%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM423+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 : n024.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 08:39:21 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 : NUM423+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 % 0.08/0.25 % Computer : n024.cluster.edu % 0.08/0.25 % Model : x86_64 x86_64 % 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.25 % Memory : 8042.1875MB % 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.25 % CPULimit : 300 % 0.08/0.25 % WCLimit : 300 % 0.08/0.25 % DateTime : Tue Jun 2 06:17:30 EDT 2026 % 0.08/0.26 % 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 $$unsorted 0) % 0.16/0.38 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.38 (declare-const tptp.xa $$unsorted) % 0.16/0.38 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.38 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.16/0.38 (declare-const tptp.sz10 $$unsorted) % 0.16/0.38 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.38 (declare-const tptp.sz00 $$unsorted) % 0.16/0.38 (declare-const tptp.xq $$unsorted) % 0.16/0.38 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.38 (declare-const tptp.aInteger0 (-> $$unsorted Bool)) % 0.16/0.38 (define @t1 () (@var "W0" $$unsorted)) % 0.16/0.38 (define @t2 () (tptp.aInteger0 @t1)) % 0.16/0.38 (define @t3 () (@list @t1)) % 0.16/0.38 (define @t4 () (tptp.aInteger0 tptp.sz00)) % 0.16/0.38 (define @t5 () (tptp.smndt0 @t1)) % 0.16/0.38 (define @t6 () (@var "W1" $$unsorted)) % 0.16/0.38 (define @t7 () (tptp.sdtpldt0 @t1 @t6)) % 0.16/0.38 (define @t8 () (tptp.aInteger0 @t6)) % 0.16/0.38 (define @t9 () (and @t2 @t8)) % 0.16/0.38 (define @t10 () (@list @t1 @t6)) % 0.16/0.38 (define @t11 () (tptp.sdtasdt0 @t1 @t6)) % 0.16/0.38 (define @t12 () (@var "W2" $$unsorted)) % 0.16/0.38 (define @t13 () (tptp.sdtpldt0 @t6 @t12)) % 0.16/0.38 (define @t14 () (tptp.aInteger0 @t12)) % 0.16/0.38 (define @t15 () (and @t2 @t8 @t14)) % 0.16/0.38 (define @t16 () (@list @t1 @t6 @t12)) % 0.16/0.38 (define @t17 () (= tptp.sz00 (tptp.sdtpldt0 @t5 @t1))) % 0.16/0.38 (define @t18 () (tptp.sdtpldt0 @t1 @t5)) % 0.16/0.38 (define @t19 () (and (= @t18 tptp.sz00) @t17)) % 0.16/0.38 (define @t20 () (=> @t2 @t19)) % 0.16/0.38 (define @t21 () (forall @t3 @t20)) % 0.16/0.38 (define @t22 () (tptp.sdtasdt0 @t6 @t12)) % 0.16/0.38 (define @t23 () (tptp.sdtasdt0 @t1 @t12)) % 0.16/0.38 (define @t24 () (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1))) % 0.16/0.38 (define @t25 () (tptp.sdtasdt0 @t1 tptp.sz00)) % 0.16/0.38 (define @t26 () (and (= @t25 tptp.sz00) @t24)) % 0.16/0.38 (define @t27 () (=> @t2 @t26)) % 0.16/0.38 (define @t28 () (forall @t3 @t27)) % 0.16/0.38 (define @t29 () (tptp.smndt0 tptp.sz10)) % 0.16/0.38 (define @t30 () (= @t6 tptp.sz00)) % 0.16/0.38 (define @t31 () (tptp.aInteger0 tptp.xq)) % 0.16/0.38 (define @t32 () (tptp.aInteger0 tptp.xa)) % 0.16/0.38 (define @t33 () (tptp.sdteqdtlpzmzozddtrp0 tptp.xa tptp.xa tptp.xq)) % 0.16/0.38 (define @t34 () (tptp.smndt0 tptp.xa)) % 0.16/0.38 (define @t35 () (tptp.sdtpldt0 tptp.xa @t34)) % 0.16/0.38 (define @t36 () (tptp.aDivisorOf0 tptp.xq @t35)) % 0.16/0.38 (define @t37 () (= (tptp.sdtasdt0 tptp.xq @t1) @t35)) % 0.16/0.38 (define @t38 () (and @t2 @t37)) % 0.16/0.38 (define @t39 () (exists @t3 @t38)) % 0.16/0.38 (define @t40 () (or @t39 @t36 @t33)) % 0.16/0.38 (define @t41 () (not @t40)) % 0.16/0.38 (define @t42 () (forall @t3 (not @t38))) % 0.16/0.38 (define @t43 () (not @t42)) % 0.16/0.38 (define @t44 () (tptp.sdtasdt0 tptp.xq tptp.sz00)) % 0.16/0.38 (define @t45 () (not (= @t44 @t35))) % 0.16/0.38 (define @t46 () (not @t4)) % 0.16/0.38 (define @t47 () (or @t46 @t45)) % 0.16/0.38 (define @t48 () (forall @t3 (or (not @t2) (not @t37)))) % 0.16/0.38 (define @t49 () (= @t35 @t44)) % 0.16/0.38 (define @t50 () (not @t49)) % 0.16/0.38 (define @t51 () (or @t46 @t50)) % 0.16/0.38 (define @t52 () (@list false)) % 0.16/0.38 (define @t53 () (@list false false)) % 0.16/0.38 (define @t54 () (and (= tptp.sz00 @t18) @t17)) % 0.16/0.38 (define @t55 () (= tptp.sz00 @t35)) % 0.16/0.38 (define @t56 () (and @t55 (= tptp.sz00 (tptp.sdtpldt0 @t34 tptp.xa)))) % 0.16/0.38 (define @t57 () (not @t32)) % 0.16/0.38 (define @t58 () (or @t57 @t56)) % 0.16/0.38 (define @t59 () (and (= tptp.sz00 @t25) @t24)) % 0.16/0.38 (define @t60 () (= tptp.sz00 @t44)) % 0.16/0.38 (define @t61 () (and @t60 (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 tptp.xq)))) % 0.16/0.38 (define @t62 () (not @t31)) % 0.16/0.38 (define @t63 () (or @t62 @t61)) % 0.16/0.38 (define @t64 () (not @t60)) % 0.16/0.38 (define @t65 () (not @t55)) % 0.16/0.38 (define @t66 () (and @t55 @t50)) % 0.16/0.38 (assume @p1 (forall @t3 (=> @t2 true))) % 0.16/0.38 (assume @p2 @t4) % 0.16/0.38 (assume @p3 (tptp.aInteger0 tptp.sz10)) % 0.16/0.38 (assume @p4 (forall @t3 (=> @t2 (tptp.aInteger0 @t5)))) % 0.16/0.38 (assume @p5 (forall @t10 (=> @t9 (tptp.aInteger0 @t7)))) % 0.16/0.38 (assume @p6 (forall @t10 (=> @t9 (tptp.aInteger0 @t11)))) % 0.16/0.38 (assume @p7 (forall @t16 (=> @t15 (= (tptp.sdtpldt0 @t1 @t13) (tptp.sdtpldt0 @t7 @t12))))) % 0.16/0.38 (assume @p8 (forall @t10 (=> @t9 (= @t7 (tptp.sdtpldt0 @t6 @t1))))) % 0.16/0.38 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.16/0.38 (assume @p10 @t21) % 0.16/0.38 (assume @p11 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t1 @t22) (tptp.sdtasdt0 @t11 @t12))))) % 0.16/0.38 (assume @p12 (forall @t10 (=> @t9 (= @t11 (tptp.sdtasdt0 @t6 @t1))))) % 0.16/0.38 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.16/0.38 (assume @p14 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t13) (tptp.sdtpldt0 @t11 @t23)) (= (tptp.sdtasdt0 @t7 @t12) (tptp.sdtpldt0 @t23 @t22)))))) % 0.16/0.38 (assume @p15 @t28) % 0.16/0.38 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t29 @t1) @t5) (= @t5 (tptp.sdtasdt0 @t1 @t29)))))) % 0.16/0.38 (assume @p17 (forall @t10 (=> @t9 (=> (= @t11 tptp.sz00) (or (= @t1 tptp.sz00) @t30))))) % 0.16/0.38 (assume @p18 (forall @t3 (=> @t2 (forall (@list @t6) (= (tptp.aDivisorOf0 @t6 @t1) (and @t8 (not @t30) (exists (@list @t12) (and @t14 (= @t22 @t1))))))))) % 0.16/0.38 (assume @p19 (forall @t16 (=> (and @t2 @t8 @t14 (not (= @t12 tptp.sz00))) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t6 @t12) (tptp.aDivisorOf0 @t12 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t6))))))) % 0.16/0.38 (assume @p20 (and @t32 @t31 (not (= tptp.xq tptp.sz00)))) % 0.16/0.38 (assume @p21 @t41) % 0.16/0.38 (assume @p22 true) % 0.16/0.38 (step @p23 :rule refl :args (@t33)) % 0.16/0.38 (step @p24 :rule refl :args (@t36)) % 0.16/0.38 (step @p25 :rule bool-and-de-morgan :args (@t2 @t37 true)) % 0.16/0.38 (step @p26 :rule cong :premises (@p25) :args (@t42)) % 0.16/0.38 (step @p27 :rule cong :premises (@p26) :args (@t43)) % 0.16/0.38 (step @p28 :rule exists-elim :args ((= @t39 @t43))) % 0.16/0.38 (step @p29 :rule trans :premises (@p28 @p27)) % 0.16/0.38 (step @p30 :rule nary_cong :premises (@p29 @p24 @p23) :args (@t40)) % 0.16/0.38 (step @p31 :rule cong :premises (@p30) :args (@t41)) % 0.16/0.38 (step @p32 :rule eq_resolve :premises (@p21 @p31)) % 0.16/0.38 (step @p33 :rule not_or_elim :premises (@p32) :args (0)) % 0.16/0.38 (step @p34 :rule not_not_elim :premises (@p33)) % 0.16/0.38 (step @p35 :rule eq-symm :args (@t44 @t35)) % 0.16/0.38 (step @p36 :rule cong :premises (@p35) :args (@t45)) % 0.16/0.38 (step @p37 :rule refl :args (@t46)) % 0.16/0.38 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t47)) % 0.16/0.38 (step @p39 :rule refl :args (@t48)) % 0.16/0.38 (step @p40 :rule cong :premises (@p39 @p38) :args ((=> @t48 @t47))) % 0.16/0.38 (assume-push @p106 @t48) % 0.16/0.38 (step @p42 :rule instantiate :premises (@p34) :args ((@list tptp.sz00))) % 0.16/0.38 (step-pop @p107 :rule scope :premises (@p42)) % 0.16/0.38 (step @p43 :rule process_scope :premises (@p107) :args (@t47)) % 0.16/0.38 (step @p45 :rule eq_resolve :premises (@p43 @p40)) % 0.16/0.38 (step @p46 :rule implies_elim :premises (@p45)) % 0.16/0.38 (step @p47 :rule chain_m_resolution :premises (@p46 @p34) :args (@t51 @t52 (@list @t48))) % 0.16/0.38 (step @p48 :rule cnf_or_pos :args (@t51)) % 0.16/0.38 (step @p49 :rule reordering :premises (@p48) :args ((or @t46 @t50 (not @t51)))) % 0.16/0.38 (step @p50 :rule chain_m_resolution :premises (@p49 @p2 @p47) :args (@t50 @t53 (@list @t4 @t51))) % 0.16/0.38 (step @p51 :rule bool-impl-elim :args (@t2 @t54)) % 0.16/0.38 (step @p52 :rule cong :premises (@p51) :args ((forall @t3 (=> @t2 @t54)))) % 0.16/0.38 (step @p53 :rule refl :args (@t17)) % 0.16/0.38 (step @p54 :rule eq-symm :args (@t18 tptp.sz00)) % 0.16/0.38 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t19)) % 0.16/0.38 (step @p56 :rule refl :args (@t2)) % 0.16/0.38 (step @p57 :rule cong :premises (@p56 @p55) :args (@t20)) % 0.16/0.38 (step @p58 :rule cong :premises (@p57) :args (@t21)) % 0.16/0.38 (step @p59 :rule trans :premises (@p58 @p52)) % 0.16/0.38 (step @p60 :rule eq_resolve :premises (@p10 @p59)) % 0.16/0.38 (step @p61 :rule instantiate :premises (@p60) :args ((@list tptp.xa))) % 0.16/0.38 (step @p62 :rule and_elim :premises (@p20) :args (0)) % 0.16/0.38 (step @p63 :rule cnf_or_pos :args (@t58)) % 0.16/0.38 (step @p64 :rule reordering :premises (@p63) :args ((or @t57 @t56 (not @t58)))) % 0.16/0.38 (step @p65 :rule chain_m_resolution :premises (@p64 @p62 @p61) :args (@t56 @t53 (@list @t32 @t58))) % 0.16/0.38 (step @p66 :rule cnf_and_pos :args (@t56 0)) % 0.16/0.38 (step @p67 :rule reordering :premises (@p66) :args ((or @t55 (not @t56)))) % 0.16/0.38 (step @p68 :rule chain_m_resolution :premises (@p67 @p65) :args (@t55 @t52 (@list @t56))) % 0.16/0.38 (step @p69 :rule bool-impl-elim :args (@t2 @t59)) % 0.16/0.38 (step @p70 :rule cong :premises (@p69) :args ((forall @t3 (=> @t2 @t59)))) % 0.16/0.38 (step @p71 :rule refl :args (@t24)) % 0.16/0.38 (step @p72 :rule eq-symm :args (@t25 tptp.sz00)) % 0.16/0.38 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t26)) % 0.16/0.38 (step @p74 :rule cong :premises (@p56 @p73) :args (@t27)) % 0.16/0.38 (step @p75 :rule cong :premises (@p74) :args (@t28)) % 0.16/0.38 (step @p76 :rule trans :premises (@p75 @p70)) % 0.16/0.38 (step @p77 :rule eq_resolve :premises (@p15 @p76)) % 0.16/0.38 (step @p78 :rule instantiate :premises (@p77) :args ((@list tptp.xq))) % 0.16/0.38 (step @p79 :rule and_elim :premises (@p20) :args (1)) % 0.16/0.38 (step @p80 :rule cnf_or_pos :args (@t63)) % 0.16/0.38 (step @p81 :rule reordering :premises (@p80) :args ((or @t62 @t61 (not @t63)))) % 0.16/0.38 (step @p82 :rule chain_m_resolution :premises (@p81 @p79 @p78) :args (@t61 @t53 (@list @t31 @t63))) % 0.16/0.38 (step @p83 :rule cnf_and_pos :args (@t61 0)) % 0.16/0.38 (step @p84 :rule reordering :premises (@p83) :args ((or @t60 (not @t61)))) % 0.16/0.38 (step @p85 :rule chain_m_resolution :premises (@p84 @p82) :args (@t60 @t52 (@list @t61))) % 0.16/0.38 (step @p86 :rule refl :args (@t64)) % 0.16/0.38 (step @p87 :rule bool-double-not-elim :args (@t49)) % 0.16/0.38 (step @p88 :rule refl :args (@t65)) % 0.16/0.38 (step @p89 :rule nary_cong :premises (@p88 @p87 @p86) :args ((or @t65 (not @t50) @t64))) % 0.16/0.38 (assume-push @p108 @t55) % 0.16/0.38 (assume-push @p109 @t50) % 0.16/0.38 (step @p92 :rule false_intro :premises (@p50)) % 0.16/0.38 (step @p93 :rule refl :args (@t44)) % 0.16/0.38 (step @p94 :rule cong :premises (@p68 @p93) :args (@t60)) % 0.16/0.38 (step @p95 :rule trans :premises (@p94 @p92)) % 0.16/0.38 (step @p96 :rule false_elim :premises (@p95)) % 0.16/0.38 (step-pop @p110 :rule scope :premises (@p96)) % 0.16/0.38 (step-pop @p111 :rule scope :premises (@p110)) % 0.16/0.38 (step @p97 :rule process_scope :premises (@p111) :args (@t64)) % 0.16/0.38 (step @p100 :rule implies_elim :premises (@p97)) % 0.16/0.38 (step @p101 :rule cnf_and_neg :args (@t66)) % 0.16/0.38 (step @p102 :rule resolution :premises (@p101 @p100) :args (true @t66)) % 0.16/0.38 (step @p103 :rule eq_resolve :premises (@p102 @p89)) % 0.16/0.38 (step @p104 :rule reordering :premises (@p103) :args ((or @t49 @t65 @t64))) % 0.16/0.38 (step @p105 false :rule chain_m_resolution :premises (@p104 @p85 @p68 @p50) :args (false (@list false false true) (@list @t60 @t55 @t49))) % 0.16/0.38 ) % 0.16/0.38 % SZS output end Proof % 0.16/0.38 % cvc5 exiting %------------------------------------------------------------------------------