%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM530+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 : n012.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 08:39:44 AM UTC 2026 % Result : Theorem 0.16s 0.38s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : NUM530+3 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Tue Jun 2 11:28:03 EDT 2026 % 0.07/0.26 % CPUTime : % 0.16/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.16/0.38 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.16/0.38 % SZS status Theorem % 0.16/0.38 % SZS output start Proof % 0.16/0.38 ( % 0.16/0.38 (declare-sort $$unsorted 0) % 0.16/0.38 (declare-const tptp.xq $$unsorted) % 0.16/0.38 (declare-const tptp.xp $$unsorted) % 0.16/0.38 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.38 (declare-const tptp.sz10 $$unsorted) % 0.16/0.38 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.38 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.38 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.16/0.38 (declare-const tptp.sz00 $$unsorted) % 0.16/0.38 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.38 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.38 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.38 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.38 (declare-const tptp.xn $$unsorted) % 0.16/0.38 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.16/0.38 (declare-const tptp.xm $$unsorted) % 0.16/0.38 (define @t1 () (@var "W0" $$unsorted)) % 0.16/0.38 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.16/0.38 (define @t3 () (@list @t1)) % 0.16/0.38 (define @t4 () (@var "W1" $$unsorted)) % 0.16/0.38 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 0.16/0.38 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 0.16/0.38 (define @t7 () (and @t2 @t6)) % 0.16/0.38 (define @t8 () (@list @t1 @t4)) % 0.16/0.38 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 0.16/0.38 (define @t10 () (tptp.sdtpldt0 @t4 @t1)) % 0.16/0.38 (define @t11 () (@var "W2" $$unsorted)) % 0.16/0.38 (define @t12 () (tptp.sdtpldt0 @t4 @t11)) % 0.16/0.38 (define @t13 () (tptp.aNaturalNumber0 @t11)) % 0.16/0.38 (define @t14 () (and @t2 @t6 @t13)) % 0.16/0.38 (define @t15 () (@list @t1 @t4 @t11)) % 0.16/0.38 (define @t16 () (tptp.sdtasdt0 @t4 @t1)) % 0.16/0.38 (define @t17 () (tptp.sdtasdt0 @t11 @t1)) % 0.16/0.38 (define @t18 () (tptp.sdtasdt0 @t1 @t11)) % 0.16/0.38 (define @t19 () (= @t4 @t11)) % 0.16/0.38 (define @t20 () (tptp.sdtpldt0 @t11 @t1)) % 0.16/0.38 (define @t21 () (tptp.sdtpldt0 @t1 @t11)) % 0.16/0.38 (define @t22 () (= @t16 @t17)) % 0.16/0.38 (define @t23 () (= @t9 @t18)) % 0.16/0.38 (define @t24 () (= @t1 tptp.sz00)) % 0.16/0.38 (define @t25 () (not @t24)) % 0.16/0.38 (define @t26 () (= @t4 tptp.sz00)) % 0.16/0.38 (define @t27 () (and @t13 (= @t21 @t4))) % 0.16/0.38 (define @t28 () (@list @t11)) % 0.16/0.38 (define @t29 () (tptp.sdtlseqdt0 @t1 @t4)) % 0.16/0.38 (define @t30 () (= @t1 @t4)) % 0.16/0.38 (define @t31 () (tptp.sdtlseqdt0 @t4 @t1)) % 0.16/0.38 (define @t32 () (tptp.sdtlseqdt0 @t4 @t11)) % 0.16/0.38 (define @t33 () (= @t4 @t1)) % 0.16/0.38 (define @t34 () (tptp.sdtpldt0 @t11 @t4)) % 0.16/0.38 (define @t35 () (and (not @t30) @t29)) % 0.16/0.38 (define @t36 () (= @t1 tptp.sz10)) % 0.16/0.38 (define @t37 () (tptp.iLess0 @t1 @t4)) % 0.16/0.38 (define @t38 () (and @t13 (= @t4 @t18))) % 0.16/0.38 (define @t39 () (tptp.doDivides0 @t1 @t4)) % 0.16/0.38 (define @t40 () (tptp.sdtsldt0 @t4 @t1)) % 0.16/0.38 (define @t41 () (and @t25 @t39)) % 0.16/0.38 (define @t42 () (tptp.doDivides0 @t1 @t11)) % 0.16/0.38 (define @t43 () (tptp.doDivides0 @t1 @t12)) % 0.16/0.38 (define @t44 () (not @t26)) % 0.16/0.38 (define @t45 () (tptp.doDivides0 @t4 @t1)) % 0.16/0.38 (define @t46 () (@list @t4)) % 0.16/0.38 (define @t47 () (not @t36)) % 0.16/0.38 (define @t48 () (tptp.isPrime0 @t11)) % 0.16/0.38 (define @t49 () (@var "W3" $$unsorted)) % 0.16/0.38 (define @t50 () (@var "W4" $$unsorted)) % 0.16/0.38 (define @t51 () (tptp.sdtasdt0 tptp.xn tptp.xn)) % 0.16/0.38 (define @t52 () (tptp.sdtasdt0 tptp.xm tptp.xm)) % 0.16/0.38 (define @t53 () (tptp.sdtasdt0 tptp.xp @t1)) % 0.16/0.38 (define @t54 () (not true)) % 0.16/0.38 (assume @p1 (forall @t3 (=> @t2 true))) % 0.16/0.38 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.16/0.38 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.16/0.38 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 0.16/0.38 (assume @p5 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t9)))) % 0.16/0.38 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t10)))) % 0.16/0.38 (assume @p7 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t5 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.16/0.38 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.16/0.38 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t16)))) % 0.16/0.38 (assume @p10 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t9 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t11)))))) % 0.16/0.38 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.16/0.38 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.16/0.38 (assume @p13 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t9 @t18)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 @t17)))))) % 0.16/0.38 (assume @p14 (forall @t15 (=> @t14 (=> (or (= @t5 @t21) (= @t10 @t20)) @t19)))) % 0.16/0.38 (assume @p15 (forall @t3 (=> @t2 (=> @t25 (forall (@list @t4 @t11) (=> (and @t6 @t13) (=> (or @t23 @t22) @t19))))))) % 0.16/0.38 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t24 @t26))))) % 0.16/0.38 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t24 @t26))))) % 0.16/0.38 (assume @p18 (forall @t8 (=> @t7 (= @t29 (exists @t28 @t27))))) % 0.16/0.38 (assume @p19 (forall @t8 (=> @t7 (=> @t29 (forall @t28 (= (= @t11 (tptp.sdtmndt0 @t4 @t1)) @t27)))))) % 0.16/0.38 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.16/0.38 (assume @p21 (forall @t8 (=> @t7 (=> (and @t29 @t31) @t30)))) % 0.16/0.38 (assume @p22 (forall @t15 (=> @t14 (=> (and @t29 @t32) (tptp.sdtlseqdt0 @t1 @t11))))) % 0.16/0.38 (assume @p23 (forall @t8 (=> @t7 (or @t29 (and (not @t33) @t31))))) % 0.16/0.38 (assume @p24 (forall @t8 (=> @t7 (=> @t35 (forall @t28 (=> @t13 (and (not (= @t20 @t34)) (tptp.sdtlseqdt0 @t20 @t34) (not (= @t21 @t12)) (tptp.sdtlseqdt0 @t21 @t12)))))))) % 0.16/0.38 (assume @p25 (forall @t15 (=> @t14 (=> (and @t25 (not @t19) @t32) (and (not @t23) (tptp.sdtlseqdt0 @t9 @t18) (not @t22) (tptp.sdtlseqdt0 @t16 @t17)))))) % 0.16/0.38 (assume @p26 (forall @t3 (=> @t2 (or @t24 @t36 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 0.16/0.38 (assume @p27 (forall @t8 (=> @t7 (=> @t25 (tptp.sdtlseqdt0 @t4 @t16))))) % 0.16/0.38 (assume @p28 (forall @t8 (=> @t7 (=> @t37 true)))) % 0.16/0.38 (assume @p29 (forall @t8 (=> @t7 (=> @t35 @t37)))) % 0.16/0.38 (assume @p30 (forall @t8 (=> @t7 (= @t39 (exists @t28 @t38))))) % 0.16/0.38 (assume @p31 (forall @t8 (=> @t7 (=> @t41 (forall @t28 (= (= @t11 @t40) @t38)))))) % 0.16/0.38 (assume @p32 (forall @t15 (=> @t14 (=> (and @t39 (tptp.doDivides0 @t4 @t11)) @t42)))) % 0.16/0.38 (assume @p33 (forall @t15 (=> @t14 (=> (and @t39 @t42) @t43)))) % 0.16/0.38 (assume @p34 (forall @t15 (=> @t14 (=> (and @t39 @t43) @t42)))) % 0.16/0.38 (assume @p35 (forall @t8 (=> @t7 (=> (and @t39 @t44) @t29)))) % 0.16/0.38 (assume @p36 (forall @t8 (=> @t7 (=> @t41 (forall @t28 (=> @t13 (= (tptp.sdtasdt0 @t11 @t40) (tptp.sdtsldt0 (tptp.sdtasdt0 @t11 @t4) @t1)))))))) % 0.16/0.38 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t25 @t47 (forall @t46 (=> (and @t6 @t45) (or (= @t4 tptp.sz10) @t33)))))))) % 0.16/0.38 (assume @p38 (forall @t3 (=> (and @t2 @t25 @t47) (exists @t46 (and @t6 @t45 (tptp.isPrime0 @t4)))))) % 0.16/0.38 (assume @p39 (forall @t15 (=> @t14 (=> (and @t48 (tptp.doDivides0 @t11 @t9)) (or (tptp.doDivides0 @t11 @t1) (tptp.doDivides0 @t11 @t4)))))) % 0.16/0.38 (assume @p40 (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp) (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00)))) % 0.16/0.38 (assume @p41 (forall @t15 (=> (and @t2 @t6 @t13 @t25 @t44 (not (= @t11 tptp.sz00))) (=> (= (tptp.sdtasdt0 @t11 (tptp.sdtasdt0 @t4 @t4)) (tptp.sdtasdt0 @t1 @t1)) (=> (tptp.iLess0 @t1 tptp.xn) (not (or (and (not (= @t11 tptp.sz10)) (forall (@list @t49) (=> (and (tptp.aNaturalNumber0 @t49) (exists (@list @t50) (and (tptp.aNaturalNumber0 @t50) (= @t11 (tptp.sdtasdt0 @t49 @t50)))) (tptp.doDivides0 @t49 @t11)) (or (= @t49 tptp.sz10) (= @t49 @t11))))) @t48))))))) % 0.16/0.38 (assume @p42 (= (tptp.sdtasdt0 tptp.xp @t52) @t51)) % 0.16/0.38 (assume @p43 (and (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t46 (and @t6 (= tptp.xp @t9))) (tptp.doDivides0 @t1 tptp.xp))) (or @t36 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp))) % 0.16/0.38 (assume @p44 (and (exists @t3 (and @t2 (= @t51 @t53))) (tptp.doDivides0 tptp.xp @t51) (exists @t3 (and @t2 (= tptp.xn @t53))) (tptp.doDivides0 tptp.xp tptp.xn))) % 0.16/0.38 (assume @p45 (and (tptp.aNaturalNumber0 tptp.xq) (= tptp.xn (tptp.sdtasdt0 tptp.xp tptp.xq)) (= tptp.xq (tptp.sdtsldt0 tptp.xn tptp.xp)))) % 0.16/0.38 (assume @p46 (= @t52 (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xq tptp.xq)))) % 0.16/0.38 (assume @p47 (and (not (= tptp.xm tptp.xn)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xm @t1) tptp.xn))) (tptp.sdtlseqdt0 tptp.xm tptp.xn))) % 0.16/0.38 (assume @p48 @t54) % 0.16/0.38 (assume @p49 (not false)) % 0.16/0.38 (assume @p50 true) % 0.16/0.38 (step @p51 :rule evaluate :args (@t54)) % 0.16/0.38 (step @p52 false :rule eq_resolve :premises (@p48 @p51)) % 0.16/0.38 ) % 0.16/0.38 % SZS output end Proof % 0.16/0.38 % cvc5 exiting %------------------------------------------------------------------------------