%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM624+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 : n004.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 08:40:03 AM UTC 2026 % Result : Theorem 0.38s 0.74s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM624+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 : n004.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 11:37:52 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.74 % SZS status Theorem % 0.38/0.74 % SZS output start Proof % 0.38/0.74 ( % 0.38/0.74 (declare-sort $$unsorted 0) % 0.38/0.74 (declare-const tptp.xx $$unsorted) % 0.38/0.74 (declare-const tptp.xn $$unsorted) % 0.38/0.74 (declare-const tptp.xp $$unsorted) % 0.38/0.74 (declare-const tptp.xQ $$unsorted) % 0.38/0.74 (declare-const tptp.xe $$unsorted) % 0.38/0.74 (declare-const tptp.xP $$unsorted) % 0.38/0.74 (declare-const tptp.xC $$unsorted) % 0.38/0.74 (declare-const tptp.xN $$unsorted) % 0.38/0.74 (declare-const tptp.sz00 $$unsorted) % 0.38/0.74 (declare-const tptp.xc $$unsorted) % 0.38/0.74 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.szNzAzT0 $$unsorted) % 0.38/0.74 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.xd $$unsorted) % 0.38/0.74 (declare-const tptp.xk $$unsorted) % 0.38/0.74 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.38/0.74 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.xm $$unsorted) % 0.38/0.74 (declare-const tptp.xK $$unsorted) % 0.38/0.74 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.xT $$unsorted) % 0.38/0.74 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.xO $$unsorted) % 0.38/0.74 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.xS $$unsorted) % 0.38/0.74 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.slcrc0 $$unsorted) % 0.38/0.74 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.74 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.74 (define @t1 () (@var "W0" $$unsorted)) % 0.38/0.74 (define @t2 () (tptp.aSet0 @t1)) % 0.38/0.74 (define @t3 () (@list @t1)) % 0.38/0.74 (define @t4 () (tptp.aElement0 @t1)) % 0.38/0.74 (define @t5 () (@var "W1" $$unsorted)) % 0.38/0.74 (define @t6 () (tptp.aElement0 @t5)) % 0.38/0.74 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.38/0.74 (define @t8 () (@list @t5)) % 0.38/0.74 (define @t9 () (tptp.isFinite0 @t1)) % 0.38/0.74 (define @t10 () (= @t1 tptp.slcrc0)) % 0.38/0.74 (define @t11 () (tptp.isCountable0 @t1)) % 0.38/0.74 (define @t12 () (not @t9)) % 0.38/0.74 (define @t13 () (and @t2 @t11)) % 0.38/0.74 (define @t14 () (not @t10)) % 0.38/0.74 (define @t15 () (@var "W2" $$unsorted)) % 0.38/0.74 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.38/0.74 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.38/0.74 (define @t18 () (@list @t15)) % 0.38/0.74 (define @t19 () (tptp.aSet0 @t5)) % 0.38/0.74 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.38/0.74 (define @t21 () (tptp.isFinite0 @t5)) % 0.38/0.74 (define @t22 () (and @t2 @t9)) % 0.38/0.74 (define @t23 () (= @t1 @t5)) % 0.38/0.74 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.38/0.74 (define @t25 () (@list @t1 @t5)) % 0.38/0.74 (define @t26 () (tptp.aSubsetOf0 @t5 @t15)) % 0.38/0.74 (define @t27 () (tptp.aSet0 @t15)) % 0.38/0.74 (define @t28 () (@list @t1 @t5 @t15)) % 0.38/0.74 (define @t29 () (@var "W3" $$unsorted)) % 0.38/0.74 (define @t30 () (= @t29 @t5)) % 0.38/0.74 (define @t31 () (tptp.aElementOf0 @t29 @t1)) % 0.38/0.74 (define @t32 () (tptp.aElement0 @t29)) % 0.38/0.74 (define @t33 () (tptp.aElementOf0 @t29 @t15)) % 0.38/0.74 (define @t34 () (@list @t29)) % 0.38/0.74 (define @t35 () (tptp.sdtpldt0 @t1 @t5)) % 0.38/0.74 (define @t36 () (and @t2 @t6)) % 0.38/0.74 (define @t37 () (tptp.sdtmndt0 @t1 @t5)) % 0.38/0.74 (define @t38 () (tptp.sdtpldt0 @t5 @t1)) % 0.38/0.74 (define @t39 () (tptp.isCountable0 @t5)) % 0.38/0.74 (define @t40 () (and @t19 @t39)) % 0.38/0.74 (define @t41 () (tptp.sdtmndt0 @t5 @t1)) % 0.38/0.74 (define @t42 () (and @t19 @t21)) % 0.38/0.74 (define @t43 () (tptp.szszuzczcdt0 @t1)) % 0.38/0.74 (define @t44 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.38/0.74 (define @t45 () (tptp.szszuzczcdt0 @t5)) % 0.38/0.74 (define @t46 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.38/0.74 (define @t47 () (and @t44 @t46)) % 0.38/0.74 (define @t48 () (= @t1 tptp.sz00)) % 0.38/0.74 (define @t49 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.38/0.74 (define @t50 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.38/0.74 (define @t51 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.38/0.74 (define @t52 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.38/0.74 (define @t53 () (tptp.sbrdtbr0 @t1)) % 0.38/0.74 (define @t54 () (and @t2 @t46)) % 0.38/0.74 (define @t55 () (tptp.szmzizndt0 @t1)) % 0.38/0.74 (define @t56 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.38/0.74 (define @t57 () (tptp.szmzizndt0 @t5)) % 0.38/0.74 (define @t58 () (= @t55 @t57)) % 0.38/0.74 (define @t59 () (tptp.aElementOf0 @t57 @t1)) % 0.38/0.74 (define @t60 () (tptp.aElementOf0 @t55 @t5)) % 0.38/0.74 (define @t61 () (and @t60 @t59)) % 0.38/0.74 (define @t62 () (=> @t61 @t58)) % 0.38/0.74 (define @t63 () (= @t5 tptp.slcrc0)) % 0.38/0.74 (define @t64 () (not @t63)) % 0.38/0.74 (define @t65 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.38/0.74 (define @t66 () (and @t56 @t65 @t14 @t64)) % 0.38/0.74 (define @t67 () (forall @t25 (=> @t66 @t62))) % 0.38/0.74 (define @t68 () (tptp.slbdtrb0 @t1)) % 0.38/0.74 (define @t69 () (tptp.slbdtrb0 @t5)) % 0.38/0.74 (define @t70 () (tptp.aSubsetOf0 @t29 @t1)) % 0.38/0.74 (define @t71 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.38/0.74 (define @t72 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.38/0.74 (define @t73 () (tptp.aFunction0 @t1)) % 0.38/0.74 (define @t74 () (tptp.szDzozmdt0 @t1)) % 0.38/0.74 (define @t75 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.38/0.74 (define @t76 () (tptp.aElementOf0 @t5 @t74)) % 0.38/0.74 (define @t77 () (tptp.sdtlpdtrp0 @t1 @t29)) % 0.38/0.74 (define @t78 () (tptp.aElementOf0 @t29 @t74)) % 0.38/0.74 (define @t79 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.38/0.74 (define @t80 () (and @t73 @t6)) % 0.38/0.74 (define @t81 () (@var "W4" $$unsorted)) % 0.38/0.74 (define @t82 () (@list @t81)) % 0.38/0.74 (define @t83 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.38/0.74 (define @t84 () (tptp.aSubsetOf0 @t5 @t74)) % 0.38/0.74 (define @t85 () (tptp.sdtlcdtrc0 @t1 @t74)) % 0.38/0.74 (define @t86 () (tptp.szDzozmdt0 @t15)) % 0.38/0.74 (define @t87 () (tptp.aFunction0 @t15)) % 0.38/0.74 (define @t88 () (tptp.szDzizrdt0 @t1)) % 0.38/0.74 (define @t89 () (tptp.szDzozmdt0 tptp.xc)) % 0.38/0.74 (define @t90 () (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) % 0.38/0.74 (define @t91 () (@var "W5" $$unsorted)) % 0.38/0.74 (define @t92 () (tptp.sdtlpdtrp0 tptp.xN @t43)) % 0.38/0.74 (define @t93 () (tptp.sdtlpdtrp0 tptp.xN @t1)) % 0.38/0.74 (define @t94 () (tptp.szmzizndt0 @t93)) % 0.38/0.74 (define @t95 () (tptp.sdtmndt0 @t93 @t94)) % 0.38/0.74 (define @t96 () (and (tptp.aSubsetOf0 @t93 tptp.szNzAzT0) (tptp.isCountable0 @t93))) % 0.38/0.74 (define @t97 () (tptp.sdtlpdtrp0 tptp.xN @t5)) % 0.38/0.74 (define @t98 () (tptp.sdtpldt0 @t5 @t94)) % 0.38/0.74 (define @t99 () (tptp.slbdtsldtrb0 @t95 tptp.xk)) % 0.38/0.74 (define @t100 () (and @t19 (tptp.aElementOf0 @t5 @t99))) % 0.38/0.74 (define @t101 () (tptp.sdtlpdtrp0 tptp.xC @t1)) % 0.38/0.74 (define @t102 () (tptp.sdtlpdtrp0 @t101 @t5)) % 0.38/0.74 (define @t103 () (tptp.szDzozmdt0 @t101)) % 0.38/0.74 (define @t104 () (tptp.aElementOf0 @t5 tptp.xT)) % 0.38/0.74 (define @t105 () (tptp.slbdtsldtrb0 @t92 tptp.xk)) % 0.38/0.74 (define @t106 () (tptp.szDzozmdt0 tptp.xd)) % 0.38/0.74 (define @t107 () (tptp.szDzizrdt0 tptp.xd)) % 0.38/0.74 (define @t108 () (tptp.sdtlbdtrb0 tptp.xd @t107)) % 0.38/0.74 (define @t109 () (tptp.aSet0 tptp.xO)) % 0.38/0.74 (define @t110 () (= tptp.xQ tptp.slcrc0)) % 0.38/0.74 (define @t111 () (not @t110)) % 0.38/0.74 (define @t112 () (tptp.aSubsetOf0 tptp.xQ tptp.szNzAzT0)) % 0.38/0.74 (define @t113 () (tptp.szmzizndt0 tptp.xQ)) % 0.38/0.74 (define @t114 () (tptp.sdtlpdtrp0 tptp.xN tptp.xm)) % 0.38/0.74 (define @t115 () (tptp.szmzizndt0 @t114)) % 0.38/0.74 (define @t116 () (= @t114 tptp.slcrc0)) % 0.38/0.74 (define @t117 () (tptp.aSubsetOf0 @t114 tptp.szNzAzT0)) % 0.38/0.74 (define @t118 () (tptp.aElementOf0 @t113 @t114)) % 0.38/0.74 (define @t119 () (not @t59)) % 0.38/0.74 (define @t120 () (not @t60)) % 0.38/0.74 (define @t121 () (not @t65)) % 0.38/0.74 (define @t122 () (not @t56)) % 0.38/0.74 (define @t123 () (or @t122 @t121 @t10 @t63 @t120 @t119 @t58)) % 0.38/0.74 (define @t124 () (or @t120 @t119 @t58)) % 0.38/0.74 (define @t125 () (not @t64)) % 0.38/0.74 (define @t126 () (not @t14)) % 0.38/0.74 (define @t127 () (or @t122 @t121 @t126 @t125)) % 0.38/0.74 (define @t128 () (= @t113 @t115)) % 0.38/0.74 (define @t129 () (tptp.aElementOf0 @t115 tptp.xQ)) % 0.38/0.74 (define @t130 () (not @t129)) % 0.38/0.74 (define @t131 () (not @t118)) % 0.38/0.74 (define @t132 () (not @t117)) % 0.38/0.74 (define @t133 () (not @t112)) % 0.38/0.74 (define @t134 () (or @t133 @t132 @t110 @t116 @t131 @t130 @t128)) % 0.38/0.74 (define @t135 () (forall @t25 @t123)) % 0.38/0.74 (define @t136 () (= tptp.slcrc0 @t114)) % 0.38/0.74 (define @t137 () (= tptp.slcrc0 tptp.xQ)) % 0.38/0.74 (define @t138 () (or @t133 @t132 @t137 @t136 @t131 @t130 @t128)) % 0.38/0.74 (assume @p1 (forall @t3 (=> @t2 true))) % 0.38/0.74 (assume @p2 (forall @t3 (=> @t4 true))) % 0.38/0.74 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.38/0.74 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.38/0.74 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.38/0.74 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.38/0.74 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.38/0.74 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.38/0.74 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.38/0.74 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.38/0.74 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.38/0.74 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.38/0.74 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.38/0.74 (assume @p14 (forall @t28 (=> (and @t2 @t19 @t27) (=> (and @t24 @t26) (tptp.aSubsetOf0 @t1 @t15))))) % 0.38/0.74 (assume @p15 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t35) (and @t27 (forall @t34 (= @t33 (and @t32 (or @t31 @t30)))))))))) % 0.38/0.74 (assume @p16 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t37) (and @t27 (forall @t34 (= @t33 (and @t32 @t31 (not @t30)))))))))) % 0.38/0.74 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t37 @t5) @t1)))))) % 0.38/0.74 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t38 @t1) @t5))))) % 0.38/0.74 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t38)))))) % 0.38/0.74 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t41)))))) % 0.38/0.74 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t38)))))) % 0.38/0.74 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t41)))))) % 0.38/0.74 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.38/0.74 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.38/0.74 (assume @p25 (forall @t3 (=> @t44 (and (tptp.aElementOf0 @t43 tptp.szNzAzT0) (not (= @t43 tptp.sz00)))))) % 0.38/0.74 (assume @p26 (forall @t25 (=> @t47 (=> (= @t43 @t45) @t23)))) % 0.38/0.74 (assume @p27 (forall @t3 (=> @t44 (or @t48 (exists @t8 (and @t46 (= @t1 @t45))))))) % 0.38/0.74 (assume @p28 (forall @t3 (=> @t44 (not (= @t1 @t43))))) % 0.38/0.74 (assume @p29 (forall @t25 (=> @t47 (=> @t49 true)))) % 0.38/0.74 (assume @p30 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.38/0.74 (assume @p31 (forall @t3 (=> @t44 (not (tptp.sdtlseqdt0 @t43 tptp.sz00))))) % 0.38/0.74 (assume @p32 (forall @t25 (=> @t47 (= @t49 (tptp.sdtlseqdt0 @t43 @t45))))) % 0.38/0.74 (assume @p33 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t43)))) % 0.38/0.74 (assume @p34 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.38/0.74 (assume @p35 (forall @t25 (=> @t47 (=> (and @t49 @t50) @t23)))) % 0.38/0.74 (assume @p36 (forall @t28 (=> (and @t44 @t46 @t52) (=> (and @t49 @t51) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.38/0.74 (assume @p37 (forall @t25 (=> @t47 (or @t49 (tptp.sdtlseqdt0 @t45 @t1))))) % 0.38/0.74 (assume @p38 (forall @t25 (=> @t47 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.38/0.74 (assume @p39 (forall @t3 (=> @t44 (tptp.iLess0 @t1 @t43)))) % 0.38/0.74 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t53)))) % 0.38/0.74 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t53 tptp.szNzAzT0) @t9)))) % 0.38/0.74 (assume @p42 (forall @t3 (=> @t2 (= (= @t53 tptp.sz00) @t10)))) % 0.38/0.74 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t35) (tptp.szszuzczcdt0 @t53)))))))) % 0.38/0.74 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t37)) @t53)))))) % 0.38/0.74 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t53)))))) % 0.38/0.74 (assume @p46 (forall @t25 (=> @t54 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t53)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.38/0.74 (assume @p47 (forall @t3 (=> (and @t56 @t14) (forall @t8 (= (= @t5 @t55) (and @t7 (forall @t18 (=> @t16 @t51)))))))) % 0.38/0.74 (assume @p48 (forall @t3 (=> (and @t56 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.38/0.74 (assume @p49 @t67) % 0.38/0.74 (assume @p50 (forall @t3 (=> @t44 (forall @t8 (= (= @t5 @t68) (and @t19 (forall @t18 (= @t17 (and @t52 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.38/0.74 (assume @p51 (forall @t3 (=> @t44 (tptp.isFinite0 @t68)))) % 0.38/0.74 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.38/0.74 (assume @p53 (forall @t25 (=> @t47 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t45)) (or (tptp.aElementOf0 @t1 @t69) @t23))))) % 0.38/0.74 (assume @p54 (forall @t25 (=> @t47 (= @t49 (tptp.aSubsetOf0 @t68 @t69))))) % 0.38/0.74 (assume @p55 (forall @t3 (=> (and @t56 @t9) (exists @t8 (and @t46 (tptp.aSubsetOf0 @t1 @t69)))))) % 0.38/0.74 (assume @p56 (forall @t3 (=> @t44 (= (tptp.sbrdtbr0 @t68) @t1)))) % 0.38/0.74 (assume @p57 (forall @t25 (=> @t54 (forall @t18 (= (= @t15 @t71) (and @t27 (forall @t34 (= @t33 (and @t70 (= (tptp.sbrdtbr0 @t29) @t5)))))))))) % 0.38/0.74 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t46 (tptp.isFinite0 @t71)))))) % 0.38/0.74 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t46 (not (= @t71 tptp.slcrc0))))))) % 0.38/0.74 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t46 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t71)))))) % 0.38/0.74 (assume @p61 (forall @t3 (=> @t44 (forall (@list @t5 @t15) (=> (and @t19 @t27 (not @t48)) (=> (and (tptp.aSubsetOf0 @t72 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t72 tptp.slcrc0))) @t26)))))) % 0.38/0.74 (assume @p62 (forall @t25 (=> @t54 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t71) (tptp.isFinite0 @t15)) (exists @t34 (and @t70 (tptp.isFinite0 @t29) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t29 @t5))))))))) % 0.38/0.74 (assume @p63 (forall @t3 (=> @t73 true))) % 0.38/0.74 (assume @p64 (forall @t3 (=> @t73 (tptp.aSet0 @t74)))) % 0.38/0.74 (assume @p65 (forall @t3 (=> @t73 (forall @t8 (=> @t76 (tptp.aElement0 @t75)))))) % 0.38/0.74 (assume @p66 (forall @t25 (=> @t80 (forall @t18 (= (= @t15 @t79) (and @t27 (forall @t34 (= @t33 (and @t78 (= @t77 @t5)))))))))) % 0.38/0.74 (assume @p67 (forall @t25 (=> @t80 (tptp.aSubsetOf0 @t79 @t74)))) % 0.38/0.74 (assume @p68 (forall @t3 (=> @t73 (forall @t8 (=> @t84 (forall @t18 (= (= @t15 @t83) (and @t27 (forall @t34 (= @t33 (exists @t82 (and (tptp.aElementOf0 @t81 @t5) (= (tptp.sdtlpdtrp0 @t1 @t81) @t29))))))))))))) % 0.38/0.74 (assume @p69 (forall @t3 (=> @t73 (forall @t8 (=> @t76 (tptp.aElementOf0 @t75 @t85)))))) % 0.38/0.74 (assume @p70 (forall @t3 (=> @t73 (forall @t8 (=> @t84 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t87 (= @t86 @t5) (forall @t34 (=> (tptp.aElementOf0 @t29 @t5) (= (tptp.sdtlpdtrp0 @t15 @t29) @t77))))))))))) % 0.38/0.74 (assume @p71 (forall @t3 (=> @t73 (forall @t8 (=> (and @t84 @t39) (=> (forall (@list @t15 @t29) (=> (and (tptp.aElementOf0 @t15 @t74) @t78 (not (= @t15 @t29))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t77)))) (tptp.isCountable0 @t83))))))) % 0.38/0.74 (assume @p72 (forall @t3 (=> @t73 (=> (and (tptp.isCountable0 @t74) (tptp.isFinite0 @t85)) (and (tptp.aElement0 @t88) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t88))))))) % 0.38/0.74 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.38/0.74 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.38/0.74 (assume @p75 (and (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.38/0.74 (assume @p76 (and (tptp.aFunction0 tptp.xc) (= @t89 @t90) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc @t89) tptp.xT))) % 0.38/0.74 (assume @p77 (forall @t3 (=> @t44 (forall @t8 (=> (and @t65 @t39) (forall @t18 (=> (and @t87 (= @t86 @t72) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t15 @t86) tptp.xT)) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t34 (and (tptp.aElementOf0 @t29 tptp.xT) (exists @t82 (and (tptp.aSubsetOf0 @t81 @t5) (tptp.isCountable0 @t81) (forall (@list @t91) (=> (tptp.aElementOf0 @t91 (tptp.slbdtsldtrb0 @t81 @t1)) (= (tptp.sdtlpdtrp0 @t15 @t91) @t29))))))))))))))) % 0.38/0.74 (assume @p78 (not (= tptp.xK tptp.sz00))) % 0.38/0.74 (assume @p79 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK))) % 0.38/0.74 (assume @p80 (and (tptp.aFunction0 tptp.xN) (= (tptp.szDzozmdt0 tptp.xN) tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall @t3 (=> @t44 (=> @t96 (and (tptp.aSubsetOf0 @t92 @t95) (tptp.isCountable0 @t92))))))) % 0.38/0.74 (assume @p81 (forall @t3 (=> @t44 @t96))) % 0.38/0.74 (assume @p82 (forall @t25 (=> @t47 (=> @t50 (tptp.aSubsetOf0 @t93 @t97))))) % 0.38/0.74 (assume @p83 (forall @t25 (=> (and @t44 @t46 (not @t23)) (not (= @t94 (tptp.szmzizndt0 @t97)))))) % 0.38/0.74 (assume @p84 (forall @t3 (=> @t44 (forall @t8 (=> @t100 (tptp.aElementOf0 @t98 @t90)))))) % 0.38/0.74 (assume @p85 (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall @t3 (=> @t44 (and (tptp.aFunction0 @t101) (= @t103 @t99) (forall @t8 (=> @t100 (= @t102 (tptp.sdtlpdtrp0 tptp.xc @t98))))))))) % 0.38/0.74 (assume @p86 (forall @t3 (=> @t44 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t101 @t103) tptp.xT)))) % 0.38/0.74 (assume @p87 (forall @t3 (=> @t44 (forall @t8 (=> (and (tptp.aSubsetOf0 @t5 @t95) @t39) (forall @t18 (=> (and @t27 (tptp.aElementOf0 @t15 (tptp.slbdtsldtrb0 @t5 tptp.xk))) (tptp.aElementOf0 @t15 @t99)))))))) % 0.38/0.74 (assume @p88 (forall @t3 (=> @t44 (exists @t8 (and @t104 (exists @t18 (and (tptp.aSubsetOf0 @t15 @t95) (tptp.isCountable0 @t15) (forall @t34 (=> (and (tptp.aSet0 @t29) (tptp.aElementOf0 @t29 (tptp.slbdtsldtrb0 @t15 tptp.xk))) (= (tptp.sdtlpdtrp0 @t101 @t29) @t5)))))))))) % 0.38/0.74 (assume @p89 (forall @t3 (=> @t44 (exists @t8 (and @t104 (forall @t18 (=> (and @t27 (tptp.aElementOf0 @t15 @t105)) (= (tptp.sdtlpdtrp0 @t101 @t15) @t5)))))))) % 0.38/0.74 (assume @p90 (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall @t3 (=> @t44 (= (tptp.sdtlpdtrp0 tptp.xe @t1) @t94))))) % 0.38/0.74 (assume @p91 (and (tptp.aFunction0 tptp.xd) (= @t106 tptp.szNzAzT0) (forall @t3 (=> @t44 (forall @t8 (=> (and @t19 (tptp.aElementOf0 @t5 @t105)) (= (tptp.sdtlpdtrp0 tptp.xd @t1) @t102))))))) % 0.38/0.74 (assume @p92 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xd @t106) tptp.xT)) % 0.38/0.74 (assume @p93 (and (tptp.aElementOf0 @t107 tptp.xT) (tptp.isCountable0 @t108))) % 0.38/0.74 (assume @p94 (and @t109 (= tptp.xO (tptp.sdtlcdtrc0 tptp.xe @t108)))) % 0.38/0.74 (assume @p95 (and @t109 (tptp.isCountable0 tptp.xO))) % 0.38/0.74 (assume @p96 (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xO) (exists @t8 (and @t46 (tptp.aElementOf0 @t5 @t108) (= (tptp.sdtlpdtrp0 tptp.xe @t5) @t1)))))) % 0.38/0.74 (assume @p97 (tptp.aSubsetOf0 tptp.xO tptp.xS)) % 0.38/0.74 (assume @p98 (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 tptp.xO tptp.xK))) % 0.38/0.74 (assume @p99 (and (tptp.aSubsetOf0 tptp.xQ tptp.xO) @t111)) % 0.38/0.74 (assume @p100 @t112) % 0.38/0.74 (assume @p101 (tptp.aElementOf0 tptp.xQ @t89)) % 0.38/0.74 (assume @p102 (= tptp.xp @t113)) % 0.38/0.74 (assume @p103 (and (tptp.aSet0 tptp.xP) (= tptp.xP (tptp.sdtmndt0 tptp.xQ @t113)))) % 0.38/0.74 (assume @p104 (tptp.aElementOf0 tptp.xp tptp.xQ)) % 0.38/0.74 (assume @p105 (tptp.aElementOf0 tptp.xp tptp.xO)) % 0.38/0.74 (assume @p106 (tptp.aSubsetOf0 tptp.xP tptp.xQ)) % 0.38/0.74 (assume @p107 (tptp.aSubsetOf0 tptp.xP tptp.xO)) % 0.38/0.74 (assume @p108 (= (tptp.sbrdtbr0 tptp.xP) tptp.xk)) % 0.38/0.74 (assume @p109 (tptp.aElementOf0 tptp.xP (tptp.slbdtsldtrb0 tptp.xO tptp.xk))) % 0.38/0.74 (assume @p110 (and (tptp.aElementOf0 tptp.xn @t108) (tptp.aElementOf0 tptp.xn tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xe tptp.xn) tptp.xp))) % 0.38/0.74 (assume @p111 (= (tptp.sdtlpdtrp0 tptp.xd tptp.xn) @t107)) % 0.38/0.74 (assume @p112 (tptp.aElementOf0 tptp.xx tptp.xP)) % 0.38/0.74 (assume @p113 (and (tptp.aElementOf0 tptp.xx tptp.szNzAzT0) (tptp.aElementOf0 tptp.xx tptp.xO))) % 0.38/0.74 (assume @p114 (and (tptp.aElementOf0 tptp.xm tptp.szNzAzT0) (= tptp.xx (tptp.sdtlpdtrp0 tptp.xe tptp.xm)))) % 0.38/0.74 (assume @p115 (= tptp.xx @t115)) % 0.38/0.74 (assume @p116 (not (tptp.aSubsetOf0 @t114 (tptp.sdtlpdtrp0 tptp.xN (tptp.szszuzczcdt0 tptp.xn))))) % 0.38/0.74 (assume @p117 (tptp.aSubsetOf0 (tptp.sdtlpdtrp0 tptp.xN tptp.xn) @t114)) % 0.38/0.74 (assume @p118 (and (tptp.aElementOf0 tptp.xp @t114) (tptp.aElementOf0 tptp.xx tptp.xQ))) % 0.38/0.74 (assume @p119 (and @t112 @t117 @t111 (not @t116))) % 0.38/0.74 (assume @p120 (not (= tptp.xp tptp.xx))) % 0.38/0.74 (assume @p121 true) % 0.38/0.74 (step @p122 :rule and_elim :premises (@p99) :args (1)) % 0.38/0.74 (step @p123 :rule symm :premises (@p122)) % 0.38/0.74 (step @p124 :rule and_elim :premises (@p119) :args (1)) % 0.38/0.74 (step @p125 :rule and_elim :premises (@p119) :args (3)) % 0.38/0.74 (step @p126 :rule symm :premises (@p125)) % 0.38/0.74 (step @p127 :rule and_elim :premises (@p118) :args (0)) % 0.38/0.74 (step @p128 :rule true_intro :premises (@p127)) % 0.38/0.74 (step @p129 :rule refl :args (@t114)) % 0.38/0.74 (step @p130 :rule symm :premises (@p102)) % 0.38/0.74 (step @p131 :rule cong :premises (@p130 @p129) :args (@t118)) % 0.38/0.74 (step @p132 :rule trans :premises (@p131 @p128)) % 0.38/0.74 (step @p133 :rule true_elim :premises (@p132)) % 0.38/0.74 (step @p134 :rule aci_norm :args ((= (or (or @t122 @t121 @t10 @t63) @t124) @t123))) % 0.38/0.74 (step @p135 :rule aci_norm :args ((= (or (or @t120 @t119) @t58) @t124))) % 0.38/0.74 (step @p136 :rule refl :args (@t58)) % 0.38/0.74 (step @p137 :rule bool-and-de-morgan :args (@t60 @t59 true)) % 0.38/0.74 (step @p138 :rule nary_cong :premises (@p137 @p136) :args ((or (not @t61) @t58))) % 0.38/0.74 (step @p139 :rule trans :premises (@p138 @p135)) % 0.38/0.74 (step @p140 :rule bool-impl-elim :args (@t61 @t58)) % 0.38/0.74 (step @p141 :rule trans :premises (@p140 @p139)) % 0.38/0.74 (step @p142 :rule bool-double-not-elim :args (@t63)) % 0.38/0.74 (step @p143 :rule bool-double-not-elim :args (@t10)) % 0.38/0.74 (step @p144 :rule refl :args (@t121)) % 0.38/0.74 (step @p145 :rule refl :args (@t122)) % 0.38/0.74 (step @p146 :rule nary_cong :premises (@p145 @p144 @p143 @p142) :args (@t127)) % 0.38/0.74 (step @p147 :rule aci_norm :args ((= (or @t122 (or @t121 (or @t126 @t125))) @t127))) % 0.38/0.74 (step @p148 :rule trans :premises (@p147 @p146)) % 0.38/0.74 (step @p149 :rule bool-and-de-morgan :args (@t14 @t64 true)) % 0.38/0.74 (step @p150 :rule nary_cong :premises (@p144 @p149) :args ((or @t121 (not (and @t14 @t64))))) % 0.38/0.74 (step @p151 :rule bool-and-de-morgan :args (@t65 @t14 (and @t64))) % 0.38/0.74 (step @p152 :rule trans :premises (@p151 @p150)) % 0.38/0.74 (step @p153 :rule nary_cong :premises (@p145 @p152) :args ((or @t122 (not (and @t65 @t14 @t64))))) % 0.38/0.74 (step @p154 :rule bool-and-de-morgan :args (@t56 @t65 (and @t14 @t64))) % 0.38/0.74 (step @p155 :rule trans :premises (@p154 @p153)) % 0.38/0.74 (step @p156 :rule trans :premises (@p155 @p148)) % 0.38/0.74 (step @p157 :rule nary_cong :premises (@p156 @p141) :args ((or (not @t66) @t62))) % 0.38/0.74 (step @p158 :rule trans :premises (@p157 @p134)) % 0.38/0.74 (step @p159 :rule bool-impl-elim :args (@t66 @t62)) % 0.38/0.74 (step @p160 :rule trans :premises (@p159 @p158)) % 0.38/0.74 (step @p161 :rule cong :premises (@p160) :args (@t67)) % 0.38/0.74 (step @p162 :rule eq_resolve :premises (@p49 @p161)) % 0.38/0.74 (step @p163 :rule refl :args (@t128)) % 0.38/0.74 (step @p164 :rule refl :args (@t130)) % 0.38/0.74 (step @p165 :rule refl :args (@t131)) % 0.38/0.74 (step @p166 :rule eq-symm :args (@t114 tptp.slcrc0)) % 0.38/0.74 (step @p167 :rule eq-symm :args (tptp.xQ tptp.slcrc0)) % 0.38/0.74 (step @p168 :rule refl :args (@t132)) % 0.38/0.74 (step @p169 :rule refl :args (@t133)) % 0.38/0.74 (step @p170 :rule nary_cong :premises (@p169 @p168 @p167 @p166 @p165 @p164 @p163) :args (@t134)) % 0.38/0.74 (step @p171 :rule refl :args (@t135)) % 0.38/0.74 (step @p172 :rule cong :premises (@p171 @p170) :args ((=> @t135 @t134))) % 0.38/0.74 (assume-push @p194 @t135) % 0.38/0.74 (step @p174 :rule instantiate :premises (@p162) :args ((@list tptp.xQ @t114))) % 0.38/0.74 (step-pop @p195 :rule scope :premises (@p174)) % 0.38/0.74 (step @p175 :rule process_scope :premises (@p195) :args (@t134)) % 0.38/0.74 (step @p177 :rule eq_resolve :premises (@p175 @p172)) % 0.38/0.74 (step @p178 :rule implies_elim :premises (@p177)) % 0.38/0.74 (step @p179 :rule chain_m_resolution :premises (@p178 @p162) :args (@t138 (@list false) (@list @t135))) % 0.38/0.74 (step @p180 :rule false_intro :premises (@p120)) % 0.38/0.74 (step @p181 :rule symm :premises (@p115)) % 0.38/0.74 (step @p182 :rule cong :premises (@p130 @p181) :args (@t128)) % 0.38/0.74 (step @p183 :rule trans :premises (@p182 @p180)) % 0.38/0.74 (step @p184 :rule false_elim :premises (@p183)) % 0.38/0.74 (step @p185 :rule and_elim :premises (@p118) :args (1)) % 0.38/0.74 (step @p186 :rule true_intro :premises (@p185)) % 0.38/0.74 (step @p187 :rule refl :args (tptp.xQ)) % 0.38/0.74 (step @p188 :rule cong :premises (@p181 @p187) :args (@t129)) % 0.38/0.74 (step @p189 :rule trans :premises (@p188 @p186)) % 0.38/0.74 (step @p190 :rule true_elim :premises (@p189)) % 0.38/0.74 (step @p191 :rule cnf_or_pos :args (@t138)) % 0.38/0.74 (step @p192 :rule reordering :premises (@p191) :args ((or @t137 @t136 @t133 @t132 @t131 @t130 @t128 (not @t138)))) % 0.38/0.74 (step @p193 false :rule chain_m_resolution :premises (@p192 @p190 @p184 @p179 @p133 @p126 @p124 @p100 @p123) :args (false (@list false true false false true false false true) (@list @t129 @t128 @t138 @t118 @t136 @t117 @t112 @t137))) % 0.38/0.74 ) % 0.38/0.74 % SZS output end Proof % 0.38/0.74 % cvc5 exiting %------------------------------------------------------------------------------