%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV282^5 : TPTP v9.2.1. Bugfixed v6.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:55:43 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEV282^5 : TPTP v9.2.1. Bugfixed v6.2.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n017.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 18:24:01 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.37/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (define tptp.cZERO () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (lambda (@list _let_2) (not (exists (@list _let_1) (_ _let_2 _let_1))))))) % 0.37/0.58 (define tptp.cSUCC () (let ((_let_1 (@var "Xt" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "Xn" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_4 _let_2) (exists (@list _let_3) (and (_ _let_2 _let_3) (_ _let_4 (lambda (@list _let_1) (and (not (= _let_1 _let_3)) (_ _let_2 _let_1)))))))))))) % 0.37/0.58 (define tptp.cNAT () (let ((_let_1 (@var "Xn" (-> (-> $$unsorted Bool) Bool)))) (let ((_let_2 (@var "Xp" (-> (-> (-> $$unsorted Bool) Bool) Bool)))) (let ((_let_3 (@var "Xx" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_1) (forall (@list _let_2) (=> (and (_ _let_2 tptp.cZERO) (forall (@list _let_3) (=> (_ _let_2 _let_3) (_ _let_2 (_ tptp.cSUCC _let_3))))) (_ _let_2 _let_1)))))))) % 0.37/0.58 (define @t1 () (not (_ tptp.cNAT tptp.cZERO))) % 0.37/0.58 (define @t2 () (@var "Xx" $$unsorted)) % 0.37/0.58 (define @t3 () (@var "Xp" (-> $$unsorted Bool))) % 0.37/0.58 (define @t4 () (_ @t3 @t2)) % 0.37/0.58 (define @t5 () (@list @t2)) % 0.37/0.58 (define @t6 () (exists @t5 @t4)) % 0.37/0.58 (define @t7 () (not @t6)) % 0.37/0.58 (define @t8 () (@list @t3)) % 0.37/0.58 (define @t9 () (lambda @t8 @t7)) % 0.37/0.58 (define @t10 () (@var "Xt" $$unsorted)) % 0.37/0.58 (define @t11 () (_ @t3 @t10)) % 0.37/0.58 (define @t12 () (not (= @t10 @t2))) % 0.37/0.58 (define @t13 () (and @t12 @t11)) % 0.37/0.58 (define @t14 () (@list @t10)) % 0.37/0.58 (define @t15 () (lambda @t14 @t13)) % 0.37/0.58 (define @t16 () (@var "Xn" (-> (-> $$unsorted Bool) Bool))) % 0.37/0.58 (define @t17 () (and @t4 (_ @t16 @t15))) % 0.37/0.58 (define @t18 () (exists @t5 @t17)) % 0.37/0.58 (define @t19 () (@list @t16 @t3)) % 0.37/0.58 (define @t20 () (lambda @t19 @t18)) % 0.37/0.58 (define @t21 () (@var "Xp" (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 0.37/0.58 (define @t22 () (_ @t21 @t16)) % 0.37/0.58 (define @t23 () (@var "Xx" (-> (-> $$unsorted Bool) Bool))) % 0.37/0.58 (define @t24 () (_ @t21 @t23)) % 0.37/0.58 (define @t25 () (=> @t24 (_ @t21 (_ tptp.cSUCC @t23)))) % 0.37/0.58 (define @t26 () (@list @t23)) % 0.37/0.58 (define @t27 () (forall @t26 @t25)) % 0.37/0.58 (define @t28 () (and (_ @t21 tptp.cZERO) @t27)) % 0.37/0.58 (define @t29 () (=> @t28 @t22)) % 0.37/0.58 (define @t30 () (@list @t21)) % 0.37/0.58 (define @t31 () (forall @t30 @t29)) % 0.37/0.58 (define @t32 () (@list @t16)) % 0.37/0.58 (define @t33 () (lambda @t32 @t31)) % 0.37/0.58 (define @t34 () (_ @t3 @t2)) % 0.37/0.58 (define @t35 () (not @t34)) % 0.37/0.58 (define @t36 () (forall @t5 @t35)) % 0.37/0.58 (define @t37 () (lambda @t8 @t36)) % 0.37/0.58 (define @t38 () (_ @t21 @t37)) % 0.37/0.58 (define @t39 () (_ @t3 @t10)) % 0.37/0.58 (define @t40 () (not (= @t2 @t10))) % 0.37/0.58 (define @t41 () (and @t40 @t39)) % 0.37/0.58 (define @t42 () (lambda @t14 @t41)) % 0.37/0.58 (define @t43 () (_ @t23 @t42)) % 0.37/0.58 (define @t44 () (not @t43)) % 0.37/0.58 (define @t45 () (or @t35 @t44)) % 0.37/0.58 (define @t46 () (forall @t5 @t45)) % 0.37/0.58 (define @t47 () (not @t46)) % 0.37/0.58 (define @t48 () (lambda @t8 @t47)) % 0.37/0.58 (define @t49 () (_ @t21 @t48)) % 0.37/0.58 (define @t50 () (_ @t21 @t23)) % 0.37/0.58 (define @t51 () (forall @t26 (or (not @t50) @t49))) % 0.37/0.58 (define @t52 () (not @t51)) % 0.37/0.58 (define @t53 () (not @t38)) % 0.37/0.58 (define @t54 () (forall @t30 (or @t53 @t52 @t38))) % 0.37/0.58 (define @t55 () (_ @t21 @t16)) % 0.37/0.58 (define @t56 () (_ (lambda @t32 (forall @t30 (or @t53 @t52 @t55))) @t37)) % 0.37/0.58 (define @t57 () (not @t4)) % 0.37/0.58 (define @t58 () (forall @t5 @t57)) % 0.37/0.58 (define @t59 () (not @t58)) % 0.37/0.58 (define @t60 () (lambda @t8 @t58)) % 0.37/0.58 (define @t61 () (_ @t21 @t37)) % 0.37/0.58 (define @t62 () (not @t61)) % 0.37/0.58 (define @t63 () (or @t62 @t52 @t22)) % 0.37/0.58 (define @t64 () (and @t61 @t51)) % 0.37/0.58 (define @t65 () (and @t40 @t11)) % 0.37/0.58 (define @t66 () (lambda @t14 @t65)) % 0.37/0.58 (define @t67 () (lambda @t8 (not (forall @t5 (or @t57 (not (_ @t23 @t66))))))) % 0.37/0.58 (define @t68 () (_ @t21 @t48)) % 0.37/0.58 (define @t69 () (not @t24)) % 0.37/0.58 (define @t70 () (or @t69 @t68)) % 0.37/0.58 (define @t71 () (_ @t16 @t42)) % 0.37/0.58 (define @t72 () (_ (lambda @t19 (not (forall @t5 (or @t35 (not @t71))))) @t23)) % 0.37/0.58 (define @t73 () (=> @t24 (_ @t21 @t72))) % 0.37/0.58 (define @t74 () (forall @t26 @t73)) % 0.37/0.58 (define @t75 () (and @t61 @t74)) % 0.37/0.58 (define @t76 () (=> @t75 @t22)) % 0.37/0.58 (define @t77 () (_ @t16 @t66)) % 0.37/0.58 (define @t78 () (not @t77)) % 0.37/0.58 (define @t79 () (or @t57 @t78)) % 0.37/0.58 (define @t80 () (and @t4 @t77)) % 0.37/0.58 (define @t81 () (forall @t5 (not @t80))) % 0.37/0.58 (define @t82 () (not @t81)) % 0.37/0.58 (assume @p1 @t1) % 0.37/0.58 (assume @p2 true) % 0.37/0.58 (step @p3 (= tptp.cZERO @t9) :rule refl :args (@t9)) % 0.37/0.58 (step @p4 (= tptp.cSUCC @t20) :rule refl :args (@t20)) % 0.37/0.58 (step @p5 (= tptp.cNAT @t33) :rule refl :args (@t33)) % 0.37/0.58 (step @p6 :rule evaluate :args ((not true))) % 0.37/0.58 (step @p7 :rule quant-unused-vars :args ((= (forall @t30 true) true))) % 0.37/0.58 (step @p8 :rule bool-or-taut2 :args (false @t38 (or @t52) false)) % 0.37/0.58 (step @p9 :rule cong :premises (@p8) :args (@t54)) % 0.37/0.58 (step @p10 :rule trans :premises (@p9 @p7)) % 0.37/0.58 (step @p11 :rule beta-reduce :args ((= @t56 @t54))) % 0.37/0.58 (step @p12 :rule trans :premises (@p11 @p10)) % 0.37/0.58 (step @p13 :rule cong :premises (@p12) :args ((not @t56))) % 0.37/0.58 (step @p14 :rule trans :premises (@p13 @p6)) % 0.37/0.58 (step @p15 :rule bool-double-not-elim :args (@t36)) % 0.37/0.58 (step @p16 :rule refl :args (@t34)) % 0.37/0.58 (step @p17 :rule refl :args (@t4)) % 0.37/0.58 (step @p18 :rule cong :premises (@p17 @p16) :args ((= @t4 @t34))) % 0.37/0.58 (step @p19 :rule symm :premises (@p18)) % 0.37/0.58 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.37/0.58 (step @p21 :rule cong :premises (@p20) :args (@t57)) % 0.37/0.58 (step @p22 :rule cong :premises (@p21) :args (@t58)) % 0.37/0.58 (step @p23 :rule cong :premises (@p22) :args (@t59)) % 0.37/0.58 (step @p24 :rule exists-elim :args ((= @t6 @t59))) % 0.37/0.58 (step @p25 :rule trans :premises (@p24 @p23)) % 0.37/0.58 (step @p26 :rule cong :premises (@p25) :args (@t7)) % 0.37/0.58 (step @p27 :rule trans :premises (@p26 @p15)) % 0.37/0.58 (step @p28 :rule cong :premises (@p27) :args (@t9)) % 0.37/0.58 (step @p29 :rule trans :premises (@p3 @p28)) % 0.37/0.58 (step @p30 :rule refl :args (@t55)) % 0.37/0.58 (step @p31 :rule refl :args (@t22)) % 0.37/0.58 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t22 @t55))) % 0.37/0.58 (step @p33 :rule symm :premises (@p32)) % 0.37/0.58 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.37/0.58 (step @p35 :rule refl :args (@t52)) % 0.37/0.58 (step @p36 :rule refl :args ((_ @t21 @t60))) % 0.37/0.58 (step @p37 :rule cong :premises (@p16) :args (@t35)) % 0.37/0.58 (step @p38 :rule cong :premises (@p37) :args (@t36)) % 0.37/0.58 (step @p39 :rule cong :premises (@p38) :args (@t37)) % 0.37/0.58 (step @p40 :rule cong :premises (@p39) :args (@t38)) % 0.37/0.58 (step @p41 :rule trans :premises (@p40 @p36)) % 0.37/0.58 (step @p42 :rule refl :args (@t21)) % 0.37/0.58 (step @p43 :rule ho_cong :premises (@p42 @p39)) % 0.37/0.58 (step @p44 :rule cong :premises (@p43 @p41) :args ((= @t61 @t38))) % 0.37/0.58 (step @p45 :rule symm :premises (@p44)) % 0.37/0.58 (step @p46 :rule refl :args ((_ @t21 @t60))) % 0.37/0.58 (step @p47 :rule eq_resolve :premises (@p46 @p45)) % 0.37/0.58 (step @p48 :rule cong :premises (@p47) :args (@t62)) % 0.37/0.58 (step @p49 :rule nary_cong :premises (@p48 @p35 @p34) :args (@t63)) % 0.37/0.58 (step @p50 :rule cong :premises (@p49) :args ((forall @t30 @t63))) % 0.37/0.58 (step @p51 :rule aci_norm :args ((= (or (or @t62 @t52) @t22) @t63))) % 0.37/0.58 (step @p52 :rule bool-and-de-morgan :args (@t61 @t51 true)) % 0.37/0.58 (step @p53 :rule nary_cong :premises (@p52 @p31) :args ((or (not @t64) @t22))) % 0.37/0.58 (step @p54 :rule trans :premises (@p53 @p51)) % 0.37/0.58 (step @p55 :rule bool-impl-elim :args (@t64 @t22)) % 0.37/0.58 (step @p56 :rule trans :premises (@p55 @p54)) % 0.37/0.58 (step @p57 :rule cong :premises (@p56) :args ((forall @t30 (=> @t64 @t22)))) % 0.37/0.58 (step @p58 :rule trans :premises (@p57 @p50)) % 0.37/0.58 (step @p59 :rule refl :args (@t22)) % 0.37/0.58 (step @p60 :rule refl :args ((_ @t21 @t67))) % 0.37/0.58 (step @p61 :rule refl :args ((_ @t23 @t66))) % 0.37/0.58 (step @p62 :rule refl :args (@t39)) % 0.37/0.58 (step @p63 :rule refl :args (@t40)) % 0.37/0.58 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t41)) % 0.37/0.58 (step @p65 :rule cong :premises (@p64) :args (@t42)) % 0.37/0.58 (step @p66 :rule cong :premises (@p65) :args (@t43)) % 0.37/0.58 (step @p67 :rule trans :premises (@p66 @p61)) % 0.37/0.58 (step @p68 :rule cong :premises (@p67) :args (@t44)) % 0.37/0.58 (step @p69 :rule nary_cong :premises (@p37 @p68) :args (@t45)) % 0.37/0.58 (step @p70 :rule cong :premises (@p69) :args (@t46)) % 0.37/0.58 (step @p71 :rule cong :premises (@p70) :args (@t47)) % 0.37/0.58 (step @p72 :rule cong :premises (@p71) :args (@t48)) % 0.37/0.58 (step @p73 :rule cong :premises (@p72) :args (@t49)) % 0.37/0.58 (step @p74 :rule trans :premises (@p73 @p60)) % 0.37/0.58 (step @p75 :rule ho_cong :premises (@p42 @p72)) % 0.37/0.58 (step @p76 :rule cong :premises (@p75 @p74) :args ((= @t68 @t49))) % 0.37/0.58 (step @p77 :rule symm :premises (@p76)) % 0.37/0.58 (step @p78 :rule refl :args ((_ @t21 @t67))) % 0.37/0.58 (step @p79 :rule eq_resolve :premises (@p78 @p77)) % 0.37/0.58 (step @p80 :rule refl :args (@t50)) % 0.37/0.58 (step @p81 :rule refl :args (@t24)) % 0.37/0.58 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t24 @t50))) % 0.37/0.58 (step @p83 :rule symm :premises (@p82)) % 0.37/0.58 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 0.37/0.58 (step @p85 :rule cong :premises (@p84) :args (@t69)) % 0.37/0.58 (step @p86 :rule nary_cong :premises (@p85 @p79) :args (@t70)) % 0.37/0.58 (step @p87 :rule cong :premises (@p86) :args ((forall @t26 @t70))) % 0.37/0.58 (step @p88 :rule bool-impl-elim :args (@t24 @t68)) % 0.37/0.58 (step @p89 :rule cong :premises (@p88) :args ((forall @t26 (=> @t24 @t68)))) % 0.37/0.58 (step @p90 :rule trans :premises (@p89 @p87)) % 0.37/0.58 (step @p91 :rule beta-reduce :args ((= @t72 @t48))) % 0.37/0.58 (step @p92 :rule refl :args (@t21)) % 0.37/0.58 (step @p93 :rule ho_cong :premises (@p92 @p91)) % 0.37/0.58 (step @p94 :rule refl :args (@t24)) % 0.37/0.58 (step @p95 :rule cong :premises (@p94 @p93) :args (@t73)) % 0.37/0.58 (step @p96 :rule cong :premises (@p95) :args (@t74)) % 0.37/0.58 (step @p97 :rule trans :premises (@p96 @p90)) % 0.37/0.58 (step @p98 :rule refl :args (@t61)) % 0.37/0.58 (step @p99 :rule nary_cong :premises (@p98 @p97) :args (@t75)) % 0.37/0.58 (step @p100 :rule cong :premises (@p99 @p59) :args (@t76)) % 0.37/0.58 (step @p101 :rule cong :premises (@p100) :args ((forall @t30 @t76))) % 0.37/0.58 (step @p102 :rule trans :premises (@p101 @p58)) % 0.37/0.58 (step @p103 :rule refl :args (@t23)) % 0.37/0.58 (step @p104 :rule refl :args ((_ @t16 @t66))) % 0.37/0.58 (step @p105 :rule cong :premises (@p65) :args (@t71)) % 0.37/0.58 (step @p106 :rule trans :premises (@p105 @p104)) % 0.37/0.58 (step @p107 :rule refl :args (@t16)) % 0.37/0.58 (step @p108 :rule ho_cong :premises (@p107 @p65)) % 0.37/0.58 (step @p109 :rule cong :premises (@p108 @p106) :args ((= (_ @t16 @t42) @t71))) % 0.37/0.58 (step @p110 :rule symm :premises (@p109)) % 0.37/0.58 (step @p111 :rule refl :args (@t77)) % 0.37/0.58 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.37/0.58 (step @p113 :rule refl :args (@t11)) % 0.37/0.58 (step @p114 :rule cong :premises (@p113 @p62) :args ((= @t11 @t39))) % 0.37/0.58 (step @p115 :rule symm :premises (@p114)) % 0.37/0.58 (step @p116 :rule eq_resolve :premises (@p113 @p115)) % 0.37/0.58 (step @p117 :rule nary_cong :premises (@p63 @p116) :args (@t65)) % 0.37/0.58 (step @p118 :rule cong :premises (@p117) :args (@t66)) % 0.37/0.58 (step @p119 :rule ho_cong :premises (@p107 @p118)) % 0.37/0.58 (step @p120 :rule trans :premises (@p119 @p112)) % 0.37/0.58 (step @p121 :rule cong :premises (@p120) :args (@t78)) % 0.37/0.58 (step @p122 :rule nary_cong :premises (@p21 @p121) :args (@t79)) % 0.37/0.58 (step @p123 :rule cong :premises (@p122) :args ((forall @t5 @t79))) % 0.37/0.58 (step @p124 :rule bool-and-de-morgan :args (@t4 @t77 true)) % 0.37/0.58 (step @p125 :rule cong :premises (@p124) :args (@t81)) % 0.37/0.58 (step @p126 :rule trans :premises (@p125 @p123)) % 0.37/0.58 (step @p127 :rule cong :premises (@p126) :args (@t82)) % 0.37/0.58 (step @p128 :rule exists-elim :args ((= (exists @t5 @t80) @t82))) % 0.37/0.58 (step @p129 :rule trans :premises (@p128 @p127)) % 0.37/0.58 (step @p130 :rule refl :args (@t11)) % 0.37/0.58 (step @p131 :rule eq-symm :args (@t10 @t2)) % 0.37/0.58 (step @p132 :rule cong :premises (@p131) :args (@t12)) % 0.37/0.58 (step @p133 :rule nary_cong :premises (@p132 @p130) :args (@t13)) % 0.37/0.58 (step @p134 :rule cong :premises (@p133) :args (@t15)) % 0.37/0.58 (step @p135 :rule refl :args (@t16)) % 0.37/0.58 (step @p136 :rule ho_cong :premises (@p135 @p134)) % 0.37/0.58 (step @p137 :rule refl :args (@t4)) % 0.37/0.58 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t17)) % 0.37/0.58 (step @p139 :rule cong :premises (@p138) :args (@t18)) % 0.37/0.58 (step @p140 :rule trans :premises (@p139 @p129)) % 0.37/0.58 (step @p141 :rule cong :premises (@p140) :args (@t20)) % 0.37/0.58 (step @p142 :rule trans :premises (@p4 @p141)) % 0.37/0.58 (step @p143 :rule ho_cong :premises (@p142 @p103)) % 0.37/0.58 (step @p144 :rule ho_cong :premises (@p92 @p143)) % 0.37/0.58 (step @p145 :rule cong :premises (@p94 @p144) :args (@t25)) % 0.37/0.58 (step @p146 :rule cong :premises (@p145) :args (@t27)) % 0.37/0.58 (step @p147 :rule ho_cong :premises (@p92 @p29)) % 0.37/0.58 (step @p148 :rule nary_cong :premises (@p147 @p146) :args (@t28)) % 0.37/0.58 (step @p149 :rule cong :premises (@p148 @p59) :args (@t29)) % 0.37/0.58 (step @p150 :rule cong :premises (@p149) :args (@t31)) % 0.37/0.58 (step @p151 :rule trans :premises (@p150 @p102)) % 0.37/0.58 (step @p152 :rule cong :premises (@p151) :args (@t33)) % 0.37/0.58 (step @p153 :rule trans :premises (@p5 @p152)) % 0.37/0.58 (step @p154 :rule ho_cong :premises (@p153 @p29)) % 0.37/0.58 (step @p155 :rule cong :premises (@p154) :args (@t1)) % 0.37/0.58 (step @p156 :rule trans :premises (@p155 @p14)) % 0.37/0.58 (step @p157 false :rule eq_resolve :premises (@p1 @p156)) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------