%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU516^1 : 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 08:52:01 AM UTC 2026 % Result : Theorem 0.36s 0.60s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU516^1 : 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 % 0.15/0.33 % Computer : n014.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 17:40:28 EDT 2026 % 0.15/0.34 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.36/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.60 % SZS status Theorem % 0.36/0.60 % SZS output start Proof % 0.36/0.60 ( % 0.36/0.60 (declare-sort $$unsorted 0) % 0.36/0.60 (declare-const tptp.emptyset $$unsorted) % 0.36/0.60 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.36/0.60 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.36/0.60 (declare-const tptp.setadjoinE Bool) % 0.36/0.60 (declare-const tptp.emptyinunitempty Bool) % 0.36/0.60 (declare-const tptp.nonemptyI1 Bool) % 0.36/0.60 (declare-const tptp.nonemptyI Bool) % 0.36/0.60 (declare-const tptp.nonemptyE1 Bool) % 0.36/0.60 (declare-const tptp.noeltsimpempty Bool) % 0.36/0.60 (declare-const tptp.emptyI Bool) % 0.36/0.60 (declare-const tptp.omegaIndAx Bool) % 0.36/0.60 (declare-const tptp.omega0Ax Bool) % 0.36/0.60 (declare-const tptp.setadjoinIL Bool) % 0.36/0.60 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.36/0.60 (declare-const tptp.powersetAx Bool) % 0.36/0.60 (declare-const tptp.omegaSAx Bool) % 0.36/0.60 (declare-const tptp.setext Bool) % 0.36/0.60 (declare-const tptp.setadjoinAx Bool) % 0.36/0.60 (declare-const tptp.setbeta Bool) % 0.36/0.60 (declare-const tptp.dsetconstrER Bool) % 0.36/0.60 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.60 (declare-const tptp.setadjoinIR Bool) % 0.36/0.60 (declare-const tptp.notinemptyset Bool) % 0.36/0.60 (declare-const tptp.foundationAx Bool) % 0.36/0.60 (declare-const tptp.setextAx Bool) % 0.36/0.60 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.60 (declare-const tptp.emptysetAx Bool) % 0.36/0.60 (declare-const tptp.dsetconstrEL Bool) % 0.36/0.60 (declare-const tptp.replAx Bool) % 0.36/0.60 (declare-const tptp.emptysetimpfalse Bool) % 0.36/0.60 (declare-const tptp.wellorderingAx Bool) % 0.36/0.60 (declare-const tptp.descr (-> (-> $$unsorted Bool) $$unsorted)) % 0.36/0.60 (declare-const tptp.exuE1 Bool) % 0.36/0.60 (declare-const tptp.descrp Bool) % 0.36/0.60 (declare-const tptp.dsetconstrI Bool) % 0.36/0.60 (declare-const tptp.omega $$unsorted) % 0.36/0.60 (declare-const tptp.exuE3e Bool) % 0.36/0.60 (declare-const tptp.prop2setE Bool) % 0.36/0.60 (declare-const tptp.setunionAx Bool) % 0.36/0.60 (declare-const tptp.emptysetE Bool) % 0.36/0.60 (define tptp.exu () (let ((_let_1 (@var "Xy" $$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)))))))))) % 0.36/0.60 (define tptp.prop2set () (let ((_let_1 (@var "Xphi" Bool))) (lambda (@list _let_1) (_ (_ tptp.dsetconstr (_ tptp.powerset tptp.emptyset)) (lambda (@list (@var "Xx" $$unsorted)) _let_1))))) % 0.36/0.60 (define tptp.nonempty () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (not (= _let_1 tptp.emptyset))))) % 0.36/0.60 (define @t1 () (@var "B" $$unsorted)) % 0.36/0.60 (define @t2 () (@var "A" $$unsorted)) % 0.36/0.60 (define @t3 () (= @t2 @t1)) % 0.36/0.60 (define @t4 () (@var "Xx" $$unsorted)) % 0.36/0.60 (define @t5 () (_ tptp.in @t4)) % 0.36/0.60 (define @t6 () (_ @t5 @t1)) % 0.36/0.60 (define @t7 () (_ @t5 @t2)) % 0.36/0.60 (define @t8 () (@list @t4)) % 0.36/0.60 (define @t9 () (@list @t2 @t1)) % 0.36/0.60 (define @t10 () (_ @t5 tptp.emptyset)) % 0.36/0.60 (define @t11 () (forall @t8 (not @t10))) % 0.36/0.60 (define @t12 () (@var "Xy" $$unsorted)) % 0.36/0.60 (define @t13 () (_ tptp.in @t12)) % 0.36/0.60 (define @t14 () (_ @t13 @t2)) % 0.36/0.60 (define @t15 () (= @t12 @t4)) % 0.36/0.60 (define @t16 () (or @t15 @t14)) % 0.36/0.60 (define @t17 () (_ tptp.setadjoin @t4)) % 0.36/0.60 (define @t18 () (_ @t17 @t2)) % 0.36/0.60 (define @t19 () (_ @t13 @t18)) % 0.36/0.60 (define @t20 () (@list @t4 @t2 @t12)) % 0.36/0.60 (define @t21 () (forall @t8 (=> @t6 @t7))) % 0.36/0.60 (define @t22 () (_ tptp.in @t1)) % 0.36/0.60 (define @t23 () (_ @t22 @t2)) % 0.36/0.60 (define @t24 () (@list @t1)) % 0.36/0.60 (define @t25 () (_ tptp.in tptp.emptyset)) % 0.36/0.60 (define @t26 () (_ tptp.in (_ @t17 @t4))) % 0.36/0.60 (define @t27 () (_ @t5 tptp.omega)) % 0.36/0.60 (define @t28 () (@list @t2)) % 0.36/0.60 (define @t29 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.36/0.60 (define @t30 () (@list @t12)) % 0.36/0.60 (define @t31 () (exists @t8 @t7)) % 0.36/0.60 (define @t32 () (@var "E" $$unsorted)) % 0.36/0.60 (define @t33 () (@var "D" $$unsorted)) % 0.36/0.60 (define @t34 () (_ @t13 @t33)) % 0.36/0.60 (define @t35 () (@var "C" $$unsorted)) % 0.36/0.60 (define @t36 () (_ @t13 @t35)) % 0.36/0.60 (define @t37 () (_ @t5 @t35)) % 0.36/0.60 (define @t38 () (_ (_ tptp.in @t33) @t1)) % 0.36/0.60 (define @t39 () (forall @t8 (=> @t37 @t7))) % 0.36/0.60 (define @t40 () (@list @t35)) % 0.36/0.60 (define @t41 () (_ @t5 @t33)) % 0.36/0.60 (define @t42 () (_ (_ tptp.in @t35) @t1)) % 0.36/0.60 (define @t43 () (= @t4 @t12)) % 0.36/0.60 (define @t44 () (@list @t4 @t12)) % 0.36/0.60 (define @t45 () (@var "Xphi" (-> $$unsorted Bool))) % 0.36/0.60 (define @t46 () (_ @t45 @t4)) % 0.36/0.60 (define @t47 () (lambda @t8 @t46)) % 0.36/0.60 (define @t48 () (_ tptp.exu @t47)) % 0.36/0.60 (define @t49 () (@list @t45)) % 0.36/0.60 (define @t50 () (_ @t45 @t12)) % 0.36/0.60 (define @t51 () (_ (_ tptp.dsetconstr @t2) (lambda @t30 @t50))) % 0.36/0.60 (define @t52 () (_ @t5 @t51)) % 0.36/0.60 (define @t53 () (@list @t2 @t45 @t4)) % 0.36/0.60 (define @t54 () (exists @t8 (and @t46 (forall @t30 (=> @t50 @t43))))) % 0.36/0.60 (define @t55 () (@var "Xphi" Bool)) % 0.36/0.60 (define @t56 () (@list @t55)) % 0.36/0.60 (define @t57 () (forall @t28 (=> (forall @t8 (not @t7)) (= @t2 tptp.emptyset)))) % 0.36/0.60 (define @t58 () (_ tptp.nonempty @t2)) % 0.36/0.60 (define @t59 () (=> @t14 @t55)) % 0.36/0.60 (define @t60 () (=> @t59 @t55)) % 0.36/0.60 (define @t61 () (=> @t15 @t55)) % 0.36/0.60 (define @t62 () (=> @t61 @t60)) % 0.36/0.60 (define @t63 () (forall @t56 @t62)) % 0.36/0.60 (define @t64 () (=> @t19 @t63)) % 0.36/0.60 (define @t65 () (forall @t20 @t64)) % 0.36/0.60 (define @t66 () (= tptp.setadjoinE @t65)) % 0.36/0.60 (define @t67 () (=> @t19 @t16)) % 0.36/0.60 (define @t68 () (forall @t20 @t67)) % 0.36/0.60 (define @t69 () (=> tptp.setadjoinE @t68)) % 0.36/0.60 (define @t70 () (=> tptp.setadjoinIR @t69)) % 0.36/0.60 (define @t71 () (=> tptp.emptyinunitempty @t70)) % 0.36/0.60 (define @t72 () (=> tptp.setadjoinIL @t71)) % 0.36/0.60 (define @t73 () (=> tptp.nonemptyI1 @t72)) % 0.36/0.60 (define @t74 () (=> tptp.nonemptyI @t73)) % 0.36/0.60 (define @t75 () (=> tptp.nonemptyE1 @t74)) % 0.36/0.60 (define @t76 () (=> tptp.setbeta @t75)) % 0.36/0.60 (define @t77 () (=> tptp.noeltsimpempty @t76)) % 0.36/0.60 (define @t78 () (=> tptp.emptyI @t77)) % 0.36/0.60 (define @t79 () (=> tptp.setext @t78)) % 0.36/0.60 (define @t80 () (=> tptp.exuE3e @t79)) % 0.36/0.60 (define @t81 () (=> tptp.notinemptyset @t80)) % 0.36/0.60 (define @t82 () (=> tptp.emptysetimpfalse @t81)) % 0.36/0.60 (define @t83 () (=> tptp.emptysetE @t82)) % 0.36/0.60 (define @t84 () (=> tptp.prop2setE @t83)) % 0.36/0.60 (define @t85 () (=> tptp.exuE1 @t84)) % 0.36/0.60 (define @t86 () (=> tptp.dsetconstrER @t85)) % 0.36/0.60 (define @t87 () (=> tptp.dsetconstrEL @t86)) % 0.36/0.60 (define @t88 () (=> tptp.dsetconstrI @t87)) % 0.36/0.60 (define @t89 () (=> tptp.descrp @t88)) % 0.36/0.60 (define @t90 () (=> tptp.wellorderingAx @t89)) % 0.36/0.60 (define @t91 () (=> tptp.foundationAx @t90)) % 0.36/0.60 (define @t92 () (=> tptp.replAx @t91)) % 0.36/0.60 (define @t93 () (=> tptp.omegaIndAx @t92)) % 0.36/0.60 (define @t94 () (=> tptp.omegaSAx @t93)) % 0.36/0.60 (define @t95 () (=> tptp.omega0Ax @t94)) % 0.36/0.60 (define @t96 () (=> tptp.setunionAx @t95)) % 0.36/0.60 (define @t97 () (=> tptp.powersetAx @t96)) % 0.36/0.60 (define @t98 () (=> tptp.setadjoinAx @t97)) % 0.36/0.60 (define @t99 () (=> tptp.emptysetAx @t98)) % 0.36/0.60 (define @t100 () (=> tptp.setextAx @t99)) % 0.36/0.60 (define @t101 () (not @t100)) % 0.36/0.60 (define @t102 () (lambda @t49 @t54)) % 0.36/0.60 (define @t103 () (lambda @t56 (_ (_ tptp.dsetconstr (_ tptp.powerset tptp.emptyset)) (lambda @t8 @t55)))) % 0.36/0.60 (define @t104 () (lambda @t8 (not (= @t4 tptp.emptyset)))) % 0.36/0.60 (define @t105 () (tptp.in @t12 @t2)) % 0.36/0.60 (define @t106 () (tptp.setadjoin @t4 @t2)) % 0.36/0.60 (define @t107 () (tptp.in @t12 @t106)) % 0.36/0.60 (define @t108 () (not @t19)) % 0.36/0.60 (define @t109 () (or @t108 @t43 @t14)) % 0.36/0.60 (define @t110 () (or @t43 @t14)) % 0.36/0.60 (define @t111 () (forall @t20 (or (not @t107) @t43 @t105))) % 0.36/0.60 (define @t112 () (or @t108 @t43 @t105)) % 0.36/0.60 (define @t113 () (or @t43 @t105)) % 0.36/0.60 (define @t114 () (not false)) % 0.36/0.60 (define @t115 () (and @t105 @t114)) % 0.36/0.60 (define @t116 () (and @t43 @t114)) % 0.36/0.60 (define @t117 () (or @t116 @t115)) % 0.36/0.60 (define @t118 () (or @t116 @t115 false)) % 0.36/0.60 (define @t119 () (not @t55)) % 0.36/0.60 (define @t120 () (and @t105 @t119)) % 0.36/0.60 (define @t121 () (and @t43 @t119)) % 0.36/0.60 (define @t122 () (or @t55 @t121 @t120 @t55)) % 0.36/0.60 (define @t123 () (or @t121 @t120 @t55)) % 0.36/0.60 (define @t124 () (and @t14 @t119)) % 0.36/0.60 (define @t125 () (or @t121 @t124 @t55)) % 0.36/0.60 (define @t126 () (=> @t43 @t55)) % 0.36/0.60 (assume @p1 (= tptp.setextAx (forall @t9 (=> (forall @t8 (= @t7 @t6)) @t3)))) % 0.36/0.60 (assume @p2 (= tptp.emptysetAx @t11)) % 0.36/0.60 (assume @p3 (= tptp.setadjoinAx (forall @t20 (= @t19 @t16)))) % 0.36/0.60 (assume @p4 (= tptp.powersetAx (forall @t9 (= (_ @t22 (_ tptp.powerset @t2)) @t21)))) % 0.36/0.60 (assume @p5 (= tptp.setunionAx (forall (@list @t2 @t4) (= (_ @t5 (_ tptp.setunion @t2)) (exists @t24 (and @t6 @t23)))))) % 0.36/0.60 (assume @p6 (= tptp.omega0Ax (_ @t25 tptp.omega))) % 0.36/0.60 (assume @p7 (= tptp.omegaSAx (forall @t8 (=> @t27 (_ @t26 tptp.omega))))) % 0.36/0.60 (assume @p8 (= tptp.omegaIndAx (forall @t28 (=> (and (_ @t25 @t2) (forall @t8 (=> (and @t27 @t7) (_ @t26 @t2)))) (forall @t8 (=> @t27 @t7)))))) % 0.36/0.60 (assume @p9 (= tptp.replAx (forall (@list @t29 @t2) (=> (forall @t8 (=> @t7 (_ tptp.exu (lambda @t30 (_ (_ @t29 @t4) @t12))))) (exists @t24 (forall @t8 (= @t6 (exists @t30 (and @t14 (_ (_ @t29 @t12) @t4)))))))))) % 0.36/0.60 (assume @p10 (= tptp.foundationAx (forall @t28 (=> @t31 (exists @t24 (and @t23 (not (exists @t8 (and @t6 @t7))))))))) % 0.36/0.60 (assume @p11 (= tptp.wellorderingAx (forall @t28 (exists @t24 (and (forall @t40 (=> @t42 @t39)) (forall @t44 (=> (and @t7 @t14) (=> (forall @t40 (=> @t42 (= @t37 @t36))) @t43))) (forall (@list @t35 @t33) (=> (and @t42 @t38) (or (forall @t8 (=> @t37 @t41)) (forall @t8 (=> @t41 @t37))))) (forall @t40 (=> (and @t39 (exists @t8 @t37)) (exists (@list @t33 @t4) (and @t38 @t37 (not (exists @t30 (and @t34 @t36))) (forall (@list @t32) (=> (_ (_ tptp.in @t32) @t1) (or (forall @t30 (=> (_ @t13 @t32) @t34)) (_ @t5 @t32))))))))))))) % 0.36/0.60 (assume @p12 (= tptp.descrp (forall @t49 (=> @t48 (_ @t45 (_ tptp.descr @t47)))))) % 0.36/0.60 (assume @p13 (= tptp.dsetconstrI (forall @t53 (=> @t7 (=> @t46 @t52))))) % 0.36/0.60 (assume @p14 (= tptp.dsetconstrEL (forall @t53 (=> @t52 @t7)))) % 0.36/0.60 (assume @p15 (= tptp.dsetconstrER (forall @t53 (=> @t52 @t46)))) % 0.36/0.60 (assume @p16 (= tptp.exuE1 (forall @t49 (=> @t48 @t54)))) % 0.36/0.60 (assume @p17 (= tptp.prop2setE (forall (@list @t55 @t4) (=> (_ @t5 (_ tptp.prop2set @t55)) @t55)))) % 0.36/0.60 (assume @p18 (= tptp.emptysetE (forall @t8 (=> @t10 (forall @t56 @t55))))) % 0.36/0.60 (assume @p19 (= tptp.emptysetimpfalse (forall @t8 (=> @t10 false)))) % 0.36/0.60 (assume @p20 (= tptp.notinemptyset @t11)) % 0.36/0.60 (assume @p21 (= tptp.exuE3e (forall @t49 (=> @t48 (exists @t8 @t46))))) % 0.36/0.60 (assume @p22 (= tptp.setext (forall @t9 (=> (forall @t8 (=> @t7 @t6)) (=> @t21 @t3))))) % 0.36/0.60 (assume @p23 (= tptp.emptyI @t57)) % 0.36/0.60 (assume @p24 (= tptp.noeltsimpempty @t57)) % 0.36/0.60 (assume @p25 (= tptp.setbeta (forall @t53 (=> @t7 (= @t52 @t46))))) % 0.36/0.60 (assume @p26 (= tptp.nonemptyE1 (forall @t28 (=> @t58 @t31)))) % 0.36/0.60 (assume @p27 (= tptp.nonemptyI (forall @t53 (=> @t7 (=> @t46 (_ tptp.nonempty @t51)))))) % 0.36/0.60 (assume @p28 (= tptp.nonemptyI1 (forall @t28 (=> @t31 @t58)))) % 0.36/0.60 (assume @p29 (= tptp.setadjoinIL (forall @t44 (_ @t5 (_ @t17 @t12))))) % 0.36/0.60 (assume @p30 (= tptp.emptyinunitempty (_ @t25 (_ (_ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) % 0.36/0.60 (assume @p31 (= tptp.setadjoinIR (forall @t20 (=> @t14 @t19)))) % 0.36/0.60 (assume @p32 @t66) % 0.36/0.60 (assume @p33 @t101) % 0.36/0.60 (assume @p34 true) % 0.36/0.60 (step @p35 (= tptp.exu @t102) :rule refl :args (@t102)) % 0.36/0.60 (step @p36 (= tptp.prop2set @t103) :rule refl :args (@t103)) % 0.36/0.60 (step @p37 (= tptp.nonempty @t104) :rule refl :args (@t104)) % 0.36/0.60 (step @p38 :rule refl :args (@t105)) % 0.36/0.60 (step @p39 :rule refl :args (@t14)) % 0.36/0.60 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t14 @t105))) % 0.36/0.60 (step @p41 :rule symm :premises (@p40)) % 0.36/0.60 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.36/0.60 (step @p43 :rule refl :args (@t43)) % 0.36/0.60 (step @p44 :rule refl :args ((tptp.in @t12 @t18))) % 0.36/0.60 (step @p45 :rule refl :args (@t106)) % 0.36/0.60 (step @p46 :rule refl :args (@t12)) % 0.36/0.60 (step @p47 :rule cong :premises (@p46 @p45) :args (@t107)) % 0.36/0.60 (step @p48 :rule trans :premises (@p47 @p44)) % 0.36/0.60 (step @p49 :rule refl :args (@t13)) % 0.36/0.60 (step @p50 :rule ho_cong :premises (@p49 @p45)) % 0.36/0.60 (step @p51 :rule cong :premises (@p50 @p48) :args ((= (_ @t13 @t106) @t107))) % 0.36/0.60 (step @p52 :rule symm :premises (@p51)) % 0.36/0.60 (step @p53 :rule refl :args (@t19)) % 0.36/0.60 (step @p54 :rule eq_resolve :premises (@p53 @p52)) % 0.36/0.60 (step @p55 :rule refl :args (@t18)) % 0.36/0.60 (step @p56 :rule cong :premises (@p55 @p45) :args ((= @t18 @t106))) % 0.36/0.60 (step @p57 :rule symm :premises (@p56)) % 0.36/0.60 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.36/0.60 (step @p59 :rule ho_cong :premises (@p49 @p58)) % 0.36/0.60 (step @p60 :rule trans :premises (@p59 @p54)) % 0.36/0.60 (step @p61 :rule cong :premises (@p60) :args (@t108)) % 0.36/0.60 (step @p62 :rule nary_cong :premises (@p61 @p43 @p42) :args (@t109)) % 0.36/0.60 (step @p63 :rule cong :premises (@p62) :args ((forall @t20 @t109))) % 0.36/0.60 (step @p64 :rule aci_norm :args ((= (or @t108 @t110) @t109))) % 0.36/0.60 (step @p65 :rule bool-impl-elim :args (@t19 @t110)) % 0.36/0.60 (step @p66 :rule trans :premises (@p65 @p64)) % 0.36/0.60 (step @p67 :rule cong :premises (@p66) :args ((forall @t20 (=> @t19 @t110)))) % 0.36/0.60 (step @p68 :rule trans :premises (@p67 @p63)) % 0.36/0.60 (step @p69 :rule refl :args (@t14)) % 0.36/0.60 (step @p70 :rule eq-symm :args (@t12 @t4)) % 0.36/0.60 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t16)) % 0.36/0.60 (step @p72 :rule refl :args (@t19)) % 0.36/0.60 (step @p73 :rule cong :premises (@p72 @p71) :args (@t67)) % 0.36/0.60 (step @p74 :rule cong :premises (@p73) :args (@t68)) % 0.36/0.60 (step @p75 :rule trans :premises (@p74 @p68)) % 0.36/0.60 (step @p76 :rule refl 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(@t76)) % 0.36/0.60 (step @p92 :rule refl :args (tptp.noeltsimpempty)) % 0.36/0.60 (step @p93 :rule cong :premises (@p92 @p91) :args (@t77)) % 0.36/0.60 (step @p94 :rule refl :args (tptp.emptyI)) % 0.36/0.60 (step @p95 :rule cong :premises (@p94 @p93) :args (@t78)) % 0.36/0.60 (step @p96 :rule refl :args (tptp.setext)) % 0.36/0.60 (step @p97 :rule cong :premises (@p96 @p95) :args (@t79)) % 0.36/0.60 (step @p98 :rule refl :args (tptp.exuE3e)) % 0.36/0.60 (step @p99 :rule cong :premises (@p98 @p97) :args (@t80)) % 0.36/0.60 (step @p100 :rule refl :args (tptp.notinemptyset)) % 0.36/0.60 (step @p101 :rule cong :premises (@p100 @p99) :args (@t81)) % 0.36/0.60 (step @p102 :rule refl :args (tptp.emptysetimpfalse)) % 0.36/0.60 (step @p103 :rule cong :premises (@p102 @p101) :args (@t82)) % 0.36/0.60 (step @p104 :rule refl :args (tptp.emptysetE)) % 0.36/0.60 (step @p105 :rule cong :premises (@p104 @p103) :args (@t83)) % 0.36/0.60 (step @p106 :rule refl :args (tptp.prop2setE)) % 0.36/0.60 (step @p107 :rule cong :premises (@p106 @p105) :args (@t84)) % 0.36/0.60 (step @p108 :rule refl :args (tptp.exuE1)) % 0.36/0.60 (step @p109 :rule cong :premises (@p108 @p107) :args (@t85)) % 0.36/0.60 (step @p110 :rule refl :args (tptp.dsetconstrER)) % 0.36/0.60 (step @p111 :rule cong :premises (@p110 @p109) :args (@t86)) % 0.36/0.60 (step @p112 :rule refl :args (tptp.dsetconstrEL)) % 0.36/0.60 (step @p113 :rule cong :premises (@p112 @p111) :args (@t87)) % 0.36/0.60 (step @p114 :rule refl :args (tptp.dsetconstrI)) % 0.36/0.60 (step @p115 :rule cong :premises (@p114 @p113) :args (@t88)) % 0.36/0.60 (step @p116 :rule refl :args (tptp.descrp)) % 0.36/0.60 (step @p117 :rule cong :premises (@p116 @p115) :args (@t89)) % 0.36/0.60 (step @p118 :rule refl :args (tptp.wellorderingAx)) % 0.36/0.60 (step @p119 :rule cong :premises (@p118 @p117) :args (@t90)) % 0.36/0.60 (step @p120 :rule refl :args (tptp.foundationAx)) % 0.36/0.60 (step @p121 :rule cong :premises (@p120 @p119) :args (@t91)) % 0.36/0.60 (step @p122 :rule refl :args (tptp.replAx)) % 0.36/0.60 (step @p123 :rule cong :premises (@p122 @p121) :args (@t92)) % 0.36/0.60 (step @p124 :rule refl :args (tptp.omegaIndAx)) % 0.36/0.60 (step @p125 :rule cong :premises (@p124 @p123) :args (@t93)) % 0.36/0.60 (step @p126 :rule refl :args (tptp.omegaSAx)) % 0.36/0.60 (step @p127 :rule cong :premises (@p126 @p125) :args (@t94)) % 0.36/0.60 (step @p128 :rule refl :args (tptp.omega0Ax)) % 0.36/0.60 (step @p129 :rule cong :premises (@p128 @p127) :args (@t95)) % 0.36/0.60 (step @p130 :rule refl :args (tptp.setunionAx)) % 0.36/0.60 (step @p131 :rule cong :premises (@p130 @p129) :args (@t96)) % 0.36/0.60 (step @p132 :rule refl :args (tptp.powersetAx)) % 0.36/0.60 (step @p133 :rule cong :premises (@p132 @p131) :args (@t97)) % 0.36/0.60 (step @p134 :rule refl :args (tptp.setadjoinAx)) % 0.36/0.60 (step @p135 :rule cong :premises (@p134 @p133) :args (@t98)) % 0.36/0.60 (step @p136 :rule refl :args (tptp.emptysetAx)) % 0.36/0.60 (step @p137 :rule cong :premises (@p136 @p135) :args (@t99)) % 0.36/0.60 (step @p138 :rule refl :args (tptp.setextAx)) % 0.36/0.60 (step @p139 :rule cong :premises (@p138 @p137) :args (@t100)) % 0.36/0.60 (step @p140 :rule cong :premises (@p139) :args (@t101)) % 0.36/0.60 (step @p141 :rule eq_resolve :premises (@p33 @p140)) % 0.36/0.60 (step @p142 :rule not_implies_elim2 :premises (@p141)) % 0.36/0.60 (step @p143 :rule not_implies_elim2 :premises (@p142)) % 0.36/0.60 (step @p144 :rule not_implies_elim2 :premises (@p143)) % 0.36/0.60 (step @p145 :rule not_implies_elim2 :premises (@p144)) % 0.36/0.60 (step @p146 :rule not_implies_elim2 :premises (@p145)) % 0.36/0.60 (step @p147 :rule not_implies_elim2 :premises (@p146)) % 0.36/0.60 (step @p148 :rule not_implies_elim2 :premises (@p147)) % 0.36/0.60 (step @p149 :rule not_implies_elim2 :premises (@p148)) % 0.36/0.60 (step @p150 :rule not_implies_elim2 :premises (@p149)) % 0.36/0.60 (step @p151 :rule not_implies_elim2 :premises (@p150)) % 0.36/0.60 (step @p152 :rule not_implies_elim2 :premises (@p151)) % 0.36/0.60 (step @p153 :rule not_implies_elim2 :premises (@p152)) % 0.36/0.60 (step @p154 :rule not_implies_elim2 :premises (@p153)) % 0.36/0.60 (step @p155 :rule not_implies_elim2 :premises (@p154)) % 0.36/0.60 (step @p156 :rule not_implies_elim2 :premises (@p155)) % 0.36/0.60 (step @p157 :rule not_implies_elim2 :premises (@p156)) % 0.36/0.60 (step @p158 :rule not_implies_elim2 :premises (@p157)) % 0.36/0.60 (step @p159 :rule not_implies_elim2 :premises (@p158)) % 0.36/0.60 (step @p160 :rule not_implies_elim2 :premises (@p159)) % 0.36/0.60 (step @p161 :rule not_implies_elim2 :premises (@p160)) % 0.36/0.60 (step @p162 :rule not_implies_elim2 :premises (@p161)) % 0.36/0.60 (step @p163 :rule not_implies_elim2 :premises (@p162)) % 0.36/0.60 (step @p164 :rule not_implies_elim2 :premises (@p163)) % 0.36/0.60 (step @p165 :rule not_implies_elim2 :premises (@p164)) % 0.36/0.60 (step @p166 :rule not_implies_elim2 :premises (@p165)) % 0.36/0.60 (step @p167 :rule not_implies_elim2 :premises (@p166)) % 0.36/0.60 (step @p168 :rule not_implies_elim2 :premises (@p167)) % 0.36/0.60 (step @p169 :rule not_implies_elim2 :premises (@p168)) % 0.36/0.60 (step @p170 :rule not_implies_elim2 :premises (@p169)) % 0.36/0.60 (step @p171 :rule not_implies_elim2 :premises (@p170)) % 0.36/0.60 (step @p172 :rule not_implies_elim2 :premises (@p171)) % 0.36/0.60 (step @p173 :rule not_implies_elim2 :premises (@p172)) % 0.36/0.60 (step @p174 :rule not_implies_elim1 :premises (@p172)) % 0.36/0.60 (step @p175 :rule cnf_equiv_pos1 :args ((= tptp.setadjoinE @t111))) % 0.36/0.60 (step @p176 :rule chain_resolution :premises (@p175 @p174 @p173) :args ((@list false true) (@list tptp.setadjoinE @t111))) % 0.36/0.60 (step @p177 :rule refl :args (@t105)) % 0.36/0.60 (step @p178 :rule nary_cong :premises (@p61 @p43 @p177) :args (@t112)) % 0.36/0.60 (step @p179 :rule cong :premises (@p178) :args ((forall @t20 @t112))) % 0.36/0.60 (step @p180 :rule 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(step @p195 :rule aci_norm :args ((= @t118 @t117))) % 0.36/0.60 (step @p196 :rule trans :premises (@p195 @p194)) % 0.36/0.60 (step @p197 :rule quant-var-elim-eq :args ((= (forall @t56 (or (not (= @t55 false)) @t121 @t120 @t55)) @t118))) % 0.36/0.60 (step @p198 :rule refl :args (@t55)) % 0.36/0.60 (step @p199 :rule refl :args (@t120)) % 0.36/0.60 (step @p200 :rule refl :args (@t121)) % 0.36/0.60 (step @p201 :rule bool-eq-false :args (@t55)) % 0.36/0.60 (step @p202 :rule symm :premises (@p201)) % 0.36/0.60 (step @p203 :rule cong :premises (@p202) :args ((not @t119))) % 0.36/0.60 (step @p204 :rule bool-double-not-elim :args (@t55)) % 0.36/0.60 (step @p205 :rule symm :premises (@p204)) % 0.36/0.60 (step @p206 :rule trans :premises (@p205 @p203)) % 0.36/0.60 (step @p207 :rule nary_cong :premises (@p206 @p200 @p199 @p198) :args (@t122)) % 0.36/0.60 (step @p208 :rule aci_norm :args ((= @t123 @t122))) % 0.36/0.60 (step @p209 :rule trans :premises (@p208 @p207)) % 0.36/0.60 (step @p210 :rule cong :premises (@p209) :args ((forall @t56 @t123))) % 0.36/0.60 (step @p211 :rule trans :premises (@p210 @p197)) % 0.36/0.60 (step @p212 :rule trans :premises (@p211 @p196)) % 0.36/0.60 (step @p213 :rule refl :args (@t119)) % 0.36/0.60 (step @p214 :rule nary_cong :premises (@p42 @p213) :args (@t124)) % 0.36/0.60 (step @p215 :rule nary_cong :premises (@p200 @p214 @p198) :args (@t125)) % 0.36/0.60 (step @p216 :rule cong :premises (@p215) :args ((forall @t56 @t125))) % 0.36/0.60 (step @p217 :rule trans :premises (@p216 @p212)) % 0.36/0.60 (step @p218 :rule aci_norm :args ((= (or @t121 (or @t124 @t55)) @t125))) % 0.36/0.60 (step @p219 :rule bool-implies-de-morgan :args (@t14 @t55)) % 0.36/0.60 (step @p220 :rule nary_cong :premises (@p219 @p198) :args ((or (not @t59) @t55))) % 0.36/0.60 (step @p221 :rule bool-impl-elim :args (@t59 @t55)) % 0.36/0.60 (step @p222 :rule trans :premises (@p221 @p220)) % 0.36/0.60 (step @p223 :rule bool-implies-de-morgan :args (@t43 @t55)) % 0.36/0.60 (step @p224 :rule nary_cong :premises (@p223 @p222) :args ((or (not @t126) @t60))) % 0.36/0.60 (step @p225 :rule trans :premises (@p224 @p218)) % 0.36/0.60 (step @p226 :rule bool-impl-elim :args (@t126 @t60)) % 0.36/0.60 (step @p227 :rule trans :premises (@p226 @p225)) % 0.36/0.60 (step @p228 :rule cong :premises (@p227) :args ((forall @t56 (=> @t126 @t60)))) % 0.36/0.60 (step @p229 :rule trans :premises (@p228 @p217)) % 0.36/0.60 (step @p230 :rule refl :args (@t60)) % 0.36/0.60 (step @p231 :rule refl :args (@t55)) % 0.36/0.60 (step @p232 :rule cong :premises (@p70 @p231) :args (@t61)) % 0.36/0.60 (step @p233 :rule cong :premises (@p232 @p230) :args (@t62)) % 0.36/0.60 (step @p234 :rule cong :premises (@p233) :args (@t63)) % 0.36/0.60 (step @p235 :rule trans :premises (@p234 @p229)) % 0.36/0.60 (step @p236 :rule cong :premises (@p72 @p235) :args (@t64)) % 0.36/0.60 (step @p237 :rule cong :premises (@p236) :args (@t65)) % 0.36/0.60 (step @p238 :rule trans :premises (@p237 @p184)) % 0.36/0.60 (step @p239 :rule cong :premises (@p76 @p238) :args (@t66)) % 0.36/0.60 (step @p240 :rule eq_resolve :premises (@p32 @p239)) % 0.36/0.60 (step @p241 false :rule contra :premises (@p240 @p176)) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.60 % cvc5 exiting %------------------------------------------------------------------------------