%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM728^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 08:40:29 AM UTC 2026 % Result : Theorem 0.30s 0.55s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM728^1 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n019.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 12:05:49 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.30/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.30/0.55 % SZS status Theorem % 0.30/0.55 % SZS output start Proof % 0.30/0.55 ( % 0.30/0.55 (declare-sort tptp.nat 0) % 0.30/0.55 (declare-sort tptp.frac 0) % 0.30/0.55 (declare-const tptp.n tptp.nat) % 0.30/0.55 (declare-const tptp.x tptp.frac) % 0.30/0.55 (declare-const tptp.fr (-> tptp.nat tptp.nat tptp.frac)) % 0.30/0.55 (declare-const tptp.c1x (-> tptp.frac tptp.nat)) % 0.30/0.55 (declare-const tptp.ts (-> tptp.nat tptp.nat tptp.nat)) % 0.30/0.55 (declare-const tptp.c2x (-> tptp.frac tptp.nat)) % 0.30/0.55 (declare-const tptp.eq (-> tptp.frac tptp.frac Bool)) % 0.30/0.55 (define @t1 () (@var "Xx" tptp.frac)) % 0.30/0.55 (define @t2 () (@var "Xy" tptp.frac)) % 0.30/0.55 (define @t3 () (_ (_ tptp.eq @t2) @t1)) % 0.30/0.55 (define @t4 () (_ tptp.eq @t1)) % 0.30/0.55 (define @t5 () (_ @t4 @t2)) % 0.30/0.55 (define @t6 () (@list @t1 @t2)) % 0.30/0.55 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.30/0.55 (define @t8 () (@var "Xn" tptp.nat)) % 0.30/0.55 (define @t9 () (_ tptp.c2x @t1)) % 0.30/0.55 (define @t10 () (_ (_ tptp.ts @t9) @t8)) % 0.30/0.55 (define @t11 () (_ tptp.c1x @t1)) % 0.30/0.55 (define @t12 () (_ (_ tptp.ts @t11) @t8)) % 0.30/0.55 (define @t13 () (_ (_ tptp.fr @t12) @t10)) % 0.30/0.55 (define @t14 () (_ @t4 @t13)) % 0.30/0.55 (define @t15 () (forall (@list @t1 @t8) @t14)) % 0.30/0.55 (define @t16 () (_ tptp.c2x tptp.x)) % 0.30/0.55 (define @t17 () (_ (_ tptp.ts @t16) tptp.n)) % 0.30/0.55 (define @t18 () (_ tptp.c1x tptp.x)) % 0.30/0.55 (define @t19 () (_ (_ tptp.ts @t18) tptp.n)) % 0.30/0.55 (define @t20 () (_ (_ tptp.fr @t19) @t17)) % 0.30/0.55 (define @t21 () (_ (_ tptp.eq @t20) tptp.x)) % 0.30/0.55 (define @t22 () (not @t21)) % 0.30/0.55 (define @t23 () (tptp.c2x tptp.x)) % 0.30/0.55 (define @t24 () (tptp.ts @t23 tptp.n)) % 0.30/0.55 (define @t25 () (tptp.c1x tptp.x)) % 0.30/0.55 (define @t26 () (tptp.ts @t25 tptp.n)) % 0.30/0.55 (define @t27 () (tptp.fr @t26 @t24)) % 0.30/0.55 (define @t28 () (tptp.eq @t27 tptp.x)) % 0.30/0.55 (define @t29 () (tptp.eq @t2 @t1)) % 0.30/0.55 (define @t30 () (tptp.eq @t1 @t2)) % 0.30/0.55 (define @t31 () (not @t5)) % 0.30/0.55 (define @t32 () (or @t31 @t3)) % 0.30/0.55 (define @t33 () (tptp.c2x @t1)) % 0.30/0.55 (define @t34 () (tptp.ts @t33 @t8)) % 0.30/0.55 (define @t35 () (tptp.c1x @t1)) % 0.30/0.55 (define @t36 () (tptp.ts @t35 @t8)) % 0.30/0.55 (define @t37 () (tptp.fr @t36 @t34)) % 0.30/0.55 (define @t38 () (tptp.eq @t1 @t37)) % 0.30/0.55 (define @t39 () (tptp.eq tptp.x @t27)) % 0.30/0.55 (define @t40 () (not @t39)) % 0.30/0.55 (define @t41 () (or @t40 @t28)) % 0.30/0.55 (assume @p1 @t7) % 0.30/0.55 (assume @p2 @t15) % 0.30/0.55 (assume @p3 @t22) % 0.30/0.55 (assume @p4 true) % 0.30/0.55 (step @p5 :rule refl :args ((tptp.eq @t20 tptp.x))) % 0.30/0.55 (step @p6 :rule refl :args (tptp.x)) % 0.30/0.55 (step @p7 :rule refl :args ((tptp.fr @t19 @t17))) % 0.30/0.55 (step @p8 :rule refl :args ((tptp.ts @t16 tptp.n))) % 0.30/0.55 (step @p9 :rule refl :args (tptp.n)) % 0.30/0.55 (step @p10 :rule refl :args (@t23)) % 0.30/0.55 (step @p11 :rule cong :premises (@p10 @p9) :args (@t24)) % 0.30/0.55 (step @p12 :rule trans :premises (@p11 @p8)) % 0.30/0.55 (step @p13 :rule refl :args ((tptp.ts @t18 tptp.n))) % 0.30/0.55 (step @p14 :rule refl :args (@t25)) % 0.30/0.55 (step @p15 :rule cong :premises (@p14 @p9) :args (@t26)) % 0.30/0.55 (step @p16 :rule trans :premises (@p15 @p13)) % 0.30/0.55 (step @p17 :rule cong :premises (@p16 @p12) :args (@t27)) % 0.30/0.55 (step @p18 :rule trans :premises (@p17 @p7)) % 0.30/0.55 (step @p19 :rule cong :premises (@p18 @p6) :args (@t28)) % 0.30/0.55 (step @p20 :rule trans :premises (@p19 @p5)) % 0.30/0.55 (step @p21 :rule refl :args (tptp.eq)) % 0.30/0.55 (step @p22 :rule ho_cong :premises (@p21 @p18)) % 0.30/0.55 (step @p23 :rule ho_cong :premises (@p22 @p6)) % 0.30/0.55 (step @p24 :rule cong :premises (@p23 @p20) :args ((= (_ (_ tptp.eq @t27) tptp.x) @t28))) % 0.30/0.55 (step @p25 :rule symm :premises (@p24)) % 0.30/0.55 (step @p26 :rule refl :args (@t21)) % 0.30/0.55 (step @p27 :rule eq_resolve :premises (@p26 @p25)) % 0.30/0.55 (step @p28 :rule refl :args (tptp.x)) % 0.30/0.55 (step @p29 :rule refl :args (tptp.fr)) % 0.30/0.55 (step @p30 :rule ho_cong :premises (@p29 @p16)) % 0.30/0.55 (step @p31 :rule ho_cong :premises (@p30 @p12)) % 0.30/0.55 (step @p32 :rule cong :premises (@p31 @p18) :args ((= (_ (_ tptp.fr @t26) @t24) @t27))) % 0.30/0.55 (step @p33 :rule symm :premises (@p32)) % 0.30/0.55 (step @p34 :rule refl :args (@t20)) % 0.30/0.55 (step @p35 :rule eq_resolve :premises (@p34 @p33)) % 0.30/0.55 (step @p36 :rule refl :args (tptp.ts)) % 0.30/0.55 (step @p37 :rule ho_cong :premises (@p36 @p10)) % 0.30/0.55 (step @p38 :rule ho_cong :premises (@p37 @p9)) % 0.30/0.55 (step @p39 :rule cong :premises (@p38 @p12) :args ((= (_ (_ tptp.ts @t23) tptp.n) @t24))) % 0.30/0.55 (step @p40 :rule symm :premises (@p39)) % 0.30/0.55 (step @p41 :rule refl :args (@t17)) % 0.30/0.55 (step @p42 :rule eq_resolve :premises (@p41 @p40)) % 0.30/0.55 (step @p43 :rule refl :args (tptp.n)) % 0.30/0.55 (step @p44 :rule refl :args (@t16)) % 0.30/0.55 (step @p45 :rule cong :premises (@p44 @p10) :args ((= @t16 @t23))) % 0.30/0.55 (step @p46 :rule symm :premises (@p45)) % 0.30/0.55 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.30/0.55 (step @p48 :rule refl :args (tptp.ts)) % 0.30/0.55 (step @p49 :rule ho_cong :premises (@p48 @p47)) % 0.30/0.55 (step @p50 :rule ho_cong :premises (@p49 @p43)) % 0.30/0.55 (step @p51 :rule trans :premises (@p50 @p42)) % 0.30/0.55 (step @p52 :rule ho_cong :premises (@p36 @p14)) % 0.30/0.55 (step @p53 :rule ho_cong :premises (@p52 @p9)) % 0.30/0.55 (step @p54 :rule cong :premises (@p53 @p16) :args ((= (_ (_ tptp.ts @t25) tptp.n) @t26))) % 0.30/0.55 (step @p55 :rule symm :premises (@p54)) % 0.30/0.55 (step @p56 :rule refl :args (@t19)) % 0.30/0.55 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 0.30/0.55 (step @p58 :rule refl :args (@t18)) % 0.30/0.55 (step @p59 :rule cong :premises (@p58 @p14) :args ((= @t18 @t25))) % 0.30/0.55 (step @p60 :rule symm :premises (@p59)) % 0.30/0.55 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 0.30/0.55 (step @p62 :rule ho_cong :premises (@p48 @p61)) % 0.30/0.55 (step @p63 :rule ho_cong :premises (@p62 @p43)) % 0.30/0.55 (step @p64 :rule trans :premises (@p63 @p57)) % 0.30/0.55 (step @p65 :rule refl :args (tptp.fr)) % 0.30/0.55 (step @p66 :rule ho_cong :premises (@p65 @p64)) % 0.30/0.55 (step @p67 :rule ho_cong :premises (@p66 @p51)) % 0.30/0.55 (step @p68 :rule trans :premises (@p67 @p35)) % 0.30/0.55 (step @p69 :rule refl :args (tptp.eq)) % 0.30/0.55 (step @p70 :rule ho_cong :premises (@p69 @p68)) % 0.30/0.55 (step @p71 :rule ho_cong :premises (@p70 @p28)) % 0.30/0.55 (step @p72 :rule trans :premises (@p71 @p27)) % 0.30/0.55 (step @p73 :rule cong :premises (@p72) :args (@t22)) % 0.30/0.55 (step @p74 :rule eq_resolve :premises (@p3 @p73)) % 0.30/0.55 (step @p75 :rule refl :args (@t29)) % 0.30/0.55 (step @p76 :rule refl :args (@t3)) % 0.30/0.55 (step @p77 :rule cong :premises (@p76 @p75) :args ((= @t3 @t29))) % 0.30/0.55 (step @p78 :rule symm :premises (@p77)) % 0.30/0.55 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.30/0.55 (step @p80 :rule refl :args (@t30)) % 0.30/0.55 (step @p81 :rule refl :args (@t5)) % 0.30/0.55 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t5 @t30))) % 0.30/0.55 (step @p83 :rule symm :premises (@p82)) % 0.30/0.55 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 0.30/0.55 (step @p85 :rule cong :premises (@p84) :args (@t31)) % 0.30/0.55 (step @p86 :rule nary_cong :premises (@p85 @p79) :args (@t32)) % 0.30/0.55 (step @p87 :rule cong :premises (@p86) :args ((forall @t6 @t32))) % 0.30/0.55 (step @p88 :rule bool-impl-elim :args (@t5 @t3)) % 0.30/0.55 (step @p89 :rule cong :premises (@p88) :args (@t7)) % 0.30/0.55 (step @p90 :rule trans :premises (@p89 @p87)) % 0.30/0.55 (step @p91 :rule eq_resolve :premises (@p1 @p90)) % 0.30/0.55 (step @p92 :rule instantiate :premises (@p91) :args ((@list tptp.x @t27))) % 0.30/0.55 (step @p93 :rule refl :args ((tptp.eq @t1 @t13))) % 0.30/0.55 (step @p94 :rule refl :args ((tptp.fr @t12 @t10))) % 0.30/0.55 (step @p95 :rule refl :args ((tptp.ts @t9 @t8))) % 0.30/0.55 (step @p96 :rule refl :args (@t8)) % 0.30/0.55 (step @p97 :rule refl :args (@t33)) % 0.30/0.55 (step @p98 :rule cong :premises (@p97 @p96) :args (@t34)) % 0.30/0.55 (step @p99 :rule trans :premises (@p98 @p95)) % 0.30/0.55 (step @p100 :rule refl :args ((tptp.ts @t11 @t8))) % 0.30/0.55 (step @p101 :rule refl :args (@t35)) % 0.30/0.55 (step @p102 :rule cong :premises (@p101 @p96) :args (@t36)) % 0.30/0.55 (step @p103 :rule trans :premises (@p102 @p100)) % 0.30/0.55 (step @p104 :rule cong :premises (@p103 @p99) :args (@t37)) % 0.30/0.55 (step @p105 :rule trans :premises (@p104 @p94)) % 0.30/0.55 (step @p106 :rule refl :args (@t1)) % 0.30/0.55 (step @p107 :rule cong :premises (@p106 @p105) :args (@t38)) % 0.30/0.55 (step @p108 :rule trans :premises (@p107 @p93)) % 0.30/0.55 (step @p109 :rule refl :args (@t4)) % 0.30/0.55 (step @p110 :rule ho_cong :premises (@p109 @p105)) % 0.30/0.55 (step @p111 :rule cong :premises (@p110 @p108) :args ((= (_ @t4 @t37) @t38))) % 0.30/0.55 (step @p112 :rule symm :premises (@p111)) % 0.30/0.55 (step @p113 :rule refl :args (@t14)) % 0.30/0.55 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 0.30/0.55 (step @p115 :rule ho_cong :premises (@p29 @p103)) % 0.30/0.55 (step @p116 :rule ho_cong :premises (@p115 @p99)) % 0.30/0.55 (step @p117 :rule cong :premises (@p116 @p105) :args ((= (_ (_ tptp.fr @t36) @t34) @t37))) % 0.30/0.55 (step @p118 :rule symm :premises (@p117)) % 0.30/0.55 (step @p119 :rule refl :args (@t13)) % 0.30/0.55 (step @p120 :rule eq_resolve :premises (@p119 @p118)) % 0.30/0.55 (step @p121 :rule ho_cong :premises (@p36 @p97)) % 0.30/0.55 (step @p122 :rule ho_cong :premises (@p121 @p96)) % 0.30/0.55 (step @p123 :rule cong :premises (@p122 @p99) :args ((= (_ (_ tptp.ts @t33) @t8) @t34))) % 0.30/0.55 (step @p124 :rule symm :premises (@p123)) % 0.30/0.55 (step @p125 :rule refl :args (@t10)) % 0.30/0.55 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 0.30/0.55 (step @p127 :rule refl :args (@t9)) % 0.38/0.55 (step @p128 :rule cong :premises (@p127 @p97) :args ((= @t9 @t33))) % 0.38/0.55 (step @p129 :rule symm :premises (@p128)) % 0.38/0.55 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 0.38/0.55 (step @p131 :rule ho_cong :premises (@p36 @p130)) % 0.38/0.55 (step @p132 :rule ho_cong :premises (@p131 @p96)) % 0.38/0.55 (step @p133 :rule trans :premises (@p132 @p126)) % 0.38/0.55 (step @p134 :rule ho_cong :premises (@p36 @p101)) % 0.38/0.55 (step @p135 :rule ho_cong :premises (@p134 @p96)) % 0.38/0.55 (step @p136 :rule cong :premises (@p135 @p103) :args ((= (_ (_ tptp.ts @t35) @t8) @t36))) % 0.38/0.55 (step @p137 :rule symm :premises (@p136)) % 0.38/0.55 (step @p138 :rule refl :args (@t12)) % 0.38/0.55 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.38/0.55 (step @p140 :rule refl :args (@t11)) % 0.38/0.55 (step @p141 :rule cong :premises (@p140 @p101) :args ((= @t11 @t35))) % 0.38/0.55 (step @p142 :rule symm :premises (@p141)) % 0.38/0.55 (step @p143 :rule eq_resolve :premises (@p140 @p142)) % 0.38/0.55 (step @p144 :rule ho_cong :premises (@p36 @p143)) % 0.38/0.55 (step @p145 :rule ho_cong :premises (@p144 @p96)) % 0.38/0.55 (step @p146 :rule trans :premises (@p145 @p139)) % 0.38/0.55 (step @p147 :rule ho_cong :premises (@p29 @p146)) % 0.38/0.55 (step @p148 :rule ho_cong :premises (@p147 @p133)) % 0.38/0.55 (step @p149 :rule trans :premises (@p148 @p120)) % 0.38/0.55 (step @p150 :rule ho_cong :premises (@p109 @p149)) % 0.38/0.55 (step @p151 :rule trans :premises (@p150 @p114)) % 0.38/0.55 (step @p152 :rule cong :premises (@p151) :args (@t15)) % 0.38/0.55 (step @p153 :rule eq_resolve :premises (@p2 @p152)) % 0.38/0.55 (step @p154 :rule instantiate :premises (@p153) :args ((@list tptp.x tptp.n))) % 0.38/0.55 (step @p155 :rule cnf_or_pos :args (@t41)) % 0.38/0.55 (step @p156 :rule reordering :premises (@p155) :args ((or @t28 @t40 (not @t41)))) % 0.38/0.55 (step @p157 false :rule chain_m_resolution :premises (@p156 @p154 @p92 @p74) :args (false (@list false false true) (@list @t39 @t41 @t28))) % 0.38/0.55 ) % 0.38/0.55 % SZS output end Proof % 0.38/0.55 % cvc5 exiting %------------------------------------------------------------------------------