%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM491+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 : n002.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 08:39:36 AM UTC 2026 % Result : Theorem 0.46s 0.63s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM491+3 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n002.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 11:24:33 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.46/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.46/0.63 % SZS status Theorem % 0.46/0.63 % SZS output start Proof % 0.46/0.63 ( % 0.46/0.63 (declare-sort $$unsorted 0) % 0.46/0.63 (declare-const tptp.xr $$unsorted) % 0.46/0.63 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.xm $$unsorted) % 0.46/0.63 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.63 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.xn $$unsorted) % 0.46/0.63 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.sz00 $$unsorted) % 0.46/0.63 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.63 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.63 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.63 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.sz10 $$unsorted) % 0.46/0.63 (declare-const tptp.xp $$unsorted) % 0.46/0.63 (define @t1 () (@var "W0" $$unsorted)) % 0.46/0.63 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.46/0.63 (define @t3 () (@list @t1)) % 0.46/0.63 (define @t4 () (@var "W1" $$unsorted)) % 0.46/0.63 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 0.46/0.63 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 0.46/0.63 (define @t7 () (and @t2 @t6)) % 0.46/0.63 (define @t8 () (@list @t1 @t4)) % 0.46/0.63 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 0.46/0.63 (define @t10 () (tptp.sdtpldt0 @t4 @t1)) % 0.46/0.63 (define @t11 () (@var "W2" $$unsorted)) % 0.46/0.63 (define @t12 () (tptp.sdtpldt0 @t4 @t11)) % 0.46/0.63 (define @t13 () (tptp.sdtpldt0 @t5 @t11)) % 0.46/0.63 (define @t14 () (tptp.aNaturalNumber0 @t11)) % 0.46/0.63 (define @t15 () (and @t2 @t6 @t14)) % 0.46/0.63 (define @t16 () (@list @t1 @t4 @t11)) % 0.46/0.63 (define @t17 () (tptp.sdtasdt0 @t4 @t1)) % 0.46/0.63 (define @t18 () (tptp.sdtasdt0 @t11 @t1)) % 0.46/0.63 (define @t19 () (tptp.sdtasdt0 @t1 @t11)) % 0.46/0.63 (define @t20 () (= @t4 @t11)) % 0.46/0.63 (define @t21 () (tptp.sdtpldt0 @t11 @t1)) % 0.46/0.63 (define @t22 () (tptp.sdtpldt0 @t1 @t11)) % 0.46/0.63 (define @t23 () (= @t17 @t18)) % 0.46/0.63 (define @t24 () (= @t9 @t19)) % 0.46/0.63 (define @t25 () (= @t1 tptp.sz00)) % 0.46/0.63 (define @t26 () (not @t25)) % 0.46/0.63 (define @t27 () (= @t4 tptp.sz00)) % 0.46/0.63 (define @t28 () (and @t14 (= @t22 @t4))) % 0.46/0.63 (define @t29 () (@list @t11)) % 0.46/0.63 (define @t30 () (tptp.sdtlseqdt0 @t1 @t4)) % 0.46/0.63 (define @t31 () (= @t1 @t4)) % 0.46/0.63 (define @t32 () (tptp.sdtlseqdt0 @t4 @t1)) % 0.46/0.63 (define @t33 () (tptp.sdtlseqdt0 @t4 @t11)) % 0.46/0.63 (define @t34 () (= @t4 @t1)) % 0.46/0.63 (define @t35 () (tptp.sdtpldt0 @t11 @t4)) % 0.46/0.63 (define @t36 () (and (not @t31) @t30)) % 0.46/0.63 (define @t37 () (= @t1 tptp.sz10)) % 0.46/0.63 (define @t38 () (tptp.iLess0 @t1 @t4)) % 0.46/0.63 (define @t39 () (and @t14 (= @t4 @t19))) % 0.46/0.63 (define @t40 () (tptp.doDivides0 @t1 @t4)) % 0.46/0.63 (define @t41 () (tptp.sdtsldt0 @t4 @t1)) % 0.46/0.63 (define @t42 () (and @t26 @t40)) % 0.46/0.63 (define @t43 () (tptp.doDivides0 @t1 @t11)) % 0.46/0.63 (define @t44 () (tptp.doDivides0 @t1 @t12)) % 0.46/0.63 (define @t45 () (tptp.doDivides0 @t4 @t1)) % 0.46/0.63 (define @t46 () (@list @t4)) % 0.46/0.63 (define @t47 () (not @t37)) % 0.46/0.63 (define @t48 () (tptp.aNaturalNumber0 tptp.xm)) % 0.46/0.63 (define @t49 () (@var "W3" $$unsorted)) % 0.46/0.63 (define @t50 () (tptp.sdtasdt0 @t11 @t49)) % 0.46/0.63 (define @t51 () (tptp.aNaturalNumber0 @t49)) % 0.46/0.63 (define @t52 () (@list @t49)) % 0.46/0.63 (define @t53 () (@var "W4" $$unsorted)) % 0.46/0.63 (define @t54 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 0.46/0.63 (define @t55 () (tptp.sdtasdt0 tptp.xp @t1)) % 0.46/0.63 (define @t56 () (tptp.sdtpldt0 tptp.xp tptp.xr)) % 0.46/0.63 (define @t57 () (tptp.sdtasdt0 tptp.xr tptp.xm)) % 0.46/0.63 (define @t58 () (tptp.sdtasdt0 tptp.xp tptp.xm)) % 0.46/0.63 (define @t59 () (tptp.sdtpldt0 @t58 @t57)) % 0.46/0.63 (define @t60 () (tptp.doDivides0 tptp.xp @t58)) % 0.46/0.63 (define @t61 () (and @t2 (= @t58 @t55))) % 0.46/0.63 (define @t62 () (exists @t3 @t61)) % 0.46/0.63 (define @t63 () (or @t62 @t60)) % 0.46/0.63 (define @t64 () (not @t63)) % 0.46/0.63 (define @t65 () (= @t55 @t58)) % 0.46/0.63 (define @t66 () (and @t2 @t65)) % 0.46/0.63 (define @t67 () (forall @t3 (not @t66))) % 0.46/0.63 (define @t68 () (not @t67)) % 0.46/0.63 (define @t69 () (not @t48)) % 0.46/0.63 (define @t70 () (not (= @t58 @t58))) % 0.46/0.63 (define @t71 () (or @t69 @t70)) % 0.46/0.63 (define @t72 () (forall @t3 (or (not @t2) (not @t65)))) % 0.46/0.63 (assume @p1 (forall @t3 (=> @t2 true))) % 0.46/0.63 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.46/0.63 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.46/0.63 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 0.46/0.63 (assume @p5 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t9)))) % 0.46/0.63 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t10)))) % 0.46/0.63 (assume @p7 (forall @t16 (=> @t15 (= @t13 (tptp.sdtpldt0 @t1 @t12))))) % 0.46/0.63 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.46/0.63 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t17)))) % 0.46/0.63 (assume @p10 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t9 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t11)))))) % 0.46/0.63 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.46/0.63 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.46/0.63 (assume @p13 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t9 @t19)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t17 @t18)))))) % 0.46/0.63 (assume @p14 (forall @t16 (=> @t15 (=> (or (= @t5 @t22) (= @t10 @t21)) @t20)))) % 0.46/0.63 (assume @p15 (forall @t3 (=> @t2 (=> @t26 (forall (@list @t4 @t11) (=> (and @t6 @t14) (=> (or @t24 @t23) @t20))))))) % 0.46/0.63 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t25 @t27))))) % 0.46/0.63 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t25 @t27))))) % 0.46/0.63 (assume @p18 (forall @t8 (=> @t7 (= @t30 (exists @t29 @t28))))) % 0.46/0.63 (assume @p19 (forall @t8 (=> @t7 (=> @t30 (forall @t29 (= (= @t11 (tptp.sdtmndt0 @t4 @t1)) @t28)))))) % 0.46/0.63 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.46/0.63 (assume @p21 (forall @t8 (=> @t7 (=> (and @t30 @t32) @t31)))) % 0.46/0.63 (assume @p22 (forall @t16 (=> @t15 (=> (and @t30 @t33) (tptp.sdtlseqdt0 @t1 @t11))))) % 0.46/0.63 (assume @p23 (forall @t8 (=> @t7 (or @t30 (and (not @t34) @t32))))) % 0.46/0.63 (assume @p24 (forall @t8 (=> @t7 (=> @t36 (forall @t29 (=> @t14 (and (not (= @t21 @t35)) (tptp.sdtlseqdt0 @t21 @t35) (not (= @t22 @t12)) (tptp.sdtlseqdt0 @t22 @t12)))))))) % 0.46/0.63 (assume @p25 (forall @t16 (=> @t15 (=> (and @t26 (not @t20) @t33) (and (not @t24) (tptp.sdtlseqdt0 @t9 @t19) (not @t23) (tptp.sdtlseqdt0 @t17 @t18)))))) % 0.46/0.63 (assume @p26 (forall @t3 (=> @t2 (or @t25 @t37 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 0.46/0.63 (assume @p27 (forall @t8 (=> @t7 (=> @t26 (tptp.sdtlseqdt0 @t4 @t17))))) % 0.46/0.63 (assume @p28 (forall @t8 (=> @t7 (=> @t38 true)))) % 0.46/0.63 (assume @p29 (forall @t8 (=> @t7 (=> @t36 @t38)))) % 0.46/0.63 (assume @p30 (forall @t8 (=> @t7 (= @t40 (exists @t29 @t39))))) % 0.46/0.63 (assume @p31 (forall @t8 (=> @t7 (=> @t42 (forall @t29 (= (= @t11 @t41) @t39)))))) % 0.46/0.63 (assume @p32 (forall @t16 (=> @t15 (=> (and @t40 (tptp.doDivides0 @t4 @t11)) @t43)))) % 0.46/0.63 (assume @p33 (forall @t16 (=> @t15 (=> (and @t40 @t43) @t44)))) % 0.46/0.63 (assume @p34 (forall @t16 (=> @t15 (=> (and @t40 @t44) @t43)))) % 0.46/0.63 (assume @p35 (forall @t8 (=> @t7 (=> (and @t40 (not @t27)) @t30)))) % 0.46/0.63 (assume @p36 (forall @t8 (=> @t7 (=> @t42 (forall @t29 (=> @t14 (= (tptp.sdtasdt0 @t11 @t41) (tptp.sdtsldt0 (tptp.sdtasdt0 @t11 @t4) @t1)))))))) % 0.46/0.63 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t26 @t47 (forall @t46 (=> (and @t6 @t45) (or (= @t4 tptp.sz10) @t34)))))))) % 0.46/0.63 (assume @p38 (forall @t3 (=> (and @t2 @t26 @t47) (exists @t46 (and @t6 @t45 (tptp.isPrime0 @t4)))))) % 0.46/0.63 (assume @p39 (and (tptp.aNaturalNumber0 tptp.xn) @t48 (tptp.aNaturalNumber0 tptp.xp))) % 0.46/0.63 (assume @p40 (forall @t16 (=> @t15 (=> (and (or (and (not (= @t11 tptp.sz00)) (not (= @t11 tptp.sz10)) (forall @t52 (=> (and @t51 (exists (@list @t53) (and (tptp.aNaturalNumber0 @t53) (= @t11 (tptp.sdtasdt0 @t49 @t53)))) (tptp.doDivides0 @t49 @t11)) (or (= @t49 tptp.sz10) (= @t49 @t11))))) (tptp.isPrime0 @t11)) (or (exists @t52 (and @t51 (= @t9 @t50))) (tptp.doDivides0 @t11 @t9))) (=> (tptp.iLess0 @t13 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists @t52 (and @t51 (= @t1 @t50))) (tptp.doDivides0 @t11 @t1)) (and (exists @t52 (and @t51 (= @t4 @t50))) (tptp.doDivides0 @t11 @t4)))))))) % 0.46/0.63 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t46 (and @t6 (= tptp.xp @t9))) (tptp.doDivides0 @t1 tptp.xp))) (or @t37 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t54 @t55))) (tptp.doDivides0 tptp.xp @t54))) % 0.46/0.63 (assume @p42 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xp @t1) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn))) % 0.46/0.63 (assume @p43 (and (tptp.aNaturalNumber0 tptp.xr) (= @t56 tptp.xn) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) % 0.46/0.63 (assume @p44 (and (not (= tptp.xr tptp.xn)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xr @t1) tptp.xn))) (tptp.sdtlseqdt0 tptp.xr tptp.xn))) % 0.46/0.63 (assume @p45 (= tptp.xn @t56)) % 0.46/0.63 (assume @p46 (= @t54 @t59)) % 0.46/0.63 (assume @p47 (and (= @t59 @t54) (= @t57 (tptp.sdtmndt0 @t54 @t58)))) % 0.46/0.63 (assume @p48 @t64) % 0.46/0.63 (assume @p49 true) % 0.46/0.63 (step @p50 :rule and_elim :premises (@p39) :args (1)) % 0.46/0.63 (step @p51 :rule refl :args (@t60)) % 0.46/0.63 (step @p52 :rule bool-and-de-morgan :args (@t2 @t65 true)) % 0.46/0.63 (step @p53 :rule cong :premises (@p52) :args (@t67)) % 0.46/0.63 (step @p54 :rule cong :premises (@p53) :args (@t68)) % 0.46/0.63 (step @p55 :rule exists-elim :args ((= (exists @t3 @t66) @t68))) % 0.46/0.63 (step @p56 :rule trans :premises (@p55 @p54)) % 0.46/0.63 (step @p57 :rule eq-symm :args (@t58 @t55)) % 0.46/0.63 (step @p58 :rule refl :args (@t2)) % 0.46/0.63 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t61)) % 0.46/0.63 (step @p60 :rule cong :premises (@p59) :args (@t62)) % 0.46/0.63 (step @p61 :rule trans :premises (@p60 @p56)) % 0.46/0.63 (step @p62 :rule nary_cong :premises (@p61 @p51) :args (@t63)) % 0.46/0.63 (step @p63 :rule cong :premises (@p62) :args (@t64)) % 0.46/0.63 (step @p64 :rule eq_resolve :premises (@p48 @p63)) % 0.46/0.63 (step @p65 :rule not_or_elim :premises (@p64) :args (0)) % 0.46/0.63 (step @p66 :rule not_not_elim :premises (@p65)) % 0.46/0.63 (step @p67 :rule aci_norm :args ((= (or @t69 false) @t69))) % 0.46/0.63 (step @p68 :rule evaluate :args ((not true))) % 0.46/0.63 (step @p69 :rule eq-refl :args (@t58)) % 0.46/0.63 (step @p70 :rule cong :premises (@p69) :args (@t70)) % 0.46/0.63 (step @p71 :rule trans :premises (@p70 @p68)) % 0.46/0.63 (step @p72 :rule refl :args (@t69)) % 0.46/0.63 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t71)) % 0.46/0.63 (step @p74 :rule trans :premises (@p73 @p67)) % 0.46/0.63 (step @p75 :rule refl :args (@t72)) % 0.46/0.63 (step @p76 :rule cong :premises (@p75 @p74) :args ((=> @t72 @t71))) % 0.46/0.63 (assume-push @p84 @t72) % 0.46/0.63 (step @p78 :rule instantiate :premises (@p66) :args ((@list tptp.xm))) % 0.46/0.63 (step-pop @p85 :rule scope :premises (@p78)) % 0.46/0.63 (step @p79 :rule process_scope :premises (@p85) :args (@t71)) % 0.46/0.63 (step @p81 :rule eq_resolve :premises (@p79 @p76)) % 0.46/0.63 (step @p82 :rule implies_elim :premises (@p81)) % 0.46/0.63 (step @p83 false :rule chain_m_resolution :premises (@p82 @p66 @p50) :args (false (@list false false) (@list @t72 @t48))) % 0.46/0.63 ) % 0.46/0.63 % SZS output end Proof % 0.46/0.64 % cvc5 exiting %------------------------------------------------------------------------------