%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM564+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 : n006.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 0.36s 0.67s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM564+3 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n006.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 11:29:49 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.67 % SZS status Theorem % 0.36/0.67 % SZS output start Proof % 0.36/0.67 ( % 0.36/0.67 (declare-sort $$unsorted 0) % 0.36/0.67 (declare-const tptp.sz00 $$unsorted) % 0.36/0.67 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.szNzAzT0 $$unsorted) % 0.36/0.67 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.36/0.67 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.xK $$unsorted) % 0.36/0.67 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.xT $$unsorted) % 0.36/0.67 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.xS $$unsorted) % 0.36/0.67 (declare-const tptp.xc $$unsorted) % 0.36/0.67 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.slcrc0 $$unsorted) % 0.36/0.67 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.67 (define @t1 () (@var "W0" $$unsorted)) % 0.36/0.67 (define @t2 () (tptp.aSet0 @t1)) % 0.36/0.67 (define @t3 () (@list @t1)) % 0.36/0.67 (define @t4 () (tptp.aElement0 @t1)) % 0.36/0.67 (define @t5 () (@var "W1" $$unsorted)) % 0.36/0.67 (define @t6 () (tptp.aElement0 @t5)) % 0.36/0.67 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.36/0.67 (define @t8 () (@list @t5)) % 0.36/0.67 (define @t9 () (tptp.isFinite0 @t1)) % 0.36/0.67 (define @t10 () (= @t1 tptp.slcrc0)) % 0.36/0.67 (define @t11 () (tptp.isCountable0 @t1)) % 0.36/0.67 (define @t12 () (not @t9)) % 0.36/0.67 (define @t13 () (and @t2 @t11)) % 0.36/0.67 (define @t14 () (not @t10)) % 0.36/0.67 (define @t15 () (@var "W2" $$unsorted)) % 0.36/0.67 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.36/0.67 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.36/0.67 (define @t18 () (@list @t15)) % 0.36/0.67 (define @t19 () (tptp.aSet0 @t5)) % 0.36/0.67 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.36/0.67 (define @t21 () (tptp.isFinite0 @t5)) % 0.36/0.67 (define @t22 () (and @t2 @t9)) % 0.36/0.67 (define @t23 () (= @t1 @t5)) % 0.36/0.67 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.36/0.67 (define @t25 () (@list @t1 @t5)) % 0.36/0.67 (define @t26 () (tptp.aSubsetOf0 @t5 @t15)) % 0.36/0.67 (define @t27 () (tptp.aSet0 @t15)) % 0.36/0.67 (define @t28 () (@list @t1 @t5 @t15)) % 0.36/0.67 (define @t29 () (@var "W3" $$unsorted)) % 0.36/0.67 (define @t30 () (= @t29 @t5)) % 0.36/0.67 (define @t31 () (tptp.aElementOf0 @t29 @t1)) % 0.36/0.67 (define @t32 () (tptp.aElement0 @t29)) % 0.36/0.67 (define @t33 () (tptp.aElementOf0 @t29 @t15)) % 0.36/0.67 (define @t34 () (@list @t29)) % 0.36/0.67 (define @t35 () (tptp.sdtpldt0 @t1 @t5)) % 0.36/0.67 (define @t36 () (and @t2 @t6)) % 0.36/0.67 (define @t37 () (tptp.sdtmndt0 @t1 @t5)) % 0.36/0.67 (define @t38 () (tptp.sdtpldt0 @t5 @t1)) % 0.36/0.67 (define @t39 () (tptp.isCountable0 @t5)) % 0.36/0.67 (define @t40 () (and @t19 @t39)) % 0.36/0.67 (define @t41 () (tptp.sdtmndt0 @t5 @t1)) % 0.36/0.67 (define @t42 () (and @t19 @t21)) % 0.36/0.67 (define @t43 () (tptp.szszuzczcdt0 @t1)) % 0.36/0.67 (define @t44 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.36/0.67 (define @t45 () (tptp.szszuzczcdt0 @t5)) % 0.36/0.67 (define @t46 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.36/0.67 (define @t47 () (and @t44 @t46)) % 0.36/0.67 (define @t48 () (= @t1 tptp.sz00)) % 0.36/0.67 (define @t49 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.36/0.67 (define @t50 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.36/0.67 (define @t51 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.36/0.67 (define @t52 () (tptp.sbrdtbr0 @t1)) % 0.36/0.67 (define @t53 () (and @t2 @t46)) % 0.36/0.67 (define @t54 () (tptp.szmzizndt0 @t1)) % 0.36/0.67 (define @t55 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.36/0.67 (define @t56 () (tptp.szmzizndt0 @t5)) % 0.36/0.67 (define @t57 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.36/0.67 (define @t58 () (tptp.slbdtrb0 @t1)) % 0.36/0.67 (define @t59 () (tptp.slbdtrb0 @t5)) % 0.36/0.67 (define @t60 () (tptp.sbrdtbr0 @t29)) % 0.36/0.67 (define @t61 () (tptp.aSubsetOf0 @t29 @t1)) % 0.36/0.67 (define @t62 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.36/0.67 (define @t63 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.36/0.67 (define @t64 () (tptp.aFunction0 @t1)) % 0.36/0.67 (define @t65 () (tptp.szDzozmdt0 @t1)) % 0.36/0.67 (define @t66 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.36/0.67 (define @t67 () (tptp.aElementOf0 @t5 @t65)) % 0.36/0.67 (define @t68 () (tptp.sdtlpdtrp0 @t1 @t29)) % 0.36/0.67 (define @t69 () (tptp.aElementOf0 @t29 @t65)) % 0.36/0.67 (define @t70 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.36/0.67 (define @t71 () (and @t64 @t6)) % 0.36/0.67 (define @t72 () (@var "W4" $$unsorted)) % 0.36/0.67 (define @t73 () (tptp.aElementOf0 @t72 @t5)) % 0.36/0.67 (define @t74 () (@list @t72)) % 0.36/0.67 (define @t75 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.36/0.67 (define @t76 () (tptp.aSubsetOf0 @t5 @t65)) % 0.36/0.67 (define @t77 () (tptp.sdtlcdtrc0 @t1 @t65)) % 0.36/0.67 (define @t78 () (tptp.szDzozmdt0 @t15)) % 0.36/0.67 (define @t79 () (tptp.aFunction0 @t15)) % 0.36/0.67 (define @t80 () (tptp.szDzizrdt0 @t1)) % 0.36/0.67 (define @t81 () (tptp.aElementOf0 @t1 tptp.xS)) % 0.36/0.67 (define @t82 () (tptp.szDzozmdt0 tptp.xc)) % 0.36/0.67 (define @t83 () (tptp.sdtlcdtrc0 tptp.xc @t82)) % 0.36/0.67 (define @t84 () (tptp.aElementOf0 @t1 @t83)) % 0.36/0.67 (define @t85 () (tptp.aElementOf0 @t1 @t82)) % 0.36/0.67 (define @t86 () (= @t52 tptp.xK)) % 0.36/0.67 (define @t87 () (tptp.aSubsetOf0 @t1 tptp.xS)) % 0.36/0.67 (define @t88 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xS)))) % 0.36/0.67 (define @t89 () (@var "W5" $$unsorted)) % 0.36/0.67 (define @t90 () (@var "W6" $$unsorted)) % 0.36/0.67 (define @t91 () (@list @t89)) % 0.36/0.67 (define @t92 () (tptp.aElementOf0 @t29 tptp.xT)) % 0.36/0.67 (define @t93 () (tptp.sdtlcdtrc0 @t15 @t78)) % 0.36/0.67 (define @t94 () (tptp.aElementOf0 @t29 @t93)) % 0.36/0.67 (define @t95 () (tptp.aElementOf0 @t29 @t78)) % 0.36/0.67 (define @t96 () (= @t60 @t1)) % 0.36/0.67 (define @t97 () (tptp.aSubsetOf0 @t29 @t5)) % 0.36/0.67 (define @t98 () (forall @t74 (=> (tptp.aElementOf0 @t72 @t29) @t73))) % 0.36/0.67 (define @t99 () (tptp.aSet0 @t29)) % 0.36/0.67 (define @t100 () (tptp.aElementOf0 tptp.slcrc0 (tptp.slbdtsldtrb0 tptp.xS tptp.sz00))) % 0.36/0.67 (define @t101 () (tptp.aSubsetOf0 tptp.slcrc0 tptp.xS)) % 0.36/0.67 (define @t102 () (tptp.aElementOf0 @t1 tptp.slcrc0)) % 0.36/0.67 (define @t103 () (forall @t3 (=> @t102 @t81))) % 0.36/0.67 (define @t104 () (or @t103 @t101 @t100)) % 0.36/0.67 (define @t105 () (exists @t3 @t102)) % 0.36/0.67 (define @t106 () (not @t105)) % 0.36/0.67 (define @t107 () (tptp.aSet0 tptp.slcrc0)) % 0.36/0.67 (define @t108 () (and @t107 @t106)) % 0.36/0.67 (define @t109 () (=> @t108 @t104)) % 0.36/0.67 (define @t110 () (not @t109)) % 0.36/0.67 (define @t111 () (not @t102)) % 0.36/0.67 (define @t112 () (forall @t3 @t111)) % 0.36/0.67 (define @t113 () (@quantifiers_skolemize (forall @t3 (or @t111 @t81)) 0)) % 0.36/0.67 (define @t114 () (tptp.aElementOf0 @t113 tptp.slcrc0)) % 0.36/0.67 (define @t115 () (not @t114)) % 0.36/0.67 (define @t116 () (or @t115 (tptp.aElementOf0 @t113 tptp.xS))) % 0.36/0.67 (assume @p1 (forall @t3 (=> @t2 true))) % 0.36/0.67 (assume @p2 (forall @t3 (=> @t4 true))) % 0.36/0.67 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.36/0.67 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.36/0.67 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.36/0.67 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.36/0.67 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.36/0.67 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.36/0.67 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.36/0.67 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.36/0.67 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.36/0.67 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.36/0.67 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.36/0.67 (assume @p14 (forall @t28 (=> (and @t2 @t19 @t27) (=> (and @t24 @t26) (tptp.aSubsetOf0 @t1 @t15))))) % 0.36/0.67 (assume @p15 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t35) (and @t27 (forall @t34 (= @t33 (and @t32 (or @t31 @t30)))))))))) % 0.36/0.67 (assume @p16 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t37) (and @t27 (forall @t34 (= @t33 (and @t32 @t31 (not @t30)))))))))) % 0.36/0.67 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t37 @t5) @t1)))))) % 0.36/0.67 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t38 @t1) @t5))))) % 0.36/0.67 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t38)))))) % 0.36/0.67 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t41)))))) % 0.36/0.67 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t38)))))) % 0.36/0.67 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t41)))))) % 0.36/0.67 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.36/0.67 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.36/0.67 (assume @p25 (forall @t3 (=> @t44 (and (tptp.aElementOf0 @t43 tptp.szNzAzT0) (not (= @t43 tptp.sz00)))))) % 0.36/0.67 (assume @p26 (forall @t25 (=> @t47 (=> (= @t43 @t45) @t23)))) % 0.36/0.67 (assume @p27 (forall @t3 (=> @t44 (or @t48 (exists @t8 (and @t46 (= @t1 @t45))))))) % 0.36/0.67 (assume @p28 (forall @t3 (=> @t44 (not (= @t1 @t43))))) % 0.36/0.67 (assume @p29 (forall @t25 (=> @t47 (=> @t49 true)))) % 0.36/0.67 (assume @p30 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.36/0.67 (assume @p31 (forall @t3 (=> @t44 (not (tptp.sdtlseqdt0 @t43 tptp.sz00))))) % 0.36/0.67 (assume @p32 (forall @t25 (=> @t47 (= @t49 (tptp.sdtlseqdt0 @t43 @t45))))) % 0.36/0.67 (assume @p33 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t43)))) % 0.36/0.67 (assume @p34 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.36/0.67 (assume @p35 (forall @t25 (=> @t47 (=> (and @t49 (tptp.sdtlseqdt0 @t5 @t1)) @t23)))) % 0.36/0.67 (assume @p36 (forall @t28 (=> (and @t44 @t46 @t51) (=> (and @t49 @t50) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.36/0.67 (assume @p37 (forall @t25 (=> @t47 (or @t49 (tptp.sdtlseqdt0 @t45 @t1))))) % 0.36/0.67 (assume @p38 (forall @t25 (=> @t47 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.36/0.67 (assume @p39 (forall @t3 (=> @t44 (tptp.iLess0 @t1 @t43)))) % 0.36/0.67 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t52)))) % 0.36/0.67 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t52 tptp.szNzAzT0) @t9)))) % 0.36/0.67 (assume @p42 (forall @t3 (=> @t2 (= (= @t52 tptp.sz00) @t10)))) % 0.36/0.67 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t35) (tptp.szszuzczcdt0 @t52)))))))) % 0.36/0.67 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t37)) @t52)))))) % 0.36/0.67 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t52)))))) % 0.36/0.67 (assume @p46 (forall @t25 (=> @t53 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t52)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.36/0.67 (assume @p47 (forall @t3 (=> (and @t55 @t14) (forall @t8 (= (= @t5 @t54) (and @t7 (forall @t18 (=> @t16 @t50)))))))) % 0.36/0.67 (assume @p48 (forall @t3 (=> (and @t55 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.36/0.67 (assume @p49 (forall @t25 (=> (and @t55 @t57 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t54 @t5) (tptp.aElementOf0 @t56 @t1)) (= @t54 @t56))))) % 0.36/0.67 (assume @p50 (forall @t3 (=> @t44 (forall @t8 (= (= @t5 @t58) (and @t19 (forall @t18 (= @t17 (and @t51 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.36/0.67 (assume @p51 (forall @t3 (=> @t44 (tptp.isFinite0 @t58)))) % 0.36/0.67 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.36/0.67 (assume @p53 (forall @t25 (=> @t47 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t45)) (or (tptp.aElementOf0 @t1 @t59) @t23))))) % 0.36/0.67 (assume @p54 (forall @t25 (=> @t47 (= @t49 (tptp.aSubsetOf0 @t58 @t59))))) % 0.36/0.67 (assume @p55 (forall @t3 (=> (and @t55 @t9) (exists @t8 (and @t46 (tptp.aSubsetOf0 @t1 @t59)))))) % 0.36/0.67 (assume @p56 (forall @t3 (=> @t44 (= (tptp.sbrdtbr0 @t58) @t1)))) % 0.36/0.67 (assume @p57 (forall @t25 (=> @t53 (forall @t18 (= (= @t15 @t62) (and @t27 (forall @t34 (= @t33 (and @t61 (= @t60 @t5)))))))))) % 0.36/0.67 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t46 (tptp.isFinite0 @t62)))))) % 0.36/0.67 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t46 (not (= @t62 tptp.slcrc0))))))) % 0.36/0.67 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t46 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t62)))))) % 0.36/0.67 (assume @p61 (forall @t3 (=> @t44 (forall (@list @t5 @t15) (=> (and @t19 @t27 (not @t48)) (=> (and (tptp.aSubsetOf0 @t63 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t63 tptp.slcrc0))) @t26)))))) % 0.36/0.67 (assume @p62 (forall @t25 (=> @t53 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t62) (tptp.isFinite0 @t15)) (exists @t34 (and @t61 (tptp.isFinite0 @t29) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t29 @t5))))))))) % 0.36/0.67 (assume @p63 (forall @t3 (=> @t64 true))) % 0.36/0.67 (assume @p64 (forall @t3 (=> @t64 (tptp.aSet0 @t65)))) % 0.36/0.67 (assume @p65 (forall @t3 (=> @t64 (forall @t8 (=> @t67 (tptp.aElement0 @t66)))))) % 0.36/0.67 (assume @p66 (forall @t25 (=> @t71 (forall @t18 (= (= @t15 @t70) (and @t27 (forall @t34 (= @t33 (and @t69 (= @t68 @t5)))))))))) % 0.36/0.67 (assume @p67 (forall @t25 (=> @t71 (tptp.aSubsetOf0 @t70 @t65)))) % 0.36/0.67 (assume @p68 (forall @t3 (=> @t64 (forall @t8 (=> @t76 (forall @t18 (= (= @t15 @t75) (and @t27 (forall @t34 (= @t33 (exists @t74 (and @t73 (= (tptp.sdtlpdtrp0 @t1 @t72) @t29))))))))))))) % 0.36/0.67 (assume @p69 (forall @t3 (=> @t64 (forall @t8 (=> @t67 (tptp.aElementOf0 @t66 @t77)))))) % 0.36/0.67 (assume @p70 (forall @t3 (=> @t64 (forall @t8 (=> @t76 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t79 (= @t78 @t5) (forall @t34 (=> (tptp.aElementOf0 @t29 @t5) (= (tptp.sdtlpdtrp0 @t15 @t29) @t68))))))))))) % 0.36/0.67 (assume @p71 (forall @t3 (=> @t64 (forall @t8 (=> (and @t76 @t39) (=> (forall (@list @t15 @t29) (=> (and (tptp.aElementOf0 @t15 @t65) @t69 (not (= @t15 @t29))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t68)))) (tptp.isCountable0 @t75))))))) % 0.36/0.67 (assume @p72 (forall @t3 (=> @t64 (=> (and (tptp.isCountable0 @t65) (tptp.isFinite0 @t77)) (and (tptp.aElement0 @t80) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t80))))))) % 0.36/0.67 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.36/0.67 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.36/0.67 (assume @p75 (and (tptp.aSet0 tptp.xS) (forall @t3 (=> @t81 @t44)) (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.36/0.67 (assume @p76 (and (tptp.aFunction0 tptp.xc) (forall @t3 (and (=> @t85 (and @t2 @t88 @t87 @t86)) (=> (and (or (and @t2 @t88) @t87) @t86) @t85))) (= @t82 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSet0 @t83) (forall @t3 (= @t84 (exists @t8 (and (tptp.aElementOf0 @t5 @t82) (= (tptp.sdtlpdtrp0 tptp.xc @t5) @t1))))) (forall @t3 (=> @t84 (tptp.aElementOf0 @t1 tptp.xT))) (tptp.aSubsetOf0 @t83 tptp.xT))) % 0.36/0.67 (assume @p77 (forall @t3 (=> @t44 (forall @t8 (=> (and (or (and @t19 (forall @t18 (=> @t17 @t51))) @t57) @t39) (forall @t18 (=> (and @t79 (or (forall @t34 (and (=> @t95 (and (or (and @t99 @t98) @t97) @t96)) (=> (and @t99 @t98 @t97 @t96) @t95))) (= @t78 @t63)) (=> (and (tptp.aSet0 @t93) (forall @t34 (= @t94 (exists @t74 (and (tptp.aElementOf0 @t72 @t78) (= (tptp.sdtlpdtrp0 @t15 @t72) @t29)))))) (or (forall @t34 (=> @t94 @t92)) (tptp.aSubsetOf0 @t93 tptp.xT)))) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t34 (and @t92 (exists @t74 (and (tptp.aSet0 @t72) (forall @t91 (=> (tptp.aElementOf0 @t89 @t72) (tptp.aElementOf0 @t89 @t5))) (tptp.aSubsetOf0 @t72 @t5) (tptp.isCountable0 @t72) (forall @t91 (=> (or (and (or (and (tptp.aSet0 @t89) (forall (@list @t90) (=> (tptp.aElementOf0 @t90 @t89) (tptp.aElementOf0 @t90 @t72)))) (tptp.aSubsetOf0 @t89 @t72)) (= (tptp.sbrdtbr0 @t89) @t1)) (tptp.aElementOf0 @t89 (tptp.slbdtsldtrb0 @t72 @t1))) (= (tptp.sdtlpdtrp0 @t15 @t89) @t29))))))))))))))) % 0.36/0.67 (assume @p78 (= tptp.xK tptp.sz00)) % 0.36/0.67 (assume @p79 @t110) % 0.36/0.67 (assume @p80 true) % 0.36/0.67 (step @p81 :rule refl :args (@t100)) % 0.36/0.67 (step @p82 :rule refl :args (@t101)) % 0.36/0.67 (step @p83 :rule bool-impl-elim :args (@t102 @t81)) % 0.36/0.67 (step @p84 :rule cong :premises (@p83) :args (@t103)) % 0.36/0.67 (step @p85 :rule nary_cong :premises (@p84 @p82 @p81) :args (@t104)) % 0.36/0.67 (step @p86 :rule bool-double-not-elim :args (@t112)) % 0.36/0.67 (step @p87 :rule exists-elim :args ((= @t105 (not @t112)))) % 0.36/0.67 (step @p88 :rule cong :premises (@p87) :args (@t106)) % 0.36/0.67 (step @p89 :rule trans :premises (@p88 @p86)) % 0.36/0.67 (step @p90 :rule refl :args (@t107)) % 0.36/0.67 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t108)) % 0.36/0.67 (step @p92 :rule cong :premises (@p91 @p85) :args (@t109)) % 0.36/0.67 (step @p93 :rule cong :premises (@p92) :args (@t110)) % 0.36/0.67 (step @p94 :rule eq_resolve :premises (@p79 @p93)) % 0.36/0.67 (step @p95 :rule not_implies_elim1 :premises (@p94)) % 0.36/0.67 (step @p96 :rule and_elim :premises (@p95) :args (1)) % 0.36/0.67 (step @p97 :rule not_implies_elim2 :premises (@p94)) % 0.36/0.67 (step @p98 :rule not_or_elim :premises (@p97) :args (0)) % 0.36/0.67 (step @p99 :rule skolemize :premises (@p98)) % 0.36/0.67 (step @p100 :rule bool-double-not-elim :args (@t114)) % 0.36/0.67 (step @p101 :rule refl :args (@t116)) % 0.36/0.67 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or @t116 (not @t115)))) % 0.36/0.67 (step @p103 :rule cnf_or_neg :args (@t116 0)) % 0.36/0.67 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.36/0.67 (step @p105 :rule reordering :premises (@p104) :args ((or @t114 @t116))) % 0.36/0.67 (step @p106 :rule chain_m_resolution :premises (@p105 @p99) :args (@t114 (@list true) (@list @t116))) % 0.36/0.67 (assume-push @p113 @t112) % 0.36/0.67 (step @p108 :rule instantiate :premises (@p96) :args ((@list @t113))) % 0.36/0.67 (step-pop @p114 :rule scope :premises (@p108)) % 0.36/0.67 (step @p109 :rule process_scope :premises (@p114) :args (@t115)) % 0.36/0.67 (step @p111 :rule implies_elim :premises (@p109)) % 0.36/0.67 (step @p112 false :rule chain_m_resolution :premises (@p111 @p106 @p96) :args (false (@list false false) (@list @t114 @t112))) % 0.36/0.67 ) % 0.36/0.67 % SZS output end Proof % 0.36/0.67 % cvc5 exiting %------------------------------------------------------------------------------