.38/0.57 (step @p39 :rule refl :args (tptp.dsetconstrER)) % 0.38/0.57 (step @p40 :rule cong :premises (@p39 @p38) :args (@t53)) % 0.38/0.57 (step @p41 :rule refl :args (tptp.dsetconstrEL)) % 0.38/0.57 (step @p42 :rule cong :premises (@p41 @p40) :args (@t54)) % 0.38/0.57 (step @p43 :rule refl :args (tptp.dsetconstrI)) % 0.38/0.57 (step @p44 :rule cong :premises (@p43 @p42) :args (@t55)) % 0.38/0.57 (step @p45 :rule refl :args (tptp.descrp)) % 0.38/0.57 (step @p46 :rule cong :premises (@p45 @p44) :args (@t56)) % 0.38/0.57 (step @p47 :rule refl :args (tptp.wellorderingAx)) % 0.38/0.57 (step @p48 :rule cong :premises (@p47 @p46) :args (@t57)) % 0.38/0.57 (step @p49 :rule refl :args (tptp.foundationAx)) % 0.38/0.57 (step @p50 :rule cong :premises (@p49 @p48) :args (@t58)) % 0.38/0.57 (step @p51 :rule refl :args (tptp.replAx)) % 0.38/0.57 (step @p52 :rule cong :premises (@p51 @p50) :args (@t59)) % 0.38/0.57 (step @p53 :rule refl :args (tptp.omegaIndAx)) % 0.38/0.57 (step @p54 :rule cong :premises (@p53 @p52) :args (@t60)) % 0.38/0.57 (step @p55 :rule refl :args (tptp.omegaSAx)) % 0.38/0.57 (step @p56 :rule cong :premises (@p55 @p54) :args (@t61)) % 0.38/0.57 (step @p57 :rule refl :args (tptp.omega0Ax)) % 0.38/0.57 (step @p58 :rule cong :premises (@p57 @p56) :args (@t62)) % 0.38/0.57 (step @p59 :rule refl :args (tptp.setunionAx)) % 0.38/0.57 (step @p60 :rule cong :premises (@p59 @p58) :args (@t63)) % 0.38/0.57 (step @p61 :rule refl :args (tptp.powersetAx)) % 0.38/0.57 (step @p62 :rule cong :premises (@p61 @p60) :args (@t64)) % 0.38/0.57 (step @p63 :rule refl :args (tptp.setadjoinAx)) % 0.38/0.57 (step @p64 :rule cong :premises (@p63 @p62) :args (@t65)) % 0.38/0.57 (step @p65 :rule refl :args (tptp.emptysetAx)) % 0.38/0.57 (step @p66 :rule cong :premises (@p65 @p64) :args (@t66)) % 0.38/0.57 (step @p67 :rule refl :args (tptp.setextAx)) % 0.38/0.57 (step @p68 :rule cong :premises (@p67 @p66) :args (@t67)) % 0.38/0.57 (step @p69 :rule cong :premises (@p68) :args (@t68)) % 0.38/0.57 (step @p70 :rule eq_resolve :premises (@p20 @p69)) % 0.38/0.57 (step @p71 :rule not_implies_elim2 :premises (@p70)) % 0.38/0.57 (step @p72 :rule not_implies_elim2 :premises (@p71)) % 0.38/0.57 (step @p73 :rule not_implies_elim2 :premises (@p72)) % 0.38/0.57 (step @p74 :rule not_implies_elim2 :premises (@p73)) % 0.38/0.57 (step @p75 :rule not_implies_elim2 :premises (@p74)) % 0.38/0.57 (step @p76 :rule not_implies_elim2 :premises (@p75)) % 0.38/0.57 (step @p77 :rule not_implies_elim2 :premises (@p76)) % 0.38/0.57 (step @p78 :rule not_implies_elim2 :premises (@p77)) % 0.38/0.57 (step @p79 :rule not_implies_elim2 :premises (@p78)) % 0.38/0.57 (step @p80 :rule not_implies_elim2 :premises (@p79)) % 0.38/0.57 (step @p81 :rule not_implies_elim2 :premises (@p80)) % 0.38/0.57 (step @p82 :rule not_implies_elim2 :premises (@p81)) % 0.38/0.57 (step @p83 :rule not_implies_elim2 :premises (@p82)) % 0.38/0.57 (step @p84 :rule not_implies_elim2 :premises (@p83)) % 0.38/0.57 (step @p85 :rule not_implies_elim2 :premises (@p84)) % 0.38/0.57 (step @p86 :rule not_implies_elim2 :premises (@p85)) % 0.38/0.57 (step @p87 :rule not_implies_elim2 :premises (@p86)) % 0.38/0.57 (step @p88 :rule cong :premises (@p65 @p30) :args (@t12)) % 0.38/0.57 (step @p89 :rule eq_resolve :premises (@p2 @p88)) % 0.38/0.57 (step @p90 :rule not_implies_elim1 :premises (@p71)) % 0.38/0.57 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.38/0.57 (step @p92 :rule cnf_implies_neg2 :args (@t73)) % 0.38/0.57 (step @p93 :rule resolution :premises (@p92 @p91) :args (false @t72)) % 0.38/0.57 (step @p94 :rule cnf_implies_neg2 :args ((=> tptp.emptysetE @t73))) % 0.38/0.57 (step @p95 :rule resolution :premises (@p94 @p93) :args (false @t73)) % 0.38/0.57 (step @p96 false :rule contra :premises (@p95 @p87)) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------