%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM491+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 : 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 08:39:35 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 : NUM491+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 % 0.17/0.34 % Computer : n027.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 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 11:23:51 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.51 %----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 $$unsorted 0) % 0.51/0.70 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.xm $$unsorted) % 0.51/0.70 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.xr $$unsorted) % 0.51/0.70 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.xn $$unsorted) % 0.51/0.70 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.sz00 $$unsorted) % 0.51/0.70 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.70 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.51/0.70 (declare-const tptp.sz10 $$unsorted) % 0.51/0.70 (declare-const tptp.xp $$unsorted) % 0.51/0.70 (define @t1 () (@var "W0" $$unsorted)) % 0.51/0.70 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.51/0.70 (define @t3 () (@list @t1)) % 0.51/0.70 (define @t4 () (@var "W1" $$unsorted)) % 0.51/0.70 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 0.51/0.70 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 0.51/0.70 (define @t7 () (and @t2 @t6)) % 0.51/0.70 (define @t8 () (@list @t1 @t4)) % 0.51/0.70 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 0.51/0.70 (define @t10 () (tptp.aNaturalNumber0 @t9)) % 0.51/0.70 (define @t11 () (forall @t8 (=> @t7 @t10))) % 0.51/0.70 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 0.51/0.70 (define @t13 () (@var "W2" $$unsorted)) % 0.51/0.70 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 0.51/0.70 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 0.51/0.70 (define @t16 () (tptp.aNaturalNumber0 @t13)) % 0.51/0.70 (define @t17 () (and @t2 @t6 @t16)) % 0.51/0.70 (define @t18 () (@list @t1 @t4 @t13)) % 0.51/0.70 (define @t19 () (tptp.sdtasdt0 @t4 @t1)) % 0.51/0.70 (define @t20 () (tptp.sdtasdt0 @t13 @t1)) % 0.51/0.70 (define @t21 () (tptp.sdtasdt0 @t1 @t13)) % 0.51/0.70 (define @t22 () (= @t4 @t13)) % 0.51/0.70 (define @t23 () (tptp.sdtpldt0 @t13 @t1)) % 0.51/0.70 (define @t24 () (tptp.sdtpldt0 @t1 @t13)) % 0.51/0.70 (define @t25 () (= @t19 @t20)) % 0.51/0.70 (define @t26 () (= @t9 @t21)) % 0.51/0.70 (define @t27 () (= @t1 tptp.sz00)) % 0.51/0.70 (define @t28 () (not @t27)) % 0.51/0.70 (define @t29 () (= @t4 tptp.sz00)) % 0.51/0.70 (define @t30 () (and @t16 (= @t24 @t4))) % 0.51/0.70 (define @t31 () (@list @t13)) % 0.51/0.70 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 0.51/0.70 (define @t33 () (= @t1 @t4)) % 0.51/0.70 (define @t34 () (tptp.sdtlseqdt0 @t4 @t1)) % 0.51/0.70 (define @t35 () (tptp.sdtlseqdt0 @t4 @t13)) % 0.51/0.70 (define @t36 () (= @t4 @t1)) % 0.51/0.70 (define @t37 () (tptp.sdtpldt0 @t13 @t4)) % 0.51/0.70 (define @t38 () (and (not @t33) @t32)) % 0.51/0.70 (define @t39 () (= @t1 tptp.sz10)) % 0.51/0.70 (define @t40 () (tptp.iLess0 @t1 @t4)) % 0.51/0.70 (define @t41 () (= @t4 @t21)) % 0.51/0.70 (define @t42 () (and @t16 @t41)) % 0.51/0.70 (define @t43 () (exists @t31 @t42)) % 0.51/0.70 (define @t44 () (tptp.doDivides0 @t1 @t4)) % 0.51/0.70 (define @t45 () (= @t44 @t43)) % 0.51/0.70 (define @t46 () (=> @t7 @t45)) % 0.51/0.70 (define @t47 () (forall @t8 @t46)) % 0.51/0.70 (define @t48 () (tptp.sdtsldt0 @t4 @t1)) % 0.51/0.70 (define @t49 () (and @t28 @t44)) % 0.51/0.70 (define @t50 () (tptp.doDivides0 @t1 @t13)) % 0.51/0.70 (define @t51 () (tptp.doDivides0 @t1 @t14)) % 0.51/0.70 (define @t52 () (tptp.doDivides0 @t4 @t1)) % 0.51/0.70 (define @t53 () (@list @t4)) % 0.51/0.70 (define @t54 () (not @t39)) % 0.51/0.70 (define @t55 () (tptp.aNaturalNumber0 tptp.xp)) % 0.51/0.70 (define @t56 () (tptp.aNaturalNumber0 tptp.xm)) % 0.51/0.70 (define @t57 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 0.51/0.70 (define @t58 () (tptp.sdtasdt0 tptp.xr tptp.xm)) % 0.51/0.70 (define @t59 () (tptp.sdtasdt0 tptp.xp tptp.xm)) % 0.51/0.70 (define @t60 () (tptp.doDivides0 tptp.xp @t59)) % 0.51/0.70 (define @t61 () (not @t16)) % 0.51/0.70 (define @t62 () (= @t44 (not (forall @t31 (or @t61 (not @t41)))))) % 0.51/0.70 (define @t63 () (not @t6)) % 0.51/0.70 (define @t64 () (not @t2)) % 0.51/0.70 (define @t65 () (or @t64 @t63)) % 0.51/0.70 (define @t66 () (not @t7)) % 0.51/0.70 (define @t67 () (forall @t31 (not @t42))) % 0.51/0.70 (define @t68 () (not @t67)) % 0.51/0.70 (define @t69 () (tptp.aNaturalNumber0 @t59)) % 0.51/0.70 (define @t70 () (not @t56)) % 0.51/0.70 (define @t71 () (not @t55)) % 0.51/0.70 (define @t72 () (or @t71 @t70 @t69)) % 0.51/0.70 (define @t73 () (@list false false false)) % 0.51/0.70 (define @t74 () (forall @t31 (or @t61 (not (= @t59 (tptp.sdtasdt0 tptp.xp @t13)))))) % 0.51/0.70 (define @t75 () (not @t74)) % 0.51/0.70 (define @t76 () (= @t60 @t75)) % 0.51/0.70 (define @t77 () (not @t69)) % 0.51/0.70 (define @t78 () (or @t71 @t77 @t76)) % 0.51/0.70 (define @t79 () (not @t76)) % 0.51/0.70 (define @t80 () (not (= @t59 @t59))) % 0.51/0.70 (define @t81 () (or @t70 @t80)) % 0.51/0.70 (assume @p1 (forall @t3 (=> @t2 true))) % 0.51/0.70 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.51/0.70 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.51/0.70 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 0.51/0.70 (assume @p5 @t11) % 0.51/0.70 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t12)))) % 0.51/0.70 (assume @p7 (forall @t18 (=> @t17 (= @t15 (tptp.sdtpldt0 @t1 @t14))))) % 0.51/0.70 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.51/0.70 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t19)))) % 0.51/0.70 (assume @p10 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t9 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 0.51/0.70 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.51/0.70 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.51/0.70 (assume @p13 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t9 @t21)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t19 @t20)))))) % 0.51/0.70 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t5 @t24) (= @t12 @t23)) @t22)))) % 0.51/0.70 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t13) (=> (and @t6 @t16) (=> (or @t26 @t25) @t22))))))) % 0.51/0.70 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 0.51/0.70 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t27 @t29))))) % 0.51/0.70 (assume @p18 (forall @t8 (=> @t7 (= @t32 (exists @t31 @t30))))) % 0.51/0.70 (assume @p19 (forall @t8 (=> @t7 (=> @t32 (forall @t31 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 0.51/0.70 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.51/0.70 (assume @p21 (forall @t8 (=> @t7 (=> (and @t32 @t34) @t33)))) % 0.51/0.70 (assume @p22 (forall @t18 (=> @t17 (=> (and @t32 @t35) (tptp.sdtlseqdt0 @t1 @t13))))) % 0.51/0.70 (assume @p23 (forall @t8 (=> @t7 (or @t32 (and (not @t36) @t34))))) % 0.51/0.70 (assume @p24 (forall @t8 (=> @t7 (=> @t38 (forall @t31 (=> @t16 (and (not (= @t23 @t37)) (tptp.sdtlseqdt0 @t23 @t37) (not (= @t24 @t14)) (tptp.sdtlseqdt0 @t24 @t14)))))))) % 0.51/0.70 (assume @p25 (forall @t18 (=> @t17 (=> (and @t28 (not @t22) @t35) (and (not @t26) (tptp.sdtlseqdt0 @t9 @t21) (not @t25) (tptp.sdtlseqdt0 @t19 @t20)))))) % 0.51/0.70 (assume @p26 (forall @t3 (=> @t2 (or @t27 @t39 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 0.51/0.70 (assume @p27 (forall @t8 (=> @t7 (=> @t28 (tptp.sdtlseqdt0 @t4 @t19))))) % 0.51/0.70 (assume @p28 (forall @t8 (=> @t7 (=> @t40 true)))) % 0.51/0.70 (assume @p29 (forall @t8 (=> @t7 (=> @t38 @t40)))) % 0.51/0.70 (assume @p30 @t47) % 0.51/0.70 (assume @p31 (forall @t8 (=> @t7 (=> @t49 (forall @t31 (= (= @t13 @t48) @t42)))))) % 0.51/0.70 (assume @p32 (forall @t18 (=> @t17 (=> (and @t44 (tptp.doDivides0 @t4 @t13)) @t50)))) % 0.51/0.70 (assume @p33 (forall @t18 (=> @t17 (=> (and @t44 @t50) @t51)))) % 0.51/0.70 (assume @p34 (forall @t18 (=> @t17 (=> (and @t44 @t51) @t50)))) % 0.51/0.70 (assume @p35 (forall @t8 (=> @t7 (=> (and @t44 (not @t29)) @t32)))) % 0.51/0.70 (assume @p36 (forall @t8 (=> @t7 (=> @t49 (forall @t31 (=> @t16 (= (tptp.sdtasdt0 @t13 @t48) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 0.51/0.70 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t28 @t54 (forall @t53 (=> (and @t6 @t52) (or (= @t4 tptp.sz10) @t36)))))))) % 0.51/0.70 (assume @p38 (forall @t3 (=> (and @t2 @t28 @t54) (exists @t53 (and @t6 @t52 (tptp.isPrime0 @t4)))))) % 0.51/0.70 (assume @p39 (and (tptp.aNaturalNumber0 tptp.xn) @t56 @t55)) % 0.51/0.70 (assume @p40 (forall @t18 (=> @t17 (=> (and (tptp.isPrime0 @t13) (tptp.doDivides0 @t13 @t9)) (=> (tptp.iLess0 @t15 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 @t13 @t1) (tptp.doDivides0 @t13 @t4))))))) % 0.51/0.70 (assume @p41 (and (tptp.isPrime0 tptp.xp) (tptp.doDivides0 tptp.xp @t57))) % 0.51/0.70 (assume @p42 (tptp.sdtlseqdt0 tptp.xp tptp.xn)) % 0.51/0.70 (assume @p43 (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp))) % 0.51/0.70 (assume @p44 (and (not (= tptp.xr tptp.xn)) (tptp.sdtlseqdt0 tptp.xr tptp.xn))) % 0.51/0.70 (assume @p45 (= tptp.xn (tptp.sdtpldt0 tptp.xp tptp.xr))) % 0.51/0.70 (assume @p46 (= @t57 (tptp.sdtpldt0 @t59 @t58))) % 0.51/0.70 (assume @p47 (= @t58 (tptp.sdtmndt0 @t57 @t59))) % 0.51/0.70 (assume @p48 (not @t60)) % 0.51/0.70 (assume @p49 true) % 0.51/0.70 (step @p50 :rule and_elim :premises (@p39) :args (1)) % 0.51/0.70 (step @p51 :rule aci_norm :args ((= (or @t65 @t62) (or @t64 @t63 @t62)))) % 0.51/0.70 (step @p52 :rule refl :args (@t62)) % 0.51/0.70 (step @p53 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 0.51/0.70 (step @p54 :rule nary_cong :premises (@p53 @p52) :args ((or @t66 @t62))) % 0.51/0.70 (step @p55 :rule trans :premises (@p54 @p51)) % 0.51/0.70 (step @p56 :rule bool-impl-elim :args (@t7 @t62)) % 0.51/0.70 (step @p57 :rule trans :premises (@p56 @p55)) % 0.51/0.70 (step @p58 :rule cong :premises (@p57) :args ((forall @t8 (=> @t7 @t62)))) % 0.51/0.70 (step @p59 :rule bool-and-de-morgan :args (@t16 @t41 true)) % 0.51/0.70 (step @p60 :rule cong :premises (@p59) :args (@t67)) % 0.51/0.70 (step @p61 :rule cong :premises (@p60) :args (@t68)) % 0.51/0.70 (step @p62 :rule exists-elim :args ((= @t43 @t68))) % 0.51/0.70 (step @p63 :rule trans :premises (@p62 @p61)) % 0.51/0.70 (step @p64 :rule refl :args (@t44)) % 0.51/0.70 (step @p65 :rule cong :premises (@p64 @p63) :args (@t45)) % 0.51/0.70 (step @p66 :rule refl :args (@t7)) % 0.51/0.70 (step @p67 :rule cong :premises (@p66 @p65) :args (@t46)) % 0.51/0.70 (step @p68 :rule cong :premises (@p67) :args (@t47)) % 0.51/0.70 (step @p69 :rule trans :premises (@p68 @p58)) % 0.51/0.70 (step @p70 :rule eq_resolve :premises (@p30 @p69)) % 0.51/0.70 (step @p71 :rule instantiate :premises (@p70) :args ((@list tptp.xp @t59))) % 0.51/0.70 (step @p72 :rule aci_norm :args ((= (or @t65 @t10) (or @t64 @t63 @t10)))) % 0.51/0.70 (step @p73 :rule refl :args (@t10)) % 0.51/0.70 (step @p74 :rule nary_cong :premises (@p53 @p73) :args ((or @t66 @t10))) % 0.51/0.70 (step @p75 :rule trans :premises (@p74 @p72)) % 0.51/0.70 (step @p76 :rule bool-impl-elim :args (@t7 @t10)) % 0.51/0.70 (step @p77 :rule trans :premises (@p76 @p75)) % 0.51/0.70 (step @p78 :rule cong :premises (@p77) :args (@t11)) % 0.51/0.70 (step @p79 :rule eq_resolve :premises (@p5 @p78)) % 0.51/0.70 (step @p80 :rule instantiate :premises (@p79) :args ((@list tptp.xp tptp.xm))) % 0.51/0.70 (step @p81 :rule and_elim :premises (@p39) :args (2)) % 0.51/0.70 (step @p82 :rule cnf_or_pos :args (@t72)) % 0.51/0.70 (step @p83 :rule reordering :premises (@p82) :args ((or @t70 @t71 @t69 (not @t72)))) % 0.51/0.70 (step @p84 :rule chain_m_resolution :premises (@p83 @p50 @p81 @p80) :args (@t69 @t73 (@list @t56 @t55 @t72))) % 0.51/0.70 (step @p85 :rule cnf_or_pos :args (@t78)) % 0.51/0.70 (step @p86 :rule reordering :premises (@p85) :args ((or @t71 @t77 @t76 (not @t78)))) % 0.51/0.70 (step @p87 :rule chain_m_resolution :premises (@p86 @p81 @p84 @p71) :args (@t76 @t73 (@list @t55 @t69 @t78))) % 0.51/0.70 (step @p88 :rule bool-double-not-elim :args (@t74)) % 0.51/0.70 (step @p89 :rule refl :args (@t60)) % 0.51/0.70 (step @p90 :rule refl :args (@t79)) % 0.51/0.70 (step @p91 :rule nary_cong :premises (@p90 @p89 @p88) :args ((or @t79 @t60 (not @t75)))) % 0.51/0.70 (step @p92 :rule cnf_equiv_pos2 :args (@t76)) % 0.51/0.70 (step @p93 :rule eq_resolve :premises (@p92 @p91)) % 0.51/0.70 (step @p94 :rule reordering :premises (@p93) :args ((or @t60 @t74 @t79))) % 0.51/0.70 (step @p95 :rule chain_m_resolution :premises (@p94 @p48 @p87) :args (@t74 (@list true false) (@list @t60 @t76))) % 0.51/0.70 (step @p96 :rule aci_norm :args ((= (or @t70 false) @t70))) % 0.51/0.70 (step @p97 :rule evaluate :args ((not true))) % 0.51/0.70 (step @p98 :rule eq-refl :args (@t59)) % 0.51/0.70 (step @p99 :rule cong :premises (@p98) :args (@t80)) % 0.51/0.70 (step @p100 :rule trans :premises (@p99 @p97)) % 0.51/0.70 (step @p101 :rule refl :args (@t70)) % 0.51/0.70 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t81)) % 0.51/0.70 (step @p103 :rule trans :premises (@p102 @p96)) % 0.51/0.70 (step @p104 :rule refl :args (@t74)) % 0.51/0.70 (step @p105 :rule cong :premises (@p104 @p103) :args ((=> @t74 @t81))) % 0.51/0.70 (assume-push @p114 @t74) % 0.51/0.70 (step @p107 :rule instantiate :premises (@p95) :args ((@list tptp.xm))) % 0.51/0.70 (step-pop @p115 :rule scope :premises (@p107)) % 0.51/0.70 (step @p108 :rule process_scope :premises (@p115) :args (@t81)) % 0.51/0.70 (step @p110 :rule eq_resolve :premises (@p108 @p105)) % 0.51/0.70 (step @p111 :rule implies_elim :premises (@p110)) % 0.51/0.70 (step @p112 :rule reordering :premises (@p111) :args ((or @t70 @t75))) % 0.51/0.70 (step @p113 false :rule chain_m_resolution :premises (@p112 @p95 @p50) :args (false (@list false false) (@list @t74 @t56))) % 0.51/0.70 ) % 0.51/0.70 % SZS output end Proof % 0.51/0.70 % cvc5 exiting %------------------------------------------------------------------------------