%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU567^1 : 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 : n001.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 08:52:13 AM UTC 2026 % Result : Theorem 0.40s 0.67s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU567^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n001.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 17:42:50 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.55 %----Proving TH0 % 0.40/0.67 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.67 % SZS status Theorem % 0.40/0.67 % SZS output start Proof % 0.40/0.67 ( % 0.40/0.67 (declare-sort $$unsorted 0) % 0.40/0.67 (declare-const tptp.emptyset $$unsorted) % 0.40/0.67 (declare-const tptp.notsubsetI Bool) % 0.40/0.67 (declare-const tptp.emptysetsubset Bool) % 0.40/0.67 (declare-const tptp.subsetI2 Bool) % 0.40/0.67 (declare-const tptp.powerset__Cong Bool) % 0.40/0.67 (declare-const tptp.setadjoin__Cong Bool) % 0.40/0.67 (declare-const tptp.emptyset__Cong Bool) % 0.40/0.67 (declare-const tptp.exu__Cong Bool) % 0.40/0.67 (declare-const tptp.in__Cong Bool) % 0.40/0.67 (declare-const tptp.inCongP Bool) % 0.40/0.67 (declare-const tptp.subsetE2 Bool) % 0.40/0.67 (declare-const tptp.exuI3 Bool) % 0.40/0.67 (declare-const tptp.subsetE Bool) % 0.40/0.67 (declare-const tptp.exuI1 Bool) % 0.40/0.67 (declare-const tptp.set2prop (-> $$unsorted Bool)) % 0.40/0.67 (declare-const tptp.subsetI1 Bool) % 0.40/0.67 (declare-const tptp.quantDeMorgan3 Bool) % 0.40/0.67 (declare-const tptp.quantDeMorgan2 Bool) % 0.40/0.67 (declare-const tptp.dsetconstr__Cong Bool) % 0.40/0.67 (declare-const tptp.quantDeMorgan1 Bool) % 0.40/0.67 (declare-const tptp.vacuousDall Bool) % 0.40/0.67 (declare-const tptp.emptyE1 Bool) % 0.40/0.67 (declare-const tptp.setunion__Cong Bool) % 0.40/0.67 (declare-const tptp.upairsetIR Bool) % 0.40/0.67 (declare-const tptp.emptysetE Bool) % 0.40/0.67 (declare-const tptp.omega__Cong Bool) % 0.40/0.67 (declare-const tptp.setadjoinIL Bool) % 0.40/0.67 (declare-const tptp.prop2setE Bool) % 0.40/0.67 (declare-const tptp.prop2set (-> Bool $$unsorted)) % 0.40/0.67 (declare-const tptp.dsetconstrI Bool) % 0.40/0.67 (declare-const tptp.setext Bool) % 0.40/0.67 (declare-const tptp.nonemptyImpWitness Bool) % 0.40/0.67 (declare-const tptp.descr (-> (-> $$unsorted Bool) $$unsorted)) % 0.40/0.67 (declare-const tptp.wellorderingAx Bool) % 0.40/0.67 (declare-const tptp.replAx Bool) % 0.40/0.67 (declare-const tptp.upairsetE Bool) % 0.40/0.67 (declare-const tptp.dsetconstrEL Bool) % 0.40/0.67 (declare-const tptp.prop2setI Bool) % 0.40/0.67 (declare-const tptp.emptyinPowerset Bool) % 0.40/0.67 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.67 (declare-const tptp.setextAx Bool) % 0.40/0.67 (declare-const tptp.setadjoinOr Bool) % 0.40/0.67 (declare-const tptp.exuE3u Bool) % 0.40/0.67 (declare-const tptp.uniqinunit Bool) % 0.40/0.67 (declare-const tptp.foundationAx Bool) % 0.40/0.67 (declare-const tptp.emptysetimpfalse Bool) % 0.40/0.67 (declare-const tptp.notinemptyset Bool) % 0.40/0.68 (declare-const tptp.setadjoinIR Bool) % 0.40/0.68 (declare-const tptp.exuE2 Bool) % 0.40/0.68 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.68 (declare-const tptp.notdallE Bool) % 0.40/0.68 (declare-const tptp.dsetconstrER Bool) % 0.40/0.68 (declare-const tptp.eqimpsubset1 Bool) % 0.40/0.68 (declare-const tptp.emptyInPowerset Bool) % 0.40/0.68 (declare-const tptp.exuEu Bool) % 0.40/0.68 (declare-const tptp.setadjoinAx Bool) % 0.40/0.68 (declare-const tptp.nonemptyE1 Bool) % 0.40/0.68 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.40/0.68 (declare-const tptp.eqimpsubset2 Bool) % 0.40/0.68 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.40/0.68 (declare-const tptp.powersetAx Bool) % 0.40/0.68 (declare-const tptp.prop2set2propI Bool) % 0.40/0.68 (declare-const tptp.powersetE Bool) % 0.40/0.68 (declare-const tptp.omegaSAx Bool) % 0.40/0.68 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.68 (declare-const tptp.descrp Bool) % 0.40/0.68 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.40/0.68 (declare-const tptp.omega0Ax Bool) % 0.40/0.68 (declare-const tptp.setoftrueEq Bool) % 0.40/0.68 (declare-const tptp.setunionAx Bool) % 0.40/0.68 (declare-const tptp.omega $$unsorted) % 0.40/0.68 (declare-const tptp.omegaIndAx Bool) % 0.40/0.68 (declare-const tptp.quantDeMorgan4 Bool) % 0.40/0.68 (declare-const tptp.powersetI Bool) % 0.40/0.68 (declare-const tptp.exuE3e Bool) % 0.40/0.68 (declare-const tptp.emptyI Bool) % 0.40/0.68 (declare-const tptp.noeltsimpempty Bool) % 0.40/0.68 (declare-const tptp.eqinunit Bool) % 0.40/0.68 (declare-const tptp.upairsetIL Bool) % 0.40/0.68 (declare-const tptp.nonemptyI Bool) % 0.40/0.68 (declare-const tptp.emptysetAx Bool) % 0.40/0.68 (declare-const tptp.nonemptyI1 Bool) % 0.40/0.68 (declare-const tptp.descr__Cong Bool) % 0.40/0.68 (declare-const tptp.emptyinunitempty Bool) % 0.40/0.68 (declare-const tptp.setadjoinE Bool) % 0.40/0.68 (declare-const tptp.notdexE Bool) % 0.40/0.68 (declare-const tptp.setunionI Bool) % 0.40/0.68 (declare-const tptp.exuE1 Bool) % 0.40/0.68 (declare-const tptp.setunionE Bool) % 0.40/0.68 (declare-const tptp.exuI2 Bool) % 0.40/0.68 (declare-const tptp.subPowSU Bool) % 0.40/0.68 (declare-const tptp.notinsingleton Bool) % 0.40/0.68 (declare-const tptp.setbeta Bool) % 0.40/0.68 (declare-const tptp.singletonsswitch Bool) % 0.40/0.68 (define tptp.exu () (let ((_let_1 (@var "Xy" $$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)))))))))) % 0.40/0.68 (define tptp.nonempty () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (not (= _let_1 tptp.emptyset))))) % 0.40/0.68 (define @t1 () (@var "B" $$unsorted)) % 0.40/0.68 (define @t2 () (@var "A" $$unsorted)) % 0.40/0.68 (define @t3 () (= @t2 @t1)) % 0.40/0.68 (define @t4 () (@var "Xx" $$unsorted)) % 0.40/0.68 (define @t5 () (_ tptp.in @t4)) % 0.40/0.68 (define @t6 () (_ @t5 @t1)) % 0.40/0.68 (define @t7 () (_ @t5 @t2)) % 0.40/0.68 (define @t8 () (@list @t4)) % 0.40/0.68 (define @t9 () (@list @t2 @t1)) % 0.40/0.68 (define @t10 () (_ @t5 tptp.emptyset)) % 0.40/0.68 (define @t11 () (forall @t8 (not @t10))) % 0.40/0.68 (define @t12 () (@var "Xy" $$unsorted)) % 0.40/0.68 (define @t13 () (_ tptp.in @t12)) % 0.40/0.68 (define @t14 () (_ @t13 @t2)) % 0.40/0.68 (define @t15 () (= @t12 @t4)) % 0.40/0.68 (define @t16 () (or @t15 @t14)) % 0.40/0.68 (define @t17 () (_ tptp.setadjoin @t4)) % 0.40/0.68 (define @t18 () (_ @t13 (_ @t17 @t2))) % 0.40/0.68 (define @t19 () (@list @t4 @t2 @t12)) % 0.40/0.68 (define @t20 () (=> @t6 @t7)) % 0.40/0.68 (define @t21 () (forall @t8 @t20)) % 0.40/0.68 (define @t22 () (_ tptp.powerset @t2)) % 0.40/0.68 (define @t23 () (_ tptp.in @t1)) % 0.40/0.68 (define @t24 () (_ @t23 @t22)) % 0.40/0.68 (define @t25 () (_ @t23 @t2)) % 0.40/0.68 (define @t26 () (@list @t1)) % 0.40/0.68 (define @t27 () (_ tptp.setunion @t2)) % 0.40/0.68 (define @t28 () (_ @t5 @t27)) % 0.40/0.68 (define @t29 () (@list @t2 @t4)) % 0.40/0.68 (define @t30 () (_ tptp.in tptp.emptyset)) % 0.40/0.68 (define @t31 () (_ tptp.in (_ @t17 @t4))) % 0.40/0.68 (define @t32 () (_ @t5 tptp.omega)) % 0.40/0.68 (define @t33 () (@list @t2)) % 0.40/0.68 (define @t34 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.40/0.68 (define @t35 () (@list @t12)) % 0.40/0.68 (define @t36 () (exists @t8 @t7)) % 0.40/0.68 (define @t37 () (@var "E" $$unsorted)) % 0.40/0.68 (define @t38 () (@var "D" $$unsorted)) % 0.40/0.68 (define @t39 () (_ @t13 @t38)) % 0.40/0.68 (define @t40 () (@var "C" $$unsorted)) % 0.40/0.68 (define @t41 () (_ @t13 @t40)) % 0.40/0.68 (define @t42 () (_ @t5 @t40)) % 0.40/0.68 (define @t43 () (_ (_ tptp.in @t38) @t1)) % 0.40/0.68 (define @t44 () (forall @t8 (=> @t42 @t7))) % 0.40/0.68 (define @t45 () (@list @t40)) % 0.40/0.68 (define @t46 () (_ @t5 @t38)) % 0.40/0.68 (define @t47 () (_ (_ tptp.in @t40) @t1)) % 0.40/0.68 (define @t48 () (= @t4 @t12)) % 0.40/0.68 (define @t49 () (@list @t4 @t12)) % 0.40/0.68 (define @t50 () (@var "Xphi" (-> $$unsorted Bool))) % 0.40/0.68 (define @t51 () (_ @t50 @t4)) % 0.40/0.68 (define @t52 () (lambda @t8 @t51)) % 0.40/0.68 (define @t53 () (_ tptp.descr @t52)) % 0.40/0.68 (define @t54 () (_ tptp.exu @t52)) % 0.40/0.68 (define @t55 () (@list @t50)) % 0.40/0.68 (define @t56 () (_ @t50 @t12)) % 0.40/0.68 (define @t57 () (_ tptp.dsetconstr @t2)) % 0.40/0.68 (define @t58 () (_ @t57 (lambda @t35 @t56))) % 0.40/0.68 (define @t59 () (_ @t5 @t58)) % 0.40/0.68 (define @t60 () (@list @t2 @t50 @t4)) % 0.40/0.68 (define @t61 () (=> @t56 @t48)) % 0.40/0.68 (define @t62 () (exists @t8 (and @t51 (forall @t35 @t61)))) % 0.40/0.68 (define @t63 () (@var "Xphi" Bool)) % 0.40/0.68 (define @t64 () (_ tptp.prop2set @t63)) % 0.40/0.68 (define @t65 () (@list @t63)) % 0.40/0.68 (define @t66 () (exists @t8 @t51)) % 0.40/0.68 (define @t67 () (=> @t7 @t6)) % 0.40/0.68 (define @t68 () (forall @t8 @t67)) % 0.40/0.68 (define @t69 () (not @t7)) % 0.40/0.68 (define @t70 () (forall @t33 (=> (forall @t8 @t69) (= @t2 tptp.emptyset)))) % 0.40/0.68 (define @t71 () (_ tptp.nonempty @t2)) % 0.40/0.68 (define @t72 () (forall @t33 (_ @t30 @t22))) % 0.40/0.68 (define @t73 () (@list @t2 @t1 @t4)) % 0.40/0.68 (define @t74 () (exists @t8 (forall @t35 (= @t56 @t15)))) % 0.40/0.68 (define @t75 () (_ tptp.setadjoin @t12)) % 0.40/0.68 (define @t76 () (_ @t75 tptp.emptyset)) % 0.40/0.68 (define @t77 () (_ @t5 @t76)) % 0.40/0.68 (define @t78 () (_ @t13 (_ @t17 tptp.emptyset))) % 0.40/0.68 (define @t79 () (@var "Xz" $$unsorted)) % 0.40/0.68 (define @t80 () (_ @t17 @t76)) % 0.40/0.68 (define @t81 () (_ @t57 @t52)) % 0.40/0.68 (define @t82 () (exists @t8 (and @t7 @t51))) % 0.40/0.68 (define @t83 () (@list @t2 @t50)) % 0.40/0.68 (define @t84 () (not @t51)) % 0.40/0.68 (define @t85 () (exists @t8 (and @t7 @t84))) % 0.40/0.68 (define @t86 () (not (forall @t8 (=> @t7 @t51)))) % 0.40/0.68 (define @t87 () (forall @t83 (=> @t86 @t85))) % 0.40/0.68 (define @t88 () (not @t82)) % 0.40/0.68 (define @t89 () (forall @t8 (=> @t7 @t84))) % 0.40/0.68 (define @t90 () (forall @t83 (=> @t88 @t89))) % 0.40/0.68 (define @t91 () (forall @t49 (=> @t51 @t61))) % 0.40/0.68 (define @t92 () (_ @t13 @t1)) % 0.40/0.68 (define @t93 () (forall @t55 (=> @t54 @t91))) % 0.40/0.68 (define @t94 () (@var "Xpsi" (-> $$unsorted Bool))) % 0.40/0.68 (define @t95 () (lambda @t8 (_ @t94 @t4))) % 0.40/0.68 (define @t96 () (_ tptp.exu @t95)) % 0.40/0.68 (define @t97 () (=> @t48 (= @t51 (_ @t94 @t12)))) % 0.40/0.68 (define @t98 () (forall @t49 @t97)) % 0.40/0.68 (define @t99 () (@list @t50 @t94)) % 0.40/0.68 (define @t100 () (@var "Xu" $$unsorted)) % 0.40/0.68 (define @t101 () (_ (_ tptp.subset @t2) @t1)) % 0.40/0.68 (define @t102 () (forall @t9 (=> @t68 @t101))) % 0.40/0.68 (define @t103 () (_ (_ tptp.subset @t1) @t2)) % 0.40/0.68 (define @t104 () (forall @t9 (=> @t3 @t103))) % 0.40/0.68 (define @t105 () (= tptp.eqimpsubset2 @t104)) % 0.40/0.68 (define @t106 () (not @t6)) % 0.40/0.68 (define @t107 () (not @t101)) % 0.40/0.68 (define @t108 () (not @t3)) % 0.40/0.68 (define @t109 () (forall @t9 (=> @t107 @t108))) % 0.40/0.68 (define @t110 () (=> tptp.notsubsetI @t109)) % 0.40/0.68 (define @t111 () (=> tptp.subsetE2 @t110)) % 0.40/0.68 (define @t112 () (=> tptp.subsetE @t111)) % 0.40/0.68 (define @t113 () (=> tptp.emptysetsubset @t112)) % 0.40/0.68 (define @t114 () (=> tptp.subsetI2 @t113)) % 0.40/0.68 (define @t115 () (=> tptp.eqimpsubset1 @t114)) % 0.40/0.68 (define @t116 () (=> tptp.eqimpsubset2 @t115)) % 0.40/0.68 (define @t117 () (=> tptp.subsetI1 @t116)) % 0.40/0.68 (define @t118 () (=> tptp.dsetconstr__Cong @t117)) % 0.40/0.68 (define @t119 () (=> tptp.descr__Cong @t118)) % 0.40/0.68 (define @t120 () (=> tptp.exuEu @t119)) % 0.40/0.68 (define @t121 () (=> tptp.omega__Cong @t120)) % 0.40/0.68 (define @t122 () (=> tptp.setunion__Cong @t121)) % 0.40/0.68 (define @t123 () (=> tptp.powerset__Cong @t122)) % 0.40/0.68 (define @t124 () (=> tptp.setadjoin__Cong @t123)) % 0.40/0.68 (define @t125 () (=> tptp.emptyset__Cong @t124)) % 0.40/0.68 (define @t126 () (=> tptp.exu__Cong @t125)) % 0.40/0.68 (define @t127 () (=> tptp.exuE3u @t126)) % 0.40/0.68 (define @t128 () (=> tptp.in__Cong @t127)) % 0.40/0.68 (define @t129 () (=> tptp.inCongP @t128)) % 0.40/0.68 (define @t130 () (=> tptp.exuI2 @t129)) % 0.40/0.68 (define @t131 () (=> tptp.exuI3 @t130)) % 0.40/0.68 (define @t132 () (=> tptp.exuI1 @t131)) % 0.40/0.68 (define @t133 () (=> tptp.notdallE @t132)) % 0.40/0.68 (define @t134 () (=> tptp.notdexE @t133)) % 0.40/0.68 (define @t135 () (=> tptp.prop2set2propI @t134)) % 0.40/0.68 (define @t136 () (=> tptp.prop2setI @t135)) % 0.40/0.68 (define @t137 () (=> tptp.quantDeMorgan4 @t136)) % 0.40/0.68 (define @t138 () (=> tptp.quantDeMorgan3 @t137)) % 0.40/0.68 (define @t139 () (=> tptp.quantDeMorgan2 @t138)) % 0.40/0.68 (define @t140 () (=> tptp.quantDeMorgan1 @t139)) % 0.40/0.68 (define @t141 () (=> tptp.vacuousDall @t140)) % 0.40/0.68 (define @t142 () (=> tptp.emptyE1 @t141)) % 0.40/0.68 (define @t143 () (=> tptp.upairsetIR @t142)) % 0.40/0.68 (define @t144 () (=> tptp.upairsetIL @t143)) % 0.40/0.68 (define @t145 () (=> tptp.upairsetE @t144)) % 0.40/0.68 (define @t146 () (=> tptp.singletonsswitch @t145)) % 0.40/0.68 (define @t147 () (=> tptp.eqinunit @t146)) % 0.40/0.68 (define @t148 () (=> tptp.notinsingleton @t147)) % 0.40/0.68 (define @t149 () (=> tptp.uniqinunit @t148)) % 0.40/0.68 (define @t150 () (=> tptp.nonemptyImpWitness @t149)) % 0.40/0.68 (define @t151 () (=> tptp.exuE2 @t150)) % 0.40/0.68 (define @t152 () (=> tptp.subPowSU @t151)) % 0.40/0.68 (define @t153 () (=> tptp.setunionE @t152)) % 0.40/0.68 (define @t154 () (=> tptp.setunionI @t153)) % 0.40/0.68 (define @t155 () (=> tptp.powersetE @t154)) % 0.40/0.68 (define @t156 () (=> tptp.emptyInPowerset @t155)) % 0.40/0.68 (define @t157 () (=> tptp.emptyinPowerset @t156)) % 0.40/0.68 (define @t158 () (=> tptp.powersetI @t157)) % 0.40/0.68 (define @t159 () (=> tptp.setoftrueEq @t158)) % 0.40/0.68 (define @t160 () (=> tptp.setadjoinOr @t159)) % 0.40/0.68 (define @t161 () (=> tptp.setadjoinE @t160)) % 0.40/0.68 (define @t162 () (=> tptp.setadjoinIR @t161)) % 0.40/0.68 (define @t163 () (=> tptp.emptyinunitempty @t162)) % 0.40/0.68 (define @t164 () (=> tptp.setadjoinIL @t163)) % 0.40/0.68 (define @t165 () (=> tptp.nonemptyI1 @t164)) % 0.40/0.68 (define @t166 () (=> tptp.nonemptyI @t165)) % 0.40/0.68 (define @t167 () (=> tptp.nonemptyE1 @t166)) % 0.40/0.68 (define @t168 () (=> tptp.setbeta @t167)) % 0.40/0.68 (define @t169 () (=> tptp.noeltsimpempty @t168)) % 0.40/0.68 (define @t170 () (=> tptp.emptyI @t169)) % 0.40/0.68 (define @t171 () (=> tptp.setext @t170)) % 0.40/0.68 (define @t172 () (=> tptp.exuE3e @t171)) % 0.40/0.68 (define @t173 () (=> tptp.notinemptyset @t172)) % 0.40/0.68 (define @t174 () (=> tptp.emptysetimpfalse @t173)) % 0.40/0.68 (define @t175 () (=> tptp.emptysetE @t174)) % 0.40/0.68 (define @t176 () (=> tptp.prop2setE @t175)) % 0.40/0.68 (define @t177 () (=> tptp.exuE1 @t176)) % 0.40/0.68 (define @t178 () (=> tptp.dsetconstrER @t177)) % 0.40/0.68 (define @t179 () (=> tptp.dsetconstrEL @t178)) % 0.40/0.68 (define @t180 () (=> tptp.dsetconstrI @t179)) % 0.40/0.68 (define @t181 () (=> tptp.descrp @t180)) % 0.40/0.68 (define @t182 () (=> tptp.wellorderingAx @t181)) % 0.40/0.68 (define @t183 () (=> tptp.foundationAx @t182)) % 0.40/0.68 (define @t184 () (=> tptp.replAx @t183)) % 0.40/0.68 (define @t185 () (=> tptp.omegaIndAx @t184)) % 0.40/0.68 (define @t186 () (=> tptp.omegaSAx @t185)) % 0.40/0.68 (define @t187 () (=> tptp.omega0Ax @t186)) % 0.40/0.68 (define @t188 () (=> tptp.setunionAx @t187)) % 0.40/0.68 (define @t189 () (=> tptp.powersetAx @t188)) % 0.40/0.68 (define @t190 () (=> tptp.setadjoinAx @t189)) % 0.40/0.68 (define @t191 () (=> tptp.emptysetAx @t190)) % 0.40/0.68 (define @t192 () (=> tptp.setextAx @t191)) % 0.40/0.68 (define @t193 () (not @t192)) % 0.40/0.68 (define @t194 () (lambda @t55 @t62)) % 0.40/0.68 (define @t195 () (lambda @t8 (not (= @t4 tptp.emptyset)))) % 0.40/0.68 (define @t196 () (tptp.subset @t1 @t1)) % 0.40/0.68 (define @t197 () (not (= @t1 @t1))) % 0.40/0.68 (define @t198 () (or @t196 @t197)) % 0.40/0.68 (define @t199 () (tptp.subset @t2 @t1)) % 0.40/0.68 (define @t200 () (or @t108 @t199 @t108)) % 0.40/0.68 (define @t201 () (or @t199 @t108)) % 0.40/0.68 (define @t202 () (forall @t33 @t201)) % 0.40/0.68 (define @t203 () (forall @t26 @t202)) % 0.40/0.68 (define @t204 () (@list @t1 @t2)) % 0.40/0.68 (define @t205 () (forall @t204 @t201)) % 0.40/0.68 (define @t206 () (or @t101 @t108)) % 0.40/0.68 (define @t207 () (or @t197 @t196)) % 0.40/0.68 (define @t208 () (tptp.subset @t1 @t2)) % 0.40/0.68 (define @t209 () (or @t108 @t108 @t208)) % 0.40/0.68 (define @t210 () (or @t108 @t208)) % 0.40/0.68 (define @t211 () (forall @t33 @t210)) % 0.40/0.68 (define @t212 () (forall @t26 @t211)) % 0.40/0.68 (define @t213 () (forall @t204 @t210)) % 0.40/0.68 (define @t214 () (or @t108 @t103)) % 0.40/0.68 (assume @p1 (= tptp.setextAx (forall @t9 (=> (forall @t8 (= @t7 @t6)) @t3)))) % 0.40/0.68 (assume @p2 (= tptp.emptysetAx @t11)) % 0.40/0.68 (assume @p3 (= tptp.setadjoinAx (forall @t19 (= @t18 @t16)))) % 0.40/0.68 (assume @p4 (= tptp.powersetAx (forall @t9 (= @t24 @t21)))) % 0.40/0.68 (assume @p5 (= tptp.setunionAx (forall @t29 (= @t28 (exists @t26 (and @t6 @t25)))))) % 0.40/0.68 (assume @p6 (= tptp.omega0Ax (_ @t30 tptp.omega))) % 0.40/0.68 (assume @p7 (= tptp.omegaSAx (forall @t8 (=> @t32 (_ @t31 tptp.omega))))) % 0.40/0.68 (assume @p8 (= tptp.omegaIndAx (forall @t33 (=> (and (_ @t30 @t2) (forall @t8 (=> (and @t32 @t7) (_ @t31 @t2)))) (forall @t8 (=> @t32 @t7)))))) % 0.40/0.68 (assume @p9 (= tptp.replAx (forall (@list @t34 @t2) (=> (forall @t8 (=> @t7 (_ tptp.exu (lambda @t35 (_ (_ @t34 @t4) @t12))))) (exists @t26 (forall @t8 (= @t6 (exists @t35 (and @t14 (_ (_ @t34 @t12) @t4)))))))))) % 0.40/0.68 (assume @p10 (= tptp.foundationAx (forall @t33 (=> @t36 (exists @t26 (and @t25 (not (exists @t8 (and @t6 @t7))))))))) % 0.40/0.68 (assume @p11 (= tptp.wellorderingAx (forall @t33 (exists @t26 (and (forall @t45 (=> @t47 @t44)) (forall @t49 (=> (and @t7 @t14) (=> (forall @t45 (=> @t47 (= @t42 @t41))) @t48))) (forall (@list @t40 @t38) (=> (and @t47 @t43) (or (forall @t8 (=> @t42 @t46)) (forall @t8 (=> @t46 @t42))))) (forall @t45 (=> (and @t44 (exists @t8 @t42)) (exists (@list @t38 @t4) (and @t43 @t42 (not (exists @t35 (and @t39 @t41))) (forall (@list @t37) (=> (_ (_ tptp.in @t37) @t1) (or (forall @t35 (=> (_ @t13 @t37) @t39)) (_ @t5 @t37))))))))))))) % 0.40/0.68 (assume @p12 (= tptp.descrp (forall @t55 (=> @t54 (_ @t50 @t53))))) % 0.40/0.68 (assume @p13 (= tptp.dsetconstrI (forall @t60 (=> @t7 (=> @t51 @t59))))) % 0.40/0.68 (assume @p14 (= tptp.dsetconstrEL (forall @t60 (=> @t59 @t7)))) % 0.40/0.68 (assume @p15 (= tptp.dsetconstrER (forall @t60 (=> @t59 @t51)))) % 0.40/0.68 (assume @p16 (= tptp.exuE1 (forall @t55 (=> @t54 @t62)))) % 0.40/0.68 (assume @p17 (= tptp.prop2setE (forall (@list @t63 @t4) (=> (_ @t5 @t64) @t63)))) % 0.40/0.68 (assume @p18 (= tptp.emptysetE (forall @t8 (=> @t10 (forall @t65 @t63))))) % 0.40/0.68 (assume @p19 (= tptp.emptysetimpfalse (forall @t8 (=> @t10 false)))) % 0.40/0.68 (assume @p20 (= tptp.notinemptyset @t11)) % 0.40/0.68 (assume @p21 (= tptp.exuE3e (forall @t55 (=> @t54 @t66)))) % 0.40/0.68 (assume @p22 (= tptp.setext (forall @t9 (=> @t68 (=> @t21 @t3))))) % 0.40/0.68 (assume @p23 (= tptp.emptyI @t70)) % 0.40/0.68 (assume @p24 (= tptp.noeltsimpempty @t70)) % 0.40/0.68 (assume @p25 (= tptp.setbeta (forall @t60 (=> @t7 (= @t59 @t51))))) % 0.40/0.68 (assume @p26 (= tptp.nonemptyE1 (forall @t33 (=> @t71 @t36)))) % 0.40/0.68 (assume @p27 (= tptp.nonemptyI (forall @t60 (=> @t7 (=> @t51 (_ tptp.nonempty @t58)))))) % 0.40/0.68 (assume @p28 (= tptp.nonemptyI1 (forall @t33 (=> @t36 @t71)))) % 0.40/0.68 (assume @p29 (= tptp.setadjoinIL (forall @t49 (_ @t5 (_ @t17 @t12))))) % 0.40/0.68 (assume @p30 (= tptp.emptyinunitempty (_ @t30 (_ (_ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) % 0.40/0.68 (assume @p31 (= tptp.setadjoinIR (forall @t19 (=> @t14 @t18)))) % 0.40/0.68 (assume @p32 (= tptp.setadjoinE (forall @t19 (=> @t18 (forall @t65 (=> (=> @t15 @t63) (=> (=> @t14 @t63) @t63))))))) % 0.40/0.68 (assume @p33 (= tptp.setadjoinOr (forall @t19 (=> @t18 @t16)))) % 0.40/0.68 (assume @p34 (= tptp.setoftrueEq (forall @t33 (= (_ @t57 (lambda @t8 true)) @t2)))) % 0.40/0.68 (assume @p35 (= tptp.powersetI (forall @t9 (=> @t21 @t24)))) % 0.40/0.68 (assume @p36 (= tptp.emptyinPowerset @t72)) % 0.40/0.68 (assume @p37 (= tptp.emptyInPowerset @t72)) % 0.40/0.68 (assume @p38 (= tptp.powersetE (forall @t73 (=> @t24 @t20)))) % 0.40/0.68 (assume @p39 (= tptp.setunionI (forall (@list @t2 @t4 @t1) (=> @t6 (=> @t25 @t28))))) % 0.40/0.68 (assume @p40 (= tptp.setunionE (forall @t29 (=> @t28 (forall @t65 (=> (forall @t26 (=> @t6 (=> @t25 @t63))) @t63)))))) % 0.40/0.68 (assume @p41 (= tptp.subPowSU (forall @t29 (=> @t7 (_ @t5 (_ tptp.powerset @t27)))))) % 0.40/0.68 (assume @p42 (= tptp.exuE2 (forall @t55 (=> @t54 @t74)))) % 0.40/0.68 (assume @p43 (= tptp.nonemptyImpWitness (forall @t33 (=> @t71 (exists @t8 (and @t7 true)))))) % 0.40/0.68 (assume @p44 (= tptp.uniqinunit (forall @t49 (=> @t77 @t48)))) % 0.40/0.68 (assume @p45 (= tptp.notinsingleton (forall @t49 (=> (not @t48) (not @t78))))) % 0.40/0.68 (assume @p46 (= tptp.eqinunit (forall @t49 (=> @t48 @t77)))) % 0.40/0.68 (assume @p47 (= tptp.singletonsswitch (forall @t49 (=> @t77 @t78)))) % 0.40/0.68 (assume @p48 (= tptp.upairsetE (forall (@list @t4 @t12 @t79) (=> (_ (_ tptp.in @t79) @t80) (or (= @t79 @t4) (= @t79 @t12)))))) % 0.40/0.68 (assume @p49 (= tptp.upairsetIL (forall @t49 (_ @t5 @t80)))) % 0.40/0.68 (assume @p50 (= tptp.upairsetIR (forall @t49 (_ @t13 @t80)))) % 0.40/0.68 (assume @p51 (= tptp.emptyE1 (forall @t83 (=> @t82 (=> (= @t81 tptp.emptyset) false))))) % 0.40/0.68 (assume @p52 (= tptp.vacuousDall (forall (@list @t50 @t4) (=> @t10 @t51)))) % 0.40/0.68 (assume @p53 (= tptp.quantDeMorgan1 @t87)) % 0.40/0.68 (assume @p54 (= tptp.quantDeMorgan2 (forall @t83 (=> @t89 @t88)))) % 0.40/0.68 (assume @p55 (= tptp.quantDeMorgan3 @t90)) % 0.40/0.68 (assume @p56 (= tptp.quantDeMorgan4 (forall @t83 (=> @t85 @t86)))) % 0.40/0.68 (assume @p57 (= tptp.prop2setI (forall @t65 (=> @t63 (_ @t30 @t64))))) % 0.40/0.68 (assume @p58 (= tptp.prop2set2propI (forall @t65 (=> @t63 (_ tptp.set2prop @t64))))) % 0.40/0.68 (assume @p59 (= tptp.notdexE @t90)) % 0.40/0.68 (assume @p60 (= tptp.notdallE @t87)) % 0.40/0.68 (assume @p61 (= tptp.exuI1 (forall @t55 (=> @t62 @t54)))) % 0.40/0.68 (assume @p62 (= tptp.exuI3 (forall @t55 (=> @t66 (=> @t91 @t54))))) % 0.40/0.68 (assume @p63 (= tptp.exuI2 (forall @t55 (=> @t74 @t54)))) % 0.40/0.68 (assume @p64 (= tptp.inCongP (forall @t9 (=> @t3 (forall @t49 (=> @t48 (=> @t7 @t92))))))) % 0.40/0.68 (assume @p65 (= tptp.in__Cong (forall @t9 (=> @t3 (forall @t49 (=> @t48 (= @t7 @t92))))))) % 0.40/0.68 (assume @p66 (= tptp.exuE3u @t93)) % 0.40/0.68 (assume @p67 (= tptp.exu__Cong (forall @t99 (=> @t98 (= @t54 @t96))))) % 0.40/0.68 (assume @p68 (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset))) % 0.40/0.68 (assume @p69 (= tptp.setadjoin__Cong (forall @t49 (=> @t48 (forall (@list @t79 @t100) (=> (= @t79 @t100) (= (_ @t17 @t79) (_ @t75 @t100)))))))) % 0.40/0.68 (assume @p70 (= tptp.powerset__Cong (forall @t9 (=> @t3 (= @t22 (_ tptp.powerset @t1)))))) % 0.40/0.68 (assume @p71 (= tptp.setunion__Cong (forall @t9 (=> @t3 (= @t27 (_ tptp.setunion @t1)))))) % 0.40/0.68 (assume @p72 (= tptp.omega__Cong (= tptp.omega tptp.omega))) % 0.40/0.68 (assume @p73 (= tptp.exuEu @t93)) % 0.40/0.68 (assume @p74 (= tptp.descr__Cong (forall @t99 (=> @t98 (=> @t54 (=> @t96 (= @t53 (_ tptp.descr @t95)))))))) % 0.40/0.68 (assume @p75 (= tptp.dsetconstr__Cong (forall @t9 (=> @t3 (forall @t99 (=> (forall @t8 (=> @t7 (forall @t35 (=> @t92 @t97)))) (= @t81 (_ (_ tptp.dsetconstr @t1) @t95)))))))) % 0.40/0.68 (assume @p76 (= tptp.subsetI1 @t102)) % 0.40/0.68 (assume @p77 @t105) % 0.40/0.68 (assume @p78 (= tptp.eqimpsubset1 (forall @t9 (=> @t3 @t101)))) % 0.40/0.68 (assume @p79 (= tptp.subsetI2 @t102)) % 0.40/0.68 (assume @p80 (= tptp.emptysetsubset (forall @t33 (_ (_ tptp.subset tptp.emptyset) @t2)))) % 0.40/0.68 (assume @p81 (= tptp.subsetE (forall @t73 (=> @t101 @t67)))) % 0.40/0.68 (assume @p82 (= tptp.subsetE2 (forall @t73 (=> @t101 (=> @t106 @t69))))) % 0.40/0.68 (assume @p83 (= tptp.notsubsetI (forall @t73 (=> @t7 (=> @t106 @t107))))) % 0.40/0.68 (assume @p84 @t193) % 0.40/0.68 (assume @p85 true) % 0.40/0.68 (step @p86 (= tptp.exu @t194) :rule refl :args (@t194)) % 0.40/0.68 (step @p87 (= tptp.nonempty @t195) :rule refl :args (@t195)) % 0.40/0.68 (step @p88 :rule aci_norm :args ((= (or @t196 false) @t196))) % 0.40/0.68 (step @p89 :rule evaluate :args ((not true))) % 0.40/0.68 (step @p90 :rule eq-refl :args (@t1)) % 0.40/0.68 (step @p91 :rule cong :premises (@p90) :args (@t197)) % 0.40/0.68 (step @p92 :rule trans :premises (@p91 @p89)) % 0.40/0.68 (step @p93 :rule refl :args (@t196)) % 0.40/0.68 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t198)) % 0.40/0.68 (step @p95 :rule trans :premises (@p94 @p88)) % 0.40/0.68 (step @p96 :rule cong :premises (@p95) :args ((forall @t26 @t198))) % 0.40/0.68 (step @p97 :rule quant-var-elim-eq :args ((= (forall @t33 @t200) @t198))) % 0.40/0.68 (step @p98 :rule aci_norm :args ((= @t201 @t200))) % 0.40/0.68 (step @p99 :rule cong :premises (@p98) :args (@t202)) % 0.40/0.68 (step @p100 :rule trans :premises (@p99 @p97)) % 0.40/0.68 (step @p101 :rule cong :premises (@p100) :args (@t203)) % 0.40/0.68 (step @p102 :rule quant-merge-prenex :args ((= @t203 @t205))) % 0.40/0.68 (step @p103 :rule symm :premises (@p102)) % 0.40/0.68 (step @p104 :rule quant_var_reordering :args ((= (forall @t9 @t201) @t205))) % 0.40/0.68 (step @p105 :rule trans :premises (@p104 @p103 @p101)) % 0.40/0.68 (step @p106 :rule trans :premises (@p105 @p96)) % 0.40/0.68 (step @p107 :rule refl :args (@t108)) % 0.40/0.68 (step @p108 :rule refl :args (@t199)) % 0.40/0.68 (step @p109 :rule refl :args (@t101)) % 0.40/0.68 (step @p110 :rule cong :premises (@p109 @p108) :args ((= @t101 @t199))) % 0.40/0.68 (step @p111 :rule symm :premises (@p110)) % 0.40/0.68 (step @p112 :rule eq_resolve :premises (@p109 @p111)) % 0.40/0.68 (step @p113 :rule nary_cong :premises (@p112 @p107) :args (@t206)) % 0.40/0.68 (step @p114 :rule cong :premises (@p113) :args ((forall @t9 @t206))) % 0.40/0.68 (step @p115 :rule trans :premises (@p114 @p106)) % 0.40/0.68 (step @p116 :rule bool-double-not-elim :args (@t101)) % 0.40/0.68 (step @p117 :rule nary_cong :premises (@p116 @p107) :args ((or (not @t107) @t108))) % 0.40/0.68 (step @p118 :rule bool-impl-elim :args (@t107 @t108)) % 0.40/0.68 (step @p119 :rule trans :premises (@p118 @p117)) % 0.40/0.68 (step @p120 :rule cong :premises (@p119) :args (@t109)) % 0.40/0.68 (step @p121 :rule trans :premises (@p120 @p115)) % 0.40/0.68 (step @p122 :rule refl :args (tptp.notsubsetI)) % 0.40/0.68 (step @p123 :rule cong :premises (@p122 @p121) :args (@t110)) % 0.40/0.68 (step @p124 :rule refl :args (tptp.subsetE2)) % 0.40/0.68 (step @p125 :rule cong :premises (@p124 @p123) :args (@t111)) % 0.40/0.68 (step @p126 :rule refl :args (tptp.subsetE)) % 0.40/0.68 (step @p127 :rule cong :premises (@p126 @p125) :args (@t112)) % 0.40/0.68 (step @p128 :rule refl :args (tptp.emptysetsubset)) % 0.40/0.68 (step @p129 :rule cong :premises (@p128 @p127) :args (@t113)) % 0.40/0.68 (step @p130 :rule refl :args (tptp.subsetI2)) % 0.40/0.68 (step @p131 :rule cong :premises (@p130 @p129) :args (@t114)) % 0.40/0.68 (step @p132 :rule refl :args (tptp.eqimpsubset1)) % 0.40/0.68 (step @p133 :rule cong :premises (@p132 @p131) :args (@t115)) % 0.40/0.68 (step @p134 :rule refl :args (tptp.eqimpsubset2)) % 0.40/0.68 (step @p135 :rule cong :premises (@p134 @p133) :args (@t116)) % 0.40/0.68 (step @p136 :rule refl :args (tptp.subsetI1)) % 0.40/0.68 (step @p137 :rule cong :premises (@p136 @p135) :args (@t117)) % 0.40/0.68 (step @p138 :rule refl :args (tptp.dsetconstr__Cong)) % 0.40/0.68 (step @p139 :rule cong :premises (@p138 @p137) :args (@t118)) % 0.40/0.68 (step @p140 :rule refl :args (tptp.descr__Cong)) % 0.40/0.68 (step @p141 :rule cong :premises (@p140 @p139) :args (@t119)) % 0.40/0.68 (step @p142 :rule refl :args (tptp.exuEu)) % 0.40/0.68 (step @p143 :rule cong :premises (@p142 @p141) :args (@t120)) % 0.40/0.68 (step @p144 :rule refl :args (tptp.omega__Cong)) % 0.40/0.68 (step @p145 :rule cong :premises (@p144 @p143) :args (@t121)) % 0.40/0.68 (step @p146 :rule refl :args (tptp.setunion__Cong)) % 0.40/0.68 (step @p147 :rule cong :premises (@p146 @p145) :args (@t122)) % 0.40/0.68 (step @p148 :rule refl :args (tptp.powerset__Cong)) % 0.40/0.68 (step @p149 :rule cong :premises (@p148 @p147) :args (@t123)) % 0.40/0.68 (step @p150 :rule refl :args (tptp.setadjoin__Cong)) % 0.40/0.68 (step @p151 :rule cong :premises (@p150 @p149) :args (@t124)) % 0.40/0.68 (step @p152 :rule refl :args (tptp.emptyset__Cong)) % 0.40/0.68 (step @p153 :rule cong :premises (@p152 @p151) :args (@t125)) % 0.40/0.68 (step @p154 :rule refl :args (tptp.exu__Cong)) % 0.40/0.68 (step @p155 :rule cong :premises (@p154 @p153) :args (@t126)) % 0.40/0.68 (step @p156 :rule refl :args (tptp.exuE3u)) % 0.40/0.68 (step @p157 :rule cong :premises (@p156 @p155) :args (@t127)) % 0.40/0.68 (step @p158 :rule refl :args (tptp.in__Cong)) % 0.40/0.68 (step @p159 :rule cong :premises (@p158 @p157) :args (@t128)) % 0.40/0.68 (step @p160 :rule refl :args (tptp.inCongP)) % 0.40/0.68 (step @p161 :rule cong :premises (@p160 @p159) :args (@t129)) % 0.40/0.68 (step @p162 :rule refl :args (tptp.exuI2)) % 0.40/0.68 (step @p163 :rule cong :premises (@p162 @p161) :args (@t130)) % 0.40/0.68 (step @p164 :rule refl :args (tptp.exuI3)) % 0.40/0.68 (step @p165 :rule cong :premises (@p164 @p163) :args (@t131)) % 0.40/0.68 (step @p166 :rule refl :args (tptp.exuI1)) % 0.40/0.68 (step @p167 :rule cong :premises (@p166 @p165) :args (@t132)) % 0.40/0.68 (step @p168 :rule refl :args (tptp.notdallE)) % 0.40/0.68 (step @p169 :rule cong :premises (@p168 @p167) :args (@t133)) % 0.40/0.68 (step @p170 :rule refl :args (tptp.notdexE)) % 0.40/0.68 (step @p171 :rule cong :premises (@p170 @p169) :args (@t134)) % 0.40/0.68 (step @p172 :rule refl :args (tptp.prop2set2propI)) % 0.40/0.68 (step @p173 :rule cong :premises (@p172 @p171) :args (@t135)) % 0.40/0.68 (step @p174 :rule refl :args (tptp.prop2setI)) % 0.40/0.68 (step @p175 :rule cong :premises (@p174 @p173) :args (@t136)) % 0.40/0.68 (step @p176 :rule refl :args (tptp.quantDeMorgan4)) % 0.40/0.68 (step @p177 :rule cong :premises (@p176 @p175) :args (@t137)) % 0.40/0.68 (step @p178 :rule refl :args (tptp.quantDeMorgan3)) % 0.40/0.68 (step @p179 :rule cong :premises (@p178 @p177) :args (@t138)) % 0.40/0.68 (step @p180 :rule refl :args (tptp.quantDeMorgan2)) % 0.40/0.68 (step @p181 :rule cong :premises (@p180 @p179) :args (@t139)) % 0.40/0.68 (step @p182 :rule refl :args (tptp.quantDeMorgan1)) % 0.40/0.68 (step @p183 :rule cong :premises (@p182 @p181) :args (@t140)) % 0.40/0.68 (step @p184 :rule refl :args (tptp.vacuousDall)) % 0.40/0.68 (step @p185 :rule cong :premises (@p184 @p183) :args (@t141)) % 0.40/0.68 (step @p186 :rule refl :args (tptp.emptyE1)) % 0.40/0.68 (step @p187 :rule cong :premises (@p186 @p185) :args (@t142)) % 0.40/0.68 (step @p188 :rule refl :args (tptp.upairsetIR)) % 0.40/0.68 (step @p189 :rule cong :premises (@p188 @p187) :args (@t143)) % 0.40/0.68 (step @p190 :rule refl :args (tptp.upairsetIL)) % 0.40/0.68 (step @p191 :rule cong :premises (@p190 @p189) :args (@t144)) % 0.40/0.68 (step @p192 :rule refl :args (tptp.upairsetE)) % 0.40/0.68 (step @p193 :rule cong :premises (@p192 @p191) :args (@t145)) % 0.40/0.68 (step @p194 :rule refl :args (tptp.singletonsswitch)) % 0.40/0.68 (step @p195 :rule cong :premises (@p194 @p193) :args (@t146)) % 0.40/0.68 (step @p196 :rule refl :args (tptp.eqinunit)) % 0.40/0.68 (step @p197 :rule cong :premises (@p196 @p195) :args (@t147)) % 0.40/0.68 (step @p198 :rule refl :args (tptp.notinsingleton)) % 0.40/0.68 (step @p199 :rule cong :premises (@p198 @p197) :args (@t148)) % 0.40/0.68 (step @p200 :rule refl :args (tptp.uniqinunit)) % 0.40/0.68 (step @p201 :rule cong :premises (@p200 @p199) :args (@t149)) % 0.40/0.68 (step @p202 :rule refl :args (tptp.nonemptyImpWitness)) % 0.40/0.68 (step @p203 :rule cong :premises (@p202 @p201) :args (@t150)) % 0.40/0.68 (step @p204 :rule refl :args (tptp.exuE2)) % 0.40/0.68 (step @p205 :rule cong :premises (@p204 @p203) :args (@t151)) % 0.40/0.68 (step @p206 :rule refl :args (tptp.subPowSU)) % 0.40/0.68 (step @p207 :rule cong :premises (@p206 @p205) :args (@t152)) % 0.40/0.68 (step @p208 :rule refl :args (tptp.setunionE)) % 0.40/0.68 (step @p209 :rule cong :premises (@p208 @p207) :args (@t153)) % 0.40/0.68 (step @p210 :rule refl :args (tptp.setunionI)) % 0.40/0.68 (step @p211 :rule cong :premises (@p210 @p209) :args (@t154)) % 0.40/0.68 (step @p212 :rule refl :args (tptp.powersetE)) % 0.40/0.68 (step @p213 :rule cong :premises (@p212 @p211) :args (@t155)) % 0.40/0.68 (step @p214 :rule refl :args (tptp.emptyInPowerset)) % 0.40/0.68 (step @p215 :rule cong :premises (@p214 @p213) :args (@t156)) % 0.40/0.68 (step @p216 :rule refl :args (tptp.emptyinPowerset)) % 0.40/0.68 (step @p217 :rule cong :premises (@p216 @p215) :args (@t157)) % 0.40/0.68 (step @p218 :rule refl :args (tptp.powersetI)) % 0.40/0.68 (step @p219 :rule cong :premises (@p218 @p217) :args (@t158)) % 0.40/0.68 (step @p220 :rule refl :args (tptp.setoftrueEq)) % 0.40/0.68 (step @p221 :rule cong :premises (@p220 @p219) :args (@t159)) % 0.40/0.68 (step @p222 :rule refl :args (tptp.setadjoinOr)) % 0.40/0.68 (step @p223 :rule cong :premises (@p222 @p221) :args (@t160)) % 0.40/0.68 (step @p224 :rule refl :args (tptp.setadjoinE)) % 0.40/0.68 (step @p225 :rule cong :premises (@p224 @p223) :args (@t161)) % 0.40/0.68 (step @p226 :rule refl :args (tptp.setadjoinIR)) % 0.40/0.68 (step @p227 :rule cong :premises (@p226 @p225) :args (@t162)) % 0.40/0.68 (step @p228 :rule refl :args (tptp.emptyinunitempty)) % 0.40/0.68 (step @p229 :rule cong :premises (@p228 @p227) :args (@t163)) % 0.40/0.68 (step @p230 :rule refl :args (tptp.setadjoinIL)) % 0.40/0.68 (step @p231 :rule cong :premises (@p230 @p229) :args (@t164)) % 0.40/0.68 (step @p232 :rule refl :args (tptp.nonemptyI1)) % 0.40/0.68 (step @p233 :rule cong :premises (@p232 @p231) :args (@t165)) % 0.40/0.68 (step @p234 :rule refl :args (tptp.nonemptyI)) % 0.40/0.68 (step @p235 :rule cong :premises (@p234 @p233) :args (@t166)) % 0.40/0.68 (step @p236 :rule refl :args (tptp.nonemptyE1)) % 0.40/0.68 (step @p237 :rule cong :premises (@p236 @p235) :args (@t167)) % 0.40/0.68 (step @p238 :rule refl :args (tptp.setbeta)) % 0.40/0.68 (step @p239 :rule cong :premises (@p238 @p237) :args (@t168)) % 0.40/0.68 (step @p240 :rule refl :args (tptp.noeltsimpempty)) % 0.40/0.68 (step @p241 :rule cong :premises (@p240 @p239) :args (@t169)) % 0.40/0.68 (step @p242 :rule refl :args (tptp.emptyI)) % 0.40/0.68 (step @p243 :rule cong :premises (@p242 @p241) :args (@t170)) % 0.40/0.68 (step @p244 :rule refl :args (tptp.setext)) % 0.40/0.68 (step @p245 :rule cong :premises (@p244 @p243) :args (@t171)) % 0.40/0.68 (step @p246 :rule refl :args (tptp.exuE3e)) % 0.40/0.68 (step @p247 :rule cong :premises (@p246 @p245) :args (@t172)) % 0.40/0.68 (step @p248 :rule refl :args (tptp.notinemptyset)) % 0.40/0.68 (step @p249 :rule cong :premises (@p248 @p247) :args (@t173)) % 0.40/0.68 (step @p250 :rule refl :args (tptp.emptysetimpfalse)) % 0.40/0.68 (step @p251 :rule cong :premises (@p250 @p249) :args (@t174)) % 0.40/0.68 (step @p252 :rule refl :args (tptp.emptysetE)) % 0.40/0.68 (step @p253 :rule cong :premises (@p252 @p251) :args (@t175)) % 0.40/0.68 (step @p254 :rule refl :args (tptp.prop2setE)) % 0.40/0.68 (step @p255 :rule cong :premises (@p254 @p253) :args (@t176)) % 0.40/0.68 (step @p256 :rule refl :args (tptp.exuE1)) % 0.40/0.68 (step @p257 :rule cong :premises (@p256 @p255) :args (@t177)) % 0.40/0.68 (step @p258 :rule refl :args (tptp.dsetconstrER)) % 0.40/0.68 (step @p259 :rule cong :premises (@p258 @p257) :args (@t178)) % 0.40/0.68 (step @p260 :rule refl :args (tptp.dsetconstrEL)) % 0.40/0.68 (step @p261 :rule cong :premises (@p260 @p259) :args (@t179)) % 0.40/0.68 (step @p262 :rule refl :args (tptp.dsetconstrI)) % 0.40/0.68 (step @p263 :rule cong :premises (@p262 @p261) :args (@t180)) % 0.40/0.68 (step @p264 :rule refl :args (tptp.descrp)) % 0.40/0.68 (step @p265 :rule cong :premises (@p264 @p263) :args (@t181)) % 0.40/0.68 (step @p266 :rule refl :args (tptp.wellorderingAx)) % 0.40/0.68 (step @p267 :rule cong :premises (@p266 @p265) :args (@t182)) % 0.40/0.68 (step @p268 :rule refl :args (tptp.foundationAx)) % 0.40/0.68 (step @p269 :rule cong :premises (@p268 @p267) :args (@t183)) % 0.40/0.68 (step @p270 :rule refl :args (tptp.replAx)) % 0.40/0.68 (step @p271 :rule cong :premises (@p270 @p269) :args (@t184)) % 0.40/0.68 (step @p272 :rule refl :args (tptp.omegaIndAx)) % 0.40/0.68 (step @p273 :rule cong :premises (@p272 @p271) :args (@t185)) % 0.40/0.68 (step @p274 :rule refl :args (tptp.omegaSAx)) % 0.40/0.68 (step @p275 :rule cong :premises (@p274 @p273) :args (@t186)) % 0.40/0.68 (step @p276 :rule refl :args (tptp.omega0Ax)) % 0.40/0.68 (step @p277 :rule cong :premises (@p276 @p275) :args (@t187)) % 0.40/0.68 (step @p278 :rule refl :args (tptp.setunionAx)) % 0.40/0.68 (step @p279 :rule cong :premises (@p278 @p277) :args (@t188)) % 0.40/0.68 (step @p280 :rule refl :args (tptp.powersetAx)) % 0.40/0.68 (step @p281 :rule cong :premises (@p280 @p279) :args (@t189)) % 0.40/0.68 (step @p282 :rule refl :args (tptp.setadjoinAx)) % 0.40/0.68 (step @p283 :rule cong :premises (@p282 @p281) :args (@t190)) % 0.40/0.68 (step @p284 :rule refl :args (tptp.emptysetAx)) % 0.40/0.68 (step @p285 :rule cong :premises (@p284 @p283) :args (@t191)) % 0.40/0.68 (step @p286 :rule refl :args (tptp.setextAx)) % 0.40/0.68 (step @p287 :rule cong :premises (@p286 @p285) :args (@t192)) % 0.40/0.68 (step @p288 :rule cong :premises (@p287) :args (@t193)) % 0.40/0.68 (step @p289 :rule eq_resolve :premises (@p84 @p288)) % 0.40/0.68 (step @p290 :rule not_implies_elim2 :premises (@p289)) % 0.40/0.68 (step @p291 :rule not_implies_elim2 :premises (@p290)) % 0.40/0.68 (step @p292 :rule not_implies_elim2 :premises (@p291)) % 0.40/0.68 (step @p293 :rule not_implies_elim2 :premises (@p292)) % 0.40/0.68 (step @p294 :rule not_implies_elim2 :premises (@p293)) % 0.40/0.68 (step @p295 :rule not_implies_elim2 :premises (@p294)) % 0.40/0.68 (step @p296 :rule not_implies_elim2 :premises (@p295)) % 0.40/0.68 (step @p297 :rule not_implies_elim2 :premises (@p296)) % 0.40/0.68 (step @p298 :rule not_implies_elim2 :premises (@p297)) % 0.40/0.68 (step @p299 :rule not_implies_elim2 :premises (@p298)) % 0.40/0.68 (step @p300 :rule not_implies_elim2 :premises (@p299)) % 0.40/0.68 (step @p301 :rule not_implies_elim2 :premises (@p300)) % 0.40/0.68 (step @p302 :rule not_implies_elim2 :premises (@p301)) % 0.40/0.68 (step @p303 :rule not_implies_elim2 :premises (@p302)) % 0.40/0.68 (step @p304 :rule not_implies_elim2 :premises (@p303)) % 0.40/0.68 (step @p305 :rule not_implies_elim2 :premises (@p304)) % 0.40/0.68 (step @p306 :rule not_implies_elim2 :premises (@p305)) % 0.40/0.68 (step @p307 :rule not_implies_elim2 :premises (@p306)) % 0.40/0.68 (step @p308 :rule not_implies_elim2 :premises (@p307)) % 0.40/0.68 (step @p309 :rule not_implies_elim2 :premises (@p308)) % 0.40/0.68 (step @p310 :rule not_implies_elim2 :premises (@p309)) % 0.40/0.68 (step @p311 :rule not_implies_elim2 :premises (@p310)) % 0.40/0.68 (step @p312 :rule not_implies_elim2 :premises (@p311)) % 0.40/0.68 (step @p313 :rule not_implies_elim2 :premises (@p312)) % 0.40/0.68 (step @p314 :rule not_implies_elim2 :premises (@p313)) % 0.40/0.68 (step @p315 :rule not_implies_elim2 :premises (@p314)) % 0.40/0.68 (step @p316 :rule not_implies_elim2 :premises (@p315)) % 0.40/0.68 (step @p317 :rule not_implies_elim2 :premises (@p316)) % 0.40/0.68 (step @p318 :rule not_implies_elim2 :premises (@p317)) % 0.40/0.68 (step @p319 :rule not_implies_elim2 :premises (@p318)) % 0.40/0.68 (step @p320 :rule not_implies_elim2 :premises (@p319)) % 0.40/0.68 (step @p321 :rule not_implies_elim2 :premises (@p320)) % 0.40/0.68 (step @p322 :rule not_implies_elim2 :premises (@p321)) % 0.40/0.68 (step @p323 :rule not_implies_elim2 :premises (@p322)) % 0.40/0.68 (step @p324 :rule not_implies_elim2 :premises (@p323)) % 0.40/0.68 (step @p325 :rule not_implies_elim2 :premises (@p324)) % 0.40/0.68 (step @p326 :rule not_implies_elim2 :premises (@p325)) % 0.40/0.68 (step @p327 :rule not_implies_elim2 :premises (@p326)) % 0.40/0.68 (step @p328 :rule not_implies_elim2 :premises (@p327)) % 0.40/0.68 (step @p329 :rule not_implies_elim2 :premises (@p328)) % 0.40/0.68 (step @p330 :rule not_implies_elim2 :premises (@p329)) % 0.40/0.68 (step @p331 :rule not_implies_elim2 :premises (@p330)) % 0.40/0.68 (step @p332 :rule not_implies_elim2 :premises (@p331)) % 0.40/0.68 (step @p333 :rule not_implies_elim2 :premises (@p332)) % 0.40/0.68 (step @p334 :rule not_implies_elim2 :premises (@p333)) % 0.40/0.68 (step @p335 :rule not_implies_elim2 :premises (@p334)) % 0.40/0.68 (step @p336 :rule not_implies_elim2 :premises (@p335)) % 0.40/0.68 (step @p337 :rule not_implies_elim2 :premises (@p336)) % 0.40/0.68 (step @p338 :rule not_implies_elim2 :premises (@p337)) % 0.40/0.68 (step @p339 :rule not_implies_elim2 :premises (@p338)) % 0.40/0.68 (step @p340 :rule not_implies_elim2 :premises (@p339)) % 0.40/0.68 (step @p341 :rule not_implies_elim2 :premises (@p340)) % 0.40/0.68 (step @p342 :rule not_implies_elim2 :premises (@p341)) % 0.40/0.68 (step @p343 :rule not_implies_elim2 :premises (@p342)) % 0.40/0.68 (step @p344 :rule not_implies_elim2 :premises (@p343)) % 0.40/0.68 (step @p345 :rule not_implies_elim2 :premises (@p344)) % 0.40/0.68 (step @p346 :rule not_implies_elim2 :premises (@p345)) % 0.40/0.68 (step @p347 :rule not_implies_elim2 :premises (@p346)) % 0.40/0.68 (step @p348 :rule not_implies_elim2 :premises (@p347)) % 0.40/0.68 (step @p349 :rule not_implies_elim2 :premises (@p348)) % 0.40/0.68 (step @p350 :rule not_implies_elim2 :premises (@p349)) % 0.40/0.68 (step @p351 :rule not_implies_elim2 :premises (@p350)) % 0.40/0.68 (step @p352 :rule not_implies_elim2 :premises (@p351)) % 0.40/0.68 (step @p353 :rule not_implies_elim2 :premises (@p352)) % 0.40/0.68 (step @p354 :rule not_implies_elim2 :premises (@p353)) % 0.40/0.68 (step @p355 :rule not_implies_elim2 :premises (@p354)) % 0.40/0.68 (step @p356 :rule not_implies_elim2 :premises (@p355)) % 0.40/0.68 (step @p357 :rule not_implies_elim2 :premises (@p356)) % 0.40/0.68 (step @p358 :rule not_implies_elim2 :premises (@p357)) % 0.40/0.68 (step @p359 :rule not_implies_elim2 :premises (@p358)) % 0.40/0.68 (step @p360 :rule not_implies_elim2 :premises (@p359)) % 0.40/0.68 (step @p361 :rule not_implies_elim2 :premises (@p360)) % 0.40/0.68 (step @p362 :rule not_implies_elim2 :premises (@p361)) % 0.40/0.68 (step @p363 :rule not_implies_elim2 :premises (@p362)) % 0.40/0.68 (step @p364 :rule not_implies_elim2 :premises (@p363)) % 0.40/0.68 (step @p365 :rule not_implies_elim2 :premises (@p364)) % 0.40/0.68 (step @p366 :rule not_implies_elim2 :premises (@p365)) % 0.40/0.68 (step @p367 :rule not_implies_elim2 :premises (@p366)) % 0.40/0.68 (step @p368 :rule not_implies_elim2 :premises (@p367)) % 0.40/0.68 (step @p369 :rule not_implies_elim2 :premises (@p368)) % 0.40/0.68 (step @p370 :rule not_implies_elim2 :premises (@p369)) % 0.40/0.68 (step @p371 :rule not_implies_elim2 :premises (@p370)) % 0.40/0.68 (step @p372 :rule not_implies_elim2 :premises (@p371)) % 0.40/0.68 (step @p373 :rule aci_norm :args ((= (or false @t196) @t196))) % 0.40/0.68 (step @p374 :rule nary_cong :premises (@p92 @p93) :args (@t207)) % 0.40/0.68 (step @p375 :rule trans :premises (@p374 @p373)) % 0.40/0.68 (step @p376 :rule cong :premises (@p375) :args ((forall @t26 @t207))) % 0.40/0.68 (step @p377 :rule quant-var-elim-eq :args ((= (forall @t33 @t209) @t207))) % 0.40/0.68 (step @p378 :rule aci_norm :args ((= @t210 @t209))) % 0.40/0.68 (step @p379 :rule cong :premises (@p378) :args (@t211)) % 0.40/0.68 (step @p380 :rule trans :premises (@p379 @p377)) % 0.40/0.68 (step @p381 :rule cong :premises (@p380) :args (@t212)) % 0.40/0.68 (step @p382 :rule quant-merge-prenex :args ((= @t212 @t213))) % 0.40/0.68 (step @p383 :rule symm :premises (@p382)) % 0.40/0.68 (step @p384 :rule quant_var_reordering :args ((= (forall @t9 @t210) @t213))) % 0.40/0.68 (step @p385 :rule trans :premises (@p384 @p383 @p381)) % 0.40/0.68 (step @p386 :rule trans :premises (@p385 @p376)) % 0.40/0.68 (step @p387 :rule refl :args (@t208)) % 0.40/0.68 (step @p388 :rule refl :args (@t103)) % 0.40/0.68 (step @p389 :rule cong :premises (@p388 @p387) :args ((= @t103 @t208))) % 0.40/0.68 (step @p390 :rule symm :premises (@p389)) % 0.40/0.68 (step @p391 :rule eq_resolve :premises (@p388 @p390)) % 0.40/0.68 (step @p392 :rule nary_cong :premises (@p107 @p391) :args (@t214)) % 0.40/0.68 (step @p393 :rule cong :premises (@p392) :args ((forall @t9 @t214))) % 0.40/0.68 (step @p394 :rule trans :premises (@p393 @p386)) % 0.40/0.68 (step @p395 :rule bool-impl-elim :args (@t3 @t103)) % 0.40/0.68 (step @p396 :rule cong :premises (@p395) :args (@t104)) % 0.40/0.68 (step @p397 :rule trans :premises (@p396 @p394)) % 0.40/0.68 (step @p398 :rule cong :premises (@p134 @p397) :args (@t105)) % 0.40/0.68 (step @p399 :rule eq_resolve :premises (@p77 @p398)) % 0.40/0.68 (step @p400 :rule not_implies_elim1 :premises (@p365)) % 0.40/0.68 (step @p401 :rule eq_resolve :premises (@p400 @p399)) % 0.40/0.68 (step @p402 false :rule contra :premises (@p401 @p372)) % 0.40/0.68 ) % 0.40/0.68 % SZS output end Proof % 0.40/0.68 % cvc5 exiting %------------------------------------------------------------------------------