%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : MGT021+1 : 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 : n008.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 06:04:44 AM UTC 2026 % Result : Theorem 0.24s 0.50s % Output : Proof 0.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT021+1 : 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 % 0.09/0.37 % Computer : n008.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Mon Sep 7 12:03:53 UTC 2026 % 0.09/0.37 % CPUTime : % 0.15/0.43 %----Proving TF0_NAR, FOF, or CNF % 0.24/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.24/0.50 % SZS status Theorem % 0.24/0.50 % SZS output start Proof % 0.24/0.50 ( % 0.24/0.50 (declare-sort $$unsorted 0) % 0.24/0.50 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.50 (declare-const tptp.disbanding_rate (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.50 (declare-const tptp.equilibrium (-> $$unsorted $$unsorted)) % 0.24/0.50 (declare-const tptp.in_environment (-> $$unsorted $$unsorted Bool)) % 0.24/0.50 (declare-const tptp.increases (-> $$unsorted Bool)) % 0.24/0.50 (declare-const tptp.efficient_producers $$unsorted) % 0.24/0.50 (declare-const tptp.greater_or_equal (-> $$unsorted $$unsorted Bool)) % 0.24/0.50 (declare-const tptp.first_movers $$unsorted) % 0.24/0.50 (declare-const tptp.greater (-> $$unsorted $$unsorted Bool)) % 0.24/0.50 (declare-const tptp.constant (-> $$unsorted Bool)) % 0.24/0.50 (declare-const tptp.subpopulations (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.24/0.50 (declare-const tptp.environment (-> $$unsorted Bool)) % 0.24/0.50 (declare-const tptp.zero $$unsorted) % 0.24/0.50 (declare-const tptp.resources (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.50 (declare-const tptp.number_of_organizations (-> $$unsorted $$unsorted $$unsorted)) % 0.24/0.50 (declare-const tptp.decreases (-> $$unsorted Bool)) % 0.24/0.50 (define @t1 () (@var "T" $$unsorted)) % 0.24/0.50 (define @t2 () (@var "E" $$unsorted)) % 0.24/0.50 (define @t3 () (tptp.in_environment @t2 @t1)) % 0.24/0.50 (define @t4 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t2 @t1)) % 0.24/0.50 (define @t5 () (tptp.environment @t2)) % 0.24/0.50 (define @t6 () (and @t5 @t4)) % 0.24/0.50 (define @t7 () (@list @t2 @t1)) % 0.24/0.50 (define @t8 () (forall @t7 (=> @t6 @t3))) % 0.24/0.50 (define @t9 () (tptp.greater (tptp.number_of_organizations @t2 @t1) tptp.zero)) % 0.24/0.50 (define @t10 () (forall @t7 (=> @t6 @t9))) % 0.24/0.50 (define @t11 () (@var "X" $$unsorted)) % 0.24/0.50 (define @t12 () (not (tptp.decreases @t11))) % 0.24/0.50 (define @t13 () (tptp.increases @t11)) % 0.24/0.50 (define @t14 () (forall (@list @t11) (=> @t13 @t12))) % 0.24/0.50 (define @t15 () (@var "Y" $$unsorted)) % 0.24/0.50 (define @t16 () (tptp.resources @t2 @t1)) % 0.24/0.50 (define @t17 () (tptp.constant @t16)) % 0.24/0.50 (define @t18 () (tptp.greater (tptp.equilibrium @t2) @t1)) % 0.24/0.50 (define @t19 () (not @t18)) % 0.24/0.50 (define @t20 () (tptp.decreases @t16)) % 0.24/0.50 (define @t21 () (and (=> @t18 @t20) (=> @t19 @t17))) % 0.24/0.50 (define @t22 () (and @t5 @t3 @t9)) % 0.24/0.50 (define @t23 () (forall @t7 (=> @t22 @t21))) % 0.24/0.50 (define @t24 () (tptp.difference (tptp.disbanding_rate tptp.first_movers @t1) (tptp.disbanding_rate tptp.efficient_producers @t1))) % 0.24/0.50 (define @t25 () (not (tptp.decreases @t24))) % 0.24/0.50 (define @t26 () (tptp.increases @t24)) % 0.24/0.50 (define @t27 () (and (=> @t20 @t26) (=> @t17 @t25))) % 0.24/0.50 (define @t28 () (forall @t7 (=> @t6 @t27))) % 0.24/0.50 (define @t29 () (forall @t7 (=> @t6 @t25))) % 0.24/0.50 (define @t30 () (not @t29)) % 0.24/0.50 (define @t31 () (and (or (not @t20) @t26) (or (not @t17) @t25))) % 0.24/0.50 (define @t32 () (not @t4)) % 0.24/0.50 (define @t33 () (not @t5)) % 0.24/0.50 (define @t34 () (or @t33 @t32)) % 0.24/0.50 (define @t35 () (not @t6)) % 0.24/0.50 (define @t36 () (or @t33 @t32 @t25)) % 0.24/0.50 (define @t37 () (forall @t7 @t36)) % 0.24/0.50 (define @t38 () (@quantifiers_skolemize @t37 1)) % 0.24/0.50 (define @t39 () (@quantifiers_skolemize @t37 0)) % 0.24/0.50 (define @t40 () (@list @t39 @t38)) % 0.24/0.50 (define @t41 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t39 @t38)) % 0.24/0.50 (define @t42 () (tptp.difference (tptp.disbanding_rate tptp.first_movers @t38) (tptp.disbanding_rate tptp.efficient_producers @t38))) % 0.24/0.50 (define @t43 () (tptp.decreases @t42)) % 0.24/0.50 (define @t44 () (not @t43)) % 0.24/0.50 (define @t45 () (not @t41)) % 0.24/0.50 (define @t46 () (tptp.environment @t39)) % 0.24/0.50 (define @t47 () (not @t46)) % 0.24/0.50 (define @t48 () (or @t47 @t45 @t44)) % 0.24/0.50 (define @t49 () (@list true)) % 0.24/0.50 (define @t50 () (@list @t48)) % 0.24/0.50 (define @t51 () (tptp.resources @t39 @t38)) % 0.24/0.50 (define @t52 () (tptp.constant @t51)) % 0.24/0.50 (define @t53 () (not @t52)) % 0.24/0.50 (define @t54 () (or @t53 @t44)) % 0.24/0.50 (define @t55 () (tptp.increases @t42)) % 0.24/0.50 (define @t56 () (tptp.decreases @t51)) % 0.24/0.50 (define @t57 () (not @t56)) % 0.24/0.50 (define @t58 () (or @t57 @t55)) % 0.24/0.50 (define @t59 () (and @t58 @t54)) % 0.24/0.50 (define @t60 () (or @t47 @t45 @t59)) % 0.24/0.50 (define @t61 () (@list false false false)) % 0.24/0.50 (define @t62 () (not @t59)) % 0.24/0.50 (define @t63 () (@list false)) % 0.24/0.50 (define @t64 () (@list @t59)) % 0.24/0.50 (define @t65 () (@list false false)) % 0.24/0.50 (define @t66 () (and (or @t19 @t20) (or @t18 @t17))) % 0.24/0.50 (define @t67 () (not @t9)) % 0.24/0.50 (define @t68 () (not @t3)) % 0.24/0.50 (define @t69 () (or @t33 @t68 @t67)) % 0.24/0.50 (define @t70 () (tptp.greater (tptp.number_of_organizations @t39 @t38) tptp.zero)) % 0.24/0.50 (define @t71 () (or @t47 @t45 @t70)) % 0.24/0.50 (define @t72 () (tptp.in_environment @t39 @t38)) % 0.24/0.50 (define @t73 () (or @t47 @t45 @t72)) % 0.24/0.50 (define @t74 () (tptp.greater (tptp.equilibrium @t39) @t38)) % 0.24/0.50 (define @t75 () (or @t74 @t52)) % 0.24/0.50 (define @t76 () (not @t74)) % 0.24/0.50 (define @t77 () (or @t76 @t56)) % 0.24/0.50 (define @t78 () (and @t77 @t75)) % 0.24/0.50 (define @t79 () (not @t70)) % 0.24/0.50 (define @t80 () (not @t72)) % 0.24/0.50 (define @t81 () (or @t47 @t80 @t79 @t78)) % 0.24/0.50 (define @t82 () (not @t78)) % 0.24/0.50 (define @t83 () (@list @t78)) % 0.24/0.50 (define @t84 () (not @t55)) % 0.24/0.50 (define @t85 () (or @t84 @t44)) % 0.24/0.50 (define @t86 () (@list true false)) % 0.24/0.50 (assume @p1 @t8) % 0.24/0.50 (assume @p2 @t10) % 0.24/0.50 (assume @p3 @t14) % 0.24/0.50 (assume @p4 (forall (@list @t11 @t15) (=> (tptp.greater_or_equal @t11 @t15) (or (tptp.greater @t11 @t15) (= @t11 @t15))))) % 0.24/0.50 (assume @p5 @t23) % 0.24/0.50 (assume @p6 @t28) % 0.24/0.50 (assume @p7 @t30) % 0.24/0.50 (assume @p8 true) % 0.24/0.50 (step @p9 :rule aci_norm :args ((= (or @t34 @t31) (or @t33 @t32 @t31)))) % 0.24/0.50 (step @p10 :rule bool-impl-elim :args (@t17 @t25)) % 0.24/0.50 (step @p11 :rule bool-impl-elim :args (@t20 @t26)) % 0.24/0.50 (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t27)) % 0.24/0.50 (step @p13 :rule bool-and-de-morgan :args (@t5 @t4 true)) % 0.24/0.50 (step @p14 :rule nary_cong :premises (@p13 @p12) :args ((or @t35 @t27))) % 0.24/0.50 (step @p15 :rule trans :premises (@p14 @p9)) % 0.24/0.50 (step @p16 :rule bool-impl-elim :args (@t6 @t27)) % 0.24/0.50 (step @p17 :rule trans :premises (@p16 @p15)) % 0.24/0.50 (step @p18 :rule cong :premises (@p17) :args (@t28)) % 0.24/0.50 (step @p19 :rule eq_resolve :premises (@p6 @p18)) % 0.24/0.50 (step @p20 :rule instantiate :premises (@p19) :args (@t40)) % 0.24/0.50 (step @p21 :rule aci_norm :args ((= (or @t34 @t25) @t36))) % 0.24/0.50 (step @p22 :rule refl :args (@t25)) % 0.24/0.50 (step @p23 :rule nary_cong :premises (@p13 @p22) :args ((or @t35 @t25))) % 0.24/0.50 (step @p24 :rule trans :premises (@p23 @p21)) % 0.24/0.50 (step @p25 :rule bool-impl-elim :args (@t6 @t25)) % 0.24/0.50 (step @p26 :rule trans :premises (@p25 @p24)) % 0.24/0.50 (step @p27 :rule cong :premises (@p26) :args (@t29)) % 0.24/0.50 (step @p28 :rule cong :premises (@p27) :args (@t30)) % 0.24/0.50 (step @p29 :rule eq_resolve :premises (@p7 @p28)) % 0.24/0.50 (step @p30 :rule skolemize :premises (@p29)) % 0.24/0.50 (step @p31 :rule bool-double-not-elim :args (@t41)) % 0.24/0.50 (step @p32 :rule refl :args (@t48)) % 0.24/0.50 (step @p33 :rule nary_cong :premises (@p32 @p31) :args ((or @t48 (not @t45)))) % 0.24/0.50 (step @p34 :rule cnf_or_neg :args (@t48 1)) % 0.24/0.50 (step @p35 :rule eq_resolve :premises (@p34 @p33)) % 0.24/0.50 (step @p36 :rule reordering :premises (@p35) :args ((or @t41 @t48))) % 0.24/0.50 (step @p37 :rule chain_m_resolution :premises (@p36 @p30) :args (@t41 @t49 @t50)) % 0.24/0.50 (step @p38 :rule bool-double-not-elim :args (@t46)) % 0.24/0.50 (step @p39 :rule nary_cong :premises (@p32 @p38) :args ((or @t48 (not @t47)))) % 0.24/0.50 (step @p40 :rule cnf_or_neg :args (@t48 0)) % 0.24/0.50 (step @p41 :rule eq_resolve :premises (@p40 @p39)) % 0.24/0.50 (step @p42 :rule reordering :premises (@p41) :args ((or @t46 @t48))) % 0.24/0.50 (step @p43 :rule chain_m_resolution :premises (@p42 @p30) :args (@t46 @t49 @t50)) % 0.24/0.50 (step @p44 :rule cnf_or_pos :args (@t60)) % 0.24/0.50 (step @p45 :rule reordering :premises (@p44) :args ((or @t47 @t45 @t59 (not @t60)))) % 0.24/0.50 (step @p46 :rule chain_m_resolution :premises (@p45 @p43 @p37 @p20) :args (@t59 @t61 (@list @t46 @t41 @t60))) % 0.24/0.50 (step @p47 :rule cnf_and_pos :args (@t59 1)) % 0.24/0.50 (step @p48 :rule reordering :premises (@p47) :args ((or @t54 @t62))) % 0.24/0.50 (step @p49 :rule chain_m_resolution :premises (@p48 @p46) :args (@t54 @t63 @t64)) % 0.24/0.50 (step @p50 :rule bool-double-not-elim :args (@t43)) % 0.24/0.50 (step @p51 :rule nary_cong :premises (@p32 @p50) :args ((or @t48 (not @t44)))) % 0.24/0.50 (step @p52 :rule cnf_or_neg :args (@t48 2)) % 0.24/0.50 (step @p53 :rule eq_resolve :premises (@p52 @p51)) % 0.24/0.50 (step @p54 :rule reordering :premises (@p53) :args ((or @t43 @t48))) % 0.24/0.50 (step @p55 :rule chain_m_resolution :premises (@p54 @p30) :args (@t43 @t49 @t50)) % 0.24/0.50 (step @p56 :rule cnf_or_pos :args (@t54)) % 0.24/0.50 (step @p57 :rule reordering :premises (@p56) :args ((or @t44 @t53 (not @t54)))) % 0.24/0.50 (step @p58 :rule chain_m_resolution :premises (@p57 @p55 @p49) :args (@t53 @t65 (@list @t43 @t54))) % 0.24/0.50 (step @p59 :rule aci_norm :args ((= (or @t69 @t66) (or @t33 @t68 @t67 @t66)))) % 0.24/0.50 (step @p60 :rule refl :args (@t17)) % 0.24/0.50 (step @p61 :rule bool-double-not-elim :args (@t18)) % 0.24/0.50 (step @p62 :rule nary_cong :premises (@p61 @p60) :args ((or (not @t19) @t17))) % 0.24/0.50 (step @p63 :rule bool-impl-elim :args (@t19 @t17)) % 0.24/0.50 (step @p64 :rule trans :premises (@p63 @p62)) % 0.24/0.50 (step @p65 :rule bool-impl-elim :args (@t18 @t20)) % 0.24/0.50 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t21)) % 0.24/0.50 (step @p67 :rule aci_norm :args ((= (or @t33 (or @t68 @t67)) @t69))) % 0.24/0.50 (step @p68 :rule bool-and-de-morgan :args (@t3 @t9 true)) % 0.24/0.50 (step @p69 :rule refl :args (@t33)) % 0.24/0.50 (step @p70 :rule nary_cong :premises (@p69 @p68) :args ((or @t33 (not (and @t3 @t9))))) % 0.24/0.50 (step @p71 :rule bool-and-de-morgan :args (@t5 @t3 (and @t9))) % 0.24/0.50 (step @p72 :rule trans :premises (@p71 @p70)) % 0.24/0.50 (step @p73 :rule trans :premises (@p72 @p67)) % 0.24/0.50 (step @p74 :rule nary_cong :premises (@p73 @p66) :args ((or (not @t22) @t21))) % 0.24/0.50 (step @p75 :rule trans :premises (@p74 @p59)) % 0.24/0.50 (step @p76 :rule bool-impl-elim :args (@t22 @t21)) % 0.24/0.50 (step @p77 :rule trans :premises (@p76 @p75)) % 0.24/0.50 (step @p78 :rule cong :premises (@p77) :args (@t23)) % 0.24/0.50 (step @p79 :rule eq_resolve :premises (@p5 @p78)) % 0.24/0.50 (step @p80 :rule instantiate :premises (@p79) :args (@t40)) % 0.24/0.50 (step @p81 :rule aci_norm :args ((= (or @t34 @t9) (or @t33 @t32 @t9)))) % 0.24/0.50 (step @p82 :rule refl :args (@t9)) % 0.24/0.50 (step @p83 :rule nary_cong :premises (@p13 @p82) :args ((or @t35 @t9))) % 0.24/0.50 (step @p84 :rule trans :premises (@p83 @p81)) % 0.24/0.50 (step @p85 :rule bool-impl-elim :args (@t6 @t9)) % 0.24/0.50 (step @p86 :rule trans :premises (@p85 @p84)) % 0.24/0.50 (step @p87 :rule cong :premises (@p86) :args (@t10)) % 0.24/0.50 (step @p88 :rule eq_resolve :premises (@p2 @p87)) % 0.24/0.50 (step @p89 :rule instantiate :premises (@p88) :args (@t40)) % 0.24/0.50 (step @p90 :rule cnf_or_pos :args (@t71)) % 0.24/0.50 (step @p91 :rule reordering :premises (@p90) :args ((or @t47 @t45 @t70 (not @t71)))) % 0.24/0.50 (step @p92 :rule chain_m_resolution :premises (@p91 @p43 @p37 @p89) :args (@t70 @t61 (@list @t46 @t41 @t71))) % 0.24/0.50 (step @p93 :rule aci_norm :args ((= (or @t34 @t3) (or @t33 @t32 @t3)))) % 0.24/0.50 (step @p94 :rule refl :args (@t3)) % 0.24/0.50 (step @p95 :rule nary_cong :premises (@p13 @p94) :args ((or @t35 @t3))) % 0.24/0.50 (step @p96 :rule trans :premises (@p95 @p93)) % 0.24/0.50 (step @p97 :rule bool-impl-elim :args (@t6 @t3)) % 0.24/0.50 (step @p98 :rule trans :premises (@p97 @p96)) % 0.24/0.50 (step @p99 :rule cong :premises (@p98) :args (@t8)) % 0.24/0.50 (step @p100 :rule eq_resolve :premises (@p1 @p99)) % 0.24/0.50 (step @p101 :rule instantiate :premises (@p100) :args (@t40)) % 0.24/0.50 (step @p102 :rule cnf_or_pos :args (@t73)) % 0.24/0.50 (step @p103 :rule reordering :premises (@p102) :args ((or @t47 @t45 @t72 (not @t73)))) % 0.24/0.50 (step @p104 :rule chain_m_resolution :premises (@p103 @p43 @p37 @p101) :args (@t72 @t61 (@list @t46 @t41 @t73))) % 0.24/0.50 (step @p105 :rule cnf_or_pos :args (@t81)) % 0.24/0.50 (step @p106 :rule reordering :premises (@p105) :args ((or @t47 @t80 @t79 @t78 (not @t81)))) % 0.24/0.50 (step @p107 :rule chain_m_resolution :premises (@p106 @p43 @p104 @p92 @p80) :args (@t78 (@list false false false false) (@list @t46 @t72 @t70 @t81))) % 0.24/0.50 (step @p108 :rule cnf_and_pos :args (@t78 1)) % 0.24/0.50 (step @p109 :rule reordering :premises (@p108) :args ((or @t75 @t82))) % 0.24/0.50 (step @p110 :rule chain_m_resolution :premises (@p109 @p107) :args (@t75 @t63 @t83)) % 0.24/0.50 (step @p111 :rule cnf_and_pos :args (@t78 0)) % 0.24/0.50 (step @p112 :rule reordering :premises (@p111) :args ((or @t77 @t82))) % 0.24/0.50 (step @p113 :rule chain_m_resolution :premises (@p112 @p107) :args (@t77 @t63 @t83)) % 0.24/0.50 (step @p114 :rule cnf_and_pos :args (@t59 0)) % 0.24/0.50 (step @p115 :rule reordering :premises (@p114) :args ((or @t58 @t62))) % 0.24/0.50 (step @p116 :rule chain_m_resolution :premises (@p115 @p46) :args (@t58 @t63 @t64)) % 0.24/0.50 (step @p117 :rule bool-impl-elim :args (@t13 @t12)) % 0.24/0.50 (step @p118 :rule cong :premises (@p117) :args (@t14)) % 0.24/0.50 (step @p119 :rule eq_resolve :premises (@p3 @p118)) % 0.24/0.50 (step @p120 :rule instantiate :premises (@p119) :args ((@list @t42))) % 0.24/0.50 (step @p121 :rule cnf_or_pos :args (@t85)) % 0.24/0.50 (step @p122 :rule reordering :premises (@p121) :args ((or @t44 @t84 (not @t85)))) % 0.24/0.50 (step @p123 :rule chain_m_resolution :premises (@p122 @p55 @p120) :args (@t84 @t65 (@list @t43 @t85))) % 0.24/0.50 (step @p124 :rule cnf_or_pos :args (@t58)) % 0.24/0.50 (step @p125 :rule reordering :premises (@p124) :args ((or @t55 @t57 (not @t58)))) % 0.24/0.50 (step @p126 :rule chain_m_resolution :premises (@p125 @p123 @p116) :args (@t57 @t86 (@list @t55 @t58))) % 0.24/0.51 (step @p127 :rule cnf_or_pos :args (@t77)) % 0.24/0.51 (step @p128 :rule reordering :premises (@p127) :args ((or @t56 @t76 (not @t77)))) % 0.24/0.51 (step @p129 :rule chain_m_resolution :premises (@p128 @p126 @p113) :args (@t76 @t86 (@list @t56 @t77))) % 0.24/0.51 (step @p130 :rule cnf_or_pos :args (@t75)) % 0.24/0.51 (step @p131 :rule reordering :premises (@p130) :args ((or @t52 @t74 (not @t75)))) % 0.24/0.51 (step @p132 false :rule chain_m_resolution :premises (@p131 @p129 @p110 @p58) :args (false (@list true false true) (@list @t74 @t75 @t52))) % 0.24/0.51 ) % 0.24/0.51 % SZS output end Proof % 0.24/0.51 % cvc5 exiting %------------------------------------------------------------------------------