%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM617+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 : n010.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 08:40:01 AM UTC 2026 % Result : Theorem 0.35s 0.98s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM617+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.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 11:36:55 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.98 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.98 % SZS status Theorem % 0.35/0.98 % SZS output start Proof % 0.35/0.98 ( % 0.35/0.98 (declare-sort $$unsorted 0) % 0.35/0.98 (declare-const tptp.xx $$unsorted) % 0.35/0.98 (declare-const tptp.xn $$unsorted) % 0.35/0.98 (declare-const tptp.xp $$unsorted) % 0.35/0.98 (declare-const tptp.xQ $$unsorted) % 0.35/0.98 (declare-const tptp.xe $$unsorted) % 0.35/0.98 (declare-const tptp.xP $$unsorted) % 0.35/0.98 (declare-const tptp.xC $$unsorted) % 0.35/0.98 (declare-const tptp.xN $$unsorted) % 0.35/0.98 (declare-const tptp.sz00 $$unsorted) % 0.35/0.98 (declare-const tptp.xc $$unsorted) % 0.35/0.98 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.35/0.98 (declare-const tptp.szNzAzT0 $$unsorted) % 0.35/0.98 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.98 (declare-const tptp.xd $$unsorted) % 0.35/0.98 (declare-const tptp.xk $$unsorted) % 0.35/0.98 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.98 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.35/0.98 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.35/0.98 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.35/0.98 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.35/0.98 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.98 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.98 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.xK $$unsorted) % 0.35/0.98 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.xT $$unsorted) % 0.35/0.98 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.xO $$unsorted) % 0.35/0.98 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.xS $$unsorted) % 0.35/0.98 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.slcrc0 $$unsorted) % 0.35/0.98 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.98 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.98 (define @t1 () (@var "W0" $$unsorted)) % 0.35/0.98 (define @t2 () (tptp.aSet0 @t1)) % 0.35/0.98 (define @t3 () (@list @t1)) % 0.35/0.98 (define @t4 () (tptp.aElement0 @t1)) % 0.35/0.98 (define @t5 () (@var "W1" $$unsorted)) % 0.35/0.98 (define @t6 () (tptp.aElement0 @t5)) % 0.35/0.98 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.35/0.98 (define @t8 () (@list @t5)) % 0.35/0.98 (define @t9 () (tptp.isFinite0 @t1)) % 0.35/0.98 (define @t10 () (= @t1 tptp.slcrc0)) % 0.35/0.98 (define @t11 () (tptp.isCountable0 @t1)) % 0.35/0.98 (define @t12 () (not @t9)) % 0.35/0.98 (define @t13 () (and @t2 @t11)) % 0.35/0.98 (define @t14 () (not @t10)) % 0.35/0.98 (define @t15 () (@var "W2" $$unsorted)) % 0.35/0.98 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.35/0.98 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.35/0.98 (define @t18 () (@list @t15)) % 0.35/0.98 (define @t19 () (forall @t18 (=> @t17 @t16))) % 0.35/0.98 (define @t20 () (tptp.aSet0 @t5)) % 0.35/0.98 (define @t21 () (and @t20 @t19)) % 0.35/0.98 (define @t22 () (tptp.aSubsetOf0 @t5 @t1)) % 0.35/0.98 (define @t23 () (= @t22 @t21)) % 0.35/0.98 (define @t24 () (forall @t8 @t23)) % 0.35/0.98 (define @t25 () (=> @t2 @t24)) % 0.35/0.98 (define @t26 () (forall @t3 @t25)) % 0.35/0.98 (define @t27 () (tptp.isFinite0 @t5)) % 0.35/0.98 (define @t28 () (and @t2 @t9)) % 0.35/0.98 (define @t29 () (= @t1 @t5)) % 0.35/0.98 (define @t30 () (tptp.aSubsetOf0 @t1 @t5)) % 0.35/0.98 (define @t31 () (@list @t1 @t5)) % 0.35/0.98 (define @t32 () (tptp.aSubsetOf0 @t5 @t15)) % 0.35/0.98 (define @t33 () (tptp.aSet0 @t15)) % 0.35/0.98 (define @t34 () (@list @t1 @t5 @t15)) % 0.35/0.98 (define @t35 () (@var "W3" $$unsorted)) % 0.35/0.98 (define @t36 () (= @t35 @t5)) % 0.35/0.98 (define @t37 () (tptp.aElementOf0 @t35 @t1)) % 0.35/0.98 (define @t38 () (tptp.aElement0 @t35)) % 0.35/0.98 (define @t39 () (tptp.aElementOf0 @t35 @t15)) % 0.35/0.98 (define @t40 () (@list @t35)) % 0.35/0.98 (define @t41 () (tptp.sdtpldt0 @t1 @t5)) % 0.35/0.98 (define @t42 () (and @t2 @t6)) % 0.35/0.98 (define @t43 () (tptp.sdtmndt0 @t1 @t5)) % 0.35/0.98 (define @t44 () (tptp.sdtpldt0 @t5 @t1)) % 0.35/0.98 (define @t45 () (tptp.isCountable0 @t5)) % 0.35/0.98 (define @t46 () (and @t20 @t45)) % 0.35/0.98 (define @t47 () (tptp.sdtmndt0 @t5 @t1)) % 0.35/0.98 (define @t48 () (and @t20 @t27)) % 0.35/0.98 (define @t49 () (tptp.aSet0 tptp.szNzAzT0)) % 0.35/0.98 (define @t50 () (tptp.szszuzczcdt0 @t1)) % 0.35/0.98 (define @t51 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.35/0.98 (define @t52 () (tptp.szszuzczcdt0 @t5)) % 0.35/0.98 (define @t53 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.35/0.98 (define @t54 () (and @t51 @t53)) % 0.35/0.98 (define @t55 () (= @t1 tptp.sz00)) % 0.35/0.98 (define @t56 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.35/0.98 (define @t57 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.35/0.98 (define @t58 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.35/0.98 (define @t59 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.35/0.98 (define @t60 () (tptp.sbrdtbr0 @t1)) % 0.35/0.98 (define @t61 () (and @t2 @t53)) % 0.35/0.98 (define @t62 () (tptp.szmzizndt0 @t1)) % 0.35/0.98 (define @t63 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.35/0.98 (define @t64 () (tptp.szmzizndt0 @t5)) % 0.35/0.98 (define @t65 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.35/0.98 (define @t66 () (tptp.slbdtrb0 @t1)) % 0.35/0.98 (define @t67 () (tptp.slbdtrb0 @t5)) % 0.35/0.98 (define @t68 () (tptp.aSubsetOf0 @t35 @t1)) % 0.35/0.98 (define @t69 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.35/0.98 (define @t70 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.35/0.98 (define @t71 () (tptp.aFunction0 @t1)) % 0.35/0.98 (define @t72 () (tptp.szDzozmdt0 @t1)) % 0.35/0.98 (define @t73 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.35/0.98 (define @t74 () (tptp.aElementOf0 @t5 @t72)) % 0.35/0.98 (define @t75 () (tptp.sdtlpdtrp0 @t1 @t35)) % 0.35/0.98 (define @t76 () (tptp.aElementOf0 @t35 @t72)) % 0.35/0.98 (define @t77 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.35/0.98 (define @t78 () (and @t71 @t6)) % 0.35/0.98 (define @t79 () (@var "W4" $$unsorted)) % 0.35/0.98 (define @t80 () (@list @t79)) % 0.35/0.98 (define @t81 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.35/0.98 (define @t82 () (tptp.aSubsetOf0 @t5 @t72)) % 0.35/0.98 (define @t83 () (tptp.sdtlcdtrc0 @t1 @t72)) % 0.35/0.98 (define @t84 () (tptp.szDzozmdt0 @t15)) % 0.35/0.98 (define @t85 () (tptp.aFunction0 @t15)) % 0.35/0.98 (define @t86 () (tptp.szDzizrdt0 @t1)) % 0.35/0.98 (define @t87 () (tptp.szDzozmdt0 tptp.xc)) % 0.35/0.98 (define @t88 () (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) % 0.35/0.98 (define @t89 () (@var "W5" $$unsorted)) % 0.35/0.98 (define @t90 () (tptp.sdtlpdtrp0 tptp.xN @t50)) % 0.35/0.98 (define @t91 () (tptp.sdtlpdtrp0 tptp.xN @t1)) % 0.35/0.98 (define @t92 () (tptp.szmzizndt0 @t91)) % 0.35/0.98 (define @t93 () (tptp.sdtmndt0 @t91 @t92)) % 0.35/0.98 (define @t94 () (and (tptp.aSubsetOf0 @t91 tptp.szNzAzT0) (tptp.isCountable0 @t91))) % 0.35/0.98 (define @t95 () (tptp.sdtlpdtrp0 tptp.xN @t5)) % 0.35/0.98 (define @t96 () (tptp.sdtpldt0 @t5 @t92)) % 0.35/0.98 (define @t97 () (tptp.slbdtsldtrb0 @t93 tptp.xk)) % 0.35/0.98 (define @t98 () (and @t20 (tptp.aElementOf0 @t5 @t97))) % 0.35/0.98 (define @t99 () (tptp.sdtlpdtrp0 tptp.xC @t1)) % 0.35/0.98 (define @t100 () (tptp.sdtlpdtrp0 @t99 @t5)) % 0.35/0.98 (define @t101 () (tptp.szDzozmdt0 @t99)) % 0.35/0.98 (define @t102 () (tptp.aElementOf0 @t5 tptp.xT)) % 0.35/0.98 (define @t103 () (tptp.slbdtsldtrb0 @t90 tptp.xk)) % 0.35/0.98 (define @t104 () (tptp.szDzozmdt0 tptp.xd)) % 0.35/0.98 (define @t105 () (tptp.szDzizrdt0 tptp.xd)) % 0.35/0.98 (define @t106 () (tptp.sdtlbdtrb0 tptp.xd @t105)) % 0.35/0.98 (define @t107 () (tptp.aSet0 tptp.xO)) % 0.35/0.98 (define @t108 () (tptp.aSubsetOf0 tptp.xQ tptp.szNzAzT0)) % 0.35/0.98 (define @t109 () (tptp.szmzizndt0 tptp.xQ)) % 0.35/0.98 (define @t110 () (tptp.aSet0 tptp.xP)) % 0.35/0.98 (define @t111 () (tptp.aSubsetOf0 tptp.xP tptp.xQ)) % 0.35/0.98 (define @t112 () (tptp.aElementOf0 tptp.xx tptp.xP)) % 0.35/0.98 (define @t113 () (tptp.aElementOf0 tptp.xx tptp.szNzAzT0)) % 0.35/0.98 (define @t114 () (@var "BOUND_VARIABLE_8248" $$unsorted)) % 0.35/0.98 (define @t115 () (= (tptp.aSubsetOf0 @t114 @t1) (and (tptp.aSet0 @t114) (forall @t18 (or (not (tptp.aElementOf0 @t15 @t114)) @t16))))) % 0.35/0.98 (define @t116 () (not @t2)) % 0.35/0.98 (define @t117 () (or @t116 @t115)) % 0.35/0.98 (define @t118 () (@list @t114)) % 0.35/0.98 (define @t119 () (forall @t118 @t117)) % 0.35/0.98 (define @t120 () (forall @t118 @t115)) % 0.35/0.98 (define @t121 () (or @t116 @t120)) % 0.35/0.98 (define @t122 () (forall @t8 (= @t22 (and @t20 (forall @t18 (or (not @t17) @t16)))))) % 0.35/0.98 (define @t123 () (tptp.aElementOf0 @t15 tptp.xQ)) % 0.35/0.98 (define @t124 () (forall @t18 (or (not @t123) @t59))) % 0.35/0.98 (define @t125 () (tptp.aSet0 tptp.xQ)) % 0.35/0.98 (define @t126 () (and @t125 @t124)) % 0.35/0.98 (define @t127 () (= @t108 @t126)) % 0.35/0.98 (define @t128 () (not @t49)) % 0.35/0.98 (define @t129 () (or @t128 @t127)) % 0.35/0.98 (define @t130 () (@list false false)) % 0.35/0.98 (define @t131 () (not @t126)) % 0.35/0.98 (define @t132 () (@list false)) % 0.35/0.98 (define @t133 () (@list @t126)) % 0.35/0.98 (define @t134 () (forall @t18 (or (not (tptp.aElementOf0 @t15 tptp.xP)) @t123))) % 0.35/0.98 (define @t135 () (and @t110 @t134)) % 0.35/0.98 (define @t136 () (= @t111 @t135)) % 0.35/0.98 (define @t137 () (not @t125)) % 0.35/0.98 (define @t138 () (or @t137 @t136)) % 0.35/0.98 (define @t139 () (@list tptp.xx)) % 0.35/0.98 (define @t140 () (tptp.aElementOf0 tptp.xx tptp.xQ)) % 0.35/0.98 (define @t141 () (not @t140)) % 0.35/0.98 (define @t142 () (or @t141 @t113)) % 0.35/0.98 (define @t143 () (not @t112)) % 0.35/0.98 (define @t144 () (or @t143 @t140)) % 0.35/0.98 (assume @p1 (forall @t3 (=> @t2 true))) % 0.35/0.98 (assume @p2 (forall @t3 (=> @t4 true))) % 0.35/0.98 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.35/0.98 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.35/0.98 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.35/0.98 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.35/0.98 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.35/0.98 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.35/0.98 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.35/0.98 (assume @p10 @t26) % 0.35/0.98 (assume @p11 (forall @t3 (=> @t28 (forall @t8 (=> @t22 @t27))))) % 0.35/0.98 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.35/0.98 (assume @p13 (forall @t31 (=> (and @t2 @t20) (=> (and @t30 @t22) @t29)))) % 0.35/0.98 (assume @p14 (forall @t34 (=> (and @t2 @t20 @t33) (=> (and @t30 @t32) (tptp.aSubsetOf0 @t1 @t15))))) % 0.35/0.98 (assume @p15 (forall @t31 (=> @t42 (forall @t18 (= (= @t15 @t41) (and @t33 (forall @t40 (= @t39 (and @t38 (or @t37 @t36)))))))))) % 0.35/0.98 (assume @p16 (forall @t31 (=> @t42 (forall @t18 (= (= @t15 @t43) (and @t33 (forall @t40 (= @t39 (and @t38 @t37 (not @t36)))))))))) % 0.35/0.98 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t43 @t5) @t1)))))) % 0.35/0.98 (assume @p18 (forall @t31 (=> (and @t4 @t20) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t44 @t1) @t5))))) % 0.35/0.98 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isCountable0 @t44)))))) % 0.35/0.98 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isCountable0 @t47)))))) % 0.35/0.98 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t48 (tptp.isFinite0 @t44)))))) % 0.35/0.98 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t48 (tptp.isFinite0 @t47)))))) % 0.35/0.98 (assume @p23 (and @t49 (tptp.isCountable0 tptp.szNzAzT0))) % 0.35/0.98 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.35/0.98 (assume @p25 (forall @t3 (=> @t51 (and (tptp.aElementOf0 @t50 tptp.szNzAzT0) (not (= @t50 tptp.sz00)))))) % 0.35/0.98 (assume @p26 (forall @t31 (=> @t54 (=> (= @t50 @t52) @t29)))) % 0.35/0.98 (assume @p27 (forall @t3 (=> @t51 (or @t55 (exists @t8 (and @t53 (= @t1 @t52))))))) % 0.35/0.98 (assume @p28 (forall @t3 (=> @t51 (not (= @t1 @t50))))) % 0.35/0.98 (assume @p29 (forall @t31 (=> @t54 (=> @t56 true)))) % 0.35/0.98 (assume @p30 (forall @t3 (=> @t51 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.35/0.98 (assume @p31 (forall @t3 (=> @t51 (not (tptp.sdtlseqdt0 @t50 tptp.sz00))))) % 0.35/0.98 (assume @p32 (forall @t31 (=> @t54 (= @t56 (tptp.sdtlseqdt0 @t50 @t52))))) % 0.35/0.98 (assume @p33 (forall @t3 (=> @t51 (tptp.sdtlseqdt0 @t1 @t50)))) % 0.35/0.98 (assume @p34 (forall @t3 (=> @t51 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.35/0.98 (assume @p35 (forall @t31 (=> @t54 (=> (and @t56 @t57) @t29)))) % 0.35/0.98 (assume @p36 (forall @t34 (=> (and @t51 @t53 @t59) (=> (and @t56 @t58) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.35/0.98 (assume @p37 (forall @t31 (=> @t54 (or @t56 (tptp.sdtlseqdt0 @t52 @t1))))) % 0.35/0.98 (assume @p38 (forall @t31 (=> @t54 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.35/0.98 (assume @p39 (forall @t3 (=> @t51 (tptp.iLess0 @t1 @t50)))) % 0.35/0.98 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t60)))) % 0.35/0.98 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t60 tptp.szNzAzT0) @t9)))) % 0.35/0.98 (assume @p42 (forall @t3 (=> @t2 (= (= @t60 tptp.sz00) @t10)))) % 0.35/0.98 (assume @p43 (forall @t3 (=> @t28 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t41) (tptp.szszuzczcdt0 @t60)))))))) % 0.35/0.98 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t43)) @t60)))))) % 0.35/0.98 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t22) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t60)))))) % 0.35/0.98 (assume @p46 (forall @t31 (=> @t61 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t60)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.35/0.98 (assume @p47 (forall @t3 (=> (and @t63 @t14) (forall @t8 (= (= @t5 @t62) (and @t7 (forall @t18 (=> @t16 @t58)))))))) % 0.35/0.98 (assume @p48 (forall @t3 (=> (and @t63 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.35/0.98 (assume @p49 (forall @t31 (=> (and @t63 @t65 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t62 @t5) (tptp.aElementOf0 @t64 @t1)) (= @t62 @t64))))) % 0.35/0.98 (assume @p50 (forall @t3 (=> @t51 (forall @t8 (= (= @t5 @t66) (and @t20 (forall @t18 (= @t17 (and @t59 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.35/0.98 (assume @p51 (forall @t3 (=> @t51 (tptp.isFinite0 @t66)))) % 0.35/0.98 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.35/0.98 (assume @p53 (forall @t31 (=> @t54 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t52)) (or (tptp.aElementOf0 @t1 @t67) @t29))))) % 0.35/0.98 (assume @p54 (forall @t31 (=> @t54 (= @t56 (tptp.aSubsetOf0 @t66 @t67))))) % 0.35/0.98 (assume @p55 (forall @t3 (=> (and @t63 @t9) (exists @t8 (and @t53 (tptp.aSubsetOf0 @t1 @t67)))))) % 0.35/0.98 (assume @p56 (forall @t3 (=> @t51 (= (tptp.sbrdtbr0 @t66) @t1)))) % 0.35/0.98 (assume @p57 (forall @t31 (=> @t61 (forall @t18 (= (= @t15 @t69) (and @t33 (forall @t40 (= @t39 (and @t68 (= (tptp.sbrdtbr0 @t35) @t5)))))))))) % 0.35/0.98 (assume @p58 (forall @t3 (=> @t28 (forall @t8 (=> @t53 (tptp.isFinite0 @t69)))))) % 0.35/0.98 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t53 (not (= @t69 tptp.slcrc0))))))) % 0.35/0.98 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t53 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t69)))))) % 0.35/0.98 (assume @p61 (forall @t3 (=> @t51 (forall (@list @t5 @t15) (=> (and @t20 @t33 (not @t55)) (=> (and (tptp.aSubsetOf0 @t70 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t70 tptp.slcrc0))) @t32)))))) % 0.35/0.98 (assume @p62 (forall @t31 (=> @t61 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t69) (tptp.isFinite0 @t15)) (exists @t40 (and @t68 (tptp.isFinite0 @t35) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t35 @t5))))))))) % 0.35/0.98 (assume @p63 (forall @t3 (=> @t71 true))) % 0.35/0.98 (assume @p64 (forall @t3 (=> @t71 (tptp.aSet0 @t72)))) % 0.35/0.98 (assume @p65 (forall @t3 (=> @t71 (forall @t8 (=> @t74 (tptp.aElement0 @t73)))))) % 0.35/0.98 (assume @p66 (forall @t31 (=> @t78 (forall @t18 (= (= @t15 @t77) (and @t33 (forall @t40 (= @t39 (and @t76 (= @t75 @t5)))))))))) % 0.35/0.98 (assume @p67 (forall @t31 (=> @t78 (tptp.aSubsetOf0 @t77 @t72)))) % 0.35/0.98 (assume @p68 (forall @t3 (=> @t71 (forall @t8 (=> @t82 (forall @t18 (= (= @t15 @t81) (and @t33 (forall @t40 (= @t39 (exists @t80 (and (tptp.aElementOf0 @t79 @t5) (= (tptp.sdtlpdtrp0 @t1 @t79) @t35))))))))))))) % 0.35/0.98 (assume @p69 (forall @t3 (=> @t71 (forall @t8 (=> @t74 (tptp.aElementOf0 @t73 @t83)))))) % 0.35/0.98 (assume @p70 (forall @t3 (=> @t71 (forall @t8 (=> @t82 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t85 (= @t84 @t5) (forall @t40 (=> (tptp.aElementOf0 @t35 @t5) (= (tptp.sdtlpdtrp0 @t15 @t35) @t75))))))))))) % 0.35/0.98 (assume @p71 (forall @t3 (=> @t71 (forall @t8 (=> (and @t82 @t45) (=> (forall (@list @t15 @t35) (=> (and (tptp.aElementOf0 @t15 @t72) @t76 (not (= @t15 @t35))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t75)))) (tptp.isCountable0 @t81))))))) % 0.35/0.98 (assume @p72 (forall @t3 (=> @t71 (=> (and (tptp.isCountable0 @t72) (tptp.isFinite0 @t83)) (and (tptp.aElement0 @t86) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t86))))))) % 0.35/0.98 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.35/0.98 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.35/0.98 (assume @p75 (and (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.35/0.98 (assume @p76 (and (tptp.aFunction0 tptp.xc) (= @t87 @t88) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc @t87) tptp.xT))) % 0.35/0.98 (assume @p77 (forall @t3 (=> @t51 (forall @t8 (=> (and @t65 @t45) (forall @t18 (=> (and @t85 (= @t84 @t70) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t15 @t84) tptp.xT)) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t40 (and (tptp.aElementOf0 @t35 tptp.xT) (exists @t80 (and (tptp.aSubsetOf0 @t79 @t5) (tptp.isCountable0 @t79) (forall (@list @t89) (=> (tptp.aElementOf0 @t89 (tptp.slbdtsldtrb0 @t79 @t1)) (= (tptp.sdtlpdtrp0 @t15 @t89) @t35))))))))))))))) % 0.35/0.98 (assume @p78 (not (= tptp.xK tptp.sz00))) % 0.35/0.98 (assume @p79 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK))) % 0.35/0.98 (assume @p80 (and (tptp.aFunction0 tptp.xN) (= (tptp.szDzozmdt0 tptp.xN) tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall @t3 (=> @t51 (=> @t94 (and (tptp.aSubsetOf0 @t90 @t93) (tptp.isCountable0 @t90))))))) % 0.35/0.98 (assume @p81 (forall @t3 (=> @t51 @t94))) % 0.35/0.98 (assume @p82 (forall @t31 (=> @t54 (=> @t57 (tptp.aSubsetOf0 @t91 @t95))))) % 0.35/0.98 (assume @p83 (forall @t31 (=> (and @t51 @t53 (not @t29)) (not (= @t92 (tptp.szmzizndt0 @t95)))))) % 0.35/0.98 (assume @p84 (forall @t3 (=> @t51 (forall @t8 (=> @t98 (tptp.aElementOf0 @t96 @t88)))))) % 0.35/0.98 (assume @p85 (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall @t3 (=> @t51 (and (tptp.aFunction0 @t99) (= @t101 @t97) (forall @t8 (=> @t98 (= @t100 (tptp.sdtlpdtrp0 tptp.xc @t96))))))))) % 0.35/0.98 (assume @p86 (forall @t3 (=> @t51 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t99 @t101) tptp.xT)))) % 0.35/0.98 (assume @p87 (forall @t3 (=> @t51 (forall @t8 (=> (and (tptp.aSubsetOf0 @t5 @t93) @t45) (forall @t18 (=> (and @t33 (tptp.aElementOf0 @t15 (tptp.slbdtsldtrb0 @t5 tptp.xk))) (tptp.aElementOf0 @t15 @t97)))))))) % 0.35/0.98 (assume @p88 (forall @t3 (=> @t51 (exists @t8 (and @t102 (exists @t18 (and (tptp.aSubsetOf0 @t15 @t93) (tptp.isCountable0 @t15) (forall @t40 (=> (and (tptp.aSet0 @t35) (tptp.aElementOf0 @t35 (tptp.slbdtsldtrb0 @t15 tptp.xk))) (= (tptp.sdtlpdtrp0 @t99 @t35) @t5)))))))))) % 0.35/0.98 (assume @p89 (forall @t3 (=> @t51 (exists @t8 (and @t102 (forall @t18 (=> (and @t33 (tptp.aElementOf0 @t15 @t103)) (= (tptp.sdtlpdtrp0 @t99 @t15) @t5)))))))) % 0.35/0.98 (assume @p90 (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall @t3 (=> @t51 (= (tptp.sdtlpdtrp0 tptp.xe @t1) @t92))))) % 0.35/0.98 (assume @p91 (and (tptp.aFunction0 tptp.xd) (= @t104 tptp.szNzAzT0) (forall @t3 (=> @t51 (forall @t8 (=> (and @t20 (tptp.aElementOf0 @t5 @t103)) (= (tptp.sdtlpdtrp0 tptp.xd @t1) @t100))))))) % 0.35/0.98 (assume @p92 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xd @t104) tptp.xT)) % 0.35/0.98 (assume @p93 (and (tptp.aElementOf0 @t105 tptp.xT) (tptp.isCountable0 @t106))) % 0.35/0.98 (assume @p94 (and @t107 (= tptp.xO (tptp.sdtlcdtrc0 tptp.xe @t106)))) % 0.35/0.98 (assume @p95 (and @t107 (tptp.isCountable0 tptp.xO))) % 0.35/0.98 (assume @p96 (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xO) (exists @t8 (and @t53 (tptp.aElementOf0 @t5 @t106) (= (tptp.sdtlpdtrp0 tptp.xe @t5) @t1)))))) % 0.35/0.98 (assume @p97 (tptp.aSubsetOf0 tptp.xO tptp.xS)) % 0.35/0.98 (assume @p98 (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 tptp.xO tptp.xK))) % 0.35/0.98 (assume @p99 (and (tptp.aSubsetOf0 tptp.xQ tptp.xO) (not (= tptp.xQ tptp.slcrc0)))) % 0.35/0.98 (assume @p100 @t108) % 0.35/0.98 (assume @p101 (tptp.aElementOf0 tptp.xQ @t87)) % 0.35/0.98 (assume @p102 (= tptp.xp @t109)) % 0.35/0.98 (assume @p103 (and @t110 (= tptp.xP (tptp.sdtmndt0 tptp.xQ @t109)))) % 0.35/0.98 (assume @p104 (tptp.aElementOf0 tptp.xp tptp.xQ)) % 0.35/0.98 (assume @p105 (tptp.aElementOf0 tptp.xp tptp.xO)) % 0.35/0.98 (assume @p106 @t111) % 0.35/0.98 (assume @p107 (tptp.aSubsetOf0 tptp.xP tptp.xO)) % 0.35/0.98 (assume @p108 (= (tptp.sbrdtbr0 tptp.xP) tptp.xk)) % 0.35/0.98 (assume @p109 (tptp.aElementOf0 tptp.xP (tptp.slbdtsldtrb0 tptp.xO tptp.xk))) % 0.35/0.98 (assume @p110 (and (tptp.aElementOf0 tptp.xn @t106) (tptp.aElementOf0 tptp.xn tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xe tptp.xn) tptp.xp))) % 0.35/0.98 (assume @p111 (= (tptp.sdtlpdtrp0 tptp.xd tptp.xn) @t105)) % 0.35/0.98 (assume @p112 @t112) % 0.35/0.98 (assume @p113 (not @t113)) % 0.35/0.98 (assume @p114 true) % 0.35/0.98 (step @p115 :rule quant-merge-prenex :args ((= (forall @t3 @t119) (forall (@list @t1 @t114) @t117)))) % 0.35/0.98 (step @p116 :rule alpha_equiv :args (@t120 (@list @t114) (@list @t5))) % 0.35/0.98 (step @p117 :rule refl :args (@t116)) % 0.35/0.98 (step @p118 :rule nary_cong :premises (@p117 @p116) :args (@t121)) % 0.35/0.98 (step @p119 :rule quant-miniscope-or :args ((= @t119 @t121))) % 0.35/0.98 (step @p120 :rule trans :premises (@p119 @p118)) % 0.35/0.98 (step @p121 :rule symm :premises (@p120)) % 0.35/0.98 (step @p122 :rule cong :premises (@p121) :args ((forall @t3 (or @t116 @t122)))) % 0.35/0.98 (step @p123 :rule trans :premises (@p122 @p115)) % 0.35/0.98 (step @p124 :rule bool-impl-elim :args (@t2 @t122)) % 0.35/0.98 (step @p125 :rule cong :premises (@p124) :args ((forall @t3 (=> @t2 @t122)))) % 0.35/0.98 (step @p126 :rule trans :premises (@p125 @p123)) % 0.35/0.98 (step @p127 :rule bool-impl-elim :args (@t17 @t16)) % 0.35/0.98 (step @p128 :rule cong :premises (@p127) :args (@t19)) % 0.35/0.98 (step @p129 :rule refl :args (@t20)) % 0.35/0.98 (step @p130 :rule nary_cong :premises (@p129 @p128) :args (@t21)) % 0.35/0.98 (step @p131 :rule refl :args (@t22)) % 0.35/0.98 (step @p132 :rule cong :premises (@p131 @p130) :args (@t23)) % 0.35/0.98 (step @p133 :rule cong :premises (@p132) :args (@t24)) % 0.35/0.98 (step @p134 :rule refl :args (@t2)) % 0.35/0.98 (step @p135 :rule cong :premises (@p134 @p133) :args (@t25)) % 0.35/0.98 (step @p136 :rule cong :premises (@p135) :args (@t26)) % 0.35/0.98 (step @p137 :rule trans :premises (@p136 @p126)) % 0.35/0.98 (step @p138 :rule eq_resolve :premises (@p10 @p137)) % 0.35/0.98 (step @p139 :rule instantiate :premises (@p138) :args ((@list tptp.xQ tptp.xP))) % 0.35/0.98 (step @p140 :rule instantiate :premises (@p138) :args ((@list tptp.szNzAzT0 tptp.xQ))) % 0.35/0.98 (step @p141 :rule and_elim :premises (@p23) :args (0)) % 0.35/0.98 (step @p142 :rule cnf_or_pos :args (@t129)) % 0.35/0.98 (step @p143 :rule reordering :premises (@p142) :args ((or @t128 @t127 (not @t129)))) % 0.35/0.98 (step @p144 :rule chain_m_resolution :premises (@p143 @p141 @p140) :args (@t127 @t130 (@list @t49 @t129))) % 0.35/0.98 (step @p145 :rule cnf_equiv_pos1 :args (@t127)) % 0.35/0.98 (step @p146 :rule reordering :premises (@p145) :args ((or (not @t108) @t126 (not @t127)))) % 0.35/0.98 (step @p147 :rule chain_m_resolution :premises (@p146 @p100 @p144) :args (@t126 @t130 (@list @t108 @t127))) % 0.35/0.98 (step @p148 :rule cnf_and_pos :args (@t126 0)) % 0.35/0.98 (step @p149 :rule reordering :premises (@p148) :args ((or @t125 @t131))) % 0.35/0.98 (step @p150 :rule chain_m_resolution :premises (@p149 @p147) :args (@t125 @t132 @t133)) % 0.35/0.98 (step @p151 :rule cnf_or_pos :args (@t138)) % 0.35/0.98 (step @p152 :rule reordering :premises (@p151) :args ((or @t137 @t136 (not @t138)))) % 0.35/0.98 (step @p153 :rule chain_m_resolution :premises (@p152 @p150 @p139) :args (@t136 @t130 (@list @t125 @t138))) % 0.35/0.98 (step @p154 :rule cnf_equiv_pos1 :args (@t136)) % 0.35/0.98 (step @p155 :rule reordering :premises (@p154) :args ((or (not @t111) @t135 (not @t136)))) % 0.35/0.98 (step @p156 :rule chain_m_resolution :premises (@p155 @p106 @p153) :args (@t135 @t130 (@list @t111 @t136))) % 0.35/0.98 (step @p157 :rule cnf_and_pos :args (@t135 1)) % 0.35/0.98 (step @p158 :rule reordering :premises (@p157) :args ((or @t134 (not @t135)))) % 0.35/0.98 (step @p159 :rule chain_m_resolution :premises (@p158 @p156) :args (@t134 @t132 (@list @t135))) % 0.35/0.98 (step @p160 :rule instantiate :premises (@p159) :args (@t139)) % 0.35/0.98 (step @p161 :rule cnf_and_pos :args (@t126 1)) % 0.35/0.98 (step @p162 :rule reordering :premises (@p161) :args ((or @t124 @t131))) % 0.35/0.98 (step @p163 :rule chain_m_resolution :premises (@p162 @p147) :args (@t124 @t132 @t133)) % 0.35/0.98 (step @p164 :rule instantiate :premises (@p163) :args (@t139)) % 0.35/0.98 (step @p165 :rule cnf_or_pos :args (@t142)) % 0.35/0.98 (step @p166 :rule reordering :premises (@p165) :args ((or @t113 @t141 (not @t142)))) % 0.35/0.98 (step @p167 :rule chain_m_resolution :premises (@p166 @p113 @p164) :args (@t141 (@list true false) (@list @t113 @t142))) % 0.35/0.98 (step @p168 :rule cnf_or_pos :args (@t144)) % 0.35/0.98 (step @p169 :rule reordering :premises (@p168) :args ((or @t143 @t140 (not @t144)))) % 0.35/0.98 (step @p170 false :rule chain_m_resolution :premises (@p169 @p167 @p160 @p112) :args (false (@list true false false) (@list @t140 @t144 @t112))) % 0.35/0.98 ) % 0.35/0.98 % SZS output end Proof % 0.35/0.98 % cvc5 exiting %------------------------------------------------------------------------------