%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM602+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n024.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 08:39:58 AM UTC 2026 % Result : Theorem 0.35s 0.59s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM602+1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.08/0.25 % Computer : n024.cluster.edu % 0.08/0.25 % Model : x86_64 x86_64 % 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.25 % Memory : 8042.1875MB % 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.25 % CPULimit : 300 % 0.08/0.25 % WCLimit : 300 % 0.08/0.25 % DateTime : Tue Jun 2 06:35:15 EDT 2026 % 0.08/0.25 % CPUTime : % 0.15/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.59 % SZS status Theorem % 0.35/0.59 % SZS output start Proof % 0.35/0.59 ( % 0.35/0.59 (declare-sort $$unsorted 0) % 0.35/0.59 (declare-const tptp.xx $$unsorted) % 0.35/0.59 (declare-const tptp.xe $$unsorted) % 0.35/0.59 (declare-const tptp.xC $$unsorted) % 0.35/0.59 (declare-const tptp.xN $$unsorted) % 0.35/0.59 (declare-const tptp.sz00 $$unsorted) % 0.35/0.59 (declare-const tptp.xc $$unsorted) % 0.35/0.59 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.szNzAzT0 $$unsorted) % 0.35/0.59 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.xd $$unsorted) % 0.35/0.59 (declare-const tptp.xk $$unsorted) % 0.35/0.59 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.59 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.xK $$unsorted) % 0.35/0.59 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.xT $$unsorted) % 0.35/0.59 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.xO $$unsorted) % 0.35/0.59 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.xS $$unsorted) % 0.35/0.59 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.slcrc0 $$unsorted) % 0.35/0.59 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.59 (define @t1 () (@var "W0" $$unsorted)) % 0.35/0.59 (define @t2 () (tptp.aSet0 @t1)) % 0.35/0.59 (define @t3 () (@list @t1)) % 0.35/0.59 (define @t4 () (tptp.aElement0 @t1)) % 0.35/0.59 (define @t5 () (@var "W1" $$unsorted)) % 0.35/0.59 (define @t6 () (tptp.aElement0 @t5)) % 0.35/0.59 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.35/0.59 (define @t8 () (@list @t5)) % 0.35/0.59 (define @t9 () (tptp.isFinite0 @t1)) % 0.35/0.59 (define @t10 () (= @t1 tptp.slcrc0)) % 0.35/0.59 (define @t11 () (tptp.isCountable0 @t1)) % 0.35/0.59 (define @t12 () (not @t9)) % 0.35/0.59 (define @t13 () (and @t2 @t11)) % 0.35/0.59 (define @t14 () (not @t10)) % 0.35/0.59 (define @t15 () (@var "W2" $$unsorted)) % 0.35/0.59 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.35/0.59 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.35/0.59 (define @t18 () (@list @t15)) % 0.35/0.59 (define @t19 () (tptp.aSet0 @t5)) % 0.35/0.59 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.35/0.59 (define @t21 () (tptp.isFinite0 @t5)) % 0.35/0.59 (define @t22 () (and @t2 @t9)) % 0.35/0.59 (define @t23 () (= @t1 @t5)) % 0.35/0.59 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.35/0.59 (define @t25 () (@list @t1 @t5)) % 0.35/0.59 (define @t26 () (tptp.aSubsetOf0 @t5 @t15)) % 0.35/0.59 (define @t27 () (tptp.aSet0 @t15)) % 0.35/0.59 (define @t28 () (@list @t1 @t5 @t15)) % 0.35/0.59 (define @t29 () (@var "W3" $$unsorted)) % 0.35/0.59 (define @t30 () (= @t29 @t5)) % 0.35/0.59 (define @t31 () (tptp.aElementOf0 @t29 @t1)) % 0.35/0.59 (define @t32 () (tptp.aElement0 @t29)) % 0.35/0.59 (define @t33 () (tptp.aElementOf0 @t29 @t15)) % 0.35/0.59 (define @t34 () (@list @t29)) % 0.35/0.59 (define @t35 () (tptp.sdtpldt0 @t1 @t5)) % 0.35/0.59 (define @t36 () (and @t2 @t6)) % 0.35/0.59 (define @t37 () (tptp.sdtmndt0 @t1 @t5)) % 0.35/0.59 (define @t38 () (tptp.sdtpldt0 @t5 @t1)) % 0.35/0.59 (define @t39 () (tptp.isCountable0 @t5)) % 0.35/0.59 (define @t40 () (and @t19 @t39)) % 0.35/0.59 (define @t41 () (tptp.sdtmndt0 @t5 @t1)) % 0.35/0.59 (define @t42 () (and @t19 @t21)) % 0.35/0.59 (define @t43 () (tptp.szszuzczcdt0 @t1)) % 0.35/0.59 (define @t44 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.35/0.59 (define @t45 () (tptp.szszuzczcdt0 @t5)) % 0.35/0.59 (define @t46 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.35/0.59 (define @t47 () (and @t44 @t46)) % 0.35/0.59 (define @t48 () (= @t1 tptp.sz00)) % 0.35/0.59 (define @t49 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.35/0.59 (define @t50 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.35/0.59 (define @t51 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.35/0.59 (define @t52 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.35/0.59 (define @t53 () (tptp.sbrdtbr0 @t1)) % 0.35/0.59 (define @t54 () (and @t2 @t46)) % 0.35/0.59 (define @t55 () (tptp.szmzizndt0 @t1)) % 0.35/0.59 (define @t56 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.35/0.59 (define @t57 () (tptp.szmzizndt0 @t5)) % 0.35/0.59 (define @t58 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.35/0.59 (define @t59 () (tptp.slbdtrb0 @t1)) % 0.35/0.59 (define @t60 () (tptp.slbdtrb0 @t5)) % 0.35/0.59 (define @t61 () (tptp.aSubsetOf0 @t29 @t1)) % 0.35/0.59 (define @t62 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.35/0.59 (define @t63 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.35/0.59 (define @t64 () (tptp.aFunction0 @t1)) % 0.35/0.59 (define @t65 () (tptp.szDzozmdt0 @t1)) % 0.35/0.59 (define @t66 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.35/0.59 (define @t67 () (tptp.aElementOf0 @t5 @t65)) % 0.35/0.59 (define @t68 () (tptp.sdtlpdtrp0 @t1 @t29)) % 0.35/0.59 (define @t69 () (tptp.aElementOf0 @t29 @t65)) % 0.35/0.59 (define @t70 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.35/0.59 (define @t71 () (and @t64 @t6)) % 0.35/0.59 (define @t72 () (@var "W4" $$unsorted)) % 0.35/0.59 (define @t73 () (@list @t72)) % 0.35/0.59 (define @t74 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.35/0.59 (define @t75 () (tptp.aSubsetOf0 @t5 @t65)) % 0.35/0.59 (define @t76 () (tptp.sdtlcdtrc0 @t1 @t65)) % 0.35/0.59 (define @t77 () (tptp.szDzozmdt0 @t15)) % 0.35/0.59 (define @t78 () (tptp.aFunction0 @t15)) % 0.35/0.59 (define @t79 () (tptp.szDzizrdt0 @t1)) % 0.35/0.59 (define @t80 () (tptp.szDzozmdt0 tptp.xc)) % 0.35/0.59 (define @t81 () (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) % 0.35/0.59 (define @t82 () (@var "W5" $$unsorted)) % 0.35/0.59 (define @t83 () (tptp.sdtlpdtrp0 tptp.xN @t43)) % 0.35/0.59 (define @t84 () (tptp.sdtlpdtrp0 tptp.xN @t1)) % 0.35/0.59 (define @t85 () (tptp.szmzizndt0 @t84)) % 0.35/0.59 (define @t86 () (tptp.sdtmndt0 @t84 @t85)) % 0.35/0.59 (define @t87 () (and (tptp.aSubsetOf0 @t84 tptp.szNzAzT0) (tptp.isCountable0 @t84))) % 0.35/0.59 (define @t88 () (tptp.sdtlpdtrp0 tptp.xN @t5)) % 0.35/0.59 (define @t89 () (tptp.sdtpldt0 @t5 @t85)) % 0.35/0.59 (define @t90 () (tptp.slbdtsldtrb0 @t86 tptp.xk)) % 0.35/0.59 (define @t91 () (and @t19 (tptp.aElementOf0 @t5 @t90))) % 0.35/0.59 (define @t92 () (tptp.sdtlpdtrp0 tptp.xC @t1)) % 0.35/0.59 (define @t93 () (tptp.sdtlpdtrp0 @t92 @t5)) % 0.35/0.59 (define @t94 () (tptp.szDzozmdt0 @t92)) % 0.35/0.59 (define @t95 () (tptp.aElementOf0 @t5 tptp.xT)) % 0.35/0.59 (define @t96 () (tptp.slbdtsldtrb0 @t83 tptp.xk)) % 0.35/0.59 (define @t97 () (tptp.sdtlpdtrp0 tptp.xe @t1)) % 0.35/0.59 (define @t98 () (tptp.szDzozmdt0 tptp.xd)) % 0.35/0.59 (define @t99 () (tptp.szDzizrdt0 tptp.xd)) % 0.35/0.59 (define @t100 () (tptp.sdtlbdtrb0 tptp.xd @t99)) % 0.35/0.59 (define @t101 () (tptp.aSet0 tptp.xO)) % 0.35/0.59 (define @t102 () (tptp.sdtlpdtrp0 tptp.xe @t5)) % 0.35/0.59 (define @t103 () (tptp.aElementOf0 @t5 @t100)) % 0.35/0.59 (define @t104 () (and @t46 @t103 (= @t102 @t1))) % 0.35/0.59 (define @t105 () (exists @t8 @t104)) % 0.35/0.59 (define @t106 () (tptp.aElementOf0 @t1 tptp.xO)) % 0.35/0.59 (define @t107 () (=> @t106 @t105)) % 0.35/0.59 (define @t108 () (forall @t3 @t107)) % 0.35/0.59 (define @t109 () (tptp.aElementOf0 tptp.xx tptp.xO)) % 0.35/0.59 (define @t110 () (= @t97 tptp.xx)) % 0.35/0.59 (define @t111 () (and @t44 @t110)) % 0.35/0.59 (define @t112 () (exists @t3 @t111)) % 0.35/0.59 (define @t113 () (not @t112)) % 0.35/0.59 (define @t114 () (forall @t3 (or (not @t44) (not @t110)))) % 0.35/0.59 (define @t115 () (forall @t3 (not @t111))) % 0.35/0.59 (define @t116 () (not @t115)) % 0.35/0.59 (define @t117 () (= @t1 @t102)) % 0.35/0.59 (define @t118 () (not @t117)) % 0.35/0.59 (define @t119 () (not @t103)) % 0.35/0.59 (define @t120 () (not @t46)) % 0.35/0.59 (define @t121 () (or @t120 @t119 @t118)) % 0.35/0.59 (define @t122 () (not (forall @t8 @t121))) % 0.35/0.59 (define @t123 () (and @t46 @t103 @t117)) % 0.35/0.59 (define @t124 () (forall @t8 (not @t123))) % 0.35/0.59 (define @t125 () (not @t124)) % 0.35/0.59 (define @t126 () (not (= tptp.xx @t102))) % 0.35/0.59 (define @t127 () (or @t120 @t119 @t126)) % 0.35/0.59 (define @t128 () (forall @t8 @t127)) % 0.35/0.59 (define @t129 () (not @t128)) % 0.35/0.59 (define @t130 () (not @t109)) % 0.35/0.59 (define @t131 () (or @t130 @t129)) % 0.35/0.59 (define @t132 () (forall @t3 (or (not @t106) @t122))) % 0.35/0.59 (define @t133 () (forall @t8 (or @t120 @t119 (not (= @t102 tptp.xx))))) % 0.35/0.59 (define @t134 () (not @t133)) % 0.35/0.59 (define @t135 () (or @t130 @t134)) % 0.35/0.59 (define @t136 () (@list false false)) % 0.35/0.59 (define @t137 () (@quantifiers_skolemize @t133 0)) % 0.35/0.59 (define @t138 () (tptp.sdtlpdtrp0 tptp.xe @t137)) % 0.35/0.59 (define @t139 () (= tptp.xx @t138)) % 0.35/0.59 (define @t140 () (not @t139)) % 0.35/0.59 (define @t141 () (not (tptp.aElementOf0 @t137 @t100))) % 0.35/0.59 (define @t142 () (tptp.aElementOf0 @t137 tptp.szNzAzT0)) % 0.35/0.59 (define @t143 () (not @t142)) % 0.35/0.59 (define @t144 () (or @t143 @t141 @t140)) % 0.35/0.59 (define @t145 () (not @t144)) % 0.35/0.59 (define @t146 () (not (= @t138 tptp.xx))) % 0.35/0.59 (define @t147 () (or @t143 @t141 @t146)) % 0.35/0.59 (define @t148 () (not @t147)) % 0.35/0.59 (define @t149 () (@list true)) % 0.35/0.59 (define @t150 () (@list @t144)) % 0.35/0.59 (define @t151 () (or @t143 @t140)) % 0.35/0.59 (define @t152 () (not @t151)) % 0.35/0.59 (define @t153 () (or @t143 @t146)) % 0.35/0.59 (assume @p1 (forall @t3 (=> @t2 true))) % 0.35/0.59 (assume @p2 (forall @t3 (=> @t4 true))) % 0.35/0.59 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.35/0.59 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.35/0.59 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.35/0.59 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.35/0.59 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.35/0.59 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.35/0.59 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.35/0.59 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.35/0.59 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.35/0.59 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.35/0.59 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.35/0.59 (assume @p14 (forall @t28 (=> (and @t2 @t19 @t27) (=> (and @t24 @t26) (tptp.aSubsetOf0 @t1 @t15))))) % 0.35/0.59 (assume @p15 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t35) (and @t27 (forall @t34 (= @t33 (and @t32 (or @t31 @t30)))))))))) % 0.35/0.59 (assume @p16 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t37) (and @t27 (forall @t34 (= @t33 (and @t32 @t31 (not @t30)))))))))) % 0.35/0.59 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t37 @t5) @t1)))))) % 0.35/0.59 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t38 @t1) @t5))))) % 0.35/0.59 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t38)))))) % 0.35/0.59 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t41)))))) % 0.35/0.59 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t38)))))) % 0.35/0.59 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t41)))))) % 0.35/0.59 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.35/0.59 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.35/0.59 (assume @p25 (forall @t3 (=> @t44 (and (tptp.aElementOf0 @t43 tptp.szNzAzT0) (not (= @t43 tptp.sz00)))))) % 0.35/0.59 (assume @p26 (forall @t25 (=> @t47 (=> (= @t43 @t45) @t23)))) % 0.35/0.59 (assume @p27 (forall @t3 (=> @t44 (or @t48 (exists @t8 (and @t46 (= @t1 @t45))))))) % 0.35/0.59 (assume @p28 (forall @t3 (=> @t44 (not (= @t1 @t43))))) % 0.35/0.59 (assume @p29 (forall @t25 (=> @t47 (=> @t49 true)))) % 0.35/0.59 (assume @p30 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.35/0.59 (assume @p31 (forall @t3 (=> @t44 (not (tptp.sdtlseqdt0 @t43 tptp.sz00))))) % 0.35/0.59 (assume @p32 (forall @t25 (=> @t47 (= @t49 (tptp.sdtlseqdt0 @t43 @t45))))) % 0.35/0.59 (assume @p33 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t43)))) % 0.35/0.59 (assume @p34 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.35/0.59 (assume @p35 (forall @t25 (=> @t47 (=> (and @t49 @t50) @t23)))) % 0.35/0.59 (assume @p36 (forall @t28 (=> (and @t44 @t46 @t52) (=> (and @t49 @t51) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.35/0.59 (assume @p37 (forall @t25 (=> @t47 (or @t49 (tptp.sdtlseqdt0 @t45 @t1))))) % 0.35/0.59 (assume @p38 (forall @t25 (=> @t47 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.35/0.59 (assume @p39 (forall @t3 (=> @t44 (tptp.iLess0 @t1 @t43)))) % 0.35/0.59 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t53)))) % 0.35/0.59 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t53 tptp.szNzAzT0) @t9)))) % 0.35/0.59 (assume @p42 (forall @t3 (=> @t2 (= (= @t53 tptp.sz00) @t10)))) % 0.35/0.59 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t35) (tptp.szszuzczcdt0 @t53)))))))) % 0.35/0.59 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t37)) @t53)))))) % 0.35/0.59 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t53)))))) % 0.35/0.59 (assume @p46 (forall @t25 (=> @t54 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t53)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.35/0.59 (assume @p47 (forall @t3 (=> (and @t56 @t14) (forall @t8 (= (= @t5 @t55) (and @t7 (forall @t18 (=> @t16 @t51)))))))) % 0.35/0.59 (assume @p48 (forall @t3 (=> (and @t56 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.35/0.59 (assume @p49 (forall @t25 (=> (and @t56 @t58 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t55 @t5) (tptp.aElementOf0 @t57 @t1)) (= @t55 @t57))))) % 0.35/0.59 (assume @p50 (forall @t3 (=> @t44 (forall @t8 (= (= @t5 @t59) (and @t19 (forall @t18 (= @t17 (and @t52 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.35/0.59 (assume @p51 (forall @t3 (=> @t44 (tptp.isFinite0 @t59)))) % 0.35/0.59 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.35/0.59 (assume @p53 (forall @t25 (=> @t47 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t45)) (or (tptp.aElementOf0 @t1 @t60) @t23))))) % 0.35/0.59 (assume @p54 (forall @t25 (=> @t47 (= @t49 (tptp.aSubsetOf0 @t59 @t60))))) % 0.35/0.59 (assume @p55 (forall @t3 (=> (and @t56 @t9) (exists @t8 (and @t46 (tptp.aSubsetOf0 @t1 @t60)))))) % 0.35/0.59 (assume @p56 (forall @t3 (=> @t44 (= (tptp.sbrdtbr0 @t59) @t1)))) % 0.35/0.59 (assume @p57 (forall @t25 (=> @t54 (forall @t18 (= (= @t15 @t62) (and @t27 (forall @t34 (= @t33 (and @t61 (= (tptp.sbrdtbr0 @t29) @t5)))))))))) % 0.35/0.59 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t46 (tptp.isFinite0 @t62)))))) % 0.35/0.59 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t46 (not (= @t62 tptp.slcrc0))))))) % 0.35/0.59 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t46 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t62)))))) % 0.35/0.59 (assume @p61 (forall @t3 (=> @t44 (forall (@list @t5 @t15) (=> (and @t19 @t27 (not @t48)) (=> (and (tptp.aSubsetOf0 @t63 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t63 tptp.slcrc0))) @t26)))))) % 0.35/0.59 (assume @p62 (forall @t25 (=> @t54 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t62) (tptp.isFinite0 @t15)) (exists @t34 (and @t61 (tptp.isFinite0 @t29) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t29 @t5))))))))) % 0.35/0.59 (assume @p63 (forall @t3 (=> @t64 true))) % 0.35/0.59 (assume @p64 (forall @t3 (=> @t64 (tptp.aSet0 @t65)))) % 0.35/0.59 (assume @p65 (forall @t3 (=> @t64 (forall @t8 (=> @t67 (tptp.aElement0 @t66)))))) % 0.35/0.59 (assume @p66 (forall @t25 (=> @t71 (forall @t18 (= (= @t15 @t70) (and @t27 (forall @t34 (= @t33 (and @t69 (= @t68 @t5)))))))))) % 0.35/0.59 (assume @p67 (forall @t25 (=> @t71 (tptp.aSubsetOf0 @t70 @t65)))) % 0.35/0.59 (assume @p68 (forall @t3 (=> @t64 (forall @t8 (=> @t75 (forall @t18 (= (= @t15 @t74) (and @t27 (forall @t34 (= @t33 (exists @t73 (and (tptp.aElementOf0 @t72 @t5) (= (tptp.sdtlpdtrp0 @t1 @t72) @t29))))))))))))) % 0.35/0.59 (assume @p69 (forall @t3 (=> @t64 (forall @t8 (=> @t67 (tptp.aElementOf0 @t66 @t76)))))) % 0.35/0.59 (assume @p70 (forall @t3 (=> @t64 (forall @t8 (=> @t75 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t78 (= @t77 @t5) (forall @t34 (=> (tptp.aElementOf0 @t29 @t5) (= (tptp.sdtlpdtrp0 @t15 @t29) @t68))))))))))) % 0.35/0.59 (assume @p71 (forall @t3 (=> @t64 (forall @t8 (=> (and @t75 @t39) (=> (forall (@list @t15 @t29) (=> (and (tptp.aElementOf0 @t15 @t65) @t69 (not (= @t15 @t29))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t68)))) (tptp.isCountable0 @t74))))))) % 0.35/0.59 (assume @p72 (forall @t3 (=> @t64 (=> (and (tptp.isCountable0 @t65) (tptp.isFinite0 @t76)) (and (tptp.aElement0 @t79) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t79))))))) % 0.35/0.59 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.35/0.59 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.35/0.59 (assume @p75 (and (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.35/0.59 (assume @p76 (and (tptp.aFunction0 tptp.xc) (= @t80 @t81) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc @t80) tptp.xT))) % 0.35/0.59 (assume @p77 (forall @t3 (=> @t44 (forall @t8 (=> (and @t58 @t39) (forall @t18 (=> (and @t78 (= @t77 @t63) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t15 @t77) tptp.xT)) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t34 (and (tptp.aElementOf0 @t29 tptp.xT) (exists @t73 (and (tptp.aSubsetOf0 @t72 @t5) (tptp.isCountable0 @t72) (forall (@list @t82) (=> (tptp.aElementOf0 @t82 (tptp.slbdtsldtrb0 @t72 @t1)) (= (tptp.sdtlpdtrp0 @t15 @t82) @t29))))))))))))))) % 0.35/0.59 (assume @p78 (not (= tptp.xK tptp.sz00))) % 0.35/0.59 (assume @p79 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK))) % 0.35/0.59 (assume @p80 (and (tptp.aFunction0 tptp.xN) (= (tptp.szDzozmdt0 tptp.xN) tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall @t3 (=> @t44 (=> @t87 (and (tptp.aSubsetOf0 @t83 @t86) (tptp.isCountable0 @t83))))))) % 0.35/0.59 (assume @p81 (forall @t3 (=> @t44 @t87))) % 0.35/0.59 (assume @p82 (forall @t25 (=> @t47 (=> @t50 (tptp.aSubsetOf0 @t84 @t88))))) % 0.35/0.59 (assume @p83 (forall @t25 (=> (and @t44 @t46 (not @t23)) (not (= @t85 (tptp.szmzizndt0 @t88)))))) % 0.35/0.59 (assume @p84 (forall @t3 (=> @t44 (forall @t8 (=> @t91 (tptp.aElementOf0 @t89 @t81)))))) % 0.35/0.59 (assume @p85 (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall @t3 (=> @t44 (and (tptp.aFunction0 @t92) (= @t94 @t90) (forall @t8 (=> @t91 (= @t93 (tptp.sdtlpdtrp0 tptp.xc @t89))))))))) % 0.35/0.59 (assume @p86 (forall @t3 (=> @t44 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t92 @t94) tptp.xT)))) % 0.35/0.59 (assume @p87 (forall @t3 (=> @t44 (forall @t8 (=> (and (tptp.aSubsetOf0 @t5 @t86) @t39) (forall @t18 (=> (and @t27 (tptp.aElementOf0 @t15 (tptp.slbdtsldtrb0 @t5 tptp.xk))) (tptp.aElementOf0 @t15 @t90)))))))) % 0.35/0.59 (assume @p88 (forall @t3 (=> @t44 (exists @t8 (and @t95 (exists @t18 (and (tptp.aSubsetOf0 @t15 @t86) (tptp.isCountable0 @t15) (forall @t34 (=> (and (tptp.aSet0 @t29) (tptp.aElementOf0 @t29 (tptp.slbdtsldtrb0 @t15 tptp.xk))) (= (tptp.sdtlpdtrp0 @t92 @t29) @t5)))))))))) % 0.35/0.59 (assume @p89 (forall @t3 (=> @t44 (exists @t8 (and @t95 (forall @t18 (=> (and @t27 (tptp.aElementOf0 @t15 @t96)) (= (tptp.sdtlpdtrp0 @t92 @t15) @t5)))))))) % 0.35/0.59 (assume @p90 (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall @t3 (=> @t44 (= @t97 @t85))))) % 0.35/0.59 (assume @p91 (and (tptp.aFunction0 tptp.xd) (= @t98 tptp.szNzAzT0) (forall @t3 (=> @t44 (forall @t8 (=> (and @t19 (tptp.aElementOf0 @t5 @t96)) (= (tptp.sdtlpdtrp0 tptp.xd @t1) @t93))))))) % 0.35/0.59 (assume @p92 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xd @t98) tptp.xT)) % 0.35/0.59 (assume @p93 (and (tptp.aElementOf0 @t99 tptp.xT) (tptp.isCountable0 @t100))) % 0.35/0.59 (assume @p94 (and @t101 (= tptp.xO (tptp.sdtlcdtrc0 tptp.xe @t100)))) % 0.35/0.59 (assume @p95 (and @t101 (tptp.isCountable0 tptp.xO))) % 0.35/0.59 (assume @p96 @t108) % 0.35/0.59 (assume @p97 @t109) % 0.35/0.59 (assume @p98 @t113) % 0.35/0.59 (assume @p99 true) % 0.35/0.59 (step @p100 :rule bool-double-not-elim :args (@t114)) % 0.35/0.59 (step @p101 :rule bool-and-de-morgan :args (@t44 @t110 true)) % 0.35/0.59 (step @p102 :rule cong :premises (@p101) :args (@t115)) % 0.35/0.59 (step @p103 :rule cong :premises (@p102) :args (@t116)) % 0.35/0.59 (step @p104 :rule exists-elim :args ((= @t112 @t116))) % 0.35/0.59 (step @p105 :rule trans :premises (@p104 @p103)) % 0.35/0.59 (step @p106 :rule cong :premises (@p105) :args (@t113)) % 0.35/0.59 (step @p107 :rule trans :premises (@p106 @p100)) % 0.35/0.59 (step @p108 :rule eq_resolve :premises (@p98 @p107)) % 0.35/0.59 (step @p109 :rule bool-impl-elim :args (@t106 @t122)) % 0.35/0.59 (step @p110 :rule cong :premises (@p109) :args ((forall @t3 (=> @t106 @t122)))) % 0.35/0.59 (step @p111 :rule aci_norm :args ((= (or @t120 (or @t119 @t118)) @t121))) % 0.35/0.59 (step @p112 :rule bool-and-de-morgan :args (@t103 @t117 true)) % 0.35/0.59 (step @p113 :rule refl :args (@t120)) % 0.35/0.59 (step @p114 :rule nary_cong :premises (@p113 @p112) :args ((or @t120 (not (and @t103 @t117))))) % 0.35/0.59 (step @p115 :rule bool-and-de-morgan :args (@t46 @t103 (and @t117))) % 0.35/0.59 (step @p116 :rule trans :premises (@p115 @p114)) % 0.35/0.59 (step @p117 :rule trans :premises (@p116 @p111)) % 0.35/0.59 (step @p118 :rule cong :premises (@p117) :args (@t124)) % 0.35/0.59 (step @p119 :rule cong :premises (@p118) :args (@t125)) % 0.35/0.59 (step @p120 :rule exists-elim :args ((= (exists @t8 @t123) @t125))) % 0.35/0.59 (step @p121 :rule trans :premises (@p120 @p119)) % 0.35/0.59 (step @p122 :rule eq-symm :args (@t102 @t1)) % 0.35/0.59 (step @p123 :rule refl :args (@t103)) % 0.35/0.59 (step @p124 :rule refl :args (@t46)) % 0.35/0.59 (step @p125 :rule nary_cong :premises (@p124 @p123 @p122) :args (@t104)) % 0.35/0.59 (step @p126 :rule cong :premises (@p125) :args (@t105)) % 0.35/0.59 (step @p127 :rule trans :premises (@p126 @p121)) % 0.35/0.59 (step @p128 :rule refl :args (@t106)) % 0.35/0.59 (step @p129 :rule cong :premises (@p128 @p127) :args (@t107)) % 0.35/0.59 (step @p130 :rule cong :premises (@p129) :args (@t108)) % 0.35/0.59 (step @p131 :rule trans :premises (@p130 @p110)) % 0.35/0.59 (step @p132 :rule eq_resolve :premises (@p96 @p131)) % 0.35/0.59 (step @p133 :rule eq-symm :args (tptp.xx @t102)) % 0.35/0.59 (step @p134 :rule cong :premises (@p133) :args (@t126)) % 0.35/0.59 (step @p135 :rule refl :args (@t119)) % 0.35/0.59 (step @p136 :rule refl :args (@t120)) % 0.35/0.59 (step @p137 :rule nary_cong :premises (@p136 @p135 @p134) :args (@t127)) % 0.35/0.59 (step @p138 :rule cong :premises (@p137) :args (@t128)) % 0.35/0.59 (step @p139 :rule cong :premises (@p138) :args (@t129)) % 0.35/0.59 (step @p140 :rule refl :args (@t130)) % 0.35/0.59 (step @p141 :rule nary_cong :premises (@p140 @p139) :args (@t131)) % 0.35/0.59 (step @p142 :rule refl :args (@t132)) % 0.35/0.59 (step @p143 :rule cong :premises (@p142 @p141) :args ((=> @t132 @t131))) % 0.35/0.59 (assume-push @p199 @t132) % 0.35/0.59 (step @p145 :rule instantiate :premises (@p132) :args ((@list tptp.xx))) % 0.35/0.59 (step-pop @p200 :rule scope :premises (@p145)) % 0.35/0.59 (step @p146 :rule process_scope :premises (@p200) :args (@t131)) % 0.35/0.59 (step @p148 :rule eq_resolve :premises (@p146 @p143)) % 0.35/0.59 (step @p149 :rule implies_elim :premises (@p148)) % 0.35/0.59 (step @p150 :rule chain_m_resolution :premises (@p149 @p132) :args (@t135 (@list false) (@list @t132))) % 0.35/0.59 (step @p151 :rule cnf_or_pos :args (@t135)) % 0.35/0.59 (step @p152 :rule reordering :premises (@p151) :args ((or @t130 @t134 (not @t135)))) % 0.35/0.59 (step @p153 :rule chain_m_resolution :premises (@p152 @p97 @p150) :args (@t134 @t136 (@list @t109 @t135))) % 0.35/0.59 (step @p154 :rule refl :args (@t145)) % 0.35/0.59 (step @p155 :rule bool-double-not-elim :args (@t133)) % 0.35/0.59 (step @p156 :rule nary_cong :premises (@p155 @p154) :args ((or (not @t134) @t145))) % 0.35/0.59 (step @p157 :rule eq-symm :args (@t138 tptp.xx)) % 0.35/0.59 (step @p158 :rule cong :premises (@p157) :args (@t146)) % 0.35/0.59 (step @p159 :rule refl :args (@t141)) % 0.35/0.59 (step @p160 :rule refl :args (@t143)) % 0.35/0.59 (step @p161 :rule nary_cong :premises (@p160 @p159 @p158) :args (@t147)) % 0.35/0.59 (step @p162 :rule cong :premises (@p161) :args (@t148)) % 0.35/0.59 (step @p163 :rule refl :args (@t134)) % 0.35/0.59 (step @p164 :rule cong :premises (@p163 @p162) :args ((=> @t134 @t148))) % 0.35/0.59 (assume-push @p201 @t134) % 0.35/0.59 (step @p166 :rule skolemize :premises (@p153)) % 0.35/0.59 (step-pop @p202 :rule scope :premises (@p166)) % 0.35/0.59 (step @p167 :rule process_scope :premises (@p202) :args (@t148)) % 0.35/0.59 (step @p169 :rule eq_resolve :premises (@p167 @p164)) % 0.35/0.59 (step @p170 :rule implies_elim :premises (@p169)) % 0.35/0.59 (step @p171 :rule eq_resolve :premises (@p170 @p156)) % 0.35/0.59 (step @p172 :rule chain_m_resolution :premises (@p171 @p153) :args (@t145 @t149 (@list @t133))) % 0.35/0.59 (step @p173 :rule bool-double-not-elim :args (@t139)) % 0.35/0.59 (step @p174 :rule refl :args (@t144)) % 0.35/0.59 (step @p175 :rule nary_cong :premises (@p174 @p173) :args ((or @t144 (not @t140)))) % 0.35/0.59 (step @p176 :rule cnf_or_neg :args (@t144 2)) % 0.35/0.59 (step @p177 :rule eq_resolve :premises (@p176 @p175)) % 0.35/0.59 (step @p178 :rule reordering :premises (@p177) :args ((or @t139 @t144))) % 0.35/0.59 (step @p179 :rule chain_m_resolution :premises (@p178 @p172) :args (@t139 @t149 @t150)) % 0.35/0.59 (step @p180 :rule bool-double-not-elim :args (@t142)) % 0.35/0.59 (step @p181 :rule nary_cong :premises (@p174 @p180) :args ((or @t144 (not @t143)))) % 0.35/0.59 (step @p182 :rule cnf_or_neg :args (@t144 0)) % 0.35/0.59 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 0.35/0.59 (step @p184 :rule reordering :premises (@p183) :args ((or @t142 @t144))) % 0.35/0.59 (step @p185 :rule chain_m_resolution :premises (@p184 @p172) :args (@t142 @t149 @t150)) % 0.35/0.59 (step @p186 :rule cnf_or_pos :args (@t151)) % 0.35/0.59 (step @p187 :rule reordering :premises (@p186) :args ((or @t143 @t140 @t152))) % 0.35/0.59 (step @p188 :rule chain_m_resolution :premises (@p187 @p185 @p179) :args (@t152 @t136 (@list @t142 @t139))) % 0.35/0.59 (step @p189 :rule nary_cong :premises (@p160 @p158) :args (@t153)) % 0.35/0.59 (step @p190 :rule refl :args (@t114)) % 0.35/0.59 (step @p191 :rule cong :premises (@p190 @p189) :args ((=> @t114 @t153))) % 0.35/0.59 (assume-push @p203 @t114) % 0.35/0.59 (step @p193 :rule instantiate :premises (@p108) :args ((@list @t137))) % 0.35/0.59 (step-pop @p204 :rule scope :premises (@p193)) % 0.35/0.59 (step @p194 :rule process_scope :premises (@p204) :args (@t153)) % 0.35/0.59 (step @p196 :rule eq_resolve :premises (@p194 @p191)) % 0.35/0.59 (step @p197 :rule implies_elim :premises (@p196)) % 0.35/0.59 (step @p198 false :rule chain_m_resolution :premises (@p197 @p188 @p108) :args (false (@list true false) (@list @t151 @t114))) % 0.35/0.59 ) % 0.35/0.59 % SZS output end Proof % 0.35/0.59 % cvc5 exiting %------------------------------------------------------------------------------