%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM587+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:39:55 AM UTC 2026 % Result : Theorem 0.37s 0.84s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM587+1 : TPTP v9.2.1. Released v4.0.0. % 0.14/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n029.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 11:33:47 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.84 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.84 % SZS status Theorem % 0.37/0.84 % SZS output start Proof % 0.37/0.84 ( % 0.37/0.84 (declare-sort $$unsorted 0) % 0.37/0.84 (declare-const tptp.xQ $$unsorted) % 0.37/0.84 (declare-const tptp.xx $$unsorted) % 0.37/0.84 (declare-const tptp.xC $$unsorted) % 0.37/0.84 (declare-const tptp.xN $$unsorted) % 0.37/0.84 (declare-const tptp.sz00 $$unsorted) % 0.37/0.84 (declare-const tptp.xc $$unsorted) % 0.37/0.84 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.37/0.84 (declare-const tptp.szNzAzT0 $$unsorted) % 0.37/0.84 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.84 (declare-const tptp.xk $$unsorted) % 0.37/0.84 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.84 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.37/0.84 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.37/0.84 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.37/0.84 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.37/0.84 (declare-const tptp.xi $$unsorted) % 0.37/0.84 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.84 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.84 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.xK $$unsorted) % 0.37/0.84 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.xT $$unsorted) % 0.37/0.84 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.xS $$unsorted) % 0.37/0.84 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.slcrc0 $$unsorted) % 0.37/0.84 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.84 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.84 (define @t1 () (@var "W0" $$unsorted)) % 0.37/0.84 (define @t2 () (tptp.aSet0 @t1)) % 0.37/0.84 (define @t3 () (@list @t1)) % 0.37/0.84 (define @t4 () (tptp.aElement0 @t1)) % 0.37/0.84 (define @t5 () (@var "W1" $$unsorted)) % 0.37/0.84 (define @t6 () (tptp.aElement0 @t5)) % 0.37/0.84 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.37/0.84 (define @t8 () (@list @t5)) % 0.37/0.84 (define @t9 () (tptp.isFinite0 @t1)) % 0.37/0.84 (define @t10 () (= @t1 tptp.slcrc0)) % 0.37/0.84 (define @t11 () (tptp.isCountable0 @t1)) % 0.37/0.84 (define @t12 () (not @t9)) % 0.37/0.84 (define @t13 () (and @t2 @t11)) % 0.37/0.84 (define @t14 () (not @t10)) % 0.37/0.84 (define @t15 () (@var "W2" $$unsorted)) % 0.37/0.84 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.37/0.84 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.37/0.84 (define @t18 () (@list @t15)) % 0.37/0.84 (define @t19 () (forall @t18 (=> @t17 @t16))) % 0.37/0.84 (define @t20 () (tptp.aSet0 @t5)) % 0.37/0.84 (define @t21 () (and @t20 @t19)) % 0.37/0.84 (define @t22 () (tptp.aSubsetOf0 @t5 @t1)) % 0.37/0.84 (define @t23 () (= @t22 @t21)) % 0.37/0.84 (define @t24 () (forall @t8 @t23)) % 0.37/0.84 (define @t25 () (=> @t2 @t24)) % 0.37/0.84 (define @t26 () (forall @t3 @t25)) % 0.37/0.84 (define @t27 () (tptp.isFinite0 @t5)) % 0.37/0.84 (define @t28 () (and @t2 @t9)) % 0.37/0.84 (define @t29 () (= @t1 @t5)) % 0.37/0.84 (define @t30 () (tptp.aSubsetOf0 @t1 @t5)) % 0.37/0.84 (define @t31 () (@list @t1 @t5)) % 0.37/0.84 (define @t32 () (tptp.aSubsetOf0 @t5 @t15)) % 0.37/0.84 (define @t33 () (tptp.aSet0 @t15)) % 0.37/0.84 (define @t34 () (@list @t1 @t5 @t15)) % 0.37/0.84 (define @t35 () (@var "W3" $$unsorted)) % 0.37/0.84 (define @t36 () (= @t35 @t5)) % 0.37/0.84 (define @t37 () (tptp.aElementOf0 @t35 @t1)) % 0.37/0.84 (define @t38 () (tptp.aElement0 @t35)) % 0.37/0.84 (define @t39 () (tptp.aElementOf0 @t35 @t15)) % 0.37/0.84 (define @t40 () (@list @t35)) % 0.37/0.84 (define @t41 () (tptp.sdtpldt0 @t1 @t5)) % 0.37/0.84 (define @t42 () (and @t2 @t6)) % 0.37/0.84 (define @t43 () (tptp.sdtmndt0 @t1 @t5)) % 0.37/0.84 (define @t44 () (tptp.sdtpldt0 @t5 @t1)) % 0.37/0.84 (define @t45 () (tptp.isCountable0 @t5)) % 0.37/0.84 (define @t46 () (and @t20 @t45)) % 0.37/0.84 (define @t47 () (tptp.sdtmndt0 @t5 @t1)) % 0.37/0.84 (define @t48 () (and @t20 @t27)) % 0.37/0.84 (define @t49 () (tptp.szszuzczcdt0 @t1)) % 0.37/0.84 (define @t50 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.37/0.84 (define @t51 () (tptp.szszuzczcdt0 @t5)) % 0.37/0.84 (define @t52 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.37/0.84 (define @t53 () (and @t50 @t52)) % 0.37/0.84 (define @t54 () (= @t1 tptp.sz00)) % 0.37/0.84 (define @t55 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.37/0.84 (define @t56 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.37/0.84 (define @t57 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.37/0.84 (define @t58 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.37/0.84 (define @t59 () (tptp.sbrdtbr0 @t1)) % 0.37/0.84 (define @t60 () (and @t2 @t52)) % 0.37/0.84 (define @t61 () (tptp.szmzizndt0 @t1)) % 0.37/0.84 (define @t62 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.37/0.84 (define @t63 () (tptp.szmzizndt0 @t5)) % 0.37/0.84 (define @t64 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.37/0.84 (define @t65 () (tptp.slbdtrb0 @t1)) % 0.37/0.84 (define @t66 () (tptp.slbdtrb0 @t5)) % 0.37/0.84 (define @t67 () (tptp.aSubsetOf0 @t35 @t1)) % 0.37/0.84 (define @t68 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.37/0.84 (define @t69 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.37/0.84 (define @t70 () (tptp.aFunction0 @t1)) % 0.37/0.84 (define @t71 () (tptp.szDzozmdt0 @t1)) % 0.37/0.84 (define @t72 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.37/0.84 (define @t73 () (tptp.aElementOf0 @t5 @t71)) % 0.37/0.84 (define @t74 () (tptp.sdtlpdtrp0 @t1 @t35)) % 0.37/0.84 (define @t75 () (tptp.aElementOf0 @t35 @t71)) % 0.37/0.84 (define @t76 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.37/0.84 (define @t77 () (and @t70 @t6)) % 0.37/0.84 (define @t78 () (@var "W4" $$unsorted)) % 0.37/0.84 (define @t79 () (@list @t78)) % 0.37/0.84 (define @t80 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.37/0.84 (define @t81 () (tptp.aSubsetOf0 @t5 @t71)) % 0.37/0.84 (define @t82 () (tptp.sdtlcdtrc0 @t1 @t71)) % 0.37/0.84 (define @t83 () (tptp.szDzozmdt0 @t15)) % 0.37/0.84 (define @t84 () (tptp.aFunction0 @t15)) % 0.37/0.84 (define @t85 () (tptp.szDzizrdt0 @t1)) % 0.37/0.84 (define @t86 () (tptp.aSet0 tptp.xT)) % 0.37/0.84 (define @t87 () (tptp.szDzozmdt0 tptp.xc)) % 0.37/0.84 (define @t88 () (tptp.sdtlcdtrc0 tptp.xc @t87)) % 0.37/0.84 (define @t89 () (tptp.aSubsetOf0 @t88 tptp.xT)) % 0.37/0.84 (define @t90 () (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) % 0.37/0.84 (define @t91 () (@var "W5" $$unsorted)) % 0.37/0.84 (define @t92 () (tptp.sdtlpdtrp0 tptp.xN @t49)) % 0.37/0.84 (define @t93 () (tptp.sdtlpdtrp0 tptp.xN @t1)) % 0.37/0.84 (define @t94 () (tptp.szmzizndt0 @t93)) % 0.37/0.84 (define @t95 () (tptp.sdtmndt0 @t93 @t94)) % 0.37/0.84 (define @t96 () (and (tptp.aSubsetOf0 @t93 tptp.szNzAzT0) (tptp.isCountable0 @t93))) % 0.37/0.84 (define @t97 () (tptp.sdtlpdtrp0 tptp.xN @t5)) % 0.37/0.84 (define @t98 () (tptp.sdtpldt0 @t5 @t94)) % 0.37/0.84 (define @t99 () (tptp.slbdtsldtrb0 @t95 tptp.xk)) % 0.37/0.84 (define @t100 () (and @t20 (tptp.aElementOf0 @t5 @t99))) % 0.37/0.84 (define @t101 () (tptp.sdtlpdtrp0 tptp.xC @t1)) % 0.37/0.84 (define @t102 () (tptp.sdtlpdtrp0 tptp.xC tptp.xi)) % 0.37/0.84 (define @t103 () (tptp.sdtlpdtrp0 tptp.xN tptp.xi)) % 0.37/0.84 (define @t104 () (tptp.szmzizndt0 @t103)) % 0.37/0.84 (define @t105 () (tptp.sdtlpdtrp0 tptp.xc (tptp.sdtpldt0 tptp.xQ @t104))) % 0.37/0.84 (define @t106 () (tptp.aElementOf0 @t105 @t88)) % 0.37/0.84 (define @t107 () (tptp.aElementOf0 tptp.xx tptp.xT)) % 0.37/0.84 (define @t108 () (@var "BOUND_VARIABLE_8140" $$unsorted)) % 0.37/0.84 (define @t109 () (= (tptp.aSubsetOf0 @t108 @t1) (and (tptp.aSet0 @t108) (forall @t18 (or (not (tptp.aElementOf0 @t15 @t108)) @t16))))) % 0.37/0.84 (define @t110 () (not @t2)) % 0.37/0.84 (define @t111 () (or @t110 @t109)) % 0.37/0.84 (define @t112 () (@list @t108)) % 0.37/0.84 (define @t113 () (forall @t112 @t111)) % 0.37/0.84 (define @t114 () (forall @t112 @t109)) % 0.37/0.84 (define @t115 () (or @t110 @t114)) % 0.37/0.84 (define @t116 () (forall @t8 (= @t22 (and @t20 (forall @t18 (or (not @t17) @t16)))))) % 0.37/0.84 (define @t117 () (forall @t18 (or (not (tptp.aElementOf0 @t15 @t88)) (tptp.aElementOf0 @t15 tptp.xT)))) % 0.37/0.84 (define @t118 () (and (tptp.aSet0 @t88) @t117)) % 0.37/0.84 (define @t119 () (= @t89 @t118)) % 0.37/0.84 (define @t120 () (not @t86)) % 0.37/0.84 (define @t121 () (or @t120 @t119)) % 0.37/0.84 (define @t122 () (@list false false)) % 0.37/0.84 (define @t123 () (tptp.aElementOf0 @t105 tptp.xT)) % 0.37/0.84 (define @t124 () (not @t106)) % 0.37/0.84 (define @t125 () (or @t124 @t123)) % 0.37/0.84 (assume @p1 (forall @t3 (=> @t2 true))) % 0.37/0.84 (assume @p2 (forall @t3 (=> @t4 true))) % 0.37/0.84 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.37/0.84 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.37/0.84 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.37/0.84 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.37/0.84 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.37/0.84 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.37/0.84 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.37/0.84 (assume @p10 @t26) % 0.37/0.84 (assume @p11 (forall @t3 (=> @t28 (forall @t8 (=> @t22 @t27))))) % 0.37/0.84 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.37/0.84 (assume @p13 (forall @t31 (=> (and @t2 @t20) (=> (and @t30 @t22) @t29)))) % 0.37/0.84 (assume @p14 (forall @t34 (=> (and @t2 @t20 @t33) (=> (and @t30 @t32) (tptp.aSubsetOf0 @t1 @t15))))) % 0.37/0.84 (assume @p15 (forall @t31 (=> @t42 (forall @t18 (= (= @t15 @t41) (and @t33 (forall @t40 (= @t39 (and @t38 (or @t37 @t36)))))))))) % 0.37/0.84 (assume @p16 (forall @t31 (=> @t42 (forall @t18 (= (= @t15 @t43) (and @t33 (forall @t40 (= @t39 (and @t38 @t37 (not @t36)))))))))) % 0.37/0.84 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t43 @t5) @t1)))))) % 0.37/0.84 (assume @p18 (forall @t31 (=> (and @t4 @t20) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t44 @t1) @t5))))) % 0.37/0.84 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isCountable0 @t44)))))) % 0.37/0.84 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isCountable0 @t47)))))) % 0.37/0.84 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t48 (tptp.isFinite0 @t44)))))) % 0.37/0.84 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t48 (tptp.isFinite0 @t47)))))) % 0.37/0.84 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.37/0.84 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.37/0.84 (assume @p25 (forall @t3 (=> @t50 (and (tptp.aElementOf0 @t49 tptp.szNzAzT0) (not (= @t49 tptp.sz00)))))) % 0.37/0.84 (assume @p26 (forall @t31 (=> @t53 (=> (= @t49 @t51) @t29)))) % 0.37/0.84 (assume @p27 (forall @t3 (=> @t50 (or @t54 (exists @t8 (and @t52 (= @t1 @t51))))))) % 0.37/0.84 (assume @p28 (forall @t3 (=> @t50 (not (= @t1 @t49))))) % 0.37/0.84 (assume @p29 (forall @t31 (=> @t53 (=> @t55 true)))) % 0.37/0.84 (assume @p30 (forall @t3 (=> @t50 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.37/0.84 (assume @p31 (forall @t3 (=> @t50 (not (tptp.sdtlseqdt0 @t49 tptp.sz00))))) % 0.37/0.84 (assume @p32 (forall @t31 (=> @t53 (= @t55 (tptp.sdtlseqdt0 @t49 @t51))))) % 0.37/0.84 (assume @p33 (forall @t3 (=> @t50 (tptp.sdtlseqdt0 @t1 @t49)))) % 0.37/0.84 (assume @p34 (forall @t3 (=> @t50 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.37/0.84 (assume @p35 (forall @t31 (=> @t53 (=> (and @t55 @t56) @t29)))) % 0.37/0.84 (assume @p36 (forall @t34 (=> (and @t50 @t52 @t58) (=> (and @t55 @t57) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.37/0.84 (assume @p37 (forall @t31 (=> @t53 (or @t55 (tptp.sdtlseqdt0 @t51 @t1))))) % 0.37/0.84 (assume @p38 (forall @t31 (=> @t53 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.37/0.84 (assume @p39 (forall @t3 (=> @t50 (tptp.iLess0 @t1 @t49)))) % 0.37/0.84 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t59)))) % 0.37/0.84 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t59 tptp.szNzAzT0) @t9)))) % 0.37/0.84 (assume @p42 (forall @t3 (=> @t2 (= (= @t59 tptp.sz00) @t10)))) % 0.37/0.84 (assume @p43 (forall @t3 (=> @t28 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t41) (tptp.szszuzczcdt0 @t59)))))))) % 0.37/0.84 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t43)) @t59)))))) % 0.37/0.84 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t22) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t59)))))) % 0.37/0.84 (assume @p46 (forall @t31 (=> @t60 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t59)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.37/0.84 (assume @p47 (forall @t3 (=> (and @t62 @t14) (forall @t8 (= (= @t5 @t61) (and @t7 (forall @t18 (=> @t16 @t57)))))))) % 0.37/0.84 (assume @p48 (forall @t3 (=> (and @t62 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.37/0.84 (assume @p49 (forall @t31 (=> (and @t62 @t64 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t61 @t5) (tptp.aElementOf0 @t63 @t1)) (= @t61 @t63))))) % 0.37/0.84 (assume @p50 (forall @t3 (=> @t50 (forall @t8 (= (= @t5 @t65) (and @t20 (forall @t18 (= @t17 (and @t58 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.37/0.84 (assume @p51 (forall @t3 (=> @t50 (tptp.isFinite0 @t65)))) % 0.37/0.84 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.37/0.84 (assume @p53 (forall @t31 (=> @t53 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t51)) (or (tptp.aElementOf0 @t1 @t66) @t29))))) % 0.37/0.84 (assume @p54 (forall @t31 (=> @t53 (= @t55 (tptp.aSubsetOf0 @t65 @t66))))) % 0.37/0.84 (assume @p55 (forall @t3 (=> (and @t62 @t9) (exists @t8 (and @t52 (tptp.aSubsetOf0 @t1 @t66)))))) % 0.37/0.84 (assume @p56 (forall @t3 (=> @t50 (= (tptp.sbrdtbr0 @t65) @t1)))) % 0.37/0.84 (assume @p57 (forall @t31 (=> @t60 (forall @t18 (= (= @t15 @t68) (and @t33 (forall @t40 (= @t39 (and @t67 (= (tptp.sbrdtbr0 @t35) @t5)))))))))) % 0.37/0.84 (assume @p58 (forall @t3 (=> @t28 (forall @t8 (=> @t52 (tptp.isFinite0 @t68)))))) % 0.37/0.84 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t52 (not (= @t68 tptp.slcrc0))))))) % 0.37/0.84 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t52 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t68)))))) % 0.37/0.84 (assume @p61 (forall @t3 (=> @t50 (forall (@list @t5 @t15) (=> (and @t20 @t33 (not @t54)) (=> (and (tptp.aSubsetOf0 @t69 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t69 tptp.slcrc0))) @t32)))))) % 0.37/0.84 (assume @p62 (forall @t31 (=> @t60 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t68) (tptp.isFinite0 @t15)) (exists @t40 (and @t67 (tptp.isFinite0 @t35) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t35 @t5))))))))) % 0.37/0.84 (assume @p63 (forall @t3 (=> @t70 true))) % 0.37/0.84 (assume @p64 (forall @t3 (=> @t70 (tptp.aSet0 @t71)))) % 0.37/0.84 (assume @p65 (forall @t3 (=> @t70 (forall @t8 (=> @t73 (tptp.aElement0 @t72)))))) % 0.37/0.84 (assume @p66 (forall @t31 (=> @t77 (forall @t18 (= (= @t15 @t76) (and @t33 (forall @t40 (= @t39 (and @t75 (= @t74 @t5)))))))))) % 0.37/0.84 (assume @p67 (forall @t31 (=> @t77 (tptp.aSubsetOf0 @t76 @t71)))) % 0.37/0.84 (assume @p68 (forall @t3 (=> @t70 (forall @t8 (=> @t81 (forall @t18 (= (= @t15 @t80) (and @t33 (forall @t40 (= @t39 (exists @t79 (and (tptp.aElementOf0 @t78 @t5) (= (tptp.sdtlpdtrp0 @t1 @t78) @t35))))))))))))) % 0.37/0.84 (assume @p69 (forall @t3 (=> @t70 (forall @t8 (=> @t73 (tptp.aElementOf0 @t72 @t82)))))) % 0.37/0.84 (assume @p70 (forall @t3 (=> @t70 (forall @t8 (=> @t81 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t84 (= @t83 @t5) (forall @t40 (=> (tptp.aElementOf0 @t35 @t5) (= (tptp.sdtlpdtrp0 @t15 @t35) @t74))))))))))) % 0.37/0.84 (assume @p71 (forall @t3 (=> @t70 (forall @t8 (=> (and @t81 @t45) (=> (forall (@list @t15 @t35) (=> (and (tptp.aElementOf0 @t15 @t71) @t75 (not (= @t15 @t35))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t74)))) (tptp.isCountable0 @t80))))))) % 0.37/0.84 (assume @p72 (forall @t3 (=> @t70 (=> (and (tptp.isCountable0 @t71) (tptp.isFinite0 @t82)) (and (tptp.aElement0 @t85) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t85))))))) % 0.37/0.84 (assume @p73 (and @t86 (tptp.isFinite0 tptp.xT))) % 0.37/0.84 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.37/0.84 (assume @p75 (and (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.37/0.84 (assume @p76 (and (tptp.aFunction0 tptp.xc) (= @t87 @t90) @t89)) % 0.37/0.84 (assume @p77 (forall @t3 (=> @t50 (forall @t8 (=> (and @t64 @t45) (forall @t18 (=> (and @t84 (= @t83 @t69) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t15 @t83) tptp.xT)) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t40 (and (tptp.aElementOf0 @t35 tptp.xT) (exists @t79 (and (tptp.aSubsetOf0 @t78 @t5) (tptp.isCountable0 @t78) (forall (@list @t91) (=> (tptp.aElementOf0 @t91 (tptp.slbdtsldtrb0 @t78 @t1)) (= (tptp.sdtlpdtrp0 @t15 @t91) @t35))))))))))))))) % 0.37/0.84 (assume @p78 (not (= tptp.xK tptp.sz00))) % 0.37/0.84 (assume @p79 (and (tptp.aElementOf0 tptp.xk tptp.szNzAzT0) (= (tptp.szszuzczcdt0 tptp.xk) tptp.xK))) % 0.37/0.84 (assume @p80 (and (tptp.aFunction0 tptp.xN) (= (tptp.szDzozmdt0 tptp.xN) tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall @t3 (=> @t50 (=> @t96 (and (tptp.aSubsetOf0 @t92 @t95) (tptp.isCountable0 @t92))))))) % 0.37/0.84 (assume @p81 (forall @t3 (=> @t50 @t96))) % 0.37/0.84 (assume @p82 (forall @t31 (=> @t53 (=> @t56 (tptp.aSubsetOf0 @t93 @t97))))) % 0.37/0.84 (assume @p83 (forall @t31 (=> (and @t50 @t52 (not @t29)) (not (= @t94 (tptp.szmzizndt0 @t97)))))) % 0.37/0.84 (assume @p84 (forall @t3 (=> @t50 (forall @t8 (=> @t100 (tptp.aElementOf0 @t98 @t90)))))) % 0.37/0.84 (assume @p85 (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall @t3 (=> @t50 (and (tptp.aFunction0 @t101) (= (tptp.szDzozmdt0 @t101) @t99) (forall @t8 (=> @t100 (= (tptp.sdtlpdtrp0 @t101 @t5) (tptp.sdtlpdtrp0 tptp.xc @t98))))))))) % 0.37/0.84 (assume @p86 (tptp.aElementOf0 tptp.xi tptp.szNzAzT0)) % 0.37/0.84 (assume @p87 (tptp.aElementOf0 tptp.xx (tptp.sdtlcdtrc0 @t102 (tptp.szDzozmdt0 @t102)))) % 0.37/0.84 (assume @p88 (and (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 (tptp.sdtmndt0 @t103 @t104) tptp.xk)) (= (tptp.sdtlpdtrp0 @t102 tptp.xQ) tptp.xx))) % 0.37/0.84 (assume @p89 (and (= tptp.xx @t105) @t106)) % 0.37/0.84 (assume @p90 (not @t107)) % 0.37/0.84 (assume @p91 true) % 0.37/0.84 (step @p92 :rule evaluate :args ((= false true))) % 0.37/0.84 (step @p93 :rule quant-merge-prenex :args ((= (forall @t3 @t113) (forall (@list @t1 @t108) @t111)))) % 0.37/0.84 (step @p94 :rule alpha_equiv :args (@t114 (@list @t108) (@list @t5))) % 0.37/0.84 (step @p95 :rule refl :args (@t110)) % 0.37/0.84 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t115)) % 0.37/0.85 (step @p97 :rule quant-miniscope-or :args ((= @t113 @t115))) % 0.37/0.85 (step @p98 :rule trans :premises (@p97 @p96)) % 0.37/0.85 (step @p99 :rule symm :premises (@p98)) % 0.37/0.85 (step @p100 :rule cong :premises (@p99) :args ((forall @t3 (or @t110 @t116)))) % 0.37/0.85 (step @p101 :rule trans :premises (@p100 @p93)) % 0.37/0.85 (step @p102 :rule bool-impl-elim :args (@t2 @t116)) % 0.37/0.85 (step @p103 :rule cong :premises (@p102) :args ((forall @t3 (=> @t2 @t116)))) % 0.37/0.85 (step @p104 :rule trans :premises (@p103 @p101)) % 0.37/0.85 (step @p105 :rule bool-impl-elim :args (@t17 @t16)) % 0.37/0.85 (step @p106 :rule cong :premises (@p105) :args (@t19)) % 0.37/0.85 (step @p107 :rule refl :args (@t20)) % 0.37/0.85 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t21)) % 0.37/0.85 (step @p109 :rule refl :args (@t22)) % 0.37/0.85 (step @p110 :rule cong :premises (@p109 @p108) :args (@t23)) % 0.37/0.85 (step @p111 :rule cong :premises (@p110) :args (@t24)) % 0.37/0.85 (step @p112 :rule refl :args (@t2)) % 0.37/0.85 (step @p113 :rule cong :premises (@p112 @p111) :args (@t25)) % 0.37/0.85 (step @p114 :rule cong :premises (@p113) :args (@t26)) % 0.37/0.85 (step @p115 :rule trans :premises (@p114 @p104)) % 0.37/0.85 (step @p116 :rule eq_resolve :premises (@p10 @p115)) % 0.37/0.85 (step @p117 :rule instantiate :premises (@p116) :args ((@list tptp.xT @t88))) % 0.37/0.85 (step @p118 :rule and_elim :premises (@p73) :args (0)) % 0.37/0.85 (step @p119 :rule cnf_or_pos :args (@t121)) % 0.37/0.85 (step @p120 :rule reordering :premises (@p119) :args ((or @t120 @t119 (not @t121)))) % 0.37/0.85 (step @p121 :rule chain_m_resolution :premises (@p120 @p118 @p117) :args (@t119 @t122 (@list @t86 @t121))) % 0.37/0.85 (step @p122 :rule and_elim :premises (@p76) :args (2)) % 0.37/0.85 (step @p123 :rule cnf_equiv_pos1 :args (@t119)) % 0.37/0.85 (step @p124 :rule reordering :premises (@p123) :args ((or (not @t89) @t118 (not @t119)))) % 0.37/0.85 (step @p125 :rule chain_m_resolution :premises (@p124 @p122 @p121) :args (@t118 @t122 (@list @t89 @t119))) % 0.37/0.85 (step @p126 :rule cnf_and_pos :args (@t118 1)) % 0.37/0.85 (step @p127 :rule reordering :premises (@p126) :args ((or @t117 (not @t118)))) % 0.37/0.85 (step @p128 :rule chain_m_resolution :premises (@p127 @p125) :args (@t117 (@list false) (@list @t118))) % 0.37/0.85 (step @p129 :rule instantiate :premises (@p128) :args ((@list @t105))) % 0.37/0.85 (step @p130 :rule and_elim :premises (@p89) :args (1)) % 0.37/0.85 (step @p131 :rule cnf_or_pos :args (@t125)) % 0.37/0.85 (step @p132 :rule reordering :premises (@p131) :args ((or @t124 @t123 (not @t125)))) % 0.37/0.85 (step @p133 :rule chain_m_resolution :premises (@p132 @p130 @p129) :args (@t123 @t122 (@list @t106 @t125))) % 0.37/0.85 (step @p134 :rule true_intro :premises (@p133)) % 0.37/0.85 (step @p135 :rule refl :args (tptp.xT)) % 0.37/0.85 (step @p136 :rule and_elim :premises (@p89) :args (0)) % 0.37/0.85 (step @p137 :rule cong :premises (@p136 @p135) :args (@t107)) % 0.37/0.85 (step @p138 :rule false_intro :premises (@p90)) % 0.37/0.85 (step @p139 :rule symm :premises (@p138)) % 0.37/0.85 (step @p140 :rule trans :premises (@p139 @p137 @p134)) % 0.37/0.85 (step @p141 false :rule eq_resolve :premises (@p140 @p92)) % 0.37/0.85 ) % 0.37/0.85 % SZS output end Proof % 0.37/0.85 % cvc5 exiting %------------------------------------------------------------------------------