%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM630+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 : n012.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 08:40:04 AM UTC 2026 % Result : Theorem 0.24s 0.47s % Output : Proof 0.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : NUM630+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 % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 11:38:18 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.35 %----Proving TF0_NAR, FOF, or CNF % 0.24/0.47 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.24/0.47 % SZS status Theorem % 0.24/0.47 % SZS output start Proof % 0.24/0.47 ( % 0.24/0.47 (declare-sort $$unsorted 0) % 0.24/0.47 (declare-const tptp.xD $$unsorted) % 0.24/0.47 (declare-const tptp.xn $$unsorted) % 0.24/0.47 (declare-const tptp.xp $$unsorted) % 0.24/0.47 (declare-const tptp.xQ $$unsorted) % 0.24/0.47 (declare-const tptp.xe $$unsorted) % 0.24/0.47 (declare-const tptp.xP $$unsorted) % 0.24/0.47 (declare-const tptp.xC $$unsorted) % 0.24/0.47 (declare-const tptp.xN $$unsorted) % 0.24/0.47 (declare-const tptp.sz00 $$unsorted) % 0.24/0.47 (declare-const tptp.xc $$unsorted) % 0.24/0.47 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.24/0.47 (declare-const tptp.szNzAzT0 $$unsorted) % 0.24/0.47 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.24/0.47 (declare-const tptp.xd $$unsorted) % 0.24/0.47 (declare-const tptp.xk $$unsorted) % 0.24/0.47 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.24/0.47 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.24/0.47 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.24/0.47 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.24/0.47 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.24/0.47 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.24/0.47 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.24/0.47 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.xK $$unsorted) % 0.24/0.47 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.xT $$unsorted) % 0.24/0.47 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.xO $$unsorted) % 0.24/0.47 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.xS $$unsorted) % 0.24/0.47 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.slcrc0 $$unsorted) % 0.24/0.47 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.47 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.47 (define @t1 () (@var "W0" $$unsorted)) % 0.24/0.47 (define @t2 () (tptp.aSet0 @t1)) % 0.24/0.47 (define @t3 () (@list @t1)) % 0.24/0.47 (define @t4 () (tptp.aElement0 @t1)) % 0.24/0.47 (define @t5 () (@var "W1" $$unsorted)) % 0.24/0.47 (define @t6 () (tptp.aElement0 @t5)) % 0.24/0.47 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.24/0.47 (define @t8 () (@list @t5)) % 0.24/0.47 (define @t9 () (tptp.isFinite0 @t1)) % 0.24/0.47 (define @t10 () (= @t1 tptp.slcrc0)) % 0.24/0.47 (define @t11 () (tptp.isCountable0 @t1)) % 0.24/0.47 (define @t12 () (not @t9)) % 0.24/0.47 (define @t13 () (and @t2 @t11)) % 0.24/0.47 (define @t14 () (not @t10)) % 0.24/0.47 (define @t15 () (@var "W2" $$unsorted)) % 0.24/0.47 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.24/0.47 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.24/0.47 (define @t18 () (@list @t15)) % 0.24/0.47 (define @t19 () (tptp.aSet0 @t5)) % 0.24/0.47 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.24/0.47 (define @t21 () (tptp.isFinite0 @t5)) % 0.24/0.47 (define @t22 () (and @t2 @t9)) % 0.24/0.47 (define @t23 () (= @t1 @t5)) % 0.24/0.47 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.24/0.47 (define @t25 () (@list @t1 @t5)) % 0.24/0.47 (define @t26 () (tptp.aSubsetOf0 @t5 @t15)) % 0.24/0.47 (define @t27 () (tptp.aSet0 @t15)) % 0.24/0.47 (define @t28 () (@list @t1 @t5 @t15)) % 0.24/0.47 (define @t29 () (@var "W3" $$unsorted)) % 0.24/0.47 (define @t30 () (= @t29 @t5)) % 0.24/0.47 (define @t31 () (tptp.aElementOf0 @t29 @t1)) % 0.24/0.47 (define @t32 () (tptp.aElement0 @t29)) % 0.24/0.47 (define @t33 () (tptp.aElementOf0 @t29 @t15)) % 0.24/0.47 (define @t34 () (@list @t29)) % 0.24/0.47 (define @t35 () (tptp.sdtpldt0 @t1 @t5)) % 0.24/0.47 (define @t36 () (and @t2 @t6)) % 0.24/0.47 (define @t37 () (tptp.sdtmndt0 @t1 @t5)) % 0.24/0.47 (define @t38 () (tptp.sdtpldt0 @t5 @t1)) % 0.24/0.47 (define @t39 () (tptp.isCountable0 @t5)) % 0.24/0.47 (define @t40 () (and @t19 @t39)) % 0.24/0.47 (define @t41 () (tptp.sdtmndt0 @t5 @t1)) % 0.24/0.47 (define @t42 () (and @t19 @t21)) % 0.24/0.47 (define @t43 () (tptp.szszuzczcdt0 @t1)) % 0.24/0.47 (define @t44 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.24/0.47 (define @t45 () (tptp.szszuzczcdt0 @t5)) % 0.24/0.47 (define @t46 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.24/0.47 (define @t47 () (and @t44 @t46)) % 0.24/0.47 (define @t48 () (= @t1 tptp.sz00)) % 0.24/0.47 (define @t49 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.24/0.47 (define @t50 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.24/0.47 (define @t51 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.24/0.47 (define @t52 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.24/0.47 (define @t53 () (tptp.sbrdtbr0 @t1)) % 0.24/0.47 (define @t54 () (and @t2 @t46)) % 0.24/0.47 (define @t55 () (tptp.szmzizndt0 @t1)) % 0.24/0.47 (define @t56 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.24/0.47 (define @t57 () (tptp.szmzizndt0 @t5)) % 0.24/0.47 (define @t58 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.24/0.47 (define @t59 () (tptp.slbdtrb0 @t1)) % 0.24/0.47 (define @t60 () (tptp.slbdtrb0 @t5)) % 0.24/0.47 (define @t61 () (tptp.aSubsetOf0 @t29 @t1)) % 0.24/0.47 (define @t62 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.24/0.47 (define @t63 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.24/0.47 (define @t64 () (tptp.aFunction0 @t1)) % 0.24/0.47 (define @t65 () (tptp.szDzozmdt0 @t1)) % 0.24/0.47 (define @t66 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.24/0.47 (define @t67 () (tptp.aElementOf0 @t5 @t65)) % 0.24/0.47 (define @t68 () (tptp.sdtlpdtrp0 @t1 @t29)) % 0.24/0.47 (define @t69 () (tptp.aElementOf0 @t29 @t65)) % 0.24/0.47 (define @t70 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.24/0.47 (define @t71 () (and @t64 @t6)) % 0.24/0.47 (define @t72 () (@var "W4" $$unsorted)) % 0.24/0.47 (define @t73 () (@list @t72)) % 0.24/0.47 (define @t74 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.24/0.47 (define @t75 () (tptp.aSubsetOf0 @t5 @t65)) % 0.24/0.47 (define @t76 () (tptp.sdtlcdtrc0 @t1 @t65)) % 0.24/0.47 (define @t77 () (tptp.szDzozmdt0 @t15)) % 0.24/0.47 (define @t78 () (tptp.aFunction0 @t15)) % 0.24/0.47 (define @t79 () (tptp.szDzizrdt0 @t1)) % 0.24/0.47 (define @t80 () (tptp.szDzozmdt0 tptp.xc)) % 0.24/0.47 (define @t81 () (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) % 0.24/0.47 (define @t82 () (@var "W5" $$unsorted)) % 0.24/0.47 (define @t83 () (tptp.sdtlpdtrp0 tptp.xN @t43)) % 0.24/0.47 (define @t84 () (tptp.sdtlpdtrp0 tptp.xN @t1)) % 0.24/0.47 (define @t85 () (tptp.szmzizndt0 @t84)) % 0.24/0.47 (define @t86 () (tptp.sdtmndt0 @t84 @t85)) % 0.24/0.47 (define @t87 () (and (tptp.aSubsetOf0 @t84 tptp.szNzAzT0) (tptp.isCountable0 @t84))) % 0.24/0.47 (define @t88 () (tptp.sdtlpdtrp0 tptp.xN @t5)) % 0.24/0.47 (define @t89 () (tptp.sdtpldt0 @t5 @t85)) % 0.24/0.47 (define @t90 () (tptp.slbdtsldtrb0 @t86 tptp.xk)) % 0.24/0.47 (define @t91 () (tptp.aElementOf0 @t5 @t90)) % 0.24/0.47 (define @t92 () (and @t19 @t91)) % 0.24/0.47 (define @t93 () (tptp.sdtlpdtrp0 tptp.xC @t1)) % 0.24/0.47 (define @t94 () (tptp.sdtlpdtrp0 @t93 @t5)) % 0.24/0.47 (define @t95 () (= @t94 (tptp.sdtlpdtrp0 tptp.xc @t89))) % 0.24/0.47 (define @t96 () (forall @t8 (=> @t92 @t95))) % 0.24/0.47 (define @t97 () (tptp.szDzozmdt0 @t93)) % 0.24/0.47 (define @t98 () (tptp.aFunction0 @t93)) % 0.24/0.47 (define @t99 () (and @t98 (= @t97 @t90) @t96)) % 0.24/0.47 (define @t100 () (=> @t44 @t99)) % 0.24/0.47 (define @t101 () (forall @t3 @t100)) % 0.24/0.47 (define @t102 () (tptp.aElementOf0 @t5 tptp.xT)) % 0.24/0.47 (define @t103 () (tptp.slbdtsldtrb0 @t83 tptp.xk)) % 0.24/0.47 (define @t104 () (tptp.szDzozmdt0 tptp.xd)) % 0.24/0.47 (define @t105 () (tptp.szDzizrdt0 tptp.xd)) % 0.24/0.47 (define @t106 () (tptp.sdtlbdtrb0 tptp.xd @t105)) % 0.24/0.47 (define @t107 () (tptp.aSet0 tptp.xO)) % 0.24/0.47 (define @t108 () (tptp.szmzizndt0 tptp.xQ)) % 0.24/0.47 (define @t109 () (tptp.aSet0 tptp.xP)) % 0.24/0.47 (define @t110 () (tptp.aElementOf0 tptp.xn tptp.szNzAzT0)) % 0.24/0.47 (define @t111 () (tptp.sdtlpdtrp0 tptp.xN tptp.xn)) % 0.24/0.47 (define @t112 () (tptp.szmzizndt0 @t111)) % 0.24/0.47 (define @t113 () (tptp.sdtmndt0 @t111 @t112)) % 0.24/0.47 (define @t114 () (tptp.slbdtsldtrb0 tptp.xD tptp.xk)) % 0.24/0.47 (define @t115 () (tptp.aElementOf0 tptp.xP @t114)) % 0.24/0.47 (define @t116 () (tptp.sdtlpdtrp0 tptp.xC tptp.xn)) % 0.24/0.47 (define @t117 () (tptp.sdtlpdtrp0 @t116 tptp.xP)) % 0.24/0.47 (define @t118 () (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 tptp.xP @t112))) % 0.24/0.47 (define @t119 () (= @t118 @t117)) % 0.24/0.47 (define @t120 () (@var "BOUND_VARIABLE_9468" $$unsorted)) % 0.24/0.47 (define @t121 () (or (not (tptp.aSet0 @t120)) (not (tptp.aElementOf0 @t120 @t90)) (= (tptp.sdtlpdtrp0 @t93 @t120) (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 @t120 @t85))))) % 0.24/0.47 (define @t122 () (= @t90 @t97)) % 0.24/0.47 (define @t123 () (and @t98 @t122 @t121)) % 0.24/0.47 (define @t124 () (not @t44)) % 0.24/0.47 (define @t125 () (or @t124 @t123)) % 0.24/0.47 (define @t126 () (forall (@list @t1 @t120) @t125)) % 0.24/0.47 (define @t127 () (@list @t120)) % 0.24/0.47 (define @t128 () (forall @t127 @t125)) % 0.24/0.47 (define @t129 () (forall @t127 @t121)) % 0.24/0.47 (define @t130 () (forall @t127 @t122)) % 0.24/0.47 (define @t131 () (forall @t127 @t98)) % 0.24/0.47 (define @t132 () (and @t131 @t130 @t129)) % 0.24/0.47 (define @t133 () (forall @t127 @t123)) % 0.24/0.47 (define @t134 () (or @t124 @t133)) % 0.24/0.47 (define @t135 () (not @t91)) % 0.24/0.47 (define @t136 () (not @t19)) % 0.24/0.47 (define @t137 () (or @t136 @t135 @t95)) % 0.24/0.47 (define @t138 () (and @t98 @t122 (forall @t8 @t137))) % 0.24/0.47 (define @t139 () (tptp.slbdtsldtrb0 @t113 tptp.xk)) % 0.24/0.47 (define @t140 () (not (tptp.aElementOf0 tptp.xP @t139))) % 0.24/0.47 (define @t141 () (not @t109)) % 0.24/0.47 (define @t142 () (or @t141 @t140 (= @t117 @t118))) % 0.24/0.47 (define @t143 () (tptp.szDzozmdt0 @t116)) % 0.24/0.47 (define @t144 () (tptp.aFunction0 @t116)) % 0.24/0.47 (define @t145 () (and @t144 (= @t139 @t143) @t142)) % 0.24/0.47 (define @t146 () (not @t110)) % 0.24/0.47 (define @t147 () (or @t146 @t145)) % 0.24/0.47 (define @t148 () (or @t141 @t140 @t119)) % 0.24/0.47 (define @t149 () (and @t144 (= @t143 @t139) @t148)) % 0.24/0.47 (define @t150 () (or @t146 @t149)) % 0.24/0.47 (define @t151 () (@list false)) % 0.24/0.47 (assume @p1 (forall @t3 (=> @t2 true))) % 0.24/0.47 (assume @p2 (forall @t3 (=> @t4 true))) % 0.24/0.47 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.24/0.47 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.24/0.47 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.24/0.47 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.24/0.47 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.24/0.47 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.24/0.47 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.24/0.47 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.24/0.47 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.24/0.47 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.24/0.47 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.24/0.47 (assume @p14 (forall @t28 (=> (and @t2 @t19 @t27) (=> (and @t24 @t26) (tptp.aSubsetOf0 @t1 @t15))))) % 0.24/0.47 (assume @p15 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t35) (and @t27 (forall @t34 (= @t33 (and @t32 (or @t31 @t30)))))))))) % 0.24/0.47 (assume @p16 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t37) (and @t27 (forall @t34 (= @t33 (and @t32 @t31 (not @t30)))))))))) % 0.24/0.47 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t37 @t5) @t1)))))) % 0.24/0.47 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t38 @t1) @t5))))) % 0.24/0.47 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t38)))))) % 0.24/0.47 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t41)))))) % 0.24/0.47 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t38)))))) % 0.24/0.47 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t41)))))) % 0.24/0.47 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.24/0.47 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.24/0.47 (assume @p25 (forall @t3 (=> @t44 (and (tptp.aElementOf0 @t43 tptp.szNzAzT0) (not (= @t43 tptp.sz00)))))) % 0.24/0.47 (assume @p26 (forall @t25 (=> @t47 (=> (= @t43 @t45) @t23)))) % 0.24/0.47 (assume @p27 (forall @t3 (=> @t44 (or @t48 (exists @t8 (and @t46 (= @t1 @t45))))))) % 0.24/0.47 (assume @p28 (forall @t3 (=> @t44 (not (= @t1 @t43))))) % 0.24/0.47 (assume @p29 (forall @t25 (=> @t47 (=> @t49 true)))) % 0.24/0.47 (assume @p30 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.24/0.47 (assume @p31 (forall @t3 (=> @t44 (not (tptp.sdtlseqdt0 @t43 tptp.sz00))))) % 0.24/0.47 (assume @p32 (forall @t25 (=> @t47 (= @t49 (tptp.sdtlseqdt0 @t43 @t45))))) % 0.24/0.47 (assume @p33 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t43)))) % 0.24/0.47 (assume @p34 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.24/0.47 (assume @p35 (forall @t25 (=> @t47 (=> (and @t49 @t50) @t23)))) % 0.24/0.47 (assume @p36 (forall @t28 (=> (and @t44 @t46 @t52) (=> (and @t49 @t51) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.24/0.47 (assume @p37 (forall @t25 (=> @t47 (or @t49 (tptp.sdtlseqdt0 @t45 @t1))))) % 0.24/0.47 (assume @p38 (forall @t25 (=> @t47 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.24/0.47 (assume @p39 (forall @t3 (=> @t44 (tptp.iLess0 @t1 @t43)))) % 0.24/0.47 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t53)))) % 0.24/0.47 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t53 tptp.szNzAzT0) @t9)))) % 0.24/0.47 (assume @p42 (forall @t3 (=> @t2 (= (= @t53 tptp.sz00) @t10)))) % 0.24/0.47 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t35) (tptp.szszuzczcdt0 @t53)))))))) % 0.24/0.47 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t37)) @t53)))))) % 0.24/0.47 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t53)))))) % 0.24/0.47 (assume @p46 (forall @t25 (=> @t54 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t53)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.24/0.47 (assume @p47 (forall @t3 (=> (and @t56 @t14) (forall @t8 (= (= @t5 @t55) (and @t7 (forall @t18 (=> @t16 @t51)))))))) % 0.24/0.47 (assume @p48 (forall @t3 (=> (and @t56 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.24/0.47 (assume @p49 (forall @t25 (=> (and @t56 @t58 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t55 @t5) (tptp.aElementOf0 @t57 @t1)) (= @t55 @t57))))) % 0.24/0.47 (assume @p50 (forall @t3 (=> @t44 (forall @t8 (= (= @t5 @t59) (and @t19 (forall @t18 (= @t17 (and @t52 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.24/0.47 (assume @p51 (forall @t3 (=> @t44 (tptp.isFinite0 @t59)))) % 0.24/0.47 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.24/0.47 (assume @p53 (forall @t25 (=> @t47 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t45)) (or (tptp.aElementOf0 @t1 @t60) @t23))))) % 0.24/0.47 (assume @p54 (forall @t25 (=> @t47 (= @t49 (tptp.aSubsetOf0 @t59 @t60))))) % 0.24/0.47 (assume @p55 (forall @t3 (=> (and @t56 @t9) (exists @t8 (and @t46 (tptp.aSubsetOf0 @t1 @t60)))))) % 0.24/0.47 (assume @p56 (forall @t3 (=> @t44 (= (tptp.sbrdtbr0 @t59) @t1)))) % 0.24/0.47 (assume @p57 (forall @t25 (=> @t54 (forall @t18 (= (= @t15 @t62) (and @t27 (forall @t34 (= @t33 (and @t61 (= (tptp.sbrdtbr0 @t29) @t5)))))))))) % 0.24/0.47 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t46 (tptp.isFinite0 @t62)))))) % 0.24/0.47 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t46 (not (= @t62 tptp.slcrc0))))))) % 0.24/0.47 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t46 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t62)))))) % 0.24/0.47 (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)))))) % 0.24/0.47 (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))))))))) % 0.24/0.47 (assume @p63 (forall @t3 (=> @t64 true))) % 0.24/0.47 (assume @p64 (forall @t3 (=> @t64 (tptp.aSet0 @t65)))) % 0.24/0.47 (assume @p65 (forall @t3 (=> @t64 (forall @t8 (=> @t67 (tptp.aElement0 @t66)))))) % 0.24/0.47 (assume @p66 (forall @t25 (=> @t71 (forall @t18 (= (= @t15 @t70) (and @t27 (forall @t34 (= @t33 (and @t69 (= @t68 @t5)))))))))) % 0.24/0.47 (assume @p67 (forall @t25 (=> @t71 (tptp.aSubsetOf0 @t70 @t65)))) % 0.24/0.47 (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))))))))))))) % 0.24/0.47 (assume @p69 (forall @t3 (=> @t64 (forall @t8 (=> @t67 (tptp.aElementOf0 @t66 @t76)))))) % 0.24/0.47 (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))))))))))) % 0.24/0.47 (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))))))) % 0.24/0.47 (assume @p72 (forall @t3 (=> @t64 (=> (and (tptp.isCountable0 @t65) (tptp.isFinite0 @t76)) (and (tptp.aElement0 @t79) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t79))))))) % 0.24/0.47 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.24/0.47 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.24/0.47 (assume @p75 (and (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.24/0.47 (assume @p76 (and (tptp.aFunction0 tptp.xc) (= @t80 @t81) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc @t80) tptp.xT))) % 0.24/0.47 (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))))))))))))))) % 0.24/0.47 (assume @p78 (not (= tptp.xK tptp.sz00))) % 0.24/0.47 (assume @p79 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK))) % 0.24/0.47 (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))))))) % 0.24/0.47 (assume @p81 (forall @t3 (=> @t44 @t87))) % 0.24/0.47 (assume @p82 (forall @t25 (=> @t47 (=> @t50 (tptp.aSubsetOf0 @t84 @t88))))) % 0.24/0.47 (assume @p83 (forall @t25 (=> (and @t44 @t46 (not @t23)) (not (= @t85 (tptp.szmzizndt0 @t88)))))) % 0.24/0.47 (assume @p84 (forall @t3 (=> @t44 (forall @t8 (=> @t92 (tptp.aElementOf0 @t89 @t81)))))) % 0.24/0.47 (assume @p85 (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) @t101)) % 0.24/0.47 (assume @p86 (forall @t3 (=> @t44 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t93 @t97) tptp.xT)))) % 0.24/0.47 (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)))))))) % 0.24/0.47 (assume @p88 (forall @t3 (=> @t44 (exists @t8 (and @t102 (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 @t93 @t29) @t5)))))))))) % 0.24/0.47 (assume @p89 (forall @t3 (=> @t44 (exists @t8 (and @t102 (forall @t18 (=> (and @t27 (tptp.aElementOf0 @t15 @t103)) (= (tptp.sdtlpdtrp0 @t93 @t15) @t5)))))))) % 0.24/0.47 (assume @p90 (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall @t3 (=> @t44 (= (tptp.sdtlpdtrp0 tptp.xe @t1) @t85))))) % 0.24/0.47 (assume @p91 (and (tptp.aFunction0 tptp.xd) (= @t104 tptp.szNzAzT0) (forall @t3 (=> @t44 (forall @t8 (=> (and @t19 (tptp.aElementOf0 @t5 @t103)) (= (tptp.sdtlpdtrp0 tptp.xd @t1) @t94))))))) % 0.24/0.47 (assume @p92 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xd @t104) tptp.xT)) % 0.24/0.47 (assume @p93 (and (tptp.aElementOf0 @t105 tptp.xT) (tptp.isCountable0 @t106))) % 0.24/0.47 (assume @p94 (and @t107 (= tptp.xO (tptp.sdtlcdtrc0 tptp.xe @t106)))) % 0.24/0.47 (assume @p95 (and @t107 (tptp.isCountable0 tptp.xO))) % 0.24/0.47 (assume @p96 (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xO) (exists @t8 (and @t46 (tptp.aElementOf0 @t5 @t106) (= (tptp.sdtlpdtrp0 tptp.xe @t5) @t1)))))) % 0.24/0.47 (assume @p97 (tptp.aSubsetOf0 tptp.xO tptp.xS)) % 0.24/0.47 (assume @p98 (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 tptp.xO tptp.xK))) % 0.24/0.47 (assume @p99 (and (tptp.aSubsetOf0 tptp.xQ tptp.xO) (not (= tptp.xQ tptp.slcrc0)))) % 0.24/0.47 (assume @p100 (tptp.aSubsetOf0 tptp.xQ tptp.szNzAzT0)) % 0.24/0.47 (assume @p101 (tptp.aElementOf0 tptp.xQ @t80)) % 0.24/0.47 (assume @p102 (= tptp.xp @t108)) % 0.24/0.47 (assume @p103 (and @t109 (= tptp.xP (tptp.sdtmndt0 tptp.xQ @t108)))) % 0.24/0.47 (assume @p104 (tptp.aElementOf0 tptp.xp tptp.xQ)) % 0.24/0.47 (assume @p105 (tptp.aElementOf0 tptp.xp tptp.xO)) % 0.24/0.47 (assume @p106 (tptp.aSubsetOf0 tptp.xP tptp.xQ)) % 0.24/0.47 (assume @p107 (tptp.aSubsetOf0 tptp.xP tptp.xO)) % 0.24/0.47 (assume @p108 (= (tptp.sbrdtbr0 tptp.xP) tptp.xk)) % 0.24/0.47 (assume @p109 (tptp.aElementOf0 tptp.xP (tptp.slbdtsldtrb0 tptp.xO tptp.xk))) % 0.24/0.47 (assume @p110 (and (tptp.aElementOf0 tptp.xn @t106) @t110 (= (tptp.sdtlpdtrp0 tptp.xe tptp.xn) tptp.xp))) % 0.24/0.47 (assume @p111 (= (tptp.sdtlpdtrp0 tptp.xd tptp.xn) @t105)) % 0.24/0.47 (assume @p112 (tptp.aSubsetOf0 tptp.xP (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xn)))) % 0.24/0.47 (assume @p113 (= tptp.xD @t113)) % 0.24/0.47 (assume @p114 @t115) % 0.24/0.47 (assume @p115 (not @t119)) % 0.24/0.47 (assume @p116 true) % 0.24/0.47 (step @p117 :rule evaluate :args ((= true false))) % 0.24/0.47 (step @p118 :rule quant-merge-prenex :args ((= (forall @t3 @t128) @t126))) % 0.24/0.47 (step @p119 :rule alpha_equiv :args (@t129 (@list @t120) (@list @t5))) % 0.24/0.47 (step @p120 :rule quant-unused-vars :args ((= @t130 @t122))) % 0.24/0.47 (step @p121 :rule quant-unused-vars :args ((= @t131 @t98))) % 0.24/0.47 (step @p122 :rule nary_cong :premises (@p121 @p120 @p119) :args (@t132)) % 0.24/0.47 (step @p123 :rule quant-miniscope-and :args ((= @t133 @t132))) % 0.24/0.47 (step @p124 :rule trans :premises (@p123 @p122)) % 0.24/0.47 (step @p125 :rule refl :args (@t124)) % 0.24/0.47 (step @p126 :rule nary_cong :premises (@p125 @p124) :args (@t134)) % 0.24/0.47 (step @p127 :rule quant-miniscope-or :args ((= @t128 @t134))) % 0.24/0.47 (step @p128 :rule trans :premises (@p127 @p126)) % 0.24/0.47 (step @p129 :rule symm :premises (@p128)) % 0.24/0.47 (step @p130 :rule cong :premises (@p129) :args ((forall @t3 (or @t124 @t138)))) % 0.24/0.47 (step @p131 :rule trans :premises (@p130 @p118)) % 0.24/0.47 (step @p132 :rule bool-impl-elim :args (@t44 @t138)) % 0.24/0.47 (step @p133 :rule cong :premises (@p132) :args ((forall @t3 (=> @t44 @t138)))) % 0.24/0.47 (step @p134 :rule trans :premises (@p133 @p131)) % 0.24/0.47 (step @p135 :rule aci_norm :args ((= (or (or @t136 @t135) @t95) @t137))) % 0.24/0.47 (step @p136 :rule refl :args (@t95)) % 0.24/0.47 (step @p137 :rule bool-and-de-morgan :args (@t19 @t91 true)) % 0.24/0.47 (step @p138 :rule nary_cong :premises (@p137 @p136) :args ((or (not @t92) @t95))) % 0.24/0.47 (step @p139 :rule trans :premises (@p138 @p135)) % 0.24/0.47 (step @p140 :rule bool-impl-elim :args (@t92 @t95)) % 0.24/0.47 (step @p141 :rule trans :premises (@p140 @p139)) % 0.24/0.47 (step @p142 :rule cong :premises (@p141) :args (@t96)) % 0.24/0.47 (step @p143 :rule eq-symm :args (@t97 @t90)) % 0.24/0.47 (step @p144 :rule refl :args (@t98)) % 0.24/0.47 (step @p145 :rule nary_cong :premises (@p144 @p143 @p142) :args (@t99)) % 0.24/0.47 (step @p146 :rule refl :args (@t44)) % 0.24/0.47 (step @p147 :rule cong :premises (@p146 @p145) :args (@t100)) % 0.24/0.47 (step @p148 :rule cong :premises (@p147) :args (@t101)) % 0.24/0.47 (step @p149 :rule trans :premises (@p148 @p134)) % 0.24/0.47 (step @p150 :rule and_elim :premises (@p85) :args (2)) % 0.24/0.47 (step @p151 :rule eq_resolve :premises (@p150 @p149)) % 0.24/0.47 (step @p152 :rule eq-symm :args (@t117 @t118)) % 0.24/0.47 (step @p153 :rule refl :args (@t140)) % 0.24/0.47 (step @p154 :rule refl :args (@t141)) % 0.24/0.47 (step @p155 :rule nary_cong :premises (@p154 @p153 @p152) :args (@t142)) % 0.24/0.47 (step @p156 :rule eq-symm :args (@t139 @t143)) % 0.24/0.47 (step @p157 :rule refl :args (@t144)) % 0.24/0.47 (step @p158 :rule nary_cong :premises (@p157 @p156 @p155) :args (@t145)) % 0.24/0.47 (step @p159 :rule refl :args (@t146)) % 0.24/0.47 (step @p160 :rule nary_cong :premises (@p159 @p158) :args (@t147)) % 0.24/0.47 (step @p161 :rule refl :args (@t126)) % 0.24/0.47 (step @p162 :rule cong :premises (@p161 @p160) :args ((=> @t126 @t147))) % 0.24/0.47 (assume-push @p190 @t126) % 0.24/0.47 (step @p164 :rule instantiate :premises (@p151) :args ((@list tptp.xn tptp.xP))) % 0.24/0.47 (step-pop @p191 :rule scope :premises (@p164)) % 0.24/0.47 (step @p165 :rule process_scope :premises (@p191) :args (@t147)) % 0.24/0.47 (step @p167 :rule eq_resolve :premises (@p165 @p162)) % 0.24/0.47 (step @p168 :rule implies_elim :premises (@p167)) % 0.24/0.47 (step @p169 :rule chain_m_resolution :premises (@p168 @p151) :args (@t150 @t151 (@list @t126))) % 0.24/0.47 (step @p170 :rule and_elim :premises (@p110) :args (1)) % 0.24/0.47 (step @p171 :rule cnf_or_pos :args (@t150)) % 0.24/0.47 (step @p172 :rule reordering :premises (@p171) :args ((or @t146 @t149 (not @t150)))) % 0.24/0.47 (step @p173 :rule chain_m_resolution :premises (@p172 @p170 @p169) :args (@t149 (@list false false) (@list @t110 @t150))) % 0.24/0.47 (step @p174 :rule cnf_and_pos :args (@t149 2)) % 0.24/0.47 (step @p175 :rule reordering :premises (@p174) :args ((or @t148 (not @t149)))) % 0.24/0.47 (step @p176 :rule chain_m_resolution :premises (@p175 @p173) :args (@t148 @t151 (@list @t149))) % 0.24/0.47 (step @p177 :rule and_elim :premises (@p103) :args (0)) % 0.24/0.47 (step @p178 :rule cnf_or_pos :args (@t148)) % 0.24/0.47 (step @p179 :rule reordering :premises (@p178) :args ((or @t119 @t141 @t140 (not @t148)))) % 0.24/0.47 (step @p180 :rule chain_m_resolution :premises (@p179 @p115 @p177 @p176) :args (@t140 (@list true false false) (@list @t119 @t109 @t148))) % 0.24/0.47 (step @p181 :rule false_intro :premises (@p180)) % 0.24/0.47 (step @p182 :rule refl :args (tptp.xk)) % 0.24/0.47 (step @p183 :rule cong :premises (@p113 @p182) :args (@t114)) % 0.24/0.47 (step @p184 :rule refl :args (tptp.xP)) % 0.24/0.47 (step @p185 :rule cong :premises (@p184 @p183) :args (@t115)) % 0.24/0.47 (step @p186 :rule true_intro :premises (@p114)) % 0.24/0.47 (step @p187 :rule symm :premises (@p186)) % 0.24/0.47 (step @p188 :rule trans :premises (@p187 @p185 @p181)) % 0.24/0.47 (step @p189 false :rule eq_resolve :premises (@p188 @p117)) % 0.24/0.47 ) % 0.24/0.47 % SZS output end Proof % 0.24/0.47 % cvc5 exiting %------------------------------------------------------------------------------