%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM419^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:39:20 AM UTC 2026 % Result : Theorem 1.86s 2.04s % Output : Proof 1.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM419^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.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 11:17:23 EDT 2026 % 0.16/0.35 % CPUTime : % 0.31/0.50 %----Proving TH0 % 1.86/2.04 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.86/2.04 % SZS status Theorem % 1.86/2.04 % SZS output start Proof % 1.86/2.04 ( % 1.86/2.04 (declare-sort $$unsorted 0) % 1.86/2.04 (define tptp.zero () (let ((_let_1 (@var "Y" $$unsorted))) (lambda (@list (@var "X" (-> $$unsorted $$unsorted)) _let_1) _let_1))) % 1.86/2.04 (define tptp.one () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 1.86/2.04 (define tptp.two () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 _let_1)))))) % 1.86/2.04 (define tptp.three () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))) % 1.86/2.04 (define tptp.four () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))) % 1.86/2.04 (define tptp.five () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))) % 1.86/2.04 (define tptp.six () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))))) % 1.86/2.04 (define tptp.seven () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))) % 1.86/2.04 (define tptp.eight () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))))))) % 1.86/2.04 (define tptp.nine () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))))) % 1.86/2.04 (define tptp.ten () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))))))))) % 1.86/2.04 (define tptp.succ () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (lambda (@list _let_3 _let_2 _let_1) (_ _let_2 (_ (_ _let_3 _let_2) _let_1))))))) % 1.86/2.04 (define tptp.plus () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (let ((_let_4 (@var "M" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (lambda (@list _let_4 _let_3 _let_2 _let_1) (_ (_ _let_4 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.86/2.04 (define tptp.mult () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (let ((_let_4 (@var "M" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (lambda (@list _let_4 _let_3 _let_2 _let_1) (_ (_ _let_4 (_ _let_3 _let_2)) _let_1))))))) % 1.86/2.04 (define @t1 () (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 1.86/2.04 (define @t2 () (= (_ (_ tptp.plus @t1) tptp.three) tptp.four)) % 1.86/2.04 (define @t3 () (@list @t1)) % 1.86/2.04 (define @t4 () (exists @t3 @t2)) % 1.86/2.04 (define @t5 () (not @t4)) % 1.86/2.04 (define @t6 () (@var "Y" $$unsorted)) % 1.86/2.04 (define @t7 () (@var "X" (-> $$unsorted $$unsorted))) % 1.86/2.04 (define @t8 () (@list @t7 @t6)) % 1.86/2.04 (define @t9 () (lambda @t8 @t6)) % 1.86/2.04 (define @t10 () (_ @t7 @t6)) % 1.86/2.04 (define @t11 () (lambda @t8 @t10)) % 1.86/2.04 (define @t12 () (_ @t7 @t10)) % 1.86/2.04 (define @t13 () (lambda @t8 @t12)) % 1.86/2.04 (define @t14 () (_ @t7 @t12)) % 1.86/2.04 (define @t15 () (lambda @t8 @t14)) % 1.86/2.04 (define @t16 () (_ @t7 @t14)) % 1.86/2.04 (define @t17 () (lambda @t8 @t16)) % 1.86/2.04 (define @t18 () (_ @t7 @t16)) % 1.86/2.04 (define @t19 () (lambda @t8 @t18)) % 1.86/2.04 (define @t20 () (_ @t7 @t18)) % 1.86/2.04 (define @t21 () (lambda @t8 @t20)) % 1.86/2.04 (define @t22 () (_ @t7 @t20)) % 1.86/2.04 (define @t23 () (lambda @t8 @t22)) % 1.86/2.04 (define @t24 () (_ @t7 @t22)) % 1.86/2.04 (define @t25 () (lambda @t8 @t24)) % 1.86/2.04 (define @t26 () (_ @t7 @t24)) % 1.86/2.04 (define @t27 () (lambda @t8 @t26)) % 1.86/2.04 (define @t28 () (lambda @t8 (_ @t7 @t26))) % 1.86/2.04 (define @t29 () (_ @t1 @t7)) % 1.86/2.04 (define @t30 () (_ @t29 @t6)) % 1.86/2.04 (define @t31 () (lambda (@list @t1 @t7 @t6) (_ @t7 @t30))) % 1.86/2.04 (define @t32 () (@var "M" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 1.86/2.04 (define @t33 () (_ @t32 @t7)) % 1.86/2.04 (define @t34 () (@list @t32 @t1 @t7 @t6)) % 1.86/2.04 (define @t35 () (lambda @t34 (_ @t33 @t30))) % 1.86/2.04 (define @t36 () (lambda @t34 (_ (_ @t32 @t29) @t6))) % 1.86/2.04 (define @t37 () (_ @t7 @t6)) % 1.86/2.04 (define @t38 () (_ @t7 @t37)) % 1.86/2.04 (define @t39 () (_ @t7 @t38)) % 1.86/2.04 (define @t40 () (_ @t1 @t7 @t39)) % 1.86/2.04 (define @t41 () (_ @t7 @t39)) % 1.86/2.04 (define @t42 () (lambda @t8 @t41)) % 1.86/2.04 (define @t43 () (forall @t3 (not (= @t42 (lambda @t8 @t40))))) % 1.86/2.04 (define @t44 () (_ @t29 @t14)) % 1.86/2.04 (define @t45 () (lambda @t8 @t44)) % 1.86/2.04 (define @t46 () (= @t17 @t45)) % 1.86/2.04 (define @t47 () (not @t46)) % 1.86/2.04 (define @t48 () (forall @t3 @t47)) % 1.86/2.04 (define @t49 () (not @t48)) % 1.86/2.04 (define @t50 () (lambda (@list @t6) @t14)) % 1.86/2.04 (define @t51 () (_ @t15 @t7)) % 1.86/2.04 (define @t52 () (lambda @t8 (_ @t29 (_ @t51 @t6)))) % 1.86/2.04 (define @t53 () (@var "BOUND_VARIABLE_7533" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 1.86/2.04 (define @t54 () (_ (_ @t53 @t7) @t6)) % 1.86/2.04 (define @t55 () (lambda (@list @t53 @t7 @t6) (_ @t29 @t54))) % 1.86/2.04 (define @t56 () (= (_ (_ @t35 @t1) @t15) @t17)) % 1.86/2.04 (define @t57 () (exists @t3 @t56)) % 1.86/2.04 (define @t58 () (@var "BOUND_VARIABLE_58238" $$unsorted)) % 1.86/2.04 (define @t59 () (@var "BOUND_VARIABLE_58237" (-> $$unsorted $$unsorted))) % 1.86/2.04 (define @t60 () (lambda (@list @t59 @t58) (_ @t59 @t58))) % 1.86/2.04 (define @t61 () (_ @t60 @t7 @t39)) % 1.86/2.04 (define @t62 () (lambda @t8 @t61)) % 1.86/2.04 (define @t63 () (= @t42 @t62)) % 1.86/2.04 (define @t64 () (not @t63)) % 1.86/2.04 (assume @p1 @t5) % 1.86/2.04 (assume @p2 true) % 1.86/2.04 (step @p3 (= tptp.zero @t9) :rule refl :args (@t9)) % 1.86/2.04 (step @p4 (= tptp.one @t11) :rule refl :args (@t11)) % 1.86/2.04 (step @p5 (= tptp.two @t13) :rule refl :args (@t13)) % 1.86/2.04 (step @p6 (= tptp.three @t15) :rule refl :args (@t15)) % 1.86/2.04 (step @p7 (= tptp.four @t17) :rule refl :args (@t17)) % 1.86/2.04 (step @p8 (= tptp.five @t19) :rule refl :args (@t19)) % 1.86/2.04 (step @p9 (= tptp.six @t21) :rule refl :args (@t21)) % 1.86/2.04 (step @p10 (= tptp.seven @t23) :rule refl :args (@t23)) % 1.86/2.04 (step @p11 (= tptp.eight @t25) :rule refl :args (@t25)) % 1.86/2.04 (step @p12 (= tptp.nine @t27) :rule refl :args (@t27)) % 1.86/2.04 (step @p13 (= tptp.ten @t28) :rule refl :args (@t28)) % 1.86/2.04 (step @p14 (= tptp.succ @t31) :rule refl :args (@t31)) % 1.86/2.04 (step @p15 (= tptp.plus @t35) :rule refl :args (@t35)) % 1.86/2.04 (step @p16 (= tptp.mult @t36) :rule refl :args (@t36)) % 1.86/2.04 (step @p17 :rule bool-double-not-elim :args (@t43)) % 1.86/2.04 (step @p18 :rule refl :args ((_ @t1 @t7 @t14))) % 1.86/2.04 (step @p19 :rule refl :args ((_ @t7 @t12))) % 1.86/2.04 (step @p20 :rule refl :args ((_ @t7 @t10))) % 1.86/2.04 (step @p21 :rule refl :args (@t37)) % 1.86/2.04 (step @p22 :rule cong :premises (@p21) :args (@t38)) % 1.86/2.04 (step @p23 :rule trans :premises (@p22 @p20)) % 1.86/2.04 (step @p24 :rule cong :premises (@p23) :args (@t39)) % 1.86/2.04 (step @p25 :rule trans :premises (@p24 @p19)) % 1.86/2.04 (step @p26 :rule refl :args (@t7)) % 1.86/2.04 (step @p27 :rule cong :premises (@p26 @p25) :args (@t40)) % 1.86/2.04 (step @p28 :rule trans :premises (@p27 @p18)) % 1.86/2.04 (step @p29 :rule refl :args (@t29)) % 1.86/2.04 (step @p30 :rule ho_cong :premises (@p29 @p25)) % 1.86/2.04 (step @p31 :rule cong :premises (@p30 @p28) :args ((= (_ @t29 @t39) @t40))) % 1.86/2.04 (step @p32 :rule symm :premises (@p31)) % 1.86/2.04 (step @p33 :rule refl :args (@t44)) % 1.86/2.04 (step @p34 :rule eq_resolve :premises (@p33 @p32)) % 1.86/2.04 (step @p35 :rule ho_cong :premises (@p26 @p23)) % 1.86/2.04 (step @p36 :rule cong :premises (@p35 @p25) :args ((= (_ @t7 @t38) @t39))) % 1.86/2.04 (step @p37 :rule symm :premises (@p36)) % 1.86/2.04 (step @p38 :rule refl :args (@t14)) % 1.86/2.04 (step @p39 :rule eq_resolve :premises (@p38 @p37)) % 1.86/2.04 (step @p40 :rule ho_cong :premises (@p26 @p21)) % 1.86/2.04 (step @p41 :rule cong :premises (@p40 @p23) :args ((= (_ @t7 @t37) @t38))) % 1.86/2.04 (step @p42 :rule symm :premises (@p41)) % 1.86/2.04 (step @p43 :rule refl :args (@t12)) % 1.86/2.04 (step @p44 :rule eq_resolve :premises (@p43 @p42)) % 1.86/2.04 (step @p45 :rule refl :args (@t10)) % 1.86/2.04 (step @p46 :rule cong :premises (@p45 @p21) :args ((= @t10 @t37))) % 1.86/2.04 (step @p47 :rule symm :premises (@p46)) % 1.86/2.04 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 1.86/2.04 (step @p49 :rule ho_cong :premises (@p26 @p48)) % 1.86/2.04 (step @p50 :rule trans :premises (@p49 @p44)) % 1.86/2.04 (step @p51 :rule ho_cong :premises (@p26 @p50)) % 1.86/2.04 (step @p52 :rule trans :premises (@p51 @p39)) % 1.86/2.04 (step @p53 :rule ho_cong :premises (@p29 @p52)) % 1.86/2.04 (step @p54 :rule trans :premises (@p53 @p34)) % 1.86/2.04 (step @p55 :rule cong :premises (@p54) :args (@t45)) % 1.86/2.04 (step @p56 :rule refl :args ((_ @t7 @t14))) % 1.86/2.04 (step @p57 :rule cong :premises (@p25) :args (@t41)) % 1.86/2.04 (step @p58 :rule trans :premises (@p57 @p56)) % 1.86/2.04 (step @p59 :rule ho_cong :premises (@p26 @p25)) % 1.86/2.04 (step @p60 :rule cong :premises (@p59 @p58) :args ((= (_ @t7 @t39) @t41))) % 1.86/2.04 (step @p61 :rule symm :premises (@p60)) % 1.86/2.04 (step @p62 :rule refl :args (@t16)) % 1.86/2.04 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 1.86/2.04 (step @p64 :rule ho_cong :premises (@p26 @p52)) % 1.86/2.04 (step @p65 :rule trans :premises (@p64 @p63)) % 1.86/2.04 (step @p66 :rule cong :premises (@p65) :args (@t17)) % 1.86/2.04 (step @p67 :rule cong :premises (@p66 @p55) :args (@t46)) % 1.86/2.04 (step @p68 :rule cong :premises (@p67) :args (@t47)) % 1.86/2.04 (step @p69 :rule cong :premises (@p68) :args (@t48)) % 1.86/2.04 (step @p70 :rule cong :premises (@p69) :args (@t49)) % 1.86/2.04 (step @p71 :rule exists-elim :args ((= (exists @t3 @t46) @t49))) % 1.86/2.04 (step @p72 :rule trans :premises (@p71 @p70)) % 1.86/2.04 (step @p73 :rule eq-symm :args (@t45 @t17)) % 1.86/2.04 (step @p74 :rule refl :args (@t17)) % 1.86/2.04 (step @p75 :rule beta-reduce :args ((= (_ @t50 @t6) @t14))) % 1.86/2.04 (step @p76 :rule refl :args (@t6)) % 1.86/2.04 (step @p77 :rule beta-reduce :args ((= @t51 @t50))) % 1.86/2.04 (step @p78 :rule ho_cong :premises (@p77 @p76)) % 1.86/2.04 (step @p79 :rule trans :premises (@p78 @p75)) % 1.86/2.04 (step @p80 :rule refl :args (@t29)) % 1.86/2.04 (step @p81 :rule ho_cong :premises (@p80 @p79)) % 1.86/2.04 (step @p82 :rule cong :premises (@p81) :args (@t52)) % 1.86/2.04 (step @p83 :rule beta-reduce :args ((= (_ @t55 @t15) @t52))) % 1.86/2.04 (step @p84 :rule trans :premises (@p83 @p82)) % 1.86/2.04 (step @p85 :rule refl :args (@t15)) % 1.86/2.04 (step @p86 :rule beta-reduce :args ((= (_ (lambda (@list @t32 @t53 @t7 @t6) (_ @t33 @t54)) @t1) @t55))) % 1.86/2.04 (step @p87 :rule refl :args (@t1)) % 1.86/2.04 (step @p88 :rule alpha_equiv :args (@t35 (@list @t1) (@list @t53))) % 1.86/2.04 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 1.86/2.04 (step @p90 :rule trans :premises (@p89 @p86)) % 1.86/2.04 (step @p91 :rule ho_cong :premises (@p90 @p85)) % 1.86/2.04 (step @p92 :rule trans :premises (@p91 @p84)) % 1.86/2.04 (step @p93 :rule cong :premises (@p92 @p74) :args (@t56)) % 1.86/2.04 (step @p94 :rule trans :premises (@p93 @p73)) % 1.86/2.04 (step @p95 :rule cong :premises (@p94) :args (@t57)) % 1.86/2.04 (step @p96 :rule trans :premises (@p95 @p72)) % 1.86/2.04 (step @p97 :rule cong :premises (@p96) :args ((not @t57))) % 1.86/2.04 (step @p98 :rule trans :premises (@p97 @p17)) % 1.86/2.04 (step @p99 :rule refl :args (@t1)) % 1.86/2.04 (step @p100 :rule ho_cong :premises (@p15 @p99)) % 1.86/2.04 (step @p101 :rule ho_cong :premises (@p100 @p6)) % 1.86/2.04 (step @p102 :rule cong :premises (@p101 @p7) :args (@t2)) % 1.86/2.04 (step @p103 :rule cong :premises (@p102) :args (@t4)) % 1.86/2.04 (step @p104 :rule cong :premises (@p103) :args (@t5)) % 1.86/2.04 (step @p105 :rule trans :premises (@p104 @p98)) % 1.86/2.04 (step @p106 :rule eq_resolve :premises (@p1 @p105)) % 1.86/2.04 (step @p107 :rule bool-impl-false1 :args (@t43)) % 1.86/2.04 (step @p108 :rule evaluate :args ((not true))) % 1.86/2.04 (step @p109 :rule eq-refl :args (@t42)) % 1.86/2.04 (step @p110 :rule beta-reduce :args ((= @t61 @t41))) % 1.86/2.04 (step @p111 :rule cong :premises (@p110) :args (@t62)) % 1.86/2.04 (step @p112 :rule refl :args (@t42)) % 1.86/2.04 (step @p113 :rule cong :premises (@p112 @p111) :args (@t63)) % 1.86/2.04 (step @p114 :rule trans :premises (@p113 @p109)) % 1.86/2.04 (step @p115 :rule cong :premises (@p114) :args (@t64)) % 1.86/2.04 (step @p116 :rule trans :premises (@p115 @p108)) % 1.86/2.04 (step @p117 :rule refl :args (@t43)) % 1.86/2.04 (step @p118 :rule cong :premises (@p117 @p116) :args ((=> @t43 @t64))) % 1.86/2.04 (step @p119 :rule trans :premises (@p118 @p107)) % 1.86/2.04 (assume-push @p126 @t43) % 1.86/2.04 (step @p121 :rule instantiate :premises (@p106) :args ((@list @t60))) % 1.86/2.04 (step-pop @p127 :rule scope :premises (@p121)) % 1.86/2.04 (step @p122 :rule process_scope :premises (@p127) :args (@t64)) % 1.86/2.04 (step @p124 :rule eq_resolve :premises (@p122 @p119)) % 1.86/2.04 (step @p125 false :rule chain_m_resolution :premises (@p124 @p106) :args (false (@list false) (@list @t43))) % 1.86/2.05 ) % 1.86/2.05 % SZS output end Proof % 1.86/2.05 % cvc5 exiting %------------------------------------------------------------------------------