%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU548^1 : TPTP v9.2.1. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:52:09 AM UTC 2026 % Result : Theorem 0.39s 0.64s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU548^1 : TPTP v9.2.1. Bugfixed v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n002.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 17:41:33 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.53 %----Proving TH0 % 0.39/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.64 % SZS status Theorem % 0.39/0.64 % SZS output start Proof % 0.39/0.64 ( % 0.39/0.64 (declare-sort $$unsorted 0) % 0.39/0.64 (declare-const tptp.emptyset $$unsorted) % 0.39/0.64 (declare-const tptp.inCongP Bool) % 0.39/0.64 (declare-const tptp.exuI3 Bool) % 0.39/0.64 (declare-const tptp.exuI1 Bool) % 0.39/0.64 (declare-const tptp.set2prop (-> $$unsorted Bool)) % 0.39/0.64 (declare-const tptp.quantDeMorgan3 Bool) % 0.39/0.64 (declare-const tptp.quantDeMorgan2 Bool) % 0.39/0.64 (declare-const tptp.quantDeMorgan1 Bool) % 0.39/0.64 (declare-const tptp.vacuousDall Bool) % 0.39/0.64 (declare-const tptp.emptyE1 Bool) % 0.39/0.64 (declare-const tptp.upairsetIR Bool) % 0.39/0.64 (declare-const tptp.emptysetE Bool) % 0.39/0.64 (declare-const tptp.setadjoinIL Bool) % 0.39/0.64 (declare-const tptp.prop2setE Bool) % 0.39/0.64 (declare-const tptp.prop2set (-> Bool $$unsorted)) % 0.39/0.64 (declare-const tptp.dsetconstrI Bool) % 0.39/0.64 (declare-const tptp.setext Bool) % 0.39/0.64 (declare-const tptp.nonemptyImpWitness Bool) % 0.39/0.64 (declare-const tptp.descr (-> (-> $$unsorted Bool) $$unsorted)) % 0.39/0.64 (declare-const tptp.wellorderingAx Bool) % 0.39/0.64 (declare-const tptp.replAx Bool) % 0.39/0.64 (declare-const tptp.upairsetE Bool) % 0.39/0.64 (declare-const tptp.dsetconstrEL Bool) % 0.39/0.64 (declare-const tptp.prop2setI Bool) % 0.39/0.64 (declare-const tptp.emptyinPowerset Bool) % 0.39/0.64 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.39/0.64 (declare-const tptp.setextAx Bool) % 0.39/0.64 (declare-const tptp.setadjoinOr Bool) % 0.39/0.64 (declare-const tptp.uniqinunit Bool) % 0.39/0.64 (declare-const tptp.foundationAx Bool) % 0.39/0.64 (declare-const tptp.emptysetimpfalse Bool) % 0.39/0.64 (declare-const tptp.notinemptyset Bool) % 0.39/0.64 (declare-const tptp.setadjoinIR Bool) % 0.39/0.64 (declare-const tptp.exuE2 Bool) % 0.39/0.64 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.64 (declare-const tptp.notdallE Bool) % 0.39/0.64 (declare-const tptp.dsetconstrER Bool) % 0.39/0.64 (declare-const tptp.emptyInPowerset Bool) % 0.39/0.64 (declare-const tptp.setadjoinAx Bool) % 0.39/0.64 (declare-const tptp.nonemptyE1 Bool) % 0.39/0.64 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.39/0.64 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.39/0.64 (declare-const tptp.powersetAx Bool) % 0.39/0.64 (declare-const tptp.prop2set2propI Bool) % 0.39/0.64 (declare-const tptp.powersetE Bool) % 0.39/0.64 (declare-const tptp.omegaSAx Bool) % 0.39/0.64 (declare-const tptp.descrp Bool) % 0.39/0.64 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.39/0.64 (declare-const tptp.omega0Ax Bool) % 0.39/0.64 (declare-const tptp.setoftrueEq Bool) % 0.39/0.64 (declare-const tptp.setunionAx Bool) % 0.39/0.64 (declare-const tptp.omega $$unsorted) % 0.39/0.64 (declare-const tptp.omegaIndAx Bool) % 0.39/0.64 (declare-const tptp.quantDeMorgan4 Bool) % 0.39/0.64 (declare-const tptp.powersetI Bool) % 0.39/0.64 (declare-const tptp.exuE3e Bool) % 0.39/0.64 (declare-const tptp.emptyI Bool) % 0.39/0.64 (declare-const tptp.noeltsimpempty Bool) % 0.39/0.64 (declare-const tptp.eqinunit Bool) % 0.39/0.64 (declare-const tptp.upairsetIL Bool) % 0.39/0.64 (declare-const tptp.nonemptyI Bool) % 0.39/0.64 (declare-const tptp.emptysetAx Bool) % 0.39/0.64 (declare-const tptp.nonemptyI1 Bool) % 0.39/0.64 (declare-const tptp.emptyinunitempty Bool) % 0.39/0.64 (declare-const tptp.setadjoinE Bool) % 0.39/0.64 (declare-const tptp.notdexE Bool) % 0.39/0.64 (declare-const tptp.setunionI Bool) % 0.39/0.64 (declare-const tptp.exuE1 Bool) % 0.39/0.64 (declare-const tptp.setunionE Bool) % 0.39/0.64 (declare-const tptp.exuI2 Bool) % 0.39/0.64 (declare-const tptp.subPowSU Bool) % 0.39/0.64 (declare-const tptp.notinsingleton Bool) % 0.39/0.64 (declare-const tptp.setbeta Bool) % 0.39/0.64 (declare-const tptp.singletonsswitch Bool) % 0.39/0.64 (define tptp.exu () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xphi" (-> $$unsorted Bool)))) (lambda (@list _let_3) (exists (@list _let_2) (and (_ _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (= _let_2 _let_1)))))))))) % 0.39/0.64 (define tptp.nonempty () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (not (= _let_1 tptp.emptyset))))) % 0.39/0.64 (define @t1 () (@var "B" $$unsorted)) % 0.39/0.64 (define @t2 () (@var "A" $$unsorted)) % 0.39/0.64 (define @t3 () (= @t2 @t1)) % 0.39/0.64 (define @t4 () (@var "Xx" $$unsorted)) % 0.39/0.64 (define @t5 () (_ tptp.in @t4)) % 0.39/0.64 (define @t6 () (_ @t5 @t1)) % 0.39/0.64 (define @t7 () (_ @t5 @t2)) % 0.39/0.64 (define @t8 () (@list @t4)) % 0.39/0.64 (define @t9 () (@list @t2 @t1)) % 0.39/0.64 (define @t10 () (_ @t5 tptp.emptyset)) % 0.39/0.64 (define @t11 () (forall @t8 (not @t10))) % 0.39/0.64 (define @t12 () (@var "Xy" $$unsorted)) % 0.39/0.64 (define @t13 () (_ tptp.in @t12)) % 0.39/0.64 (define @t14 () (_ @t13 @t2)) % 0.39/0.64 (define @t15 () (= @t12 @t4)) % 0.39/0.64 (define @t16 () (or @t15 @t14)) % 0.39/0.64 (define @t17 () (_ tptp.setadjoin @t4)) % 0.39/0.64 (define @t18 () (_ @t13 (_ @t17 @t2))) % 0.39/0.64 (define @t19 () (@list @t4 @t2 @t12)) % 0.39/0.64 (define @t20 () (=> @t6 @t7)) % 0.39/0.64 (define @t21 () (forall @t8 @t20)) % 0.39/0.64 (define @t22 () (_ tptp.powerset @t2)) % 0.39/0.64 (define @t23 () (_ tptp.in @t1)) % 0.39/0.64 (define @t24 () (_ @t23 @t22)) % 0.39/0.64 (define @t25 () (_ @t23 @t2)) % 0.39/0.64 (define @t26 () (@list @t1)) % 0.39/0.64 (define @t27 () (_ tptp.setunion @t2)) % 0.39/0.64 (define @t28 () (_ @t5 @t27)) % 0.39/0.64 (define @t29 () (@list @t2 @t4)) % 0.39/0.64 (define @t30 () (_ tptp.in tptp.emptyset)) % 0.39/0.64 (define @t31 () (_ tptp.in (_ @t17 @t4))) % 0.39/0.64 (define @t32 () (_ @t5 tptp.omega)) % 0.39/0.64 (define @t33 () (@list @t2)) % 0.39/0.64 (define @t34 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.39/0.64 (define @t35 () (@list @t12)) % 0.39/0.64 (define @t36 () (exists @t8 @t7)) % 0.39/0.64 (define @t37 () (@var "E" $$unsorted)) % 0.39/0.64 (define @t38 () (@var "D" $$unsorted)) % 0.39/0.64 (define @t39 () (_ @t13 @t38)) % 0.39/0.64 (define @t40 () (@var "C" $$unsorted)) % 0.39/0.64 (define @t41 () (_ @t13 @t40)) % 0.39/0.64 (define @t42 () (_ @t5 @t40)) % 0.39/0.64 (define @t43 () (_ (_ tptp.in @t38) @t1)) % 0.39/0.64 (define @t44 () (forall @t8 (=> @t42 @t7))) % 0.39/0.64 (define @t45 () (@list @t40)) % 0.39/0.64 (define @t46 () (_ @t5 @t38)) % 0.39/0.64 (define @t47 () (_ (_ tptp.in @t40) @t1)) % 0.39/0.64 (define @t48 () (= @t4 @t12)) % 0.39/0.64 (define @t49 () (@list @t4 @t12)) % 0.39/0.64 (define @t50 () (@var "Xphi" (-> $$unsorted Bool))) % 0.39/0.64 (define @t51 () (_ @t50 @t4)) % 0.39/0.64 (define @t52 () (lambda @t8 @t51)) % 0.39/0.64 (define @t53 () (_ tptp.exu @t52)) % 0.39/0.64 (define @t54 () (@list @t50)) % 0.39/0.64 (define @t55 () (_ @t50 @t12)) % 0.39/0.64 (define @t56 () (_ tptp.dsetconstr @t2)) % 0.39/0.64 (define @t57 () (_ @t56 (lambda @t35 @t55))) % 0.39/0.64 (define @t58 () (_ @t5 @t57)) % 0.39/0.64 (define @t59 () (@list @t2 @t50 @t4)) % 0.39/0.64 (define @t60 () (=> @t55 @t48)) % 0.39/0.64 (define @t61 () (exists @t8 (and @t51 (forall @t35 @t60)))) % 0.39/0.64 (define @t62 () (@var "Xphi" Bool)) % 0.39/0.64 (define @t63 () (_ tptp.prop2set @t62)) % 0.39/0.64 (define @t64 () (@list @t62)) % 0.39/0.64 (define @t65 () (exists @t8 @t51)) % 0.39/0.64 (define @t66 () (forall @t33 (=> (forall @t8 (not @t7)) (= @t2 tptp.emptyset)))) % 0.39/0.64 (define @t67 () (_ tptp.nonempty @t2)) % 0.39/0.64 (define @t68 () (forall @t33 (_ @t30 @t22))) % 0.39/0.64 (define @t69 () (exists @t8 (forall @t35 (= @t55 @t15)))) % 0.39/0.64 (define @t70 () (_ (_ tptp.setadjoin @t12) tptp.emptyset)) % 0.39/0.64 (define @t71 () (_ @t5 @t70)) % 0.39/0.64 (define @t72 () (_ @t13 (_ @t17 tptp.emptyset))) % 0.39/0.64 (define @t73 () (not @t48)) % 0.39/0.64 (define @t74 () (@var "Xz" $$unsorted)) % 0.39/0.64 (define @t75 () (_ @t17 @t70)) % 0.39/0.64 (define @t76 () (exists @t8 (and @t7 @t51))) % 0.39/0.64 (define @t77 () (@list @t2 @t50)) % 0.39/0.64 (define @t78 () (not @t51)) % 0.39/0.64 (define @t79 () (exists @t8 (and @t7 @t78))) % 0.39/0.64 (define @t80 () (not (forall @t8 (=> @t7 @t51)))) % 0.39/0.64 (define @t81 () (forall @t77 (=> @t80 @t79))) % 0.39/0.64 (define @t82 () (not @t76)) % 0.39/0.64 (define @t83 () (forall @t8 (=> @t7 @t78))) % 0.39/0.64 (define @t84 () (forall @t77 (=> @t82 @t83))) % 0.39/0.64 (define @t85 () (_ @t13 @t1)) % 0.39/0.64 (define @t86 () (= @t7 @t85)) % 0.39/0.64 (define @t87 () (forall @t49 (=> @t48 @t86))) % 0.39/0.64 (define @t88 () (=> @t3 @t87)) % 0.39/0.64 (define @t89 () (forall @t9 @t88)) % 0.39/0.64 (define @t90 () (=> tptp.inCongP @t89)) % 0.39/0.64 (define @t91 () (=> tptp.exuI2 @t90)) % 0.39/0.64 (define @t92 () (=> tptp.exuI3 @t91)) % 0.39/0.64 (define @t93 () (=> tptp.exuI1 @t92)) % 0.39/0.64 (define @t94 () (=> tptp.notdallE @t93)) % 0.39/0.64 (define @t95 () (=> tptp.notdexE @t94)) % 0.39/0.64 (define @t96 () (=> tptp.prop2set2propI @t95)) % 0.39/0.64 (define @t97 () (=> tptp.prop2setI @t96)) % 0.39/0.64 (define @t98 () (=> tptp.quantDeMorgan4 @t97)) % 0.39/0.64 (define @t99 () (=> tptp.quantDeMorgan3 @t98)) % 0.39/0.64 (define @t100 () (=> tptp.quantDeMorgan2 @t99)) % 0.39/0.64 (define @t101 () (=> tptp.quantDeMorgan1 @t100)) % 0.39/0.64 (define @t102 () (=> tptp.vacuousDall @t101)) % 0.39/0.64 (define @t103 () (=> tptp.emptyE1 @t102)) % 0.39/0.64 (define @t104 () (=> tptp.upairsetIR @t103)) % 0.39/0.64 (define @t105 () (=> tptp.upairsetIL @t104)) % 0.39/0.64 (define @t106 () (=> tptp.upairsetE @t105)) % 0.39/0.64 (define @t107 () (=> tptp.singletonsswitch @t106)) % 0.39/0.64 (define @t108 () (=> tptp.eqinunit @t107)) % 0.39/0.64 (define @t109 () (=> tptp.notinsingleton @t108)) % 0.39/0.64 (define @t110 () (=> tptp.uniqinunit @t109)) % 0.39/0.64 (define @t111 () (=> tptp.nonemptyImpWitness @t110)) % 0.39/0.64 (define @t112 () (=> tptp.exuE2 @t111)) % 0.39/0.64 (define @t113 () (=> tptp.subPowSU @t112)) % 0.39/0.64 (define @t114 () (=> tptp.setunionE @t113)) % 0.39/0.64 (define @t115 () (=> tptp.setunionI @t114)) % 0.39/0.64 (define @t116 () (=> tptp.powersetE @t115)) % 0.39/0.64 (define @t117 () (=> tptp.emptyInPowerset @t116)) % 0.39/0.64 (define @t118 () (=> tptp.emptyinPowerset @t117)) % 0.39/0.64 (define @t119 () (=> tptp.powersetI @t118)) % 0.39/0.64 (define @t120 () (=> tptp.setoftrueEq @t119)) % 0.39/0.64 (define @t121 () (=> tptp.setadjoinOr @t120)) % 0.39/0.64 (define @t122 () (=> tptp.setadjoinE @t121)) % 0.39/0.64 (define @t123 () (=> tptp.setadjoinIR @t122)) % 0.39/0.64 (define @t124 () (=> tptp.emptyinunitempty @t123)) % 0.39/0.64 (define @t125 () (=> tptp.setadjoinIL @t124)) % 0.39/0.64 (define @t126 () (=> tptp.nonemptyI1 @t125)) % 0.39/0.64 (define @t127 () (=> tptp.nonemptyI @t126)) % 0.39/0.64 (define @t128 () (=> tptp.nonemptyE1 @t127)) % 0.39/0.64 (define @t129 () (=> tptp.setbeta @t128)) % 0.39/0.64 (define @t130 () (=> tptp.noeltsimpempty @t129)) % 0.39/0.64 (define @t131 () (=> tptp.emptyI @t130)) % 0.39/0.64 (define @t132 () (=> tptp.setext @t131)) % 0.39/0.64 (define @t133 () (=> tptp.exuE3e @t132)) % 0.39/0.64 (define @t134 () (=> tptp.notinemptyset @t133)) % 0.39/0.64 (define @t135 () (=> tptp.emptysetimpfalse @t134)) % 0.39/0.64 (define @t136 () (=> tptp.emptysetE @t135)) % 0.39/0.64 (define @t137 () (=> tptp.prop2setE @t136)) % 0.39/0.64 (define @t138 () (=> tptp.exuE1 @t137)) % 0.39/0.64 (define @t139 () (=> tptp.dsetconstrER @t138)) % 0.39/0.64 (define @t140 () (=> tptp.dsetconstrEL @t139)) % 0.39/0.64 (define @t141 () (=> tptp.dsetconstrI @t140)) % 0.39/0.64 (define @t142 () (=> tptp.descrp @t141)) % 0.39/0.64 (define @t143 () (=> tptp.wellorderingAx @t142)) % 0.39/0.64 (define @t144 () (=> tptp.foundationAx @t143)) % 0.39/0.64 (define @t145 () (=> tptp.replAx @t144)) % 0.39/0.64 (define @t146 () (=> tptp.omegaIndAx @t145)) % 0.39/0.64 (define @t147 () (=> tptp.omegaSAx @t146)) % 0.39/0.64 (define @t148 () (=> tptp.omega0Ax @t147)) % 0.39/0.64 (define @t149 () (=> tptp.setunionAx @t148)) % 0.39/0.64 (define @t150 () (=> tptp.powersetAx @t149)) % 0.39/0.64 (define @t151 () (=> tptp.setadjoinAx @t150)) % 0.39/0.64 (define @t152 () (=> tptp.emptysetAx @t151)) % 0.39/0.64 (define @t153 () (=> tptp.setextAx @t152)) % 0.39/0.64 (define @t154 () (not @t153)) % 0.39/0.64 (define @t155 () (lambda @t54 @t61)) % 0.39/0.64 (define @t156 () (lambda @t8 (not (= @t4 tptp.emptyset)))) % 0.39/0.64 (define @t157 () (@var "BOUND_VARIABLE_9104" $$unsorted)) % 0.39/0.64 (define @t158 () (@list @t1 @t157)) % 0.39/0.64 (define @t159 () (tptp.in @t157 @t1)) % 0.39/0.64 (define @t160 () (not (= @t1 @t1))) % 0.39/0.64 (define @t161 () (or @t160 (= @t159 @t159))) % 0.39/0.64 (define @t162 () (= (tptp.in @t157 @t2) @t159)) % 0.39/0.64 (define @t163 () (not @t3)) % 0.39/0.64 (define @t164 () (or @t163 @t163 @t162)) % 0.39/0.64 (define @t165 () (or @t163 @t162)) % 0.39/0.65 (define @t166 () (forall @t33 @t165)) % 0.39/0.65 (define @t167 () (forall @t158 @t166)) % 0.39/0.65 (define @t168 () (forall (@list @t1 @t157 @t2) @t165)) % 0.39/0.65 (define @t169 () (forall (@list @t2 @t1 @t157) @t165)) % 0.39/0.65 (define @t170 () (@list @t157)) % 0.39/0.65 (define @t171 () (forall @t170 @t165)) % 0.39/0.65 (define @t172 () (forall @t170 @t162)) % 0.39/0.65 (define @t173 () (or @t163 @t172)) % 0.39/0.65 (define @t174 () (tptp.in @t12 @t1)) % 0.39/0.65 (define @t175 () (= (tptp.in @t12 @t2) @t174)) % 0.39/0.65 (define @t176 () (forall @t35 @t175)) % 0.39/0.65 (define @t177 () (not (= @t12 @t12))) % 0.39/0.65 (define @t178 () (or @t177 @t175)) % 0.39/0.65 (define @t179 () (tptp.in @t4 @t2)) % 0.39/0.65 (define @t180 () (= @t179 @t174)) % 0.39/0.65 (define @t181 () (or @t73 @t73 @t180)) % 0.39/0.65 (define @t182 () (or @t73 @t180)) % 0.39/0.65 (define @t183 () (forall @t8 @t182)) % 0.39/0.65 (define @t184 () (forall @t35 @t183)) % 0.39/0.65 (define @t185 () (forall (@list @t12 @t4) @t182)) % 0.39/0.65 (define @t186 () (or @t73 @t86)) % 0.39/0.65 (assume @p1 (= tptp.setextAx (forall @t9 (=> (forall @t8 (= @t7 @t6)) @t3)))) % 0.39/0.65 (assume @p2 (= tptp.emptysetAx @t11)) % 0.39/0.65 (assume @p3 (= tptp.setadjoinAx (forall @t19 (= @t18 @t16)))) % 0.39/0.65 (assume @p4 (= tptp.powersetAx (forall @t9 (= @t24 @t21)))) % 0.39/0.65 (assume @p5 (= tptp.setunionAx (forall @t29 (= @t28 (exists @t26 (and @t6 @t25)))))) % 0.39/0.65 (assume @p6 (= tptp.omega0Ax (_ @t30 tptp.omega))) % 0.39/0.65 (assume @p7 (= tptp.omegaSAx (forall @t8 (=> @t32 (_ @t31 tptp.omega))))) % 0.39/0.65 (assume @p8 (= tptp.omegaIndAx (forall @t33 (=> (and (_ @t30 @t2) (forall @t8 (=> (and @t32 @t7) (_ @t31 @t2)))) (forall @t8 (=> @t32 @t7)))))) % 0.39/0.65 (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)))))))))) % 0.39/0.65 (assume @p10 (= tptp.foundationAx (forall @t33 (=> @t36 (exists @t26 (and @t25 (not (exists @t8 (and @t6 @t7))))))))) % 0.39/0.65 (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))))))))))))) % 0.39/0.65 (assume @p12 (= tptp.descrp (forall @t54 (=> @t53 (_ @t50 (_ tptp.descr @t52)))))) % 0.39/0.65 (assume @p13 (= tptp.dsetconstrI (forall @t59 (=> @t7 (=> @t51 @t58))))) % 0.39/0.65 (assume @p14 (= tptp.dsetconstrEL (forall @t59 (=> @t58 @t7)))) % 0.39/0.65 (assume @p15 (= tptp.dsetconstrER (forall @t59 (=> @t58 @t51)))) % 0.39/0.65 (assume @p16 (= tptp.exuE1 (forall @t54 (=> @t53 @t61)))) % 0.39/0.65 (assume @p17 (= tptp.prop2setE (forall (@list @t62 @t4) (=> (_ @t5 @t63) @t62)))) % 0.39/0.65 (assume @p18 (= tptp.emptysetE (forall @t8 (=> @t10 (forall @t64 @t62))))) % 0.39/0.65 (assume @p19 (= tptp.emptysetimpfalse (forall @t8 (=> @t10 false)))) % 0.39/0.65 (assume @p20 (= tptp.notinemptyset @t11)) % 0.39/0.65 (assume @p21 (= tptp.exuE3e (forall @t54 (=> @t53 @t65)))) % 0.39/0.65 (assume @p22 (= tptp.setext (forall @t9 (=> (forall @t8 (=> @t7 @t6)) (=> @t21 @t3))))) % 0.39/0.65 (assume @p23 (= tptp.emptyI @t66)) % 0.39/0.65 (assume @p24 (= tptp.noeltsimpempty @t66)) % 0.39/0.65 (assume @p25 (= tptp.setbeta (forall @t59 (=> @t7 (= @t58 @t51))))) % 0.39/0.65 (assume @p26 (= tptp.nonemptyE1 (forall @t33 (=> @t67 @t36)))) % 0.39/0.65 (assume @p27 (= tptp.nonemptyI (forall @t59 (=> @t7 (=> @t51 (_ tptp.nonempty @t57)))))) % 0.39/0.65 (assume @p28 (= tptp.nonemptyI1 (forall @t33 (=> @t36 @t67)))) % 0.39/0.65 (assume @p29 (= tptp.setadjoinIL (forall @t49 (_ @t5 (_ @t17 @t12))))) % 0.39/0.65 (assume @p30 (= tptp.emptyinunitempty (_ @t30 (_ (_ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) % 0.39/0.65 (assume @p31 (= tptp.setadjoinIR (forall @t19 (=> @t14 @t18)))) % 0.39/0.65 (assume @p32 (= tptp.setadjoinE (forall @t19 (=> @t18 (forall @t64 (=> (=> @t15 @t62) (=> (=> @t14 @t62) @t62))))))) % 0.39/0.65 (assume @p33 (= tptp.setadjoinOr (forall @t19 (=> @t18 @t16)))) % 0.39/0.65 (assume @p34 (= tptp.setoftrueEq (forall @t33 (= (_ @t56 (lambda @t8 true)) @t2)))) % 0.39/0.65 (assume @p35 (= tptp.powersetI (forall @t9 (=> @t21 @t24)))) % 0.39/0.65 (assume @p36 (= tptp.emptyinPowerset @t68)) % 0.39/0.65 (assume @p37 (= tptp.emptyInPowerset @t68)) % 0.39/0.65 (assume @p38 (= tptp.powersetE (forall (@list @t2 @t1 @t4) (=> @t24 @t20)))) % 0.39/0.65 (assume @p39 (= tptp.setunionI (forall (@list @t2 @t4 @t1) (=> @t6 (=> @t25 @t28))))) % 0.39/0.65 (assume @p40 (= tptp.setunionE (forall @t29 (=> @t28 (forall @t64 (=> (forall @t26 (=> @t6 (=> @t25 @t62))) @t62)))))) % 0.39/0.65 (assume @p41 (= tptp.subPowSU (forall @t29 (=> @t7 (_ @t5 (_ tptp.powerset @t27)))))) % 0.39/0.65 (assume @p42 (= tptp.exuE2 (forall @t54 (=> @t53 @t69)))) % 0.39/0.65 (assume @p43 (= tptp.nonemptyImpWitness (forall @t33 (=> @t67 (exists @t8 (and @t7 true)))))) % 0.39/0.65 (assume @p44 (= tptp.uniqinunit (forall @t49 (=> @t71 @t48)))) % 0.39/0.65 (assume @p45 (= tptp.notinsingleton (forall @t49 (=> @t73 (not @t72))))) % 0.39/0.65 (assume @p46 (= tptp.eqinunit (forall @t49 (=> @t48 @t71)))) % 0.39/0.65 (assume @p47 (= tptp.singletonsswitch (forall @t49 (=> @t71 @t72)))) % 0.39/0.65 (assume @p48 (= tptp.upairsetE (forall (@list @t4 @t12 @t74) (=> (_ (_ tptp.in @t74) @t75) (or (= @t74 @t4) (= @t74 @t12)))))) % 0.39/0.65 (assume @p49 (= tptp.upairsetIL (forall @t49 (_ @t5 @t75)))) % 0.39/0.65 (assume @p50 (= tptp.upairsetIR (forall @t49 (_ @t13 @t75)))) % 0.39/0.65 (assume @p51 (= tptp.emptyE1 (forall @t77 (=> @t76 (=> (= (_ @t56 @t52) tptp.emptyset) false))))) % 0.39/0.65 (assume @p52 (= tptp.vacuousDall (forall (@list @t50 @t4) (=> @t10 @t51)))) % 0.39/0.65 (assume @p53 (= tptp.quantDeMorgan1 @t81)) % 0.39/0.65 (assume @p54 (= tptp.quantDeMorgan2 (forall @t77 (=> @t83 @t82)))) % 0.39/0.65 (assume @p55 (= tptp.quantDeMorgan3 @t84)) % 0.39/0.65 (assume @p56 (= tptp.quantDeMorgan4 (forall @t77 (=> @t79 @t80)))) % 0.39/0.65 (assume @p57 (= tptp.prop2setI (forall @t64 (=> @t62 (_ @t30 @t63))))) % 0.39/0.65 (assume @p58 (= tptp.prop2set2propI (forall @t64 (=> @t62 (_ tptp.set2prop @t63))))) % 0.39/0.65 (assume @p59 (= tptp.notdexE @t84)) % 0.39/0.65 (assume @p60 (= tptp.notdallE @t81)) % 0.39/0.65 (assume @p61 (= tptp.exuI1 (forall @t54 (=> @t61 @t53)))) % 0.39/0.65 (assume @p62 (= tptp.exuI3 (forall @t54 (=> @t65 (=> (forall @t49 (=> @t51 @t60)) @t53))))) % 0.39/0.65 (assume @p63 (= tptp.exuI2 (forall @t54 (=> @t69 @t53)))) % 0.39/0.65 (assume @p64 (= tptp.inCongP (forall @t9 (=> @t3 (forall @t49 (=> @t48 (=> @t7 @t85))))))) % 0.39/0.65 (assume @p65 @t154) % 0.39/0.65 (assume @p66 true) % 0.39/0.65 (step @p67 (= tptp.exu @t155) :rule refl :args (@t155)) % 0.39/0.65 (step @p68 (= tptp.nonempty @t156) :rule refl :args (@t156)) % 0.39/0.65 (step @p69 :rule evaluate :args ((not true))) % 0.39/0.65 (step @p70 :rule bool-impl-true1 :args (tptp.setextAx)) % 0.39/0.65 (step @p71 :rule bool-impl-true1 :args (tptp.emptysetAx)) % 0.39/0.65 (step @p72 :rule bool-impl-true1 :args (tptp.setadjoinAx)) % 0.39/0.65 (step @p73 :rule bool-impl-true1 :args (tptp.powersetAx)) % 0.39/0.65 (step @p74 :rule bool-impl-true1 :args (tptp.setunionAx)) % 0.39/0.65 (step @p75 :rule bool-impl-true1 :args (tptp.omega0Ax)) % 0.39/0.65 (step @p76 :rule bool-impl-true1 :args (tptp.omegaSAx)) % 0.39/0.65 (step @p77 :rule bool-impl-true1 :args (tptp.omegaIndAx)) % 0.39/0.65 (step @p78 :rule bool-impl-true1 :args (tptp.replAx)) % 0.39/0.65 (step @p79 :rule bool-impl-true1 :args (tptp.foundationAx)) % 0.39/0.65 (step @p80 :rule bool-impl-true1 :args (tptp.wellorderingAx)) % 0.39/0.65 (step @p81 :rule bool-impl-true1 :args (tptp.descrp)) % 0.39/0.65 (step @p82 :rule bool-impl-true1 :args (tptp.dsetconstrI)) % 0.39/0.65 (step @p83 :rule bool-impl-true1 :args (tptp.dsetconstrEL)) % 0.39/0.65 (step @p84 :rule bool-impl-true1 :args (tptp.dsetconstrER)) % 0.39/0.65 (step @p85 :rule bool-impl-true1 :args (tptp.exuE1)) % 0.39/0.65 (step @p86 :rule bool-impl-true1 :args (tptp.prop2setE)) % 0.39/0.65 (step @p87 :rule bool-impl-true1 :args (tptp.emptysetE)) % 0.39/0.65 (step @p88 :rule bool-impl-true1 :args (tptp.emptysetimpfalse)) % 0.39/0.65 (step @p89 :rule bool-impl-true1 :args (tptp.notinemptyset)) % 0.39/0.65 (step @p90 :rule bool-impl-true1 :args (tptp.exuE3e)) % 0.39/0.65 (step @p91 :rule bool-impl-true1 :args (tptp.setext)) % 0.39/0.65 (step @p92 :rule bool-impl-true1 :args (tptp.emptyI)) % 0.39/0.65 (step @p93 :rule bool-impl-true1 :args (tptp.noeltsimpempty)) % 0.39/0.65 (step @p94 :rule bool-impl-true1 :args (tptp.setbeta)) % 0.39/0.65 (step @p95 :rule bool-impl-true1 :args (tptp.nonemptyE1)) % 0.39/0.65 (step @p96 :rule bool-impl-true1 :args (tptp.nonemptyI)) % 0.39/0.65 (step @p97 :rule bool-impl-true1 :args (tptp.nonemptyI1)) % 0.39/0.65 (step @p98 :rule bool-impl-true1 :args (tptp.setadjoinIL)) % 0.39/0.65 (step @p99 :rule bool-impl-true1 :args (tptp.emptyinunitempty)) % 0.39/0.65 (step @p100 :rule bool-impl-true1 :args (tptp.setadjoinIR)) % 0.39/0.65 (step @p101 :rule bool-impl-true1 :args (tptp.setadjoinE)) % 0.39/0.65 (step @p102 :rule bool-impl-true1 :args (tptp.setadjoinOr)) % 0.39/0.65 (step @p103 :rule bool-impl-true1 :args (tptp.setoftrueEq)) % 0.39/0.65 (step @p104 :rule bool-impl-true1 :args (tptp.powersetI)) % 0.39/0.65 (step @p105 :rule bool-impl-true1 :args (tptp.emptyinPowerset)) % 0.39/0.65 (step @p106 :rule bool-impl-true1 :args (tptp.emptyInPowerset)) % 0.39/0.65 (step @p107 :rule bool-impl-true1 :args (tptp.powersetE)) % 0.39/0.65 (step @p108 :rule bool-impl-true1 :args (tptp.setunionI)) % 0.39/0.65 (step @p109 :rule bool-impl-true1 :args (tptp.setunionE)) % 0.39/0.65 (step @p110 :rule bool-impl-true1 :args (tptp.subPowSU)) % 0.39/0.65 (step @p111 :rule bool-impl-true1 :args (tptp.exuE2)) % 0.39/0.65 (step @p112 :rule bool-impl-true1 :args (tptp.nonemptyImpWitness)) % 0.39/0.65 (step @p113 :rule bool-impl-true1 :args (tptp.uniqinunit)) % 0.39/0.65 (step @p114 :rule bool-impl-true1 :args (tptp.notinsingleton)) % 0.39/0.65 (step @p115 :rule bool-impl-true1 :args (tptp.eqinunit)) % 0.39/0.65 (step @p116 :rule bool-impl-true1 :args (tptp.singletonsswitch)) % 0.39/0.65 (step @p117 :rule bool-impl-true1 :args (tptp.upairsetE)) % 0.39/0.65 (step @p118 :rule bool-impl-true1 :args (tptp.upairsetIL)) % 0.39/0.65 (step @p119 :rule bool-impl-true1 :args (tptp.upairsetIR)) % 0.39/0.65 (step @p120 :rule bool-impl-true1 :args (tptp.emptyE1)) % 0.39/0.65 (step @p121 :rule bool-impl-true1 :args (tptp.vacuousDall)) % 0.39/0.65 (step @p122 :rule bool-impl-true1 :args (tptp.quantDeMorgan1)) % 0.39/0.65 (step @p123 :rule bool-impl-true1 :args (tptp.quantDeMorgan2)) % 0.39/0.65 (step @p124 :rule bool-impl-true1 :args (tptp.quantDeMorgan3)) % 0.39/0.65 (step @p125 :rule bool-impl-true1 :args (tptp.quantDeMorgan4)) % 0.39/0.65 (step @p126 :rule bool-impl-true1 :args (tptp.prop2setI)) % 0.39/0.65 (step @p127 :rule bool-impl-true1 :args (tptp.prop2set2propI)) % 0.39/0.65 (step @p128 :rule bool-impl-true1 :args (tptp.notdexE)) % 0.39/0.65 (step @p129 :rule bool-impl-true1 :args (tptp.notdallE)) % 0.39/0.65 (step @p130 :rule bool-impl-true1 :args (tptp.exuI1)) % 0.39/0.65 (step @p131 :rule bool-impl-true1 :args (tptp.exuI3)) % 0.39/0.65 (step @p132 :rule bool-impl-true1 :args (tptp.exuI2)) % 0.39/0.65 (step @p133 :rule bool-impl-true1 :args (tptp.inCongP)) % 0.39/0.65 (step @p134 :rule quant-unused-vars :args ((= (forall @t158 true) true))) % 0.39/0.65 (step @p135 :rule evaluate :args ((or false true))) % 0.39/0.65 (step @p136 :rule eq-refl :args (@t159)) % 0.39/0.65 (step @p137 :rule eq-refl :args (@t1)) % 0.39/0.65 (step @p138 :rule cong :premises (@p137) :args (@t160)) % 0.39/0.65 (step @p139 :rule trans :premises (@p138 @p69)) % 0.39/0.65 (step @p140 :rule nary_cong :premises (@p139 @p136) :args (@t161)) % 0.39/0.65 (step @p141 :rule trans :premises (@p140 @p135)) % 0.39/0.65 (step @p142 :rule cong :premises (@p141) :args ((forall @t158 @t161))) % 0.39/0.65 (step @p143 :rule trans :premises (@p142 @p134)) % 0.39/0.65 (step @p144 :rule quant-var-elim-eq :args ((= (forall @t33 @t164) @t161))) % 0.39/0.65 (step @p145 :rule aci_norm :args ((= @t165 @t164))) % 0.39/0.65 (step @p146 :rule cong :premises (@p145) :args (@t166)) % 0.39/0.65 (step @p147 :rule trans :premises (@p146 @p144)) % 0.39/0.65 (step @p148 :rule cong :premises (@p147) :args (@t167)) % 0.39/0.65 (step @p149 :rule quant-merge-prenex :args ((= @t167 @t168))) % 0.39/0.65 (step @p150 :rule symm :premises (@p149)) % 0.39/0.65 (step @p151 :rule quant_var_reordering :args ((= @t169 @t168))) % 0.39/0.65 (step @p152 :rule trans :premises (@p151 @p150 @p148)) % 0.39/0.65 (step @p153 :rule trans :premises (@p152 @p143)) % 0.39/0.65 (step @p154 :rule quant-merge-prenex :args ((= (forall @t9 @t171) @t169))) % 0.39/0.65 (step @p155 :rule alpha_equiv :args (@t172 (@list @t157) (@list @t12))) % 0.39/0.65 (step @p156 :rule refl :args (@t163)) % 0.39/0.65 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t173)) % 0.39/0.65 (step @p158 :rule quant-miniscope-or :args ((= @t171 @t173))) % 0.39/0.65 (step @p159 :rule trans :premises (@p158 @p157)) % 0.39/0.65 (step @p160 :rule symm :premises (@p159)) % 0.39/0.65 (step @p161 :rule cong :premises (@p160) :args ((forall @t9 (or @t163 @t176)))) % 0.39/0.65 (step @p162 :rule trans :premises (@p161 @p154)) % 0.39/0.65 (step @p163 :rule trans :premises (@p162 @p153)) % 0.39/0.65 (step @p164 :rule bool-impl-elim :args (@t3 @t176)) % 0.39/0.65 (step @p165 :rule cong :premises (@p164) :args ((forall @t9 (=> @t3 @t176)))) % 0.39/0.65 (step @p166 :rule trans :premises (@p165 @p163)) % 0.39/0.65 (step @p167 :rule aci_norm :args ((= (or false @t175) @t175))) % 0.39/0.65 (step @p168 :rule refl :args (@t175)) % 0.39/0.65 (step @p169 :rule eq-refl :args (@t12)) % 0.39/0.65 (step @p170 :rule cong :premises (@p169) :args (@t177)) % 0.39/0.65 (step @p171 :rule trans :premises (@p170 @p69)) % 0.39/0.65 (step @p172 :rule nary_cong :premises (@p171 @p168) :args (@t178)) % 0.39/0.65 (step @p173 :rule trans :premises (@p172 @p167)) % 0.39/0.65 (step @p174 :rule cong :premises (@p173) :args ((forall @t35 @t178))) % 0.39/0.65 (step @p175 :rule quant-var-elim-eq :args ((= (forall @t8 @t181) @t178))) % 0.39/0.65 (step @p176 :rule aci_norm :args ((= @t182 @t181))) % 0.39/0.65 (step @p177 :rule cong :premises (@p176) :args (@t183)) % 0.39/0.65 (step @p178 :rule trans :premises (@p177 @p175)) % 0.39/0.65 (step @p179 :rule cong :premises (@p178) :args (@t184)) % 0.39/0.65 (step @p180 :rule quant-merge-prenex :args ((= @t184 @t185))) % 0.39/0.65 (step @p181 :rule symm :premises (@p180)) % 0.39/0.65 (step @p182 :rule quant_var_reordering :args ((= (forall @t49 @t182) @t185))) % 0.39/0.65 (step @p183 :rule trans :premises (@p182 @p181 @p179)) % 0.39/0.65 (step @p184 :rule trans :premises (@p183 @p174)) % 0.39/0.65 (step @p185 :rule refl :args (@t174)) % 0.39/0.65 (step @p186 :rule refl :args (@t85)) % 0.39/0.65 (step @p187 :rule cong :premises (@p186 @p185) :args ((= @t85 @t174))) % 0.39/0.65 (step @p188 :rule symm :premises (@p187)) % 0.39/0.65 (step @p189 :rule eq_resolve :premises (@p186 @p188)) % 0.39/0.65 (step @p190 :rule refl :args (@t179)) % 0.39/0.65 (step @p191 :rule refl :args (@t7)) % 0.39/0.65 (step @p192 :rule cong :premises (@p191 @p190) :args ((= @t7 @t179))) % 0.39/0.65 (step @p193 :rule symm :premises (@p192)) % 0.39/0.65 (step @p194 :rule eq_resolve :premises (@p191 @p193)) % 0.39/0.65 (step @p195 :rule cong :premises (@p194 @p189) :args (@t86)) % 0.39/0.65 (step @p196 :rule refl :args (@t73)) % 0.39/0.65 (step @p197 :rule nary_cong :premises (@p196 @p195) :args (@t186)) % 0.39/0.65 (step @p198 :rule cong :premises (@p197) :args ((forall @t49 @t186))) % 0.39/0.65 (step @p199 :rule trans :premises (@p198 @p184)) % 0.39/0.65 (step @p200 :rule bool-impl-elim :args (@t48 @t86)) % 0.39/0.65 (step @p201 :rule cong :premises (@p200) :args (@t87)) % 0.39/0.65 (step @p202 :rule trans :premises (@p201 @p199)) % 0.39/0.65 (step @p203 :rule refl :args (@t3)) % 0.39/0.65 (step @p204 :rule cong :premises (@p203 @p202) :args (@t88)) % 0.39/0.65 (step @p205 :rule cong :premises (@p204) :args (@t89)) % 0.39/0.65 (step @p206 :rule trans :premises (@p205 @p166)) % 0.39/0.65 (step @p207 :rule refl :args (tptp.inCongP)) % 0.39/0.65 (step @p208 :rule cong :premises (@p207 @p206) :args (@t90)) % 0.39/0.65 (step @p209 :rule trans :premises (@p208 @p133)) % 0.39/0.65 (step @p210 :rule refl :args (tptp.exuI2)) % 0.39/0.65 (step @p211 :rule cong :premises (@p210 @p209) :args (@t91)) % 0.39/0.65 (step @p212 :rule trans :premises (@p211 @p132)) % 0.39/0.65 (step @p213 :rule refl :args (tptp.exuI3)) % 0.39/0.65 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(step @p352 :rule cong :premises (@p351 @p350) :args (@t138)) % 0.39/0.65 (step @p353 :rule trans :premises (@p352 @p85)) % 0.39/0.65 (step @p354 :rule refl :args (tptp.dsetconstrER)) % 0.39/0.65 (step @p355 :rule cong :premises (@p354 @p353) :args (@t139)) % 0.39/0.65 (step @p356 :rule trans :premises (@p355 @p84)) % 0.39/0.65 (step @p357 :rule refl :args (tptp.dsetconstrEL)) % 0.39/0.65 (step @p358 :rule cong :premises (@p357 @p356) :args (@t140)) % 0.39/0.65 (step @p359 :rule trans :premises (@p358 @p83)) % 0.39/0.65 (step @p360 :rule refl :args (tptp.dsetconstrI)) % 0.39/0.65 (step @p361 :rule cong :premises (@p360 @p359) :args (@t141)) % 0.39/0.65 (step @p362 :rule trans :premises (@p361 @p82)) % 0.39/0.65 (step @p363 :rule refl :args (tptp.descrp)) % 0.39/0.65 (step @p364 :rule cong :premises (@p363 @p362) :args (@t142)) % 0.39/0.65 (step @p365 :rule trans :premises (@p364 @p81)) % 0.39/0.65 (step @p366 :rule refl :args (tptp.wellorderingAx)) % 0.39/0.65 (step @p367 :rule cong 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@p398 :rule trans :premises (@p397 @p70)) % 0.39/0.65 (step @p399 :rule cong :premises (@p398) :args (@t154)) % 0.39/0.65 (step @p400 :rule trans :premises (@p399 @p69)) % 0.39/0.65 (step @p401 false :rule eq_resolve :premises (@p65 @p400)) % 0.39/0.65 ) % 0.39/0.65 % SZS output end Proof % 0.39/0.65 % cvc5 exiting %------------------------------------------------------------------------------