%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM568+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 : n027.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 08:39:52 AM UTC 2026 % Result : Theorem 0.44s 0.66s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM568+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 % 0.16/0.34 % Computer : n027.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 11:30:36 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.66 % SZS status Theorem % 0.44/0.66 % SZS output start Proof % 0.44/0.66 ( % 0.44/0.66 (declare-sort $$unsorted 0) % 0.44/0.66 (declare-const tptp.sz00 $$unsorted) % 0.44/0.66 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.szNzAzT0 $$unsorted) % 0.44/0.66 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.sdtexdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.szDzizrdt0 (-> $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.xK $$unsorted) % 0.44/0.66 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.xT $$unsorted) % 0.44/0.66 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.xS $$unsorted) % 0.44/0.66 (declare-const tptp.xc $$unsorted) % 0.44/0.66 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.slcrc0 $$unsorted) % 0.44/0.66 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (define @t1 () (@var "W0" $$unsorted)) % 0.44/0.66 (define @t2 () (tptp.aSet0 @t1)) % 0.44/0.66 (define @t3 () (@list @t1)) % 0.44/0.66 (define @t4 () (tptp.aElement0 @t1)) % 0.44/0.66 (define @t5 () (@var "W1" $$unsorted)) % 0.44/0.66 (define @t6 () (tptp.aElement0 @t5)) % 0.44/0.66 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.44/0.66 (define @t8 () (@list @t5)) % 0.44/0.66 (define @t9 () (tptp.isFinite0 @t1)) % 0.44/0.66 (define @t10 () (= @t1 tptp.slcrc0)) % 0.44/0.66 (define @t11 () (tptp.isCountable0 @t1)) % 0.44/0.66 (define @t12 () (not @t9)) % 0.44/0.66 (define @t13 () (and @t2 @t11)) % 0.44/0.66 (define @t14 () (not @t10)) % 0.44/0.66 (define @t15 () (@var "W2" $$unsorted)) % 0.44/0.66 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.44/0.66 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.44/0.66 (define @t18 () (@list @t15)) % 0.44/0.66 (define @t19 () (tptp.aSet0 @t5)) % 0.44/0.66 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.44/0.66 (define @t21 () (tptp.isFinite0 @t5)) % 0.44/0.66 (define @t22 () (and @t2 @t9)) % 0.44/0.66 (define @t23 () (= @t1 @t5)) % 0.44/0.66 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.44/0.66 (define @t25 () (@list @t1 @t5)) % 0.44/0.66 (define @t26 () (tptp.aSubsetOf0 @t5 @t15)) % 0.44/0.66 (define @t27 () (tptp.aSet0 @t15)) % 0.44/0.66 (define @t28 () (@list @t1 @t5 @t15)) % 0.44/0.66 (define @t29 () (@var "W3" $$unsorted)) % 0.44/0.66 (define @t30 () (= @t29 @t5)) % 0.44/0.66 (define @t31 () (tptp.aElementOf0 @t29 @t1)) % 0.44/0.66 (define @t32 () (tptp.aElement0 @t29)) % 0.44/0.66 (define @t33 () (tptp.aElementOf0 @t29 @t15)) % 0.44/0.66 (define @t34 () (@list @t29)) % 0.44/0.66 (define @t35 () (tptp.sdtpldt0 @t1 @t5)) % 0.44/0.66 (define @t36 () (and @t2 @t6)) % 0.44/0.66 (define @t37 () (tptp.sdtmndt0 @t1 @t5)) % 0.44/0.66 (define @t38 () (tptp.sdtpldt0 @t5 @t1)) % 0.44/0.66 (define @t39 () (tptp.isCountable0 @t5)) % 0.44/0.66 (define @t40 () (and @t19 @t39)) % 0.44/0.66 (define @t41 () (tptp.sdtmndt0 @t5 @t1)) % 0.44/0.66 (define @t42 () (and @t19 @t21)) % 0.44/0.66 (define @t43 () (tptp.szszuzczcdt0 @t1)) % 0.44/0.66 (define @t44 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.44/0.66 (define @t45 () (tptp.szszuzczcdt0 @t5)) % 0.44/0.66 (define @t46 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.44/0.66 (define @t47 () (and @t44 @t46)) % 0.44/0.66 (define @t48 () (= @t1 @t45)) % 0.44/0.66 (define @t49 () (and @t46 @t48)) % 0.44/0.66 (define @t50 () (exists @t8 @t49)) % 0.44/0.66 (define @t51 () (= @t1 tptp.sz00)) % 0.44/0.66 (define @t52 () (or @t51 @t50)) % 0.44/0.66 (define @t53 () (=> @t44 @t52)) % 0.44/0.66 (define @t54 () (forall @t3 @t53)) % 0.44/0.66 (define @t55 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.44/0.66 (define @t56 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.44/0.66 (define @t57 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.44/0.66 (define @t58 () (tptp.sbrdtbr0 @t1)) % 0.44/0.66 (define @t59 () (and @t2 @t46)) % 0.44/0.66 (define @t60 () (tptp.szmzizndt0 @t1)) % 0.44/0.66 (define @t61 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.44/0.66 (define @t62 () (tptp.szmzizndt0 @t5)) % 0.44/0.66 (define @t63 () (tptp.aSubsetOf0 @t5 tptp.szNzAzT0)) % 0.44/0.66 (define @t64 () (tptp.slbdtrb0 @t1)) % 0.44/0.66 (define @t65 () (tptp.slbdtrb0 @t5)) % 0.44/0.66 (define @t66 () (tptp.sbrdtbr0 @t29)) % 0.44/0.66 (define @t67 () (tptp.aSubsetOf0 @t29 @t1)) % 0.44/0.66 (define @t68 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.44/0.66 (define @t69 () (tptp.slbdtsldtrb0 @t5 @t1)) % 0.44/0.66 (define @t70 () (tptp.aFunction0 @t1)) % 0.44/0.66 (define @t71 () (tptp.szDzozmdt0 @t1)) % 0.44/0.66 (define @t72 () (tptp.sdtlpdtrp0 @t1 @t5)) % 0.44/0.66 (define @t73 () (tptp.aElementOf0 @t5 @t71)) % 0.44/0.66 (define @t74 () (tptp.sdtlpdtrp0 @t1 @t29)) % 0.44/0.66 (define @t75 () (tptp.aElementOf0 @t29 @t71)) % 0.44/0.66 (define @t76 () (tptp.sdtlbdtrb0 @t1 @t5)) % 0.44/0.66 (define @t77 () (and @t70 @t6)) % 0.44/0.66 (define @t78 () (@var "W4" $$unsorted)) % 0.44/0.66 (define @t79 () (tptp.aElementOf0 @t78 @t5)) % 0.44/0.66 (define @t80 () (@list @t78)) % 0.44/0.66 (define @t81 () (tptp.sdtlcdtrc0 @t1 @t5)) % 0.44/0.66 (define @t82 () (tptp.aSubsetOf0 @t5 @t71)) % 0.44/0.66 (define @t83 () (tptp.sdtlcdtrc0 @t1 @t71)) % 0.44/0.66 (define @t84 () (tptp.szDzozmdt0 @t15)) % 0.44/0.66 (define @t85 () (tptp.aFunction0 @t15)) % 0.44/0.66 (define @t86 () (tptp.szDzizrdt0 @t1)) % 0.44/0.66 (define @t87 () (tptp.aElementOf0 tptp.xK tptp.szNzAzT0)) % 0.44/0.66 (define @t88 () (tptp.szDzozmdt0 tptp.xc)) % 0.44/0.66 (define @t89 () (tptp.sdtlcdtrc0 tptp.xc @t88)) % 0.44/0.66 (define @t90 () (tptp.aElementOf0 @t1 @t89)) % 0.44/0.66 (define @t91 () (tptp.aElementOf0 @t1 @t88)) % 0.44/0.66 (define @t92 () (= @t58 tptp.xK)) % 0.44/0.66 (define @t93 () (tptp.aSubsetOf0 @t1 tptp.xS)) % 0.44/0.66 (define @t94 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xS)))) % 0.44/0.66 (define @t95 () (@var "W5" $$unsorted)) % 0.44/0.66 (define @t96 () (@var "W6" $$unsorted)) % 0.44/0.66 (define @t97 () (@list @t95)) % 0.44/0.66 (define @t98 () (tptp.aElementOf0 @t29 tptp.xT)) % 0.44/0.66 (define @t99 () (tptp.sdtlcdtrc0 @t15 @t84)) % 0.44/0.66 (define @t100 () (tptp.aElementOf0 @t29 @t99)) % 0.44/0.66 (define @t101 () (tptp.aElementOf0 @t29 @t84)) % 0.44/0.66 (define @t102 () (= @t66 @t1)) % 0.44/0.66 (define @t103 () (tptp.aSubsetOf0 @t29 @t5)) % 0.44/0.66 (define @t104 () (forall @t80 (=> (tptp.aElementOf0 @t78 @t29) @t79))) % 0.44/0.66 (define @t105 () (tptp.aSet0 @t29)) % 0.44/0.66 (define @t106 () (= tptp.xK tptp.sz00)) % 0.44/0.66 (define @t107 () (= @t43 tptp.xK)) % 0.44/0.66 (define @t108 () (and @t44 @t107)) % 0.44/0.66 (define @t109 () (exists @t3 @t108)) % 0.44/0.66 (define @t110 () (not @t109)) % 0.44/0.66 (define @t111 () (not @t44)) % 0.44/0.66 (define @t112 () (forall @t3 (or @t111 (not @t107)))) % 0.44/0.66 (define @t113 () (forall @t3 (not @t108))) % 0.44/0.66 (define @t114 () (not @t113)) % 0.44/0.66 (define @t115 () (not @t46)) % 0.44/0.66 (define @t116 () (forall @t8 (or @t115 (not (= @t45 tptp.xK))))) % 0.44/0.66 (define @t117 () (@list false)) % 0.44/0.66 (define @t118 () (not (forall @t8 (or @t115 (not @t48))))) % 0.44/0.66 (define @t119 () (or @t111 @t51 @t118)) % 0.44/0.66 (define @t120 () (or @t51 @t118)) % 0.44/0.66 (define @t121 () (forall @t8 (not @t49))) % 0.44/0.66 (define @t122 () (not @t121)) % 0.44/0.66 (define @t123 () (not (= tptp.xK @t45))) % 0.44/0.66 (define @t124 () (or @t115 @t123)) % 0.44/0.66 (define @t125 () (forall @t8 @t124)) % 0.44/0.66 (define @t126 () (not @t125)) % 0.44/0.66 (define @t127 () (not @t87)) % 0.44/0.66 (define @t128 () (or @t127 @t106 @t126)) % 0.44/0.66 (define @t129 () (forall @t3 @t119)) % 0.44/0.66 (define @t130 () (not @t116)) % 0.44/0.66 (define @t131 () (= tptp.sz00 tptp.xK)) % 0.44/0.66 (define @t132 () (or @t127 @t131 @t130)) % 0.44/0.66 (assume @p1 (forall @t3 (=> @t2 true))) % 0.44/0.66 (assume @p2 (forall @t3 (=> @t4 true))) % 0.44/0.66 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.44/0.66 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.44/0.66 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.44/0.66 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.44/0.66 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.44/0.66 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.44/0.66 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.44/0.66 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.44/0.66 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.44/0.66 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.44/0.66 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.44/0.66 (assume @p14 (forall @t28 (=> (and @t2 @t19 @t27) (=> (and @t24 @t26) (tptp.aSubsetOf0 @t1 @t15))))) % 0.44/0.66 (assume @p15 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t35) (and @t27 (forall @t34 (= @t33 (and @t32 (or @t31 @t30)))))))))) % 0.44/0.66 (assume @p16 (forall @t25 (=> @t36 (forall @t18 (= (= @t15 @t37) (and @t27 (forall @t34 (= @t33 (and @t32 @t31 (not @t30)))))))))) % 0.44/0.66 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t37 @t5) @t1)))))) % 0.44/0.66 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t38 @t1) @t5))))) % 0.44/0.66 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t38)))))) % 0.44/0.66 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isCountable0 @t41)))))) % 0.44/0.66 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t38)))))) % 0.44/0.66 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t42 (tptp.isFinite0 @t41)))))) % 0.44/0.66 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.44/0.66 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.44/0.66 (assume @p25 (forall @t3 (=> @t44 (and (tptp.aElementOf0 @t43 tptp.szNzAzT0) (not (= @t43 tptp.sz00)))))) % 0.44/0.66 (assume @p26 (forall @t25 (=> @t47 (=> (= @t43 @t45) @t23)))) % 0.44/0.66 (assume @p27 @t54) % 0.44/0.66 (assume @p28 (forall @t3 (=> @t44 (not (= @t1 @t43))))) % 0.44/0.66 (assume @p29 (forall @t25 (=> @t47 (=> @t55 true)))) % 0.44/0.66 (assume @p30 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.44/0.66 (assume @p31 (forall @t3 (=> @t44 (not (tptp.sdtlseqdt0 @t43 tptp.sz00))))) % 0.44/0.66 (assume @p32 (forall @t25 (=> @t47 (= @t55 (tptp.sdtlseqdt0 @t43 @t45))))) % 0.44/0.66 (assume @p33 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t43)))) % 0.44/0.66 (assume @p34 (forall @t3 (=> @t44 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.44/0.66 (assume @p35 (forall @t25 (=> @t47 (=> (and @t55 (tptp.sdtlseqdt0 @t5 @t1)) @t23)))) % 0.44/0.66 (assume @p36 (forall @t28 (=> (and @t44 @t46 @t57) (=> (and @t55 @t56) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.44/0.66 (assume @p37 (forall @t25 (=> @t47 (or @t55 (tptp.sdtlseqdt0 @t45 @t1))))) % 0.44/0.66 (assume @p38 (forall @t25 (=> @t47 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.44/0.66 (assume @p39 (forall @t3 (=> @t44 (tptp.iLess0 @t1 @t43)))) % 0.44/0.66 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t58)))) % 0.44/0.66 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t58 tptp.szNzAzT0) @t9)))) % 0.44/0.66 (assume @p42 (forall @t3 (=> @t2 (= (= @t58 tptp.sz00) @t10)))) % 0.44/0.66 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t35) (tptp.szszuzczcdt0 @t58)))))))) % 0.44/0.66 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t37)) @t58)))))) % 0.44/0.66 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t58)))))) % 0.44/0.66 (assume @p46 (forall @t25 (=> @t59 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t58)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.44/0.66 (assume @p47 (forall @t3 (=> (and @t61 @t14) (forall @t8 (= (= @t5 @t60) (and @t7 (forall @t18 (=> @t16 @t56)))))))) % 0.44/0.66 (assume @p48 (forall @t3 (=> (and @t61 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.44/0.66 (assume @p49 (forall @t25 (=> (and @t61 @t63 @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t60 @t5) (tptp.aElementOf0 @t62 @t1)) (= @t60 @t62))))) % 0.44/0.66 (assume @p50 (forall @t3 (=> @t44 (forall @t8 (= (= @t5 @t64) (and @t19 (forall @t18 (= @t17 (and @t57 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.44/0.66 (assume @p51 (forall @t3 (=> @t44 (tptp.isFinite0 @t64)))) % 0.44/0.66 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.44/0.66 (assume @p53 (forall @t25 (=> @t47 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t45)) (or (tptp.aElementOf0 @t1 @t65) @t23))))) % 0.44/0.66 (assume @p54 (forall @t25 (=> @t47 (= @t55 (tptp.aSubsetOf0 @t64 @t65))))) % 0.44/0.66 (assume @p55 (forall @t3 (=> (and @t61 @t9) (exists @t8 (and @t46 (tptp.aSubsetOf0 @t1 @t65)))))) % 0.44/0.66 (assume @p56 (forall @t3 (=> @t44 (= (tptp.sbrdtbr0 @t64) @t1)))) % 0.44/0.66 (assume @p57 (forall @t25 (=> @t59 (forall @t18 (= (= @t15 @t68) (and @t27 (forall @t34 (= @t33 (and @t67 (= @t66 @t5)))))))))) % 0.44/0.66 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t46 (tptp.isFinite0 @t68)))))) % 0.44/0.66 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t46 (not (= @t68 tptp.slcrc0))))))) % 0.44/0.66 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t46 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t68)))))) % 0.44/0.66 (assume @p61 (forall @t3 (=> @t44 (forall (@list @t5 @t15) (=> (and @t19 @t27 (not @t51)) (=> (and (tptp.aSubsetOf0 @t69 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t69 tptp.slcrc0))) @t26)))))) % 0.44/0.66 (assume @p62 (forall @t25 (=> @t59 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t68) (tptp.isFinite0 @t15)) (exists @t34 (and @t67 (tptp.isFinite0 @t29) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t29 @t5))))))))) % 0.44/0.66 (assume @p63 (forall @t3 (=> @t70 true))) % 0.44/0.66 (assume @p64 (forall @t3 (=> @t70 (tptp.aSet0 @t71)))) % 0.44/0.66 (assume @p65 (forall @t3 (=> @t70 (forall @t8 (=> @t73 (tptp.aElement0 @t72)))))) % 0.44/0.66 (assume @p66 (forall @t25 (=> @t77 (forall @t18 (= (= @t15 @t76) (and @t27 (forall @t34 (= @t33 (and @t75 (= @t74 @t5)))))))))) % 0.44/0.66 (assume @p67 (forall @t25 (=> @t77 (tptp.aSubsetOf0 @t76 @t71)))) % 0.44/0.66 (assume @p68 (forall @t3 (=> @t70 (forall @t8 (=> @t82 (forall @t18 (= (= @t15 @t81) (and @t27 (forall @t34 (= @t33 (exists @t80 (and @t79 (= (tptp.sdtlpdtrp0 @t1 @t78) @t29))))))))))))) % 0.44/0.66 (assume @p69 (forall @t3 (=> @t70 (forall @t8 (=> @t73 (tptp.aElementOf0 @t72 @t83)))))) % 0.44/0.66 (assume @p70 (forall @t3 (=> @t70 (forall @t8 (=> @t82 (forall @t18 (= (= @t15 (tptp.sdtexdt0 @t1 @t5)) (and @t85 (= @t84 @t5) (forall @t34 (=> (tptp.aElementOf0 @t29 @t5) (= (tptp.sdtlpdtrp0 @t15 @t29) @t74))))))))))) % 0.44/0.66 (assume @p71 (forall @t3 (=> @t70 (forall @t8 (=> (and @t82 @t39) (=> (forall (@list @t15 @t29) (=> (and (tptp.aElementOf0 @t15 @t71) @t75 (not (= @t15 @t29))) (not (= (tptp.sdtlpdtrp0 @t1 @t15) @t74)))) (tptp.isCountable0 @t81))))))) % 0.44/0.66 (assume @p72 (forall @t3 (=> @t70 (=> (and (tptp.isCountable0 @t71) (tptp.isFinite0 @t83)) (and (tptp.aElement0 @t86) (tptp.isCountable0 (tptp.sdtlbdtrb0 @t1 @t86))))))) % 0.44/0.66 (assume @p73 (and (tptp.aSet0 tptp.xT) (tptp.isFinite0 tptp.xT))) % 0.44/0.66 (assume @p74 @t87) % 0.44/0.66 (assume @p75 (and (tptp.aSet0 tptp.xS) (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xS) @t44)) (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0) (tptp.isCountable0 tptp.xS))) % 0.44/0.66 (assume @p76 (and (tptp.aFunction0 tptp.xc) (forall @t3 (and (=> @t91 (and @t2 @t94 @t93 @t92)) (=> (and (or (and @t2 @t94) @t93) @t92) @t91))) (= @t88 (tptp.slbdtsldtrb0 tptp.xS tptp.xK)) (tptp.aSet0 @t89) (forall @t3 (= @t90 (exists @t8 (and (tptp.aElementOf0 @t5 @t88) (= (tptp.sdtlpdtrp0 tptp.xc @t5) @t1))))) (forall @t3 (=> @t90 (tptp.aElementOf0 @t1 tptp.xT))) (tptp.aSubsetOf0 @t89 tptp.xT))) % 0.44/0.66 (assume @p77 (forall @t3 (=> @t44 (forall @t8 (=> (and (or (and @t19 (forall @t18 (=> @t17 @t57))) @t63) @t39) (forall @t18 (=> (and @t85 (or (forall @t34 (and (=> @t101 (and (or (and @t105 @t104) @t103) @t102)) (=> (and @t105 @t104 @t103 @t102) @t101))) (= @t84 @t69)) (=> (and (tptp.aSet0 @t99) (forall @t34 (= @t100 (exists @t80 (and (tptp.aElementOf0 @t78 @t84) (= (tptp.sdtlpdtrp0 @t15 @t78) @t29)))))) (or (forall @t34 (=> @t100 @t98)) (tptp.aSubsetOf0 @t99 tptp.xT)))) (=> (tptp.iLess0 @t1 tptp.xK) (exists @t34 (and @t98 (exists @t80 (and (tptp.aSet0 @t78) (forall @t97 (=> (tptp.aElementOf0 @t95 @t78) (tptp.aElementOf0 @t95 @t5))) (tptp.aSubsetOf0 @t78 @t5) (tptp.isCountable0 @t78) (forall @t97 (=> (or (and (or (and (tptp.aSet0 @t95) (forall (@list @t96) (=> (tptp.aElementOf0 @t96 @t95) (tptp.aElementOf0 @t96 @t78)))) (tptp.aSubsetOf0 @t95 @t78)) (= (tptp.sbrdtbr0 @t95) @t1)) (tptp.aElementOf0 @t95 (tptp.slbdtsldtrb0 @t78 @t1))) (= (tptp.sdtlpdtrp0 @t15 @t95) @t29))))))))))))))) % 0.44/0.66 (assume @p78 (not @t106)) % 0.44/0.66 (assume @p79 @t110) % 0.44/0.66 (assume @p80 true) % 0.44/0.66 (step @p81 :rule symm :premises (@p78)) % 0.44/0.66 (step @p82 :rule bool-double-not-elim :args (@t112)) % 0.44/0.66 (step @p83 :rule bool-and-de-morgan :args (@t44 @t107 true)) % 0.44/0.66 (step @p84 :rule cong :premises (@p83) :args (@t113)) % 0.44/0.66 (step @p85 :rule cong :premises (@p84) :args (@t114)) % 0.44/0.66 (step @p86 :rule exists-elim :args ((= @t109 @t114))) % 0.44/0.66 (step @p87 :rule trans :premises (@p86 @p85)) % 0.44/0.66 (step @p88 :rule cong :premises (@p87) :args (@t110)) % 0.44/0.66 (step @p89 :rule trans :premises (@p88 @p82)) % 0.44/0.66 (step @p90 :rule eq_resolve :premises (@p79 @p89)) % 0.44/0.66 (step @p91 :rule alpha_equiv :args (@t112 (@list @t1) (@list @t5))) % 0.44/0.66 (step @p92 :rule equiv_elim1 :premises (@p91)) % 0.44/0.66 (step @p93 :rule chain_m_resolution :premises (@p92 @p90) :args (@t116 @t117 (@list @t112))) % 0.44/0.66 (step @p94 :rule aci_norm :args ((= (or @t111 @t120) @t119))) % 0.44/0.66 (step @p95 :rule bool-impl-elim :args (@t44 @t120)) % 0.44/0.66 (step @p96 :rule trans :premises (@p95 @p94)) % 0.44/0.66 (step @p97 :rule cong :premises (@p96) :args ((forall @t3 (=> @t44 @t120)))) % 0.44/0.66 (step @p98 :rule bool-and-de-morgan :args (@t46 @t48 true)) % 0.44/0.66 (step @p99 :rule cong :premises (@p98) :args (@t121)) % 0.44/0.66 (step @p100 :rule cong :premises (@p99) :args (@t122)) % 0.44/0.66 (step @p101 :rule exists-elim :args ((= @t50 @t122))) % 0.44/0.66 (step @p102 :rule trans :premises (@p101 @p100)) % 0.44/0.66 (step @p103 :rule refl :args (@t51)) % 0.44/0.66 (step @p104 :rule nary_cong :premises (@p103 @p102) :args (@t52)) % 0.44/0.66 (step @p105 :rule refl :args (@t44)) % 0.44/0.66 (step @p106 :rule cong :premises (@p105 @p104) :args (@t53)) % 0.44/0.66 (step @p107 :rule cong :premises (@p106) :args (@t54)) % 0.44/0.66 (step @p108 :rule trans :premises (@p107 @p97)) % 0.44/0.66 (step @p109 :rule eq_resolve :premises (@p27 @p108)) % 0.44/0.66 (step @p110 :rule eq-symm :args (tptp.xK @t45)) % 0.44/0.66 (step @p111 :rule cong :premises (@p110) :args (@t123)) % 0.44/0.66 (step @p112 :rule refl :args (@t115)) % 0.44/0.66 (step @p113 :rule nary_cong :premises (@p112 @p111) :args (@t124)) % 0.44/0.66 (step @p114 :rule cong :premises (@p113) :args (@t125)) % 0.44/0.66 (step @p115 :rule cong :premises (@p114) :args (@t126)) % 0.44/0.66 (step @p116 :rule eq-symm :args (tptp.xK tptp.sz00)) % 0.44/0.66 (step @p117 :rule refl :args (@t127)) % 0.44/0.66 (step @p118 :rule nary_cong :premises (@p117 @p116 @p115) :args (@t128)) % 0.44/0.66 (step @p119 :rule refl :args (@t129)) % 0.44/0.66 (step @p120 :rule cong :premises (@p119 @p118) :args ((=> @t129 @t128))) % 0.44/0.66 (assume-push @p131 @t129) % 0.44/0.66 (step @p122 :rule instantiate :premises (@p109) :args ((@list tptp.xK))) % 0.44/0.66 (step-pop @p132 :rule scope :premises (@p122)) % 0.44/0.66 (step @p123 :rule process_scope :premises (@p132) :args (@t128)) % 0.44/0.66 (step @p125 :rule eq_resolve :premises (@p123 @p120)) % 0.44/0.66 (step @p126 :rule implies_elim :premises (@p125)) % 0.44/0.66 (step @p127 :rule chain_m_resolution :premises (@p126 @p109) :args (@t132 @t117 (@list @t129))) % 0.44/0.66 (step @p128 :rule cnf_or_pos :args (@t132)) % 0.44/0.66 (step @p129 :rule reordering :premises (@p128) :args ((or @t131 @t127 @t130 (not @t132)))) % 0.44/0.66 (step @p130 false :rule chain_m_resolution :premises (@p129 @p127 @p93 @p81 @p74) :args (false (@list false false true false) (@list @t132 @t116 @t131 @t87))) % 0.44/0.66 ) % 0.44/0.66 % SZS output end Proof % 0.44/0.66 % cvc5 exiting %------------------------------------------------------------------------------