%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM607+3 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:39:59 AM UTC 2026 % Result : Theorem 0.37s 0.75s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM607+3 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n021.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 11:37:35 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.75 % SZS status Theorem % 0.37/0.75 % SZS output start Proof % 0.37/0.75 ( % 0.37/0.75 (declare-sort $$unsorted 0) % 0.37/0.75 (declare-const tptp.xQ $$unsorted) % 0.37/0.75 (declare-const tptp.xN $$unsorted) % 0.37/0.75 (declare-const tptp.sz00 $$unsorted) % 0.37/0.75 (declare-const tptp.xC $$unsorted) % 0.37/0.75 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.szNzAzT0 $$unsorted) % 0.37/0.75 (declare-const tptp.xk $$unsorted) % 0.37/0.75 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.xd $$unsorted) % 0.37/0.75 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.xO $$unsorted) % 0.37/0.75 (declare-const tptp.xe $$unsorted) % 0.37/0.75 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.75 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.xK $$unsorted) % 0.37/0.75 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.xT $$unsorted) % 0.37/0.75 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.xS $$unsorted) % 0.37/0.75 (declare-const tptp.xc $$unsorted) % 0.37/0.75 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.slcrc0 $$unsorted) % 0.37/0.75 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.75 (define @t1 () (@var "W0" $$unsorted)) % 0.37/0.75 (define @t2 () (tptp.aSet0 @t1)) % 0.37/0.75 (define @t3 () (@list @t1)) % 0.37/0.75 (define @t4 () (tptp.aElement0 @t1)) % 0.37/0.75 (define @t5 () (@var "W1" $$unsorted)) % 0.37/0.75 (define @t6 () (tptp.aElement0 @t5)) % 0.37/0.75 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.37/0.75 (define @t8 () (@list @t5)) % 0.37/0.75 (define @t9 () (tptp.isFinite0 @t1)) % 0.37/0.75 (define @t10 () (= @t1 tptp.slcrc0)) % 0.37/0.75 (define @t11 () (tptp.isCountable0 @t1)) % 0.37/0.75 (define @t12 () (not @t9)) % 0.37/0.75 (define @t13 () (and @t2 @t11)) % 0.37/0.75 (define @t14 () (not @t10)) % 0.37/0.75 (define @t15 () (@var "W2" $$unsorted)) % 0.37/0.75 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.37/0.75 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.37/0.75 (define @t18 () (@list @t15)) % 0.37/0.75 (define @t19 () (tptp.aSet0 @t5)) % 0.37/0.75 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.37/0.75 (define @t21 () (tptp.isFinite0 @t5)) % 0.37/0.75 (define @t22 () (and @t2 @t9)) % 0.37/0.75 (define @t23 () (= @t1 @t5)) % 0.37/0.75 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.37/0.75 (define @t25 () (@list @t1 @t5)) % 0.37/0.75 (define @t26 () (tptp.aSubsetOf0 @t5 @t15)) % 0.37/0.75 (define @t27 () (tptp.aSet0 @t15)) % 0.37/0.75 (define @t28 () (@list @t1 @t5 @t15)) % 0.37/0.75 (define @t29 () (@var "W3" $$unsorted)) % 0.37/0.75 (define @t30 () (= @t29 @t5)) % 0.37/0.75 (define @t31 () (tptp.aElementOf0 @t29 @t1)) % 0.37/0.75 (define @t32 () (tptp.aElement0 @t29)) % 0.37/0.75 (define @t33 () (tptp.aElementOf0 @t29 @t15)) % 0.37/0.75 (define @t34 () (@list @t29)) % 0.37/0.75 (define @t35 () (tptp.sdtpldt0 @t1 @t5)) % 0.37/0.75 (define @t36 () (and @t2 @t6)) % 0.37/0.75 (define @t37 () (tptp.sdtmndt0 @t1 @t5)) % 0.37/0.75 (define @t38 () (tptp.sdtpldt0 @t5 @t1)) % 0.37/0.75 (define @t39 () (tptp.isCountable0 @t5)) % 0.37/0.75 (define @t40 () (and @t19 @t39)) % 0.37/0.75 (define @t41 () (tptp.sdtmndt0 @t5 @t1)) % 0.37/0.75 (define @t42 () (and @t19 @t21)) % 0.37/0.75 (define @t43 () (tptp.szszuzczcdt0 @t1)) % 0.37/0.75 (define @t44 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.37/0.75 (define @t45 () (tptp.szszuzczcdt0 @t5)) % 0.37/0.75 (define @t46 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.37/0.75 (define @t47 () (and @t44 @t46)) % 0.37/0.75 (define @t48 () (= @t1 tptp.sz00)) % 0.37/0.75 (define @t49 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.37/0.75 (define @t50 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.37/0.75 (define @t51 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.37/0.75 (define @t52 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.37/0.75 (define @t53 () (tptp.sbrdtbr0 @t1)) % 0.37/0.75 (define @t54 () (tptp.sbrdtbr0 @t5)) % 0.37/0.75 (define @t55 () (tptp.sbrdtbr0 @t15)) % 0.37/0.75 (define @t56 () (and @t2 @t46)) % 0.37/0.75 (define @t57 () (tptp.szmzizndt0 @t1)) % 0.37/0.75 (define @t58 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.37/0.75 (define @t59 () (tptp.szmzizndt0 @t5)) % 0.37/0.75 (define @t60 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.37/0.75 (define @t61 () (tptp.slbdtrb0 @t1)) % 0.37/0.75 (define @t62 () (tptp.slbdtrb0 @t5)) % 0.37/0.75 (define @t63 () (tptp.sbrdtbr0 @t29)) % 0.37/0.75 (define @t64 () (tptp.aSubsetOf0 @t29 @t1)) % 0.37/0.75 (define @t65 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.37/0.75 (define @t66 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.37/0.75 (define @t67 () (tptp.aFunction0 @t1)) % 0.37/0.75 (define @t68 () (tptp.szDzozmdt0 @t1)) % 0.37/0.75 (define @t69 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.37/0.75 (define @t70 () (tptp.aElementOf0 @t5 @t68)) % 0.37/0.75 (define @t71 () (tptp.sdtlpdtrp0 @t1 @t29)) % 0.37/0.75 (define @t72 () (tptp.aElementOf0 @t29 @t68)) % 0.37/0.75 (define @t73 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.37/0.75 (define @t74 () (and @t67 @t6)) % 0.37/0.75 (define @t75 () (@var "W4" $$unsorted)) % 0.37/0.75 (define @t76 () (tptp.aElementOf0 @t75 @t5)) % 0.37/0.75 (define @t77 () (@list @t75)) % 0.37/0.75 (define @t78 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.37/0.75 (define @t79 () (tptp.aSubsetOf0 @t5 @t68)) % 0.37/0.75 (define @t80 () (tptp.sdtlcdtrc0 @t1 @t68)) % 0.37/0.75 (define @t81 () (tptp.aElementOf0 @t29 @t5)) % 0.37/0.75 (define @t82 () (tptp.szDzozmdt0 @t15)) % 0.37/0.75 (define @t83 () (tptp.aFunction0 @t15)) % 0.37/0.75 (define @t84 () (tptp.szDzizrdt0 @t1)) % 0.37/0.75 (define @t85 () (tptp.aElementOf0 @t1 tptp.xS)) % 0.37/0.75 (define @t86 () (tptp.szDzozmdt0 tptp.xc)) % 0.37/0.75 (define @t87 () (tptp.sdtlcdtrc0 tptp.xc @t86)) % 0.37/0.75 (define @t88 () (tptp.aElementOf0 @t1 tptp.xT)) % 0.37/0.75 (define @t89 () (tptp.aElementOf0 @t1 @t87)) % 0.37/0.75 (define @t90 () (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) % 0.37/0.75 (define @t91 () (tptp.aElementOf0 @t1 @t86)) % 0.37/0.75 (define @t92 () (= @t53 tptp.xK)) % 0.37/0.75 (define @t93 () (tptp.aSubsetOf0 @t1 tptp.xS)) % 0.37/0.75 (define @t94 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xS)))) % 0.37/0.75 (define @t95 () (@var "W5" $$unsorted)) % 0.37/0.75 (define @t96 () (@var "W6" $$unsorted)) % 0.37/0.75 (define @t97 () (@list @t95)) % 0.37/0.75 (define @t98 () (tptp.aElementOf0 @t29 tptp.xT)) % 0.37/0.75 (define @t99 () (tptp.sdtlcdtrc0 @t15 @t82)) % 0.37/0.75 (define @t100 () (tptp.aElementOf0 @t29 @t99)) % 0.37/0.75 (define @t101 () (tptp.aElementOf0 @t29 @t82)) % 0.37/0.75 (define @t102 () (= @t63 @t1)) % 0.37/0.75 (define @t103 () (tptp.aSubsetOf0 @t29 @t5)) % 0.37/0.75 (define @t104 () (tptp.aElementOf0 @t75 @t29)) % 0.37/0.75 (define @t105 () (forall @t77 (=> @t104 @t76))) % 0.37/0.75 (define @t106 () (tptp.aSet0 @t29)) % 0.37/0.75 (define @t107 () (tptp.sdtlpdtrp0 tptp.xN @t43)) % 0.37/0.75 (define @t108 () (tptp.sdtlpdtrp0 tptp.xN @t1)) % 0.37/0.75 (define @t109 () (tptp.szmzizndt0 @t108)) % 0.37/0.75 (define @t110 () (tptp.sdtmndt0 @t108 @t109)) % 0.37/0.75 (define @t111 () (tptp.aElementOf0 @t5 @t110)) % 0.37/0.75 (define @t112 () (tptp.aElementOf0 @t5 @t108)) % 0.37/0.75 (define @t113 () (forall @t8 (= @t111 (and @t6 @t112 (not (= @t5 @t109)))))) % 0.37/0.75 (define @t114 () (tptp.aSet0 @t110)) % 0.37/0.75 (define @t115 () (forall @t8 (=> @t112 (tptp.sdtlseqdt0 @t109 @t5)))) % 0.37/0.75 (define @t116 () (tptp.aElementOf0 @t109 @t108)) % 0.37/0.75 (define @t117 () (tptp.isCountable0 @t108)) % 0.37/0.75 (define @t118 () (tptp.aSubsetOf0 @t108 tptp.szNzAzT0)) % 0.37/0.75 (define @t119 () (forall @t8 (=> @t112 @t46))) % 0.37/0.75 (define @t120 () (tptp.aSet0 @t108)) % 0.37/0.75 (define @t121 () (tptp.sdtlpdtrp0 tptp.xN @t5)) % 0.37/0.75 (define @t122 () (tptp.aElementOf0 @t15 @t121)) % 0.37/0.75 (define @t123 () (tptp.aElementOf0 @t15 @t108)) % 0.37/0.75 (define @t124 () (tptp.sdtlseqdt0 @t109 @t15)) % 0.37/0.75 (define @t125 () (forall @t18 (=> @t123 @t124))) % 0.37/0.75 (define @t126 () (and @t116 @t125)) % 0.37/0.75 (define @t127 () (tptp.sdtpldt0 @t5 @t109)) % 0.37/0.75 (define @t128 () (tptp.aElementOf0 @t15 @t127)) % 0.37/0.75 (define @t129 () (= @t15 @t109)) % 0.37/0.75 (define @t130 () (tptp.aElement0 @t15)) % 0.37/0.75 (define @t131 () (forall @t18 (= @t128 (and @t130 (or @t17 @t129))))) % 0.37/0.75 (define @t132 () (tptp.slbdtsldtrb0 @t110 tptp.xk)) % 0.37/0.75 (define @t133 () (= @t54 tptp.xk)) % 0.37/0.75 (define @t134 () (tptp.aSubsetOf0 @t5 @t110)) % 0.37/0.75 (define @t135 () (tptp.aElementOf0 @t15 @t110)) % 0.37/0.75 (define @t136 () (forall @t18 (=> @t17 @t135))) % 0.37/0.75 (define @t137 () (and @t114 (forall @t18 (= @t135 (and @t130 @t123 (not @t129)))))) % 0.37/0.75 (define @t138 () (and @t19 (=> @t126 (=> @t137 (or (and (or @t136 @t134) @t133) (tptp.aElementOf0 @t5 @t132)))))) % 0.37/0.75 (define @t139 () (tptp.sdtlpdtrp0 tptp.xC @t1)) % 0.37/0.75 (define @t140 () (tptp.sdtlpdtrp0 @t139 @t5)) % 0.37/0.75 (define @t141 () (tptp.szDzozmdt0 @t139)) % 0.37/0.75 (define @t142 () (tptp.aElementOf0 @t5 @t141)) % 0.37/0.75 (define @t143 () (or (and @t19 @t136) @t134)) % 0.37/0.75 (define @t144 () (tptp.sdtlcdtrc0 @t139 @t141)) % 0.37/0.75 (define @t145 () (tptp.aElementOf0 @t5 tptp.xT)) % 0.37/0.75 (define @t146 () (tptp.aElementOf0 @t5 @t144)) % 0.37/0.75 (define @t147 () (= (tptp.sdtlpdtrp0 @t139 @t15) @t5)) % 0.37/0.75 (define @t148 () (tptp.aSubsetOf0 @t15 @t110)) % 0.37/0.75 (define @t149 () (tptp.aElementOf0 @t29 @t110)) % 0.37/0.75 (define @t150 () (forall @t34 (=> @t33 @t149))) % 0.37/0.75 (define @t151 () (tptp.aElementOf0 @t29 @t108)) % 0.37/0.75 (define @t152 () (forall @t34 (= @t149 (and @t32 @t151 (not (= @t29 @t109)))))) % 0.37/0.75 (define @t153 () (forall @t34 (=> @t151 (tptp.sdtlseqdt0 @t109 @t29)))) % 0.37/0.75 (define @t154 () (= @t55 tptp.xk)) % 0.37/0.75 (define @t155 () (tptp.slbdtsldtrb0 @t107 tptp.xk)) % 0.37/0.75 (define @t156 () (tptp.sdtlpdtrp0 tptp.xe @t1)) % 0.37/0.75 (define @t157 () (tptp.sdtlpdtrp0 tptp.xd @t1)) % 0.37/0.75 (define @t158 () (tptp.szDzozmdt0 tptp.xd)) % 0.37/0.75 (define @t159 () (tptp.sdtlcdtrc0 tptp.xd @t158)) % 0.37/0.75 (define @t160 () (tptp.aElementOf0 @t1 @t159)) % 0.37/0.75 (define @t161 () (tptp.sdtlpdtrp0 tptp.xd @t5)) % 0.37/0.75 (define @t162 () (tptp.szDzizrdt0 tptp.xd)) % 0.37/0.75 (define @t163 () (tptp.sdtlbdtrb0 tptp.xd @t162)) % 0.37/0.75 (define @t164 () (forall @t3 (= (tptp.aElementOf0 @t1 @t163) (and (tptp.aElementOf0 @t1 @t158) (= @t157 @t162))))) % 0.37/0.75 (define @t165 () (tptp.aSet0 @t163)) % 0.37/0.75 (define @t166 () (= (tptp.sdtlpdtrp0 tptp.xe @t5) @t1)) % 0.37/0.75 (define @t167 () (tptp.aElementOf0 @t5 @t163)) % 0.37/0.75 (define @t168 () (exists @t8 (and @t167 @t166))) % 0.37/0.75 (define @t169 () (tptp.aElementOf0 @t1 tptp.xO)) % 0.37/0.75 (define @t170 () (tptp.aSet0 tptp.xO)) % 0.37/0.75 (define @t171 () (forall @t3 (=> @t169 @t85))) % 0.37/0.75 (define @t172 () (tptp.aElementOf0 @t1 tptp.xQ)) % 0.37/0.75 (define @t173 () (forall @t3 (=> @t172 @t169))) % 0.37/0.75 (define @t174 () (tptp.aElementOf0 tptp.xQ @t86)) % 0.37/0.75 (define @t175 () (tptp.aSubsetOf0 tptp.xQ tptp.xS)) % 0.37/0.75 (define @t176 () (forall @t3 (=> @t172 @t85))) % 0.37/0.75 (define @t177 () (or @t176 @t175 @t176 @t175 @t174)) % 0.37/0.75 (define @t178 () (not @t177)) % 0.37/0.75 (define @t179 () (@quantifiers_skolemize (forall @t3 (or (not @t172) @t85)) 0)) % 0.37/0.75 (define @t180 () (tptp.aElementOf0 @t179 tptp.xQ)) % 0.37/0.75 (define @t181 () (tptp.aElementOf0 @t179 tptp.xS)) % 0.37/0.75 (define @t182 () (not @t180)) % 0.37/0.75 (define @t183 () (or @t182 @t181)) % 0.37/0.75 (define @t184 () (@list true)) % 0.37/0.75 (define @t185 () (@list @t183)) % 0.37/0.75 (define @t186 () (@list @t179)) % 0.37/0.75 (define @t187 () (tptp.aElementOf0 @t179 tptp.xO)) % 0.37/0.75 (define @t188 () (not @t187)) % 0.37/0.75 (define @t189 () (or @t188 @t181)) % 0.37/0.75 (define @t190 () (or @t182 @t187)) % 0.37/0.75 (assume @p1 (forall @t3 (=> @t2 true))) % 0.37/0.75 (assume @p2 (forall @t3 (=> @t4 true))) % 0.37/0.75 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.37/0.75 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.37/0.75 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.37/0.75 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.37/0.75 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.37/0.75 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.37/0.75 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.37/0.75 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.37/0.75 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.37/0.75 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.37/0.75 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.37/0.75 (assume @p14 (forall @t28 (=> (and @t2 @t19 @t27) (=> (and @t24 @t26) (tptp.aSubsetOf0 @t1 @t15))))) % 0.37/0.75 (assume @p15 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t35) (and @t27 (forall @t34 (= @t33 (and @t32 (or @t31 @t30)))))))))) % 0.37/0.75 (assume @p16 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t37) (and @t27 (forall @t34 (= @t33 (and @t32 @t31 (not @t30)))))))))) % 0.37/0.75 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t37 @t5) @t1)))))) % 0.37/0.75 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t38 @t1) @t5))))) % 0.37/0.75 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t38)))))) % 0.37/0.75 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t41)))))) % 0.37/0.75 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t38)))))) % 0.37/0.75 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t41)))))) % 0.37/0.75 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.37/0.75 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.37/0.75 (assume @p25 (forall @t3 (=> @t44 (and (tptp.aElementOf0 @t43 tptp.szNzAzT0) (not (= @t43 tptp.sz00)))))) % 0.37/0.75 (assume @p26 (forall @t25 (=> @t47 (=> (= @t43 @t45) @t23)))) % 0.37/0.75 (assume @p27 (forall @t3 (=> @t44 (or @t48 (exists @t8 (and @t46 (= @t1 @t45))))))) % 0.37/0.75 (assume @p28 (forall @t3 (=> @t44 (not (= @t1 @t43))))) % 0.37/0.75 (assume @p29 (forall @t25 (=> @t47 (=> @t49 true)))) % 0.37/0.75 (assume @p30 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.37/0.75 (assume @p31 (forall @t3 (=> @t44 (not (tptp.sdtlseqdt0 @t43 tptp.sz00))))) % 0.37/0.75 (assume @p32 (forall @t25 (=> @t47 (= @t49 (tptp.sdtlseqdt0 @t43 @t45))))) % 0.37/0.75 (assume @p33 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t43)))) % 0.37/0.75 (assume @p34 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.37/0.75 (assume @p35 (forall @t25 (=> @t47 (=> (and @t49 @t50) @t23)))) % 0.37/0.75 (assume @p36 (forall @t28 (=> (and @t44 @t46 @t52) (=> (and @t49 @t51) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.37/0.75 (assume @p37 (forall @t25 (=> @t47 (or @t49 (tptp.sdtlseqdt0 @t45 @t1))))) % 0.37/0.75 (assume @p38 (forall @t25 (=> @t47 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.37/0.75 (assume @p39 (forall @t3 (=> @t44 (tptp.iLess0 @t1 @t43)))) % 0.37/0.75 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t53)))) % 0.37/0.75 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t53 tptp.szNzAzT0) @t9)))) % 0.37/0.75 (assume @p42 (forall @t3 (=> @t2 (= (= @t53 tptp.sz00) @t10)))) % 0.37/0.75 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t35) (tptp.szszuzczcdt0 @t53)))))))) % 0.37/0.75 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t37)) @t53)))))) % 0.37/0.75 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 @t54 @t53)))))) % 0.37/0.75 (assume @p46 (forall @t25 (=> @t56 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t53)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= @t55 @t5))))))) % 0.37/0.75 (assume @p47 (forall @t3 (=> (and @t58 @t14) (forall @t8 (= (= @t5 @t57) (and @t7 (forall @t18 (=> @t16 @t51)))))))) % 0.37/0.75 (assume @p48 (forall @t3 (=> (and @t58 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.37/0.75 (assume @p49 (forall @t25 (=> (and @t58 @t60 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t57 @t5) (tptp.aElementOf0 @t59 @t1)) (= @t57 @t59))))) % 0.37/0.75 (assume @p50 (forall @t3 (=> @t44 (forall @t8 (= (= @t5 @t61) (and @t19 (forall @t18 (= @t17 (and @t52 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.37/0.75 (assume @p51 (forall @t3 (=> @t44 (tptp.isFinite0 @t61)))) % 0.37/0.75 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.37/0.75 (assume @p53 (forall @t25 (=> @t47 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t45)) (or (tptp.aElementOf0 @t1 @t62) @t23))))) % 0.37/0.75 (assume @p54 (forall @t25 (=> @t47 (= @t49 (tptp.aSubsetOf0 @t61 @t62))))) % 0.37/0.75 (assume @p55 (forall @t3 (=> (and @t58 @t9) (exists @t8 (and @t46 (tptp.aSubsetOf0 @t1 @t62)))))) % 0.37/0.75 (assume @p56 (forall @t3 (=> @t44 (= (tptp.sbrdtbr0 @t61) @t1)))) % 0.37/0.75 (assume @p57 (forall @t25 (=> @t56 (forall @t18 (= (= @t15 @t65) (and @t27 (forall @t34 (= @t33 (and @t64 (= @t63 @t5)))))))))) % 0.37/0.75 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t46 (tptp.isFinite0 @t65)))))) % 0.37/0.75 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t46 (not (= @t65 tptp.slcrc0))))))) % 0.37/0.75 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t46 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t65)))))) % 0.37/0.75 (assume @p61 (forall @t3 (=> @t44 (forall (@list @t5 @t15) (=> (and @t19 @t27 (not @t48)) (=> (and (tptp.aSubsetOf0 @t66 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t66 tptp.slcrc0))) @t26)))))) % 0.37/0.75 (assume @p62 (forall @t25 (=> @t56 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t65) (tptp.isFinite0 @t15)) (exists @t34 (and @t64 (tptp.isFinite0 @t29) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t29 @t5))))))))) % 0.37/0.75 (assume @p63 (forall @t3 (=> @t67 true))) % 0.37/0.75 (assume @p64 (forall @t3 (=> @t67 (tptp.aSet0 @t68)))) % 0.37/0.75 (assume @p65 (forall @t3 (=> @t67 (forall @t8 (=> @t70 (tptp.aElement0 @t69)))))) % 0.37/0.75 (assume @p66 (forall @t25 (=> @t74 (forall @t18 (= (= @t15 @t73) (and @t27 (forall @t34 (= @t33 (and @t72 (= @t71 @t5)))))))))) % 0.37/0.75 (assume @p67 (forall @t25 (=> @t74 (tptp.aSubsetOf0 @t73 @t68)))) % 0.37/0.75 (assume @p68 (forall @t3 (=> @t67 (forall @t8 (=> @t79 (forall @t18 (= (= @t15 @t78) (and @t27 (forall @t34 (= @t33 (exists @t77 (and @t76 (= (tptp.sdtlpdtrp0 @t1 @t75) @t29))))))))))))) % 0.37/0.75 (assume @p69 (forall @t3 (=> @t67 (forall @t8 (=> @t70 (tptp.aElementOf0 @t69 @t80)))))) % 0.37/0.75 (assume @p70 (forall @t3 (=> @t67 (forall @t8 (=> @t79 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t83 (= @t82 @t5) (forall @t34 (=> @t81 (= (tptp.sdtlpdtrp0 @t15 @t29) @t71))))))))))) % 0.37/0.75 (assume @p71 (forall @t3 (=> @t67 (forall @t8 (=> (and @t79 @t39) (=> (forall (@list @t15 @t29) (=> (and (tptp.aElementOf0 @t15 @t68) @t72 (not (= @t15 @t29))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t71)))) (tptp.isCountable0 @t78))))))) % 0.37/0.75 (assume @p72 (forall @t3 (=> @t67 (=> (and (tptp.isCountable0 @t68) (tptp.isFinite0 @t80)) (and (tptp.aElement0 @t84) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t84))))))) % 0.37/0.75 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.37/0.75 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.37/0.75 (assume @p75 (and (tptp.aSet0 tptp.xS) (forall @t3 (=> @t85 @t44)) (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.37/0.75 (assume @p76 (and (tptp.aFunction0 tptp.xc) (forall @t3 (and (=> @t91 (and @t2 @t94 @t93 @t92)) (=> (and (or (and @t2 @t94) @t93) @t92) @t91))) (= @t86 @t90) (tptp.aSet0 @t87) (forall @t3 (= @t89 (exists @t8 (and (tptp.aElementOf0 @t5 @t86) (= (tptp.sdtlpdtrp0 tptp.xc @t5) @t1))))) (forall @t3 (=> @t89 @t88)) (tptp.aSubsetOf0 @t87 tptp.xT))) % 0.37/0.75 (assume @p77 (forall @t3 (=> @t44 (forall @t8 (=> (and (or (and @t19 (forall @t18 (=> @t17 @t52))) @t60) @t39) (forall @t18 (=> (and @t83 (or (forall @t34 (and (=> @t101 (and (or (and @t106 @t105) @t103) @t102)) (=> (and @t106 @t105 @t103 @t102) @t101))) (= @t82 @t66)) (=> (and (tptp.aSet0 @t99) (forall @t34 (= @t100 (exists @t77 (and (tptp.aElementOf0 @t75 @t82) (= (tptp.sdtlpdtrp0 @t15 @t75) @t29)))))) (or (forall @t34 (=> @t100 @t98)) (tptp.aSubsetOf0 @t99 tptp.xT)))) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t34 (and @t98 (exists @t77 (and (tptp.aSet0 @t75) (forall @t97 (=> (tptp.aElementOf0 @t95 @t75) (tptp.aElementOf0 @t95 @t5))) (tptp.aSubsetOf0 @t75 @t5) (tptp.isCountable0 @t75) (forall @t97 (=> (or (and (or (and (tptp.aSet0 @t95) (forall (@list @t96) (=> (tptp.aElementOf0 @t96 @t95) (tptp.aElementOf0 @t96 @t75)))) (tptp.aSubsetOf0 @t95 @t75)) (= (tptp.sbrdtbr0 @t95) @t1)) (tptp.aElementOf0 @t95 (tptp.slbdtsldtrb0 @t75 @t1))) (= (tptp.sdtlpdtrp0 @t15 @t95) @t29))))))))))))))) % 0.37/0.75 (assume @p78 (not (= tptp.xK tptp.sz00))) % 0.37/0.75 (assume @p79 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK))) % 0.37/0.75 (assume @p80 (and (tptp.aFunction0 tptp.xN) (= (tptp.szDzozmdt0 tptp.xN) tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall @t3 (=> @t44 (=> (and (or (and @t120 @t119) @t118) @t117) (and @t116 @t115 @t114 @t113 (tptp.aSet0 @t107) (forall @t8 (=> (tptp.aElementOf0 @t5 @t107) @t111)) (tptp.aSubsetOf0 @t107 @t110) (tptp.isCountable0 @t107))))))) % 0.37/0.75 (assume @p81 (forall @t3 (=> @t44 (and @t120 @t119 @t118 @t117)))) % 0.37/0.75 (assume @p82 (forall @t25 (=> @t47 (=> @t50 (and (forall @t18 (=> @t123 @t122)) (tptp.aSubsetOf0 @t108 @t121)))))) % 0.37/0.75 (assume @p83 (forall @t25 (=> (and @t44 @t46 (not @t23)) (not (=> @t126 (or (and (tptp.aElementOf0 @t109 @t121) (forall @t18 (=> @t122 @t124))) (= @t109 (tptp.szmzizndt0 @t121)))))))) % 0.37/0.75 (assume @p84 (forall @t3 (=> @t44 (forall @t8 (=> @t138 (and @t116 @t125 (tptp.aSet0 @t127) @t131 (forall @t18 (=> @t128 (tptp.aElementOf0 @t15 tptp.xS))) (tptp.aSubsetOf0 @t127 tptp.xS) (= (tptp.sbrdtbr0 @t127) tptp.xK) (tptp.aElementOf0 @t127 @t90))))))) % 0.37/0.75 (assume @p85 (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall @t3 (=> @t44 (and (tptp.aFunction0 @t139) @t116 @t115 @t114 @t113 (forall @t8 (and (=> @t142 (and @t19 @t136 @t134 @t133)) (=> (and @t143 @t133) @t142))) (= @t141 @t132) (forall @t8 (=> @t138 (and @t116 @t125 @t131 (= @t140 (tptp.sdtlpdtrp0 tptp.xc @t127)))))))))) % 0.37/0.75 (assume @p86 (forall @t3 (=> @t44 (and (tptp.aSet0 @t144) (forall @t8 (= @t146 (exists @t18 (and (tptp.aElementOf0 @t15 @t141) @t147)))) (forall @t8 (=> @t146 @t145)) (tptp.aSubsetOf0 @t144 tptp.xT))))) % 0.37/0.75 (assume @p87 (forall @t3 (=> @t44 (forall @t8 (=> (and (=> @t126 (=> @t137 @t143)) @t39) (forall @t18 (=> (and @t27 (or (and (or (forall @t34 (=> @t33 @t81)) (tptp.aSubsetOf0 @t15 @t5)) @t154) (tptp.aElementOf0 @t15 (tptp.slbdtsldtrb0 @t5 tptp.xk)))) (and @t116 @t153 @t114 @t152 @t150 @t148 (tptp.aElementOf0 @t15 @t132))))))))) % 0.37/0.75 (assume @p88 (forall @t3 (=> @t44 (exists @t8 (and @t145 (exists @t18 (and @t116 @t153 @t114 @t152 @t27 @t150 @t148 (tptp.isCountable0 @t15) (forall @t34 (=> (and @t106 (or (and (or (forall @t77 (=> @t104 (tptp.aElementOf0 @t75 @t15))) (tptp.aSubsetOf0 @t29 @t15)) (= @t63 tptp.xk)) (tptp.aElementOf0 @t29 (tptp.slbdtsldtrb0 @t15 tptp.xk)))) (= (tptp.sdtlpdtrp0 @t139 @t29) @t5)))))))))) % 0.37/0.75 (assume @p89 (forall @t3 (=> @t44 (exists @t8 (and @t145 (forall @t18 (=> (and @t27 (or (and (or (forall @t34 (=> @t33 (tptp.aElementOf0 @t29 @t107))) (tptp.aSubsetOf0 @t15 @t107)) @t154) (tptp.aElementOf0 @t15 @t155))) @t147))))))) % 0.37/0.75 (assume @p90 (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall @t3 (=> @t44 (and (tptp.aElementOf0 @t156 @t108) (forall @t8 (=> @t112 (tptp.sdtlseqdt0 @t156 @t5))) (= @t156 @t109)))))) % 0.37/0.75 (assume @p91 (and (tptp.aFunction0 tptp.xd) (= @t158 tptp.szNzAzT0) (forall @t3 (=> @t44 (forall @t8 (=> (and @t19 (or (and (or (forall @t18 (=> @t17 (tptp.aElementOf0 @t15 @t107))) (tptp.aSubsetOf0 @t5 @t107)) @t133) (tptp.aElementOf0 @t5 @t155))) (= @t157 @t140))))))) % 0.37/0.75 (assume @p92 (and (tptp.aSet0 @t159) (forall @t3 (= @t160 (exists @t8 (and (tptp.aElementOf0 @t5 @t158) (= @t161 @t1))))) (forall @t3 (=> @t160 @t88)) (tptp.aSubsetOf0 @t159 tptp.xT))) % 0.37/0.75 (assume @p93 (and (tptp.aElementOf0 @t162 tptp.xT) @t165 @t164)) % 0.37/0.75 (assume @p94 (and @t170 @t165 @t164 (forall @t3 (= @t169 @t168)) (= tptp.xO (tptp.sdtlcdtrc0 tptp.xe @t163)))) % 0.37/0.75 (assume @p95 (and @t170 (tptp.isCountable0 tptp.xO))) % 0.37/0.75 (assume @p96 (forall @t3 (=> (or @t168 @t169) (exists @t8 (and @t46 (= @t161 @t162) @t167 @t166))))) % 0.37/0.75 (assume @p97 (and @t171 (tptp.aSubsetOf0 tptp.xO tptp.xS))) % 0.37/0.75 (assume @p98 (and (tptp.aSet0 tptp.xQ) @t173 (tptp.aSubsetOf0 tptp.xQ tptp.xO) (= (tptp.sbrdtbr0 tptp.xQ) tptp.xK) (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 tptp.xO tptp.xK)))) % 0.37/0.75 (assume @p99 (and @t173 (not (or (not (exists @t3 @t172)) (= tptp.xQ tptp.slcrc0))))) % 0.37/0.75 (assume @p100 (and (forall @t3 (=> @t172 @t44)) (tptp.aSubsetOf0 tptp.xQ tptp.szNzAzT0))) % 0.37/0.75 (assume @p101 @t178) % 0.37/0.75 (assume @p102 true) % 0.37/0.75 (step @p103 :rule refl :args (@t174)) % 0.37/0.75 (step @p104 :rule refl :args (@t175)) % 0.37/0.75 (step @p105 :rule bool-impl-elim :args (@t172 @t85)) % 0.37/0.75 (step @p106 :rule cong :premises (@p105) :args (@t176)) % 0.37/0.75 (step @p107 :rule nary_cong :premises (@p106 @p104 @p106 @p104 @p103) :args (@t177)) % 0.37/0.75 (step @p108 :rule cong :premises (@p107) :args (@t178)) % 0.37/0.75 (step @p109 :rule eq_resolve :premises (@p101 @p108)) % 0.37/0.75 (step @p110 :rule not_or_elim :premises (@p109) :args (0)) % 0.37/0.75 (step @p111 :rule skolemize :premises (@p110)) % 0.37/0.75 (step @p112 :rule bool-double-not-elim :args (@t180)) % 0.37/0.75 (step @p113 :rule refl :args (@t183)) % 0.37/0.75 (step @p114 :rule nary_cong :premises (@p113 @p112) :args ((or @t183 (not @t182)))) % 0.37/0.75 (step @p115 :rule cnf_or_neg :args (@t183 0)) % 0.37/0.75 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 0.37/0.75 (step @p117 :rule reordering :premises (@p116) :args ((or @t180 @t183))) % 0.37/0.75 (step @p118 :rule chain_m_resolution :premises (@p117 @p111) :args (@t180 @t184 @t185)) % 0.37/0.75 (step @p119 :rule bool-impl-elim :args (@t172 @t169)) % 0.37/0.75 (step @p120 :rule cong :premises (@p119) :args (@t173)) % 0.37/0.75 (step @p121 :rule and_elim :premises (@p98) :args (1)) % 0.37/0.75 (step @p122 :rule eq_resolve :premises (@p121 @p120)) % 0.37/0.75 (step @p123 :rule instantiate :premises (@p122) :args (@t186)) % 0.37/0.75 (step @p124 :rule bool-impl-elim :args (@t169 @t85)) % 0.37/0.75 (step @p125 :rule cong :premises (@p124) :args (@t171)) % 0.37/0.75 (step @p126 :rule and_elim :premises (@p97) :args (0)) % 0.37/0.75 (step @p127 :rule eq_resolve :premises (@p126 @p125)) % 0.37/0.75 (step @p128 :rule instantiate :premises (@p127) :args (@t186)) % 0.37/0.75 (step @p129 :rule cnf_or_neg :args (@t183 1)) % 0.37/0.75 (step @p130 :rule chain_m_resolution :premises (@p129 @p111) :args ((not @t181) @t184 @t185)) % 0.37/0.75 (step @p131 :rule cnf_or_pos :args (@t189)) % 0.37/0.75 (step @p132 :rule reordering :premises (@p131) :args ((or @t181 @t188 (not @t189)))) % 0.37/0.75 (step @p133 :rule chain_m_resolution :premises (@p132 @p130 @p128) :args (@t188 (@list true false) (@list @t181 @t189))) % 0.37/0.75 (step @p134 :rule cnf_or_pos :args (@t190)) % 0.37/0.75 (step @p135 :rule reordering :premises (@p134) :args ((or @t182 @t187 (not @t190)))) % 0.37/0.75 (step @p136 false :rule chain_m_resolution :premises (@p135 @p133 @p123 @p118) :args (false (@list true false false) (@list @t187 @t190 @t180))) % 0.37/0.75 ) % 0.37/0.75 % SZS output end Proof % 0.37/0.75 % cvc5 exiting %------------------------------------------------------------------------------