%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM582+3 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n009.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 08:39:55 AM UTC 2026 % Result : Theorem 0.38s 0.71s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM582+3 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n009.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 11:33:14 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.71 % SZS status Theorem % 0.38/0.71 % SZS output start Proof % 0.38/0.71 ( % 0.38/0.71 (declare-sort $$unsorted 0) % 0.38/0.71 (declare-const tptp.xQ $$unsorted) % 0.38/0.71 (declare-const tptp.xi $$unsorted) % 0.38/0.71 (declare-const tptp.xN $$unsorted) % 0.38/0.71 (declare-const tptp.sz00 $$unsorted) % 0.38/0.71 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.38/0.71 (declare-const tptp.szNzAzT0 $$unsorted) % 0.38/0.71 (declare-const tptp.xk $$unsorted) % 0.38/0.71 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.71 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.71 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.38/0.71 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.38/0.71 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.38/0.71 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.38/0.71 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.71 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.71 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.xK $$unsorted) % 0.38/0.71 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.xT $$unsorted) % 0.38/0.71 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.xS $$unsorted) % 0.38/0.71 (declare-const tptp.xc $$unsorted) % 0.38/0.71 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.slcrc0 $$unsorted) % 0.38/0.71 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.71 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.71 (define @t1 () (@var "W0" $$unsorted)) % 0.38/0.71 (define @t2 () (tptp.aSet0 @t1)) % 0.38/0.71 (define @t3 () (@list @t1)) % 0.38/0.71 (define @t4 () (tptp.aElement0 @t1)) % 0.38/0.71 (define @t5 () (@var "W1" $$unsorted)) % 0.38/0.71 (define @t6 () (tptp.aElement0 @t5)) % 0.38/0.71 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.38/0.71 (define @t8 () (@list @t5)) % 0.38/0.71 (define @t9 () (tptp.isFinite0 @t1)) % 0.38/0.71 (define @t10 () (= @t1 tptp.slcrc0)) % 0.38/0.71 (define @t11 () (tptp.isCountable0 @t1)) % 0.38/0.71 (define @t12 () (not @t9)) % 0.38/0.71 (define @t13 () (and @t2 @t11)) % 0.38/0.71 (define @t14 () (not @t10)) % 0.38/0.71 (define @t15 () (@var "W2" $$unsorted)) % 0.38/0.71 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.38/0.71 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.38/0.71 (define @t18 () (@list @t15)) % 0.38/0.71 (define @t19 () (tptp.aSet0 @t5)) % 0.38/0.71 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.38/0.71 (define @t21 () (tptp.isFinite0 @t5)) % 0.38/0.71 (define @t22 () (and @t2 @t9)) % 0.38/0.71 (define @t23 () (= @t1 @t5)) % 0.38/0.71 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.38/0.71 (define @t25 () (@list @t1 @t5)) % 0.38/0.71 (define @t26 () (tptp.aSubsetOf0 @t5 @t15)) % 0.38/0.71 (define @t27 () (tptp.aSet0 @t15)) % 0.38/0.71 (define @t28 () (@list @t1 @t5 @t15)) % 0.38/0.71 (define @t29 () (@var "W3" $$unsorted)) % 0.38/0.71 (define @t30 () (= @t29 @t5)) % 0.38/0.71 (define @t31 () (tptp.aElementOf0 @t29 @t1)) % 0.38/0.71 (define @t32 () (tptp.aElement0 @t29)) % 0.38/0.71 (define @t33 () (tptp.aElementOf0 @t29 @t15)) % 0.38/0.71 (define @t34 () (@list @t29)) % 0.38/0.71 (define @t35 () (tptp.sdtpldt0 @t1 @t5)) % 0.38/0.71 (define @t36 () (and @t2 @t6)) % 0.38/0.71 (define @t37 () (tptp.sdtmndt0 @t1 @t5)) % 0.38/0.71 (define @t38 () (tptp.sdtpldt0 @t5 @t1)) % 0.38/0.71 (define @t39 () (tptp.isCountable0 @t5)) % 0.38/0.71 (define @t40 () (and @t19 @t39)) % 0.38/0.71 (define @t41 () (tptp.sdtmndt0 @t5 @t1)) % 0.38/0.71 (define @t42 () (and @t19 @t21)) % 0.38/0.71 (define @t43 () (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.38/0.71 (define @t44 () (tptp.szszuzczcdt0 @t1)) % 0.38/0.71 (define @t45 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.38/0.71 (define @t46 () (tptp.szszuzczcdt0 @t5)) % 0.38/0.71 (define @t47 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.38/0.71 (define @t48 () (and @t45 @t47)) % 0.38/0.71 (define @t49 () (= @t1 tptp.sz00)) % 0.38/0.71 (define @t50 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.38/0.71 (define @t51 () (tptp.sdtlseqdt0 tptp.sz00 @t1)) % 0.38/0.71 (define @t52 () (forall @t3 (=> @t45 @t51))) % 0.38/0.71 (define @t53 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.38/0.71 (define @t54 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.38/0.71 (define @t55 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.38/0.71 (define @t56 () (tptp.sbrdtbr0 @t1)) % 0.38/0.71 (define @t57 () (and @t2 @t47)) % 0.38/0.71 (define @t58 () (tptp.szmzizndt0 @t1)) % 0.38/0.71 (define @t59 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.38/0.71 (define @t60 () (tptp.szmzizndt0 @t5)) % 0.38/0.71 (define @t61 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.38/0.71 (define @t62 () (tptp.slbdtrb0 @t1)) % 0.38/0.71 (define @t63 () (tptp.slbdtrb0 @t5)) % 0.38/0.71 (define @t64 () (tptp.sbrdtbr0 @t29)) % 0.38/0.71 (define @t65 () (tptp.aSubsetOf0 @t29 @t1)) % 0.38/0.71 (define @t66 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.38/0.71 (define @t67 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.38/0.71 (define @t68 () (tptp.aFunction0 @t1)) % 0.38/0.71 (define @t69 () (tptp.szDzozmdt0 @t1)) % 0.38/0.71 (define @t70 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.38/0.71 (define @t71 () (tptp.aElementOf0 @t5 @t69)) % 0.38/0.71 (define @t72 () (tptp.sdtlpdtrp0 @t1 @t29)) % 0.38/0.71 (define @t73 () (tptp.aElementOf0 @t29 @t69)) % 0.38/0.71 (define @t74 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.38/0.71 (define @t75 () (and @t68 @t6)) % 0.38/0.71 (define @t76 () (@var "W4" $$unsorted)) % 0.38/0.71 (define @t77 () (tptp.aElementOf0 @t76 @t5)) % 0.38/0.71 (define @t78 () (@list @t76)) % 0.38/0.71 (define @t79 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.38/0.71 (define @t80 () (tptp.aSubsetOf0 @t5 @t69)) % 0.38/0.71 (define @t81 () (tptp.sdtlcdtrc0 @t1 @t69)) % 0.38/0.71 (define @t82 () (tptp.szDzozmdt0 @t15)) % 0.38/0.71 (define @t83 () (tptp.aFunction0 @t15)) % 0.38/0.71 (define @t84 () (tptp.szDzizrdt0 @t1)) % 0.38/0.71 (define @t85 () (tptp.aElementOf0 @t1 tptp.xS)) % 0.38/0.71 (define @t86 () (tptp.szDzozmdt0 tptp.xc)) % 0.38/0.71 (define @t87 () (tptp.sdtlcdtrc0 tptp.xc @t86)) % 0.38/0.71 (define @t88 () (tptp.aElementOf0 @t1 @t87)) % 0.38/0.71 (define @t89 () (tptp.aElementOf0 @t1 @t86)) % 0.38/0.71 (define @t90 () (= @t56 tptp.xK)) % 0.38/0.71 (define @t91 () (tptp.aSubsetOf0 @t1 tptp.xS)) % 0.38/0.71 (define @t92 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xS)))) % 0.38/0.71 (define @t93 () (@var "W5" $$unsorted)) % 0.38/0.71 (define @t94 () (@var "W6" $$unsorted)) % 0.38/0.71 (define @t95 () (@list @t93)) % 0.38/0.71 (define @t96 () (tptp.aElementOf0 @t29 tptp.xT)) % 0.38/0.71 (define @t97 () (tptp.sdtlcdtrc0 @t15 @t82)) % 0.38/0.71 (define @t98 () (tptp.aElementOf0 @t29 @t97)) % 0.38/0.71 (define @t99 () (tptp.aElementOf0 @t29 @t82)) % 0.38/0.71 (define @t100 () (= @t64 @t1)) % 0.38/0.71 (define @t101 () (tptp.aSubsetOf0 @t29 @t5)) % 0.38/0.71 (define @t102 () (forall @t78 (=> (tptp.aElementOf0 @t76 @t29) @t77))) % 0.38/0.71 (define @t103 () (tptp.aSet0 @t29)) % 0.38/0.71 (define @t104 () (tptp.sdtlpdtrp0 tptp.xN @t44)) % 0.38/0.71 (define @t105 () (tptp.sdtlpdtrp0 tptp.xN @t1)) % 0.38/0.71 (define @t106 () (tptp.szmzizndt0 @t105)) % 0.38/0.71 (define @t107 () (tptp.sdtmndt0 @t105 @t106)) % 0.38/0.71 (define @t108 () (tptp.aElementOf0 @t5 @t107)) % 0.38/0.71 (define @t109 () (tptp.aElementOf0 @t5 @t105)) % 0.38/0.71 (define @t110 () (tptp.aElementOf0 @t106 @t105)) % 0.38/0.71 (define @t111 () (tptp.isCountable0 @t105)) % 0.38/0.71 (define @t112 () (tptp.aSubsetOf0 @t105 tptp.szNzAzT0)) % 0.38/0.71 (define @t113 () (forall @t8 (=> @t109 @t47))) % 0.38/0.71 (define @t114 () (tptp.aSet0 @t105)) % 0.38/0.71 (define @t115 () (tptp.sdtlpdtrp0 tptp.xN tptp.sz00)) % 0.38/0.71 (define @t116 () (tptp.sdtlpdtrp0 tptp.xN @t5)) % 0.38/0.71 (define @t117 () (tptp.aSubsetOf0 @t105 @t116)) % 0.38/0.71 (define @t118 () (tptp.aElementOf0 @t15 @t116)) % 0.38/0.71 (define @t119 () (tptp.aElementOf0 @t15 @t105)) % 0.38/0.71 (define @t120 () (forall @t18 (=> @t119 @t118))) % 0.38/0.71 (define @t121 () (and @t120 @t117)) % 0.38/0.71 (define @t122 () (=> @t53 @t121)) % 0.38/0.71 (define @t123 () (=> @t48 @t122)) % 0.38/0.71 (define @t124 () (forall @t25 @t123)) % 0.38/0.71 (define @t125 () (tptp.sdtlseqdt0 @t106 @t15)) % 0.38/0.71 (define @t126 () (tptp.aElementOf0 tptp.xi tptp.szNzAzT0)) % 0.38/0.71 (define @t127 () (tptp.sdtlpdtrp0 tptp.xN tptp.xi)) % 0.38/0.71 (define @t128 () (tptp.szmzizndt0 @t127)) % 0.38/0.71 (define @t129 () (tptp.sdtmndt0 @t127 @t128)) % 0.38/0.71 (define @t130 () (tptp.aElementOf0 @t1 @t129)) % 0.38/0.71 (define @t131 () (tptp.aElementOf0 @t1 tptp.xQ)) % 0.38/0.71 (define @t132 () (= @t1 @t128)) % 0.38/0.71 (define @t133 () (tptp.aElementOf0 @t1 @t127)) % 0.38/0.71 (define @t134 () (forall @t3 (=> @t133 (tptp.sdtlseqdt0 @t128 @t1)))) % 0.38/0.71 (define @t135 () (tptp.aElementOf0 @t128 @t127)) % 0.38/0.71 (define @t136 () (tptp.sdtpldt0 tptp.xQ @t128)) % 0.38/0.71 (define @t137 () (tptp.aSubsetOf0 @t127 tptp.xS)) % 0.38/0.71 (define @t138 () (forall @t3 (=> @t133 @t85))) % 0.38/0.71 (define @t139 () (or @t138 @t137)) % 0.38/0.71 (define @t140 () (not @t139)) % 0.38/0.71 (define @t141 () (@var "BOUND_VARIABLE_9877" $$unsorted)) % 0.38/0.71 (define @t142 () (or (not (tptp.aElementOf0 @t141 @t105)) (tptp.aElementOf0 @t141 @t116))) % 0.38/0.71 (define @t143 () (and @t142 @t117)) % 0.38/0.71 (define @t144 () (not @t53)) % 0.38/0.71 (define @t145 () (not @t47)) % 0.38/0.71 (define @t146 () (not @t45)) % 0.38/0.71 (define @t147 () (or @t146 @t145 @t144 @t143)) % 0.38/0.71 (define @t148 () (@list @t141)) % 0.38/0.71 (define @t149 () (forall @t148 @t147)) % 0.38/0.71 (define @t150 () (forall @t148 @t117)) % 0.38/0.71 (define @t151 () (forall @t148 @t142)) % 0.38/0.71 (define @t152 () (and @t151 @t150)) % 0.38/0.71 (define @t153 () (forall @t148 @t143)) % 0.38/0.71 (define @t154 () (or @t146 @t145 @t144 @t153)) % 0.38/0.71 (define @t155 () (and (forall @t18 (or (not @t119) @t118)) @t117)) % 0.38/0.71 (define @t156 () (or @t146 @t145 @t144 @t155)) % 0.38/0.71 (define @t157 () (=> @t53 @t155)) % 0.38/0.71 (define @t158 () (tptp.sdtlseqdt0 tptp.sz00 tptp.xi)) % 0.38/0.71 (define @t159 () (not @t126)) % 0.38/0.71 (define @t160 () (or @t159 @t158)) % 0.38/0.71 (define @t161 () (tptp.aSubsetOf0 @t127 @t115)) % 0.38/0.71 (define @t162 () (and (or (not @t135) (tptp.aElementOf0 @t128 @t115)) @t161)) % 0.38/0.71 (define @t163 () (not @t158)) % 0.38/0.71 (define @t164 () (not @t43)) % 0.38/0.71 (define @t165 () (or @t159 @t164 @t163 @t162)) % 0.38/0.71 (assume @p1 (forall @t3 (=> @t2 true))) % 0.38/0.71 (assume @p2 (forall @t3 (=> @t4 true))) % 0.38/0.71 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.38/0.71 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.38/0.71 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.38/0.71 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.38/0.71 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.38/0.71 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.38/0.71 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.38/0.71 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.38/0.71 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.38/0.71 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.38/0.71 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.38/0.71 (assume @p14 (forall @t28 (=> (and @t2 @t19 @t27) (=> (and @t24 @t26) (tptp.aSubsetOf0 @t1 @t15))))) % 0.38/0.71 (assume @p15 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t35) (and @t27 (forall @t34 (= @t33 (and @t32 (or @t31 @t30)))))))))) % 0.38/0.71 (assume @p16 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t37) (and @t27 (forall @t34 (= @t33 (and @t32 @t31 (not @t30)))))))))) % 0.38/0.71 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t37 @t5) @t1)))))) % 0.38/0.71 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t38 @t1) @t5))))) % 0.38/0.71 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t38)))))) % 0.38/0.71 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t41)))))) % 0.38/0.71 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t38)))))) % 0.38/0.71 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t41)))))) % 0.38/0.71 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.38/0.71 (assume @p24 @t43) % 0.38/0.71 (assume @p25 (forall @t3 (=> @t45 (and (tptp.aElementOf0 @t44 tptp.szNzAzT0) (not (= @t44 tptp.sz00)))))) % 0.38/0.71 (assume @p26 (forall @t25 (=> @t48 (=> (= @t44 @t46) @t23)))) % 0.38/0.71 (assume @p27 (forall @t3 (=> @t45 (or @t49 (exists @t8 (and @t47 (= @t1 @t46))))))) % 0.38/0.71 (assume @p28 (forall @t3 (=> @t45 (not (= @t1 @t44))))) % 0.38/0.71 (assume @p29 (forall @t25 (=> @t48 (=> @t50 true)))) % 0.38/0.71 (assume @p30 @t52) % 0.38/0.71 (assume @p31 (forall @t3 (=> @t45 (not (tptp.sdtlseqdt0 @t44 tptp.sz00))))) % 0.38/0.71 (assume @p32 (forall @t25 (=> @t48 (= @t50 (tptp.sdtlseqdt0 @t44 @t46))))) % 0.38/0.71 (assume @p33 (forall @t3 (=> @t45 (tptp.sdtlseqdt0 @t1 @t44)))) % 0.38/0.71 (assume @p34 (forall @t3 (=> @t45 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.38/0.71 (assume @p35 (forall @t25 (=> @t48 (=> (and @t50 @t53) @t23)))) % 0.38/0.71 (assume @p36 (forall @t28 (=> (and @t45 @t47 @t55) (=> (and @t50 @t54) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.38/0.71 (assume @p37 (forall @t25 (=> @t48 (or @t50 (tptp.sdtlseqdt0 @t46 @t1))))) % 0.38/0.71 (assume @p38 (forall @t25 (=> @t48 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.38/0.71 (assume @p39 (forall @t3 (=> @t45 (tptp.iLess0 @t1 @t44)))) % 0.38/0.71 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t56)))) % 0.38/0.71 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t56 tptp.szNzAzT0) @t9)))) % 0.38/0.71 (assume @p42 (forall @t3 (=> @t2 (= (= @t56 tptp.sz00) @t10)))) % 0.38/0.71 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t35) (tptp.szszuzczcdt0 @t56)))))))) % 0.38/0.71 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t37)) @t56)))))) % 0.38/0.71 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t56)))))) % 0.38/0.71 (assume @p46 (forall @t25 (=> @t57 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t56)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.38/0.71 (assume @p47 (forall @t3 (=> (and @t59 @t14) (forall @t8 (= (= @t5 @t58) (and @t7 (forall @t18 (=> @t16 @t54)))))))) % 0.38/0.71 (assume @p48 (forall @t3 (=> (and @t59 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.38/0.71 (assume @p49 (forall @t25 (=> (and @t59 @t61 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t58 @t5) (tptp.aElementOf0 @t60 @t1)) (= @t58 @t60))))) % 0.38/0.71 (assume @p50 (forall @t3 (=> @t45 (forall @t8 (= (= @t5 @t62) (and @t19 (forall @t18 (= @t17 (and @t55 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.38/0.71 (assume @p51 (forall @t3 (=> @t45 (tptp.isFinite0 @t62)))) % 0.38/0.71 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.38/0.71 (assume @p53 (forall @t25 (=> @t48 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t46)) (or (tptp.aElementOf0 @t1 @t63) @t23))))) % 0.38/0.71 (assume @p54 (forall @t25 (=> @t48 (= @t50 (tptp.aSubsetOf0 @t62 @t63))))) % 0.38/0.71 (assume @p55 (forall @t3 (=> (and @t59 @t9) (exists @t8 (and @t47 (tptp.aSubsetOf0 @t1 @t63)))))) % 0.38/0.71 (assume @p56 (forall @t3 (=> @t45 (= (tptp.sbrdtbr0 @t62) @t1)))) % 0.38/0.71 (assume @p57 (forall @t25 (=> @t57 (forall @t18 (= (= @t15 @t66) (and @t27 (forall @t34 (= @t33 (and @t65 (= @t64 @t5)))))))))) % 0.38/0.71 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t47 (tptp.isFinite0 @t66)))))) % 0.38/0.71 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t47 (not (= @t66 tptp.slcrc0))))))) % 0.38/0.71 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t47 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t66)))))) % 0.38/0.71 (assume @p61 (forall @t3 (=> @t45 (forall (@list @t5 @t15) (=> (and @t19 @t27 (not @t49)) (=> (and (tptp.aSubsetOf0 @t67 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t67 tptp.slcrc0))) @t26)))))) % 0.38/0.71 (assume @p62 (forall @t25 (=> @t57 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t66) (tptp.isFinite0 @t15)) (exists @t34 (and @t65 (tptp.isFinite0 @t29) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t29 @t5))))))))) % 0.38/0.71 (assume @p63 (forall @t3 (=> @t68 true))) % 0.38/0.71 (assume @p64 (forall @t3 (=> @t68 (tptp.aSet0 @t69)))) % 0.38/0.71 (assume @p65 (forall @t3 (=> @t68 (forall @t8 (=> @t71 (tptp.aElement0 @t70)))))) % 0.38/0.71 (assume @p66 (forall @t25 (=> @t75 (forall @t18 (= (= @t15 @t74) (and @t27 (forall @t34 (= @t33 (and @t73 (= @t72 @t5)))))))))) % 0.38/0.71 (assume @p67 (forall @t25 (=> @t75 (tptp.aSubsetOf0 @t74 @t69)))) % 0.38/0.71 (assume @p68 (forall @t3 (=> @t68 (forall @t8 (=> @t80 (forall @t18 (= (= @t15 @t79) (and @t27 (forall @t34 (= @t33 (exists @t78 (and @t77 (= (tptp.sdtlpdtrp0 @t1 @t76) @t29))))))))))))) % 0.38/0.71 (assume @p69 (forall @t3 (=> @t68 (forall @t8 (=> @t71 (tptp.aElementOf0 @t70 @t81)))))) % 0.38/0.71 (assume @p70 (forall @t3 (=> @t68 (forall @t8 (=> @t80 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t83 (= @t82 @t5) (forall @t34 (=> (tptp.aElementOf0 @t29 @t5) (= (tptp.sdtlpdtrp0 @t15 @t29) @t72))))))))))) % 0.38/0.71 (assume @p71 (forall @t3 (=> @t68 (forall @t8 (=> (and @t80 @t39) (=> (forall (@list @t15 @t29) (=> (and (tptp.aElementOf0 @t15 @t69) @t73 (not (= @t15 @t29))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t72)))) (tptp.isCountable0 @t79))))))) % 0.38/0.71 (assume @p72 (forall @t3 (=> @t68 (=> (and (tptp.isCountable0 @t69) (tptp.isFinite0 @t81)) (and (tptp.aElement0 @t84) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t84))))))) % 0.38/0.71 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.38/0.71 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.38/0.71 (assume @p75 (and (tptp.aSet0 tptp.xS) (forall @t3 (=> @t85 @t45)) (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.38/0.71 (assume @p76 (and (tptp.aFunction0 tptp.xc) (forall @t3 (and (=> @t89 (and @t2 @t92 @t91 @t90)) (=> (and (or (and @t2 @t92) @t91) @t90) @t89))) (= @t86 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSet0 @t87) (forall @t3 (= @t88 (exists @t8 (and (tptp.aElementOf0 @t5 @t86) (= (tptp.sdtlpdtrp0 tptp.xc @t5) @t1))))) (forall @t3 (=> @t88 (tptp.aElementOf0 @t1 tptp.xT))) (tptp.aSubsetOf0 @t87 tptp.xT))) % 0.38/0.71 (assume @p77 (forall @t3 (=> @t45 (forall @t8 (=> (and (or (and @t19 (forall @t18 (=> @t17 @t55))) @t61) @t39) (forall @t18 (=> (and @t83 (or (forall @t34 (and (=> @t99 (and (or (and @t103 @t102) @t101) @t100)) (=> (and @t103 @t102 @t101 @t100) @t99))) (= @t82 @t67)) (=> (and (tptp.aSet0 @t97) (forall @t34 (= @t98 (exists @t78 (and (tptp.aElementOf0 @t76 @t82) (= (tptp.sdtlpdtrp0 @t15 @t76) @t29)))))) (or (forall @t34 (=> @t98 @t96)) (tptp.aSubsetOf0 @t97 tptp.xT)))) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t34 (and @t96 (exists @t78 (and (tptp.aSet0 @t76) (forall @t95 (=> (tptp.aElementOf0 @t93 @t76) (tptp.aElementOf0 @t93 @t5))) (tptp.aSubsetOf0 @t76 @t5) (tptp.isCountable0 @t76) (forall @t95 (=> (or (and (or (and (tptp.aSet0 @t93) (forall (@list @t94) (=> (tptp.aElementOf0 @t94 @t93) (tptp.aElementOf0 @t94 @t76)))) (tptp.aSubsetOf0 @t93 @t76)) (= (tptp.sbrdtbr0 @t93) @t1)) (tptp.aElementOf0 @t93 (tptp.slbdtsldtrb0 @t76 @t1))) (= (tptp.sdtlpdtrp0 @t15 @t93) @t29))))))))))))))) % 0.38/0.71 (assume @p78 (not (= tptp.xK tptp.sz00))) % 0.38/0.71 (assume @p79 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK))) % 0.38/0.71 (assume @p80 (and (tptp.aFunction0 tptp.xN) (= (tptp.szDzozmdt0 tptp.xN) tptp.szNzAzT0) (= @t115 tptp.xS) (forall @t3 (=> @t45 (=> (and (or (and @t114 @t113) @t112) @t111) (and @t110 (forall @t8 (=> @t109 (tptp.sdtlseqdt0 @t106 @t5))) (tptp.aSet0 @t107) (forall @t8 (= @t108 (and @t6 @t109 (not (= @t5 @t106))))) (tptp.aSet0 @t104) (forall @t8 (=> (tptp.aElementOf0 @t5 @t104) @t108)) (tptp.aSubsetOf0 @t104 @t107) (tptp.isCountable0 @t104))))))) % 0.38/0.71 (assume @p81 (forall @t3 (=> @t45 (and @t114 @t113 @t112 @t111)))) % 0.38/0.71 (assume @p82 @t124) % 0.38/0.71 (assume @p83 (forall @t25 (=> (and @t45 @t47 (not @t23)) (not (=> (and @t110 (forall @t18 (=> @t119 @t125))) (or (and (tptp.aElementOf0 @t106 @t116) (forall @t18 (=> @t118 @t125))) (= @t106 (tptp.szmzizndt0 @t116)))))))) % 0.38/0.71 (assume @p84 @t126) % 0.38/0.71 (assume @p85 (and @t135 @t134 (tptp.aSet0 @t129) (forall @t3 (= @t130 (and @t4 @t133 (not @t132)))) (tptp.aSet0 tptp.xQ) (forall @t3 (=> @t131 @t130)) (tptp.aSubsetOf0 tptp.xQ @t129) (= (tptp.sbrdtbr0 tptp.xQ) tptp.xk) (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 @t129 tptp.xk)))) % 0.38/0.71 (assume @p86 (and @t135 @t134 (tptp.aSet0 @t136) (forall @t3 (= (tptp.aElementOf0 @t1 @t136) (and @t4 (or @t131 @t132)))) (= (tptp.sbrdtbr0 @t136) tptp.xK))) % 0.38/0.71 (assume @p87 @t140) % 0.38/0.71 (assume @p88 true) % 0.38/0.71 (step @p89 :rule evaluate :args ((= false true))) % 0.38/0.71 (step @p90 :rule quant-merge-prenex :args ((= (forall @t25 @t149) (forall (@list @t1 @t5 @t141) @t147)))) % 0.38/0.71 (step @p91 :rule quant-unused-vars :args ((= @t150 @t117))) % 0.38/0.71 (step @p92 :rule alpha_equiv :args (@t151 (@list @t141) (@list @t15))) % 0.38/0.71 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t152)) % 0.38/0.71 (step @p94 :rule quant-miniscope-and :args ((= @t153 @t152))) % 0.38/0.71 (step @p95 :rule trans :premises (@p94 @p93)) % 0.38/0.71 (step @p96 :rule refl :args (@t144)) % 0.38/0.71 (step @p97 :rule refl :args (@t145)) % 0.38/0.71 (step @p98 :rule refl :args (@t146)) % 0.38/0.71 (step @p99 :rule nary_cong :premises (@p98 @p97 @p96 @p95) :args (@t154)) % 0.38/0.71 (step @p100 :rule quant-miniscope-or :args ((= @t149 @t154))) % 0.38/0.71 (step @p101 :rule trans :premises (@p100 @p99)) % 0.38/0.71 (step @p102 :rule symm :premises (@p101)) % 0.38/0.71 (step @p103 :rule cong :premises (@p102) :args ((forall @t25 @t156))) % 0.38/0.71 (step @p104 :rule trans :premises (@p103 @p90)) % 0.38/0.71 (step @p105 :rule aci_norm :args ((= (or (or @t146 @t145) (or @t144 @t155)) @t156))) % 0.38/0.71 (step @p106 :rule bool-impl-elim :args (@t53 @t155)) % 0.38/0.71 (step @p107 :rule bool-and-de-morgan :args (@t45 @t47 true)) % 0.38/0.71 (step @p108 :rule nary_cong :premises (@p107 @p106) :args ((or (not @t48) @t157))) % 0.38/0.71 (step @p109 :rule trans :premises (@p108 @p105)) % 0.38/0.71 (step @p110 :rule bool-impl-elim :args (@t48 @t157)) % 0.38/0.71 (step @p111 :rule trans :premises (@p110 @p109)) % 0.38/0.71 (step @p112 :rule cong :premises (@p111) :args ((forall @t25 (=> @t48 @t157)))) % 0.38/0.71 (step @p113 :rule trans :premises (@p112 @p104)) % 0.38/0.71 (step @p114 :rule refl :args (@t117)) % 0.38/0.71 (step @p115 :rule bool-impl-elim :args (@t119 @t118)) % 0.38/0.71 (step @p116 :rule cong :premises (@p115) :args (@t120)) % 0.38/0.71 (step @p117 :rule nary_cong :premises (@p116 @p114) :args (@t121)) % 0.38/0.71 (step @p118 :rule refl :args (@t53)) % 0.38/0.71 (step @p119 :rule cong :premises (@p118 @p117) :args (@t122)) % 0.38/0.71 (step @p120 :rule refl :args (@t48)) % 0.38/0.72 (step @p121 :rule cong :premises (@p120 @p119) :args (@t123)) % 0.38/0.72 (step @p122 :rule cong :premises (@p121) :args (@t124)) % 0.38/0.72 (step @p123 :rule trans :premises (@p122 @p113)) % 0.38/0.72 (step @p124 :rule eq_resolve :premises (@p82 @p123)) % 0.38/0.72 (step @p125 :rule instantiate :premises (@p124) :args ((@list tptp.xi tptp.sz00 @t128))) % 0.38/0.72 (step @p126 :rule bool-impl-elim :args (@t45 @t51)) % 0.38/0.72 (step @p127 :rule cong :premises (@p126) :args (@t52)) % 0.38/0.72 (step @p128 :rule eq_resolve :premises (@p30 @p127)) % 0.38/0.72 (step @p129 :rule instantiate :premises (@p128) :args ((@list tptp.xi))) % 0.38/0.72 (step @p130 :rule cnf_or_pos :args (@t160)) % 0.38/0.72 (step @p131 :rule reordering :premises (@p130) :args ((or @t159 @t158 (not @t160)))) % 0.38/0.72 (step @p132 :rule chain_m_resolution :premises (@p131 @p84 @p129) :args (@t158 (@list false false) (@list @t126 @t160))) % 0.38/0.72 (step @p133 :rule cnf_or_pos :args (@t165)) % 0.38/0.72 (step @p134 :rule reordering :premises (@p133) :args ((or @t164 @t159 @t163 @t162 (not @t165)))) % 0.38/0.72 (step @p135 :rule chain_m_resolution :premises (@p134 @p24 @p84 @p132 @p125) :args (@t162 (@list false false false false) (@list @t43 @t126 @t158 @t165))) % 0.38/0.72 (step @p136 :rule cnf_and_pos :args (@t162 1)) % 0.38/0.72 (step @p137 :rule reordering :premises (@p136) :args ((or @t161 (not @t162)))) % 0.38/0.72 (step @p138 :rule chain_m_resolution :premises (@p137 @p135) :args (@t161 (@list false) (@list @t162))) % 0.38/0.72 (step @p139 :rule true_intro :premises (@p138)) % 0.38/0.72 (step @p140 :rule and_elim :premises (@p80) :args (2)) % 0.38/0.72 (step @p141 :rule symm :premises (@p140)) % 0.38/0.72 (step @p142 :rule refl :args (@t127)) % 0.38/0.72 (step @p143 :rule cong :premises (@p142 @p141) :args (@t137)) % 0.38/0.72 (step @p144 :rule refl :args (@t137)) % 0.38/0.72 (step @p145 :rule bool-impl-elim :args (@t133 @t85)) % 0.38/0.72 (step @p146 :rule cong :premises (@p145) :args (@t138)) % 0.38/0.72 (step @p147 :rule nary_cong :premises (@p146 @p144) :args (@t139)) % 0.38/0.72 (step @p148 :rule cong :premises (@p147) :args (@t140)) % 0.38/0.72 (step @p149 :rule eq_resolve :premises (@p87 @p148)) % 0.38/0.72 (step @p150 :rule not_or_elim :premises (@p149) :args (1)) % 0.38/0.72 (step @p151 :rule false_intro :premises (@p150)) % 0.38/0.72 (step @p152 :rule symm :premises (@p151)) % 0.38/0.72 (step @p153 :rule trans :premises (@p152 @p143 @p139)) % 0.38/0.72 (step @p154 false :rule eq_resolve :premises (@p153 @p89)) % 0.38/0.72 ) % 0.38/0.72 % SZS output end Proof % 0.38/0.72 % cvc5 exiting %------------------------------------------------------------------------------