%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM688^1 : 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 : n029.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 08:40:22 AM UTC 2026 % Result : Theorem 0.30s 0.55s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM688^1 : 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 : n029.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 11:54:17 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-const tptp.pl (-> tptp.nat tptp.nat tptp.nat)) % 0.30/0.55 (declare-const tptp.z tptp.nat) % 0.30/0.55 (declare-const tptp.u tptp.nat) % 0.30/0.55 (declare-const tptp.more (-> tptp.nat tptp.nat Bool)) % 0.30/0.55 (declare-const tptp.x tptp.nat) % 0.30/0.55 (declare-const tptp.y tptp.nat) % 0.30/0.55 (define @t1 () (_ (_ tptp.more tptp.x) tptp.y)) % 0.30/0.55 (define @t2 () (= tptp.z tptp.u)) % 0.30/0.55 (define @t3 () (_ (_ tptp.more tptp.z) tptp.u)) % 0.30/0.55 (define @t4 () (not @t3)) % 0.30/0.55 (define @t5 () (=> @t4 @t2)) % 0.30/0.55 (define @t6 () (@var "Xa" Bool)) % 0.30/0.55 (define @t7 () (@var "Xy" tptp.nat)) % 0.30/0.55 (define @t8 () (@var "Xu" tptp.nat)) % 0.30/0.55 (define @t9 () (_ (_ tptp.pl @t8) @t7)) % 0.30/0.55 (define @t10 () (@var "Xx" tptp.nat)) % 0.30/0.55 (define @t11 () (@var "Xz" tptp.nat)) % 0.30/0.55 (define @t12 () (_ (_ tptp.pl @t11) @t10)) % 0.30/0.55 (define @t13 () (_ (_ tptp.more @t12) @t9)) % 0.30/0.55 (define @t14 () (_ (_ tptp.more @t11) @t8)) % 0.30/0.55 (define @t15 () (=> @t14 @t13)) % 0.30/0.55 (define @t16 () (= @t10 @t7)) % 0.30/0.55 (define @t17 () (@list @t10 @t7 @t11 @t8)) % 0.30/0.55 (define @t18 () (forall @t17 (=> @t16 @t15))) % 0.30/0.55 (define @t19 () (_ (_ tptp.pl @t7) @t8)) % 0.30/0.55 (define @t20 () (_ (_ tptp.pl @t10) @t11)) % 0.30/0.55 (define @t21 () (_ (_ tptp.more @t20) @t19)) % 0.30/0.55 (define @t22 () (=> @t14 @t21)) % 0.30/0.55 (define @t23 () (_ (_ tptp.more @t10) @t7)) % 0.30/0.55 (define @t24 () (forall @t17 (=> @t23 @t22))) % 0.30/0.55 (define @t25 () (_ (_ tptp.pl tptp.y) tptp.u)) % 0.30/0.55 (define @t26 () (_ (_ tptp.pl tptp.x) tptp.z)) % 0.30/0.55 (define @t27 () (_ (_ tptp.more @t26) @t25)) % 0.30/0.55 (define @t28 () (not @t27)) % 0.30/0.55 (define @t29 () (tptp.pl @t8 @t7)) % 0.30/0.55 (define @t30 () (tptp.more (tptp.pl @t11 @t7) @t29)) % 0.30/0.55 (define @t31 () (tptp.more @t11 @t8)) % 0.30/0.55 (define @t32 () (not @t31)) % 0.30/0.55 (define @t33 () (or @t32 @t30)) % 0.30/0.55 (define @t34 () (not (= @t7 @t7))) % 0.30/0.55 (define @t35 () (or @t34 @t32 @t30)) % 0.30/0.55 (define @t36 () (@list @t7 @t11 @t8)) % 0.30/0.55 (define @t37 () (tptp.pl @t11 @t10)) % 0.30/0.55 (define @t38 () (tptp.more @t37 @t29)) % 0.30/0.55 (define @t39 () (not @t16)) % 0.30/0.55 (define @t40 () (or @t39 @t39 @t32 @t38)) % 0.30/0.55 (define @t41 () (@list @t10)) % 0.30/0.55 (define @t42 () (or @t39 @t32 @t38)) % 0.30/0.55 (define @t43 () (forall @t41 @t42)) % 0.30/0.55 (define @t44 () (forall @t36 @t43)) % 0.30/0.55 (define @t45 () (forall (@list @t7 @t11 @t8 @t10) @t42)) % 0.30/0.55 (define @t46 () (not @t14)) % 0.30/0.55 (define @t47 () (or @t39 @t46 @t13)) % 0.30/0.55 (define @t48 () (tptp.pl tptp.y tptp.u)) % 0.30/0.55 (define @t49 () (tptp.pl tptp.x tptp.z)) % 0.30/0.55 (define @t50 () (tptp.more @t49 @t48)) % 0.30/0.55 (define @t51 () (tptp.pl @t7 @t8)) % 0.30/0.55 (define @t52 () (tptp.pl @t10 @t11)) % 0.30/0.55 (define @t53 () (tptp.more @t52 @t51)) % 0.30/0.55 (define @t54 () (tptp.more @t10 @t7)) % 0.30/0.55 (define @t55 () (not @t23)) % 0.30/0.55 (define @t56 () (or @t55 @t46 @t21)) % 0.30/0.55 (define @t57 () (tptp.more tptp.x tptp.y)) % 0.30/0.55 (define @t58 () (tptp.more tptp.z tptp.u)) % 0.30/0.55 (define @t59 () (not @t58)) % 0.30/0.55 (define @t60 () (not @t57)) % 0.30/0.55 (define @t61 () (or @t60 @t59 @t50)) % 0.30/0.55 (define @t62 () (tptp.pl tptp.y tptp.z)) % 0.30/0.55 (define @t63 () (tptp.more @t49 @t62)) % 0.30/0.55 (define @t64 () (or @t60 @t63)) % 0.30/0.55 (define @t65 () (not @t64)) % 0.30/0.55 (define @t66 () (forall @t36 @t33)) % 0.30/0.55 (assume @p1 @t1) % 0.30/0.55 (assume @p2 @t5) % 0.30/0.55 (assume @p3 (forall (@list @t6) (=> (not (not @t6)) @t6))) % 0.30/0.55 (assume @p4 @t18) % 0.30/0.55 (assume @p5 @t24) % 0.30/0.55 (assume @p6 @t28) % 0.30/0.55 (assume @p7 true) % 0.30/0.55 (step @p8 :rule aci_norm :args ((= (or false @t32 @t30) @t33))) % 0.30/0.55 (step @p9 :rule refl :args (@t30)) % 0.30/0.55 (step @p10 :rule refl :args (@t32)) % 0.30/0.55 (step @p11 :rule evaluate :args ((not true))) % 0.30/0.55 (step @p12 :rule eq-refl :args (@t7)) % 0.30/0.55 (step @p13 :rule cong :premises (@p12) :args (@t34)) % 0.30/0.55 (step @p14 :rule trans :premises (@p13 @p11)) % 0.30/0.55 (step @p15 :rule nary_cong :premises (@p14 @p10 @p9) :args (@t35)) % 0.30/0.55 (step @p16 :rule trans :premises (@p15 @p8)) % 0.30/0.55 (step @p17 :rule cong :premises (@p16) :args ((forall @t36 @t35))) % 0.30/0.55 (step @p18 :rule quant-var-elim-eq :args ((= (forall @t41 @t40) @t35))) % 0.30/0.55 (step @p19 :rule aci_norm :args ((= @t42 @t40))) % 0.30/0.55 (step @p20 :rule cong :premises (@p19) :args (@t43)) % 0.30/0.55 (step @p21 :rule trans :premises (@p20 @p18)) % 0.30/0.55 (step @p22 :rule cong :premises (@p21) :args (@t44)) % 0.30/0.55 (step @p23 :rule quant-merge-prenex :args ((= @t44 @t45))) % 0.30/0.55 (step @p24 :rule symm :premises (@p23)) % 0.30/0.55 (step @p25 :rule quant_var_reordering :args ((= (forall @t17 @t42) @t45))) % 0.30/0.55 (step @p26 :rule trans :premises (@p25 @p24 @p22)) % 0.30/0.55 (step @p27 :rule trans :premises (@p26 @p17)) % 0.30/0.55 (step @p28 :rule refl :args ((tptp.more @t12 @t9))) % 0.30/0.55 (step @p29 :rule refl :args (@t29)) % 0.30/0.55 (step @p30 :rule refl :args (@t37)) % 0.30/0.55 (step @p31 :rule cong :premises (@p30 @p29) :args (@t38)) % 0.30/0.55 (step @p32 :rule trans :premises (@p31 @p28)) % 0.30/0.55 (step @p33 :rule refl :args (tptp.more)) % 0.30/0.55 (step @p34 :rule ho_cong :premises (@p33 @p30)) % 0.30/0.55 (step @p35 :rule ho_cong :premises (@p34 @p29)) % 0.30/0.55 (step @p36 :rule cong :premises (@p35 @p32) :args ((= (_ (_ tptp.more @t37) @t29) @t38))) % 0.30/0.55 (step @p37 :rule symm :premises (@p36)) % 0.30/0.55 (step @p38 :rule refl :args (@t13)) % 0.30/0.55 (step @p39 :rule eq_resolve :premises (@p38 @p37)) % 0.30/0.55 (step @p40 :rule refl :args (@t9)) % 0.30/0.55 (step @p41 :rule cong :premises (@p40 @p29) :args ((= @t9 @t29))) % 0.30/0.55 (step @p42 :rule symm :premises (@p41)) % 0.30/0.55 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 0.30/0.55 (step @p44 :rule refl :args (@t12)) % 0.30/0.55 (step @p45 :rule cong :premises (@p44 @p30) :args ((= @t12 @t37))) % 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 ho_cong :premises (@p33 @p47)) % 0.30/0.55 (step @p49 :rule ho_cong :premises (@p48 @p43)) % 0.30/0.55 (step @p50 :rule trans :premises (@p49 @p39)) % 0.30/0.55 (step @p51 :rule refl :args (@t31)) % 0.30/0.55 (step @p52 :rule refl :args (@t14)) % 0.30/0.55 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t14 @t31))) % 0.30/0.55 (step @p54 :rule symm :premises (@p53)) % 0.30/0.55 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 0.30/0.55 (step @p56 :rule cong :premises (@p55) :args (@t46)) % 0.30/0.55 (step @p57 :rule refl :args (@t39)) % 0.30/0.55 (step @p58 :rule nary_cong :premises (@p57 @p56 @p50) :args (@t47)) % 0.30/0.55 (step @p59 :rule cong :premises (@p58) :args ((forall @t17 @t47))) % 0.30/0.55 (step @p60 :rule trans :premises (@p59 @p27)) % 0.30/0.55 (step @p61 :rule aci_norm :args ((= (or @t39 (or @t46 @t13)) @t47))) % 0.30/0.55 (step @p62 :rule bool-impl-elim :args (@t14 @t13)) % 0.30/0.55 (step @p63 :rule nary_cong :premises (@p57 @p62) :args ((or @t39 @t15))) % 0.30/0.55 (step @p64 :rule trans :premises (@p63 @p61)) % 0.30/0.55 (step @p65 :rule bool-impl-elim :args (@t16 @t15)) % 0.30/0.55 (step @p66 :rule trans :premises (@p65 @p64)) % 0.30/0.55 (step @p67 :rule cong :premises (@p66) :args (@t18)) % 0.30/0.55 (step @p68 :rule trans :premises (@p67 @p60)) % 0.30/0.55 (step @p69 :rule eq_resolve :premises (@p4 @p68)) % 0.30/0.55 (step @p70 :rule refl :args ((tptp.more @t26 @t25))) % 0.30/0.55 (step @p71 :rule refl :args (@t48)) % 0.30/0.55 (step @p72 :rule refl :args (@t49)) % 0.30/0.55 (step @p73 :rule cong :premises (@p72 @p71) :args (@t50)) % 0.30/0.55 (step @p74 :rule trans :premises (@p73 @p70)) % 0.30/0.55 (step @p75 :rule ho_cong :premises (@p33 @p72)) % 0.30/0.55 (step @p76 :rule ho_cong :premises (@p75 @p71)) % 0.30/0.55 (step @p77 :rule cong :premises (@p76 @p74) :args ((= (_ (_ tptp.more @t49) @t48) @t50))) % 0.30/0.55 (step @p78 :rule symm :premises (@p77)) % 0.30/0.55 (step @p79 :rule refl :args (@t27)) % 0.30/0.55 (step @p80 :rule eq_resolve :premises (@p79 @p78)) % 0.30/0.55 (step @p81 :rule refl :args (@t25)) % 0.30/0.55 (step @p82 :rule cong :premises (@p81 @p71) :args ((= @t25 @t48))) % 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 refl :args (@t26)) % 0.30/0.55 (step @p86 :rule cong :premises (@p85 @p72) :args ((= @t26 @t49))) % 0.30/0.55 (step @p87 :rule symm :premises (@p86)) % 0.30/0.55 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.30/0.55 (step @p89 :rule refl :args (tptp.more)) % 0.30/0.55 (step @p90 :rule ho_cong :premises (@p89 @p88)) % 0.30/0.55 (step @p91 :rule ho_cong :premises (@p90 @p84)) % 0.30/0.55 (step @p92 :rule trans :premises (@p91 @p80)) % 0.30/0.55 (step @p93 :rule cong :premises (@p92) :args (@t28)) % 0.30/0.55 (step @p94 :rule eq_resolve :premises (@p6 @p93)) % 0.30/0.55 (step @p95 :rule false_intro :premises (@p94)) % 0.30/0.55 (step @p96 :rule refl :args ((tptp.more @t20 @t19))) % 0.30/0.55 (step @p97 :rule refl :args (@t51)) % 0.30/0.55 (step @p98 :rule refl :args (@t52)) % 0.30/0.55 (step @p99 :rule cong :premises (@p98 @p97) :args (@t53)) % 0.30/0.55 (step @p100 :rule trans :premises (@p99 @p96)) % 0.30/0.55 (step @p101 :rule ho_cong :premises (@p33 @p98)) % 0.30/0.55 (step @p102 :rule ho_cong :premises (@p101 @p97)) % 0.30/0.55 (step @p103 :rule cong :premises (@p102 @p100) :args ((= (_ (_ tptp.more @t52) @t51) @t53))) % 0.30/0.55 (step @p104 :rule symm :premises (@p103)) % 0.30/0.55 (step @p105 :rule refl :args (@t21)) % 0.30/0.55 (step @p106 :rule eq_resolve :premises (@p105 @p104)) % 0.30/0.55 (step @p107 :rule refl :args (@t19)) % 0.30/0.55 (step @p108 :rule cong :premises (@p107 @p97) :args ((= @t19 @t51))) % 0.30/0.55 (step @p109 :rule symm :premises (@p108)) % 0.37/0.56 (step @p110 :rule eq_resolve :premises (@p107 @p109)) % 0.37/0.56 (step @p111 :rule refl :args (@t20)) % 0.37/0.56 (step @p112 :rule cong :premises (@p111 @p98) :args ((= @t20 @t52))) % 0.37/0.56 (step @p113 :rule symm :premises (@p112)) % 0.37/0.56 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 0.37/0.56 (step @p115 :rule ho_cong :premises (@p33 @p114)) % 0.37/0.56 (step @p116 :rule ho_cong :premises (@p115 @p110)) % 0.37/0.56 (step @p117 :rule trans :premises (@p116 @p106)) % 0.37/0.56 (step @p118 :rule refl :args (@t54)) % 0.37/0.56 (step @p119 :rule refl :args (@t23)) % 0.37/0.56 (step @p120 :rule cong :premises (@p119 @p118) :args ((= @t23 @t54))) % 0.37/0.56 (step @p121 :rule symm :premises (@p120)) % 0.37/0.56 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 0.37/0.56 (step @p123 :rule cong :premises (@p122) :args (@t55)) % 0.37/0.56 (step @p124 :rule nary_cong :premises (@p123 @p56 @p117) :args (@t56)) % 0.37/0.56 (step @p125 :rule cong :premises (@p124) :args ((forall @t17 @t56))) % 0.37/0.56 (step @p126 :rule aci_norm :args ((= (or @t55 (or @t46 @t21)) @t56))) % 0.37/0.56 (step @p127 :rule bool-impl-elim :args (@t14 @t21)) % 0.37/0.56 (step @p128 :rule refl :args (@t55)) % 0.37/0.56 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or @t55 @t22))) % 0.37/0.56 (step @p130 :rule trans :premises (@p129 @p126)) % 0.37/0.56 (step @p131 :rule bool-impl-elim :args (@t23 @t22)) % 0.37/0.56 (step @p132 :rule trans :premises (@p131 @p130)) % 0.37/0.56 (step @p133 :rule cong :premises (@p132) :args (@t24)) % 0.37/0.56 (step @p134 :rule trans :premises (@p133 @p125)) % 0.37/0.56 (step @p135 :rule eq_resolve :premises (@p5 @p134)) % 0.37/0.56 (step @p136 :rule instantiate :premises (@p135) :args ((@list tptp.x tptp.y tptp.z tptp.u))) % 0.37/0.56 (step @p137 :rule refl :args (@t57)) % 0.37/0.56 (step @p138 :rule refl :args (@t1)) % 0.37/0.56 (step @p139 :rule cong :premises (@p138 @p137) :args ((= @t1 @t57))) % 0.37/0.56 (step @p140 :rule symm :premises (@p139)) % 0.37/0.56 (step @p141 :rule eq_resolve :premises (@p138 @p140)) % 0.37/0.56 (step @p142 :rule eq_resolve :premises (@p1 @p141)) % 0.37/0.56 (step @p143 :rule cnf_or_pos :args (@t61)) % 0.37/0.56 (step @p144 :rule reordering :premises (@p143) :args ((or @t59 @t50 @t60 (not @t61)))) % 0.37/0.56 (step @p145 :rule chain_m_resolution :premises (@p144 @p94 @p142 @p136) :args (@t59 (@list true false false) (@list @t50 @t57 @t61))) % 0.37/0.56 (step @p146 :rule refl :args (@t2)) % 0.37/0.56 (step @p147 :rule bool-double-not-elim :args (@t58)) % 0.37/0.56 (step @p148 :rule nary_cong :premises (@p147 @p146) :args ((or (not @t59) @t2))) % 0.37/0.56 (step @p149 :rule refl :args (@t58)) % 0.37/0.56 (step @p150 :rule refl :args (@t3)) % 0.37/0.56 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t3 @t58))) % 0.37/0.56 (step @p152 :rule symm :premises (@p151)) % 0.37/0.56 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.37/0.56 (step @p154 :rule cong :premises (@p153) :args (@t4)) % 0.37/0.56 (step @p155 :rule cong :premises (@p154 @p146) :args (@t5)) % 0.37/0.56 (step @p156 :rule eq_resolve :premises (@p2 @p155)) % 0.37/0.56 (step @p157 :rule implies_elim :premises (@p156)) % 0.37/0.56 (step @p158 :rule eq_resolve :premises (@p157 @p148)) % 0.37/0.56 (step @p159 :rule reordering :premises (@p158) :args ((or @t2 @t58))) % 0.37/0.56 (step @p160 :rule chain_m_resolution :premises (@p159 @p145) :args (@t2 (@list true) (@list @t58))) % 0.37/0.56 (step @p161 :rule refl :args (tptp.y)) % 0.37/0.56 (step @p162 :rule cong :premises (@p161 @p160) :args (@t62)) % 0.37/0.56 (step @p163 :rule refl :args (@t49)) % 0.37/0.56 (step @p164 :rule cong :premises (@p163 @p162) :args (@t63)) % 0.37/0.56 (step @p165 :rule trans :premises (@p164 @p95)) % 0.37/0.56 (step @p166 :rule false_elim :premises (@p165)) % 0.37/0.56 (step @p167 :rule cnf_or_pos :args (@t64)) % 0.37/0.56 (step @p168 :rule reordering :premises (@p167) :args ((or @t60 @t63 @t65))) % 0.37/0.56 (step @p169 :rule chain_m_resolution :premises (@p168 @p142 @p166) :args (@t65 (@list false true) (@list @t57 @t63))) % 0.37/0.56 (assume-push @p176 @t66) % 0.37/0.56 (step @p171 :rule instantiate :premises (@p69) :args ((@list tptp.z tptp.x tptp.y))) % 0.37/0.56 (step-pop @p177 :rule scope :premises (@p171)) % 0.37/0.56 (step @p172 :rule process_scope :premises (@p177) :args (@t64)) % 0.37/0.56 (step @p174 :rule implies_elim :premises (@p172)) % 0.37/0.56 (step @p175 false :rule chain_m_resolution :premises (@p174 @p169 @p69) :args (false (@list true false) (@list @t64 @t66))) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------