%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM613+1 : 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 : n008.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 08:40:01 AM UTC 2026 % Result : Theorem 0.51s 0.70s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM613+1 : 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 % 0.17/0.35 % Computer : n008.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 11:36:33 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.51/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.51/0.70 % SZS status Theorem % 0.51/0.70 % SZS output start Proof % 0.51/0.70 ( % 0.51/0.70 (declare-sort $$unsorted 0) % 0.51/0.70 (declare-const tptp.xp $$unsorted) % 0.51/0.70 (declare-const tptp.xQ $$unsorted) % 0.51/0.70 (declare-const tptp.xe $$unsorted) % 0.51/0.70 (declare-const tptp.xP $$unsorted) % 0.51/0.70 (declare-const tptp.xC $$unsorted) % 0.51/0.70 (declare-const tptp.xN $$unsorted) % 0.51/0.70 (declare-const tptp.sz00 $$unsorted) % 0.51/0.70 (declare-const tptp.xc $$unsorted) % 0.51/0.70 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.szNzAzT0 $$unsorted) % 0.51/0.70 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.xd $$unsorted) % 0.51/0.70 (declare-const tptp.xk $$unsorted) % 0.51/0.70 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.xK $$unsorted) % 0.51/0.70 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.xT $$unsorted) % 0.51/0.70 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.xO $$unsorted) % 0.51/0.70 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.xS $$unsorted) % 0.51/0.70 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.slcrc0 $$unsorted) % 0.51/0.70 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (define @t1 () (@var "W0" $$unsorted)) % 0.51/0.70 (define @t2 () (tptp.aSet0 @t1)) % 0.51/0.70 (define @t3 () (@list @t1)) % 0.51/0.70 (define @t4 () (tptp.aElement0 @t1)) % 0.51/0.70 (define @t5 () (@var "W1" $$unsorted)) % 0.51/0.70 (define @t6 () (tptp.aElement0 @t5)) % 0.51/0.70 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.51/0.70 (define @t8 () (@list @t5)) % 0.51/0.70 (define @t9 () (tptp.isFinite0 @t1)) % 0.51/0.70 (define @t10 () (= @t1 tptp.slcrc0)) % 0.51/0.70 (define @t11 () (tptp.isCountable0 @t1)) % 0.51/0.70 (define @t12 () (not @t9)) % 0.51/0.70 (define @t13 () (and @t2 @t11)) % 0.51/0.70 (define @t14 () (not @t10)) % 0.51/0.70 (define @t15 () (@var "W2" $$unsorted)) % 0.51/0.70 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.51/0.70 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.51/0.70 (define @t18 () (@list @t15)) % 0.51/0.70 (define @t19 () (tptp.aSet0 @t5)) % 0.51/0.70 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.51/0.70 (define @t21 () (tptp.isFinite0 @t5)) % 0.51/0.70 (define @t22 () (and @t2 @t9)) % 0.51/0.70 (define @t23 () (= @t1 @t5)) % 0.51/0.70 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.51/0.70 (define @t25 () (@list @t1 @t5)) % 0.51/0.70 (define @t26 () (tptp.aSubsetOf0 @t5 @t15)) % 0.51/0.70 (define @t27 () (tptp.aSet0 @t15)) % 0.51/0.70 (define @t28 () (@list @t1 @t5 @t15)) % 0.51/0.70 (define @t29 () (@var "W3" $$unsorted)) % 0.51/0.70 (define @t30 () (= @t29 @t5)) % 0.51/0.70 (define @t31 () (tptp.aElementOf0 @t29 @t1)) % 0.51/0.70 (define @t32 () (tptp.aElement0 @t29)) % 0.51/0.70 (define @t33 () (tptp.aElementOf0 @t29 @t15)) % 0.51/0.70 (define @t34 () (@list @t29)) % 0.51/0.70 (define @t35 () (tptp.sdtpldt0 @t1 @t5)) % 0.51/0.70 (define @t36 () (and @t2 @t6)) % 0.51/0.70 (define @t37 () (tptp.sdtmndt0 @t1 @t5)) % 0.51/0.70 (define @t38 () (tptp.sdtpldt0 @t5 @t1)) % 0.51/0.70 (define @t39 () (tptp.isCountable0 @t5)) % 0.51/0.70 (define @t40 () (and @t19 @t39)) % 0.51/0.70 (define @t41 () (tptp.sdtmndt0 @t5 @t1)) % 0.51/0.70 (define @t42 () (and @t19 @t21)) % 0.51/0.70 (define @t43 () (tptp.szszuzczcdt0 @t1)) % 0.51/0.70 (define @t44 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.51/0.70 (define @t45 () (tptp.szszuzczcdt0 @t5)) % 0.51/0.70 (define @t46 () (= @t43 @t45)) % 0.51/0.70 (define @t47 () (=> @t46 @t23)) % 0.51/0.70 (define @t48 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.51/0.70 (define @t49 () (and @t44 @t48)) % 0.51/0.70 (define @t50 () (forall @t25 (=> @t49 @t47))) % 0.51/0.70 (define @t51 () (= @t1 tptp.sz00)) % 0.51/0.70 (define @t52 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.51/0.70 (define @t53 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.51/0.70 (define @t54 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.51/0.70 (define @t55 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.51/0.70 (define @t56 () (tptp.sbrdtbr0 @t1)) % 0.51/0.70 (define @t57 () (and @t2 @t48)) % 0.51/0.70 (define @t58 () (tptp.szmzizndt0 @t1)) % 0.51/0.70 (define @t59 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.51/0.70 (define @t60 () (tptp.szmzizndt0 @t5)) % 0.51/0.70 (define @t61 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.51/0.70 (define @t62 () (tptp.slbdtrb0 @t1)) % 0.51/0.70 (define @t63 () (tptp.slbdtrb0 @t5)) % 0.51/0.70 (define @t64 () (tptp.aSubsetOf0 @t29 @t1)) % 0.51/0.70 (define @t65 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.51/0.70 (define @t66 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.51/0.70 (define @t67 () (tptp.aFunction0 @t1)) % 0.51/0.70 (define @t68 () (tptp.szDzozmdt0 @t1)) % 0.51/0.70 (define @t69 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.51/0.70 (define @t70 () (tptp.aElementOf0 @t5 @t68)) % 0.51/0.70 (define @t71 () (tptp.sdtlpdtrp0 @t1 @t29)) % 0.51/0.70 (define @t72 () (tptp.aElementOf0 @t29 @t68)) % 0.51/0.70 (define @t73 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.51/0.70 (define @t74 () (and @t67 @t6)) % 0.51/0.70 (define @t75 () (@var "W4" $$unsorted)) % 0.51/0.70 (define @t76 () (@list @t75)) % 0.51/0.70 (define @t77 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.51/0.70 (define @t78 () (tptp.aSubsetOf0 @t5 @t68)) % 0.51/0.70 (define @t79 () (tptp.sdtlcdtrc0 @t1 @t68)) % 0.51/0.70 (define @t80 () (tptp.szDzozmdt0 @t15)) % 0.51/0.70 (define @t81 () (tptp.aFunction0 @t15)) % 0.51/0.70 (define @t82 () (tptp.szDzizrdt0 @t1)) % 0.51/0.70 (define @t83 () (tptp.szDzozmdt0 tptp.xc)) % 0.51/0.70 (define @t84 () (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) % 0.51/0.70 (define @t85 () (@var "W5" $$unsorted)) % 0.51/0.70 (define @t86 () (tptp.szszuzczcdt0 tptp.xk)) % 0.51/0.70 (define @t87 () (tptp.aElementOf0 tptp.xk tptp.szNzAzT0)) % 0.51/0.70 (define @t88 () (tptp.sdtlpdtrp0 tptp.xN @t43)) % 0.51/0.70 (define @t89 () (tptp.sdtlpdtrp0 tptp.xN @t1)) % 0.51/0.70 (define @t90 () (tptp.szmzizndt0 @t89)) % 0.51/0.70 (define @t91 () (tptp.sdtmndt0 @t89 @t90)) % 0.51/0.70 (define @t92 () (and (tptp.aSubsetOf0 @t89 tptp.szNzAzT0) (tptp.isCountable0 @t89))) % 0.51/0.70 (define @t93 () (tptp.sdtlpdtrp0 tptp.xN @t5)) % 0.51/0.70 (define @t94 () (tptp.sdtpldt0 @t5 @t90)) % 0.51/0.70 (define @t95 () (tptp.slbdtsldtrb0 @t91 tptp.xk)) % 0.51/0.70 (define @t96 () (and @t19 (tptp.aElementOf0 @t5 @t95))) % 0.51/0.70 (define @t97 () (tptp.sdtlpdtrp0 tptp.xC @t1)) % 0.51/0.70 (define @t98 () (tptp.sdtlpdtrp0 @t97 @t5)) % 0.51/0.70 (define @t99 () (tptp.szDzozmdt0 @t97)) % 0.51/0.70 (define @t100 () (tptp.aElementOf0 @t5 tptp.xT)) % 0.51/0.70 (define @t101 () (tptp.slbdtsldtrb0 @t88 tptp.xk)) % 0.51/0.70 (define @t102 () (tptp.szDzozmdt0 tptp.xd)) % 0.51/0.70 (define @t103 () (tptp.szDzizrdt0 tptp.xd)) % 0.51/0.70 (define @t104 () (tptp.sdtlbdtrb0 tptp.xd @t103)) % 0.51/0.70 (define @t105 () (tptp.aSet0 tptp.xO)) % 0.51/0.70 (define @t106 () (tptp.szmzizndt0 tptp.xQ)) % 0.51/0.70 (define @t107 () (tptp.sbrdtbr0 tptp.xP)) % 0.51/0.70 (define @t108 () (tptp.aElementOf0 @t107 tptp.szNzAzT0)) % 0.51/0.70 (define @t109 () (tptp.sbrdtbr0 tptp.xQ)) % 0.51/0.70 (define @t110 () (tptp.szszuzczcdt0 @t107)) % 0.51/0.70 (define @t111 () (not @t46)) % 0.51/0.70 (define @t112 () (not @t48)) % 0.51/0.70 (define @t113 () (not @t44)) % 0.51/0.70 (define @t114 () (= tptp.xk @t107)) % 0.51/0.70 (define @t115 () (not (= @t86 @t110))) % 0.51/0.70 (define @t116 () (not @t108)) % 0.51/0.70 (define @t117 () (not @t87)) % 0.51/0.70 (define @t118 () (or @t117 @t116 @t115 @t114)) % 0.51/0.70 (assume @p1 (forall @t3 (=> @t2 true))) % 0.51/0.70 (assume @p2 (forall @t3 (=> @t4 true))) % 0.51/0.70 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.51/0.70 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.51/0.70 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.51/0.70 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.51/0.70 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.51/0.70 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.51/0.70 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.51/0.70 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.51/0.70 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.51/0.70 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.51/0.70 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.51/0.70 (assume @p14 (forall @t28 (=> (and @t2 @t19 @t27) (=> (and @t24 @t26) (tptp.aSubsetOf0 @t1 @t15))))) % 0.51/0.70 (assume @p15 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t35) (and @t27 (forall @t34 (= @t33 (and @t32 (or @t31 @t30)))))))))) % 0.51/0.70 (assume @p16 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t37) (and @t27 (forall @t34 (= @t33 (and @t32 @t31 (not @t30)))))))))) % 0.51/0.70 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t37 @t5) @t1)))))) % 0.51/0.70 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t38 @t1) @t5))))) % 0.51/0.70 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t38)))))) % 0.51/0.70 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t41)))))) % 0.51/0.70 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t38)))))) % 0.51/0.70 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t41)))))) % 0.51/0.70 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.51/0.70 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.51/0.70 (assume @p25 (forall @t3 (=> @t44 (and (tptp.aElementOf0 @t43 tptp.szNzAzT0) (not (= @t43 tptp.sz00)))))) % 0.51/0.70 (assume @p26 @t50) % 0.51/0.70 (assume @p27 (forall @t3 (=> @t44 (or @t51 (exists @t8 (and @t48 (= @t1 @t45))))))) % 0.51/0.70 (assume @p28 (forall @t3 (=> @t44 (not (= @t1 @t43))))) % 0.51/0.70 (assume @p29 (forall @t25 (=> @t49 (=> @t52 true)))) % 0.51/0.70 (assume @p30 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.51/0.70 (assume @p31 (forall @t3 (=> @t44 (not (tptp.sdtlseqdt0 @t43 tptp.sz00))))) % 0.51/0.70 (assume @p32 (forall @t25 (=> @t49 (= @t52 (tptp.sdtlseqdt0 @t43 @t45))))) % 0.51/0.70 (assume @p33 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t43)))) % 0.51/0.70 (assume @p34 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.51/0.70 (assume @p35 (forall @t25 (=> @t49 (=> (and @t52 @t53) @t23)))) % 0.51/0.70 (assume @p36 (forall @t28 (=> (and @t44 @t48 @t55) (=> (and @t52 @t54) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.51/0.70 (assume @p37 (forall @t25 (=> @t49 (or @t52 (tptp.sdtlseqdt0 @t45 @t1))))) % 0.51/0.70 (assume @p38 (forall @t25 (=> @t49 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.51/0.70 (assume @p39 (forall @t3 (=> @t44 (tptp.iLess0 @t1 @t43)))) % 0.51/0.70 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t56)))) % 0.51/0.70 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t56 tptp.szNzAzT0) @t9)))) % 0.51/0.70 (assume @p42 (forall @t3 (=> @t2 (= (= @t56 tptp.sz00) @t10)))) % 0.51/0.70 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t35) (tptp.szszuzczcdt0 @t56)))))))) % 0.51/0.70 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t37)) @t56)))))) % 0.51/0.70 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t56)))))) % 0.51/0.70 (assume @p46 (forall @t25 (=> @t57 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t56)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.51/0.70 (assume @p47 (forall @t3 (=> (and @t59 @t14) (forall @t8 (= (= @t5 @t58) (and @t7 (forall @t18 (=> @t16 @t54)))))))) % 0.51/0.70 (assume @p48 (forall @t3 (=> (and @t59 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.51/0.70 (assume @p49 (forall @t25 (=> (and @t59 @t61 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t58 @t5) (tptp.aElementOf0 @t60 @t1)) (= @t58 @t60))))) % 0.51/0.70 (assume @p50 (forall @t3 (=> @t44 (forall @t8 (= (= @t5 @t62) (and @t19 (forall @t18 (= @t17 (and @t55 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.51/0.70 (assume @p51 (forall @t3 (=> @t44 (tptp.isFinite0 @t62)))) % 0.51/0.70 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.51/0.70 (assume @p53 (forall @t25 (=> @t49 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t45)) (or (tptp.aElementOf0 @t1 @t63) @t23))))) % 0.51/0.70 (assume @p54 (forall @t25 (=> @t49 (= @t52 (tptp.aSubsetOf0 @t62 @t63))))) % 0.51/0.70 (assume @p55 (forall @t3 (=> (and @t59 @t9) (exists @t8 (and @t48 (tptp.aSubsetOf0 @t1 @t63)))))) % 0.51/0.70 (assume @p56 (forall @t3 (=> @t44 (= (tptp.sbrdtbr0 @t62) @t1)))) % 0.51/0.70 (assume @p57 (forall @t25 (=> @t57 (forall @t18 (= (= @t15 @t65) (and @t27 (forall @t34 (= @t33 (and @t64 (= (tptp.sbrdtbr0 @t29) @t5)))))))))) % 0.51/0.70 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t48 (tptp.isFinite0 @t65)))))) % 0.51/0.70 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t48 (not (= @t65 tptp.slcrc0))))))) % 0.51/0.70 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t48 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t65)))))) % 0.51/0.70 (assume @p61 (forall @t3 (=> @t44 (forall (@list @t5 @t15) (=> (and @t19 @t27 (not @t51)) (=> (and (tptp.aSubsetOf0 @t66 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t66 tptp.slcrc0))) @t26)))))) % 0.51/0.70 (assume @p62 (forall @t25 (=> @t57 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t65) (tptp.isFinite0 @t15)) (exists @t34 (and @t64 (tptp.isFinite0 @t29) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t29 @t5))))))))) % 0.51/0.70 (assume @p63 (forall @t3 (=> @t67 true))) % 0.51/0.70 (assume @p64 (forall @t3 (=> @t67 (tptp.aSet0 @t68)))) % 0.51/0.70 (assume @p65 (forall @t3 (=> @t67 (forall @t8 (=> @t70 (tptp.aElement0 @t69)))))) % 0.51/0.70 (assume @p66 (forall @t25 (=> @t74 (forall @t18 (= (= @t15 @t73) (and @t27 (forall @t34 (= @t33 (and @t72 (= @t71 @t5)))))))))) % 0.51/0.70 (assume @p67 (forall @t25 (=> @t74 (tptp.aSubsetOf0 @t73 @t68)))) % 0.51/0.70 (assume @p68 (forall @t3 (=> @t67 (forall @t8 (=> @t78 (forall @t18 (= (= @t15 @t77) (and @t27 (forall @t34 (= @t33 (exists @t76 (and (tptp.aElementOf0 @t75 @t5) (= (tptp.sdtlpdtrp0 @t1 @t75) @t29))))))))))))) % 0.51/0.70 (assume @p69 (forall @t3 (=> @t67 (forall @t8 (=> @t70 (tptp.aElementOf0 @t69 @t79)))))) % 0.51/0.70 (assume @p70 (forall @t3 (=> @t67 (forall @t8 (=> @t78 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t81 (= @t80 @t5) (forall @t34 (=> (tptp.aElementOf0 @t29 @t5) (= (tptp.sdtlpdtrp0 @t15 @t29) @t71))))))))))) % 0.51/0.70 (assume @p71 (forall @t3 (=> @t67 (forall @t8 (=> (and @t78 @t39) (=> (forall (@list @t15 @t29) (=> (and (tptp.aElementOf0 @t15 @t68) @t72 (not (= @t15 @t29))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t71)))) (tptp.isCountable0 @t77))))))) % 0.51/0.70 (assume @p72 (forall @t3 (=> @t67 (=> (and (tptp.isCountable0 @t68) (tptp.isFinite0 @t79)) (and (tptp.aElement0 @t82) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t82))))))) % 0.51/0.70 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.51/0.70 (assume @p74 (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.51/0.70 (assume @p75 (and (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.51/0.70 (assume @p76 (and (tptp.aFunction0 tptp.xc) (= @t83 @t84) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xc @t83) tptp.xT))) % 0.51/0.70 (assume @p77 (forall @t3 (=> @t44 (forall @t8 (=> (and @t61 @t39) (forall @t18 (=> (and @t81 (= @t80 @t66) (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t15 @t80) tptp.xT)) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t34 (and (tptp.aElementOf0 @t29 tptp.xT) (exists @t76 (and (tptp.aSubsetOf0 @t75 @t5) (tptp.isCountable0 @t75) (forall (@list @t85) (=> (tptp.aElementOf0 @t85 (tptp.slbdtsldtrb0 @t75 @t1)) (= (tptp.sdtlpdtrp0 @t15 @t85) @t29))))))))))))))) % 0.51/0.70 (assume @p78 (not (= tptp.xK tptp.sz00))) % 0.51/0.70 (assume @p79 (and @t87 (= @t86 tptp.xK))) % 0.51/0.70 (assume @p80 (and (tptp.aFunction0 tptp.xN) (= (tptp.szDzozmdt0 tptp.xN) tptp.szNzAzT0) (= (tptp.sdtlpdtrp0 tptp.xN tptp.sz00) tptp.xS) (forall @t3 (=> @t44 (=> @t92 (and (tptp.aSubsetOf0 @t88 @t91) (tptp.isCountable0 @t88))))))) % 0.51/0.70 (assume @p81 (forall @t3 (=> @t44 @t92))) % 0.51/0.70 (assume @p82 (forall @t25 (=> @t49 (=> @t53 (tptp.aSubsetOf0 @t89 @t93))))) % 0.51/0.70 (assume @p83 (forall @t25 (=> (and @t44 @t48 (not @t23)) (not (= @t90 (tptp.szmzizndt0 @t93)))))) % 0.51/0.70 (assume @p84 (forall @t3 (=> @t44 (forall @t8 (=> @t96 (tptp.aElementOf0 @t94 @t84)))))) % 0.51/0.70 (assume @p85 (and (tptp.aFunction0 tptp.xC) (= (tptp.szDzozmdt0 tptp.xC) tptp.szNzAzT0) (forall @t3 (=> @t44 (and (tptp.aFunction0 @t97) (= @t99 @t95) (forall @t8 (=> @t96 (= @t98 (tptp.sdtlpdtrp0 tptp.xc @t94))))))))) % 0.51/0.70 (assume @p86 (forall @t3 (=> @t44 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 @t97 @t99) tptp.xT)))) % 0.51/0.70 (assume @p87 (forall @t3 (=> @t44 (forall @t8 (=> (and (tptp.aSubsetOf0 @t5 @t91) @t39) (forall @t18 (=> (and @t27 (tptp.aElementOf0 @t15 (tptp.slbdtsldtrb0 @t5 tptp.xk))) (tptp.aElementOf0 @t15 @t95)))))))) % 0.51/0.70 (assume @p88 (forall @t3 (=> @t44 (exists @t8 (and @t100 (exists @t18 (and (tptp.aSubsetOf0 @t15 @t91) (tptp.isCountable0 @t15) (forall @t34 (=> (and (tptp.aSet0 @t29) (tptp.aElementOf0 @t29 (tptp.slbdtsldtrb0 @t15 tptp.xk))) (= (tptp.sdtlpdtrp0 @t97 @t29) @t5)))))))))) % 0.51/0.70 (assume @p89 (forall @t3 (=> @t44 (exists @t8 (and @t100 (forall @t18 (=> (and @t27 (tptp.aElementOf0 @t15 @t101)) (= (tptp.sdtlpdtrp0 @t97 @t15) @t5)))))))) % 0.51/0.70 (assume @p90 (and (tptp.aFunction0 tptp.xe) (= (tptp.szDzozmdt0 tptp.xe) tptp.szNzAzT0) (forall @t3 (=> @t44 (= (tptp.sdtlpdtrp0 tptp.xe @t1) @t90))))) % 0.51/0.70 (assume @p91 (and (tptp.aFunction0 tptp.xd) (= @t102 tptp.szNzAzT0) (forall @t3 (=> @t44 (forall @t8 (=> (and @t19 (tptp.aElementOf0 @t5 @t101)) (= (tptp.sdtlpdtrp0 tptp.xd @t1) @t98))))))) % 0.51/0.70 (assume @p92 (tptp.aSubsetOf0 (tptp.sdtlcdtrc0 tptp.xd @t102) tptp.xT)) % 0.51/0.70 (assume @p93 (and (tptp.aElementOf0 @t103 tptp.xT) (tptp.isCountable0 @t104))) % 0.51/0.70 (assume @p94 (and @t105 (= tptp.xO (tptp.sdtlcdtrc0 tptp.xe @t104)))) % 0.51/0.70 (assume @p95 (and @t105 (tptp.isCountable0 tptp.xO))) % 0.51/0.70 (assume @p96 (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xO) (exists @t8 (and @t48 (tptp.aElementOf0 @t5 @t104) (= (tptp.sdtlpdtrp0 tptp.xe @t5) @t1)))))) % 0.51/0.70 (assume @p97 (tptp.aSubsetOf0 tptp.xO tptp.xS)) % 0.51/0.70 (assume @p98 (tptp.aElementOf0 tptp.xQ (tptp.slbdtsldtrb0 tptp.xO tptp.xK))) % 0.51/0.70 (assume @p99 (and (tptp.aSubsetOf0 tptp.xQ tptp.xO) (not (= tptp.xQ tptp.slcrc0)))) % 0.51/0.70 (assume @p100 (tptp.aSubsetOf0 tptp.xQ tptp.szNzAzT0)) % 0.51/0.70 (assume @p101 (tptp.aElementOf0 tptp.xQ @t83)) % 0.51/0.70 (assume @p102 (= tptp.xp @t106)) % 0.51/0.70 (assume @p103 (and (tptp.aSet0 tptp.xP) (= tptp.xP (tptp.sdtmndt0 tptp.xQ @t106)))) % 0.51/0.70 (assume @p104 (tptp.aElementOf0 tptp.xp tptp.xQ)) % 0.51/0.70 (assume @p105 (tptp.aElementOf0 tptp.xp tptp.xO)) % 0.51/0.70 (assume @p106 (tptp.aSubsetOf0 tptp.xP tptp.xQ)) % 0.51/0.70 (assume @p107 (tptp.aSubsetOf0 tptp.xP tptp.xO)) % 0.51/0.70 (assume @p108 (and (= @t109 @t86) (= @t110 @t109) @t108)) % 0.51/0.70 (assume @p109 (not (= @t107 tptp.xk))) % 0.51/0.70 (assume @p110 true) % 0.51/0.70 (step @p111 :rule evaluate :args ((= true false))) % 0.51/0.70 (step @p112 :rule aci_norm :args ((= (or (or @t113 @t112) (or @t111 @t23)) (or @t113 @t112 @t111 @t23)))) % 0.51/0.70 (step @p113 :rule bool-impl-elim :args (@t46 @t23)) % 0.51/0.70 (step @p114 :rule bool-and-de-morgan :args (@t44 @t48 true)) % 0.51/0.70 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or (not @t49) @t47))) % 0.51/0.70 (step @p116 :rule trans :premises (@p115 @p112)) % 0.51/0.70 (step @p117 :rule bool-impl-elim :args (@t49 @t47)) % 0.51/0.70 (step @p118 :rule trans :premises (@p117 @p116)) % 0.51/0.70 (step @p119 :rule cong :premises (@p118) :args (@t50)) % 0.51/0.70 (step @p120 :rule eq_resolve :premises (@p26 @p119)) % 0.51/0.70 (step @p121 :rule instantiate :premises (@p120) :args ((@list tptp.xk @t107))) % 0.51/0.70 (step @p122 :rule and_elim :premises (@p108) :args (2)) % 0.51/0.70 (step @p123 :rule and_elim :premises (@p79) :args (0)) % 0.51/0.70 (step @p124 :rule symm :premises (@p109)) % 0.51/0.70 (step @p125 :rule cnf_or_pos :args (@t118)) % 0.51/0.70 (step @p126 :rule reordering :premises (@p125) :args ((or @t114 @t117 @t116 @t115 (not @t118)))) % 0.51/0.70 (step @p127 :rule chain_m_resolution :premises (@p126 @p124 @p123 @p122 @p121) :args (@t115 (@list true false false false) (@list @t114 @t87 @t108 @t118))) % 0.51/0.70 (step @p128 :rule false_intro :premises (@p127)) % 0.51/0.70 (step @p129 :rule and_elim :premises (@p108) :args (1)) % 0.51/0.70 (step @p130 :rule symm :premises (@p129)) % 0.51/0.70 (step @p131 :rule and_elim :premises (@p108) :args (0)) % 0.51/0.70 (step @p132 :rule symm :premises (@p131)) % 0.51/0.70 (step @p133 :rule trans :premises (@p132 @p130)) % 0.51/0.70 (step @p134 :rule true_intro :premises (@p133)) % 0.51/0.70 (step @p135 :rule symm :premises (@p134)) % 0.51/0.70 (step @p136 :rule trans :premises (@p135 @p128)) % 0.51/0.70 (step @p137 false :rule eq_resolve :premises (@p136 @p111)) % 0.51/0.70 ) % 0.51/0.70 % SZS output end Proof % 0.51/0.70 % cvc5 exiting %------------------------------------------------------------------------------