%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET086^1 : 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 : n005.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 08:47:20 AM UTC 2026 % Result : Theorem 0.32s 0.52s % Output : Proof 0.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET086^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.33 % Computer : n005.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Jun 2 14:51:48 EDT 2026 % 0.16/0.33 % CPUTime : % 0.19/0.48 %----Proving TH0 % 0.32/0.52 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.32/0.52 % SZS status Theorem % 0.32/0.52 % SZS output start Proof % 0.32/0.52 ( % 0.32/0.52 (declare-sort $$unsorted 0) % 0.32/0.52 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.32/0.52 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.32/0.52 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.32/0.52 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.32/0.52 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.32/0.52 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.32/0.52 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.32/0.52 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.32/0.52 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.32/0.52 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.32/0.52 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.32/0.52 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.32/0.52 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.32/0.52 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.32/0.52 (define @t1 () (@var "Y" $$unsorted)) % 0.32/0.52 (define @t2 () (@var "X" $$unsorted)) % 0.32/0.52 (define @t3 () (@list @t1)) % 0.32/0.52 (define @t4 () (exists @t3 (_ (_ tptp.singleton @t2) @t1))) % 0.32/0.52 (define @t5 () (@list @t2)) % 0.32/0.52 (define @t6 () (forall @t5 @t4)) % 0.32/0.52 (define @t7 () (not @t6)) % 0.32/0.52 (define @t8 () (@var "M" (-> $$unsorted Bool))) % 0.32/0.52 (define @t9 () (lambda (@list @t2 @t8) (_ @t8 @t2))) % 0.32/0.52 (define @t10 () (lambda @t5 false)) % 0.32/0.52 (define @t11 () (@var "U" $$unsorted)) % 0.32/0.52 (define @t12 () (= @t11 @t2)) % 0.32/0.52 (define @t13 () (lambda (@list @t2 @t1 @t11) (or @t12 (= @t11 @t1)))) % 0.32/0.52 (define @t14 () (@list @t2 @t11)) % 0.32/0.52 (define @t15 () (lambda @t14 @t12)) % 0.32/0.52 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 0.32/0.52 (define @t17 () (_ @t16 @t11)) % 0.32/0.52 (define @t18 () (@var "X" (-> $$unsorted Bool))) % 0.32/0.52 (define @t19 () (_ @t18 @t11)) % 0.32/0.52 (define @t20 () (@list @t18 @t16 @t11)) % 0.32/0.52 (define @t21 () (lambda @t20 (or @t19 @t17))) % 0.32/0.52 (define @t22 () (not @t19)) % 0.32/0.52 (define @t23 () (and @t19 (not @t17))) % 0.32/0.52 (define @t24 () (lambda @t20 (or @t23 (and @t22 @t17)))) % 0.32/0.52 (define @t25 () (and @t19 @t17)) % 0.32/0.52 (define @t26 () (lambda @t20 @t25)) % 0.32/0.52 (define @t27 () (lambda @t20 @t23)) % 0.32/0.52 (define @t28 () (lambda (@list @t18 @t11) @t22)) % 0.32/0.52 (define @t29 () (@list @t18 @t16)) % 0.32/0.52 (define @t30 () (lambda @t29 (= (_ (_ tptp.intersection @t18) @t16) tptp.emptyset))) % 0.32/0.52 (define @t31 () (@list @t11)) % 0.32/0.52 (define @t32 () (lambda @t29 (forall @t31 (=> @t19 @t17)))) % 0.32/0.52 (define @t33 () (exists @t31 @t25)) % 0.32/0.52 (define @t34 () (lambda @t29 @t33)) % 0.32/0.52 (define @t35 () (lambda @t29 (not @t33))) % 0.32/0.52 (define @t36 () (not (= @t2 @t2))) % 0.32/0.52 (define @t37 () (= @t2 @t1)) % 0.32/0.52 (define @t38 () (not @t37)) % 0.32/0.52 (define @t39 () (or @t38 @t38)) % 0.32/0.52 (define @t40 () (forall @t3 @t38)) % 0.32/0.52 (define @t41 () (not @t40)) % 0.32/0.52 (define @t42 () (= @t2 @t11)) % 0.32/0.52 (define @t43 () (lambda @t31 @t42)) % 0.32/0.52 (define @t44 () (_ (lambda @t14 @t42) @t2)) % 0.32/0.52 (define @t45 () (exists @t3 (_ @t44 @t1))) % 0.32/0.52 (define @t46 () (forall @t5 @t45)) % 0.32/0.52 (assume @p1 @t7) % 0.32/0.52 (assume @p2 true) % 0.32/0.52 (step @p3 (= tptp.in @t9) :rule refl :args (@t9)) % 0.32/0.52 (step @p4 (= tptp.is_a @t9) :rule refl :args (@t9)) % 0.32/0.52 (step @p5 (= tptp.emptyset @t10) :rule refl :args (@t10)) % 0.32/0.52 (step @p6 (= tptp.unord_pair @t13) :rule refl :args (@t13)) % 0.32/0.52 (step @p7 (= tptp.singleton @t15) :rule refl :args (@t15)) % 0.32/0.52 (step @p8 (= tptp.union @t21) :rule refl :args (@t21)) % 0.32/0.52 (step @p9 (= tptp.excl_union @t24) :rule refl :args (@t24)) % 0.32/0.52 (step @p10 (= tptp.intersection @t26) :rule refl :args (@t26)) % 0.32/0.52 (step @p11 (= tptp.setminus @t27) :rule refl :args (@t27)) % 0.32/0.52 (step @p12 (= tptp.complement @t28) :rule refl :args (@t28)) % 0.32/0.52 (step @p13 (= tptp.disjoint @t30) :rule refl :args (@t30)) % 0.32/0.52 (step @p14 (= tptp.subset @t32) :rule refl :args (@t32)) % 0.32/0.52 (step @p15 (= tptp.meets @t34) :rule refl :args (@t34)) % 0.32/0.52 (step @p16 (= tptp.misses @t35) :rule refl :args (@t35)) % 0.32/0.52 (step @p17 :rule evaluate :args ((not true))) % 0.32/0.52 (step @p18 :rule quant-unused-vars :args ((= (forall @t5 true) true))) % 0.32/0.52 (step @p19 :rule evaluate :args ((not false))) % 0.32/0.52 (step @p20 :rule eq-refl :args (@t2)) % 0.32/0.52 (step @p21 :rule cong :premises (@p20) :args (@t36)) % 0.32/0.52 (step @p22 :rule trans :premises (@p21 @p17)) % 0.32/0.52 (step @p23 :rule quant-var-elim-eq :args ((= (forall @t3 (or (not (= @t1 @t2)) @t38)) @t36))) % 0.32/0.52 (step @p24 :rule refl :args (@t38)) % 0.32/0.52 (step @p25 :rule eq-symm :args (@t2 @t1)) % 0.32/0.52 (step @p26 :rule cong :premises (@p25) :args (@t38)) % 0.32/0.52 (step @p27 :rule nary_cong :premises (@p26 @p24) :args (@t39)) % 0.32/0.52 (step @p28 :rule aci_norm :args ((= @t38 @t39))) % 0.32/0.52 (step @p29 :rule trans :premises (@p28 @p27)) % 0.32/0.52 (step @p30 :rule cong :premises (@p29) :args (@t40)) % 0.32/0.52 (step @p31 :rule trans :premises (@p30 @p23)) % 0.32/0.52 (step @p32 :rule trans :premises (@p31 @p22)) % 0.32/0.52 (step @p33 :rule cong :premises (@p32) :args (@t41)) % 0.32/0.52 (step @p34 :rule trans :premises (@p33 @p19)) % 0.32/0.52 (step @p35 :rule exists-elim :args ((= (exists @t3 @t37) @t41))) % 0.32/0.52 (step @p36 :rule trans :premises (@p35 @p34)) % 0.32/0.52 (step @p37 :rule beta-reduce :args ((= (_ @t43 @t1) @t37))) % 0.32/0.52 (step @p38 :rule refl :args (@t1)) % 0.32/0.52 (step @p39 :rule beta-reduce :args ((= @t44 @t43))) % 0.32/0.52 (step @p40 :rule ho_cong :premises (@p39 @p38)) % 0.32/0.52 (step @p41 :rule trans :premises (@p40 @p37)) % 0.32/0.52 (step @p42 :rule cong :premises (@p41) :args (@t45)) % 0.32/0.52 (step @p43 :rule trans :premises (@p42 @p36)) % 0.32/0.52 (step @p44 :rule cong :premises (@p43) :args (@t46)) % 0.32/0.52 (step @p45 :rule trans :premises (@p44 @p18)) % 0.32/0.52 (step @p46 :rule cong :premises (@p45) :args ((not @t46))) % 0.32/0.52 (step @p47 :rule trans :premises (@p46 @p17)) % 0.32/0.52 (step @p48 :rule refl :args (@t2)) % 0.32/0.52 (step @p49 :rule eq-symm :args (@t11 @t2)) % 0.32/0.52 (step @p50 :rule cong :premises (@p49) :args (@t15)) % 0.32/0.52 (step @p51 :rule trans :premises (@p7 @p50)) % 0.32/0.52 (step @p52 :rule ho_cong :premises (@p51 @p48)) % 0.32/0.52 (step @p53 :rule ho_cong :premises (@p52 @p38)) % 0.32/0.52 (step @p54 :rule cong :premises (@p53) :args (@t4)) % 0.32/0.52 (step @p55 :rule cong :premises (@p54) :args (@t6)) % 0.32/0.52 (step @p56 :rule cong :premises (@p55) :args (@t7)) % 0.32/0.52 (step @p57 :rule trans :premises (@p56 @p47)) % 0.32/0.52 (step @p58 false :rule eq_resolve :premises (@p1 @p57)) % 0.32/0.52 ) % 0.32/0.52 % SZS output end Proof % 0.32/0.52 % cvc5 exiting %------------------------------------------------------------------------------