%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU526^1 : 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 : n016.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 08:52:03 AM UTC 2026 % Result : Theorem 0.38s 0.61s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU526^1 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n016.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:41:09 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.51 %----Proving TH0 % 0.38/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.61 % SZS status Theorem % 0.38/0.61 % SZS output start Proof % 0.38/0.61 ( % 0.38/0.61 (declare-sort $$unsorted 0) % 0.38/0.61 (declare-const tptp.emptyset $$unsorted) % 0.38/0.61 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.38/0.61 (declare-const tptp.subPowSU Bool) % 0.38/0.61 (declare-const tptp.setunionE Bool) % 0.38/0.61 (declare-const tptp.setunionI Bool) % 0.38/0.61 (declare-const tptp.powersetE Bool) % 0.38/0.61 (declare-const tptp.emptyInPowerset Bool) % 0.38/0.61 (declare-const tptp.setoftrueEq Bool) % 0.38/0.61 (declare-const tptp.setadjoinOr Bool) % 0.38/0.61 (declare-const tptp.setadjoinE Bool) % 0.38/0.61 (declare-const tptp.emptyinunitempty Bool) % 0.38/0.61 (declare-const tptp.nonemptyI1 Bool) % 0.38/0.61 (declare-const tptp.nonemptyI Bool) % 0.38/0.61 (declare-const tptp.nonemptyE1 Bool) % 0.38/0.61 (declare-const tptp.noeltsimpempty Bool) % 0.38/0.61 (declare-const tptp.emptyI Bool) % 0.38/0.61 (declare-const tptp.omegaIndAx Bool) % 0.38/0.61 (declare-const tptp.omega0Ax Bool) % 0.38/0.61 (declare-const tptp.setadjoinIL Bool) % 0.38/0.61 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.powersetAx Bool) % 0.38/0.61 (declare-const tptp.omegaSAx Bool) % 0.38/0.61 (declare-const tptp.setext Bool) % 0.38/0.61 (declare-const tptp.setadjoinAx Bool) % 0.38/0.61 (declare-const tptp.powersetI Bool) % 0.38/0.61 (declare-const tptp.setbeta Bool) % 0.38/0.61 (declare-const tptp.dsetconstrER Bool) % 0.38/0.61 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.exuE2 Bool) % 0.38/0.61 (declare-const tptp.setadjoinIR Bool) % 0.38/0.61 (declare-const tptp.notinemptyset Bool) % 0.38/0.61 (declare-const tptp.foundationAx Bool) % 0.38/0.61 (declare-const tptp.setextAx Bool) % 0.38/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.emptysetAx Bool) % 0.38/0.61 (declare-const tptp.dsetconstrEL Bool) % 0.38/0.61 (declare-const tptp.replAx Bool) % 0.38/0.61 (declare-const tptp.emptysetimpfalse Bool) % 0.38/0.61 (declare-const tptp.wellorderingAx Bool) % 0.38/0.61 (declare-const tptp.descr (-> (-> $$unsorted Bool) $$unsorted)) % 0.38/0.61 (declare-const tptp.emptyinPowerset Bool) % 0.38/0.61 (declare-const tptp.exuE1 Bool) % 0.38/0.61 (declare-const tptp.descrp Bool) % 0.38/0.61 (declare-const tptp.dsetconstrI Bool) % 0.38/0.61 (declare-const tptp.omega $$unsorted) % 0.38/0.61 (declare-const tptp.exuE3e Bool) % 0.38/0.61 (declare-const tptp.prop2setE Bool) % 0.38/0.61 (declare-const tptp.setunionAx Bool) % 0.38/0.61 (declare-const tptp.emptysetE Bool) % 0.38/0.61 (define tptp.exu () (let ((_let_1 (@var "Xy" $$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)))))))))) % 0.38/0.61 (define tptp.prop2set () (let ((_let_1 (@var "Xphi" Bool))) (lambda (@list _let_1) (_ (_ tptp.dsetconstr (_ tptp.powerset tptp.emptyset)) (lambda (@list (@var "Xx" $$unsorted)) _let_1))))) % 0.38/0.61 (define tptp.nonempty () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (not (= _let_1 tptp.emptyset))))) % 0.38/0.61 (define @t1 () (@var "B" $$unsorted)) % 0.38/0.61 (define @t2 () (@var "A" $$unsorted)) % 0.38/0.61 (define @t3 () (= @t2 @t1)) % 0.38/0.61 (define @t4 () (@var "Xx" $$unsorted)) % 0.38/0.61 (define @t5 () (_ tptp.in @t4)) % 0.38/0.61 (define @t6 () (_ @t5 @t1)) % 0.38/0.61 (define @t7 () (_ @t5 @t2)) % 0.38/0.61 (define @t8 () (@list @t4)) % 0.38/0.61 (define @t9 () (@list @t2 @t1)) % 0.38/0.61 (define @t10 () (_ @t5 tptp.emptyset)) % 0.38/0.61 (define @t11 () (forall @t8 (not @t10))) % 0.38/0.61 (define @t12 () (@var "Xy" $$unsorted)) % 0.38/0.61 (define @t13 () (_ tptp.in @t12)) % 0.38/0.61 (define @t14 () (_ @t13 @t2)) % 0.38/0.61 (define @t15 () (= @t12 @t4)) % 0.38/0.61 (define @t16 () (or @t15 @t14)) % 0.38/0.61 (define @t17 () (_ tptp.setadjoin @t4)) % 0.38/0.61 (define @t18 () (_ @t13 (_ @t17 @t2))) % 0.38/0.61 (define @t19 () (@list @t4 @t2 @t12)) % 0.38/0.61 (define @t20 () (=> @t6 @t7)) % 0.38/0.61 (define @t21 () (forall @t8 @t20)) % 0.38/0.61 (define @t22 () (_ tptp.powerset @t2)) % 0.38/0.61 (define @t23 () (_ tptp.in @t1)) % 0.38/0.61 (define @t24 () (_ @t23 @t22)) % 0.38/0.61 (define @t25 () (_ @t23 @t2)) % 0.38/0.61 (define @t26 () (@list @t1)) % 0.38/0.61 (define @t27 () (_ tptp.setunion @t2)) % 0.38/0.61 (define @t28 () (_ @t5 @t27)) % 0.38/0.61 (define @t29 () (@list @t2 @t4)) % 0.38/0.61 (define @t30 () (_ tptp.in tptp.emptyset)) % 0.38/0.61 (define @t31 () (_ tptp.in (_ @t17 @t4))) % 0.38/0.61 (define @t32 () (_ @t5 tptp.omega)) % 0.38/0.61 (define @t33 () (@list @t2)) % 0.38/0.61 (define @t34 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.38/0.61 (define @t35 () (@list @t12)) % 0.38/0.61 (define @t36 () (exists @t8 @t7)) % 0.38/0.61 (define @t37 () (@var "E" $$unsorted)) % 0.38/0.61 (define @t38 () (@var "D" $$unsorted)) % 0.38/0.61 (define @t39 () (_ @t13 @t38)) % 0.38/0.61 (define @t40 () (@var "C" $$unsorted)) % 0.38/0.61 (define @t41 () (_ @t13 @t40)) % 0.38/0.61 (define @t42 () (_ @t5 @t40)) % 0.38/0.61 (define @t43 () (_ (_ tptp.in @t38) @t1)) % 0.38/0.61 (define @t44 () (forall @t8 (=> @t42 @t7))) % 0.38/0.61 (define @t45 () (@list @t40)) % 0.38/0.61 (define @t46 () (_ @t5 @t38)) % 0.38/0.61 (define @t47 () (_ (_ tptp.in @t40) @t1)) % 0.38/0.61 (define @t48 () (= @t4 @t12)) % 0.38/0.61 (define @t49 () (@list @t4 @t12)) % 0.38/0.61 (define @t50 () (@var "Xphi" (-> $$unsorted Bool))) % 0.38/0.61 (define @t51 () (_ @t50 @t4)) % 0.38/0.61 (define @t52 () (lambda @t8 @t51)) % 0.38/0.61 (define @t53 () (_ tptp.exu @t52)) % 0.38/0.61 (define @t54 () (@list @t50)) % 0.38/0.61 (define @t55 () (_ @t50 @t12)) % 0.38/0.61 (define @t56 () (_ tptp.dsetconstr @t2)) % 0.38/0.61 (define @t57 () (_ @t56 (lambda @t35 @t55))) % 0.38/0.61 (define @t58 () (_ @t5 @t57)) % 0.38/0.61 (define @t59 () (@list @t2 @t50 @t4)) % 0.38/0.61 (define @t60 () (exists @t8 (and @t51 (forall @t35 (=> @t55 @t48))))) % 0.38/0.61 (define @t61 () (@var "Xphi" Bool)) % 0.38/0.61 (define @t62 () (@list @t61)) % 0.38/0.61 (define @t63 () (= @t2 tptp.emptyset)) % 0.38/0.61 (define @t64 () (not @t7)) % 0.38/0.61 (define @t65 () (forall @t8 @t64)) % 0.38/0.61 (define @t66 () (forall @t33 (=> @t65 @t63))) % 0.38/0.61 (define @t67 () (_ tptp.nonempty @t2)) % 0.38/0.61 (define @t68 () (=> @t67 @t36)) % 0.38/0.61 (define @t69 () (forall @t33 @t68)) % 0.38/0.61 (define @t70 () (= tptp.nonemptyE1 @t69)) % 0.38/0.61 (define @t71 () (forall @t33 (_ @t30 @t22))) % 0.38/0.61 (define @t72 () (and @t7 true)) % 0.38/0.61 (define @t73 () (exists @t8 @t72)) % 0.38/0.61 (define @t74 () (=> @t67 @t73)) % 0.38/0.61 (define @t75 () (forall @t33 @t74)) % 0.38/0.61 (define @t76 () (=> tptp.exuE2 @t75)) % 0.38/0.61 (define @t77 () (=> tptp.subPowSU @t76)) % 0.38/0.61 (define @t78 () (=> tptp.setunionE @t77)) % 0.38/0.61 (define @t79 () (=> tptp.setunionI @t78)) % 0.38/0.61 (define @t80 () (=> tptp.powersetE @t79)) % 0.38/0.61 (define @t81 () (=> tptp.emptyInPowerset @t80)) % 0.38/0.61 (define @t82 () (=> tptp.emptyinPowerset @t81)) % 0.38/0.61 (define @t83 () (=> tptp.powersetI @t82)) % 0.38/0.61 (define @t84 () (=> tptp.setoftrueEq @t83)) % 0.38/0.61 (define @t85 () (=> tptp.setadjoinOr @t84)) % 0.38/0.61 (define @t86 () (=> tptp.setadjoinE @t85)) % 0.38/0.61 (define @t87 () (=> tptp.setadjoinIR @t86)) % 0.38/0.61 (define @t88 () (=> tptp.emptyinunitempty @t87)) % 0.38/0.61 (define @t89 () (=> tptp.setadjoinIL @t88)) % 0.38/0.61 (define @t90 () (=> tptp.nonemptyI1 @t89)) % 0.38/0.61 (define @t91 () (=> tptp.nonemptyI @t90)) % 0.38/0.61 (define @t92 () (=> tptp.nonemptyE1 @t91)) % 0.38/0.61 (define @t93 () (=> tptp.setbeta @t92)) % 0.38/0.61 (define @t94 () (=> tptp.noeltsimpempty @t93)) % 0.38/0.61 (define @t95 () (=> tptp.emptyI @t94)) % 0.38/0.61 (define @t96 () (=> tptp.setext @t95)) % 0.38/0.61 (define @t97 () (=> tptp.exuE3e @t96)) % 0.38/0.61 (define @t98 () (=> tptp.notinemptyset @t97)) % 0.38/0.61 (define @t99 () (=> tptp.emptysetimpfalse @t98)) % 0.38/0.61 (define @t100 () (=> tptp.emptysetE @t99)) % 0.38/0.61 (define @t101 () (=> tptp.prop2setE @t100)) % 0.38/0.61 (define @t102 () (=> tptp.exuE1 @t101)) % 0.38/0.61 (define @t103 () (=> tptp.dsetconstrER @t102)) % 0.38/0.61 (define @t104 () (=> tptp.dsetconstrEL @t103)) % 0.38/0.61 (define @t105 () (=> tptp.dsetconstrI @t104)) % 0.38/0.61 (define @t106 () (=> tptp.descrp @t105)) % 0.38/0.61 (define @t107 () (=> tptp.wellorderingAx @t106)) % 0.38/0.61 (define @t108 () (=> tptp.foundationAx @t107)) % 0.38/0.61 (define @t109 () (=> tptp.replAx @t108)) % 0.38/0.61 (define @t110 () (=> tptp.omegaIndAx @t109)) % 0.38/0.61 (define @t111 () (=> tptp.omegaSAx @t110)) % 0.38/0.61 (define @t112 () (=> tptp.omega0Ax @t111)) % 0.38/0.61 (define @t113 () (=> tptp.setunionAx @t112)) % 0.38/0.61 (define @t114 () (=> tptp.powersetAx @t113)) % 0.38/0.61 (define @t115 () (=> tptp.setadjoinAx @t114)) % 0.38/0.61 (define @t116 () (=> tptp.emptysetAx @t115)) % 0.38/0.61 (define @t117 () (=> tptp.setextAx @t116)) % 0.38/0.61 (define @t118 () (not @t117)) % 0.38/0.61 (define @t119 () (lambda @t54 @t60)) % 0.38/0.61 (define @t120 () (lambda @t62 (_ (_ tptp.dsetconstr (_ tptp.powerset tptp.emptyset)) (lambda @t8 @t61)))) % 0.38/0.61 (define @t121 () (lambda @t8 (not (= @t4 tptp.emptyset)))) % 0.38/0.61 (define @t122 () (tptp.in @t4 @t2)) % 0.38/0.61 (define @t123 () (not (forall @t8 (not @t122)))) % 0.38/0.61 (define @t124 () (not @t63)) % 0.38/0.61 (define @t125 () (not @t65)) % 0.38/0.61 (define @t126 () (_ @t121 @t2)) % 0.38/0.61 (define @t127 () (=> @t126 @t73)) % 0.38/0.61 (define @t128 () (forall @t33 @t127)) % 0.38/0.61 (define @t129 () (=> tptp.exuE2 @t128)) % 0.38/0.61 (define @t130 () (=> tptp.subPowSU @t129)) % 0.38/0.61 (define @t131 () (=> tptp.setunionE @t130)) % 0.38/0.61 (define @t132 () (=> tptp.setunionI @t131)) % 0.38/0.61 (define @t133 () (=> tptp.powersetE @t132)) % 0.38/0.61 (define @t134 () (=> tptp.emptyInPowerset @t133)) % 0.38/0.61 (define @t135 () (=> tptp.emptyinPowerset @t134)) % 0.38/0.61 (define @t136 () (=> tptp.powersetI @t135)) % 0.38/0.61 (define @t137 () (=> tptp.setoftrueEq @t136)) % 0.38/0.61 (define @t138 () (=> tptp.setadjoinOr @t137)) % 0.38/0.61 (define @t139 () (=> tptp.setadjoinE @t138)) % 0.38/0.61 (define @t140 () (=> tptp.setadjoinIR @t139)) % 0.38/0.61 (define @t141 () (=> tptp.emptyinunitempty @t140)) % 0.38/0.61 (define @t142 () (=> tptp.setadjoinIL @t141)) % 0.38/0.61 (define @t143 () (=> tptp.nonemptyI1 @t142)) % 0.38/0.61 (define @t144 () (=> tptp.nonemptyI @t143)) % 0.38/0.61 (define @t145 () (=> tptp.nonemptyE1 @t144)) % 0.38/0.61 (define @t146 () (=> tptp.setbeta @t145)) % 0.38/0.61 (define @t147 () (=> tptp.noeltsimpempty @t146)) % 0.38/0.61 (define @t148 () (=> tptp.emptyI @t147)) % 0.38/0.61 (define @t149 () (=> tptp.setext @t148)) % 0.38/0.61 (define @t150 () (=> tptp.exuE3e @t149)) % 0.38/0.61 (define @t151 () (=> tptp.notinemptyset @t150)) % 0.38/0.61 (define @t152 () (=> tptp.emptysetimpfalse @t151)) % 0.38/0.61 (define @t153 () (=> tptp.emptysetE @t152)) % 0.38/0.61 (define @t154 () (=> tptp.prop2setE @t153)) % 0.38/0.61 (define @t155 () (=> tptp.exuE1 @t154)) % 0.38/0.61 (define @t156 () (=> tptp.dsetconstrER @t155)) % 0.38/0.61 (define @t157 () (=> tptp.dsetconstrEL @t156)) % 0.38/0.61 (define @t158 () (=> tptp.dsetconstrI @t157)) % 0.38/0.61 (define @t159 () (=> tptp.descrp @t158)) % 0.38/0.61 (define @t160 () (=> tptp.wellorderingAx @t159)) % 0.38/0.61 (define @t161 () (=> tptp.foundationAx @t160)) % 0.38/0.61 (define @t162 () (=> tptp.replAx @t161)) % 0.38/0.61 (define @t163 () (=> tptp.omegaIndAx @t162)) % 0.38/0.61 (define @t164 () (=> tptp.omegaSAx @t163)) % 0.38/0.61 (define @t165 () (=> tptp.omega0Ax @t164)) % 0.38/0.61 (define @t166 () (=> tptp.setunionAx @t165)) % 0.38/0.61 (define @t167 () (=> tptp.powersetAx @t166)) % 0.38/0.61 (define @t168 () (=> tptp.setadjoinAx @t167)) % 0.38/0.61 (define @t169 () (=> tptp.emptysetAx @t168)) % 0.38/0.61 (define @t170 () (=> tptp.setextAx @t169)) % 0.38/0.61 (define @t171 () (=> @t126 @t36)) % 0.38/0.61 (define @t172 () (forall @t33 @t171)) % 0.38/0.61 (assume @p1 (= tptp.setextAx (forall @t9 (=> (forall @t8 (= @t7 @t6)) @t3)))) % 0.38/0.61 (assume @p2 (= tptp.emptysetAx @t11)) % 0.38/0.61 (assume @p3 (= tptp.setadjoinAx (forall @t19 (= @t18 @t16)))) % 0.38/0.61 (assume @p4 (= tptp.powersetAx (forall @t9 (= @t24 @t21)))) % 0.38/0.61 (assume @p5 (= tptp.setunionAx (forall @t29 (= @t28 (exists @t26 (and @t6 @t25)))))) % 0.38/0.61 (assume @p6 (= tptp.omega0Ax (_ @t30 tptp.omega))) % 0.38/0.61 (assume @p7 (= tptp.omegaSAx (forall @t8 (=> @t32 (_ @t31 tptp.omega))))) % 0.38/0.61 (assume @p8 (= tptp.omegaIndAx (forall @t33 (=> (and (_ @t30 @t2) (forall @t8 (=> (and @t32 @t7) (_ @t31 @t2)))) (forall @t8 (=> @t32 @t7)))))) % 0.38/0.61 (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)))))))))) % 0.38/0.61 (assume @p10 (= tptp.foundationAx (forall @t33 (=> @t36 (exists @t26 (and @t25 (not (exists @t8 (and @t6 @t7))))))))) % 0.38/0.61 (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))))))))))))) % 0.38/0.61 (assume @p12 (= tptp.descrp (forall @t54 (=> @t53 (_ @t50 (_ tptp.descr @t52)))))) % 0.38/0.61 (assume @p13 (= tptp.dsetconstrI (forall @t59 (=> @t7 (=> @t51 @t58))))) % 0.38/0.61 (assume @p14 (= tptp.dsetconstrEL (forall @t59 (=> @t58 @t7)))) % 0.38/0.61 (assume @p15 (= tptp.dsetconstrER (forall @t59 (=> @t58 @t51)))) % 0.38/0.61 (assume @p16 (= tptp.exuE1 (forall @t54 (=> @t53 @t60)))) % 0.38/0.61 (assume @p17 (= tptp.prop2setE (forall (@list @t61 @t4) (=> (_ @t5 (_ tptp.prop2set @t61)) @t61)))) % 0.38/0.61 (assume @p18 (= tptp.emptysetE (forall @t8 (=> @t10 (forall @t62 @t61))))) % 0.38/0.61 (assume @p19 (= tptp.emptysetimpfalse (forall @t8 (=> @t10 false)))) % 0.38/0.61 (assume @p20 (= tptp.notinemptyset @t11)) % 0.38/0.61 (assume @p21 (= tptp.exuE3e (forall @t54 (=> @t53 (exists @t8 @t51))))) % 0.38/0.61 (assume @p22 (= tptp.setext (forall @t9 (=> (forall @t8 (=> @t7 @t6)) (=> @t21 @t3))))) % 0.38/0.61 (assume @p23 (= tptp.emptyI @t66)) % 0.38/0.61 (assume @p24 (= tptp.noeltsimpempty @t66)) % 0.38/0.61 (assume @p25 (= tptp.setbeta (forall @t59 (=> @t7 (= @t58 @t51))))) % 0.38/0.61 (assume @p26 @t70) % 0.38/0.61 (assume @p27 (= tptp.nonemptyI (forall @t59 (=> @t7 (=> @t51 (_ tptp.nonempty @t57)))))) % 0.38/0.61 (assume @p28 (= tptp.nonemptyI1 (forall @t33 (=> @t36 @t67)))) % 0.38/0.61 (assume @p29 (= tptp.setadjoinIL (forall @t49 (_ @t5 (_ @t17 @t12))))) % 0.38/0.61 (assume @p30 (= tptp.emptyinunitempty (_ @t30 (_ (_ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) % 0.38/0.61 (assume @p31 (= tptp.setadjoinIR (forall @t19 (=> @t14 @t18)))) % 0.38/0.61 (assume @p32 (= tptp.setadjoinE (forall @t19 (=> @t18 (forall @t62 (=> (=> @t15 @t61) (=> (=> @t14 @t61) @t61))))))) % 0.38/0.61 (assume @p33 (= tptp.setadjoinOr (forall @t19 (=> @t18 @t16)))) % 0.38/0.61 (assume @p34 (= tptp.setoftrueEq (forall @t33 (= (_ @t56 (lambda @t8 true)) @t2)))) % 0.38/0.61 (assume @p35 (= tptp.powersetI (forall @t9 (=> @t21 @t24)))) % 0.38/0.61 (assume @p36 (= tptp.emptyinPowerset @t71)) % 0.38/0.61 (assume @p37 (= tptp.emptyInPowerset @t71)) % 0.38/0.61 (assume @p38 (= tptp.powersetE (forall (@list @t2 @t1 @t4) (=> @t24 @t20)))) % 0.38/0.61 (assume @p39 (= tptp.setunionI (forall (@list @t2 @t4 @t1) (=> @t6 (=> @t25 @t28))))) % 0.38/0.61 (assume @p40 (= tptp.setunionE (forall @t29 (=> @t28 (forall @t62 (=> (forall @t26 (=> @t6 (=> @t25 @t61))) @t61)))))) % 0.38/0.61 (assume @p41 (= tptp.subPowSU (forall @t29 (=> @t7 (_ @t5 (_ tptp.powerset @t27)))))) % 0.38/0.61 (assume @p42 (= tptp.exuE2 (forall @t54 (=> @t53 (exists @t8 (forall @t35 (= @t55 @t15))))))) % 0.38/0.61 (assume @p43 @t118) % 0.38/0.61 (assume @p44 true) % 0.38/0.61 (step @p45 (= tptp.exu @t119) :rule refl :args (@t119)) % 0.38/0.61 (step @p46 (= tptp.prop2set @t120) :rule refl :args (@t120)) % 0.38/0.61 (step @p47 (= tptp.nonempty @t121) :rule refl :args (@t121)) % 0.38/0.61 (step @p48 :rule refl :args (@t123)) % 0.38/0.61 (step @p49 :rule bool-double-not-elim :args (@t63)) % 0.38/0.61 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((or (not @t124) @t123))) % 0.38/0.61 (step @p51 :rule bool-impl-elim :args (@t124 @t123)) % 0.38/0.61 (step @p52 :rule trans :premises (@p51 @p50)) % 0.38/0.61 (step @p53 :rule cong :premises (@p52) :args ((forall @t33 (=> @t124 @t123)))) % 0.38/0.61 (step @p54 :rule refl :args (@t122)) % 0.38/0.61 (step @p55 :rule refl :args (@t7)) % 0.38/0.61 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t7 @t122))) % 0.38/0.61 (step @p57 :rule symm :premises (@p56)) % 0.38/0.61 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.38/0.61 (step @p59 :rule cong :premises (@p58) :args (@t64)) % 0.38/0.61 (step @p60 :rule cong :premises (@p59) :args (@t65)) % 0.38/0.61 (step @p61 :rule cong :premises (@p60) :args (@t125)) % 0.38/0.61 (step @p62 :rule exists-elim :args ((= @t36 @t125))) % 0.38/0.61 (step @p63 :rule trans :premises (@p62 @p61)) % 0.38/0.61 (step @p64 :rule aci_norm :args ((= @t72 @t7))) % 0.38/0.61 (step @p65 :rule cong :premises (@p64) :args (@t73)) % 0.38/0.61 (step @p66 :rule trans :premises (@p65 @p63)) % 0.38/0.61 (step @p67 :rule beta-reduce :args ((= @t126 @t124))) % 0.38/0.61 (step @p68 :rule cong :premises (@p67 @p66) :args (@t127)) % 0.38/0.61 (step @p69 :rule cong :premises (@p68) :args (@t128)) % 0.38/0.61 (step @p70 :rule trans :premises (@p69 @p53)) % 0.38/0.61 (step @p71 :rule refl :args (tptp.exuE2)) % 0.38/0.61 (step @p72 :rule cong :premises (@p71 @p70) :args (@t129)) % 0.38/0.61 (step @p73 :rule refl :args (tptp.subPowSU)) % 0.38/0.61 (step @p74 :rule cong :premises (@p73 @p72) :args (@t130)) % 0.38/0.61 (step @p75 :rule refl :args (tptp.setunionE)) % 0.38/0.61 (step @p76 :rule cong :premises (@p75 @p74) :args (@t131)) % 0.38/0.61 (step @p77 :rule refl :args (tptp.setunionI)) % 0.38/0.61 (step @p78 :rule cong :premises (@p77 @p76) :args (@t132)) % 0.38/0.61 (step @p79 :rule refl :args (tptp.powersetE)) % 0.38/0.61 (step @p80 :rule cong :premises (@p79 @p78) :args (@t133)) % 0.38/0.61 (step @p81 :rule refl :args (tptp.emptyInPowerset)) % 0.38/0.61 (step @p82 :rule cong :premises (@p81 @p80) :args (@t134)) % 0.38/0.61 (step @p83 :rule refl :args (tptp.emptyinPowerset)) % 0.38/0.61 (step @p84 :rule cong :premises (@p83 @p82) :args (@t135)) % 0.38/0.61 (step @p85 :rule refl :args (tptp.powersetI)) % 0.38/0.61 (step @p86 :rule cong :premises (@p85 @p84) :args (@t136)) % 0.38/0.61 (step @p87 :rule refl :args (tptp.setoftrueEq)) % 0.38/0.61 (step @p88 :rule cong :premises (@p87 @p86) :args (@t137)) % 0.38/0.61 (step @p89 :rule refl :args (tptp.setadjoinOr)) % 0.38/0.61 (step @p90 :rule cong :premises (@p89 @p88) :args (@t138)) % 0.38/0.61 (step @p91 :rule refl :args (tptp.setadjoinE)) % 0.38/0.61 (step @p92 :rule cong :premises (@p91 @p90) :args (@t139)) % 0.38/0.61 (step @p93 :rule refl :args (tptp.setadjoinIR)) % 0.38/0.61 (step @p94 :rule cong :premises (@p93 @p92) :args (@t140)) % 0.38/0.61 (step @p95 :rule refl :args (tptp.emptyinunitempty)) % 0.38/0.61 (step @p96 :rule cong :premises (@p95 @p94) :args (@t141)) % 0.38/0.61 (step @p97 :rule refl :args (tptp.setadjoinIL)) % 0.38/0.61 (step @p98 :rule cong :premises (@p97 @p96) :args (@t142)) % 0.38/0.61 (step @p99 :rule refl :args (tptp.nonemptyI1)) % 0.38/0.61 (step @p100 :rule cong :premises (@p99 @p98) :args (@t143)) % 0.38/0.61 (step @p101 :rule refl :args (tptp.nonemptyI)) % 0.38/0.61 (step @p102 :rule cong :premises (@p101 @p100) :args (@t144)) % 0.38/0.61 (step @p103 :rule refl :args (tptp.nonemptyE1)) % 0.38/0.61 (step @p104 :rule cong :premises (@p103 @p102) :args (@t145)) % 0.38/0.61 (step @p105 :rule refl :args (tptp.setbeta)) % 0.38/0.61 (step @p106 :rule cong :premises (@p105 @p104) :args (@t146)) % 0.38/0.61 (step @p107 :rule refl :args (tptp.noeltsimpempty)) % 0.38/0.61 (step @p108 :rule cong :premises (@p107 @p106) :args (@t147)) % 0.38/0.61 (step @p109 :rule refl :args (tptp.emptyI)) % 0.38/0.61 (step @p110 :rule cong :premises (@p109 @p108) :args (@t148)) % 0.38/0.61 (step @p111 :rule refl :args (tptp.setext)) % 0.38/0.61 (step @p112 :rule cong :premises (@p111 @p110) :args (@t149)) % 0.38/0.61 (step @p113 :rule refl :args (tptp.exuE3e)) % 0.38/0.61 (step @p114 :rule cong :premises (@p113 @p112) :args (@t150)) % 0.38/0.61 (step @p115 :rule refl :args (tptp.notinemptyset)) % 0.38/0.61 (step @p116 :rule cong :premises (@p115 @p114) :args (@t151)) % 0.38/0.61 (step @p117 :rule refl :args (tptp.emptysetimpfalse)) % 0.38/0.61 (step @p118 :rule cong :premises (@p117 @p116) :args (@t152)) % 0.38/0.61 (step @p119 :rule refl :args (tptp.emptysetE)) % 0.38/0.61 (step @p120 :rule cong :premises (@p119 @p118) :args (@t153)) % 0.38/0.61 (step @p121 :rule refl :args (tptp.prop2setE)) % 0.38/0.61 (step @p122 :rule cong :premises (@p121 @p120) :args (@t154)) % 0.38/0.61 (step @p123 :rule refl :args (tptp.exuE1)) % 0.38/0.61 (step @p124 :rule cong :premises (@p123 @p122) :args (@t155)) % 0.38/0.61 (step @p125 :rule refl :args (tptp.dsetconstrER)) % 0.38/0.61 (step @p126 :rule cong :premises (@p125 @p124) :args (@t156)) % 0.38/0.61 (step @p127 :rule refl :args (tptp.dsetconstrEL)) % 0.38/0.61 (step @p128 :rule cong :premises (@p127 @p126) :args (@t157)) % 0.38/0.61 (step @p129 :rule refl :args (tptp.dsetconstrI)) % 0.38/0.61 (step @p130 :rule cong :premises (@p129 @p128) :args (@t158)) % 0.38/0.61 (step @p131 :rule refl :args (tptp.descrp)) % 0.38/0.61 (step @p132 :rule cong :premises (@p131 @p130) :args (@t159)) % 0.38/0.61 (step @p133 :rule refl :args (tptp.wellorderingAx)) % 0.38/0.61 (step @p134 :rule cong :premises (@p133 @p132) :args (@t160)) % 0.38/0.61 (step @p135 :rule refl :args (tptp.foundationAx)) % 0.38/0.61 (step @p136 :rule cong :premises (@p135 @p134) :args (@t161)) % 0.38/0.61 (step @p137 :rule refl :args (tptp.replAx)) % 0.38/0.61 (step @p138 :rule cong :premises (@p137 @p136) :args (@t162)) % 0.38/0.61 (step @p139 :rule refl :args (tptp.omegaIndAx)) % 0.38/0.61 (step @p140 :rule cong :premises (@p139 @p138) :args (@t163)) % 0.38/0.61 (step @p141 :rule refl :args (tptp.omegaSAx)) % 0.38/0.61 (step @p142 :rule cong :premises (@p141 @p140) :args (@t164)) % 0.38/0.61 (step @p143 :rule refl :args (tptp.omega0Ax)) % 0.38/0.61 (step @p144 :rule cong :premises (@p143 @p142) :args (@t165)) % 0.38/0.61 (step @p145 :rule refl :args (tptp.setunionAx)) % 0.38/0.61 (step @p146 :rule cong :premises (@p145 @p144) :args (@t166)) % 0.38/0.61 (step @p147 :rule refl :args (tptp.powersetAx)) % 0.38/0.61 (step @p148 :rule cong :premises (@p147 @p146) :args (@t167)) % 0.38/0.61 (step @p149 :rule refl :args (tptp.setadjoinAx)) % 0.38/0.61 (step @p150 :rule cong :premises (@p149 @p148) :args (@t168)) % 0.38/0.61 (step @p151 :rule refl :args (tptp.emptysetAx)) % 0.38/0.61 (step @p152 :rule cong :premises (@p151 @p150) :args (@t169)) % 0.38/0.61 (step @p153 :rule refl :args (tptp.setextAx)) % 0.38/0.61 (step @p154 :rule cong :premises (@p153 @p152) :args (@t170)) % 0.38/0.61 (step @p155 :rule cong :premises (@p154) :args ((not @t170))) % 0.38/0.61 (step @p156 :rule refl :args (@t73)) % 0.38/0.61 (step @p157 :rule refl :args (@t2)) % 0.38/0.61 (step @p158 :rule ho_cong :premises (@p47 @p157)) % 0.38/0.61 (step @p159 :rule cong :premises (@p158 @p156) :args (@t74)) % 0.38/0.61 (step @p160 :rule cong :premises (@p159) :args (@t75)) % 0.38/0.61 (step @p161 :rule cong :premises (@p71 @p160) :args (@t76)) % 0.38/0.61 (step @p162 :rule cong :premises (@p73 @p161) :args (@t77)) % 0.38/0.61 (step @p163 :rule cong :premises (@p75 @p162) :args (@t78)) % 0.38/0.61 (step @p164 :rule cong :premises (@p77 @p163) :args (@t79)) % 0.38/0.61 (step @p165 :rule cong :premises (@p79 @p164) :args (@t80)) % 0.38/0.61 (step @p166 :rule cong :premises (@p81 @p165) :args (@t81)) % 0.38/0.61 (step @p167 :rule cong :premises (@p83 @p166) :args (@t82)) % 0.38/0.61 (step @p168 :rule cong :premises (@p85 @p167) :args (@t83)) % 0.38/0.61 (step @p169 :rule cong :premises (@p87 @p168) :args (@t84)) % 0.38/0.61 (step @p170 :rule cong :premises (@p89 @p169) :args (@t85)) % 0.38/0.61 (step @p171 :rule cong :premises (@p91 @p170) :args (@t86)) % 0.38/0.61 (step @p172 :rule cong :premises (@p93 @p171) :args (@t87)) % 0.38/0.61 (step @p173 :rule cong :premises (@p95 @p172) :args (@t88)) % 0.38/0.61 (step @p174 :rule cong :premises (@p97 @p173) :args (@t89)) % 0.38/0.61 (step @p175 :rule cong :premises (@p99 @p174) :args (@t90)) % 0.38/0.61 (step @p176 :rule cong :premises (@p101 @p175) :args (@t91)) % 0.38/0.61 (step @p177 :rule cong :premises (@p103 @p176) :args (@t92)) % 0.38/0.61 (step @p178 :rule cong :premises (@p105 @p177) :args (@t93)) % 0.38/0.61 (step @p179 :rule cong :premises (@p107 @p178) :args (@t94)) % 0.38/0.61 (step @p180 :rule cong :premises (@p109 @p179) :args (@t95)) % 0.38/0.61 (step @p181 :rule cong :premises (@p111 @p180) :args (@t96)) % 0.38/0.61 (step @p182 :rule cong :premises (@p113 @p181) :args (@t97)) % 0.38/0.61 (step @p183 :rule cong :premises (@p115 @p182) :args (@t98)) % 0.38/0.61 (step @p184 :rule cong :premises (@p117 @p183) :args (@t99)) % 0.38/0.61 (step @p185 :rule cong :premises (@p119 @p184) :args (@t100)) % 0.38/0.61 (step @p186 :rule cong :premises (@p121 @p185) :args (@t101)) % 0.38/0.61 (step @p187 :rule cong :premises (@p123 @p186) :args (@t102)) % 0.38/0.61 (step @p188 :rule cong :premises (@p125 @p187) :args (@t103)) % 0.38/0.61 (step @p189 :rule cong :premises (@p127 @p188) :args (@t104)) % 0.38/0.61 (step @p190 :rule cong :premises (@p129 @p189) :args (@t105)) % 0.38/0.61 (step @p191 :rule cong :premises (@p131 @p190) :args (@t106)) % 0.38/0.61 (step @p192 :rule cong :premises (@p133 @p191) :args (@t107)) % 0.38/0.61 (step @p193 :rule cong :premises (@p135 @p192) :args (@t108)) % 0.38/0.61 (step @p194 :rule cong :premises (@p137 @p193) :args (@t109)) % 0.38/0.61 (step @p195 :rule cong :premises (@p139 @p194) :args (@t110)) % 0.38/0.61 (step @p196 :rule cong :premises (@p141 @p195) :args (@t111)) % 0.38/0.61 (step @p197 :rule cong :premises (@p143 @p196) :args (@t112)) % 0.38/0.61 (step @p198 :rule cong :premises (@p145 @p197) :args (@t113)) % 0.38/0.61 (step @p199 :rule cong :premises (@p147 @p198) :args (@t114)) % 0.38/0.61 (step @p200 :rule cong :premises (@p149 @p199) :args (@t115)) % 0.38/0.61 (step @p201 :rule cong :premises (@p151 @p200) :args (@t116)) % 0.38/0.61 (step @p202 :rule cong :premises (@p153 @p201) :args (@t117)) % 0.38/0.61 (step @p203 :rule cong :premises (@p202) :args (@t118)) % 0.38/0.61 (step @p204 :rule trans :premises (@p203 @p155)) % 0.38/0.61 (step @p205 :rule eq_resolve :premises (@p43 @p204)) % 0.38/0.61 (step @p206 :rule not_implies_elim2 :premises (@p205)) % 0.38/0.61 (step @p207 :rule not_implies_elim2 :premises (@p206)) % 0.38/0.61 (step @p208 :rule not_implies_elim2 :premises (@p207)) % 0.38/0.61 (step @p209 :rule not_implies_elim2 :premises (@p208)) % 0.38/0.61 (step @p210 :rule not_implies_elim2 :premises (@p209)) % 0.38/0.61 (step @p211 :rule not_implies_elim2 :premises (@p210)) % 0.38/0.61 (step @p212 :rule not_implies_elim2 :premises (@p211)) % 0.38/0.61 (step @p213 :rule not_implies_elim2 :premises (@p212)) % 0.38/0.61 (step @p214 :rule not_implies_elim2 :premises (@p213)) % 0.38/0.61 (step @p215 :rule not_implies_elim2 :premises (@p214)) % 0.38/0.61 (step @p216 :rule not_implies_elim2 :premises (@p215)) % 0.38/0.61 (step @p217 :rule not_implies_elim2 :premises (@p216)) % 0.38/0.61 (step @p218 :rule not_implies_elim2 :premises (@p217)) % 0.38/0.61 (step @p219 :rule not_implies_elim2 :premises (@p218)) % 0.38/0.61 (step @p220 :rule not_implies_elim2 :premises (@p219)) % 0.38/0.61 (step @p221 :rule not_implies_elim2 :premises (@p220)) % 0.38/0.61 (step @p222 :rule not_implies_elim2 :premises (@p221)) % 0.38/0.61 (step @p223 :rule not_implies_elim2 :premises (@p222)) % 0.38/0.61 (step @p224 :rule not_implies_elim2 :premises (@p223)) % 0.38/0.61 (step @p225 :rule not_implies_elim2 :premises (@p224)) % 0.38/0.61 (step @p226 :rule not_implies_elim2 :premises (@p225)) % 0.38/0.61 (step @p227 :rule not_implies_elim2 :premises (@p226)) % 0.38/0.61 (step @p228 :rule not_implies_elim2 :premises (@p227)) % 0.38/0.61 (step @p229 :rule not_implies_elim2 :premises (@p228)) % 0.38/0.61 (step @p230 :rule not_implies_elim2 :premises (@p229)) % 0.38/0.61 (step @p231 :rule not_implies_elim2 :premises (@p230)) % 0.38/0.61 (step @p232 :rule not_implies_elim2 :premises (@p231)) % 0.38/0.61 (step @p233 :rule not_implies_elim2 :premises (@p232)) % 0.38/0.61 (step @p234 :rule not_implies_elim2 :premises (@p233)) % 0.38/0.61 (step @p235 :rule not_implies_elim2 :premises (@p234)) % 0.38/0.61 (step @p236 :rule not_implies_elim2 :premises (@p235)) % 0.38/0.61 (step @p237 :rule not_implies_elim2 :premises (@p236)) % 0.38/0.61 (step @p238 :rule not_implies_elim2 :premises (@p237)) % 0.38/0.61 (step @p239 :rule not_implies_elim2 :premises (@p238)) % 0.38/0.61 (step @p240 :rule not_implies_elim2 :premises (@p239)) % 0.38/0.61 (step @p241 :rule not_implies_elim2 :premises (@p240)) % 0.38/0.61 (step @p242 :rule not_implies_elim2 :premises (@p241)) % 0.38/0.61 (step @p243 :rule not_implies_elim2 :premises (@p242)) % 0.38/0.61 (step @p244 :rule not_implies_elim2 :premises (@p243)) % 0.38/0.61 (step @p245 :rule not_implies_elim2 :premises (@p244)) % 0.38/0.61 (step @p246 :rule not_implies_elim2 :premises (@p245)) % 0.38/0.61 (step @p247 :rule not_implies_elim2 :premises (@p246)) % 0.38/0.61 (step @p248 :rule cong :premises (@p67 @p63) :args (@t171)) % 0.38/0.61 (step @p249 :rule cong :premises (@p248) :args (@t172)) % 0.38/0.61 (step @p250 :rule trans :premises (@p249 @p53)) % 0.38/0.61 (step @p251 :rule cong :premises (@p103 @p250) :args ((= tptp.nonemptyE1 @t172))) % 0.38/0.61 (step @p252 :rule refl :args (@t36)) % 0.38/0.61 (step @p253 :rule cong :premises (@p158 @p252) :args (@t68)) % 0.38/0.61 (step @p254 :rule cong :premises (@p253) :args (@t69)) % 0.38/0.61 (step @p255 :rule cong :premises (@p103 @p254) :args (@t70)) % 0.38/0.61 (step @p256 :rule trans :premises (@p255 @p251)) % 0.38/0.61 (step @p257 :rule eq_resolve :premises (@p26 @p256)) % 0.38/0.61 (step @p258 :rule not_implies_elim1 :premises (@p230)) % 0.38/0.61 (step @p259 :rule eq_resolve :premises (@p258 @p257)) % 0.38/0.61 (step @p260 false :rule contra :premises (@p259 @p247)) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------