%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU520^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:52:02 AM UTC 2026 % Result : Theorem 0.39s 0.59s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU520^1 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:41:35 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.39/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.59 % SZS status Theorem % 0.39/0.59 % SZS output start Proof % 0.39/0.59 ( % 0.39/0.59 (declare-sort $$unsorted 0) % 0.39/0.59 (declare-const tptp.emptyset $$unsorted) % 0.39/0.59 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.39/0.59 (declare-const tptp.setoftrueEq Bool) % 0.39/0.59 (declare-const tptp.setadjoinOr Bool) % 0.39/0.59 (declare-const tptp.setadjoinE Bool) % 0.39/0.59 (declare-const tptp.emptyinunitempty Bool) % 0.39/0.59 (declare-const tptp.nonemptyI1 Bool) % 0.39/0.59 (declare-const tptp.nonemptyI Bool) % 0.39/0.59 (declare-const tptp.nonemptyE1 Bool) % 0.39/0.59 (declare-const tptp.noeltsimpempty Bool) % 0.39/0.59 (declare-const tptp.emptyI Bool) % 0.39/0.59 (declare-const tptp.omegaIndAx Bool) % 0.39/0.59 (declare-const tptp.omega0Ax Bool) % 0.39/0.59 (declare-const tptp.setadjoinIL Bool) % 0.39/0.59 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.powersetAx Bool) % 0.39/0.59 (declare-const tptp.omegaSAx Bool) % 0.39/0.59 (declare-const tptp.setext Bool) % 0.39/0.59 (declare-const tptp.setadjoinAx Bool) % 0.39/0.59 (declare-const tptp.powersetI Bool) % 0.39/0.59 (declare-const tptp.setbeta Bool) % 0.39/0.59 (declare-const tptp.dsetconstrER Bool) % 0.39/0.59 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.setadjoinIR Bool) % 0.39/0.59 (declare-const tptp.notinemptyset Bool) % 0.39/0.59 (declare-const tptp.foundationAx Bool) % 0.39/0.59 (declare-const tptp.setextAx Bool) % 0.39/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.emptysetAx Bool) % 0.39/0.59 (declare-const tptp.dsetconstrEL Bool) % 0.39/0.59 (declare-const tptp.replAx Bool) % 0.39/0.59 (declare-const tptp.emptysetimpfalse Bool) % 0.39/0.59 (declare-const tptp.wellorderingAx Bool) % 0.39/0.59 (declare-const tptp.descr (-> (-> $$unsorted Bool) $$unsorted)) % 0.39/0.59 (declare-const tptp.emptyinPowerset Bool) % 0.39/0.59 (declare-const tptp.exuE1 Bool) % 0.39/0.59 (declare-const tptp.descrp Bool) % 0.39/0.59 (declare-const tptp.dsetconstrI Bool) % 0.39/0.59 (declare-const tptp.omega $$unsorted) % 0.39/0.59 (declare-const tptp.exuE3e Bool) % 0.39/0.59 (declare-const tptp.prop2setE Bool) % 0.39/0.59 (declare-const tptp.setunionAx Bool) % 0.39/0.59 (declare-const tptp.emptysetE Bool) % 0.39/0.59 (define tptp.exu () (let ((_let_1 (@var "Xy" $$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)))))))))) % 0.39/0.59 (define tptp.prop2set () (let ((_let_1 (@var "Xphi" Bool))) (lambda (@list _let_1) (_ (_ tptp.dsetconstr (_ tptp.powerset tptp.emptyset)) (lambda (@list (@var "Xx" $$unsorted)) _let_1))))) % 0.39/0.59 (define tptp.nonempty () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (not (= _let_1 tptp.emptyset))))) % 0.39/0.59 (define @t1 () (@var "B" $$unsorted)) % 0.39/0.59 (define @t2 () (@var "A" $$unsorted)) % 0.39/0.59 (define @t3 () (= @t2 @t1)) % 0.39/0.59 (define @t4 () (@var "Xx" $$unsorted)) % 0.39/0.59 (define @t5 () (_ tptp.in @t4)) % 0.39/0.59 (define @t6 () (_ @t5 @t1)) % 0.39/0.59 (define @t7 () (_ @t5 @t2)) % 0.39/0.59 (define @t8 () (@list @t4)) % 0.39/0.59 (define @t9 () (@list @t2 @t1)) % 0.39/0.59 (define @t10 () (_ @t5 tptp.emptyset)) % 0.39/0.59 (define @t11 () (forall @t8 (not @t10))) % 0.39/0.59 (define @t12 () (@var "Xy" $$unsorted)) % 0.39/0.59 (define @t13 () (_ tptp.in @t12)) % 0.39/0.59 (define @t14 () (_ @t13 @t2)) % 0.39/0.59 (define @t15 () (= @t12 @t4)) % 0.39/0.59 (define @t16 () (or @t15 @t14)) % 0.39/0.59 (define @t17 () (_ tptp.setadjoin @t4)) % 0.39/0.59 (define @t18 () (_ @t13 (_ @t17 @t2))) % 0.39/0.59 (define @t19 () (@list @t4 @t2 @t12)) % 0.39/0.59 (define @t20 () (forall @t8 (=> @t6 @t7))) % 0.39/0.59 (define @t21 () (_ tptp.powerset @t2)) % 0.39/0.59 (define @t22 () (_ tptp.in @t1)) % 0.39/0.59 (define @t23 () (_ @t22 @t21)) % 0.39/0.59 (define @t24 () (_ @t22 @t2)) % 0.39/0.59 (define @t25 () (@list @t1)) % 0.39/0.59 (define @t26 () (_ tptp.in tptp.emptyset)) % 0.39/0.59 (define @t27 () (_ tptp.in (_ @t17 @t4))) % 0.39/0.59 (define @t28 () (_ @t5 tptp.omega)) % 0.39/0.59 (define @t29 () (@list @t2)) % 0.39/0.59 (define @t30 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.39/0.59 (define @t31 () (@list @t12)) % 0.39/0.59 (define @t32 () (exists @t8 @t7)) % 0.39/0.59 (define @t33 () (@var "E" $$unsorted)) % 0.39/0.59 (define @t34 () (@var "D" $$unsorted)) % 0.39/0.59 (define @t35 () (_ @t13 @t34)) % 0.39/0.59 (define @t36 () (@var "C" $$unsorted)) % 0.39/0.59 (define @t37 () (_ @t13 @t36)) % 0.39/0.59 (define @t38 () (_ @t5 @t36)) % 0.39/0.59 (define @t39 () (_ (_ tptp.in @t34) @t1)) % 0.39/0.59 (define @t40 () (forall @t8 (=> @t38 @t7))) % 0.39/0.59 (define @t41 () (@list @t36)) % 0.39/0.59 (define @t42 () (_ @t5 @t34)) % 0.39/0.59 (define @t43 () (_ (_ tptp.in @t36) @t1)) % 0.39/0.59 (define @t44 () (= @t4 @t12)) % 0.39/0.59 (define @t45 () (@list @t4 @t12)) % 0.39/0.59 (define @t46 () (@var "Xphi" (-> $$unsorted Bool))) % 0.39/0.59 (define @t47 () (_ @t46 @t4)) % 0.39/0.59 (define @t48 () (lambda @t8 @t47)) % 0.39/0.59 (define @t49 () (_ tptp.exu @t48)) % 0.39/0.59 (define @t50 () (@list @t46)) % 0.39/0.59 (define @t51 () (_ @t46 @t12)) % 0.39/0.59 (define @t52 () (_ tptp.dsetconstr @t2)) % 0.39/0.59 (define @t53 () (_ @t52 (lambda @t31 @t51))) % 0.39/0.59 (define @t54 () (_ @t5 @t53)) % 0.39/0.59 (define @t55 () (@list @t2 @t46 @t4)) % 0.39/0.59 (define @t56 () (exists @t8 (and @t47 (forall @t31 (=> @t51 @t44))))) % 0.39/0.59 (define @t57 () (@var "Xphi" Bool)) % 0.39/0.59 (define @t58 () (@list @t57)) % 0.39/0.59 (define @t59 () (forall @t29 (=> (forall @t8 (not @t7)) (= @t2 tptp.emptyset)))) % 0.39/0.59 (define @t60 () (_ tptp.nonempty @t2)) % 0.39/0.59 (define @t61 () (_ @t26 @t21)) % 0.39/0.59 (define @t62 () (forall @t29 @t61)) % 0.39/0.59 (define @t63 () (= tptp.emptyinPowerset @t62)) % 0.39/0.59 (define @t64 () (=> tptp.emptyinPowerset @t62)) % 0.39/0.59 (define @t65 () (=> tptp.powersetI @t64)) % 0.39/0.59 (define @t66 () (=> tptp.setoftrueEq @t65)) % 0.39/0.59 (define @t67 () (=> tptp.setadjoinOr @t66)) % 0.39/0.59 (define @t68 () (=> tptp.setadjoinE @t67)) % 0.39/0.59 (define @t69 () (=> tptp.setadjoinIR @t68)) % 0.39/0.59 (define @t70 () (=> tptp.emptyinunitempty @t69)) % 0.39/0.59 (define @t71 () (=> tptp.setadjoinIL @t70)) % 0.39/0.59 (define @t72 () (=> tptp.nonemptyI1 @t71)) % 0.39/0.59 (define @t73 () (=> tptp.nonemptyI @t72)) % 0.39/0.59 (define @t74 () (=> tptp.nonemptyE1 @t73)) % 0.39/0.59 (define @t75 () (=> tptp.setbeta @t74)) % 0.39/0.59 (define @t76 () (=> tptp.noeltsimpempty @t75)) % 0.39/0.59 (define @t77 () (=> tptp.emptyI @t76)) % 0.39/0.59 (define @t78 () (=> tptp.setext @t77)) % 0.39/0.59 (define @t79 () (=> tptp.exuE3e @t78)) % 0.39/0.59 (define @t80 () (=> tptp.notinemptyset @t79)) % 0.39/0.59 (define @t81 () (=> tptp.emptysetimpfalse @t80)) % 0.39/0.59 (define @t82 () (=> tptp.emptysetE @t81)) % 0.39/0.59 (define @t83 () (=> tptp.prop2setE @t82)) % 0.39/0.59 (define @t84 () (=> tptp.exuE1 @t83)) % 0.39/0.59 (define @t85 () (=> tptp.dsetconstrER @t84)) % 0.39/0.59 (define @t86 () (=> tptp.dsetconstrEL @t85)) % 0.39/0.59 (define @t87 () (=> tptp.dsetconstrI @t86)) % 0.39/0.59 (define @t88 () (=> tptp.descrp @t87)) % 0.39/0.59 (define @t89 () (=> tptp.wellorderingAx @t88)) % 0.39/0.59 (define @t90 () (=> tptp.foundationAx @t89)) % 0.39/0.59 (define @t91 () (=> tptp.replAx @t90)) % 0.39/0.59 (define @t92 () (=> tptp.omegaIndAx @t91)) % 0.39/0.59 (define @t93 () (=> tptp.omegaSAx @t92)) % 0.39/0.59 (define @t94 () (=> tptp.omega0Ax @t93)) % 0.39/0.59 (define @t95 () (=> tptp.setunionAx @t94)) % 0.39/0.59 (define @t96 () (=> tptp.powersetAx @t95)) % 0.39/0.59 (define @t97 () (=> tptp.setadjoinAx @t96)) % 0.39/0.59 (define @t98 () (=> tptp.emptysetAx @t97)) % 0.39/0.59 (define @t99 () (=> tptp.setextAx @t98)) % 0.39/0.59 (define @t100 () (not @t99)) % 0.39/0.59 (define @t101 () (lambda @t50 @t56)) % 0.39/0.59 (define @t102 () (lambda @t58 (_ (_ tptp.dsetconstr (_ tptp.powerset tptp.emptyset)) (lambda @t8 @t57)))) % 0.39/0.59 (define @t103 () (lambda @t8 (not (= @t4 tptp.emptyset)))) % 0.39/0.59 (define @t104 () (tptp.powerset @t2)) % 0.39/0.59 (define @t105 () (tptp.in tptp.emptyset @t104)) % 0.39/0.59 (define @t106 () (forall @t29 @t105)) % 0.39/0.59 (assume @p1 (= tptp.setextAx (forall @t9 (=> (forall @t8 (= @t7 @t6)) @t3)))) % 0.39/0.59 (assume @p2 (= tptp.emptysetAx @t11)) % 0.39/0.59 (assume @p3 (= tptp.setadjoinAx (forall @t19 (= @t18 @t16)))) % 0.39/0.59 (assume @p4 (= tptp.powersetAx (forall @t9 (= @t23 @t20)))) % 0.39/0.59 (assume @p5 (= tptp.setunionAx (forall (@list @t2 @t4) (= (_ @t5 (_ tptp.setunion @t2)) (exists @t25 (and @t6 @t24)))))) % 0.39/0.59 (assume @p6 (= tptp.omega0Ax (_ @t26 tptp.omega))) % 0.39/0.59 (assume @p7 (= tptp.omegaSAx (forall @t8 (=> @t28 (_ @t27 tptp.omega))))) % 0.39/0.59 (assume @p8 (= tptp.omegaIndAx (forall @t29 (=> (and (_ @t26 @t2) (forall @t8 (=> (and @t28 @t7) (_ @t27 @t2)))) (forall @t8 (=> @t28 @t7)))))) % 0.39/0.59 (assume @p9 (= tptp.replAx (forall (@list @t30 @t2) (=> (forall @t8 (=> @t7 (_ tptp.exu (lambda @t31 (_ (_ @t30 @t4) @t12))))) (exists @t25 (forall @t8 (= @t6 (exists @t31 (and @t14 (_ (_ @t30 @t12) @t4)))))))))) % 0.39/0.59 (assume @p10 (= tptp.foundationAx (forall @t29 (=> @t32 (exists @t25 (and @t24 (not (exists @t8 (and @t6 @t7))))))))) % 0.39/0.59 (assume @p11 (= tptp.wellorderingAx (forall @t29 (exists @t25 (and (forall @t41 (=> @t43 @t40)) (forall @t45 (=> (and @t7 @t14) (=> (forall @t41 (=> @t43 (= @t38 @t37))) @t44))) (forall (@list @t36 @t34) (=> (and @t43 @t39) (or (forall @t8 (=> @t38 @t42)) (forall @t8 (=> @t42 @t38))))) (forall @t41 (=> (and @t40 (exists @t8 @t38)) (exists (@list @t34 @t4) (and @t39 @t38 (not (exists @t31 (and @t35 @t37))) (forall (@list @t33) (=> (_ (_ tptp.in @t33) @t1) (or (forall @t31 (=> (_ @t13 @t33) @t35)) (_ @t5 @t33))))))))))))) % 0.39/0.59 (assume @p12 (= tptp.descrp (forall @t50 (=> @t49 (_ @t46 (_ tptp.descr @t48)))))) % 0.39/0.59 (assume @p13 (= tptp.dsetconstrI (forall @t55 (=> @t7 (=> @t47 @t54))))) % 0.39/0.59 (assume @p14 (= tptp.dsetconstrEL (forall @t55 (=> @t54 @t7)))) % 0.39/0.59 (assume @p15 (= tptp.dsetconstrER (forall @t55 (=> @t54 @t47)))) % 0.39/0.59 (assume @p16 (= tptp.exuE1 (forall @t50 (=> @t49 @t56)))) % 0.39/0.59 (assume @p17 (= tptp.prop2setE (forall (@list @t57 @t4) (=> (_ @t5 (_ tptp.prop2set @t57)) @t57)))) % 0.39/0.59 (assume @p18 (= tptp.emptysetE (forall @t8 (=> @t10 (forall @t58 @t57))))) % 0.39/0.59 (assume @p19 (= tptp.emptysetimpfalse (forall @t8 (=> @t10 false)))) % 0.39/0.59 (assume @p20 (= tptp.notinemptyset @t11)) % 0.39/0.59 (assume @p21 (= tptp.exuE3e (forall @t50 (=> @t49 (exists @t8 @t47))))) % 0.39/0.59 (assume @p22 (= tptp.setext (forall @t9 (=> (forall @t8 (=> @t7 @t6)) (=> @t20 @t3))))) % 0.39/0.59 (assume @p23 (= tptp.emptyI @t59)) % 0.39/0.59 (assume @p24 (= tptp.noeltsimpempty @t59)) % 0.39/0.59 (assume @p25 (= tptp.setbeta (forall @t55 (=> @t7 (= @t54 @t47))))) % 0.39/0.59 (assume @p26 (= tptp.nonemptyE1 (forall @t29 (=> @t60 @t32)))) % 0.39/0.59 (assume @p27 (= tptp.nonemptyI (forall @t55 (=> @t7 (=> @t47 (_ tptp.nonempty @t53)))))) % 0.39/0.59 (assume @p28 (= tptp.nonemptyI1 (forall @t29 (=> @t32 @t60)))) % 0.39/0.59 (assume @p29 (= tptp.setadjoinIL (forall @t45 (_ @t5 (_ @t17 @t12))))) % 0.39/0.59 (assume @p30 (= tptp.emptyinunitempty (_ @t26 (_ (_ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) % 0.39/0.59 (assume @p31 (= tptp.setadjoinIR (forall @t19 (=> @t14 @t18)))) % 0.39/0.59 (assume @p32 (= tptp.setadjoinE (forall @t19 (=> @t18 (forall @t58 (=> (=> @t15 @t57) (=> (=> @t14 @t57) @t57))))))) % 0.39/0.59 (assume @p33 (= tptp.setadjoinOr (forall @t19 (=> @t18 @t16)))) % 0.39/0.59 (assume @p34 (= tptp.setoftrueEq (forall @t29 (= (_ @t52 (lambda @t8 true)) @t2)))) % 0.39/0.59 (assume @p35 (= tptp.powersetI (forall @t9 (=> @t20 @t23)))) % 0.39/0.59 (assume @p36 @t63) % 0.39/0.59 (assume @p37 @t100) % 0.39/0.59 (assume @p38 true) % 0.39/0.59 (step @p39 (= tptp.exu @t101) :rule refl :args (@t101)) % 0.39/0.59 (step @p40 (= tptp.prop2set @t102) :rule refl :args (@t102)) % 0.39/0.59 (step @p41 (= tptp.nonempty @t103) :rule refl :args (@t103)) % 0.39/0.59 (step @p42 :rule refl :args ((tptp.in tptp.emptyset @t21))) % 0.39/0.59 (step @p43 :rule refl :args (@t104)) % 0.39/0.59 (step @p44 :rule refl :args (tptp.emptyset)) % 0.39/0.59 (step @p45 :rule cong :premises (@p44 @p43) :args (@t105)) % 0.39/0.59 (step @p46 :rule trans :premises (@p45 @p42)) % 0.39/0.59 (step @p47 :rule refl :args (@t26)) % 0.39/0.59 (step @p48 :rule ho_cong :premises (@p47 @p43)) % 0.39/0.59 (step @p49 :rule cong :premises (@p48 @p46) :args ((= (_ @t26 @t104) @t105))) % 0.39/0.59 (step @p50 :rule symm :premises (@p49)) % 0.39/0.59 (step @p51 :rule refl :args (@t61)) % 0.39/0.59 (step @p52 :rule eq_resolve :premises (@p51 @p50)) % 0.39/0.59 (step @p53 :rule refl :args (@t21)) % 0.39/0.59 (step @p54 :rule cong :premises (@p53 @p43) :args ((= @t21 @t104))) % 0.39/0.59 (step @p55 :rule symm :premises (@p54)) % 0.39/0.59 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.39/0.59 (step @p57 :rule ho_cong :premises (@p47 @p56)) % 0.39/0.59 (step @p58 :rule trans :premises (@p57 @p52)) % 0.39/0.59 (step @p59 :rule cong :premises (@p58) :args (@t62)) % 0.39/0.59 (step @p60 :rule refl :args (tptp.emptyinPowerset)) % 0.39/0.59 (step @p61 :rule cong :premises (@p60 @p59) :args (@t64)) % 0.39/0.59 (step @p62 :rule refl :args (tptp.powersetI)) % 0.39/0.59 (step @p63 :rule cong :premises (@p62 @p61) :args (@t65)) % 0.39/0.59 (step @p64 :rule refl :args (tptp.setoftrueEq)) % 0.39/0.59 (step @p65 :rule cong :premises (@p64 @p63) :args (@t66)) % 0.39/0.59 (step @p66 :rule refl :args (tptp.setadjoinOr)) % 0.39/0.59 (step @p67 :rule cong :premises (@p66 @p65) :args (@t67)) % 0.39/0.59 (step @p68 :rule refl :args (tptp.setadjoinE)) % 0.39/0.59 (step @p69 :rule cong :premises (@p68 @p67) :args (@t68)) % 0.39/0.59 (step @p70 :rule refl :args (tptp.setadjoinIR)) % 0.39/0.59 (step @p71 :rule cong :premises (@p70 @p69) :args (@t69)) % 0.39/0.59 (step @p72 :rule refl :args (tptp.emptyinunitempty)) % 0.39/0.59 (step @p73 :rule cong :premises (@p72 @p71) :args (@t70)) % 0.39/0.59 (step @p74 :rule refl :args (tptp.setadjoinIL)) % 0.39/0.59 (step @p75 :rule cong :premises (@p74 @p73) :args (@t71)) % 0.39/0.59 (step @p76 :rule refl :args (tptp.nonemptyI1)) % 0.39/0.59 (step @p77 :rule cong :premises (@p76 @p75) :args (@t72)) % 0.39/0.59 (step @p78 :rule refl :args (tptp.nonemptyI)) % 0.39/0.59 (step @p79 :rule cong :premises (@p78 @p77) :args (@t73)) % 0.39/0.59 (step @p80 :rule refl :args (tptp.nonemptyE1)) % 0.39/0.59 (step @p81 :rule cong :premises (@p80 @p79) :args (@t74)) % 0.39/0.59 (step @p82 :rule refl :args (tptp.setbeta)) % 0.39/0.59 (step @p83 :rule cong :premises (@p82 @p81) :args (@t75)) % 0.39/0.59 (step @p84 :rule refl :args (tptp.noeltsimpempty)) % 0.39/0.59 (step @p85 :rule cong :premises (@p84 @p83) :args (@t76)) % 0.39/0.59 (step @p86 :rule refl :args (tptp.emptyI)) % 0.39/0.59 (step @p87 :rule cong :premises (@p86 @p85) :args (@t77)) % 0.39/0.59 (step @p88 :rule refl :args (tptp.setext)) % 0.39/0.59 (step @p89 :rule cong :premises (@p88 @p87) :args (@t78)) % 0.39/0.59 (step @p90 :rule refl :args (tptp.exuE3e)) % 0.39/0.59 (step @p91 :rule cong :premises (@p90 @p89) :args (@t79)) % 0.39/0.59 (step @p92 :rule refl :args (tptp.notinemptyset)) % 0.39/0.59 (step @p93 :rule cong :premises (@p92 @p91) :args (@t80)) % 0.39/0.59 (step @p94 :rule refl :args (tptp.emptysetimpfalse)) % 0.39/0.59 (step @p95 :rule cong :premises (@p94 @p93) :args (@t81)) % 0.39/0.59 (step @p96 :rule refl :args (tptp.emptysetE)) % 0.39/0.59 (step @p97 :rule cong :premises (@p96 @p95) :args (@t82)) % 0.39/0.59 (step @p98 :rule refl :args (tptp.prop2setE)) % 0.39/0.59 (step @p99 :rule cong :premises (@p98 @p97) :args (@t83)) % 0.39/0.59 (step @p100 :rule refl :args (tptp.exuE1)) % 0.39/0.59 (step @p101 :rule cong :premises (@p100 @p99) :args (@t84)) % 0.39/0.59 (step @p102 :rule refl :args (tptp.dsetconstrER)) % 0.39/0.59 (step @p103 :rule cong :premises (@p102 @p101) :args (@t85)) % 0.39/0.59 (step @p104 :rule refl :args (tptp.dsetconstrEL)) % 0.39/0.59 (step @p105 :rule cong :premises (@p104 @p103) :args (@t86)) % 0.39/0.59 (step @p106 :rule refl :args (tptp.dsetconstrI)) % 0.39/0.59 (step @p107 :rule cong :premises (@p106 @p105) :args (@t87)) % 0.39/0.59 (step @p108 :rule refl :args (tptp.descrp)) % 0.39/0.59 (step @p109 :rule cong :premises (@p108 @p107) :args (@t88)) % 0.39/0.59 (step @p110 :rule refl :args (tptp.wellorderingAx)) % 0.39/0.59 (step @p111 :rule cong :premises (@p110 @p109) :args (@t89)) % 0.39/0.59 (step @p112 :rule refl :args (tptp.foundationAx)) % 0.39/0.59 (step @p113 :rule cong :premises (@p112 @p111) :args (@t90)) % 0.39/0.59 (step @p114 :rule refl :args (tptp.replAx)) % 0.39/0.59 (step @p115 :rule cong :premises (@p114 @p113) :args (@t91)) % 0.39/0.59 (step @p116 :rule refl :args (tptp.omegaIndAx)) % 0.39/0.59 (step @p117 :rule cong :premises (@p116 @p115) :args (@t92)) % 0.39/0.59 (step @p118 :rule refl :args (tptp.omegaSAx)) % 0.39/0.59 (step @p119 :rule cong :premises (@p118 @p117) :args (@t93)) % 0.39/0.59 (step @p120 :rule refl :args (tptp.omega0Ax)) % 0.39/0.59 (step @p121 :rule cong :premises (@p120 @p119) :args (@t94)) % 0.39/0.59 (step @p122 :rule refl :args (tptp.setunionAx)) % 0.39/0.59 (step @p123 :rule cong :premises (@p122 @p121) :args (@t95)) % 0.39/0.59 (step @p124 :rule refl :args (tptp.powersetAx)) % 0.39/0.59 (step @p125 :rule cong :premises (@p124 @p123) :args (@t96)) % 0.39/0.59 (step @p126 :rule refl :args (tptp.setadjoinAx)) % 0.39/0.59 (step @p127 :rule cong :premises (@p126 @p125) :args (@t97)) % 0.39/0.59 (step @p128 :rule refl :args (tptp.emptysetAx)) % 0.39/0.59 (step @p129 :rule cong :premises (@p128 @p127) :args (@t98)) % 0.39/0.59 (step @p130 :rule refl :args (tptp.setextAx)) % 0.39/0.59 (step @p131 :rule cong :premises (@p130 @p129) :args (@t99)) % 0.39/0.59 (step @p132 :rule cong :premises (@p131) :args (@t100)) % 0.39/0.59 (step @p133 :rule eq_resolve :premises (@p37 @p132)) % 0.39/0.59 (step @p134 :rule not_implies_elim2 :premises (@p133)) % 0.39/0.59 (step @p135 :rule not_implies_elim2 :premises (@p134)) % 0.39/0.59 (step @p136 :rule not_implies_elim2 :premises (@p135)) % 0.39/0.59 (step @p137 :rule not_implies_elim2 :premises (@p136)) % 0.39/0.59 (step @p138 :rule not_implies_elim2 :premises (@p137)) % 0.39/0.59 (step @p139 :rule not_implies_elim2 :premises (@p138)) % 0.39/0.59 (step @p140 :rule not_implies_elim2 :premises (@p139)) % 0.39/0.59 (step @p141 :rule not_implies_elim2 :premises (@p140)) % 0.39/0.59 (step @p142 :rule not_implies_elim2 :premises (@p141)) % 0.39/0.59 (step @p143 :rule not_implies_elim2 :premises (@p142)) % 0.39/0.59 (step @p144 :rule not_implies_elim2 :premises (@p143)) % 0.39/0.59 (step @p145 :rule not_implies_elim2 :premises (@p144)) % 0.39/0.59 (step @p146 :rule not_implies_elim2 :premises (@p145)) % 0.39/0.59 (step @p147 :rule not_implies_elim2 :premises (@p146)) % 0.39/0.59 (step @p148 :rule not_implies_elim2 :premises (@p147)) % 0.39/0.59 (step @p149 :rule not_implies_elim2 :premises (@p148)) % 0.39/0.59 (step @p150 :rule not_implies_elim2 :premises (@p149)) % 0.39/0.59 (step @p151 :rule not_implies_elim2 :premises (@p150)) % 0.39/0.59 (step @p152 :rule not_implies_elim2 :premises (@p151)) % 0.39/0.59 (step @p153 :rule not_implies_elim2 :premises (@p152)) % 0.39/0.59 (step @p154 :rule not_implies_elim2 :premises (@p153)) % 0.39/0.59 (step @p155 :rule not_implies_elim2 :premises (@p154)) % 0.39/0.59 (step @p156 :rule not_implies_elim2 :premises (@p155)) % 0.39/0.59 (step @p157 :rule not_implies_elim2 :premises (@p156)) % 0.39/0.59 (step @p158 :rule not_implies_elim2 :premises (@p157)) % 0.39/0.59 (step @p159 :rule not_implies_elim2 :premises (@p158)) % 0.39/0.59 (step @p160 :rule not_implies_elim2 :premises (@p159)) % 0.39/0.59 (step @p161 :rule not_implies_elim2 :premises (@p160)) % 0.39/0.59 (step @p162 :rule not_implies_elim2 :premises (@p161)) % 0.39/0.59 (step @p163 :rule not_implies_elim2 :premises (@p162)) % 0.39/0.59 (step @p164 :rule not_implies_elim2 :premises (@p163)) % 0.39/0.59 (step @p165 :rule not_implies_elim2 :premises (@p164)) % 0.39/0.59 (step @p166 :rule not_implies_elim2 :premises (@p165)) % 0.39/0.59 (step @p167 :rule not_implies_elim2 :premises (@p166)) % 0.39/0.59 (step @p168 :rule not_implies_elim2 :premises (@p167)) % 0.39/0.59 (step @p169 :rule not_implies_elim2 :premises (@p168)) % 0.39/0.59 (step @p170 :rule not_implies_elim1 :premises (@p168)) % 0.39/0.59 (step @p171 :rule cnf_equiv_pos1 :args ((= tptp.emptyinPowerset @t106))) % 0.39/0.59 (step @p172 :rule chain_resolution :premises (@p171 @p170 @p169) :args ((@list false true) (@list tptp.emptyinPowerset @t106))) % 0.39/0.59 (step @p173 :rule cong :premises (@p60 @p59) :args (@t63)) % 0.39/0.59 (step @p174 :rule eq_resolve :premises (@p36 @p173)) % 0.39/0.59 (step @p175 false :rule contra :premises (@p174 @p172)) % 0.39/0.59 ) % 0.39/0.59 % SZS output end Proof % 0.39/0.59 % cvc5 exiting %------------------------------------------------------------------------------