%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU561^1 : 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 : n020.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 08:52:12 AM UTC 2026 % Result : Theorem 0.38s 0.66s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU561^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n020.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 17:41:56 EDT 2026 % 0.18/0.35 % CPUTime : % 0.31/0.53 %----Proving TH0 % 0.38/0.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.66 % SZS status Theorem % 0.38/0.66 % SZS output start Proof % 0.38/0.66 ( % 0.38/0.66 (declare-sort $$unsorted 0) % 0.38/0.66 (declare-const tptp.emptyset $$unsorted) % 0.38/0.66 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.powerset__Cong Bool) % 0.38/0.66 (declare-const tptp.setadjoin__Cong Bool) % 0.38/0.66 (declare-const tptp.emptyset__Cong Bool) % 0.38/0.66 (declare-const tptp.exu__Cong Bool) % 0.38/0.66 (declare-const tptp.in__Cong Bool) % 0.38/0.66 (declare-const tptp.inCongP Bool) % 0.38/0.66 (declare-const tptp.exuI3 Bool) % 0.38/0.66 (declare-const tptp.eqimpsubset2 Bool) % 0.38/0.66 (declare-const tptp.exuI1 Bool) % 0.38/0.66 (declare-const tptp.set2prop (-> $$unsorted Bool)) % 0.38/0.66 (declare-const tptp.quantDeMorgan3 Bool) % 0.38/0.66 (declare-const tptp.quantDeMorgan2 Bool) % 0.38/0.66 (declare-const tptp.dsetconstr__Cong Bool) % 0.38/0.66 (declare-const tptp.quantDeMorgan1 Bool) % 0.38/0.66 (declare-const tptp.vacuousDall Bool) % 0.38/0.66 (declare-const tptp.emptyE1 Bool) % 0.38/0.66 (declare-const tptp.exuE3e Bool) % 0.38/0.66 (declare-const tptp.emptysetE Bool) % 0.38/0.66 (declare-const tptp.omega__Cong Bool) % 0.38/0.66 (declare-const tptp.setadjoinIL Bool) % 0.38/0.66 (declare-const tptp.prop2setE Bool) % 0.38/0.66 (declare-const tptp.prop2set (-> Bool $$unsorted)) % 0.38/0.66 (declare-const tptp.subsetI1 Bool) % 0.38/0.66 (declare-const tptp.dsetconstrEL Bool) % 0.38/0.66 (declare-const tptp.prop2setI Bool) % 0.38/0.66 (declare-const tptp.emptyinPowerset Bool) % 0.38/0.66 (declare-const tptp.dsetconstrI Bool) % 0.38/0.66 (declare-const tptp.setext Bool) % 0.38/0.66 (declare-const tptp.nonemptyImpWitness Bool) % 0.38/0.66 (declare-const tptp.descr (-> (-> $$unsorted Bool) $$unsorted)) % 0.38/0.66 (declare-const tptp.wellorderingAx Bool) % 0.38/0.66 (declare-const tptp.replAx Bool) % 0.38/0.66 (declare-const tptp.upairsetE Bool) % 0.38/0.66 (declare-const tptp.setextAx Bool) % 0.38/0.66 (declare-const tptp.setadjoinOr Bool) % 0.38/0.66 (declare-const tptp.exuE3u Bool) % 0.38/0.66 (declare-const tptp.uniqinunit Bool) % 0.38/0.66 (declare-const tptp.foundationAx Bool) % 0.38/0.66 (declare-const tptp.emptysetimpfalse Bool) % 0.38/0.66 (declare-const tptp.notinemptyset Bool) % 0.38/0.66 (declare-const tptp.setadjoinIR Bool) % 0.38/0.66 (declare-const tptp.exuE2 Bool) % 0.38/0.66 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.notdallE Bool) % 0.38/0.66 (declare-const tptp.dsetconstrER Bool) % 0.38/0.66 (declare-const tptp.emptyInPowerset Bool) % 0.38/0.66 (declare-const tptp.exuEu Bool) % 0.38/0.66 (declare-const tptp.setadjoinAx Bool) % 0.38/0.66 (declare-const tptp.nonemptyE1 Bool) % 0.38/0.66 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.38/0.66 (declare-const tptp.powersetAx Bool) % 0.38/0.66 (declare-const tptp.prop2set2propI Bool) % 0.38/0.66 (declare-const tptp.powersetE Bool) % 0.38/0.66 (declare-const tptp.omegaSAx Bool) % 0.38/0.66 (declare-const tptp.descrp Bool) % 0.38/0.66 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.38/0.66 (declare-const tptp.omega0Ax Bool) % 0.38/0.66 (declare-const tptp.setoftrueEq Bool) % 0.38/0.66 (declare-const tptp.setunionAx Bool) % 0.38/0.66 (declare-const tptp.omega $$unsorted) % 0.38/0.66 (declare-const tptp.omegaIndAx Bool) % 0.38/0.66 (declare-const tptp.quantDeMorgan4 Bool) % 0.38/0.66 (declare-const tptp.powersetI Bool) % 0.38/0.66 (declare-const tptp.emptyI Bool) % 0.38/0.66 (declare-const tptp.noeltsimpempty Bool) % 0.38/0.66 (declare-const tptp.eqinunit Bool) % 0.38/0.66 (declare-const tptp.upairsetIL Bool) % 0.38/0.66 (declare-const tptp.nonemptyI Bool) % 0.38/0.66 (declare-const tptp.emptysetAx Bool) % 0.38/0.66 (declare-const tptp.nonemptyI1 Bool) % 0.38/0.66 (declare-const tptp.descr__Cong Bool) % 0.38/0.66 (declare-const tptp.emptyinunitempty Bool) % 0.38/0.66 (declare-const tptp.setadjoinE Bool) % 0.38/0.66 (declare-const tptp.notdexE Bool) % 0.38/0.66 (declare-const tptp.setunionI Bool) % 0.38/0.66 (declare-const tptp.exuE1 Bool) % 0.38/0.66 (declare-const tptp.setunionE Bool) % 0.38/0.66 (declare-const tptp.exuI2 Bool) % 0.38/0.66 (declare-const tptp.subPowSU Bool) % 0.38/0.66 (declare-const tptp.notinsingleton Bool) % 0.38/0.66 (declare-const tptp.setbeta Bool) % 0.38/0.66 (declare-const tptp.singletonsswitch Bool) % 0.38/0.66 (declare-const tptp.setunion__Cong Bool) % 0.38/0.66 (declare-const tptp.upairsetIR Bool) % 0.38/0.66 (define tptp.exu () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xphi" (-> $$unsorted Bool)))) (lambda (@list _let_3) (exists (@list _let_2) (and (_ _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (= _let_2 _let_1)))))))))) % 0.38/0.66 (define tptp.nonempty () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (not (= _let_1 tptp.emptyset))))) % 0.38/0.66 (define tptp.subset () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.in _let_2))) (let ((_let_4 (@var "A" $$unsorted))) (lambda (@list _let_4 _let_1) (forall (@list _let_2) (=> (_ _let_3 _let_4) (_ _let_3 _let_1))))))))) % 0.38/0.66 (define @t1 () (@var "B" $$unsorted)) % 0.38/0.66 (define @t2 () (@var "A" $$unsorted)) % 0.38/0.66 (define @t3 () (= @t2 @t1)) % 0.38/0.66 (define @t4 () (@var "Xx" $$unsorted)) % 0.38/0.66 (define @t5 () (_ tptp.in @t4)) % 0.38/0.66 (define @t6 () (_ @t5 @t1)) % 0.38/0.66 (define @t7 () (_ @t5 @t2)) % 0.38/0.66 (define @t8 () (@list @t4)) % 0.38/0.66 (define @t9 () (@list @t2 @t1)) % 0.38/0.66 (define @t10 () (_ @t5 tptp.emptyset)) % 0.38/0.66 (define @t11 () (forall @t8 (not @t10))) % 0.38/0.66 (define @t12 () (@var "Xy" $$unsorted)) % 0.38/0.66 (define @t13 () (_ tptp.in @t12)) % 0.38/0.66 (define @t14 () (_ @t13 @t2)) % 0.38/0.66 (define @t15 () (= @t12 @t4)) % 0.38/0.66 (define @t16 () (or @t15 @t14)) % 0.38/0.66 (define @t17 () (_ tptp.setadjoin @t4)) % 0.38/0.66 (define @t18 () (_ @t13 (_ @t17 @t2))) % 0.38/0.66 (define @t19 () (@list @t4 @t2 @t12)) % 0.38/0.66 (define @t20 () (=> @t6 @t7)) % 0.38/0.66 (define @t21 () (forall @t8 @t20)) % 0.38/0.66 (define @t22 () (_ tptp.powerset @t2)) % 0.38/0.66 (define @t23 () (_ tptp.in @t1)) % 0.38/0.66 (define @t24 () (_ @t23 @t22)) % 0.38/0.66 (define @t25 () (_ @t23 @t2)) % 0.38/0.66 (define @t26 () (@list @t1)) % 0.38/0.66 (define @t27 () (_ tptp.setunion @t2)) % 0.38/0.66 (define @t28 () (_ @t5 @t27)) % 0.38/0.66 (define @t29 () (@list @t2 @t4)) % 0.38/0.66 (define @t30 () (_ tptp.in tptp.emptyset)) % 0.38/0.66 (define @t31 () (_ tptp.in (_ @t17 @t4))) % 0.38/0.66 (define @t32 () (_ @t5 tptp.omega)) % 0.38/0.66 (define @t33 () (@list @t2)) % 0.38/0.66 (define @t34 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.38/0.66 (define @t35 () (@list @t12)) % 0.38/0.66 (define @t36 () (exists @t8 @t7)) % 0.38/0.66 (define @t37 () (@var "E" $$unsorted)) % 0.38/0.66 (define @t38 () (@var "D" $$unsorted)) % 0.38/0.66 (define @t39 () (_ @t13 @t38)) % 0.38/0.66 (define @t40 () (@var "C" $$unsorted)) % 0.38/0.66 (define @t41 () (_ @t13 @t40)) % 0.38/0.66 (define @t42 () (_ @t5 @t40)) % 0.38/0.66 (define @t43 () (_ (_ tptp.in @t38) @t1)) % 0.38/0.66 (define @t44 () (forall @t8 (=> @t42 @t7))) % 0.38/0.66 (define @t45 () (@list @t40)) % 0.38/0.66 (define @t46 () (_ @t5 @t38)) % 0.38/0.66 (define @t47 () (_ (_ tptp.in @t40) @t1)) % 0.38/0.66 (define @t48 () (= @t4 @t12)) % 0.38/0.66 (define @t49 () (@list @t4 @t12)) % 0.38/0.66 (define @t50 () (@var "Xphi" (-> $$unsorted Bool))) % 0.38/0.66 (define @t51 () (_ @t50 @t4)) % 0.38/0.66 (define @t52 () (lambda @t8 @t51)) % 0.38/0.66 (define @t53 () (_ tptp.descr @t52)) % 0.38/0.66 (define @t54 () (_ tptp.exu @t52)) % 0.38/0.66 (define @t55 () (@list @t50)) % 0.38/0.66 (define @t56 () (_ @t50 @t12)) % 0.38/0.66 (define @t57 () (_ tptp.dsetconstr @t2)) % 0.38/0.66 (define @t58 () (_ @t57 (lambda @t35 @t56))) % 0.38/0.66 (define @t59 () (_ @t5 @t58)) % 0.38/0.66 (define @t60 () (@list @t2 @t50 @t4)) % 0.38/0.66 (define @t61 () (=> @t56 @t48)) % 0.38/0.66 (define @t62 () (exists @t8 (and @t51 (forall @t35 @t61)))) % 0.38/0.66 (define @t63 () (@var "Xphi" Bool)) % 0.38/0.66 (define @t64 () (_ tptp.prop2set @t63)) % 0.38/0.66 (define @t65 () (@list @t63)) % 0.38/0.66 (define @t66 () (exists @t8 @t51)) % 0.38/0.66 (define @t67 () (forall @t8 (=> @t7 @t6))) % 0.38/0.66 (define @t68 () (not @t7)) % 0.38/0.66 (define @t69 () (forall @t33 (=> (forall @t8 @t68) (= @t2 tptp.emptyset)))) % 0.38/0.66 (define @t70 () (_ tptp.nonempty @t2)) % 0.38/0.66 (define @t71 () (forall @t33 (_ @t30 @t22))) % 0.38/0.66 (define @t72 () (exists @t8 (forall @t35 (= @t56 @t15)))) % 0.38/0.66 (define @t73 () (_ tptp.setadjoin @t12)) % 0.38/0.66 (define @t74 () (_ @t73 tptp.emptyset)) % 0.38/0.66 (define @t75 () (_ @t5 @t74)) % 0.38/0.66 (define @t76 () (_ @t13 (_ @t17 tptp.emptyset))) % 0.38/0.66 (define @t77 () (@var "Xz" $$unsorted)) % 0.38/0.66 (define @t78 () (_ @t17 @t74)) % 0.38/0.66 (define @t79 () (_ @t57 @t52)) % 0.38/0.66 (define @t80 () (exists @t8 (and @t7 @t51))) % 0.38/0.66 (define @t81 () (@list @t2 @t50)) % 0.38/0.66 (define @t82 () (not @t51)) % 0.38/0.66 (define @t83 () (exists @t8 (and @t7 @t82))) % 0.38/0.66 (define @t84 () (not (forall @t8 (=> @t7 @t51)))) % 0.38/0.66 (define @t85 () (forall @t81 (=> @t84 @t83))) % 0.38/0.66 (define @t86 () (not @t80)) % 0.38/0.66 (define @t87 () (forall @t8 (=> @t7 @t82))) % 0.38/0.66 (define @t88 () (forall @t81 (=> @t86 @t87))) % 0.38/0.66 (define @t89 () (forall @t49 (=> @t51 @t61))) % 0.38/0.66 (define @t90 () (_ @t13 @t1)) % 0.38/0.66 (define @t91 () (forall @t55 (=> @t54 @t89))) % 0.38/0.66 (define @t92 () (@var "Xpsi" (-> $$unsorted Bool))) % 0.38/0.66 (define @t93 () (lambda @t8 (_ @t92 @t4))) % 0.38/0.66 (define @t94 () (_ tptp.exu @t93)) % 0.38/0.66 (define @t95 () (=> @t48 (= @t51 (_ @t92 @t12)))) % 0.38/0.66 (define @t96 () (forall @t49 @t95)) % 0.38/0.66 (define @t97 () (@list @t50 @t92)) % 0.38/0.66 (define @t98 () (@var "Xu" $$unsorted)) % 0.38/0.66 (define @t99 () (_ (_ tptp.subset @t2) @t1)) % 0.38/0.66 (define @t100 () (=> @t3 @t99)) % 0.38/0.66 (define @t101 () (forall @t9 @t100)) % 0.38/0.66 (define @t102 () (=> tptp.eqimpsubset2 @t101)) % 0.38/0.66 (define @t103 () (=> tptp.subsetI1 @t102)) % 0.38/0.66 (define @t104 () (=> tptp.dsetconstr__Cong @t103)) % 0.38/0.66 (define @t105 () (=> tptp.descr__Cong @t104)) % 0.38/0.66 (define @t106 () (=> tptp.exuEu @t105)) % 0.38/0.66 (define @t107 () (=> tptp.omega__Cong @t106)) % 0.38/0.66 (define @t108 () (=> tptp.setunion__Cong @t107)) % 0.38/0.66 (define @t109 () (=> tptp.powerset__Cong @t108)) % 0.38/0.66 (define @t110 () (=> tptp.setadjoin__Cong @t109)) % 0.38/0.66 (define @t111 () (=> tptp.emptyset__Cong @t110)) % 0.38/0.66 (define @t112 () (=> tptp.exu__Cong @t111)) % 0.38/0.66 (define @t113 () (=> tptp.exuE3u @t112)) % 0.38/0.66 (define @t114 () (=> tptp.in__Cong @t113)) % 0.38/0.66 (define @t115 () (=> tptp.inCongP @t114)) % 0.38/0.66 (define @t116 () (=> tptp.exuI2 @t115)) % 0.38/0.66 (define @t117 () (=> tptp.exuI3 @t116)) % 0.38/0.66 (define @t118 () (=> tptp.exuI1 @t117)) % 0.38/0.66 (define @t119 () (=> tptp.notdallE @t118)) % 0.38/0.66 (define @t120 () (=> tptp.notdexE @t119)) % 0.38/0.66 (define @t121 () (=> tptp.prop2set2propI @t120)) % 0.38/0.66 (define @t122 () (=> tptp.prop2setI @t121)) % 0.38/0.66 (define @t123 () (=> tptp.quantDeMorgan4 @t122)) % 0.38/0.66 (define @t124 () (=> tptp.quantDeMorgan3 @t123)) % 0.38/0.66 (define @t125 () (=> tptp.quantDeMorgan2 @t124)) % 0.38/0.66 (define @t126 () (=> tptp.quantDeMorgan1 @t125)) % 0.38/0.66 (define @t127 () (=> tptp.vacuousDall @t126)) % 0.38/0.66 (define @t128 () (=> tptp.emptyE1 @t127)) % 0.38/0.66 (define @t129 () (=> tptp.upairsetIR @t128)) % 0.38/0.66 (define @t130 () (=> tptp.upairsetIL @t129)) % 0.38/0.66 (define @t131 () (=> tptp.upairsetE @t130)) % 0.38/0.66 (define @t132 () (=> tptp.singletonsswitch @t131)) % 0.38/0.66 (define @t133 () (=> tptp.eqinunit @t132)) % 0.38/0.66 (define @t134 () (=> tptp.notinsingleton @t133)) % 0.38/0.66 (define @t135 () (=> tptp.uniqinunit @t134)) % 0.38/0.66 (define @t136 () (=> tptp.nonemptyImpWitness @t135)) % 0.38/0.66 (define @t137 () (=> tptp.exuE2 @t136)) % 0.38/0.66 (define @t138 () (=> tptp.subPowSU @t137)) % 0.38/0.66 (define @t139 () (=> tptp.setunionE @t138)) % 0.38/0.66 (define @t140 () (=> tptp.setunionI @t139)) % 0.38/0.66 (define @t141 () (=> tptp.powersetE @t140)) % 0.38/0.66 (define @t142 () (=> tptp.emptyInPowerset @t141)) % 0.38/0.66 (define @t143 () (=> tptp.emptyinPowerset @t142)) % 0.38/0.66 (define @t144 () (=> tptp.powersetI @t143)) % 0.38/0.66 (define @t145 () (=> tptp.setoftrueEq @t144)) % 0.38/0.66 (define @t146 () (=> tptp.setadjoinOr @t145)) % 0.38/0.66 (define @t147 () (=> tptp.setadjoinE @t146)) % 0.38/0.66 (define @t148 () (=> tptp.setadjoinIR @t147)) % 0.38/0.66 (define @t149 () (=> tptp.emptyinunitempty @t148)) % 0.38/0.66 (define @t150 () (=> tptp.setadjoinIL @t149)) % 0.38/0.66 (define @t151 () (=> tptp.nonemptyI1 @t150)) % 0.38/0.66 (define @t152 () (=> tptp.nonemptyI @t151)) % 0.38/0.66 (define @t153 () (=> tptp.nonemptyE1 @t152)) % 0.38/0.66 (define @t154 () (=> tptp.setbeta @t153)) % 0.38/0.66 (define @t155 () (=> tptp.noeltsimpempty @t154)) % 0.38/0.66 (define @t156 () (=> tptp.emptyI @t155)) % 0.38/0.66 (define @t157 () (=> tptp.setext @t156)) % 0.38/0.66 (define @t158 () (=> tptp.exuE3e @t157)) % 0.38/0.66 (define @t159 () (=> tptp.notinemptyset @t158)) % 0.38/0.66 (define @t160 () (=> tptp.emptysetimpfalse @t159)) % 0.38/0.66 (define @t161 () (=> tptp.emptysetE @t160)) % 0.38/0.66 (define @t162 () (=> tptp.prop2setE @t161)) % 0.38/0.66 (define @t163 () (=> tptp.exuE1 @t162)) % 0.38/0.66 (define @t164 () (=> tptp.dsetconstrER @t163)) % 0.38/0.66 (define @t165 () (=> tptp.dsetconstrEL @t164)) % 0.38/0.66 (define @t166 () (=> tptp.dsetconstrI @t165)) % 0.38/0.66 (define @t167 () (=> tptp.descrp @t166)) % 0.38/0.66 (define @t168 () (=> tptp.wellorderingAx @t167)) % 0.38/0.66 (define @t169 () (=> tptp.foundationAx @t168)) % 0.38/0.66 (define @t170 () (=> tptp.replAx @t169)) % 0.38/0.66 (define @t171 () (=> tptp.omegaIndAx @t170)) % 0.38/0.66 (define @t172 () (=> tptp.omegaSAx @t171)) % 0.38/0.66 (define @t173 () (=> tptp.omega0Ax @t172)) % 0.38/0.66 (define @t174 () (=> tptp.setunionAx @t173)) % 0.38/0.66 (define @t175 () (=> tptp.powersetAx @t174)) % 0.38/0.66 (define @t176 () (=> tptp.setadjoinAx @t175)) % 0.38/0.66 (define @t177 () (=> tptp.emptysetAx @t176)) % 0.38/0.66 (define @t178 () (=> tptp.setextAx @t177)) % 0.38/0.66 (define @t179 () (not @t178)) % 0.38/0.66 (define @t180 () (lambda @t55 @t62)) % 0.38/0.66 (define @t181 () (lambda @t8 (not (= @t4 tptp.emptyset)))) % 0.38/0.66 (define @t182 () (lambda @t9 @t67)) % 0.38/0.66 (define @t183 () (@var "BOUND_VARIABLE_9656" $$unsorted)) % 0.38/0.66 (define @t184 () (@list @t1 @t183)) % 0.38/0.66 (define @t185 () (tptp.in @t183 @t1)) % 0.38/0.66 (define @t186 () (not @t185)) % 0.38/0.66 (define @t187 () (or @t186 @t185)) % 0.38/0.66 (define @t188 () (not (= @t1 @t1))) % 0.38/0.66 (define @t189 () (or @t188 @t186 @t185)) % 0.38/0.66 (define @t190 () (not (tptp.in @t183 @t2))) % 0.38/0.66 (define @t191 () (not @t3)) % 0.38/0.66 (define @t192 () (or @t191 @t191 @t190 @t185)) % 0.38/0.66 (define @t193 () (or @t191 @t190 @t185)) % 0.38/0.66 (define @t194 () (forall @t33 @t193)) % 0.38/0.66 (define @t195 () (forall @t184 @t194)) % 0.38/0.66 (define @t196 () (forall (@list @t1 @t183 @t2) @t193)) % 0.38/0.66 (define @t197 () (@list @t2 @t1 @t183)) % 0.38/0.66 (define @t198 () (or @t190 @t185)) % 0.38/0.66 (define @t199 () (or @t191 @t198)) % 0.38/0.66 (define @t200 () (forall @t197 @t199)) % 0.38/0.66 (define @t201 () (@list @t183)) % 0.38/0.66 (define @t202 () (forall @t201 @t199)) % 0.38/0.66 (define @t203 () (forall @t201 @t198)) % 0.38/0.66 (define @t204 () (or @t191 @t203)) % 0.38/0.66 (define @t205 () (tptp.in @t4 @t1)) % 0.38/0.66 (define @t206 () (tptp.in @t4 @t2)) % 0.38/0.66 (define @t207 () (forall @t8 (or (not @t206) @t205))) % 0.38/0.66 (define @t208 () (lambda @t26 @t207)) % 0.38/0.66 (define @t209 () (_ (lambda @t9 @t207) @t2)) % 0.38/0.66 (define @t210 () (=> @t3 (_ @t209 @t1))) % 0.38/0.66 (define @t211 () (forall @t9 @t210)) % 0.38/0.66 (define @t212 () (=> tptp.eqimpsubset2 @t211)) % 0.38/0.66 (define @t213 () (=> tptp.subsetI1 @t212)) % 0.38/0.66 (define @t214 () (=> tptp.dsetconstr__Cong @t213)) % 0.38/0.66 (define @t215 () (=> tptp.descr__Cong @t214)) % 0.38/0.66 (define @t216 () (=> tptp.exuEu @t215)) % 0.38/0.66 (define @t217 () (=> tptp.omega__Cong @t216)) % 0.38/0.66 (define @t218 () (=> tptp.setunion__Cong @t217)) % 0.38/0.66 (define @t219 () (=> tptp.powerset__Cong @t218)) % 0.38/0.66 (define @t220 () (=> tptp.setadjoin__Cong @t219)) % 0.38/0.66 (define @t221 () (=> tptp.emptyset__Cong @t220)) % 0.38/0.66 (define @t222 () (=> tptp.exu__Cong @t221)) % 0.38/0.66 (define @t223 () (=> tptp.exuE3u @t222)) % 0.38/0.66 (define @t224 () (=> tptp.in__Cong @t223)) % 0.38/0.66 (define @t225 () (=> tptp.inCongP @t224)) % 0.38/0.66 (define @t226 () (=> tptp.exuI2 @t225)) % 0.38/0.66 (define @t227 () (=> tptp.exuI3 @t226)) % 0.38/0.66 (define @t228 () (=> tptp.exuI1 @t227)) % 0.38/0.66 (define @t229 () (=> tptp.notdallE @t228)) % 0.38/0.66 (define @t230 () (=> tptp.notdexE @t229)) % 0.38/0.66 (define @t231 () (=> tptp.prop2set2propI @t230)) % 0.38/0.66 (define @t232 () (=> tptp.prop2setI @t231)) % 0.38/0.66 (define @t233 () (=> tptp.quantDeMorgan4 @t232)) % 0.38/0.66 (define @t234 () (=> tptp.quantDeMorgan3 @t233)) % 0.38/0.66 (define @t235 () (=> tptp.quantDeMorgan2 @t234)) % 0.38/0.66 (define @t236 () (=> tptp.quantDeMorgan1 @t235)) % 0.38/0.66 (define @t237 () (=> tptp.vacuousDall @t236)) % 0.38/0.66 (define @t238 () (=> tptp.emptyE1 @t237)) % 0.38/0.66 (define @t239 () (=> tptp.upairsetIR @t238)) % 0.38/0.66 (define @t240 () (=> tptp.upairsetIL @t239)) % 0.38/0.66 (define @t241 () (=> tptp.upairsetE @t240)) % 0.38/0.66 (define @t242 () (=> tptp.singletonsswitch @t241)) % 0.38/0.66 (define @t243 () (=> tptp.eqinunit @t242)) % 0.38/0.66 (define @t244 () (=> tptp.notinsingleton @t243)) % 0.38/0.66 (define @t245 () (=> tptp.uniqinunit @t244)) % 0.38/0.66 (define @t246 () (=> tptp.nonemptyImpWitness @t245)) % 0.38/0.66 (define @t247 () (=> tptp.exuE2 @t246)) % 0.38/0.66 (define @t248 () (=> tptp.subPowSU @t247)) % 0.38/0.66 (define @t249 () (=> tptp.setunionE @t248)) % 0.38/0.66 (define @t250 () (=> tptp.setunionI @t249)) % 0.38/0.66 (define @t251 () (=> tptp.powersetE @t250)) % 0.38/0.66 (define @t252 () (=> tptp.emptyInPowerset @t251)) % 0.38/0.66 (define @t253 () (=> tptp.emptyinPowerset @t252)) % 0.38/0.66 (define @t254 () (=> tptp.powersetI @t253)) % 0.38/0.66 (define @t255 () (=> tptp.setoftrueEq @t254)) % 0.38/0.66 (define @t256 () (=> tptp.setadjoinOr @t255)) % 0.38/0.66 (define @t257 () (=> tptp.setadjoinE @t256)) % 0.38/0.66 (define @t258 () (=> tptp.setadjoinIR @t257)) % 0.38/0.66 (define @t259 () (=> tptp.emptyinunitempty @t258)) % 0.38/0.66 (define @t260 () (=> tptp.setadjoinIL @t259)) % 0.38/0.66 (define @t261 () (=> tptp.nonemptyI1 @t260)) % 0.38/0.66 (define @t262 () (=> tptp.nonemptyI @t261)) % 0.38/0.66 (define @t263 () (=> tptp.nonemptyE1 @t262)) % 0.38/0.66 (define @t264 () (=> tptp.setbeta @t263)) % 0.38/0.66 (define @t265 () (=> tptp.noeltsimpempty @t264)) % 0.38/0.66 (define @t266 () (=> tptp.emptyI @t265)) % 0.38/0.66 (define @t267 () (=> tptp.setext @t266)) % 0.38/0.66 (define @t268 () (=> tptp.exuE3e @t267)) % 0.38/0.66 (define @t269 () (=> tptp.notinemptyset @t268)) % 0.38/0.66 (define @t270 () (=> tptp.emptysetimpfalse @t269)) % 0.38/0.66 (define @t271 () (=> tptp.emptysetE @t270)) % 0.38/0.66 (define @t272 () (=> tptp.prop2setE @t271)) % 0.38/0.66 (define @t273 () (=> tptp.exuE1 @t272)) % 0.38/0.66 (define @t274 () (=> tptp.dsetconstrER @t273)) % 0.38/0.66 (define @t275 () (=> tptp.dsetconstrEL @t274)) % 0.38/0.66 (define @t276 () (=> tptp.dsetconstrI @t275)) % 0.38/0.66 (define @t277 () (=> tptp.descrp @t276)) % 0.38/0.66 (define @t278 () (=> tptp.wellorderingAx @t277)) % 0.38/0.66 (define @t279 () (=> tptp.foundationAx @t278)) % 0.38/0.66 (define @t280 () (=> tptp.replAx @t279)) % 0.38/0.66 (define @t281 () (=> tptp.omegaIndAx @t280)) % 0.38/0.66 (define @t282 () (=> tptp.omegaSAx @t281)) % 0.38/0.66 (define @t283 () (=> tptp.omega0Ax @t282)) % 0.38/0.66 (define @t284 () (=> tptp.setunionAx @t283)) % 0.38/0.66 (define @t285 () (=> tptp.powersetAx @t284)) % 0.38/0.66 (define @t286 () (=> tptp.setadjoinAx @t285)) % 0.38/0.66 (define @t287 () (=> tptp.emptysetAx @t286)) % 0.38/0.66 (define @t288 () (=> tptp.setextAx @t287)) % 0.38/0.66 (define @t289 () (or @t68 @t6)) % 0.38/0.66 (assume @p1 (= tptp.setextAx (forall @t9 (=> (forall @t8 (= @t7 @t6)) @t3)))) % 0.38/0.66 (assume @p2 (= tptp.emptysetAx @t11)) % 0.38/0.66 (assume @p3 (= tptp.setadjoinAx (forall @t19 (= @t18 @t16)))) % 0.38/0.66 (assume @p4 (= tptp.powersetAx (forall @t9 (= @t24 @t21)))) % 0.38/0.66 (assume @p5 (= tptp.setunionAx (forall @t29 (= @t28 (exists @t26 (and @t6 @t25)))))) % 0.38/0.66 (assume @p6 (= tptp.omega0Ax (_ @t30 tptp.omega))) % 0.38/0.66 (assume @p7 (= tptp.omegaSAx (forall @t8 (=> @t32 (_ @t31 tptp.omega))))) % 0.38/0.66 (assume @p8 (= tptp.omegaIndAx (forall @t33 (=> (and (_ @t30 @t2) (forall @t8 (=> (and @t32 @t7) (_ @t31 @t2)))) (forall @t8 (=> @t32 @t7)))))) % 0.38/0.66 (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)))))))))) % 0.38/0.66 (assume @p10 (= tptp.foundationAx (forall @t33 (=> @t36 (exists @t26 (and @t25 (not (exists @t8 (and @t6 @t7))))))))) % 0.38/0.66 (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))))))))))))) % 0.38/0.66 (assume @p12 (= tptp.descrp (forall @t55 (=> @t54 (_ @t50 @t53))))) % 0.38/0.66 (assume @p13 (= tptp.dsetconstrI (forall @t60 (=> @t7 (=> @t51 @t59))))) % 0.38/0.66 (assume @p14 (= tptp.dsetconstrEL (forall @t60 (=> @t59 @t7)))) % 0.38/0.66 (assume @p15 (= tptp.dsetconstrER (forall @t60 (=> @t59 @t51)))) % 0.38/0.66 (assume @p16 (= tptp.exuE1 (forall @t55 (=> @t54 @t62)))) % 0.38/0.66 (assume @p17 (= tptp.prop2setE (forall (@list @t63 @t4) (=> (_ @t5 @t64) @t63)))) % 0.38/0.66 (assume @p18 (= tptp.emptysetE (forall @t8 (=> @t10 (forall @t65 @t63))))) % 0.38/0.66 (assume @p19 (= tptp.emptysetimpfalse (forall @t8 (=> @t10 false)))) % 0.38/0.66 (assume @p20 (= tptp.notinemptyset @t11)) % 0.38/0.66 (assume @p21 (= tptp.exuE3e (forall @t55 (=> @t54 @t66)))) % 0.38/0.66 (assume @p22 (= tptp.setext (forall @t9 (=> @t67 (=> @t21 @t3))))) % 0.38/0.66 (assume @p23 (= tptp.emptyI @t69)) % 0.38/0.66 (assume @p24 (= tptp.noeltsimpempty @t69)) % 0.38/0.66 (assume @p25 (= tptp.setbeta (forall @t60 (=> @t7 (= @t59 @t51))))) % 0.38/0.66 (assume @p26 (= tptp.nonemptyE1 (forall @t33 (=> @t70 @t36)))) % 0.38/0.66 (assume @p27 (= tptp.nonemptyI (forall @t60 (=> @t7 (=> @t51 (_ tptp.nonempty @t58)))))) % 0.38/0.66 (assume @p28 (= tptp.nonemptyI1 (forall @t33 (=> @t36 @t70)))) % 0.38/0.66 (assume @p29 (= tptp.setadjoinIL (forall @t49 (_ @t5 (_ @t17 @t12))))) % 0.38/0.66 (assume @p30 (= tptp.emptyinunitempty (_ @t30 (_ (_ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) % 0.38/0.66 (assume @p31 (= tptp.setadjoinIR (forall @t19 (=> @t14 @t18)))) % 0.38/0.66 (assume @p32 (= tptp.setadjoinE (forall @t19 (=> @t18 (forall @t65 (=> (=> @t15 @t63) (=> (=> @t14 @t63) @t63))))))) % 0.38/0.66 (assume @p33 (= tptp.setadjoinOr (forall @t19 (=> @t18 @t16)))) % 0.38/0.66 (assume @p34 (= tptp.setoftrueEq (forall @t33 (= (_ @t57 (lambda @t8 true)) @t2)))) % 0.38/0.66 (assume @p35 (= tptp.powersetI (forall @t9 (=> @t21 @t24)))) % 0.38/0.66 (assume @p36 (= tptp.emptyinPowerset @t71)) % 0.38/0.66 (assume @p37 (= tptp.emptyInPowerset @t71)) % 0.38/0.66 (assume @p38 (= tptp.powersetE (forall (@list @t2 @t1 @t4) (=> @t24 @t20)))) % 0.38/0.66 (assume @p39 (= tptp.setunionI (forall (@list @t2 @t4 @t1) (=> @t6 (=> @t25 @t28))))) % 0.38/0.66 (assume @p40 (= tptp.setunionE (forall @t29 (=> @t28 (forall @t65 (=> (forall @t26 (=> @t6 (=> @t25 @t63))) @t63)))))) % 0.38/0.66 (assume @p41 (= tptp.subPowSU (forall @t29 (=> @t7 (_ @t5 (_ tptp.powerset @t27)))))) % 0.38/0.66 (assume @p42 (= tptp.exuE2 (forall @t55 (=> @t54 @t72)))) % 0.38/0.66 (assume @p43 (= tptp.nonemptyImpWitness (forall @t33 (=> @t70 (exists @t8 (and @t7 true)))))) % 0.38/0.66 (assume @p44 (= tptp.uniqinunit (forall @t49 (=> @t75 @t48)))) % 0.38/0.66 (assume @p45 (= tptp.notinsingleton (forall @t49 (=> (not @t48) (not @t76))))) % 0.38/0.66 (assume @p46 (= tptp.eqinunit (forall @t49 (=> @t48 @t75)))) % 0.38/0.66 (assume @p47 (= tptp.singletonsswitch (forall @t49 (=> @t75 @t76)))) % 0.38/0.66 (assume @p48 (= tptp.upairsetE (forall (@list @t4 @t12 @t77) (=> (_ (_ tptp.in @t77) @t78) (or (= @t77 @t4) (= @t77 @t12)))))) % 0.38/0.66 (assume @p49 (= tptp.upairsetIL (forall @t49 (_ @t5 @t78)))) % 0.38/0.66 (assume @p50 (= tptp.upairsetIR (forall @t49 (_ @t13 @t78)))) % 0.38/0.66 (assume @p51 (= tptp.emptyE1 (forall @t81 (=> @t80 (=> (= @t79 tptp.emptyset) false))))) % 0.38/0.66 (assume @p52 (= tptp.vacuousDall (forall (@list @t50 @t4) (=> @t10 @t51)))) % 0.38/0.66 (assume @p53 (= tptp.quantDeMorgan1 @t85)) % 0.38/0.66 (assume @p54 (= tptp.quantDeMorgan2 (forall @t81 (=> @t87 @t86)))) % 0.38/0.66 (assume @p55 (= tptp.quantDeMorgan3 @t88)) % 0.38/0.66 (assume @p56 (= tptp.quantDeMorgan4 (forall @t81 (=> @t83 @t84)))) % 0.38/0.66 (assume @p57 (= tptp.prop2setI (forall @t65 (=> @t63 (_ @t30 @t64))))) % 0.38/0.66 (assume @p58 (= tptp.prop2set2propI (forall @t65 (=> @t63 (_ tptp.set2prop @t64))))) % 0.38/0.66 (assume @p59 (= tptp.notdexE @t88)) % 0.38/0.66 (assume @p60 (= tptp.notdallE @t85)) % 0.38/0.66 (assume @p61 (= tptp.exuI1 (forall @t55 (=> @t62 @t54)))) % 0.38/0.66 (assume @p62 (= tptp.exuI3 (forall @t55 (=> @t66 (=> @t89 @t54))))) % 0.38/0.66 (assume @p63 (= tptp.exuI2 (forall @t55 (=> @t72 @t54)))) % 0.38/0.66 (assume @p64 (= tptp.inCongP (forall @t9 (=> @t3 (forall @t49 (=> @t48 (=> @t7 @t90))))))) % 0.38/0.66 (assume @p65 (= tptp.in__Cong (forall @t9 (=> @t3 (forall @t49 (=> @t48 (= @t7 @t90))))))) % 0.38/0.66 (assume @p66 (= tptp.exuE3u @t91)) % 0.38/0.66 (assume @p67 (= tptp.exu__Cong (forall @t97 (=> @t96 (= @t54 @t94))))) % 0.38/0.66 (assume @p68 (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset))) % 0.38/0.66 (assume @p69 (= tptp.setadjoin__Cong (forall @t49 (=> @t48 (forall (@list @t77 @t98) (=> (= @t77 @t98) (= (_ @t17 @t77) (_ @t73 @t98)))))))) % 0.38/0.66 (assume @p70 (= tptp.powerset__Cong (forall @t9 (=> @t3 (= @t22 (_ tptp.powerset @t1)))))) % 0.38/0.66 (assume @p71 (= tptp.setunion__Cong (forall @t9 (=> @t3 (= @t27 (_ tptp.setunion @t1)))))) % 0.38/0.66 (assume @p72 (= tptp.omega__Cong (= tptp.omega tptp.omega))) % 0.38/0.66 (assume @p73 (= tptp.exuEu @t91)) % 0.38/0.66 (assume @p74 (= tptp.descr__Cong (forall @t97 (=> @t96 (=> @t54 (=> @t94 (= @t53 (_ tptp.descr @t93)))))))) % 0.38/0.66 (assume @p75 (= tptp.dsetconstr__Cong (forall @t9 (=> @t3 (forall @t97 (=> (forall @t8 (=> @t7 (forall @t35 (=> @t90 @t95)))) (= @t79 (_ (_ tptp.dsetconstr @t1) @t93)))))))) % 0.38/0.66 (assume @p76 (= tptp.subsetI1 (forall @t9 (=> @t67 @t99)))) % 0.38/0.66 (assume @p77 (= tptp.eqimpsubset2 (forall @t9 (=> @t3 (_ (_ tptp.subset @t1) @t2))))) % 0.38/0.66 (assume @p78 @t179) % 0.38/0.66 (assume @p79 true) % 0.38/0.66 (step @p80 (= tptp.exu @t180) :rule refl :args (@t180)) % 0.38/0.66 (step @p81 (= tptp.nonempty @t181) :rule refl :args (@t181)) % 0.38/0.66 (step @p82 (= tptp.subset @t182) :rule refl :args (@t182)) % 0.38/0.66 (step @p83 :rule evaluate :args ((not true))) % 0.38/0.66 (step @p84 :rule bool-impl-true1 :args (tptp.setextAx)) % 0.38/0.66 (step @p85 :rule bool-impl-true1 :args (tptp.emptysetAx)) % 0.38/0.66 (step @p86 :rule bool-impl-true1 :args (tptp.setadjoinAx)) % 0.38/0.66 (step @p87 :rule bool-impl-true1 :args (tptp.powersetAx)) % 0.38/0.66 (step @p88 :rule bool-impl-true1 :args (tptp.setunionAx)) % 0.38/0.66 (step @p89 :rule bool-impl-true1 :args (tptp.omega0Ax)) % 0.38/0.66 (step @p90 :rule bool-impl-true1 :args (tptp.omegaSAx)) % 0.38/0.66 (step @p91 :rule bool-impl-true1 :args (tptp.omegaIndAx)) % 0.38/0.66 (step @p92 :rule bool-impl-true1 :args (tptp.replAx)) % 0.38/0.66 (step @p93 :rule bool-impl-true1 :args (tptp.foundationAx)) % 0.38/0.66 (step @p94 :rule bool-impl-true1 :args (tptp.wellorderingAx)) % 0.38/0.66 (step @p95 :rule bool-impl-true1 :args (tptp.descrp)) % 0.38/0.66 (step @p96 :rule bool-impl-true1 :args (tptp.dsetconstrI)) % 0.38/0.66 (step @p97 :rule bool-impl-true1 :args (tptp.dsetconstrEL)) % 0.38/0.66 (step @p98 :rule bool-impl-true1 :args (tptp.dsetconstrER)) % 0.38/0.66 (step @p99 :rule bool-impl-true1 :args (tptp.exuE1)) % 0.38/0.66 (step @p100 :rule bool-impl-true1 :args (tptp.prop2setE)) % 0.38/0.66 (step @p101 :rule bool-impl-true1 :args (tptp.emptysetE)) % 0.38/0.66 (step @p102 :rule bool-impl-true1 :args (tptp.emptysetimpfalse)) % 0.38/0.66 (step @p103 :rule bool-impl-true1 :args (tptp.notinemptyset)) % 0.38/0.66 (step @p104 :rule bool-impl-true1 :args (tptp.exuE3e)) % 0.38/0.66 (step @p105 :rule bool-impl-true1 :args (tptp.setext)) % 0.38/0.66 (step @p106 :rule bool-impl-true1 :args (tptp.emptyI)) % 0.38/0.66 (step @p107 :rule bool-impl-true1 :args (tptp.noeltsimpempty)) % 0.38/0.66 (step @p108 :rule bool-impl-true1 :args (tptp.setbeta)) % 0.38/0.66 (step @p109 :rule bool-impl-true1 :args (tptp.nonemptyE1)) % 0.38/0.66 (step @p110 :rule bool-impl-true1 :args (tptp.nonemptyI)) % 0.38/0.66 (step @p111 :rule bool-impl-true1 :args (tptp.nonemptyI1)) % 0.38/0.66 (step @p112 :rule bool-impl-true1 :args (tptp.setadjoinIL)) % 0.38/0.66 (step @p113 :rule bool-impl-true1 :args (tptp.emptyinunitempty)) % 0.38/0.66 (step @p114 :rule bool-impl-true1 :args (tptp.setadjoinIR)) % 0.38/0.66 (step @p115 :rule bool-impl-true1 :args (tptp.setadjoinE)) % 0.38/0.66 (step @p116 :rule bool-impl-true1 :args (tptp.setadjoinOr)) % 0.38/0.66 (step @p117 :rule bool-impl-true1 :args (tptp.setoftrueEq)) % 0.38/0.66 (step @p118 :rule bool-impl-true1 :args (tptp.powersetI)) % 0.38/0.66 (step @p119 :rule bool-impl-true1 :args (tptp.emptyinPowerset)) % 0.38/0.66 (step @p120 :rule bool-impl-true1 :args (tptp.emptyInPowerset)) % 0.38/0.66 (step @p121 :rule bool-impl-true1 :args (tptp.powersetE)) % 0.38/0.66 (step @p122 :rule bool-impl-true1 :args (tptp.setunionI)) % 0.38/0.66 (step @p123 :rule bool-impl-true1 :args (tptp.setunionE)) % 0.38/0.66 (step @p124 :rule bool-impl-true1 :args (tptp.subPowSU)) % 0.38/0.66 (step @p125 :rule bool-impl-true1 :args (tptp.exuE2)) % 0.38/0.66 (step @p126 :rule bool-impl-true1 :args (tptp.nonemptyImpWitness)) % 0.38/0.66 (step @p127 :rule bool-impl-true1 :args (tptp.uniqinunit)) % 0.38/0.66 (step @p128 :rule bool-impl-true1 :args (tptp.notinsingleton)) % 0.38/0.66 (step @p129 :rule bool-impl-true1 :args (tptp.eqinunit)) % 0.38/0.66 (step @p130 :rule bool-impl-true1 :args (tptp.singletonsswitch)) % 0.38/0.66 (step @p131 :rule bool-impl-true1 :args (tptp.upairsetE)) % 0.38/0.66 (step @p132 :rule bool-impl-true1 :args (tptp.upairsetIL)) % 0.38/0.66 (step @p133 :rule bool-impl-true1 :args (tptp.upairsetIR)) % 0.38/0.66 (step @p134 :rule bool-impl-true1 :args (tptp.emptyE1)) % 0.38/0.66 (step @p135 :rule bool-impl-true1 :args (tptp.vacuousDall)) % 0.38/0.66 (step @p136 :rule bool-impl-true1 :args (tptp.quantDeMorgan1)) % 0.38/0.66 (step @p137 :rule bool-impl-true1 :args (tptp.quantDeMorgan2)) % 0.38/0.66 (step @p138 :rule bool-impl-true1 :args (tptp.quantDeMorgan3)) % 0.38/0.66 (step @p139 :rule bool-impl-true1 :args (tptp.quantDeMorgan4)) % 0.38/0.66 (step @p140 :rule bool-impl-true1 :args (tptp.prop2setI)) % 0.38/0.66 (step @p141 :rule bool-impl-true1 :args (tptp.prop2set2propI)) % 0.38/0.66 (step @p142 :rule bool-impl-true1 :args (tptp.notdexE)) % 0.38/0.66 (step @p143 :rule bool-impl-true1 :args (tptp.notdallE)) % 0.38/0.66 (step @p144 :rule bool-impl-true1 :args (tptp.exuI1)) % 0.38/0.66 (step @p145 :rule bool-impl-true1 :args (tptp.exuI3)) % 0.38/0.66 (step @p146 :rule bool-impl-true1 :args (tptp.exuI2)) % 0.38/0.66 (step @p147 :rule bool-impl-true1 :args (tptp.inCongP)) % 0.38/0.66 (step @p148 :rule bool-impl-true1 :args (tptp.in__Cong)) % 0.38/0.66 (step @p149 :rule bool-impl-true1 :args (tptp.exuE3u)) % 0.38/0.66 (step @p150 :rule bool-impl-true1 :args (tptp.exu__Cong)) % 0.38/0.66 (step @p151 :rule bool-impl-true1 :args (tptp.emptyset__Cong)) % 0.38/0.66 (step @p152 :rule bool-impl-true1 :args (tptp.setadjoin__Cong)) % 0.38/0.66 (step @p153 :rule bool-impl-true1 :args (tptp.powerset__Cong)) % 0.38/0.66 (step @p154 :rule bool-impl-true1 :args (tptp.setunion__Cong)) % 0.38/0.66 (step @p155 :rule bool-impl-true1 :args (tptp.omega__Cong)) % 0.38/0.66 (step @p156 :rule bool-impl-true1 :args (tptp.exuEu)) % 0.38/0.66 (step @p157 :rule bool-impl-true1 :args (tptp.descr__Cong)) % 0.38/0.66 (step @p158 :rule bool-impl-true1 :args (tptp.dsetconstr__Cong)) % 0.38/0.66 (step @p159 :rule bool-impl-true1 :args (tptp.subsetI1)) % 0.38/0.66 (step @p160 :rule bool-impl-true1 :args (tptp.eqimpsubset2)) % 0.38/0.66 (step @p161 :rule quant-unused-vars :args ((= (forall @t184 true) true))) % 0.38/0.66 (step @p162 :rule bool-or-taut2 :args (false @t185 false false)) % 0.38/0.66 (step @p163 :rule cong :premises (@p162) :args ((forall @t184 @t187))) % 0.38/0.66 (step @p164 :rule trans :premises (@p163 @p161)) % 0.38/0.66 (step @p165 :rule aci_norm :args ((= (or false @t186 @t185) @t187))) % 0.38/0.66 (step @p166 :rule refl :args (@t185)) % 0.38/0.66 (step @p167 :rule refl :args (@t186)) % 0.38/0.66 (step @p168 :rule eq-refl :args (@t1)) % 0.38/0.66 (step @p169 :rule cong :premises (@p168) :args (@t188)) % 0.38/0.66 (step @p170 :rule trans :premises (@p169 @p83)) % 0.38/0.66 (step @p171 :rule nary_cong :premises (@p170 @p167 @p166) :args (@t189)) % 0.38/0.66 (step @p172 :rule trans :premises (@p171 @p165)) % 0.38/0.66 (step @p173 :rule cong :premises (@p172) :args ((forall @t184 @t189))) % 0.38/0.66 (step @p174 :rule trans :premises (@p173 @p164)) % 0.38/0.66 (step @p175 :rule quant-var-elim-eq :args ((= (forall @t33 @t192) @t189))) % 0.38/0.66 (step @p176 :rule aci_norm :args ((= @t193 @t192))) % 0.38/0.66 (step @p177 :rule cong :premises (@p176) :args (@t194)) % 0.38/0.66 (step @p178 :rule trans :premises (@p177 @p175)) % 0.38/0.66 (step @p179 :rule cong :premises (@p178) :args (@t195)) % 0.38/0.66 (step @p180 :rule quant-merge-prenex :args ((= @t195 @t196))) % 0.38/0.66 (step @p181 :rule symm :premises (@p180)) % 0.38/0.66 (step @p182 :rule quant_var_reordering :args ((= (forall @t197 @t193) @t196))) % 0.38/0.66 (step @p183 :rule trans :premises (@p182 @p181 @p179)) % 0.38/0.66 (step @p184 :rule trans :premises (@p183 @p174)) % 0.38/0.66 (step @p185 :rule aci_norm :args ((= @t199 @t193))) % 0.38/0.66 (step @p186 :rule cong :premises (@p185) :args (@t200)) % 0.38/0.66 (step @p187 :rule trans :premises (@p186 @p184)) % 0.38/0.66 (step @p188 :rule quant-merge-prenex :args ((= (forall @t9 @t202) @t200))) % 0.38/0.66 (step @p189 :rule alpha_equiv :args (@t203 (@list @t183) (@list @t4))) % 0.38/0.66 (step @p190 :rule refl :args (@t191)) % 0.38/0.66 (step @p191 :rule nary_cong :premises (@p190 @p189) :args (@t204)) % 0.38/0.66 (step @p192 :rule quant-miniscope-or :args ((= @t202 @t204))) % 0.38/0.66 (step @p193 :rule trans :premises (@p192 @p191)) % 0.38/0.66 (step @p194 :rule symm :premises (@p193)) % 0.38/0.66 (step @p195 :rule cong :premises (@p194) :args ((forall @t9 (or @t191 @t207)))) % 0.38/0.66 (step @p196 :rule trans :premises (@p195 @p188)) % 0.38/0.66 (step @p197 :rule trans :premises (@p196 @p187)) % 0.38/0.66 (step @p198 :rule bool-impl-elim :args (@t3 @t207)) % 0.38/0.66 (step @p199 :rule cong :premises (@p198) :args ((forall @t9 (=> @t3 @t207)))) % 0.38/0.66 (step @p200 :rule trans :premises (@p199 @p197)) % 0.38/0.66 (step @p201 :rule beta-reduce :args ((= (_ @t208 @t1) @t207))) % 0.38/0.66 (step @p202 :rule refl :args (@t1)) % 0.38/0.66 (step @p203 :rule beta-reduce :args ((= @t209 @t208))) % 0.38/0.66 (step @p204 :rule ho_cong :premises (@p203 @p202)) % 0.38/0.66 (step @p205 :rule trans :premises (@p204 @p201)) % 0.38/0.66 (step @p206 :rule refl :args (@t3)) % 0.38/0.66 (step @p207 :rule cong :premises (@p206 @p205) :args (@t210)) % 0.38/0.66 (step @p208 :rule cong :premises (@p207) :args (@t211)) % 0.38/0.66 (step @p209 :rule trans :premises (@p208 @p200)) % 0.38/0.66 (step @p210 :rule refl :args (tptp.eqimpsubset2)) % 0.38/0.66 (step @p211 :rule cong :premises (@p210 @p209) :args (@t212)) % 0.38/0.66 (step @p212 :rule trans :premises (@p211 @p160)) % 0.38/0.66 (step @p213 :rule refl :args (tptp.subsetI1)) % 0.38/0.66 (step @p214 :rule cong :premises (@p213 @p212) :args (@t213)) % 0.38/0.66 (step @p215 :rule trans :premises (@p214 @p159)) % 0.38/0.66 (step @p216 :rule refl :args (tptp.dsetconstr__Cong)) % 0.38/0.66 (step @p217 :rule cong :premises (@p216 @p215) :args (@t214)) % 0.38/0.66 (step @p218 :rule trans :premises (@p217 @p158)) % 0.38/0.66 (step @p219 :rule refl :args (tptp.descr__Cong)) % 0.38/0.66 (step @p220 :rule cong :premises (@p219 @p218) :args (@t215)) % 0.38/0.66 (step @p221 :rule trans :premises (@p220 @p157)) % 0.38/0.66 (step @p222 :rule refl :args (tptp.exuEu)) % 0.38/0.66 (step @p223 :rule cong :premises (@p222 @p221) :args (@t216)) % 0.38/0.66 (step @p224 :rule trans :premises (@p223 @p156)) % 0.38/0.66 (step @p225 :rule refl :args (tptp.omega__Cong)) % 0.38/0.66 (step @p226 :rule cong :premises (@p225 @p224) :args (@t217)) % 0.38/0.66 (step @p227 :rule trans :premises (@p226 @p155)) % 0.38/0.66 (step @p228 :rule refl :args (tptp.setunion__Cong)) % 0.38/0.66 (step @p229 :rule cong :premises (@p228 @p227) :args (@t218)) % 0.38/0.66 (step @p230 :rule trans :premises (@p229 @p154)) % 0.38/0.66 (step @p231 :rule refl :args (tptp.powerset__Cong)) % 0.38/0.66 (step @p232 :rule cong :premises (@p231 @p230) :args (@t219)) % 0.38/0.66 (step @p233 :rule trans :premises (@p232 @p153)) % 0.38/0.66 (step @p234 :rule refl :args (tptp.setadjoin__Cong)) % 0.38/0.66 (step @p235 :rule cong :premises (@p234 @p233) :args (@t220)) % 0.38/0.66 (step @p236 :rule trans :premises (@p235 @p152)) % 0.38/0.66 (step @p237 :rule refl :args (tptp.emptyset__Cong)) % 0.38/0.66 (step @p238 :rule cong :premises (@p237 @p236) :args (@t221)) % 0.38/0.66 (step @p239 :rule trans :premises (@p238 @p151)) % 0.38/0.66 (step @p240 :rule refl :args (tptp.exu__Cong)) % 0.38/0.66 (step @p241 :rule cong :premises (@p240 @p239) :args (@t222)) % 0.38/0.66 (step @p242 :rule trans :premises (@p241 @p150)) % 0.38/0.66 (step @p243 :rule refl :args (tptp.exuE3u)) % 0.38/0.66 (step @p244 :rule cong :premises (@p243 @p242) :args (@t223)) % 0.38/0.66 (step @p245 :rule trans :premises (@p244 @p149)) % 0.38/0.66 (step @p246 :rule refl :args (tptp.in__Cong)) % 0.38/0.66 (step @p247 :rule cong :premises (@p246 @p245) :args (@t224)) % 0.38/0.66 (step @p248 :rule trans :premises (@p247 @p148)) % 0.38/0.66 (step @p249 :rule refl :args (tptp.inCongP)) % 0.38/0.66 (step @p250 :rule cong :premises (@p249 @p248) :args (@t225)) % 0.38/0.66 (step @p251 :rule trans :premises (@p250 @p147)) % 0.38/0.66 (step @p252 :rule refl :args (tptp.exuI2)) % 0.38/0.66 (step @p253 :rule cong :premises (@p252 @p251) :args (@t226)) % 0.38/0.66 (step @p254 :rule trans :premises (@p253 @p146)) % 0.38/0.66 (step @p255 :rule refl :args (tptp.exuI3)) % 0.38/0.66 (step @p256 :rule cong :premises (@p255 @p254) :args (@t227)) % 0.38/0.66 (step @p257 :rule trans :premises (@p256 @p145)) % 0.38/0.66 (step @p258 :rule refl :args (tptp.exuI1)) % 0.38/0.66 (step @p259 :rule cong :premises (@p258 @p257) :args (@t228)) % 0.38/0.66 (step @p260 :rule trans :premises (@p259 @p144)) % 0.38/0.66 (step @p261 :rule refl :args (tptp.notdallE)) % 0.38/0.66 (step @p262 :rule cong :premises (@p261 @p260) :args (@t229)) % 0.38/0.66 (step @p263 :rule trans :premises (@p262 @p143)) % 0.38/0.66 (step @p264 :rule refl :args (tptp.notdexE)) % 0.38/0.66 (step @p265 :rule cong :premises (@p264 @p263) :args (@t230)) % 0.38/0.66 (step @p266 :rule trans :premises (@p265 @p142)) % 0.38/0.66 (step @p267 :rule refl :args (tptp.prop2set2propI)) % 0.38/0.66 (step @p268 :rule cong :premises (@p267 @p266) :args (@t231)) % 0.38/0.66 (step @p269 :rule trans :premises (@p268 @p141)) % 0.38/0.66 (step @p270 :rule refl :args (tptp.prop2setI)) % 0.38/0.66 (step @p271 :rule cong :premises (@p270 @p269) :args (@t232)) % 0.38/0.66 (step @p272 :rule trans :premises (@p271 @p140)) % 0.38/0.66 (step @p273 :rule refl :args (tptp.quantDeMorgan4)) % 0.38/0.66 (step @p274 :rule cong :premises (@p273 @p272) :args (@t233)) % 0.38/0.66 (step @p275 :rule trans :premises (@p274 @p139)) % 0.38/0.66 (step @p276 :rule refl :args (tptp.quantDeMorgan3)) % 0.38/0.66 (step @p277 :rule cong :premises (@p276 @p275) :args (@t234)) % 0.38/0.66 (step @p278 :rule trans :premises (@p277 @p138)) % 0.38/0.66 (step @p279 :rule refl :args (tptp.quantDeMorgan2)) % 0.38/0.66 (step @p280 :rule cong :premises (@p279 @p278) :args (@t235)) % 0.38/0.66 (step @p281 :rule trans :premises (@p280 @p137)) % 0.38/0.66 (step @p282 :rule refl :args (tptp.quantDeMorgan1)) % 0.38/0.66 (step @p283 :rule cong :premises (@p282 @p281) :args (@t236)) % 0.38/0.66 (step @p284 :rule trans :premises (@p283 @p136)) % 0.38/0.66 (step @p285 :rule refl :args (tptp.vacuousDall)) % 0.38/0.66 (step @p286 :rule cong :premises (@p285 @p284) :args (@t237)) % 0.38/0.66 (step @p287 :rule trans :premises (@p286 @p135)) % 0.38/0.66 (step @p288 :rule refl :args (tptp.emptyE1)) % 0.38/0.66 (step @p289 :rule cong :premises (@p288 @p287) :args (@t238)) % 0.38/0.66 (step @p290 :rule trans :premises (@p289 @p134)) % 0.38/0.66 (step @p291 :rule refl :args (tptp.upairsetIR)) % 0.38/0.66 (step @p292 :rule cong :premises (@p291 @p290) :args (@t239)) % 0.38/0.66 (step @p293 :rule trans :premises (@p292 @p133)) % 0.38/0.66 (step @p294 :rule refl :args (tptp.upairsetIL)) % 0.38/0.66 (step @p295 :rule cong :premises (@p294 @p293) :args (@t240)) % 0.38/0.66 (step @p296 :rule trans :premises (@p295 @p132)) % 0.38/0.66 (step @p297 :rule refl :args (tptp.upairsetE)) % 0.38/0.66 (step @p298 :rule cong :premises (@p297 @p296) :args (@t241)) % 0.38/0.66 (step @p299 :rule trans :premises (@p298 @p131)) % 0.38/0.66 (step @p300 :rule refl :args (tptp.singletonsswitch)) % 0.38/0.66 (step @p301 :rule cong :premises (@p300 @p299) :args (@t242)) % 0.38/0.66 (step @p302 :rule trans :premises (@p301 @p130)) % 0.38/0.66 (step @p303 :rule refl :args (tptp.eqinunit)) % 0.38/0.66 (step @p304 :rule cong :premises (@p303 @p302) :args (@t243)) % 0.38/0.66 (step @p305 :rule trans :premises (@p304 @p129)) % 0.38/0.66 (step @p306 :rule refl :args (tptp.notinsingleton)) % 0.38/0.66 (step @p307 :rule cong :premises (@p306 @p305) :args (@t244)) % 0.38/0.66 (step @p308 :rule trans :premises (@p307 @p128)) % 0.38/0.66 (step @p309 :rule refl :args (tptp.uniqinunit)) % 0.38/0.66 (step @p310 :rule cong :premises (@p309 @p308) :args (@t245)) % 0.38/0.66 (step @p311 :rule trans :premises (@p310 @p127)) % 0.38/0.66 (step @p312 :rule refl :args (tptp.nonemptyImpWitness)) % 0.38/0.66 (step @p313 :rule cong :premises (@p312 @p311) :args (@t246)) % 0.38/0.66 (step @p314 :rule trans :premises (@p313 @p126)) % 0.38/0.66 (step @p315 :rule refl :args (tptp.exuE2)) % 0.38/0.66 (step @p316 :rule cong :premises (@p315 @p314) :args (@t247)) % 0.38/0.66 (step @p317 :rule trans :premises (@p316 @p125)) % 0.38/0.66 (step @p318 :rule refl :args (tptp.subPowSU)) % 0.38/0.66 (step @p319 :rule cong :premises (@p318 @p317) :args (@t248)) % 0.38/0.66 (step @p320 :rule trans :premises (@p319 @p124)) % 0.38/0.66 (step @p321 :rule refl :args (tptp.setunionE)) % 0.38/0.66 (step @p322 :rule cong :premises (@p321 @p320) :args (@t249)) % 0.38/0.66 (step @p323 :rule trans :premises (@p322 @p123)) % 0.38/0.66 (step @p324 :rule refl :args (tptp.setunionI)) % 0.38/0.66 (step @p325 :rule cong :premises (@p324 @p323) :args (@t250)) % 0.38/0.66 (step @p326 :rule trans :premises (@p325 @p122)) % 0.38/0.66 (step @p327 :rule refl :args (tptp.powersetE)) % 0.38/0.66 (step @p328 :rule cong :premises (@p327 @p326) :args (@t251)) % 0.38/0.66 (step @p329 :rule trans :premises (@p328 @p121)) % 0.38/0.66 (step @p330 :rule refl :args (tptp.emptyInPowerset)) % 0.38/0.66 (step @p331 :rule cong :premises (@p330 @p329) :args (@t252)) % 0.38/0.66 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(step @p409 :rule cong :premises (@p408 @p407) :args (@t278)) % 0.38/0.66 (step @p410 :rule trans :premises (@p409 @p94)) % 0.38/0.66 (step @p411 :rule refl :args (tptp.foundationAx)) % 0.38/0.66 (step @p412 :rule cong :premises (@p411 @p410) :args (@t279)) % 0.38/0.66 (step @p413 :rule trans :premises (@p412 @p93)) % 0.38/0.66 (step @p414 :rule refl :args (tptp.replAx)) % 0.38/0.66 (step @p415 :rule cong :premises (@p414 @p413) :args (@t280)) % 0.38/0.66 (step @p416 :rule trans :premises (@p415 @p92)) % 0.38/0.66 (step @p417 :rule refl :args (tptp.omegaIndAx)) % 0.38/0.66 (step @p418 :rule cong :premises (@p417 @p416) :args (@t281)) % 0.38/0.66 (step @p419 :rule trans :premises (@p418 @p91)) % 0.38/0.66 (step @p420 :rule refl :args (tptp.omegaSAx)) % 0.38/0.66 (step @p421 :rule cong :premises (@p420 @p419) :args (@t282)) % 0.38/0.66 (step @p422 :rule trans :premises (@p421 @p90)) % 0.38/0.66 (step @p423 :rule refl :args (tptp.omega0Ax)) % 0.38/0.66 (step @p424 :rule cong :premises 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(step @p456 :rule cong :premises (@p455) :args ((forall @t8 @t289))) % 0.38/0.66 (step @p457 :rule bool-impl-elim :args (@t7 @t6)) % 0.38/0.66 (step @p458 :rule cong :premises (@p457) :args (@t67)) % 0.38/0.66 (step @p459 :rule trans :premises (@p458 @p456)) % 0.38/0.66 (step @p460 :rule cong :premises (@p459) :args (@t182)) % 0.38/0.66 (step @p461 :rule trans :premises (@p82 @p460)) % 0.38/0.66 (step @p462 :rule ho_cong :premises (@p461 @p443)) % 0.38/0.66 (step @p463 :rule ho_cong :premises (@p462 @p202)) % 0.38/0.66 (step @p464 :rule cong :premises (@p206 @p463) :args (@t100)) % 0.38/0.66 (step @p465 :rule cong :premises (@p464) :args (@t101)) % 0.38/0.66 (step @p466 :rule cong :premises (@p210 @p465) :args (@t102)) % 0.38/0.66 (step @p467 :rule cong :premises (@p213 @p466) :args (@t103)) % 0.38/0.66 (step @p468 :rule cong :premises (@p216 @p467) :args (@t104)) % 0.38/0.66 (step @p469 :rule cong :premises (@p219 @p468) :args (@t105)) % 0.38/0.66 (step @p470 :rule cong :premises 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% 0.38/0.66 (step @p511 :rule cong :premises (@p345 @p510) :args (@t147)) % 0.38/0.66 (step @p512 :rule cong :premises (@p348 @p511) :args (@t148)) % 0.38/0.66 (step @p513 :rule cong :premises (@p351 @p512) :args (@t149)) % 0.38/0.66 (step @p514 :rule cong :premises (@p354 @p513) :args (@t150)) % 0.38/0.66 (step @p515 :rule cong :premises (@p357 @p514) :args (@t151)) % 0.38/0.66 (step @p516 :rule cong :premises (@p360 @p515) :args (@t152)) % 0.38/0.66 (step @p517 :rule cong :premises (@p363 @p516) :args (@t153)) % 0.38/0.66 (step @p518 :rule cong :premises (@p366 @p517) :args (@t154)) % 0.38/0.66 (step @p519 :rule cong :premises (@p369 @p518) :args (@t155)) % 0.38/0.66 (step @p520 :rule cong :premises (@p372 @p519) :args (@t156)) % 0.38/0.66 (step @p521 :rule cong :premises (@p375 @p520) :args (@t157)) % 0.38/0.66 (step @p522 :rule cong :premises (@p378 @p521) :args (@t158)) % 0.38/0.66 (step @p523 :rule cong :premises (@p381 @p522) :args (@t159)) % 0.38/0.66 (step @p524 :rule cong 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% 0.38/0.66 (step @p538 :rule cong :premises (@p426 @p537) :args (@t174)) % 0.38/0.66 (step @p539 :rule cong :premises (@p429 @p538) :args (@t175)) % 0.38/0.66 (step @p540 :rule cong :premises (@p432 @p539) :args (@t176)) % 0.38/0.66 (step @p541 :rule cong :premises (@p435 @p540) :args (@t177)) % 0.38/0.66 (step @p542 :rule cong :premises (@p438 @p541) :args (@t178)) % 0.38/0.66 (step @p543 :rule cong :premises (@p542) :args (@t179)) % 0.38/0.66 (step @p544 :rule trans :premises (@p543 @p442)) % 0.38/0.66 (step @p545 false :rule eq_resolve :premises (@p78 @p544)) % 0.38/0.66 ) % 0.38/0.66 % SZS output end Proof % 0.38/0.66 % cvc5 exiting %------------------------------------------------------------------------------