%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM565+3 : 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 : n023.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 08:39:51 AM UTC 2026 % Result : Theorem 0.44s 0.67s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM565+3 : 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 : n023.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 11:30:43 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.67 % SZS status Theorem % 0.44/0.67 % SZS output start Proof % 0.44/0.67 ( % 0.44/0.67 (declare-sort $$unsorted 0) % 0.44/0.67 (declare-const tptp.sz00 $$unsorted) % 0.44/0.67 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.szNzAzT0 $$unsorted) % 0.44/0.67 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.xK $$unsorted) % 0.44/0.67 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.xT $$unsorted) % 0.44/0.67 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.xS $$unsorted) % 0.44/0.67 (declare-const tptp.xc $$unsorted) % 0.44/0.67 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.slcrc0 $$unsorted) % 0.44/0.67 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.67 (define @t1 () (@var "W0" $$unsorted)) % 0.44/0.67 (define @t2 () (tptp.aSet0 @t1)) % 0.44/0.67 (define @t3 () (@list @t1)) % 0.44/0.67 (define @t4 () (tptp.aElement0 @t1)) % 0.44/0.67 (define @t5 () (@var "W1" $$unsorted)) % 0.44/0.67 (define @t6 () (tptp.aElement0 @t5)) % 0.44/0.67 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.44/0.67 (define @t8 () (@list @t5)) % 0.44/0.67 (define @t9 () (tptp.isFinite0 @t1)) % 0.44/0.67 (define @t10 () (= @t1 tptp.slcrc0)) % 0.44/0.67 (define @t11 () (tptp.isCountable0 @t1)) % 0.44/0.67 (define @t12 () (not @t9)) % 0.44/0.67 (define @t13 () (and @t2 @t11)) % 0.44/0.67 (define @t14 () (not @t10)) % 0.44/0.67 (define @t15 () (@var "W2" $$unsorted)) % 0.44/0.67 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.44/0.67 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.44/0.67 (define @t18 () (@list @t15)) % 0.44/0.67 (define @t19 () (tptp.aSet0 @t5)) % 0.44/0.67 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.44/0.67 (define @t21 () (tptp.isFinite0 @t5)) % 0.44/0.67 (define @t22 () (and @t2 @t9)) % 0.44/0.67 (define @t23 () (= @t1 @t5)) % 0.44/0.67 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.44/0.67 (define @t25 () (@list @t1 @t5)) % 0.44/0.67 (define @t26 () (tptp.aSubsetOf0 @t5 @t15)) % 0.44/0.67 (define @t27 () (tptp.aSet0 @t15)) % 0.44/0.67 (define @t28 () (@list @t1 @t5 @t15)) % 0.44/0.67 (define @t29 () (@var "W3" $$unsorted)) % 0.44/0.67 (define @t30 () (= @t29 @t5)) % 0.44/0.67 (define @t31 () (tptp.aElementOf0 @t29 @t1)) % 0.44/0.67 (define @t32 () (tptp.aElement0 @t29)) % 0.44/0.67 (define @t33 () (tptp.aElementOf0 @t29 @t15)) % 0.44/0.67 (define @t34 () (@list @t29)) % 0.44/0.67 (define @t35 () (tptp.sdtpldt0 @t1 @t5)) % 0.44/0.67 (define @t36 () (and @t2 @t6)) % 0.44/0.67 (define @t37 () (tptp.sdtmndt0 @t1 @t5)) % 0.44/0.67 (define @t38 () (tptp.sdtpldt0 @t5 @t1)) % 0.44/0.67 (define @t39 () (tptp.isCountable0 @t5)) % 0.44/0.67 (define @t40 () (and @t19 @t39)) % 0.44/0.67 (define @t41 () (tptp.sdtmndt0 @t5 @t1)) % 0.44/0.67 (define @t42 () (and @t19 @t21)) % 0.44/0.67 (define @t43 () (tptp.szszuzczcdt0 @t1)) % 0.44/0.67 (define @t44 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.44/0.67 (define @t45 () (tptp.szszuzczcdt0 @t5)) % 0.44/0.67 (define @t46 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.44/0.67 (define @t47 () (and @t44 @t46)) % 0.44/0.67 (define @t48 () (= @t1 tptp.sz00)) % 0.44/0.67 (define @t49 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.44/0.67 (define @t50 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.44/0.67 (define @t51 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.44/0.67 (define @t52 () (tptp.sbrdtbr0 @t1)) % 0.44/0.67 (define @t53 () (= @t52 tptp.sz00)) % 0.44/0.67 (define @t54 () (=> @t2 (= @t53 @t10))) % 0.44/0.67 (define @t55 () (forall @t3 @t54)) % 0.44/0.67 (define @t56 () (not @t7)) % 0.44/0.67 (define @t57 () (and @t2 @t46)) % 0.44/0.67 (define @t58 () (tptp.szmzizndt0 @t1)) % 0.44/0.67 (define @t59 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.44/0.67 (define @t60 () (tptp.szmzizndt0 @t5)) % 0.44/0.67 (define @t61 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.44/0.67 (define @t62 () (tptp.slbdtrb0 @t1)) % 0.44/0.67 (define @t63 () (tptp.slbdtrb0 @t5)) % 0.44/0.67 (define @t64 () (tptp.sbrdtbr0 @t29)) % 0.44/0.67 (define @t65 () (tptp.aSubsetOf0 @t29 @t1)) % 0.44/0.67 (define @t66 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.44/0.67 (define @t67 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.44/0.67 (define @t68 () (tptp.aFunction0 @t1)) % 0.44/0.67 (define @t69 () (tptp.szDzozmdt0 @t1)) % 0.44/0.67 (define @t70 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.44/0.67 (define @t71 () (tptp.aElementOf0 @t5 @t69)) % 0.44/0.67 (define @t72 () (tptp.sdtlpdtrp0 @t1 @t29)) % 0.44/0.67 (define @t73 () (tptp.aElementOf0 @t29 @t69)) % 0.44/0.67 (define @t74 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.44/0.67 (define @t75 () (and @t68 @t6)) % 0.44/0.67 (define @t76 () (@var "W4" $$unsorted)) % 0.44/0.67 (define @t77 () (tptp.aElementOf0 @t76 @t5)) % 0.44/0.67 (define @t78 () (@list @t76)) % 0.44/0.67 (define @t79 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.44/0.67 (define @t80 () (tptp.aSubsetOf0 @t5 @t69)) % 0.44/0.67 (define @t81 () (tptp.sdtlcdtrc0 @t1 @t69)) % 0.44/0.67 (define @t82 () (tptp.szDzozmdt0 @t15)) % 0.44/0.67 (define @t83 () (tptp.aFunction0 @t15)) % 0.44/0.67 (define @t84 () (tptp.szDzizrdt0 @t1)) % 0.44/0.67 (define @t85 () (tptp.aElementOf0 @t1 tptp.xS)) % 0.44/0.67 (define @t86 () (tptp.szDzozmdt0 tptp.xc)) % 0.44/0.67 (define @t87 () (tptp.sdtlcdtrc0 tptp.xc @t86)) % 0.44/0.67 (define @t88 () (tptp.aElementOf0 @t1 @t87)) % 0.44/0.67 (define @t89 () (tptp.aElementOf0 @t1 @t86)) % 0.44/0.67 (define @t90 () (= @t52 tptp.xK)) % 0.44/0.67 (define @t91 () (tptp.aSubsetOf0 @t1 tptp.xS)) % 0.44/0.67 (define @t92 () (tptp.aElementOf0 @t5 tptp.xS)) % 0.44/0.67 (define @t93 () (forall @t8 (=> @t7 @t92))) % 0.44/0.67 (define @t94 () (@var "W5" $$unsorted)) % 0.44/0.67 (define @t95 () (@var "W6" $$unsorted)) % 0.44/0.67 (define @t96 () (@list @t94)) % 0.44/0.67 (define @t97 () (tptp.aElementOf0 @t29 tptp.xT)) % 0.44/0.67 (define @t98 () (tptp.sdtlcdtrc0 @t15 @t82)) % 0.44/0.67 (define @t99 () (tptp.aElementOf0 @t29 @t98)) % 0.44/0.67 (define @t100 () (tptp.aElementOf0 @t29 @t82)) % 0.44/0.67 (define @t101 () (= @t64 @t1)) % 0.44/0.67 (define @t102 () (tptp.aSubsetOf0 @t29 @t5)) % 0.44/0.67 (define @t103 () (forall @t78 (=> (tptp.aElementOf0 @t76 @t29) @t77))) % 0.44/0.67 (define @t104 () (tptp.aSet0 @t29)) % 0.44/0.67 (define @t105 () (tptp.slbdtsldtrb0 tptp.xS tptp.sz00)) % 0.44/0.67 (define @t106 () (tptp.aElementOf0 @t1 tptp.slcrc0)) % 0.44/0.67 (define @t107 () (tptp.aSet0 tptp.slcrc0)) % 0.44/0.67 (define @t108 () (tptp.sdtlpdtrp0 tptp.xc tptp.slcrc0)) % 0.44/0.67 (define @t109 () (= (tptp.sdtlpdtrp0 tptp.xc @t1) @t108)) % 0.44/0.67 (define @t110 () (tptp.aElementOf0 @t5 tptp.slcrc0)) % 0.44/0.67 (define @t111 () (exists @t8 @t110)) % 0.44/0.67 (define @t112 () (not @t111)) % 0.44/0.67 (define @t113 () (and @t107 @t112)) % 0.44/0.67 (define @t114 () (=> @t113 @t109)) % 0.44/0.67 (define @t115 () (tptp.aElementOf0 @t1 @t105)) % 0.44/0.67 (define @t116 () (and @t2 @t93 @t91 @t53 @t115)) % 0.44/0.67 (define @t117 () (=> @t116 @t114)) % 0.44/0.67 (define @t118 () (forall @t3 @t117)) % 0.44/0.67 (define @t119 () (not @t118)) % 0.44/0.67 (define @t120 () (not @t115)) % 0.44/0.67 (define @t121 () (= tptp.sz00 @t52)) % 0.44/0.67 (define @t122 () (not @t121)) % 0.44/0.67 (define @t123 () (not @t91)) % 0.44/0.67 (define @t124 () (forall @t8 (or @t56 @t92))) % 0.44/0.67 (define @t125 () (not @t124)) % 0.44/0.67 (define @t126 () (not @t2)) % 0.44/0.67 (define @t127 () (or @t126 @t125 @t123 @t122 @t120 @t109)) % 0.44/0.67 (define @t128 () (forall @t3 @t127)) % 0.44/0.67 (define @t129 () (forall @t8 (not @t110))) % 0.44/0.67 (define @t130 () (not @t129)) % 0.44/0.67 (define @t131 () (not @t107)) % 0.44/0.67 (define @t132 () (or @t131 @t130 @t127)) % 0.44/0.67 (define @t133 () (or @t126 @t125 @t123 @t122 @t120 @t131 @t130 @t109)) % 0.44/0.67 (define @t134 () (or @t131 @t130 @t109)) % 0.44/0.67 (define @t135 () (or @t126 @t125 @t123 @t122 @t120)) % 0.44/0.67 (define @t136 () (and @t107 @t129)) % 0.44/0.67 (define @t137 () (=> @t136 @t109)) % 0.44/0.67 (define @t138 () (and @t2 @t124 @t91 @t121 @t115)) % 0.44/0.67 (define @t139 () (@quantifiers_skolemize @t128 0)) % 0.44/0.67 (define @t140 () (tptp.sdtlpdtrp0 tptp.xc @t139)) % 0.44/0.67 (define @t141 () (= @t108 @t140)) % 0.44/0.67 (define @t142 () (not (tptp.aElementOf0 @t139 @t105))) % 0.44/0.67 (define @t143 () (= tptp.sz00 (tptp.sbrdtbr0 @t139))) % 0.44/0.67 (define @t144 () (not @t143)) % 0.44/0.67 (define @t145 () (not (tptp.aSubsetOf0 @t139 tptp.xS))) % 0.44/0.67 (define @t146 () (not (forall @t8 (or (not (tptp.aElementOf0 @t5 @t139)) @t92)))) % 0.44/0.67 (define @t147 () (tptp.aSet0 @t139)) % 0.44/0.67 (define @t148 () (not @t147)) % 0.44/0.67 (define @t149 () (or @t148 @t146 @t145 @t144 @t142 @t141)) % 0.44/0.67 (define @t150 () (not @t149)) % 0.44/0.67 (define @t151 () (not @t128)) % 0.44/0.67 (define @t152 () (or @t148 @t146 @t145 @t144 @t142 (= @t140 @t108))) % 0.44/0.67 (define @t153 () (not @t152)) % 0.44/0.67 (define @t154 () (@list true)) % 0.44/0.67 (define @t155 () (@list @t149)) % 0.44/0.67 (define @t156 () (= @t10 @t121)) % 0.44/0.67 (define @t157 () (= @t139 tptp.slcrc0)) % 0.44/0.67 (define @t158 () (or @t148 (= @t157 @t143))) % 0.44/0.67 (define @t159 () (forall @t3 (or @t126 @t156))) % 0.44/0.67 (define @t160 () (= tptp.slcrc0 @t139)) % 0.44/0.67 (define @t161 () (= @t143 @t160)) % 0.44/0.67 (define @t162 () (or @t148 @t161)) % 0.44/0.67 (define @t163 () (@list false false)) % 0.44/0.67 (assume @p1 (forall @t3 (=> @t2 true))) % 0.44/0.67 (assume @p2 (forall @t3 (=> @t4 true))) % 0.44/0.67 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.44/0.67 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.44/0.67 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.44/0.67 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.44/0.67 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.44/0.67 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.44/0.67 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.44/0.67 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.44/0.67 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.44/0.67 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.44/0.67 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.44/0.67 (assume @p14 (forall @t28 (=> (and @t2 @t19 @t27) (=> (and @t24 @t26) (tptp.aSubsetOf0 @t1 @t15))))) % 0.44/0.67 (assume @p15 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t35) (and @t27 (forall @t34 (= @t33 (and @t32 (or @t31 @t30)))))))))) % 0.44/0.67 (assume @p16 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t37) (and @t27 (forall @t34 (= @t33 (and @t32 @t31 (not @t30)))))))))) % 0.44/0.67 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t37 @t5) @t1)))))) % 0.44/0.67 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t38 @t1) @t5))))) % 0.44/0.67 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t38)))))) % 0.44/0.67 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t41)))))) % 0.44/0.67 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t38)))))) % 0.44/0.67 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t41)))))) % 0.44/0.67 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.44/0.67 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.44/0.67 (assume @p25 (forall @t3 (=> @t44 (and (tptp.aElementOf0 @t43 tptp.szNzAzT0) (not (= @t43 tptp.sz00)))))) % 0.44/0.67 (assume @p26 (forall @t25 (=> @t47 (=> (= @t43 @t45) @t23)))) % 0.44/0.67 (assume @p27 (forall @t3 (=> @t44 (or @t48 (exists @t8 (and @t46 (= @t1 @t45))))))) % 0.44/0.67 (assume @p28 (forall @t3 (=> @t44 (not (= @t1 @t43))))) % 0.44/0.67 (assume @p29 (forall @t25 (=> @t47 (=> @t49 true)))) % 0.44/0.67 (assume @p30 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.44/0.67 (assume @p31 (forall @t3 (=> @t44 (not (tptp.sdtlseqdt0 @t43 tptp.sz00))))) % 0.44/0.67 (assume @p32 (forall @t25 (=> @t47 (= @t49 (tptp.sdtlseqdt0 @t43 @t45))))) % 0.44/0.67 (assume @p33 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t43)))) % 0.44/0.67 (assume @p34 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.44/0.67 (assume @p35 (forall @t25 (=> @t47 (=> (and @t49 (tptp.sdtlseqdt0 @t5 @t1)) @t23)))) % 0.44/0.67 (assume @p36 (forall @t28 (=> (and @t44 @t46 @t51) (=> (and @t49 @t50) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.44/0.67 (assume @p37 (forall @t25 (=> @t47 (or @t49 (tptp.sdtlseqdt0 @t45 @t1))))) % 0.44/0.67 (assume @p38 (forall @t25 (=> @t47 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.44/0.67 (assume @p39 (forall @t3 (=> @t44 (tptp.iLess0 @t1 @t43)))) % 0.44/0.67 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t52)))) % 0.44/0.67 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t52 tptp.szNzAzT0) @t9)))) % 0.44/0.67 (assume @p42 @t55) % 0.44/0.67 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> @t56 (= (tptp.sbrdtbr0 @t35) (tptp.szszuzczcdt0 @t52)))))))) % 0.44/0.67 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t37)) @t52)))))) % 0.44/0.67 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t52)))))) % 0.44/0.67 (assume @p46 (forall @t25 (=> @t57 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t52)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.44/0.67 (assume @p47 (forall @t3 (=> (and @t59 @t14) (forall @t8 (= (= @t5 @t58) (and @t7 (forall @t18 (=> @t16 @t50)))))))) % 0.44/0.67 (assume @p48 (forall @t3 (=> (and @t59 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.44/0.67 (assume @p49 (forall @t25 (=> (and @t59 @t61 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t58 @t5) (tptp.aElementOf0 @t60 @t1)) (= @t58 @t60))))) % 0.44/0.67 (assume @p50 (forall @t3 (=> @t44 (forall @t8 (= (= @t5 @t62) (and @t19 (forall @t18 (= @t17 (and @t51 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.44/0.67 (assume @p51 (forall @t3 (=> @t44 (tptp.isFinite0 @t62)))) % 0.44/0.67 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.44/0.67 (assume @p53 (forall @t25 (=> @t47 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t45)) (or (tptp.aElementOf0 @t1 @t63) @t23))))) % 0.44/0.67 (assume @p54 (forall @t25 (=> @t47 (= @t49 (tptp.aSubsetOf0 @t62 @t63))))) % 0.44/0.67 (assume @p55 (forall @t3 (=> (and @t59 @t9) (exists @t8 (and @t46 (tptp.aSubsetOf0 @t1 @t63)))))) % 0.44/0.67 (assume @p56 (forall @t3 (=> @t44 (= (tptp.sbrdtbr0 @t62) @t1)))) % 0.44/0.67 (assume @p57 (forall @t25 (=> @t57 (forall @t18 (= (= @t15 @t66) (and @t27 (forall @t34 (= @t33 (and @t65 (= @t64 @t5)))))))))) % 0.44/0.67 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t46 (tptp.isFinite0 @t66)))))) % 0.44/0.67 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t46 (not (= @t66 tptp.slcrc0))))))) % 0.44/0.67 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t46 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t66)))))) % 0.44/0.67 (assume @p61 (forall @t3 (=> @t44 (forall (@list @t5 @t15) (=> (and @t19 @t27 (not @t48)) (=> (and (tptp.aSubsetOf0 @t67 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t67 tptp.slcrc0))) @t26)))))) % 0.44/0.67 (assume @p62 (forall @t25 (=> @t57 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t66) (tptp.isFinite0 @t15)) (exists @t34 (and @t65 (tptp.isFinite0 @t29) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t29 @t5))))))))) % 0.44/0.67 (assume @p63 (forall @t3 (=> @t68 true))) % 0.44/0.67 (assume @p64 (forall @t3 (=> @t68 (tptp.aSet0 @t69)))) % 0.44/0.67 (assume @p65 (forall @t3 (=> @t68 (forall @t8 (=> @t71 (tptp.aElement0 @t70)))))) % 0.44/0.67 (assume @p66 (forall @t25 (=> @t75 (forall @t18 (= (= @t15 @t74) (and @t27 (forall @t34 (= @t33 (and @t73 (= @t72 @t5)))))))))) % 0.44/0.67 (assume @p67 (forall @t25 (=> @t75 (tptp.aSubsetOf0 @t74 @t69)))) % 0.44/0.67 (assume @p68 (forall @t3 (=> @t68 (forall @t8 (=> @t80 (forall @t18 (= (= @t15 @t79) (and @t27 (forall @t34 (= @t33 (exists @t78 (and @t77 (= (tptp.sdtlpdtrp0 @t1 @t76) @t29))))))))))))) % 0.44/0.67 (assume @p69 (forall @t3 (=> @t68 (forall @t8 (=> @t71 (tptp.aElementOf0 @t70 @t81)))))) % 0.44/0.67 (assume @p70 (forall @t3 (=> @t68 (forall @t8 (=> @t80 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t83 (= @t82 @t5) (forall @t34 (=> (tptp.aElementOf0 @t29 @t5) (= (tptp.sdtlpdtrp0 @t15 @t29) @t72))))))))))) % 0.44/0.67 (assume @p71 (forall @t3 (=> @t68 (forall @t8 (=> (and @t80 @t39) (=> (forall (@list @t15 @t29) (=> (and (tptp.aElementOf0 @t15 @t69) @t73 (not (= @t15 @t29))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t72)))) (tptp.isCountable0 @t79))))))) % 0.44/0.67 (assume @p72 (forall @t3 (=> @t68 (=> (and (tptp.isCountable0 @t69) (tptp.isFinite0 @t81)) (and (tptp.aElement0 @t84) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t84))))))) % 0.44/0.67 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.44/0.67 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.44/0.67 (assume @p75 (and (tptp.aSet0 tptp.xS) (forall @t3 (=> @t85 @t44)) (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.44/0.67 (assume @p76 (and (tptp.aFunction0 tptp.xc) (forall @t3 (and (=> @t89 (and @t2 @t93 @t91 @t90)) (=> (and (or (and @t2 @t93) @t91) @t90) @t89))) (= @t86 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSet0 @t87) (forall @t3 (= @t88 (exists @t8 (and (tptp.aElementOf0 @t5 @t86) (= (tptp.sdtlpdtrp0 tptp.xc @t5) @t1))))) (forall @t3 (=> @t88 (tptp.aElementOf0 @t1 tptp.xT))) (tptp.aSubsetOf0 @t87 tptp.xT))) % 0.44/0.67 (assume @p77 (forall @t3 (=> @t44 (forall @t8 (=> (and (or (and @t19 (forall @t18 (=> @t17 @t51))) @t61) @t39) (forall @t18 (=> (and @t83 (or (forall @t34 (and (=> @t100 (and (or (and @t104 @t103) @t102) @t101)) (=> (and @t104 @t103 @t102 @t101) @t100))) (= @t82 @t67)) (=> (and (tptp.aSet0 @t98) (forall @t34 (= @t99 (exists @t78 (and (tptp.aElementOf0 @t76 @t82) (= (tptp.sdtlpdtrp0 @t15 @t76) @t29)))))) (or (forall @t34 (=> @t99 @t97)) (tptp.aSubsetOf0 @t98 tptp.xT)))) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t34 (and @t97 (exists @t78 (and (tptp.aSet0 @t76) (forall @t96 (=> (tptp.aElementOf0 @t94 @t76) (tptp.aElementOf0 @t94 @t5))) (tptp.aSubsetOf0 @t76 @t5) (tptp.isCountable0 @t76) (forall @t96 (=> (or (and (or (and (tptp.aSet0 @t94) (forall (@list @t95) (=> (tptp.aElementOf0 @t95 @t94) (tptp.aElementOf0 @t95 @t76)))) (tptp.aSubsetOf0 @t94 @t76)) (= (tptp.sbrdtbr0 @t94) @t1)) (tptp.aElementOf0 @t94 (tptp.slbdtsldtrb0 @t76 @t1))) (= (tptp.sdtlpdtrp0 @t15 @t94) @t29))))))))))))))) % 0.44/0.67 (assume @p78 (= tptp.xK tptp.sz00)) % 0.44/0.67 (assume @p79 (and @t107 (not (exists @t3 @t106)) (forall @t3 (=> @t106 @t85)) (tptp.aSubsetOf0 tptp.slcrc0 tptp.xS) (tptp.aElementOf0 tptp.slcrc0 @t105))) % 0.44/0.67 (assume @p80 @t119) % 0.44/0.67 (assume @p81 true) % 0.44/0.67 (step @p82 :rule quant-miniscope-or :args ((= (forall @t3 @t132) (or @t131 @t130 @t128)))) % 0.44/0.67 (step @p83 :rule aci_norm :args ((= @t133 @t132))) % 0.44/0.67 (step @p84 :rule cong :premises (@p83) :args ((forall @t3 @t133))) % 0.44/0.67 (step @p85 :rule trans :premises (@p84 @p82)) % 0.44/0.67 (step @p86 :rule aci_norm :args ((= (or @t135 @t134) @t133))) % 0.44/0.67 (step @p87 :rule aci_norm :args ((= (or (or @t131 @t130) @t109) @t134))) % 0.44/0.67 (step @p88 :rule refl :args (@t109)) % 0.44/0.67 (step @p89 :rule bool-and-de-morgan :args (@t107 @t129 true)) % 0.44/0.67 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or (not @t136) @t109))) % 0.44/0.67 (step @p91 :rule trans :premises (@p90 @p87)) % 0.44/0.67 (step @p92 :rule bool-impl-elim :args (@t136 @t109)) % 0.44/0.67 (step @p93 :rule trans :premises (@p92 @p91)) % 0.44/0.67 (step @p94 :rule aci_norm :args ((= (or @t126 (or @t125 (or @t123 (or @t122 @t120)))) @t135))) % 0.44/0.67 (step @p95 :rule bool-and-de-morgan :args (@t121 @t115 true)) % 0.44/0.67 (step @p96 :rule refl :args (@t123)) % 0.44/0.67 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or @t123 (not (and @t121 @t115))))) % 0.44/0.67 (step @p98 :rule bool-and-de-morgan :args (@t91 @t121 (and @t115))) % 0.44/0.67 (step @p99 :rule trans :premises (@p98 @p97)) % 0.44/0.67 (step @p100 :rule refl :args (@t125)) % 0.44/0.67 (step @p101 :rule nary_cong :premises (@p100 @p99) :args ((or @t125 (not (and @t91 @t121 @t115))))) % 0.44/0.67 (step @p102 :rule bool-and-de-morgan :args (@t124 @t91 (and @t121 @t115))) % 0.44/0.67 (step @p103 :rule trans :premises (@p102 @p101)) % 0.44/0.67 (step @p104 :rule refl :args (@t126)) % 0.44/0.67 (step @p105 :rule nary_cong :premises (@p104 @p103) :args ((or @t126 (not (and @t124 @t91 @t121 @t115))))) % 0.44/0.67 (step @p106 :rule bool-and-de-morgan :args (@t2 @t124 (and @t91 @t121 @t115))) % 0.44/0.67 (step @p107 :rule trans :premises (@p106 @p105)) % 0.44/0.67 (step @p108 :rule trans :premises (@p107 @p94)) % 0.44/0.67 (step @p109 :rule nary_cong :premises (@p108 @p93) :args ((or (not @t138) @t137))) % 0.44/0.67 (step @p110 :rule trans :premises (@p109 @p86)) % 0.44/0.67 (step @p111 :rule bool-impl-elim :args (@t138 @t137)) % 0.44/0.67 (step @p112 :rule trans :premises (@p111 @p110)) % 0.44/0.67 (step @p113 :rule cong :premises (@p112) :args ((forall @t3 (=> @t138 @t137)))) % 0.44/0.67 (step @p114 :rule trans :premises (@p113 @p85)) % 0.44/0.67 (step @p115 :rule refl :args (@t109)) % 0.44/0.67 (step @p116 :rule bool-double-not-elim :args (@t129)) % 0.44/0.67 (step @p117 :rule exists-elim :args ((= @t111 @t130))) % 0.44/0.67 (step @p118 :rule cong :premises (@p117) :args (@t112)) % 0.44/0.67 (step @p119 :rule trans :premises (@p118 @p116)) % 0.44/0.67 (step @p120 :rule refl :args (@t107)) % 0.44/0.67 (step @p121 :rule nary_cong :premises (@p120 @p119) :args (@t113)) % 0.44/0.67 (step @p122 :rule cong :premises (@p121 @p115) :args (@t114)) % 0.44/0.67 (step @p123 :rule refl :args (@t115)) % 0.44/0.67 (step @p124 :rule eq-symm :args (@t52 tptp.sz00)) % 0.44/0.67 (step @p125 :rule refl :args (@t91)) % 0.44/0.67 (step @p126 :rule bool-impl-elim :args (@t7 @t92)) % 0.44/0.67 (step @p127 :rule cong :premises (@p126) :args (@t93)) % 0.44/0.67 (step @p128 :rule refl :args (@t2)) % 0.44/0.67 (step @p129 :rule nary_cong :premises (@p128 @p127 @p125 @p124 @p123) :args (@t116)) % 0.44/0.67 (step @p130 :rule cong :premises (@p129 @p122) :args (@t117)) % 0.44/0.67 (step @p131 :rule cong :premises (@p130) :args (@t118)) % 0.44/0.67 (step @p132 :rule trans :premises (@p131 @p114)) % 0.44/0.67 (step @p133 :rule cong :premises (@p132) :args (@t119)) % 0.44/0.67 (step @p134 :rule eq_resolve :premises (@p80 @p133)) % 0.44/0.67 (step @p135 :rule not_or_elim :premises (@p134) :args (2)) % 0.44/0.67 (step @p136 :rule refl :args (@t150)) % 0.44/0.67 (step @p137 :rule bool-double-not-elim :args (@t128)) % 0.44/0.67 (step @p138 :rule nary_cong :premises (@p137 @p136) :args ((or (not @t151) @t150))) % 0.44/0.67 (step @p139 :rule eq-symm :args (@t140 @t108)) % 0.44/0.67 (step @p140 :rule refl :args (@t142)) % 0.44/0.67 (step @p141 :rule refl :args (@t144)) % 0.44/0.67 (step @p142 :rule refl :args (@t145)) % 0.44/0.67 (step @p143 :rule refl :args (@t146)) % 0.44/0.67 (step @p144 :rule refl :args (@t148)) % 0.44/0.67 (step @p145 :rule nary_cong :premises (@p144 @p143 @p142 @p141 @p140 @p139) :args (@t152)) % 0.44/0.67 (step @p146 :rule cong :premises (@p145) :args (@t153)) % 0.44/0.67 (step @p147 :rule refl :args (@t151)) % 0.44/0.67 (step @p148 :rule cong :premises (@p147 @p146) :args ((=> @t151 @t153))) % 0.44/0.67 (assume-push @p211 @t151) % 0.44/0.67 (step @p150 :rule skolemize :premises (@p135)) % 0.44/0.67 (step-pop @p212 :rule scope :premises (@p150)) % 0.44/0.67 (step @p151 :rule process_scope :premises (@p212) :args (@t153)) % 0.44/0.67 (step @p153 :rule eq_resolve :premises (@p151 @p148)) % 0.44/0.67 (step @p154 :rule implies_elim :premises (@p153)) % 0.44/0.67 (step @p155 :rule eq_resolve :premises (@p154 @p138)) % 0.44/0.67 (step @p156 :rule chain_m_resolution :premises (@p155 @p135) :args (@t150 @t154 (@list @t128))) % 0.44/0.67 (step @p157 :rule cnf_or_neg :args (@t149 5)) % 0.44/0.67 (step @p158 :rule chain_m_resolution :premises (@p157 @p156) :args ((not @t141) @t154 @t155)) % 0.44/0.67 (step @p159 :rule bool-impl-elim :args (@t2 @t156)) % 0.44/0.67 (step @p160 :rule cong :premises (@p159) :args ((forall @t3 (=> @t2 @t156)))) % 0.44/0.67 (step @p161 :rule refl :args (@t10)) % 0.44/0.67 (step @p162 :rule cong :premises (@p161 @p124) :args ((= @t10 @t53))) % 0.44/0.67 (step @p163 :rule eq-symm :args (@t53 @t10)) % 0.44/0.67 (step @p164 :rule trans :premises (@p163 @p162)) % 0.44/0.67 (step @p165 :rule cong :premises (@p128 @p164) :args (@t54)) % 0.44/0.67 (step @p166 :rule cong :premises (@p165) :args (@t55)) % 0.44/0.67 (step @p167 :rule trans :premises (@p166 @p160)) % 0.44/0.67 (step @p168 :rule eq_resolve :premises (@p42 @p167)) % 0.44/0.67 (step @p169 :rule eq-symm :args (@t139 tptp.slcrc0)) % 0.44/0.67 (step @p170 :rule refl :args (@t143)) % 0.44/0.67 (step @p171 :rule cong :premises (@p170 @p169) :args ((= @t143 @t157))) % 0.44/0.67 (step @p172 :rule eq-symm :args (@t157 @t143)) % 0.44/0.67 (step @p173 :rule trans :premises (@p172 @p171)) % 0.44/0.67 (step @p174 :rule nary_cong :premises (@p144 @p173) :args (@t158)) % 0.44/0.67 (step @p175 :rule refl :args (@t159)) % 0.44/0.67 (step @p176 :rule cong :premises (@p175 @p174) :args ((=> @t159 @t158))) % 0.44/0.67 (assume-push @p213 @t159) % 0.44/0.67 (step @p178 :rule instantiate :premises (@p168) :args ((@list @t139))) % 0.44/0.67 (step-pop @p214 :rule scope :premises (@p178)) % 0.44/0.67 (step @p179 :rule process_scope :premises (@p214) :args (@t158)) % 0.44/0.67 (step @p181 :rule eq_resolve :premises (@p179 @p176)) % 0.44/0.67 (step @p182 :rule implies_elim :premises (@p181)) % 0.44/0.67 (step @p183 :rule chain_m_resolution :premises (@p182 @p168) :args (@t162 (@list false) (@list @t159))) % 0.44/0.67 (step @p184 :rule bool-double-not-elim :args (@t147)) % 0.44/0.67 (step @p185 :rule refl :args (@t149)) % 0.44/0.67 (step @p186 :rule nary_cong :premises (@p185 @p184) :args ((or @t149 (not @t148)))) % 0.44/0.67 (step @p187 :rule cnf_or_neg :args (@t149 0)) % 0.44/0.67 (step @p188 :rule eq_resolve :premises (@p187 @p186)) % 0.44/0.67 (step @p189 :rule reordering :premises (@p188) :args ((or @t147 @t149))) % 0.44/0.67 (step @p190 :rule chain_m_resolution :premises (@p189 @p156) :args (@t147 @t154 @t155)) % 0.44/0.67 (step @p191 :rule cnf_or_pos :args (@t162)) % 0.44/0.67 (step @p192 :rule reordering :premises (@p191) :args ((or @t148 @t161 (not @t162)))) % 0.44/0.67 (step @p193 :rule chain_m_resolution :premises (@p192 @p190 @p183) :args (@t161 @t163 (@list @t147 @t162))) % 0.44/0.67 (step @p194 :rule bool-double-not-elim :args (@t143)) % 0.44/0.67 (step @p195 :rule nary_cong :premises (@p185 @p194) :args ((or @t149 (not @t144)))) % 0.44/0.67 (step @p196 :rule cnf_or_neg :args (@t149 3)) % 0.44/0.67 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 0.44/0.67 (step @p198 :rule reordering :premises (@p197) :args ((or @t143 @t149))) % 0.44/0.67 (step @p199 :rule chain_m_resolution :premises (@p198 @p156) :args (@t143 @t154 @t155)) % 0.44/0.67 (step @p200 :rule cnf_equiv_pos1 :args (@t161)) % 0.44/0.67 (step @p201 :rule reordering :premises (@p200) :args ((or @t144 @t160 (not @t161)))) % 0.44/0.67 (step @p202 :rule chain_m_resolution :premises (@p201 @p199 @p193) :args (@t160 @t163 (@list @t143 @t161))) % 0.44/0.67 (assume-push @p215 @t160) % 0.44/0.67 (step @p204 :rule refl :args (tptp.xc)) % 0.44/0.67 (step @p205 :rule cong :premises (@p204 @p202) :args (@t108)) % 0.44/0.67 (step-pop @p216 :rule scope :premises (@p205)) % 0.44/0.67 (step @p206 :rule process_scope :premises (@p216) :args (@t141)) % 0.44/0.67 (step @p208 :rule implies_elim :premises (@p206)) % 0.44/0.67 (step @p209 :rule reordering :premises (@p208) :args ((or @t141 (not @t160)))) % 0.44/0.67 (step @p210 false :rule chain_m_resolution :premises (@p209 @p202 @p158) :args (false (@list false true) (@list @t160 @t141))) % 0.44/0.67 ) % 0.44/0.67 % SZS output end Proof % 0.44/0.67 % cvc5 exiting %------------------------------------------------------------------------------