%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM748^1 : 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 : n009.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 08:40:33 AM UTC 2026 % Result : Theorem 0.37s 0.56s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM748^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n009.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 12:10:29 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.37/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.56 % SZS status Theorem % 0.37/0.56 % SZS output start Proof % 0.37/0.56 ( % 0.37/0.56 (declare-sort tptp.nat 0) % 0.37/0.56 (declare-sort tptp.frac 0) % 0.37/0.56 (declare-const tptp.fr (-> tptp.nat tptp.nat tptp.frac)) % 0.37/0.56 (declare-const tptp.num (-> tptp.frac tptp.nat)) % 0.37/0.56 (declare-const tptp.y tptp.frac) % 0.37/0.56 (declare-const tptp.den (-> tptp.frac tptp.nat)) % 0.37/0.56 (declare-const tptp.x tptp.frac) % 0.37/0.56 (declare-const tptp.pl (-> tptp.nat tptp.nat tptp.nat)) % 0.37/0.56 (declare-const tptp.ts (-> tptp.nat tptp.nat tptp.nat)) % 0.37/0.56 (declare-const tptp.eq (-> tptp.frac tptp.frac Bool)) % 0.37/0.56 (define @t1 () (@var "Xx" tptp.frac)) % 0.37/0.56 (define @t2 () (_ (_ tptp.eq @t1) @t1)) % 0.37/0.56 (define @t3 () (@list @t1)) % 0.37/0.56 (define @t4 () (forall @t3 @t2)) % 0.37/0.56 (define @t5 () (@var "Xx" tptp.nat)) % 0.37/0.56 (define @t6 () (@var "Xy" tptp.nat)) % 0.37/0.56 (define @t7 () (_ (_ tptp.ts @t6) @t5)) % 0.37/0.56 (define @t8 () (_ (_ tptp.ts @t5) @t6)) % 0.37/0.56 (define @t9 () (= @t8 @t7)) % 0.37/0.56 (define @t10 () (@list @t5 @t6)) % 0.37/0.56 (define @t11 () (forall @t10 @t9)) % 0.37/0.56 (define @t12 () (_ (_ tptp.pl @t6) @t5)) % 0.37/0.56 (define @t13 () (_ (_ tptp.pl @t5) @t6)) % 0.37/0.56 (define @t14 () (= @t13 @t12)) % 0.37/0.56 (define @t15 () (forall @t10 @t14)) % 0.37/0.56 (define @t16 () (_ tptp.den tptp.x)) % 0.37/0.56 (define @t17 () (_ tptp.den tptp.y)) % 0.37/0.56 (define @t18 () (_ (_ tptp.ts @t17) @t16)) % 0.37/0.56 (define @t19 () (_ tptp.num tptp.x)) % 0.37/0.56 (define @t20 () (_ (_ tptp.ts @t19) @t17)) % 0.37/0.56 (define @t21 () (_ tptp.num tptp.y)) % 0.37/0.56 (define @t22 () (_ (_ tptp.ts @t21) @t16)) % 0.37/0.56 (define @t23 () (_ (_ tptp.pl @t22) @t20)) % 0.37/0.56 (define @t24 () (_ (_ tptp.fr @t23) @t18)) % 0.37/0.56 (define @t25 () (_ (_ tptp.ts @t16) @t17)) % 0.37/0.56 (define @t26 () (_ (_ tptp.pl @t20) @t22)) % 0.37/0.56 (define @t27 () (_ (_ tptp.fr @t26) @t25)) % 0.37/0.56 (define @t28 () (_ (_ tptp.eq @t27) @t24)) % 0.37/0.56 (define @t29 () (not @t28)) % 0.37/0.56 (define @t30 () (tptp.eq @t1 @t1)) % 0.37/0.56 (define @t31 () (tptp.den tptp.x)) % 0.37/0.56 (define @t32 () (tptp.den tptp.y)) % 0.37/0.56 (define @t33 () (tptp.ts @t32 @t31)) % 0.37/0.56 (define @t34 () (tptp.num tptp.x)) % 0.37/0.56 (define @t35 () (tptp.ts @t34 @t32)) % 0.37/0.56 (define @t36 () (tptp.num tptp.y)) % 0.37/0.56 (define @t37 () (tptp.ts @t36 @t31)) % 0.37/0.56 (define @t38 () (tptp.pl @t37 @t35)) % 0.37/0.56 (define @t39 () (tptp.fr @t38 @t33)) % 0.37/0.56 (define @t40 () (tptp.ts @t31 @t32)) % 0.37/0.56 (define @t41 () (tptp.pl @t35 @t37)) % 0.37/0.56 (define @t42 () (tptp.fr @t41 @t40)) % 0.37/0.56 (define @t43 () (tptp.eq @t42 @t39)) % 0.37/0.56 (define @t44 () (tptp.ts @t6 @t5)) % 0.37/0.56 (define @t45 () (tptp.ts @t5 @t6)) % 0.37/0.56 (define @t46 () (tptp.pl @t6 @t5)) % 0.37/0.56 (define @t47 () (tptp.pl @t5 @t6)) % 0.37/0.56 (define @t48 () (tptp.eq @t42 @t42)) % 0.37/0.56 (define @t49 () (forall @t3 @t30)) % 0.37/0.56 (assume @p1 @t4) % 0.37/0.56 (assume @p2 @t11) % 0.37/0.56 (assume @p3 @t15) % 0.37/0.56 (assume @p4 @t29) % 0.37/0.56 (assume @p5 true) % 0.37/0.56 (step @p6 :rule refl :args (@t30)) % 0.37/0.56 (step @p7 :rule refl :args (@t2)) % 0.37/0.56 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t2 @t30))) % 0.37/0.56 (step @p9 :rule symm :premises (@p8)) % 0.37/0.56 (step @p10 :rule eq_resolve :premises (@p7 @p9)) % 0.37/0.56 (step @p11 :rule cong :premises (@p10) :args (@t4)) % 0.37/0.56 (step @p12 :rule eq_resolve :premises (@p1 @p11)) % 0.37/0.56 (step @p13 :rule refl :args ((tptp.eq @t27 @t24))) % 0.37/0.56 (step @p14 :rule refl :args ((tptp.fr @t23 @t18))) % 0.37/0.56 (step @p15 :rule refl :args ((tptp.ts @t17 @t16))) % 0.37/0.56 (step @p16 :rule refl :args (@t31)) % 0.37/0.56 (step @p17 :rule refl :args (@t32)) % 0.37/0.56 (step @p18 :rule cong :premises (@p17 @p16) :args (@t33)) % 0.37/0.56 (step @p19 :rule trans :premises (@p18 @p15)) % 0.37/0.56 (step @p20 :rule refl :args ((tptp.pl @t22 @t20))) % 0.37/0.56 (step @p21 :rule refl :args ((tptp.ts @t19 @t17))) % 0.37/0.56 (step @p22 :rule refl :args (@t34)) % 0.37/0.56 (step @p23 :rule cong :premises (@p22 @p17) :args (@t35)) % 0.37/0.56 (step @p24 :rule trans :premises (@p23 @p21)) % 0.37/0.56 (step @p25 :rule refl :args ((tptp.ts @t21 @t16))) % 0.37/0.56 (step @p26 :rule refl :args (@t36)) % 0.37/0.56 (step @p27 :rule cong :premises (@p26 @p16) :args (@t37)) % 0.37/0.56 (step @p28 :rule trans :premises (@p27 @p25)) % 0.37/0.56 (step @p29 :rule cong :premises (@p28 @p24) :args (@t38)) % 0.37/0.56 (step @p30 :rule trans :premises (@p29 @p20)) % 0.37/0.56 (step @p31 :rule cong :premises (@p30 @p19) :args (@t39)) % 0.37/0.56 (step @p32 :rule trans :premises (@p31 @p14)) % 0.37/0.56 (step @p33 :rule refl :args ((tptp.fr @t26 @t25))) % 0.37/0.56 (step @p34 :rule refl :args ((tptp.ts @t16 @t17))) % 0.37/0.56 (step @p35 :rule cong :premises (@p16 @p17) :args (@t40)) % 0.37/0.56 (step @p36 :rule trans :premises (@p35 @p34)) % 0.37/0.56 (step @p37 :rule refl :args ((tptp.pl @t20 @t22))) % 0.37/0.56 (step @p38 :rule cong :premises (@p24 @p28) :args (@t41)) % 0.37/0.56 (step @p39 :rule trans :premises (@p38 @p37)) % 0.37/0.56 (step @p40 :rule cong :premises (@p39 @p36) :args (@t42)) % 0.37/0.56 (step @p41 :rule trans :premises (@p40 @p33)) % 0.37/0.56 (step @p42 :rule cong :premises (@p41 @p32) :args (@t43)) % 0.37/0.56 (step @p43 :rule trans :premises (@p42 @p13)) % 0.37/0.56 (step @p44 :rule refl :args (tptp.eq)) % 0.37/0.56 (step @p45 :rule ho_cong :premises (@p44 @p41)) % 0.37/0.56 (step @p46 :rule ho_cong :premises (@p45 @p32)) % 0.37/0.56 (step @p47 :rule cong :premises (@p46 @p43) :args ((= (_ (_ tptp.eq @t42) @t39) @t43))) % 0.37/0.56 (step @p48 :rule symm :premises (@p47)) % 0.37/0.56 (step @p49 :rule refl :args (@t28)) % 0.37/0.56 (step @p50 :rule eq_resolve :premises (@p49 @p48)) % 0.37/0.56 (step @p51 :rule refl :args (tptp.fr)) % 0.37/0.56 (step @p52 :rule ho_cong :premises (@p51 @p30)) % 0.37/0.56 (step @p53 :rule ho_cong :premises (@p52 @p19)) % 0.37/0.56 (step @p54 :rule cong :premises (@p53 @p32) :args ((= (_ (_ tptp.fr @t38) @t33) @t39))) % 0.37/0.56 (step @p55 :rule symm :premises (@p54)) % 0.37/0.56 (step @p56 :rule refl :args (@t24)) % 0.37/0.56 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 0.37/0.56 (step @p58 :rule refl :args (tptp.ts)) % 0.37/0.56 (step @p59 :rule ho_cong :premises (@p58 @p17)) % 0.37/0.56 (step @p60 :rule ho_cong :premises (@p59 @p16)) % 0.37/0.56 (step @p61 :rule cong :premises (@p60 @p19) :args ((= (_ (_ tptp.ts @t32) @t31) @t33))) % 0.37/0.56 (step @p62 :rule symm :premises (@p61)) % 0.37/0.56 (step @p63 :rule refl :args (@t18)) % 0.37/0.56 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 0.37/0.56 (step @p65 :rule refl :args (@t16)) % 0.37/0.56 (step @p66 :rule cong :premises (@p65 @p16) :args ((= @t16 @t31))) % 0.37/0.56 (step @p67 :rule symm :premises (@p66)) % 0.37/0.56 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.37/0.56 (step @p69 :rule refl :args (@t17)) % 0.37/0.56 (step @p70 :rule cong :premises (@p69 @p17) :args ((= @t17 @t32))) % 0.37/0.56 (step @p71 :rule symm :premises (@p70)) % 0.37/0.56 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 0.37/0.56 (step @p73 :rule refl :args (tptp.ts)) % 0.37/0.56 (step @p74 :rule ho_cong :premises (@p73 @p72)) % 0.37/0.56 (step @p75 :rule ho_cong :premises (@p74 @p68)) % 0.37/0.56 (step @p76 :rule trans :premises (@p75 @p64)) % 0.37/0.56 (step @p77 :rule refl :args (tptp.pl)) % 0.37/0.56 (step @p78 :rule ho_cong :premises (@p77 @p28)) % 0.37/0.56 (step @p79 :rule ho_cong :premises (@p78 @p24)) % 0.37/0.56 (step @p80 :rule cong :premises (@p79 @p30) :args ((= (_ (_ tptp.pl @t37) @t35) @t38))) % 0.37/0.56 (step @p81 :rule symm :premises (@p80)) % 0.37/0.56 (step @p82 :rule refl :args (@t23)) % 0.37/0.56 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.37/0.56 (step @p84 :rule ho_cong :premises (@p58 @p22)) % 0.37/0.56 (step @p85 :rule ho_cong :premises (@p84 @p17)) % 0.37/0.56 (step @p86 :rule cong :premises (@p85 @p24) :args ((= (_ (_ tptp.ts @t34) @t32) @t35))) % 0.37/0.56 (step @p87 :rule symm :premises (@p86)) % 0.37/0.56 (step @p88 :rule refl :args (@t20)) % 0.37/0.56 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 0.37/0.56 (step @p90 :rule refl :args (@t19)) % 0.37/0.56 (step @p91 :rule cong :premises (@p90 @p22) :args ((= @t19 @t34))) % 0.37/0.56 (step @p92 :rule symm :premises (@p91)) % 0.37/0.56 (step @p93 :rule eq_resolve :premises (@p90 @p92)) % 0.37/0.56 (step @p94 :rule ho_cong :premises (@p73 @p93)) % 0.37/0.56 (step @p95 :rule ho_cong :premises (@p94 @p72)) % 0.37/0.56 (step @p96 :rule trans :premises (@p95 @p89)) % 0.37/0.56 (step @p97 :rule ho_cong :premises (@p58 @p26)) % 0.37/0.56 (step @p98 :rule ho_cong :premises (@p97 @p16)) % 0.37/0.56 (step @p99 :rule cong :premises (@p98 @p28) :args ((= (_ (_ tptp.ts @t36) @t31) @t37))) % 0.37/0.56 (step @p100 :rule symm :premises (@p99)) % 0.37/0.56 (step @p101 :rule refl :args (@t22)) % 0.37/0.56 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 0.37/0.56 (step @p103 :rule refl :args (@t21)) % 0.37/0.56 (step @p104 :rule cong :premises (@p103 @p26) :args ((= @t21 @t36))) % 0.37/0.56 (step @p105 :rule symm :premises (@p104)) % 0.37/0.56 (step @p106 :rule eq_resolve :premises (@p103 @p105)) % 0.37/0.56 (step @p107 :rule ho_cong :premises (@p73 @p106)) % 0.37/0.56 (step @p108 :rule ho_cong :premises (@p107 @p68)) % 0.37/0.56 (step @p109 :rule trans :premises (@p108 @p102)) % 0.37/0.56 (step @p110 :rule refl :args (tptp.pl)) % 0.37/0.56 (step @p111 :rule ho_cong :premises (@p110 @p109)) % 0.37/0.56 (step @p112 :rule ho_cong :premises (@p111 @p96)) % 0.37/0.56 (step @p113 :rule trans :premises (@p112 @p83)) % 0.37/0.56 (step @p114 :rule refl :args (tptp.fr)) % 0.37/0.56 (step @p115 :rule ho_cong :premises (@p114 @p113)) % 0.37/0.56 (step @p116 :rule ho_cong :premises (@p115 @p76)) % 0.37/0.56 (step @p117 :rule trans :premises (@p116 @p57)) % 0.37/0.56 (step @p118 :rule ho_cong :premises (@p51 @p39)) % 0.37/0.56 (step @p119 :rule ho_cong :premises (@p118 @p36)) % 0.37/0.56 (step @p120 :rule cong :premises (@p119 @p41) :args ((= (_ (_ tptp.fr @t41) @t40) @t42))) % 0.37/0.56 (step @p121 :rule symm :premises (@p120)) % 0.37/0.56 (step @p122 :rule refl :args (@t27)) % 0.37/0.56 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.37/0.56 (step @p124 :rule ho_cong :premises (@p58 @p16)) % 0.37/0.56 (step @p125 :rule ho_cong :premises (@p124 @p17)) % 0.37/0.56 (step @p126 :rule cong :premises (@p125 @p36) :args ((= (_ (_ tptp.ts @t31) @t32) @t40))) % 0.37/0.56 (step @p127 :rule symm :premises (@p126)) % 0.37/0.56 (step @p128 :rule refl :args (@t25)) % 0.37/0.56 (step @p129 :rule eq_resolve :premises (@p128 @p127)) % 0.37/0.56 (step @p130 :rule ho_cong :premises (@p73 @p68)) % 0.37/0.56 (step @p131 :rule ho_cong :premises (@p130 @p72)) % 0.37/0.56 (step @p132 :rule trans :premises (@p131 @p129)) % 0.37/0.56 (step @p133 :rule ho_cong :premises (@p77 @p24)) % 0.37/0.56 (step @p134 :rule ho_cong :premises (@p133 @p28)) % 0.37/0.56 (step @p135 :rule cong :premises (@p134 @p39) :args ((= (_ (_ tptp.pl @t35) @t37) @t41))) % 0.37/0.56 (step @p136 :rule symm :premises (@p135)) % 0.37/0.56 (step @p137 :rule refl :args (@t26)) % 0.37/0.56 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.37/0.56 (step @p139 :rule ho_cong :premises (@p110 @p96)) % 0.37/0.56 (step @p140 :rule ho_cong :premises (@p139 @p109)) % 0.37/0.56 (step @p141 :rule trans :premises (@p140 @p138)) % 0.37/0.56 (step @p142 :rule ho_cong :premises (@p114 @p141)) % 0.37/0.56 (step @p143 :rule ho_cong :premises (@p142 @p132)) % 0.37/0.56 (step @p144 :rule trans :premises (@p143 @p123)) % 0.37/0.56 (step @p145 :rule refl :args (tptp.eq)) % 0.37/0.56 (step @p146 :rule ho_cong :premises (@p145 @p144)) % 0.37/0.56 (step @p147 :rule ho_cong :premises (@p146 @p117)) % 0.37/0.56 (step @p148 :rule trans :premises (@p147 @p50)) % 0.37/0.56 (step @p149 :rule cong :premises (@p148) :args (@t29)) % 0.37/0.56 (step @p150 :rule eq_resolve :premises (@p4 @p149)) % 0.37/0.56 (step @p151 :rule false_intro :premises (@p150)) % 0.37/0.56 (step @p152 :rule refl :args (@t44)) % 0.37/0.56 (step @p153 :rule refl :args (@t7)) % 0.37/0.56 (step @p154 :rule cong :premises (@p153 @p152) :args ((= @t7 @t44))) % 0.37/0.56 (step @p155 :rule symm :premises (@p154)) % 0.37/0.56 (step @p156 :rule eq_resolve :premises (@p153 @p155)) % 0.37/0.56 (step @p157 :rule refl :args (@t45)) % 0.37/0.56 (step @p158 :rule refl :args (@t8)) % 0.37/0.56 (step @p159 :rule cong :premises (@p158 @p157) :args ((= @t8 @t45))) % 0.37/0.56 (step @p160 :rule symm :premises (@p159)) % 0.37/0.56 (step @p161 :rule eq_resolve :premises (@p158 @p160)) % 0.37/0.56 (step @p162 :rule cong :premises (@p161 @p156) :args (@t9)) % 0.37/0.56 (step @p163 :rule cong :premises (@p162) :args (@t11)) % 0.37/0.56 (step @p164 :rule eq_resolve :premises (@p2 @p163)) % 0.37/0.56 (step @p165 :rule instantiate :premises (@p164) :args ((@list @t32 @t31))) % 0.37/0.56 (step @p166 :rule symm :premises (@p165)) % 0.37/0.56 (step @p167 :rule refl :args (@t46)) % 0.37/0.56 (step @p168 :rule refl :args (@t12)) % 0.37/0.56 (step @p169 :rule cong :premises (@p168 @p167) :args ((= @t12 @t46))) % 0.37/0.56 (step @p170 :rule symm :premises (@p169)) % 0.37/0.56 (step @p171 :rule eq_resolve :premises (@p168 @p170)) % 0.37/0.56 (step @p172 :rule refl :args (@t47)) % 0.37/0.56 (step @p173 :rule refl :args (@t13)) % 0.37/0.56 (step @p174 :rule cong :premises (@p173 @p172) :args ((= @t13 @t47))) % 0.37/0.56 (step @p175 :rule symm :premises (@p174)) % 0.37/0.56 (step @p176 :rule eq_resolve :premises (@p173 @p175)) % 0.37/0.56 (step @p177 :rule cong :premises (@p176 @p171) :args (@t14)) % 0.37/0.56 (step @p178 :rule cong :premises (@p177) :args (@t15)) % 0.37/0.56 (step @p179 :rule eq_resolve :premises (@p3 @p178)) % 0.37/0.56 (step @p180 :rule instantiate :premises (@p179) :args ((@list @t37 @t35))) % 0.37/0.56 (step @p181 :rule symm :premises (@p180)) % 0.37/0.56 (step @p182 :rule cong :premises (@p181 @p166) :args (@t42)) % 0.37/0.56 (step @p183 :rule refl :args (@t42)) % 0.37/0.56 (step @p184 :rule cong :premises (@p183 @p182) :args (@t48)) % 0.37/0.56 (step @p185 :rule trans :premises (@p184 @p151)) % 0.37/0.56 (step @p186 :rule false_elim :premises (@p185)) % 0.37/0.56 (assume-push @p193 @t49) % 0.37/0.56 (step @p188 :rule instantiate :premises (@p12) :args ((@list @t42))) % 0.37/0.56 (step-pop @p194 :rule scope :premises (@p188)) % 0.37/0.56 (step @p189 :rule process_scope :premises (@p194) :args (@t48)) % 0.37/0.56 (step @p191 :rule implies_elim :premises (@p189)) % 0.37/0.56 (step @p192 false :rule chain_m_resolution :premises (@p191 @p186 @p12) :args (false (@list true false) (@list @t48 @t49))) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------