%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : MGT023+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 : n005.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 0.21s 0.50s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT023+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 % 0.10/0.36 % Computer : n005.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Mon Sep 7 12:06:35 UTC 2026 % 0.10/0.36 % CPUTime : % 0.10/0.43 %----Proving TF0_NAR, FOF, or CNF % 0.21/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.21/0.50 % SZS status Theorem % 0.21/0.50 % SZS output start Proof % 0.21/0.50 ( % 0.21/0.50 (declare-sort $$unsorted 0) % 0.21/0.50 (declare-const tptp.stable (-> $$unsorted Bool)) % 0.21/0.50 (declare-const tptp.environment (-> $$unsorted Bool)) % 0.21/0.50 (declare-const tptp.in_environment (-> $$unsorted $$unsorted Bool)) % 0.21/0.50 (declare-const tptp.subpopulations (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.21/0.50 (declare-const tptp.greater (-> $$unsorted $$unsorted Bool)) % 0.21/0.50 (declare-const tptp.efficient_producers $$unsorted) % 0.21/0.50 (declare-const tptp.growth_rate (-> $$unsorted $$unsorted $$unsorted)) % 0.21/0.50 (declare-const tptp.first_movers $$unsorted) % 0.21/0.50 (declare-const tptp.critical_point (-> $$unsorted $$unsorted)) % 0.21/0.50 (define @t1 () (@var "E" $$unsorted)) % 0.21/0.50 (define @t2 () (tptp.critical_point @t1)) % 0.21/0.50 (define @t3 () (@var "To" $$unsorted)) % 0.21/0.50 (define @t4 () (= @t3 @t2)) % 0.21/0.50 (define @t5 () (@var "T" $$unsorted)) % 0.21/0.50 (define @t6 () (tptp.greater (tptp.growth_rate tptp.efficient_producers @t5) (tptp.growth_rate tptp.first_movers @t5))) % 0.21/0.50 (define @t7 () (tptp.greater @t5 @t3)) % 0.21/0.50 (define @t8 () (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t1 @t5)) % 0.21/0.50 (define @t9 () (and @t8 @t7)) % 0.21/0.50 (define @t10 () (@list @t5)) % 0.21/0.50 (define @t11 () (forall @t10 (=> @t9 @t6))) % 0.21/0.50 (define @t12 () (tptp.in_environment @t1 @t3)) % 0.21/0.50 (define @t13 () (tptp.greater (tptp.growth_rate tptp.efficient_producers @t3) (tptp.growth_rate tptp.first_movers @t3))) % 0.21/0.50 (define @t14 () (not @t13)) % 0.21/0.50 (define @t15 () (tptp.environment @t1)) % 0.21/0.50 (define @t16 () (and @t15 @t14 @t12 @t11)) % 0.21/0.50 (define @t17 () (=> @t16 @t4)) % 0.21/0.50 (define @t18 () (@list @t1 @t3)) % 0.21/0.50 (define @t19 () (forall @t18 @t17)) % 0.21/0.50 (define @t20 () (and @t12 @t14 @t11)) % 0.21/0.50 (define @t21 () (@list @t3)) % 0.21/0.50 (define @t22 () (exists @t21 @t20)) % 0.21/0.50 (define @t23 () (tptp.stable @t1)) % 0.21/0.50 (define @t24 () (and @t15 @t23)) % 0.21/0.50 (define @t25 () (=> @t24 @t22)) % 0.21/0.50 (define @t26 () (@list @t1)) % 0.21/0.50 (define @t27 () (forall @t26 @t25)) % 0.21/0.50 (define @t28 () (tptp.in_environment @t1 @t2)) % 0.21/0.50 (define @t29 () (forall @t26 (=> @t24 @t28))) % 0.21/0.50 (define @t30 () (not @t29)) % 0.21/0.50 (define @t31 () (not @t23)) % 0.21/0.50 (define @t32 () (not @t15)) % 0.21/0.50 (define @t33 () (or @t32 @t31 @t28)) % 0.21/0.50 (define @t34 () (or @t32 @t31)) % 0.21/0.50 (define @t35 () (not @t24)) % 0.21/0.50 (define @t36 () (@quantifiers_skolemize (forall @t26 @t33) 0)) % 0.21/0.50 (define @t37 () (tptp.critical_point @t36)) % 0.21/0.50 (define @t38 () (tptp.in_environment @t36 @t37)) % 0.21/0.50 (define @t39 () (tptp.stable @t36)) % 0.21/0.50 (define @t40 () (not @t39)) % 0.21/0.50 (define @t41 () (tptp.environment @t36)) % 0.21/0.50 (define @t42 () (not @t41)) % 0.21/0.50 (define @t43 () (or @t42 @t40 @t38)) % 0.21/0.50 (define @t44 () (@list true)) % 0.21/0.50 (define @t45 () (@list @t43)) % 0.21/0.50 (define @t46 () (not @t7)) % 0.21/0.50 (define @t47 () (not @t8)) % 0.21/0.50 (define @t48 () (or @t47 @t46 @t6)) % 0.21/0.50 (define @t49 () (forall @t10 @t48)) % 0.21/0.50 (define @t50 () (not @t49)) % 0.21/0.50 (define @t51 () (not @t12)) % 0.21/0.50 (define @t52 () (or @t32 @t13 @t51 @t50 @t4)) % 0.21/0.50 (define @t53 () (not @t14)) % 0.21/0.50 (define @t54 () (or @t32 @t53 @t51 @t50)) % 0.21/0.50 (define @t55 () (and @t15 @t14 @t12 @t49)) % 0.21/0.50 (define @t56 () (not (tptp.subpopulations tptp.first_movers tptp.efficient_producers @t36 @t5))) % 0.21/0.50 (define @t57 () (forall @t21 (or (not (tptp.in_environment @t36 @t3)) @t13 (not (forall @t10 (or @t56 @t46 @t6)))))) % 0.21/0.50 (define @t58 () (@quantifiers_skolemize @t57 0)) % 0.21/0.50 (define @t59 () (forall @t10 (or @t56 (not (tptp.greater @t5 @t58)) @t6))) % 0.21/0.50 (define @t60 () (not @t59)) % 0.21/0.50 (define @t61 () (tptp.in_environment @t36 @t58)) % 0.21/0.50 (define @t62 () (not @t61)) % 0.21/0.50 (define @t63 () (tptp.greater (tptp.growth_rate tptp.efficient_producers @t58) (tptp.growth_rate tptp.first_movers @t58))) % 0.21/0.50 (define @t64 () (or @t42 @t63 @t62 @t60 (= @t58 @t37))) % 0.21/0.50 (define @t65 () (forall @t18 @t52)) % 0.21/0.50 (define @t66 () (= @t37 @t58)) % 0.21/0.50 (define @t67 () (or @t42 @t63 @t62 @t60 @t66)) % 0.21/0.50 (define @t68 () (not (forall @t21 (or @t51 @t13 @t50)))) % 0.21/0.50 (define @t69 () (or @t51 @t53 @t50)) % 0.21/0.50 (define @t70 () (and @t12 @t14 @t49)) % 0.21/0.50 (define @t71 () (forall @t21 (not @t70))) % 0.21/0.50 (define @t72 () (not @t71)) % 0.21/0.50 (define @t73 () (not @t57)) % 0.21/0.50 (define @t74 () (or @t42 @t40 @t73)) % 0.21/0.50 (define @t75 () (or @t62 @t63 @t60)) % 0.21/0.50 (define @t76 () (@list @t75)) % 0.21/0.50 (assume @p1 @t19) % 0.21/0.50 (assume @p2 @t27) % 0.21/0.50 (assume @p3 @t30) % 0.21/0.50 (assume @p4 true) % 0.21/0.50 (step @p5 :rule evaluate :args ((= true false))) % 0.21/0.50 (step @p6 :rule aci_norm :args ((= (or @t34 @t28) @t33))) % 0.21/0.50 (step @p7 :rule refl :args (@t28)) % 0.21/0.50 (step @p8 :rule bool-and-de-morgan :args (@t15 @t23 true)) % 0.21/0.50 (step @p9 :rule nary_cong :premises (@p8 @p7) :args ((or @t35 @t28))) % 0.21/0.50 (step @p10 :rule trans :premises (@p9 @p6)) % 0.21/0.50 (step @p11 :rule bool-impl-elim :args (@t24 @t28)) % 0.21/0.50 (step @p12 :rule trans :premises (@p11 @p10)) % 0.21/0.50 (step @p13 :rule cong :premises (@p12) :args (@t29)) % 0.21/0.50 (step @p14 :rule cong :premises (@p13) :args (@t30)) % 0.21/0.50 (step @p15 :rule eq_resolve :premises (@p3 @p14)) % 0.21/0.50 (step @p16 :rule skolemize :premises (@p15)) % 0.21/0.50 (step @p17 :rule cnf_or_neg :args (@t43 2)) % 0.21/0.50 (step @p18 :rule chain_m_resolution :premises (@p17 @p16) :args ((not @t38) @t44 @t45)) % 0.21/0.50 (step @p19 :rule false_intro :premises (@p18)) % 0.21/0.50 (step @p20 :rule aci_norm :args ((= (or (or @t32 @t13 @t51 @t50) @t4) @t52))) % 0.21/0.50 (step @p21 :rule refl :args (@t4)) % 0.21/0.50 (step @p22 :rule refl :args (@t50)) % 0.21/0.50 (step @p23 :rule refl :args (@t51)) % 0.21/0.50 (step @p24 :rule bool-double-not-elim :args (@t13)) % 0.21/0.50 (step @p25 :rule refl :args (@t32)) % 0.21/0.50 (step @p26 :rule nary_cong :premises (@p25 @p24 @p23 @p22) :args (@t54)) % 0.21/0.50 (step @p27 :rule aci_norm :args ((= (or @t32 (or @t53 (or @t51 @t50))) @t54))) % 0.21/0.50 (step @p28 :rule trans :premises (@p27 @p26)) % 0.21/0.50 (step @p29 :rule bool-and-de-morgan :args (@t12 @t49 true)) % 0.21/0.50 (step @p30 :rule refl :args (@t53)) % 0.21/0.50 (step @p31 :rule nary_cong :premises (@p30 @p29) :args ((or @t53 (not (and @t12 @t49))))) % 0.21/0.50 (step @p32 :rule bool-and-de-morgan :args (@t14 @t12 (and @t49))) % 0.21/0.50 (step @p33 :rule trans :premises (@p32 @p31)) % 0.21/0.50 (step @p34 :rule nary_cong :premises (@p25 @p33) :args ((or @t32 (not (and @t14 @t12 @t49))))) % 0.21/0.50 (step @p35 :rule bool-and-de-morgan :args (@t15 @t14 (and @t12 @t49))) % 0.21/0.50 (step @p36 :rule trans :premises (@p35 @p34)) % 0.21/0.50 (step @p37 :rule trans :premises (@p36 @p28)) % 0.21/0.50 (step @p38 :rule nary_cong :premises (@p37 @p21) :args ((or (not @t55) @t4))) % 0.21/0.50 (step @p39 :rule trans :premises (@p38 @p20)) % 0.21/0.50 (step @p40 :rule bool-impl-elim :args (@t55 @t4)) % 0.21/0.50 (step @p41 :rule trans :premises (@p40 @p39)) % 0.21/0.50 (step @p42 :rule cong :premises (@p41) :args ((forall @t18 (=> @t55 @t4)))) % 0.21/0.50 (step @p43 :rule refl :args (@t4)) % 0.21/0.50 (step @p44 :rule aci_norm :args ((= (or (or @t47 @t46) @t6) @t48))) % 0.21/0.50 (step @p45 :rule refl :args (@t6)) % 0.21/0.50 (step @p46 :rule bool-and-de-morgan :args (@t8 @t7 true)) % 0.21/0.50 (step @p47 :rule nary_cong :premises (@p46 @p45) :args ((or (not @t9) @t6))) % 0.21/0.50 (step @p48 :rule trans :premises (@p47 @p44)) % 0.21/0.50 (step @p49 :rule bool-impl-elim :args (@t9 @t6)) % 0.21/0.50 (step @p50 :rule trans :premises (@p49 @p48)) % 0.21/0.50 (step @p51 :rule cong :premises (@p50) :args (@t11)) % 0.21/0.50 (step @p52 :rule refl :args (@t12)) % 0.21/0.50 (step @p53 :rule refl :args (@t14)) % 0.21/0.50 (step @p54 :rule refl :args (@t15)) % 0.21/0.50 (step @p55 :rule nary_cong :premises (@p54 @p53 @p52 @p51) :args (@t16)) % 0.21/0.50 (step @p56 :rule cong :premises (@p55 @p43) :args (@t17)) % 0.21/0.50 (step @p57 :rule cong :premises (@p56) :args (@t19)) % 0.21/0.50 (step @p58 :rule trans :premises (@p57 @p42)) % 0.21/0.50 (step @p59 :rule eq_resolve :premises (@p1 @p58)) % 0.21/0.50 (step @p60 :rule eq-symm :args (@t58 @t37)) % 0.21/0.50 (step @p61 :rule refl :args (@t60)) % 0.21/0.50 (step @p62 :rule refl :args (@t62)) % 0.21/0.50 (step @p63 :rule refl :args (@t63)) % 0.21/0.50 (step @p64 :rule refl :args (@t42)) % 0.21/0.50 (step @p65 :rule nary_cong :premises (@p64 @p63 @p62 @p61 @p60) :args (@t64)) % 0.21/0.50 (step @p66 :rule refl :args (@t65)) % 0.21/0.50 (step @p67 :rule cong :premises (@p66 @p65) :args ((=> @t65 @t64))) % 0.21/0.50 (assume-push @p145 @t65) % 0.21/0.50 (step @p69 :rule instantiate :premises (@p59) :args ((@list @t36 @t58))) % 0.21/0.50 (step-pop @p146 :rule scope :premises (@p69)) % 0.21/0.50 (step @p70 :rule process_scope :premises (@p146) :args (@t64)) % 0.21/0.50 (step @p72 :rule eq_resolve :premises (@p70 @p67)) % 0.21/0.50 (step @p73 :rule implies_elim :premises (@p72)) % 0.21/0.50 (step @p74 :rule chain_m_resolution :premises (@p73 @p59) :args (@t67 (@list false) (@list @t65))) % 0.21/0.50 (step @p75 :rule aci_norm :args ((= (or @t34 @t68) (or @t32 @t31 @t68)))) % 0.21/0.50 (step @p76 :rule refl :args (@t68)) % 0.21/0.50 (step @p77 :rule nary_cong :premises (@p8 @p76) :args ((or @t35 @t68))) % 0.21/0.50 (step @p78 :rule trans :premises (@p77 @p75)) % 0.21/0.50 (step @p79 :rule bool-impl-elim :args (@t24 @t68)) % 0.21/0.50 (step @p80 :rule trans :premises (@p79 @p78)) % 0.21/0.50 (step @p81 :rule cong :premises (@p80) :args ((forall @t26 (=> @t24 @t68)))) % 0.21/0.51 (step @p82 :rule nary_cong :premises (@p23 @p24 @p22) :args (@t69)) % 0.21/0.51 (step @p83 :rule aci_norm :args ((= (or @t51 (or @t53 @t50)) @t69))) % 0.21/0.51 (step @p84 :rule trans :premises (@p83 @p82)) % 0.21/0.51 (step @p85 :rule bool-and-de-morgan :args (@t14 @t49 true)) % 0.21/0.51 (step @p86 :rule nary_cong :premises (@p23 @p85) :args ((or @t51 (not (and @t14 @t49))))) % 0.21/0.51 (step @p87 :rule bool-and-de-morgan :args (@t12 @t14 (and @t49))) % 0.21/0.51 (step @p88 :rule trans :premises (@p87 @p86)) % 0.21/0.51 (step @p89 :rule trans :premises (@p88 @p84)) % 0.21/0.51 (step @p90 :rule cong :premises (@p89) :args (@t71)) % 0.21/0.51 (step @p91 :rule cong :premises (@p90) :args (@t72)) % 0.21/0.51 (step @p92 :rule exists-elim :args ((= (exists @t21 @t70) @t72))) % 0.21/0.51 (step @p93 :rule trans :premises (@p92 @p91)) % 0.21/0.51 (step @p94 :rule nary_cong :premises (@p52 @p53 @p51) :args (@t20)) % 0.21/0.51 (step @p95 :rule cong :premises (@p94) :args (@t22)) % 0.21/0.51 (step @p96 :rule trans :premises (@p95 @p93)) % 0.21/0.51 (step @p97 :rule refl :args (@t24)) % 0.21/0.51 (step @p98 :rule cong :premises (@p97 @p96) :args (@t25)) % 0.21/0.51 (step @p99 :rule cong :premises (@p98) :args (@t27)) % 0.21/0.51 (step @p100 :rule trans :premises (@p99 @p81)) % 0.21/0.51 (step @p101 :rule eq_resolve :premises (@p2 @p100)) % 0.21/0.51 (step @p102 :rule instantiate :premises (@p101) :args ((@list @t36))) % 0.21/0.51 (step @p103 :rule bool-double-not-elim :args (@t39)) % 0.21/0.51 (step @p104 :rule refl :args (@t43)) % 0.21/0.51 (step @p105 :rule nary_cong :premises (@p104 @p103) :args ((or @t43 (not @t40)))) % 0.21/0.51 (step @p106 :rule cnf_or_neg :args (@t43 1)) % 0.21/0.51 (step @p107 :rule eq_resolve :premises (@p106 @p105)) % 0.21/0.51 (step @p108 :rule reordering :premises (@p107) :args ((or @t39 @t43))) % 0.21/0.51 (step @p109 :rule chain_m_resolution :premises (@p108 @p16) :args (@t39 @t44 @t45)) % 0.21/0.51 (step @p110 :rule bool-double-not-elim :args (@t41)) % 0.21/0.51 (step @p111 :rule nary_cong :premises (@p104 @p110) :args ((or @t43 (not @t42)))) % 0.21/0.51 (step @p112 :rule cnf_or_neg :args (@t43 0)) % 0.21/0.51 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 0.21/0.51 (step @p114 :rule reordering :premises (@p113) :args ((or @t41 @t43))) % 0.21/0.51 (step @p115 :rule chain_m_resolution :premises (@p114 @p16) :args (@t41 @t44 @t45)) % 0.21/0.51 (step @p116 :rule cnf_or_pos :args (@t74)) % 0.21/0.51 (step @p117 :rule reordering :premises (@p116) :args ((or @t42 @t40 @t73 (not @t74)))) % 0.21/0.51 (step @p118 :rule chain_m_resolution :premises (@p117 @p115 @p109 @p102) :args (@t73 (@list false false false) (@list @t41 @t39 @t74))) % 0.21/0.51 (step @p119 :rule skolemize :premises (@p118)) % 0.21/0.51 (step @p120 :rule bool-double-not-elim :args (@t59)) % 0.21/0.51 (step @p121 :rule refl :args (@t75)) % 0.21/0.51 (step @p122 :rule nary_cong :premises (@p121 @p120) :args ((or @t75 (not @t60)))) % 0.21/0.51 (step @p123 :rule cnf_or_neg :args (@t75 2)) % 0.21/0.51 (step @p124 :rule eq_resolve :premises (@p123 @p122)) % 0.21/0.51 (step @p125 :rule reordering :premises (@p124) :args ((or @t59 @t75))) % 0.21/0.51 (step @p126 :rule chain_m_resolution :premises (@p125 @p119) :args (@t59 @t44 @t76)) % 0.21/0.51 (step @p127 :rule cnf_or_neg :args (@t75 1)) % 0.21/0.51 (step @p128 :rule chain_m_resolution :premises (@p127 @p119) :args ((not @t63) @t44 @t76)) % 0.21/0.51 (step @p129 :rule bool-double-not-elim :args (@t61)) % 0.21/0.51 (step @p130 :rule nary_cong :premises (@p121 @p129) :args ((or @t75 (not @t62)))) % 0.21/0.51 (step @p131 :rule cnf_or_neg :args (@t75 0)) % 0.21/0.51 (step @p132 :rule eq_resolve :premises (@p131 @p130)) % 0.21/0.51 (step @p133 :rule reordering :premises (@p132) :args ((or @t61 @t75))) % 0.21/0.51 (step @p134 :rule chain_m_resolution :premises (@p133 @p119) :args (@t61 @t44 @t76)) % 0.21/0.51 (step @p135 :rule cnf_or_pos :args (@t67)) % 0.21/0.51 (step @p136 :rule reordering :premises (@p135) :args ((or @t42 @t62 @t63 @t60 @t66 (not @t67)))) % 0.21/0.51 (step @p137 :rule chain_m_resolution :premises (@p136 @p115 @p134 @p128 @p126 @p74) :args (@t66 (@list false false true false false) (@list @t41 @t61 @t63 @t59 @t67))) % 0.21/0.51 (step @p138 :rule symm :premises (@p137)) % 0.21/0.51 (step @p139 :rule refl :args (@t36)) % 0.21/0.51 (step @p140 :rule cong :premises (@p139 @p138) :args (@t61)) % 0.21/0.51 (step @p141 :rule true_intro :premises (@p134)) % 0.21/0.51 (step @p142 :rule symm :premises (@p141)) % 0.21/0.51 (step @p143 :rule trans :premises (@p142 @p140 @p19)) % 0.21/0.51 (step @p144 false :rule eq_resolve :premises (@p143 @p5)) % 0.21/0.51 ) % 0.21/0.51 % SZS output end Proof % 0.21/0.51 % cvc5 exiting %------------------------------------------------------------------------------