%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU544^1 : 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 : n011.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 08:52:08 AM UTC 2026 % Result : Theorem 0.37s 0.63s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU544^1 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n011.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 17:40:50 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.52 %----Proving TH0 % 0.37/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.63 % SZS status Theorem % 0.37/0.63 % SZS output start Proof % 0.37/0.63 ( % 0.37/0.63 (declare-sort $$unsorted 0) % 0.37/0.63 (declare-const tptp.emptyset $$unsorted) % 0.37/0.63 (declare-const tptp.set2prop (-> $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.quantDeMorgan3 Bool) % 0.37/0.63 (declare-const tptp.quantDeMorgan2 Bool) % 0.37/0.63 (declare-const tptp.quantDeMorgan1 Bool) % 0.37/0.63 (declare-const tptp.vacuousDall Bool) % 0.37/0.63 (declare-const tptp.emptyE1 Bool) % 0.37/0.63 (declare-const tptp.upairsetIR Bool) % 0.37/0.63 (declare-const tptp.emptysetE Bool) % 0.37/0.63 (declare-const tptp.setadjoinIL Bool) % 0.37/0.63 (declare-const tptp.prop2setE Bool) % 0.37/0.63 (declare-const tptp.prop2set (-> Bool $$unsorted)) % 0.37/0.63 (declare-const tptp.dsetconstrI Bool) % 0.37/0.63 (declare-const tptp.setext Bool) % 0.37/0.63 (declare-const tptp.nonemptyImpWitness Bool) % 0.37/0.63 (declare-const tptp.descr (-> (-> $$unsorted Bool) $$unsorted)) % 0.37/0.63 (declare-const tptp.wellorderingAx Bool) % 0.37/0.63 (declare-const tptp.replAx Bool) % 0.37/0.63 (declare-const tptp.upairsetE Bool) % 0.37/0.63 (declare-const tptp.dsetconstrEL Bool) % 0.37/0.63 (declare-const tptp.prop2setI Bool) % 0.37/0.63 (declare-const tptp.emptyinPowerset Bool) % 0.37/0.63 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.63 (declare-const tptp.setextAx Bool) % 0.37/0.63 (declare-const tptp.setadjoinOr Bool) % 0.37/0.63 (declare-const tptp.uniqinunit Bool) % 0.37/0.63 (declare-const tptp.foundationAx Bool) % 0.37/0.63 (declare-const tptp.emptysetimpfalse Bool) % 0.37/0.63 (declare-const tptp.notinemptyset Bool) % 0.37/0.63 (declare-const tptp.setadjoinIR Bool) % 0.37/0.63 (declare-const tptp.exuE2 Bool) % 0.37/0.63 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.notdallE Bool) % 0.37/0.63 (declare-const tptp.dsetconstrER Bool) % 0.37/0.63 (declare-const tptp.emptyInPowerset Bool) % 0.37/0.63 (declare-const tptp.setadjoinAx Bool) % 0.37/0.63 (declare-const tptp.nonemptyE1 Bool) % 0.37/0.63 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.37/0.63 (declare-const tptp.powersetAx Bool) % 0.37/0.63 (declare-const tptp.prop2set2propI Bool) % 0.37/0.63 (declare-const tptp.powersetE Bool) % 0.37/0.63 (declare-const tptp.omegaSAx Bool) % 0.37/0.63 (declare-const tptp.descrp Bool) % 0.37/0.63 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.37/0.63 (declare-const tptp.omega0Ax Bool) % 0.37/0.63 (declare-const tptp.setoftrueEq Bool) % 0.37/0.63 (declare-const tptp.setunionAx Bool) % 0.37/0.63 (declare-const tptp.omega $$unsorted) % 0.37/0.63 (declare-const tptp.omegaIndAx Bool) % 0.37/0.63 (declare-const tptp.quantDeMorgan4 Bool) % 0.37/0.63 (declare-const tptp.powersetI Bool) % 0.37/0.63 (declare-const tptp.exuE3e Bool) % 0.37/0.63 (declare-const tptp.emptyI Bool) % 0.37/0.63 (declare-const tptp.noeltsimpempty Bool) % 0.37/0.63 (declare-const tptp.eqinunit Bool) % 0.37/0.63 (declare-const tptp.upairsetIL Bool) % 0.37/0.63 (declare-const tptp.nonemptyI Bool) % 0.37/0.63 (declare-const tptp.emptysetAx Bool) % 0.37/0.63 (declare-const tptp.nonemptyI1 Bool) % 0.37/0.63 (declare-const tptp.emptyinunitempty Bool) % 0.37/0.63 (declare-const tptp.setadjoinE Bool) % 0.37/0.63 (declare-const tptp.notdexE Bool) % 0.37/0.63 (declare-const tptp.setunionI Bool) % 0.37/0.63 (declare-const tptp.exuE1 Bool) % 0.37/0.63 (declare-const tptp.setunionE Bool) % 0.37/0.63 (declare-const tptp.subPowSU Bool) % 0.37/0.63 (declare-const tptp.notinsingleton Bool) % 0.37/0.63 (declare-const tptp.setbeta Bool) % 0.37/0.63 (declare-const tptp.singletonsswitch Bool) % 0.37/0.63 (define tptp.exu () (let ((_let_1 (@var "Xy" $$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)))))))))) % 0.37/0.63 (define tptp.nonempty () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (not (= _let_1 tptp.emptyset))))) % 0.37/0.63 (define @t1 () (@var "B" $$unsorted)) % 0.37/0.63 (define @t2 () (@var "A" $$unsorted)) % 0.37/0.63 (define @t3 () (= @t2 @t1)) % 0.37/0.63 (define @t4 () (@var "Xx" $$unsorted)) % 0.37/0.63 (define @t5 () (_ tptp.in @t4)) % 0.37/0.63 (define @t6 () (_ @t5 @t1)) % 0.37/0.63 (define @t7 () (_ @t5 @t2)) % 0.37/0.63 (define @t8 () (@list @t4)) % 0.37/0.63 (define @t9 () (@list @t2 @t1)) % 0.37/0.63 (define @t10 () (_ @t5 tptp.emptyset)) % 0.37/0.63 (define @t11 () (forall @t8 (not @t10))) % 0.37/0.63 (define @t12 () (@var "Xy" $$unsorted)) % 0.37/0.63 (define @t13 () (_ tptp.in @t12)) % 0.37/0.63 (define @t14 () (_ @t13 @t2)) % 0.37/0.63 (define @t15 () (= @t12 @t4)) % 0.37/0.63 (define @t16 () (or @t15 @t14)) % 0.37/0.63 (define @t17 () (_ tptp.setadjoin @t4)) % 0.37/0.63 (define @t18 () (_ @t13 (_ @t17 @t2))) % 0.37/0.63 (define @t19 () (@list @t4 @t2 @t12)) % 0.37/0.63 (define @t20 () (=> @t6 @t7)) % 0.37/0.63 (define @t21 () (forall @t8 @t20)) % 0.37/0.63 (define @t22 () (_ tptp.powerset @t2)) % 0.37/0.63 (define @t23 () (_ tptp.in @t1)) % 0.37/0.63 (define @t24 () (_ @t23 @t22)) % 0.37/0.63 (define @t25 () (_ @t23 @t2)) % 0.37/0.63 (define @t26 () (@list @t1)) % 0.37/0.63 (define @t27 () (_ tptp.setunion @t2)) % 0.37/0.63 (define @t28 () (_ @t5 @t27)) % 0.37/0.63 (define @t29 () (@list @t2 @t4)) % 0.37/0.63 (define @t30 () (_ tptp.in tptp.emptyset)) % 0.37/0.63 (define @t31 () (_ tptp.in (_ @t17 @t4))) % 0.37/0.63 (define @t32 () (_ @t5 tptp.omega)) % 0.37/0.63 (define @t33 () (@list @t2)) % 0.37/0.63 (define @t34 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.37/0.63 (define @t35 () (@list @t12)) % 0.37/0.63 (define @t36 () (exists @t8 @t7)) % 0.37/0.63 (define @t37 () (@var "E" $$unsorted)) % 0.37/0.63 (define @t38 () (@var "D" $$unsorted)) % 0.37/0.63 (define @t39 () (_ @t13 @t38)) % 0.37/0.63 (define @t40 () (@var "C" $$unsorted)) % 0.37/0.63 (define @t41 () (_ @t13 @t40)) % 0.37/0.63 (define @t42 () (_ @t5 @t40)) % 0.37/0.63 (define @t43 () (_ (_ tptp.in @t38) @t1)) % 0.37/0.63 (define @t44 () (forall @t8 (=> @t42 @t7))) % 0.37/0.63 (define @t45 () (@list @t40)) % 0.37/0.63 (define @t46 () (_ @t5 @t38)) % 0.37/0.63 (define @t47 () (_ (_ tptp.in @t40) @t1)) % 0.37/0.63 (define @t48 () (= @t4 @t12)) % 0.37/0.63 (define @t49 () (@list @t4 @t12)) % 0.37/0.63 (define @t50 () (@var "Xphi" (-> $$unsorted Bool))) % 0.37/0.63 (define @t51 () (_ @t50 @t4)) % 0.37/0.63 (define @t52 () (lambda @t8 @t51)) % 0.37/0.63 (define @t53 () (_ tptp.exu @t52)) % 0.37/0.63 (define @t54 () (@list @t50)) % 0.37/0.63 (define @t55 () (_ @t50 @t12)) % 0.37/0.63 (define @t56 () (_ tptp.dsetconstr @t2)) % 0.37/0.63 (define @t57 () (_ @t56 (lambda @t35 @t55))) % 0.37/0.63 (define @t58 () (_ @t5 @t57)) % 0.37/0.63 (define @t59 () (@list @t2 @t50 @t4)) % 0.37/0.63 (define @t60 () (forall @t35 (=> @t55 @t48))) % 0.37/0.63 (define @t61 () (and @t51 @t60)) % 0.37/0.63 (define @t62 () (exists @t8 @t61)) % 0.37/0.63 (define @t63 () (@var "Xphi" Bool)) % 0.37/0.63 (define @t64 () (_ tptp.prop2set @t63)) % 0.37/0.63 (define @t65 () (@list @t63)) % 0.37/0.63 (define @t66 () (forall @t33 (=> (forall @t8 (not @t7)) (= @t2 tptp.emptyset)))) % 0.37/0.63 (define @t67 () (_ tptp.nonempty @t2)) % 0.37/0.63 (define @t68 () (forall @t33 (_ @t30 @t22))) % 0.37/0.63 (define @t69 () (_ (_ tptp.setadjoin @t12) tptp.emptyset)) % 0.37/0.63 (define @t70 () (_ @t5 @t69)) % 0.37/0.63 (define @t71 () (_ @t13 (_ @t17 tptp.emptyset))) % 0.37/0.63 (define @t72 () (@var "Xz" $$unsorted)) % 0.37/0.63 (define @t73 () (_ @t17 @t69)) % 0.37/0.63 (define @t74 () (exists @t8 (and @t7 @t51))) % 0.37/0.63 (define @t75 () (@list @t2 @t50)) % 0.37/0.63 (define @t76 () (not @t51)) % 0.37/0.63 (define @t77 () (exists @t8 (and @t7 @t76))) % 0.37/0.63 (define @t78 () (not (forall @t8 (=> @t7 @t51)))) % 0.37/0.63 (define @t79 () (forall @t75 (=> @t78 @t77))) % 0.37/0.63 (define @t80 () (not @t74)) % 0.37/0.63 (define @t81 () (forall @t8 (=> @t7 @t76))) % 0.37/0.63 (define @t82 () (forall @t75 (=> @t80 @t81))) % 0.37/0.63 (define @t83 () (=> @t62 @t53)) % 0.37/0.63 (define @t84 () (forall @t54 @t83)) % 0.37/0.63 (define @t85 () (=> tptp.notdallE @t84)) % 0.37/0.63 (define @t86 () (=> tptp.notdexE @t85)) % 0.37/0.63 (define @t87 () (=> tptp.prop2set2propI @t86)) % 0.37/0.63 (define @t88 () (=> tptp.prop2setI @t87)) % 0.37/0.63 (define @t89 () (=> tptp.quantDeMorgan4 @t88)) % 0.37/0.63 (define @t90 () (=> tptp.quantDeMorgan3 @t89)) % 0.37/0.63 (define @t91 () (=> tptp.quantDeMorgan2 @t90)) % 0.37/0.63 (define @t92 () (=> tptp.quantDeMorgan1 @t91)) % 0.37/0.63 (define @t93 () (=> tptp.vacuousDall @t92)) % 0.37/0.63 (define @t94 () (=> tptp.emptyE1 @t93)) % 0.37/0.63 (define @t95 () (=> tptp.upairsetIR @t94)) % 0.37/0.63 (define @t96 () (=> tptp.upairsetIL @t95)) % 0.37/0.63 (define @t97 () (=> tptp.upairsetE @t96)) % 0.37/0.63 (define @t98 () (=> tptp.singletonsswitch @t97)) % 0.37/0.63 (define @t99 () (=> tptp.eqinunit @t98)) % 0.37/0.63 (define @t100 () (=> tptp.notinsingleton @t99)) % 0.37/0.63 (define @t101 () (=> tptp.uniqinunit @t100)) % 0.37/0.63 (define @t102 () (=> tptp.nonemptyImpWitness @t101)) % 0.37/0.63 (define @t103 () (=> tptp.exuE2 @t102)) % 0.37/0.63 (define @t104 () (=> tptp.subPowSU @t103)) % 0.37/0.63 (define @t105 () (=> tptp.setunionE @t104)) % 0.37/0.63 (define @t106 () (=> tptp.setunionI @t105)) % 0.37/0.63 (define @t107 () (=> tptp.powersetE @t106)) % 0.37/0.63 (define @t108 () (=> tptp.emptyInPowerset @t107)) % 0.37/0.63 (define @t109 () (=> tptp.emptyinPowerset @t108)) % 0.37/0.63 (define @t110 () (=> tptp.powersetI @t109)) % 0.37/0.63 (define @t111 () (=> tptp.setoftrueEq @t110)) % 0.37/0.63 (define @t112 () (=> tptp.setadjoinOr @t111)) % 0.37/0.63 (define @t113 () (=> tptp.setadjoinE @t112)) % 0.37/0.63 (define @t114 () (=> tptp.setadjoinIR @t113)) % 0.37/0.63 (define @t115 () (=> tptp.emptyinunitempty @t114)) % 0.37/0.63 (define @t116 () (=> tptp.setadjoinIL @t115)) % 0.37/0.63 (define @t117 () (=> tptp.nonemptyI1 @t116)) % 0.37/0.63 (define @t118 () (=> tptp.nonemptyI @t117)) % 0.37/0.63 (define @t119 () (=> tptp.nonemptyE1 @t118)) % 0.37/0.63 (define @t120 () (=> tptp.setbeta @t119)) % 0.37/0.63 (define @t121 () (=> tptp.noeltsimpempty @t120)) % 0.37/0.63 (define @t122 () (=> tptp.emptyI @t121)) % 0.37/0.63 (define @t123 () (=> tptp.setext @t122)) % 0.37/0.63 (define @t124 () (=> tptp.exuE3e @t123)) % 0.37/0.63 (define @t125 () (=> tptp.notinemptyset @t124)) % 0.37/0.63 (define @t126 () (=> tptp.emptysetimpfalse @t125)) % 0.37/0.63 (define @t127 () (=> tptp.emptysetE @t126)) % 0.37/0.63 (define @t128 () (=> tptp.prop2setE @t127)) % 0.37/0.63 (define @t129 () (=> tptp.exuE1 @t128)) % 0.37/0.63 (define @t130 () (=> tptp.dsetconstrER @t129)) % 0.37/0.63 (define @t131 () (=> tptp.dsetconstrEL @t130)) % 0.37/0.63 (define @t132 () (=> tptp.dsetconstrI @t131)) % 0.37/0.63 (define @t133 () (=> tptp.descrp @t132)) % 0.37/0.63 (define @t134 () (=> tptp.wellorderingAx @t133)) % 0.37/0.63 (define @t135 () (=> tptp.foundationAx @t134)) % 0.37/0.63 (define @t136 () (=> tptp.replAx @t135)) % 0.37/0.63 (define @t137 () (=> tptp.omegaIndAx @t136)) % 0.37/0.63 (define @t138 () (=> tptp.omegaSAx @t137)) % 0.37/0.63 (define @t139 () (=> tptp.omega0Ax @t138)) % 0.37/0.63 (define @t140 () (=> tptp.setunionAx @t139)) % 0.37/0.63 (define @t141 () (=> tptp.powersetAx @t140)) % 0.37/0.63 (define @t142 () (=> tptp.setadjoinAx @t141)) % 0.37/0.63 (define @t143 () (=> tptp.emptysetAx @t142)) % 0.37/0.63 (define @t144 () (=> tptp.setextAx @t143)) % 0.37/0.63 (define @t145 () (not @t144)) % 0.37/0.63 (define @t146 () (lambda @t54 @t62)) % 0.37/0.63 (define @t147 () (lambda @t8 (not (= @t4 tptp.emptyset)))) % 0.37/0.63 (define @t148 () (_ @t50 @t12)) % 0.37/0.63 (define @t149 () (forall @t35 (or (not @t148) @t48))) % 0.37/0.63 (define @t150 () (not @t149)) % 0.37/0.63 (define @t151 () (_ @t50 @t4)) % 0.37/0.63 (define @t152 () (forall @t8 (or (not @t151) @t150))) % 0.37/0.63 (define @t153 () (not @t152)) % 0.37/0.63 (define @t154 () (or @t76 @t150)) % 0.37/0.63 (define @t155 () (not @t55)) % 0.37/0.63 (define @t156 () (or @t155 @t48)) % 0.37/0.63 (define @t157 () (_ @t52 @t12)) % 0.37/0.63 (define @t158 () (not @t157)) % 0.37/0.63 (define @t159 () (or @t158 @t48)) % 0.37/0.63 (define @t160 () (forall @t35 @t159)) % 0.37/0.63 (define @t161 () (not @t160)) % 0.37/0.63 (define @t162 () (_ @t52 @t4)) % 0.37/0.63 (define @t163 () (not @t162)) % 0.37/0.63 (define @t164 () (or @t163 @t161)) % 0.37/0.63 (define @t165 () (forall @t8 @t164)) % 0.37/0.63 (define @t166 () (not @t165)) % 0.37/0.63 (define @t167 () (_ (lambda @t54 @t153) @t52)) % 0.37/0.63 (define @t168 () (and @t51 @t149)) % 0.37/0.63 (define @t169 () (forall @t8 (not @t168))) % 0.37/0.63 (define @t170 () (not @t169)) % 0.37/0.63 (define @t171 () (=> @t62 @t167)) % 0.37/0.63 (define @t172 () (forall @t54 @t171)) % 0.37/0.63 (define @t173 () (=> tptp.notdallE @t172)) % 0.37/0.63 (define @t174 () (=> tptp.notdexE @t173)) % 0.37/0.63 (define @t175 () (=> tptp.prop2set2propI @t174)) % 0.37/0.63 (define @t176 () (=> tptp.prop2setI @t175)) % 0.37/0.63 (define @t177 () (=> tptp.quantDeMorgan4 @t176)) % 0.37/0.63 (define @t178 () (=> tptp.quantDeMorgan3 @t177)) % 0.37/0.63 (define @t179 () (=> tptp.quantDeMorgan2 @t178)) % 0.37/0.63 (define @t180 () (=> tptp.quantDeMorgan1 @t179)) % 0.37/0.63 (define @t181 () (=> tptp.vacuousDall @t180)) % 0.37/0.63 (define @t182 () (=> tptp.emptyE1 @t181)) % 0.37/0.63 (define @t183 () (=> tptp.upairsetIR @t182)) % 0.37/0.63 (define @t184 () (=> tptp.upairsetIL @t183)) % 0.37/0.63 (define @t185 () (=> tptp.upairsetE @t184)) % 0.37/0.63 (define @t186 () (=> tptp.singletonsswitch @t185)) % 0.37/0.63 (define @t187 () (=> tptp.eqinunit @t186)) % 0.37/0.63 (define @t188 () (=> tptp.notinsingleton @t187)) % 0.37/0.63 (define @t189 () (=> tptp.uniqinunit @t188)) % 0.37/0.63 (define @t190 () (=> tptp.nonemptyImpWitness @t189)) % 0.37/0.63 (define @t191 () (=> tptp.exuE2 @t190)) % 0.37/0.63 (define @t192 () (=> tptp.subPowSU @t191)) % 0.37/0.63 (define @t193 () (=> tptp.setunionE @t192)) % 0.37/0.63 (define @t194 () (=> tptp.setunionI @t193)) % 0.37/0.63 (define @t195 () (=> tptp.powersetE @t194)) % 0.37/0.63 (define @t196 () (=> tptp.emptyInPowerset @t195)) % 0.37/0.63 (define @t197 () (=> tptp.emptyinPowerset @t196)) % 0.37/0.63 (define @t198 () (=> tptp.powersetI @t197)) % 0.37/0.63 (define @t199 () (=> tptp.setoftrueEq @t198)) % 0.37/0.63 (define @t200 () (=> tptp.setadjoinOr @t199)) % 0.37/0.63 (define @t201 () (=> tptp.setadjoinE @t200)) % 0.37/0.63 (define @t202 () (=> tptp.setadjoinIR @t201)) % 0.37/0.63 (define @t203 () (=> tptp.emptyinunitempty @t202)) % 0.37/0.63 (define @t204 () (=> tptp.setadjoinIL @t203)) % 0.37/0.63 (define @t205 () (=> tptp.nonemptyI1 @t204)) % 0.37/0.63 (define @t206 () (=> tptp.nonemptyI @t205)) % 0.37/0.63 (define @t207 () (=> tptp.nonemptyE1 @t206)) % 0.37/0.63 (define @t208 () (=> tptp.setbeta @t207)) % 0.37/0.63 (define @t209 () (=> tptp.noeltsimpempty @t208)) % 0.37/0.63 (define @t210 () (=> tptp.emptyI @t209)) % 0.37/0.63 (define @t211 () (=> tptp.setext @t210)) % 0.37/0.63 (define @t212 () (=> tptp.exuE3e @t211)) % 0.37/0.63 (define @t213 () (=> tptp.notinemptyset @t212)) % 0.37/0.63 (define @t214 () (=> tptp.emptysetimpfalse @t213)) % 0.37/0.63 (define @t215 () (=> tptp.emptysetE @t214)) % 0.37/0.63 (define @t216 () (=> tptp.prop2setE @t215)) % 0.37/0.63 (define @t217 () (=> tptp.exuE1 @t216)) % 0.37/0.63 (define @t218 () (=> tptp.dsetconstrER @t217)) % 0.37/0.63 (define @t219 () (=> tptp.dsetconstrEL @t218)) % 0.37/0.63 (define @t220 () (=> tptp.dsetconstrI @t219)) % 0.37/0.63 (define @t221 () (=> tptp.descrp @t220)) % 0.37/0.63 (define @t222 () (=> tptp.wellorderingAx @t221)) % 0.37/0.63 (define @t223 () (=> tptp.foundationAx @t222)) % 0.37/0.63 (define @t224 () (=> tptp.replAx @t223)) % 0.37/0.63 (define @t225 () (=> tptp.omegaIndAx @t224)) % 0.37/0.63 (define @t226 () (=> tptp.omegaSAx @t225)) % 0.37/0.63 (define @t227 () (=> tptp.omega0Ax @t226)) % 0.37/0.63 (define @t228 () (=> tptp.setunionAx @t227)) % 0.37/0.63 (define @t229 () (=> tptp.powersetAx @t228)) % 0.37/0.63 (define @t230 () (=> tptp.setadjoinAx @t229)) % 0.37/0.63 (define @t231 () (=> tptp.emptysetAx @t230)) % 0.37/0.63 (define @t232 () (=> tptp.setextAx @t231)) % 0.37/0.63 (assume @p1 (= tptp.setextAx (forall @t9 (=> (forall @t8 (= @t7 @t6)) @t3)))) % 0.37/0.63 (assume @p2 (= tptp.emptysetAx @t11)) % 0.37/0.63 (assume @p3 (= tptp.setadjoinAx (forall @t19 (= @t18 @t16)))) % 0.37/0.63 (assume @p4 (= tptp.powersetAx (forall @t9 (= @t24 @t21)))) % 0.37/0.63 (assume @p5 (= tptp.setunionAx (forall @t29 (= @t28 (exists @t26 (and @t6 @t25)))))) % 0.37/0.63 (assume @p6 (= tptp.omega0Ax (_ @t30 tptp.omega))) % 0.37/0.63 (assume @p7 (= tptp.omegaSAx (forall @t8 (=> @t32 (_ @t31 tptp.omega))))) % 0.37/0.63 (assume @p8 (= tptp.omegaIndAx (forall @t33 (=> (and (_ @t30 @t2) (forall @t8 (=> (and @t32 @t7) (_ @t31 @t2)))) (forall @t8 (=> @t32 @t7)))))) % 0.37/0.63 (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)))))))))) % 0.37/0.63 (assume @p10 (= tptp.foundationAx (forall @t33 (=> @t36 (exists @t26 (and @t25 (not (exists @t8 (and @t6 @t7))))))))) % 0.37/0.63 (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))))))))))))) % 0.37/0.63 (assume @p12 (= tptp.descrp (forall @t54 (=> @t53 (_ @t50 (_ tptp.descr @t52)))))) % 0.37/0.63 (assume @p13 (= tptp.dsetconstrI (forall @t59 (=> @t7 (=> @t51 @t58))))) % 0.37/0.63 (assume @p14 (= tptp.dsetconstrEL (forall @t59 (=> @t58 @t7)))) % 0.37/0.63 (assume @p15 (= tptp.dsetconstrER (forall @t59 (=> @t58 @t51)))) % 0.37/0.63 (assume @p16 (= tptp.exuE1 (forall @t54 (=> @t53 @t62)))) % 0.37/0.63 (assume @p17 (= tptp.prop2setE (forall (@list @t63 @t4) (=> (_ @t5 @t64) @t63)))) % 0.37/0.63 (assume @p18 (= tptp.emptysetE (forall @t8 (=> @t10 (forall @t65 @t63))))) % 0.37/0.63 (assume @p19 (= tptp.emptysetimpfalse (forall @t8 (=> @t10 false)))) % 0.37/0.63 (assume @p20 (= tptp.notinemptyset @t11)) % 0.37/0.63 (assume @p21 (= tptp.exuE3e (forall @t54 (=> @t53 (exists @t8 @t51))))) % 0.37/0.63 (assume @p22 (= tptp.setext (forall @t9 (=> (forall @t8 (=> @t7 @t6)) (=> @t21 @t3))))) % 0.37/0.63 (assume @p23 (= tptp.emptyI @t66)) % 0.37/0.63 (assume @p24 (= tptp.noeltsimpempty @t66)) % 0.37/0.63 (assume @p25 (= tptp.setbeta (forall @t59 (=> @t7 (= @t58 @t51))))) % 0.37/0.63 (assume @p26 (= tptp.nonemptyE1 (forall @t33 (=> @t67 @t36)))) % 0.37/0.63 (assume @p27 (= tptp.nonemptyI (forall @t59 (=> @t7 (=> @t51 (_ tptp.nonempty @t57)))))) % 0.37/0.63 (assume @p28 (= tptp.nonemptyI1 (forall @t33 (=> @t36 @t67)))) % 0.37/0.63 (assume @p29 (= tptp.setadjoinIL (forall @t49 (_ @t5 (_ @t17 @t12))))) % 0.37/0.63 (assume @p30 (= tptp.emptyinunitempty (_ @t30 (_ (_ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) % 0.37/0.63 (assume @p31 (= tptp.setadjoinIR (forall @t19 (=> @t14 @t18)))) % 0.37/0.63 (assume @p32 (= tptp.setadjoinE (forall @t19 (=> @t18 (forall @t65 (=> (=> @t15 @t63) (=> (=> @t14 @t63) @t63))))))) % 0.37/0.63 (assume @p33 (= tptp.setadjoinOr (forall @t19 (=> @t18 @t16)))) % 0.37/0.63 (assume @p34 (= tptp.setoftrueEq (forall @t33 (= (_ @t56 (lambda @t8 true)) @t2)))) % 0.37/0.63 (assume @p35 (= tptp.powersetI (forall @t9 (=> @t21 @t24)))) % 0.37/0.63 (assume @p36 (= tptp.emptyinPowerset @t68)) % 0.37/0.63 (assume @p37 (= tptp.emptyInPowerset @t68)) % 0.37/0.63 (assume @p38 (= tptp.powersetE (forall (@list @t2 @t1 @t4) (=> @t24 @t20)))) % 0.37/0.63 (assume @p39 (= tptp.setunionI (forall (@list @t2 @t4 @t1) (=> @t6 (=> @t25 @t28))))) % 0.37/0.63 (assume @p40 (= tptp.setunionE (forall @t29 (=> @t28 (forall @t65 (=> (forall @t26 (=> @t6 (=> @t25 @t63))) @t63)))))) % 0.37/0.63 (assume @p41 (= tptp.subPowSU (forall @t29 (=> @t7 (_ @t5 (_ tptp.powerset @t27)))))) % 0.37/0.63 (assume @p42 (= tptp.exuE2 (forall @t54 (=> @t53 (exists @t8 (forall @t35 (= @t55 @t15))))))) % 0.37/0.63 (assume @p43 (= tptp.nonemptyImpWitness (forall @t33 (=> @t67 (exists @t8 (and @t7 true)))))) % 0.37/0.63 (assume @p44 (= tptp.uniqinunit (forall @t49 (=> @t70 @t48)))) % 0.37/0.63 (assume @p45 (= tptp.notinsingleton (forall @t49 (=> (not @t48) (not @t71))))) % 0.37/0.63 (assume @p46 (= tptp.eqinunit (forall @t49 (=> @t48 @t70)))) % 0.37/0.63 (assume @p47 (= tptp.singletonsswitch (forall @t49 (=> @t70 @t71)))) % 0.37/0.63 (assume @p48 (= tptp.upairsetE (forall (@list @t4 @t12 @t72) (=> (_ (_ tptp.in @t72) @t73) (or (= @t72 @t4) (= @t72 @t12)))))) % 0.37/0.63 (assume @p49 (= tptp.upairsetIL (forall @t49 (_ @t5 @t73)))) % 0.37/0.63 (assume @p50 (= tptp.upairsetIR (forall @t49 (_ @t13 @t73)))) % 0.37/0.63 (assume @p51 (= tptp.emptyE1 (forall @t75 (=> @t74 (=> (= (_ @t56 @t52) tptp.emptyset) false))))) % 0.37/0.63 (assume @p52 (= tptp.vacuousDall (forall (@list @t50 @t4) (=> @t10 @t51)))) % 0.37/0.63 (assume @p53 (= tptp.quantDeMorgan1 @t79)) % 0.37/0.63 (assume @p54 (= tptp.quantDeMorgan2 (forall @t75 (=> @t81 @t80)))) % 0.37/0.63 (assume @p55 (= tptp.quantDeMorgan3 @t82)) % 0.37/0.63 (assume @p56 (= tptp.quantDeMorgan4 (forall @t75 (=> @t77 @t78)))) % 0.37/0.63 (assume @p57 (= tptp.prop2setI (forall @t65 (=> @t63 (_ @t30 @t64))))) % 0.37/0.63 (assume @p58 (= tptp.prop2set2propI (forall @t65 (=> @t63 (_ tptp.set2prop @t64))))) % 0.37/0.63 (assume @p59 (= tptp.notdexE @t82)) % 0.37/0.63 (assume @p60 (= tptp.notdallE @t79)) % 0.37/0.63 (assume @p61 @t145) % 0.37/0.63 (assume @p62 true) % 0.37/0.63 (step @p63 (= tptp.exu @t146) :rule refl :args (@t146)) % 0.37/0.63 (step @p64 (= tptp.nonempty @t147) :rule refl :args (@t147)) % 0.37/0.63 (step @p65 :rule evaluate :args ((not true))) % 0.37/0.63 (step @p66 :rule bool-impl-true1 :args (tptp.setextAx)) % 0.37/0.63 (step @p67 :rule bool-impl-true1 :args (tptp.emptysetAx)) % 0.37/0.63 (step @p68 :rule bool-impl-true1 :args (tptp.setadjoinAx)) % 0.37/0.63 (step @p69 :rule bool-impl-true1 :args (tptp.powersetAx)) % 0.37/0.63 (step @p70 :rule bool-impl-true1 :args (tptp.setunionAx)) % 0.37/0.63 (step @p71 :rule bool-impl-true1 :args (tptp.omega0Ax)) % 0.37/0.63 (step @p72 :rule bool-impl-true1 :args (tptp.omegaSAx)) % 0.37/0.63 (step @p73 :rule bool-impl-true1 :args (tptp.omegaIndAx)) % 0.37/0.63 (step @p74 :rule bool-impl-true1 :args (tptp.replAx)) % 0.37/0.63 (step @p75 :rule bool-impl-true1 :args (tptp.foundationAx)) % 0.37/0.63 (step @p76 :rule bool-impl-true1 :args (tptp.wellorderingAx)) % 0.37/0.63 (step @p77 :rule bool-impl-true1 :args (tptp.descrp)) % 0.37/0.63 (step @p78 :rule bool-impl-true1 :args (tptp.dsetconstrI)) % 0.37/0.63 (step @p79 :rule bool-impl-true1 :args (tptp.dsetconstrEL)) % 0.37/0.63 (step @p80 :rule bool-impl-true1 :args (tptp.dsetconstrER)) % 0.37/0.63 (step @p81 :rule bool-impl-true1 :args (tptp.exuE1)) % 0.37/0.63 (step @p82 :rule bool-impl-true1 :args (tptp.prop2setE)) % 0.37/0.63 (step @p83 :rule bool-impl-true1 :args (tptp.emptysetE)) % 0.37/0.63 (step @p84 :rule bool-impl-true1 :args (tptp.emptysetimpfalse)) % 0.37/0.63 (step @p85 :rule bool-impl-true1 :args (tptp.notinemptyset)) % 0.37/0.63 (step @p86 :rule bool-impl-true1 :args (tptp.exuE3e)) % 0.37/0.63 (step @p87 :rule bool-impl-true1 :args (tptp.setext)) % 0.37/0.63 (step @p88 :rule bool-impl-true1 :args (tptp.emptyI)) % 0.37/0.63 (step @p89 :rule bool-impl-true1 :args (tptp.noeltsimpempty)) % 0.37/0.63 (step @p90 :rule bool-impl-true1 :args (tptp.setbeta)) % 0.37/0.63 (step @p91 :rule bool-impl-true1 :args (tptp.nonemptyE1)) % 0.37/0.63 (step @p92 :rule bool-impl-true1 :args (tptp.nonemptyI)) % 0.37/0.63 (step @p93 :rule bool-impl-true1 :args (tptp.nonemptyI1)) % 0.37/0.63 (step @p94 :rule bool-impl-true1 :args (tptp.setadjoinIL)) % 0.37/0.63 (step @p95 :rule bool-impl-true1 :args (tptp.emptyinunitempty)) % 0.37/0.63 (step @p96 :rule bool-impl-true1 :args (tptp.setadjoinIR)) % 0.37/0.63 (step @p97 :rule bool-impl-true1 :args (tptp.setadjoinE)) % 0.37/0.63 (step @p98 :rule bool-impl-true1 :args (tptp.setadjoinOr)) % 0.37/0.63 (step @p99 :rule bool-impl-true1 :args (tptp.setoftrueEq)) % 0.37/0.63 (step @p100 :rule bool-impl-true1 :args (tptp.powersetI)) % 0.37/0.63 (step @p101 :rule bool-impl-true1 :args (tptp.emptyinPowerset)) % 0.37/0.63 (step @p102 :rule bool-impl-true1 :args (tptp.emptyInPowerset)) % 0.37/0.63 (step @p103 :rule bool-impl-true1 :args (tptp.powersetE)) % 0.37/0.63 (step @p104 :rule bool-impl-true1 :args (tptp.setunionI)) % 0.37/0.63 (step @p105 :rule bool-impl-true1 :args (tptp.setunionE)) % 0.37/0.63 (step @p106 :rule bool-impl-true1 :args (tptp.subPowSU)) % 0.37/0.63 (step @p107 :rule bool-impl-true1 :args (tptp.exuE2)) % 0.37/0.63 (step @p108 :rule bool-impl-true1 :args (tptp.nonemptyImpWitness)) % 0.37/0.63 (step @p109 :rule bool-impl-true1 :args (tptp.uniqinunit)) % 0.37/0.63 (step @p110 :rule bool-impl-true1 :args (tptp.notinsingleton)) % 0.37/0.63 (step @p111 :rule bool-impl-true1 :args (tptp.eqinunit)) % 0.37/0.63 (step @p112 :rule bool-impl-true1 :args (tptp.singletonsswitch)) % 0.37/0.63 (step @p113 :rule bool-impl-true1 :args (tptp.upairsetE)) % 0.37/0.63 (step @p114 :rule bool-impl-true1 :args (tptp.upairsetIL)) % 0.37/0.63 (step @p115 :rule bool-impl-true1 :args (tptp.upairsetIR)) % 0.37/0.63 (step @p116 :rule bool-impl-true1 :args (tptp.emptyE1)) % 0.37/0.63 (step @p117 :rule bool-impl-true1 :args (tptp.vacuousDall)) % 0.37/0.63 (step @p118 :rule bool-impl-true1 :args (tptp.quantDeMorgan1)) % 0.37/0.63 (step @p119 :rule bool-impl-true1 :args (tptp.quantDeMorgan2)) % 0.37/0.63 (step @p120 :rule bool-impl-true1 :args (tptp.quantDeMorgan3)) % 0.37/0.63 (step @p121 :rule bool-impl-true1 :args (tptp.quantDeMorgan4)) % 0.37/0.63 (step @p122 :rule bool-impl-true1 :args (tptp.prop2setI)) % 0.37/0.63 (step @p123 :rule bool-impl-true1 :args (tptp.prop2set2propI)) % 0.37/0.63 (step @p124 :rule bool-impl-true1 :args (tptp.notdexE)) % 0.37/0.63 (step @p125 :rule bool-impl-true1 :args (tptp.notdallE)) % 0.37/0.63 (step @p126 :rule quant-unused-vars :args ((= (forall @t54 true) true))) % 0.37/0.63 (step @p127 :rule bool-or-taut :args (false @t152 false false)) % 0.37/0.63 (step @p128 :rule refl :args (@t153)) % 0.37/0.63 (step @p129 :rule bool-double-not-elim :args (@t152)) % 0.37/0.63 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((or (not @t153) @t153))) % 0.37/0.63 (step @p131 :rule bool-impl-elim :args (@t153 @t153)) % 0.37/0.63 (step @p132 :rule trans :premises (@p131 @p130)) % 0.37/0.63 (step @p133 :rule trans :premises (@p132 @p127)) % 0.37/0.63 (step @p134 :rule cong :premises (@p133) :args ((forall @t54 (=> @t153 @t153)))) % 0.37/0.63 (step @p135 :rule trans :premises (@p134 @p126)) % 0.37/0.63 (step @p136 :rule refl :args (@t150)) % 0.37/0.63 (step @p137 :rule refl :args (@t151)) % 0.37/0.63 (step @p138 :rule refl :args (@t51)) % 0.37/0.63 (step @p139 :rule cong :premises (@p138 @p137) :args ((= @t51 @t151))) % 0.37/0.63 (step @p140 :rule symm :premises (@p139)) % 0.37/0.63 (step @p141 :rule eq_resolve :premises (@p138 @p140)) % 0.37/0.63 (step @p142 :rule cong :premises (@p141) :args (@t76)) % 0.37/0.63 (step @p143 :rule nary_cong :premises (@p142 @p136) :args (@t154)) % 0.37/0.63 (step @p144 :rule cong :premises (@p143) :args ((forall @t8 @t154))) % 0.37/0.63 (step @p145 :rule refl :args (@t48)) % 0.37/0.63 (step @p146 :rule refl :args (@t148)) % 0.37/0.63 (step @p147 :rule refl :args (@t55)) % 0.37/0.63 (step @p148 :rule cong :premises (@p147 @p146) :args ((= @t55 @t148))) % 0.37/0.63 (step @p149 :rule symm :premises (@p148)) % 0.37/0.63 (step @p150 :rule eq_resolve :premises (@p147 @p149)) % 0.37/0.63 (step @p151 :rule cong :premises (@p150) :args (@t155)) % 0.37/0.63 (step @p152 :rule nary_cong :premises (@p151 @p145) :args (@t156)) % 0.37/0.63 (step @p153 :rule cong :premises (@p152) :args ((forall @t35 @t156))) % 0.37/0.63 (step @p154 :rule refl :args (@t48)) % 0.37/0.63 (step @p155 :rule beta-reduce :args ((= @t157 @t55))) % 0.37/0.63 (step @p156 :rule cong :premises (@p155) :args (@t158)) % 0.37/0.63 (step @p157 :rule nary_cong :premises (@p156 @p154) :args (@t159)) % 0.37/0.63 (step @p158 :rule cong :premises (@p157) :args (@t160)) % 0.37/0.63 (step @p159 :rule trans :premises (@p158 @p153)) % 0.37/0.63 (step @p160 :rule cong :premises (@p159) :args (@t161)) % 0.37/0.63 (step @p161 :rule beta-reduce :args ((= @t162 @t51))) % 0.37/0.63 (step @p162 :rule cong :premises (@p161) :args (@t163)) % 0.37/0.63 (step @p163 :rule nary_cong :premises (@p162 @p160) :args (@t164)) % 0.37/0.63 (step @p164 :rule cong :premises (@p163) :args (@t165)) % 0.37/0.63 (step @p165 :rule trans :premises (@p164 @p144)) % 0.37/0.63 (step @p166 :rule cong :premises (@p165) :args (@t166)) % 0.37/0.63 (step @p167 :rule beta-reduce :args ((= @t167 @t166))) % 0.37/0.63 (step @p168 :rule trans :premises (@p167 @p166)) % 0.37/0.63 (step @p169 :rule bool-and-de-morgan :args (@t51 @t149 true)) % 0.37/0.63 (step @p170 :rule cong :premises (@p169) :args (@t169)) % 0.37/0.63 (step @p171 :rule trans :premises (@p170 @p144)) % 0.37/0.63 (step @p172 :rule cong :premises (@p171) :args (@t170)) % 0.37/0.63 (step @p173 :rule exists-elim :args ((= (exists @t8 @t168) @t170))) % 0.37/0.63 (step @p174 :rule trans :premises (@p173 @p172)) % 0.37/0.63 (step @p175 :rule bool-impl-elim :args (@t55 @t48)) % 0.37/0.63 (step @p176 :rule cong :premises (@p175) :args (@t60)) % 0.37/0.63 (step @p177 :rule trans :premises (@p176 @p153)) % 0.37/0.63 (step @p178 :rule refl :args (@t51)) 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:args (@t129)) % 0.37/0.63 (step @p419 :rule cong :premises (@p320 @p418) :args (@t130)) % 0.37/0.63 (step @p420 :rule cong :premises (@p323 @p419) :args (@t131)) % 0.37/0.63 (step @p421 :rule cong :premises (@p326 @p420) :args (@t132)) % 0.37/0.63 (step @p422 :rule cong :premises (@p329 @p421) :args (@t133)) % 0.37/0.63 (step @p423 :rule cong :premises (@p332 @p422) :args (@t134)) % 0.37/0.63 (step @p424 :rule cong :premises (@p335 @p423) :args (@t135)) % 0.37/0.63 (step @p425 :rule cong :premises (@p338 @p424) :args (@t136)) % 0.37/0.63 (step @p426 :rule cong :premises (@p341 @p425) :args (@t137)) % 0.37/0.63 (step @p427 :rule cong :premises (@p344 @p426) :args (@t138)) % 0.37/0.63 (step @p428 :rule cong :premises (@p347 @p427) :args (@t139)) % 0.37/0.63 (step @p429 :rule cong :premises (@p350 @p428) :args (@t140)) % 0.37/0.63 (step @p430 :rule cong :premises (@p353 @p429) :args (@t141)) % 0.37/0.63 (step @p431 :rule cong :premises (@p356 @p430) :args (@t142)) % 0.37/0.63 (step @p432 :rule cong :premises (@p359 @p431) :args (@t143)) % 0.37/0.63 (step @p433 :rule cong :premises (@p362 @p432) :args (@t144)) % 0.37/0.63 (step @p434 :rule cong :premises (@p433) :args (@t145)) % 0.37/0.63 (step @p435 :rule trans :premises (@p434 @p366)) % 0.37/0.63 (step @p436 false :rule eq_resolve :premises (@p61 @p435)) % 0.37/0.63 ) % 0.37/0.63 % SZS output end Proof % 0.37/0.63 % cvc5 exiting %------------------------------------------------------------------------------