%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:04:48 AM UTC 2026 % Result : Theorem 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.35 % Computer : n026.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Mon Sep 7 12:44:57 UTC 2026 % 0.09/0.35 % CPUTime : % 0.13/0.43 %----Proving TF0_NAR, FOF, or CNF % 0.19/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.19/0.50 % SZS status Theorem % 0.19/0.50 % SZS output start Proof % 0.19/0.50 ( % 0.19/0.50 (declare-sort $$unsorted 0) % 0.19/0.50 (declare-const tptp.efficient_producers $$unsorted) % 0.19/0.50 (declare-const tptp.greater (-> $$unsorted $$unsorted Bool)) % 0.19/0.50 (declare-const tptp.zero $$unsorted) % 0.19/0.50 (declare-const tptp.growth_rate (-> $$unsorted $$unsorted $$unsorted)) % 0.19/0.50 (declare-const tptp.outcompetes (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.19/0.50 (declare-const tptp.first_movers $$unsorted) % 0.19/0.50 (declare-const tptp.greater_or_equal (-> $$unsorted $$unsorted Bool)) % 0.19/0.50 (declare-const tptp.environment (-> $$unsorted Bool)) % 0.19/0.50 (declare-const tptp.subpopulations (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.19/0.50 (define @t1 () (@var "T" $$unsorted)) % 0.19/0.50 (define @t2 () (@var "E" $$unsorted)) % 0.19/0.50 (define @t3 () (@var "S1" $$unsorted)) % 0.19/0.50 (define @t4 () (@var "S2" $$unsorted)) % 0.19/0.50 (define @t5 () (tptp.subpopulations @t4 @t3 @t2 @t1)) % 0.19/0.50 (define @t6 () (tptp.subpopulations @t3 @t4 @t2 @t1)) % 0.19/0.50 (define @t7 () (tptp.environment @t2)) % 0.19/0.50 (define @t8 () (and @t7 @t6)) % 0.19/0.50 (define @t9 () (@list @t2 @t3 @t4 @t1)) % 0.19/0.50 (define @t10 () (forall @t9 (=> @t8 @t5))) % 0.19/0.50 (define @t11 () (= (and (tptp.greater_or_equal (tptp.growth_rate @t4 @t1) tptp.zero) (tptp.greater tptp.zero (tptp.growth_rate @t3 @t1))) (tptp.outcompetes @t4 @t3 @t1))) % 0.19/0.50 (define @t12 () (forall @t9 (=> @t8 @t11))) % 0.19/0.50 (define @t13 () (tptp.greater tptp.zero (tptp.growth_rate tptp.efficient_producers @t1))) % 0.19/0.50 (define @t14 () (tptp.greater_or_equal (tptp.growth_rate tptp.first_movers @t1) tptp.zero)) % 0.19/0.50 (define @t15 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t2 @t1)) % 0.19/0.50 (define @t16 () (and @t7 @t15 @t14 @t13)) % 0.19/0.50 (define @t17 () (@list @t2 @t1)) % 0.19/0.50 (define @t18 () (exists @t17 @t16)) % 0.19/0.50 (define @t19 () (tptp.outcompetes tptp.first_movers tptp.efficient_producers @t1)) % 0.19/0.50 (define @t20 () (and @t7 @t15 @t19)) % 0.19/0.50 (define @t21 () (exists @t17 @t20)) % 0.19/0.50 (define @t22 () (not @t21)) % 0.19/0.50 (define @t23 () (not @t13)) % 0.19/0.50 (define @t24 () (not @t14)) % 0.19/0.50 (define @t25 () (not @t15)) % 0.19/0.50 (define @t26 () (not @t7)) % 0.19/0.50 (define @t27 () (or @t26 @t25 @t24 @t23)) % 0.19/0.50 (define @t28 () (forall @t17 (not @t16))) % 0.19/0.50 (define @t29 () (not @t28)) % 0.19/0.50 (define @t30 () (forall @t17 @t27)) % 0.19/0.50 (define @t31 () (@quantifiers_skolemize @t30 0)) % 0.19/0.50 (define @t32 () (tptp.environment @t31)) % 0.19/0.50 (define @t33 () (@quantifiers_skolemize @t30 1)) % 0.19/0.50 (define @t34 () (tptp.greater tptp.zero (tptp.growth_rate tptp.efficient_producers @t33))) % 0.19/0.50 (define @t35 () (not @t34)) % 0.19/0.50 (define @t36 () (tptp.greater_or_equal (tptp.growth_rate tptp.first_movers @t33) tptp.zero)) % 0.19/0.50 (define @t37 () (not @t36)) % 0.19/0.50 (define @t38 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t31 @t33)) % 0.19/0.50 (define @t39 () (not @t38)) % 0.19/0.50 (define @t40 () (not @t32)) % 0.19/0.50 (define @t41 () (or @t40 @t39 @t37 @t35)) % 0.19/0.50 (define @t42 () (@list true)) % 0.19/0.50 (define @t43 () (@list @t41)) % 0.19/0.50 (define @t44 () (not @t6)) % 0.19/0.50 (define @t45 () (or @t26 @t44)) % 0.19/0.50 (define @t46 () (not @t8)) % 0.19/0.50 (define @t47 () (tptp.subpopulations tptp.efficient_producers tptp.first_movers @t31 @t33)) % 0.19/0.50 (define @t48 () (or @t40 @t39 @t47)) % 0.19/0.50 (define @t49 () (@list false false false)) % 0.19/0.50 (define @t50 () (or @t26 @t44 @t11)) % 0.19/0.50 (define @t51 () (and @t36 @t34)) % 0.19/0.50 (define @t52 () (tptp.outcompetes tptp.first_movers tptp.efficient_producers @t33)) % 0.19/0.50 (define @t53 () (not @t47)) % 0.19/0.50 (define @t54 () (or @t40 @t53 (= @t51 @t52))) % 0.19/0.50 (define @t55 () (forall @t9 @t50)) % 0.19/0.50 (define @t56 () (= @t52 @t51)) % 0.19/0.50 (define @t57 () (or @t40 @t53 @t56)) % 0.19/0.50 (define @t58 () (not @t19)) % 0.19/0.50 (define @t59 () (or @t26 @t25 @t58)) % 0.19/0.50 (define @t60 () (forall @t17 (not @t20))) % 0.19/0.50 (define @t61 () (not @t60)) % 0.19/0.50 (define @t62 () (not @t52)) % 0.19/0.50 (define @t63 () (or @t40 @t39 @t62)) % 0.19/0.50 (define @t64 () (not @t56)) % 0.19/0.50 (assume @p1 @t10) % 0.19/0.50 (assume @p2 @t12) % 0.19/0.50 (assume @p3 @t18) % 0.19/0.50 (assume @p4 @t22) % 0.19/0.50 (assume @p5 true) % 0.19/0.50 (step @p6 :rule aci_norm :args ((= (or @t26 (or @t25 (or @t24 @t23))) @t27))) % 0.19/0.50 (step @p7 :rule bool-and-de-morgan :args (@t14 @t13 true)) % 0.19/0.50 (step @p8 :rule refl :args (@t25)) % 0.19/0.50 (step @p9 :rule nary_cong :premises (@p8 @p7) :args ((or @t25 (not (and @t14 @t13))))) % 0.19/0.50 (step @p10 :rule bool-and-de-morgan :args (@t15 @t14 (and @t13))) % 0.19/0.50 (step @p11 :rule trans :premises (@p10 @p9)) % 0.19/0.50 (step @p12 :rule refl :args (@t26)) % 0.19/0.50 (step @p13 :rule nary_cong :premises (@p12 @p11) :args ((or @t26 (not (and @t15 @t14 @t13))))) % 0.19/0.50 (step @p14 :rule bool-and-de-morgan :args (@t7 @t15 (and @t14 @t13))) % 0.19/0.50 (step @p15 :rule trans :premises (@p14 @p13)) % 0.19/0.50 (step @p16 :rule trans :premises (@p15 @p6)) % 0.19/0.50 (step @p17 :rule cong :premises (@p16) :args (@t28)) % 0.19/0.50 (step @p18 :rule cong :premises (@p17) :args (@t29)) % 0.19/0.50 (step @p19 :rule exists-elim :args ((= @t18 @t29))) % 0.19/0.50 (step @p20 :rule trans :premises (@p19 @p18)) % 0.19/0.50 (step @p21 :rule eq_resolve :premises (@p3 @p20)) % 0.19/0.50 (step @p22 :rule skolemize :premises (@p21)) % 0.19/0.50 (step @p23 :rule bool-double-not-elim :args (@t32)) % 0.19/0.50 (step @p24 :rule refl :args (@t41)) % 0.19/0.50 (step @p25 :rule nary_cong :premises (@p24 @p23) :args ((or @t41 (not @t40)))) % 0.19/0.50 (step @p26 :rule cnf_or_neg :args (@t41 0)) % 0.19/0.50 (step @p27 :rule eq_resolve :premises (@p26 @p25)) % 0.19/0.50 (step @p28 :rule reordering :premises (@p27) :args ((or @t32 @t41))) % 0.19/0.50 (step @p29 :rule chain_m_resolution :premises (@p28 @p22) :args (@t32 @t42 @t43)) % 0.19/0.50 (step @p30 :rule aci_norm :args ((= (or @t45 @t5) (or @t26 @t44 @t5)))) % 0.19/0.50 (step @p31 :rule refl :args (@t5)) % 0.19/0.50 (step @p32 :rule bool-and-de-morgan :args (@t7 @t6 true)) % 0.19/0.50 (step @p33 :rule nary_cong :premises (@p32 @p31) :args ((or @t46 @t5))) % 0.19/0.50 (step @p34 :rule trans :premises (@p33 @p30)) % 0.19/0.50 (step @p35 :rule bool-impl-elim :args (@t8 @t5)) % 0.19/0.50 (step @p36 :rule trans :premises (@p35 @p34)) % 0.19/0.50 (step @p37 :rule cong :premises (@p36) :args (@t10)) % 0.19/0.50 (step @p38 :rule eq_resolve :premises (@p1 @p37)) % 0.19/0.50 (step @p39 :rule instantiate :premises (@p38) :args ((@list @t31 tptp.first_movers tptp.efficient_producers @t33))) % 0.19/0.50 (step @p40 :rule bool-double-not-elim :args (@t38)) % 0.19/0.50 (step @p41 :rule nary_cong :premises (@p24 @p40) :args ((or @t41 (not @t39)))) % 0.19/0.50 (step @p42 :rule cnf_or_neg :args (@t41 1)) % 0.19/0.50 (step @p43 :rule eq_resolve :premises (@p42 @p41)) % 0.19/0.50 (step @p44 :rule reordering :premises (@p43) :args ((or @t38 @t41))) % 0.19/0.50 (step @p45 :rule chain_m_resolution :premises (@p44 @p22) :args (@t38 @t42 @t43)) % 0.19/0.50 (step @p46 :rule cnf_or_pos :args (@t48)) % 0.19/0.50 (step @p47 :rule reordering :premises (@p46) :args ((or @t40 @t39 @t47 (not @t48)))) % 0.19/0.50 (step @p48 :rule chain_m_resolution :premises (@p47 @p29 @p45 @p39) :args (@t47 @t49 (@list @t32 @t38 @t48))) % 0.19/0.50 (step @p49 :rule aci_norm :args ((= (or @t45 @t11) @t50))) % 0.19/0.50 (step @p50 :rule refl :args (@t11)) % 0.19/0.50 (step @p51 :rule nary_cong :premises (@p32 @p50) :args ((or @t46 @t11))) % 0.19/0.50 (step @p52 :rule trans :premises (@p51 @p49)) % 0.19/0.50 (step @p53 :rule bool-impl-elim :args (@t8 @t11)) % 0.19/0.50 (step @p54 :rule trans :premises (@p53 @p52)) % 0.19/0.50 (step @p55 :rule cong :premises (@p54) :args (@t12)) % 0.19/0.50 (step @p56 :rule eq_resolve :premises (@p2 @p55)) % 0.19/0.50 (step @p57 :rule eq-symm :args (@t51 @t52)) % 0.19/0.50 (step @p58 :rule refl :args (@t53)) % 0.19/0.50 (step @p59 :rule refl :args (@t40)) % 0.19/0.50 (step @p60 :rule nary_cong :premises (@p59 @p58 @p57) :args (@t54)) % 0.19/0.50 (step @p61 :rule refl :args (@t55)) % 0.19/0.50 (step @p62 :rule cong :premises (@p61 @p60) :args ((=> @t55 @t54))) % 0.19/0.50 (assume-push @p109 @t55) % 0.19/0.50 (step @p64 :rule instantiate :premises (@p56) :args ((@list @t31 tptp.efficient_producers tptp.first_movers @t33))) % 0.19/0.50 (step-pop @p110 :rule scope :premises (@p64)) % 0.19/0.50 (step @p65 :rule process_scope :premises (@p110) :args (@t54)) % 0.19/0.50 (step @p67 :rule eq_resolve :premises (@p65 @p62)) % 0.19/0.50 (step @p68 :rule implies_elim :premises (@p67)) % 0.19/0.50 (step @p69 :rule chain_m_resolution :premises (@p68 @p56) :args (@t57 (@list false) (@list @t55))) % 0.19/0.50 (step @p70 :rule bool-double-not-elim :args (@t34)) % 0.19/0.50 (step @p71 :rule nary_cong :premises (@p24 @p70) :args ((or @t41 (not @t35)))) % 0.19/0.50 (step @p72 :rule cnf_or_neg :args (@t41 3)) % 0.19/0.50 (step @p73 :rule eq_resolve :premises (@p72 @p71)) % 0.19/0.50 (step @p74 :rule reordering :premises (@p73) :args ((or @t34 @t41))) % 0.19/0.50 (step @p75 :rule chain_m_resolution :premises (@p74 @p22) :args (@t34 @t42 @t43)) % 0.19/0.50 (step @p76 :rule bool-double-not-elim :args (@t36)) % 0.19/0.50 (step @p77 :rule nary_cong :premises (@p24 @p76) :args ((or @t41 (not @t37)))) % 0.19/0.50 (step @p78 :rule cnf_or_neg :args (@t41 2)) % 0.19/0.50 (step @p79 :rule eq_resolve :premises (@p78 @p77)) % 0.19/0.50 (step @p80 :rule reordering :premises (@p79) :args ((or @t36 @t41))) % 0.19/0.50 (step @p81 :rule chain_m_resolution :premises (@p80 @p22) :args (@t36 @t42 @t43)) % 0.19/0.50 (step @p82 :rule cnf_and_neg :args (@t51)) % 0.19/0.50 (step @p83 :rule reordering :premises (@p82) :args ((or @t37 @t35 @t51))) % 0.19/0.50 (step @p84 :rule chain_m_resolution :premises (@p83 @p81 @p75) :args (@t51 (@list false false) (@list @t36 @t34))) % 0.19/0.50 (step @p85 :rule bool-double-not-elim :args ((forall @t17 @t59))) % 0.19/0.50 (step @p86 :rule aci_norm :args ((= (or @t26 (or @t25 @t58)) @t59))) % 0.19/0.50 (step @p87 :rule bool-and-de-morgan :args (@t15 @t19 true)) % 0.19/0.50 (step @p88 :rule nary_cong :premises (@p12 @p87) :args ((or @t26 (not (and @t15 @t19))))) % 0.19/0.50 (step @p89 :rule bool-and-de-morgan :args (@t7 @t15 (and @t19))) % 0.19/0.50 (step @p90 :rule trans :premises (@p89 @p88)) % 0.19/0.50 (step @p91 :rule trans :premises (@p90 @p86)) % 0.19/0.50 (step @p92 :rule cong :premises (@p91) :args (@t60)) % 0.19/0.50 (step @p93 :rule cong :premises (@p92) :args (@t61)) % 0.19/0.50 (step @p94 :rule exists-elim :args ((= @t21 @t61))) % 0.19/0.50 (step @p95 :rule trans :premises (@p94 @p93)) % 0.19/0.50 (step @p96 :rule cong :premises (@p95) :args (@t22)) % 0.19/0.50 (step @p97 :rule trans :premises (@p96 @p85)) % 0.19/0.50 (step @p98 :rule eq_resolve :premises (@p4 @p97)) % 0.19/0.50 (step @p99 :rule instantiate :premises (@p98) :args ((@list @t31 @t33))) % 0.19/0.50 (step @p100 :rule cnf_or_pos :args (@t63)) % 0.19/0.50 (step @p101 :rule reordering :premises (@p100) :args ((or @t40 @t39 @t62 (not @t63)))) % 0.19/0.50 (step @p102 :rule chain_m_resolution :premises (@p101 @p29 @p45 @p99) :args (@t62 @t49 (@list @t32 @t38 @t63))) % 0.19/0.50 (step @p103 :rule cnf_equiv_pos2 :args (@t56)) % 0.19/0.50 (step @p104 :rule reordering :premises (@p103) :args ((or @t52 (not @t51) @t64))) % 0.19/0.50 (step @p105 :rule chain_m_resolution :premises (@p104 @p102 @p84) :args (@t64 (@list true false) (@list @t52 @t51))) % 0.19/0.50 (step @p106 :rule cnf_or_pos :args (@t57)) % 0.19/0.50 (step @p107 :rule reordering :premises (@p106) :args ((or @t40 @t53 @t56 (not @t57)))) % 0.19/0.50 (step @p108 false :rule chain_m_resolution :premises (@p107 @p105 @p69 @p48 @p29) :args (false (@list true false false false) (@list @t56 @t57 @t47 @t32))) % 0.19/0.50 ) % 0.19/0.50 % SZS output end Proof % 0.19/0.50 % cvc5 exiting %------------------------------------------------------------------------------