%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM559+3 : 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 : n003.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 08:39:50 AM UTC 2026 % Result : Theorem 0.40s 0.60s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM559+3 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n003.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 11:28:59 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.60 % SZS status Theorem % 0.40/0.60 % SZS output start Proof % 0.40/0.60 ( % 0.40/0.60 (declare-sort $$unsorted 0) % 0.40/0.60 (declare-const tptp.xQ $$unsorted) % 0.40/0.60 (declare-const tptp.xx $$unsorted) % 0.40/0.60 (declare-const tptp.xT $$unsorted) % 0.40/0.60 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.xS $$unsorted) % 0.40/0.60 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.xy $$unsorted) % 0.40/0.60 (declare-const tptp.slcrc0 $$unsorted) % 0.40/0.60 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.xk $$unsorted) % 0.40/0.60 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.szNzAzT0 $$unsorted) % 0.40/0.60 (declare-const tptp.sz00 $$unsorted) % 0.40/0.60 (define @t1 () (@var "W0" $$unsorted)) % 0.40/0.60 (define @t2 () (tptp.aSet0 @t1)) % 0.40/0.60 (define @t3 () (@list @t1)) % 0.40/0.60 (define @t4 () (tptp.aElement0 @t1)) % 0.40/0.60 (define @t5 () (@var "W1" $$unsorted)) % 0.40/0.60 (define @t6 () (tptp.aElement0 @t5)) % 0.40/0.60 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.40/0.60 (define @t8 () (@list @t5)) % 0.40/0.60 (define @t9 () (tptp.isFinite0 @t1)) % 0.40/0.60 (define @t10 () (= @t1 tptp.slcrc0)) % 0.40/0.60 (define @t11 () (tptp.isCountable0 @t1)) % 0.40/0.60 (define @t12 () (not @t9)) % 0.40/0.60 (define @t13 () (and @t2 @t11)) % 0.40/0.60 (define @t14 () (not @t10)) % 0.40/0.60 (define @t15 () (@var "W2" $$unsorted)) % 0.40/0.60 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 0.40/0.60 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 0.40/0.60 (define @t18 () (@list @t15)) % 0.40/0.60 (define @t19 () (tptp.aSet0 @t5)) % 0.40/0.60 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.40/0.60 (define @t21 () (tptp.isFinite0 @t5)) % 0.40/0.60 (define @t22 () (and @t2 @t9)) % 0.40/0.60 (define @t23 () (= @t1 @t5)) % 0.40/0.60 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.40/0.60 (define @t25 () (@list @t1 @t5)) % 0.40/0.60 (define @t26 () (tptp.aSet0 @t15)) % 0.40/0.60 (define @t27 () (@list @t1 @t5 @t15)) % 0.40/0.60 (define @t28 () (@var "W3" $$unsorted)) % 0.40/0.60 (define @t29 () (= @t28 @t5)) % 0.40/0.60 (define @t30 () (tptp.aElementOf0 @t28 @t1)) % 0.40/0.60 (define @t31 () (tptp.aElement0 @t28)) % 0.40/0.60 (define @t32 () (tptp.aElementOf0 @t28 @t15)) % 0.40/0.60 (define @t33 () (@list @t28)) % 0.40/0.60 (define @t34 () (tptp.sdtpldt0 @t1 @t5)) % 0.40/0.60 (define @t35 () (and @t2 @t6)) % 0.40/0.60 (define @t36 () (tptp.sdtmndt0 @t1 @t5)) % 0.40/0.60 (define @t37 () (tptp.sdtpldt0 @t5 @t1)) % 0.40/0.60 (define @t38 () (and @t19 (tptp.isCountable0 @t5))) % 0.40/0.60 (define @t39 () (tptp.sdtmndt0 @t5 @t1)) % 0.40/0.60 (define @t40 () (and @t19 @t21)) % 0.40/0.60 (define @t41 () (tptp.szszuzczcdt0 @t1)) % 0.40/0.60 (define @t42 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.40/0.60 (define @t43 () (tptp.szszuzczcdt0 @t5)) % 0.40/0.60 (define @t44 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.40/0.60 (define @t45 () (and @t42 @t44)) % 0.40/0.60 (define @t46 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.40/0.60 (define @t47 () (tptp.sdtlseqdt0 @t5 @t15)) % 0.40/0.60 (define @t48 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 0.40/0.60 (define @t49 () (tptp.sbrdtbr0 @t1)) % 0.40/0.60 (define @t50 () (and @t2 @t44)) % 0.40/0.60 (define @t51 () (tptp.szmzizndt0 @t1)) % 0.40/0.60 (define @t52 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 0.40/0.60 (define @t53 () (tptp.szmzizndt0 @t5)) % 0.40/0.60 (define @t54 () (tptp.slbdtrb0 @t1)) % 0.40/0.60 (define @t55 () (tptp.slbdtrb0 @t5)) % 0.40/0.60 (define @t56 () (tptp.slbdtsldtrb0 @t1 @t5)) % 0.40/0.60 (define @t57 () (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) % 0.40/0.60 (define @t58 () (tptp.aElementOf0 @t1 @t57)) % 0.40/0.60 (define @t59 () (= @t49 tptp.xk)) % 0.40/0.60 (define @t60 () (tptp.aSubsetOf0 @t1 tptp.xS)) % 0.40/0.60 (define @t61 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xS)))) % 0.40/0.60 (define @t62 () (forall @t3 (and (=> @t58 (and @t2 @t61 @t60 @t59)) (=> (and (or (and @t2 @t61) @t60) @t59) @t58)))) % 0.40/0.60 (define @t63 () (tptp.slbdtsldtrb0 tptp.xT tptp.xk)) % 0.40/0.60 (define @t64 () (tptp.aElementOf0 @t1 @t63)) % 0.40/0.60 (define @t65 () (tptp.aSubsetOf0 @t1 tptp.xT)) % 0.40/0.60 (define @t66 () (forall @t8 (=> @t7 (tptp.aElementOf0 @t5 tptp.xT)))) % 0.40/0.60 (define @t67 () (= (tptp.sbrdtbr0 tptp.xQ) tptp.xk)) % 0.40/0.60 (define @t68 () (tptp.aSet0 tptp.xQ)) % 0.40/0.60 (define @t69 () (tptp.aElementOf0 tptp.xx tptp.xQ)) % 0.40/0.60 (define @t70 () (not @t69)) % 0.40/0.60 (assume @p1 (forall @t3 (=> @t2 true))) % 0.40/0.60 (assume @p2 (forall @t3 (=> @t4 true))) % 0.40/0.60 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 0.40/0.60 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 0.40/0.60 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 0.40/0.60 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.40/0.60 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.40/0.60 (assume @p8 (forall @t3 (=> @t13 @t12))) % 0.40/0.60 (assume @p9 (forall @t3 (=> @t13 @t14))) % 0.40/0.60 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 0.40/0.60 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.40/0.60 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.40/0.60 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.40/0.60 (assume @p14 (forall @t27 (=> (and @t2 @t19 @t26) (=> (and @t24 (tptp.aSubsetOf0 @t5 @t15)) (tptp.aSubsetOf0 @t1 @t15))))) % 0.40/0.60 (assume @p15 (forall @t25 (=> @t35 (forall @t18 (= (= @t15 @t34) (and @t26 (forall @t33 (= @t32 (and @t31 (or @t30 @t29)))))))))) % 0.40/0.60 (assume @p16 (forall @t25 (=> @t35 (forall @t18 (= (= @t15 @t36) (and @t26 (forall @t33 (= @t32 (and @t31 @t30 (not @t29)))))))))) % 0.40/0.60 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t36 @t5) @t1)))))) % 0.40/0.60 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t37 @t1) @t5))))) % 0.40/0.60 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t38 (tptp.isCountable0 @t37)))))) % 0.40/0.60 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t38 (tptp.isCountable0 @t39)))))) % 0.40/0.60 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isFinite0 @t37)))))) % 0.40/0.60 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isFinite0 @t39)))))) % 0.40/0.60 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.40/0.60 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.40/0.60 (assume @p25 (forall @t3 (=> @t42 (and (tptp.aElementOf0 @t41 tptp.szNzAzT0) (not (= @t41 tptp.sz00)))))) % 0.40/0.60 (assume @p26 (forall @t25 (=> @t45 (=> (= @t41 @t43) @t23)))) % 0.40/0.60 (assume @p27 (forall @t3 (=> @t42 (or (= @t1 tptp.sz00) (exists @t8 (and @t44 (= @t1 @t43))))))) % 0.40/0.60 (assume @p28 (forall @t3 (=> @t42 (not (= @t1 @t41))))) % 0.40/0.60 (assume @p29 (forall @t25 (=> @t45 (=> @t46 true)))) % 0.40/0.60 (assume @p30 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.40/0.60 (assume @p31 (forall @t3 (=> @t42 (not (tptp.sdtlseqdt0 @t41 tptp.sz00))))) % 0.40/0.60 (assume @p32 (forall @t25 (=> @t45 (= @t46 (tptp.sdtlseqdt0 @t41 @t43))))) % 0.40/0.60 (assume @p33 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 @t1 @t41)))) % 0.40/0.60 (assume @p34 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.40/0.60 (assume @p35 (forall @t25 (=> @t45 (=> (and @t46 (tptp.sdtlseqdt0 @t5 @t1)) @t23)))) % 0.40/0.60 (assume @p36 (forall @t27 (=> (and @t42 @t44 @t48) (=> (and @t46 @t47) (tptp.sdtlseqdt0 @t1 @t15))))) % 0.40/0.60 (assume @p37 (forall @t25 (=> @t45 (or @t46 (tptp.sdtlseqdt0 @t43 @t1))))) % 0.40/0.60 (assume @p38 (forall @t25 (=> @t45 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.40/0.60 (assume @p39 (forall @t3 (=> @t42 (tptp.iLess0 @t1 @t41)))) % 0.40/0.60 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t49)))) % 0.40/0.60 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t49 tptp.szNzAzT0) @t9)))) % 0.40/0.60 (assume @p42 (forall @t3 (=> @t2 (= (= @t49 tptp.sz00) @t10)))) % 0.40/0.60 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t34) (tptp.szszuzczcdt0 @t49)))))))) % 0.40/0.60 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t36)) @t49)))))) % 0.40/0.60 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t49)))))) % 0.40/0.60 (assume @p46 (forall @t25 (=> @t50 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t49)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 0.40/0.60 (assume @p47 (forall @t3 (=> (and @t52 @t14) (forall @t8 (= (= @t5 @t51) (and @t7 (forall @t18 (=> @t16 @t47)))))))) % 0.40/0.60 (assume @p48 (forall @t3 (=> (and @t52 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 0.40/0.60 (assume @p49 (forall @t25 (=> (and @t52 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t51 @t5) (tptp.aElementOf0 @t53 @t1)) (= @t51 @t53))))) % 0.40/0.60 (assume @p50 (forall @t3 (=> @t42 (forall @t8 (= (= @t5 @t54) (and @t19 (forall @t18 (= @t17 (and @t48 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 0.40/0.60 (assume @p51 (forall @t3 (=> @t42 (tptp.isFinite0 @t54)))) % 0.40/0.60 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 0.40/0.60 (assume @p53 (forall @t25 (=> @t45 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t43)) (or (tptp.aElementOf0 @t1 @t55) @t23))))) % 0.40/0.60 (assume @p54 (forall @t25 (=> @t45 (= @t46 (tptp.aSubsetOf0 @t54 @t55))))) % 0.40/0.60 (assume @p55 (forall @t3 (=> (and @t52 @t9) (exists @t8 (and @t44 (tptp.aSubsetOf0 @t1 @t55)))))) % 0.40/0.60 (assume @p56 (forall @t3 (=> @t42 (= (tptp.sbrdtbr0 @t54) @t1)))) % 0.40/0.60 (assume @p57 (forall @t25 (=> @t50 (forall @t18 (= (= @t15 @t56) (and @t26 (forall @t33 (= @t32 (and (tptp.aSubsetOf0 @t28 @t1) (= (tptp.sbrdtbr0 @t28) @t5)))))))))) % 0.40/0.60 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t44 (tptp.isFinite0 @t56)))))) % 0.40/0.60 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t44 (not (= @t56 tptp.slcrc0))))))) % 0.40/0.60 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t44 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t56)))))) % 0.40/0.60 (assume @p61 (tptp.aElementOf0 tptp.xk tptp.szNzAzT0)) % 0.40/0.60 (assume @p62 (and (tptp.aSet0 tptp.xS) (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00)))) % 0.40/0.60 (assume @p63 (and (tptp.aSet0 @t57) @t62 (tptp.aSet0 @t63) (forall @t3 (and (=> @t64 (and @t2 @t66 @t65 @t59)) (=> (and (or (and @t2 @t66) @t65) @t59) @t64))) (forall @t3 (=> @t58 @t64)) (tptp.aSubsetOf0 @t57 @t63) (not (=> @t62 (or (not (exists @t3 @t58)) (= @t57 tptp.slcrc0)))))) % 0.40/0.60 (assume @p64 (tptp.aElementOf0 tptp.xx tptp.xS)) % 0.40/0.60 (assume @p65 (and @t68 (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xQ) (tptp.aElementOf0 @t1 tptp.xS))) (tptp.aSubsetOf0 tptp.xQ tptp.xS) @t67 (tptp.aElementOf0 tptp.xQ @t57))) % 0.40/0.60 (assume @p66 (and @t68 (tptp.isFinite0 tptp.xQ) @t67)) % 0.40/0.60 (assume @p67 (and (tptp.aElement0 tptp.xy) (tptp.aElementOf0 tptp.xy tptp.xQ))) % 0.40/0.60 (assume @p68 @t70) % 0.40/0.60 (assume @p69 (not @t70)) % 0.40/0.60 (assume @p70 (not (tptp.aElementOf0 tptp.xx tptp.xT))) % 0.40/0.60 (assume @p71 true) % 0.40/0.60 (step @p72 :rule bool-double-not-elim :args (@t69)) % 0.40/0.60 (step @p73 :rule eq_resolve :premises (@p69 @p72)) % 0.40/0.60 (step @p74 false :rule chain_m_resolution :premises (@p73 @p68) :args (false (@list true) (@list @t69))) % 0.40/0.60 ) % 0.40/0.60 % SZS output end Proof % 0.40/0.60 % cvc5 exiting %------------------------------------------------------------------------------