%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM547+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 : n009.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 08:39:48 AM UTC 2026 % Result : Theorem 0.35s 0.60s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : NUM547+3 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n009.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 11:28:44 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.60 % SZS status Theorem % 0.35/0.60 % SZS output start Proof % 0.35/0.60 ( % 0.35/0.60 (declare-sort $$unsorted 0) % 0.35/0.60 (declare-const tptp.xx $$unsorted) % 0.35/0.60 (declare-const tptp.xT $$unsorted) % 0.35/0.60 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.60 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.35/0.60 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.35/0.60 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.35/0.60 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.35/0.60 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.60 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.35/0.60 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.35/0.60 (declare-const tptp.xS $$unsorted) % 0.35/0.60 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.35/0.60 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.35/0.60 (declare-const tptp.slcrc0 $$unsorted) % 0.35/0.60 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.60 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.60 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.60 (declare-const tptp.xk $$unsorted) % 0.35/0.60 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.35/0.60 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.60 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.35/0.60 (declare-const tptp.szNzAzT0 $$unsorted) % 0.35/0.60 (declare-const tptp.sz00 $$unsorted) % 0.35/0.60 (define @t1 () (@var "W0" $$unsorted)) % 0.35/0.60 (define @t2 () (tptp.aSet0 @t1)) % 0.35/0.60 (define @t3 () (@list @t1)) % 0.35/0.60 (define @t4 () (tptp.aElement0 @t1)) % 0.35/0.60 (define @t5 () (@var "W1" $$unsorted)) % 0.35/0.60 (define @t6 () (tptp.aElement0 @t5)) % 0.35/0.60 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.35/0.60 (define @t8 () (@list @t5)) % 0.35/0.60 (define @t9 () (tptp.isFinite0 @t1)) % 0.35/0.60 (define @t10 () (= @t1 tptp.slcrc0)) % 0.35/0.60 (define @t11 () (tptp.isCountable0 @t1)) % 0.35/0.60 (define @t12 () (not @t9)) % 0.35/0.60 (define @t13 () (and @t2 @t11)) % 0.35/0.60 (define @t14 () (not @t10)) % 0.35/0.60 (define @t15 () (@var "W2" $$unsorted)) % 0.35/0.60 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.35/0.60 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.35/0.60 (define @t18 () (@list @t15)) % 0.35/0.60 (define @t19 () (tptp.aSet0 @t5)) % 0.35/0.60 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.35/0.60 (define @t21 () (tptp.isFinite0 @t5)) % 0.35/0.60 (define @t22 () (and @t2 @t9)) % 0.35/0.60 (define @t23 () (= @t1 @t5)) % 0.35/0.60 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.35/0.60 (define @t25 () (@list @t1 @t5)) % 0.35/0.60 (define @t26 () (tptp.aSet0 @t15)) % 0.35/0.60 (define @t27 () (@list @t1 @t5 @t15)) % 0.35/0.60 (define @t28 () (@var "W3" $$unsorted)) % 0.35/0.60 (define @t29 () (= @t28 @t5)) % 0.35/0.60 (define @t30 () (tptp.aElementOf0 @t28 @t1)) % 0.35/0.60 (define @t31 () (tptp.aElement0 @t28)) % 0.35/0.60 (define @t32 () (tptp.aElementOf0 @t28 @t15)) % 0.35/0.60 (define @t33 () (@list @t28)) % 0.35/0.60 (define @t34 () (tptp.sdtpldt0 @t1 @t5)) % 0.35/0.60 (define @t35 () (and @t2 @t6)) % 0.35/0.60 (define @t36 () (tptp.sdtmndt0 @t1 @t5)) % 0.35/0.60 (define @t37 () (tptp.sdtpldt0 @t5 @t1)) % 0.35/0.60 (define @t38 () (and @t19 (tptp.isCountable0 @t5))) % 0.35/0.60 (define @t39 () (tptp.sdtmndt0 @t5 @t1)) % 0.35/0.60 (define @t40 () (and @t19 @t21)) % 0.35/0.60 (define @t41 () (tptp.szszuzczcdt0 @t1)) % 0.35/0.60 (define @t42 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.35/0.60 (define @t43 () (tptp.szszuzczcdt0 @t5)) % 0.35/0.60 (define @t44 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.35/0.60 (define @t45 () (and @t42 @t44)) % 0.35/0.60 (define @t46 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.35/0.60 (define @t47 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.35/0.60 (define @t48 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.35/0.60 (define @t49 () (tptp.sbrdtbr0 @t1)) % 0.35/0.60 (define @t50 () (not @t7)) % 0.35/0.60 (define @t51 () (and @t2 @t44)) % 0.35/0.60 (define @t52 () (tptp.szmzizndt0 @t1)) % 0.35/0.60 (define @t53 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.35/0.60 (define @t54 () (tptp.szmzizndt0 @t5)) % 0.35/0.60 (define @t55 () (tptp.slbdtrb0 @t1)) % 0.35/0.60 (define @t56 () (tptp.slbdtrb0 @t5)) % 0.35/0.60 (define @t57 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.35/0.60 (define @t58 () (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) % 0.35/0.60 (define @t59 () (tptp.aElementOf0 @t1 @t58)) % 0.35/0.60 (define @t60 () (exists @t3 @t59)) % 0.35/0.60 (define @t61 () (not @t60)) % 0.35/0.60 (define @t62 () (or @t61 (= @t58 tptp.slcrc0))) % 0.35/0.60 (define @t63 () (= @t49 tptp.xk)) % 0.35/0.60 (define @t64 () (tptp.aSubsetOf0 @t1 tptp.xS)) % 0.35/0.60 (define @t65 () (tptp.aElementOf0 @t5 tptp.xS)) % 0.35/0.60 (define @t66 () (forall @t8 (=> @t7 @t65))) % 0.35/0.60 (define @t67 () (and @t2 @t66)) % 0.35/0.60 (define @t68 () (or @t67 @t64)) % 0.35/0.60 (define @t69 () (and @t68 @t63)) % 0.35/0.60 (define @t70 () (=> @t69 @t59)) % 0.35/0.60 (define @t71 () (and @t2 @t66 @t64 @t63)) % 0.35/0.60 (define @t72 () (=> @t59 @t71)) % 0.35/0.60 (define @t73 () (and @t72 @t70)) % 0.35/0.60 (define @t74 () (forall @t3 @t73)) % 0.35/0.60 (define @t75 () (=> @t74 @t62)) % 0.35/0.60 (define @t76 () (not @t75)) % 0.35/0.60 (define @t77 () (tptp.slbdtsldtrb0 tptp.xT tptp.xk)) % 0.35/0.60 (define @t78 () (tptp.aElementOf0 @t1 @t77)) % 0.35/0.60 (define @t79 () (tptp.aSubsetOf0 @t1 tptp.xT)) % 0.35/0.60 (define @t80 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xT)))) % 0.35/0.60 (define @t81 () (or @t69 @t59)) % 0.35/0.60 (define @t82 () (exists @t3 @t81)) % 0.35/0.60 (define @t83 () (not @t82)) % 0.35/0.60 (define @t84 () (not @t59)) % 0.35/0.60 (define @t85 () (forall @t3 @t84)) % 0.35/0.60 (define @t86 () (@var "BOUND_VARIABLE_8629" $$unsorted)) % 0.35/0.60 (define @t87 () (tptp.aElementOf0 @t86 @t58)) % 0.35/0.60 (define @t88 () (tptp.sbrdtbr0 @t86)) % 0.35/0.60 (define @t89 () (not (= @t88 tptp.xk))) % 0.35/0.60 (define @t90 () (and (or (not (tptp.aSet0 @t86)) (not (forall @t8 (or (not (tptp.aElementOf0 @t5 @t86)) @t65)))) (not (tptp.aSubsetOf0 @t86 tptp.xS)))) % 0.35/0.60 (define @t91 () (or @t90 @t89 @t87)) % 0.35/0.60 (define @t92 () (forall (@list @t86) @t91)) % 0.35/0.60 (define @t93 () (@var "BOUND_VARIABLE_8613" $$unsorted)) % 0.35/0.60 (define @t94 () (tptp.sbrdtbr0 @t93)) % 0.35/0.60 (define @t95 () (= tptp.xk @t94)) % 0.35/0.60 (define @t96 () (tptp.aSubsetOf0 @t93 tptp.xS)) % 0.35/0.60 (define @t97 () (@var "BOUND_VARIABLE_8654" $$unsorted)) % 0.35/0.60 (define @t98 () (or (not (tptp.aElementOf0 @t97 @t93)) (tptp.aElementOf0 @t97 tptp.xS))) % 0.35/0.60 (define @t99 () (tptp.aSet0 @t93)) % 0.35/0.60 (define @t100 () (and @t99 @t98 @t96 @t95)) % 0.35/0.60 (define @t101 () (not (tptp.aElementOf0 @t93 @t58))) % 0.35/0.60 (define @t102 () (or @t101 @t100)) % 0.35/0.60 (define @t103 () (@list @t97)) % 0.35/0.60 (define @t104 () (forall @t103 @t102)) % 0.35/0.60 (define @t105 () (@list @t93)) % 0.35/0.60 (define @t106 () (forall @t103 @t95)) % 0.35/0.60 (define @t107 () (forall @t103 @t96)) % 0.35/0.60 (define @t108 () (forall @t103 @t98)) % 0.35/0.60 (define @t109 () (forall @t103 @t99)) % 0.35/0.60 (define @t110 () (and @t109 @t108 @t107 @t106)) % 0.35/0.60 (define @t111 () (forall @t103 @t100)) % 0.35/0.60 (define @t112 () (or @t101 @t111)) % 0.35/0.60 (define @t113 () (forall @t8 (or (not (tptp.aElementOf0 @t5 @t93)) @t65))) % 0.35/0.60 (define @t114 () (and @t99 @t113 @t96 (= @t94 tptp.xk))) % 0.35/0.60 (define @t115 () (or @t101 @t114)) % 0.35/0.60 (define @t116 () (forall @t105 @t115)) % 0.35/0.60 (define @t117 () (not @t63)) % 0.35/0.60 (define @t118 () (not @t64)) % 0.35/0.60 (define @t119 () (forall @t8 (or @t50 @t65))) % 0.35/0.60 (define @t120 () (and (or (not @t2) (not @t119)) @t118)) % 0.35/0.60 (define @t121 () (or @t120 @t117 @t59)) % 0.35/0.60 (define @t122 () (forall @t3 @t121)) % 0.35/0.60 (define @t123 () (@list @t1)) % 0.35/0.60 (define @t124 () (and @t2 @t119 @t64 @t63)) % 0.35/0.60 (define @t125 () (or @t84 @t124)) % 0.35/0.60 (define @t126 () (forall @t3 @t125)) % 0.35/0.60 (define @t127 () (and @t126 @t122)) % 0.35/0.60 (define @t128 () (or @t120 @t117)) % 0.35/0.60 (define @t129 () (and @t2 @t119)) % 0.35/0.60 (define @t130 () (or @t129 @t64)) % 0.35/0.60 (define @t131 () (and @t130 @t63)) % 0.35/0.60 (define @t132 () (not @t131)) % 0.35/0.60 (define @t133 () (and (=> @t59 @t124) (=> @t131 @t59))) % 0.35/0.60 (define @t134 () (@var "BOUND_VARIABLE_8787" $$unsorted)) % 0.35/0.60 (define @t135 () (@list @t134)) % 0.35/0.60 (define @t136 () (forall (@list @t134) (not (tptp.aElementOf0 @t134 @t58)))) % 0.35/0.60 (define @t137 () (@list true)) % 0.35/0.60 (define @t138 () (@var "BOUND_VARIABLE_8768" $$unsorted)) % 0.35/0.60 (define @t139 () (tptp.sbrdtbr0 @t138)) % 0.35/0.60 (define @t140 () (and (or (not (tptp.aSet0 @t138)) (not (forall @t8 (or (not (tptp.aElementOf0 @t5 @t138)) @t65)))) (not (tptp.aSubsetOf0 @t138 tptp.xS)))) % 0.35/0.60 (define @t141 () (@list @t138)) % 0.35/0.60 (define @t142 () (not (= @t139 tptp.xk))) % 0.35/0.60 (define @t143 () (or @t140 @t142)) % 0.35/0.60 (define @t144 () (forall @t141 @t143)) % 0.35/0.60 (define @t145 () (forall @t3 @t128)) % 0.35/0.60 (define @t146 () (and @t145 @t85)) % 0.35/0.60 (define @t147 () (or @t131 @t59)) % 0.35/0.60 (define @t148 () (forall @t3 (not @t147))) % 0.35/0.60 (define @t149 () (not @t148)) % 0.35/0.60 (assume @p1 (forall @t3 (=> @t2 true))) % 0.35/0.60 (assume @p2 (forall @t3 (=> @t4 true))) % 0.35/0.60 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.35/0.60 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.35/0.60 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.35/0.60 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.35/0.60 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.35/0.60 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.35/0.60 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.35/0.60 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.35/0.60 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.35/0.60 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.35/0.60 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.35/0.60 (assume @p14 (forall @t27 (=> (and @t2 @t19 @t26) (=> (and @t24 (tptp.aSubsetOf0 @t5 @t15)) (tptp.aSubsetOf0 @t1 @t15))))) % 0.35/0.60 (assume @p15 (forall @t25 (=> @t35 (forall @t18 (= (= @t15 @t34) (and @t26 (forall @t33 (= @t32 (and @t31 (or @t30 @t29)))))))))) % 0.35/0.60 (assume @p16 (forall @t25 (=> @t35 (forall @t18 (= (= @t15 @t36) (and @t26 (forall @t33 (= @t32 (and @t31 @t30 (not @t29)))))))))) % 0.35/0.60 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t36 @t5) @t1)))))) % 0.35/0.60 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t37 @t1) @t5))))) % 0.35/0.60 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t38 (tptp.isCountable0 @t37)))))) % 0.35/0.60 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t38 (tptp.isCountable0 @t39)))))) % 0.35/0.60 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isFinite0 @t37)))))) % 0.35/0.60 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isFinite0 @t39)))))) % 0.35/0.60 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.35/0.60 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.35/0.60 (assume @p25 (forall @t3 (=> @t42 (and (tptp.aElementOf0 @t41 tptp.szNzAzT0) (not (= @t41 tptp.sz00)))))) % 0.35/0.60 (assume @p26 (forall @t25 (=> @t45 (=> (= @t41 @t43) @t23)))) % 0.35/0.60 (assume @p27 (forall @t3 (=> @t42 (or (= @t1 tptp.sz00) (exists @t8 (and @t44 (= @t1 @t43))))))) % 0.35/0.60 (assume @p28 (forall @t3 (=> @t42 (not (= @t1 @t41))))) % 0.35/0.60 (assume @p29 (forall @t25 (=> @t45 (=> @t46 true)))) % 0.35/0.60 (assume @p30 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.35/0.60 (assume @p31 (forall @t3 (=> @t42 (not (tptp.sdtlseqdt0 @t41 tptp.sz00))))) % 0.35/0.60 (assume @p32 (forall @t25 (=> @t45 (= @t46 (tptp.sdtlseqdt0 @t41 @t43))))) % 0.35/0.60 (assume @p33 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 @t1 @t41)))) % 0.35/0.60 (assume @p34 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.35/0.60 (assume @p35 (forall @t25 (=> @t45 (=> (and @t46 (tptp.sdtlseqdt0 @t5 @t1)) @t23)))) % 0.35/0.60 (assume @p36 (forall @t27 (=> (and @t42 @t44 @t48) (=> (and @t46 @t47) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.35/0.60 (assume @p37 (forall @t25 (=> @t45 (or @t46 (tptp.sdtlseqdt0 @t43 @t1))))) % 0.35/0.60 (assume @p38 (forall @t25 (=> @t45 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.35/0.60 (assume @p39 (forall @t3 (=> @t42 (tptp.iLess0 @t1 @t41)))) % 0.35/0.60 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t49)))) % 0.35/0.60 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t49 tptp.szNzAzT0) @t9)))) % 0.35/0.60 (assume @p42 (forall @t3 (=> @t2 (= (= @t49 tptp.sz00) @t10)))) % 0.35/0.60 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> @t50 (= (tptp.sbrdtbr0 @t34) (tptp.szszuzczcdt0 @t49)))))))) % 0.35/0.60 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t36)) @t49)))))) % 0.35/0.60 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t49)))))) % 0.35/0.60 (assume @p46 (forall @t25 (=> @t51 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t49)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.35/0.60 (assume @p47 (forall @t3 (=> (and @t53 @t14) (forall @t8 (= (= @t5 @t52) (and @t7 (forall @t18 (=> @t16 @t47)))))))) % 0.35/0.60 (assume @p48 (forall @t3 (=> (and @t53 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.35/0.60 (assume @p49 (forall @t25 (=> (and @t53 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t52 @t5) (tptp.aElementOf0 @t54 @t1)) (= @t52 @t54))))) % 0.35/0.60 (assume @p50 (forall @t3 (=> @t42 (forall @t8 (= (= @t5 @t55) (and @t19 (forall @t18 (= @t17 (and @t48 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.35/0.60 (assume @p51 (forall @t3 (=> @t42 (tptp.isFinite0 @t55)))) % 0.35/0.60 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.35/0.60 (assume @p53 (forall @t25 (=> @t45 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t43)) (or (tptp.aElementOf0 @t1 @t56) @t23))))) % 0.35/0.60 (assume @p54 (forall @t25 (=> @t45 (= @t46 (tptp.aSubsetOf0 @t55 @t56))))) % 0.35/0.60 (assume @p55 (forall @t3 (=> (and @t53 @t9) (exists @t8 (and @t44 (tptp.aSubsetOf0 @t1 @t56)))))) % 0.35/0.60 (assume @p56 (forall @t3 (=> @t42 (= (tptp.sbrdtbr0 @t55) @t1)))) % 0.35/0.60 (assume @p57 (forall @t25 (=> @t51 (forall @t18 (= (= @t15 @t57) (and @t26 (forall @t33 (= @t32 (and (tptp.aSubsetOf0 @t28 @t1) (= (tptp.sbrdtbr0 @t28) @t5)))))))))) % 0.35/0.60 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t44 (tptp.isFinite0 @t57)))))) % 0.35/0.60 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t44 (not (= @t57 tptp.slcrc0))))))) % 0.35/0.60 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t44 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t57)))))) % 0.35/0.60 (assume @p61 (tptp.aElementOf0 tptp.xk tptp.szNzAzT0)) % 0.35/0.60 (assume @p62 (and (tptp.aSet0 tptp.xS) (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00)))) % 0.35/0.60 (assume @p63 (and (tptp.aSet0 @t58) @t74 (tptp.aSet0 @t77) (forall @t3 (and (=> @t78 (and @t2 @t80 @t79 @t63)) (=> (and (or (and @t2 @t80) @t79) @t63) @t78))) (forall @t3 (=> @t59 @t78)) (tptp.aSubsetOf0 @t58 @t77) @t76)) % 0.35/0.60 (assume @p64 (tptp.aElementOf0 tptp.xx tptp.xS)) % 0.35/0.60 (assume @p65 @t83) % 0.35/0.60 (assume @p66 true) % 0.35/0.60 (step @p67 :rule eq-symm :args (@t58 tptp.slcrc0)) % 0.35/0.60 (step @p68 :rule bool-double-not-elim :args (@t85)) % 0.35/0.60 (step @p69 :rule exists-elim :args ((= @t60 (not @t85)))) % 0.35/0.60 (step @p70 :rule cong :premises (@p69) :args (@t61)) % 0.35/0.60 (step @p71 :rule trans :premises (@p70 @p68)) % 0.35/0.60 (step @p72 :rule nary_cong :premises (@p71 @p67) :args (@t62)) % 0.35/0.60 (step @p73 :rule refl :args (@t87)) % 0.35/0.60 (step @p74 :rule eq-symm :args (@t88 tptp.xk)) % 0.35/0.60 (step @p75 :rule cong :premises (@p74) :args (@t89)) % 0.35/0.60 (step @p76 :rule refl :args (@t90)) % 0.35/0.60 (step @p77 :rule nary_cong :premises (@p76 @p75 @p73) :args (@t91)) % 0.35/0.60 (step @p78 :rule cong :premises (@p77) :args (@t92)) % 0.35/0.60 (step @p79 :rule quant-merge-prenex :args ((= (forall @t105 @t104) (forall (@list @t93 @t97) @t102)))) % 0.35/0.60 (step @p80 :rule quant-unused-vars :args ((= @t106 @t95))) % 0.35/0.60 (step @p81 :rule quant-unused-vars :args ((= @t107 @t96))) % 0.35/0.60 (step @p82 :rule alpha_equiv :args (@t108 (@list @t97) (@list @t5))) % 0.35/0.60 (step @p83 :rule quant-unused-vars :args ((= @t109 @t99))) % 0.35/0.60 (step @p84 :rule nary_cong :premises (@p83 @p82 @p81 @p80) :args (@t110)) % 0.35/0.60 (step @p85 :rule quant-miniscope-and :args ((= @t111 @t110))) % 0.35/0.60 (step @p86 :rule trans :premises (@p85 @p84)) % 0.35/0.60 (step @p87 :rule refl :args (@t101)) % 0.35/0.60 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t112)) % 0.35/0.60 (step @p89 :rule quant-miniscope-or :args ((= @t104 @t112))) % 0.35/0.60 (step @p90 :rule trans :premises (@p89 @p88)) % 0.35/0.60 (step @p91 :rule symm :premises (@p90)) % 0.35/0.60 (step @p92 :rule cong :premises (@p91) :args ((forall @t105 (or @t101 (and @t99 @t113 @t96 @t95))))) % 0.35/0.60 (step @p93 :rule trans :premises (@p92 @p79)) % 0.35/0.60 (step @p94 :rule eq-symm :args (@t94 tptp.xk)) % 0.35/0.60 (step @p95 :rule refl :args (@t96)) % 0.35/0.60 (step @p96 :rule refl :args (@t113)) % 0.35/0.60 (step @p97 :rule refl :args (@t99)) % 0.35/0.60 (step @p98 :rule nary_cong :premises (@p97 @p96 @p95 @p94) :args (@t114)) % 0.35/0.60 (step @p99 :rule refl :args (@t101)) % 0.35/0.60 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t115)) % 0.35/0.60 (step @p101 :rule cong :premises (@p100) :args (@t116)) % 0.35/0.60 (step @p102 :rule trans :premises (@p101 @p93)) % 0.35/0.60 (step @p103 :rule nary_cong :premises (@p102 @p78) :args ((and @t116 @t92))) % 0.35/0.60 (step @p104 :rule alpha_equiv :args (@t122 @t123 (@list @t86))) % 0.35/0.60 (step @p105 :rule alpha_equiv :args (@t126 @t123 (@list @t93))) % 0.35/0.60 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t127)) % 0.35/0.60 (step @p107 :rule quant-miniscope-and :args ((= (forall @t3 (and @t125 @t121)) @t127))) % 0.35/0.60 (step @p108 :rule trans :premises (@p107 @p106)) % 0.35/0.60 (step @p109 :rule trans :premises (@p108 @p103)) % 0.35/0.60 (step @p110 :rule aci_norm :args ((= (or @t128 @t59) @t121))) % 0.35/0.60 (step @p111 :rule refl :args (@t59)) % 0.35/0.60 (step @p112 :rule refl :args (@t117)) % 0.35/0.60 (step @p113 :rule refl :args (@t118)) % 0.35/0.60 (step @p114 :rule bool-and-de-morgan :args (@t2 @t119 true)) % 0.35/0.60 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((and (not @t129) @t118))) % 0.35/0.60 (step @p116 :rule bool-or-de-morgan :args (@t129 @t64 false)) % 0.35/0.60 (step @p117 :rule trans :premises (@p116 @p115)) % 0.35/0.60 (step @p118 :rule nary_cong :premises (@p117 @p112) :args ((or (not @t130) @t117))) % 0.35/0.60 (step @p119 :rule bool-and-de-morgan :args (@t130 @t63 true)) % 0.35/0.60 (step @p120 :rule trans :premises (@p119 @p118)) % 0.35/0.60 (step @p121 :rule nary_cong :premises (@p120 @p111) :args ((or @t132 @t59))) % 0.35/0.60 (step @p122 :rule trans :premises (@p121 @p110)) % 0.35/0.60 (step @p123 :rule bool-impl-elim :args (@t131 @t59)) % 0.35/0.60 (step @p124 :rule trans :premises (@p123 @p122)) % 0.35/0.60 (step @p125 :rule bool-impl-elim :args (@t59 @t124)) % 0.35/0.60 (step @p126 :rule nary_cong :premises (@p125 @p124) :args (@t133)) % 0.35/0.60 (step @p127 :rule cong :premises (@p126) :args ((forall @t3 @t133))) % 0.35/0.60 (step @p128 :rule trans :premises (@p127 @p109)) % 0.35/0.60 (step @p129 :rule refl :args (@t59)) % 0.35/0.60 (step @p130 :rule refl :args (@t63)) % 0.35/0.60 (step @p131 :rule refl :args (@t64)) % 0.35/0.60 (step @p132 :rule bool-impl-elim :args (@t7 @t65)) % 0.35/0.60 (step @p133 :rule cong :premises (@p132) :args (@t66)) % 0.35/0.60 (step @p134 :rule refl :args (@t2)) % 0.35/0.60 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t67)) % 0.35/0.60 (step @p136 :rule nary_cong :premises (@p135 @p131) :args (@t68)) % 0.35/0.60 (step @p137 :rule nary_cong :premises (@p136 @p130) :args (@t69)) % 0.35/0.60 (step @p138 :rule cong :premises (@p137 @p129) :args (@t70)) % 0.35/0.60 (step @p139 :rule nary_cong :premises (@p134 @p133 @p131 @p130) :args (@t71)) % 0.35/0.60 (step @p140 :rule cong :premises (@p129 @p139) :args (@t72)) % 0.35/0.60 (step @p141 :rule nary_cong :premises (@p140 @p138) :args (@t73)) % 0.35/0.60 (step @p142 :rule cong :premises (@p141) :args (@t74)) % 0.35/0.60 (step @p143 :rule trans :premises (@p142 @p128)) % 0.35/0.60 (step @p144 :rule cong :premises (@p143 @p72) :args (@t75)) % 0.35/0.60 (step @p145 :rule cong :premises (@p144) :args (@t76)) % 0.35/0.60 (step @p146 :rule and_elim :premises (@p63) :args (6)) % 0.35/0.60 (step @p147 :rule eq_resolve :premises (@p146 @p145)) % 0.35/0.60 (step @p148 :rule not_implies_elim2 :premises (@p147)) % 0.35/0.60 (step @p149 :rule not_or_elim :premises (@p148) :args (0)) % 0.35/0.60 (step @p150 :rule alpha_equiv :args (@t85 @t123 @t135)) % 0.35/0.60 (step @p151 :rule equiv_elim2 :premises (@p150)) % 0.35/0.60 (step @p152 :rule chain_m_resolution :premises (@p151 @p149) :args ((not @t136) @t137 (@list @t85))) % 0.35/0.60 (step @p153 :rule bool-double-not-elim :args ((and (forall @t141 (or @t140 (not (= tptp.xk @t139)))) @t136))) % 0.35/0.60 (step @p154 :rule refl :args (@t136)) % 0.35/0.60 (step @p155 :rule eq-symm :args (@t139 tptp.xk)) % 0.35/0.60 (step @p156 :rule cong :premises (@p155) :args (@t142)) % 0.35/0.60 (step @p157 :rule refl :args (@t140)) % 0.35/0.60 (step @p158 :rule nary_cong :premises (@p157 @p156) :args (@t143)) % 0.35/0.60 (step @p159 :rule cong :premises (@p158) :args (@t144)) % 0.35/0.60 (step @p160 :rule nary_cong :premises (@p159 @p154) :args ((and @t144 @t136))) % 0.35/0.60 (step @p161 :rule alpha_equiv :args (@t85 @t123 @t135)) % 0.35/0.60 (step @p162 :rule alpha_equiv :args (@t145 @t123 (@list @t138))) % 0.35/0.60 (step @p163 :rule nary_cong :premises (@p162 @p161) :args (@t146)) % 0.35/0.60 (step @p164 :rule quant-miniscope-and :args ((= (forall @t3 (and @t128 @t84)) @t146))) % 0.35/0.60 (step @p165 :rule trans :premises (@p164 @p163)) % 0.35/0.60 (step @p166 :rule trans :premises (@p165 @p160)) % 0.35/0.60 (step @p167 :rule refl :args (@t84)) % 0.35/0.60 (step @p168 :rule nary_cong :premises (@p120 @p167) :args ((and @t132 @t84))) % 0.35/0.60 (step @p169 :rule bool-or-de-morgan :args (@t131 @t59 false)) % 0.35/0.60 (step @p170 :rule trans :premises (@p169 @p168)) % 0.35/0.60 (step @p171 :rule cong :premises (@p170) :args (@t148)) % 0.35/0.60 (step @p172 :rule trans :premises (@p171 @p166)) % 0.35/0.60 (step @p173 :rule cong :premises (@p172) :args (@t149)) % 0.35/0.60 (step @p174 :rule exists-elim :args ((= (exists @t3 @t147) @t149))) % 0.35/0.60 (step @p175 :rule trans :premises (@p174 @p173)) % 0.35/0.60 (step @p176 :rule nary_cong :premises (@p137 @p129) :args (@t81)) % 0.35/0.60 (step @p177 :rule cong :premises (@p176) :args (@t82)) % 0.35/0.60 (step @p178 :rule trans :premises (@p177 @p175)) % 0.35/0.60 (step @p179 :rule cong :premises (@p178) :args (@t83)) % 0.35/0.60 (step @p180 :rule trans :premises (@p179 @p153)) % 0.35/0.60 (step @p181 :rule eq_resolve :premises (@p65 @p180)) % 0.35/0.60 (step @p182 :rule and_elim :premises (@p181) :args (1)) % 0.35/0.60 (step @p183 false :rule chain_m_resolution :premises (@p182 @p152) :args (false @t137 (@list @t136))) % 0.35/0.60 ) % 0.35/0.60 % SZS output end Proof % 0.35/0.60 % cvc5 exiting %------------------------------------------------------------------------------