%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM798^1 : 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 : n010.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 08:40:43 AM UTC 2026 % Result : Theorem 0.31s 0.55s % Output : Proof 0.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM798^1 : 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 : n010.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 12:24:40 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.31/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.31/0.55 % SZS status Theorem % 0.31/0.55 % SZS output start Proof % 0.31/0.55 ( % 0.31/0.55 (declare-sort $$unsorted 0) % 0.31/0.55 (define tptp.zero () (let ((_let_1 (@var "Y" $$unsorted))) (lambda (@list (@var "X" (-> $$unsorted $$unsorted)) _let_1) _let_1))) % 0.31/0.55 (define tptp.one () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.31/0.55 (define tptp.two () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 _let_1)))))) % 0.31/0.55 (define tptp.three () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))) % 0.31/0.55 (define tptp.four () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))) % 0.31/0.55 (define tptp.five () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))) % 0.31/0.55 (define tptp.six () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.31/0.55 (define tptp.seven () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))) % 0.31/0.55 (define tptp.eight () (let ((_let_1 (@var "Y" $$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)))))))))))) % 0.31/0.55 (define tptp.nine () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))))) % 0.31/0.55 (define tptp.ten () (let ((_let_1 (@var "Y" $$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)))))))))))))) % 0.31/0.55 (define tptp.succ () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (lambda (@list _let_3 _let_2 _let_1) (_ _let_2 (_ (_ _let_3 _let_2) _let_1))))))) % 0.31/0.55 (define tptp.plus () (let ((_let_1 (@var "Y" $$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)))))))) % 0.31/0.55 (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 $$unsorted)))) (lambda (@list _let_4 _let_3 _let_2 _let_1) (_ (_ _let_4 (_ _let_3 _let_2)) _let_1))))))) % 0.31/0.55 (define @t1 () (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 0.31/0.55 (define @t2 () (= (_ (_ tptp.mult @t1) tptp.one) tptp.one)) % 0.31/0.55 (define @t3 () (@list @t1)) % 0.31/0.55 (define @t4 () (exists @t3 @t2)) % 0.31/0.55 (define @t5 () (not @t4)) % 0.31/0.55 (define @t6 () (@var "Y" $$unsorted)) % 0.31/0.55 (define @t7 () (@var "X" (-> $$unsorted $$unsorted))) % 0.31/0.55 (define @t8 () (@list @t7 @t6)) % 0.31/0.55 (define @t9 () (lambda @t8 @t6)) % 0.31/0.55 (define @t10 () (_ @t7 @t6)) % 0.31/0.55 (define @t11 () (lambda @t8 @t10)) % 0.31/0.55 (define @t12 () (_ @t7 @t10)) % 0.31/0.55 (define @t13 () (lambda @t8 @t12)) % 0.31/0.55 (define @t14 () (_ @t7 @t12)) % 0.31/0.55 (define @t15 () (lambda @t8 @t14)) % 0.31/0.55 (define @t16 () (_ @t7 @t14)) % 0.31/0.55 (define @t17 () (lambda @t8 @t16)) % 0.31/0.55 (define @t18 () (_ @t7 @t16)) % 0.31/0.55 (define @t19 () (lambda @t8 @t18)) % 0.31/0.55 (define @t20 () (_ @t7 @t18)) % 0.31/0.55 (define @t21 () (lambda @t8 @t20)) % 0.31/0.55 (define @t22 () (_ @t7 @t20)) % 0.31/0.55 (define @t23 () (lambda @t8 @t22)) % 0.31/0.55 (define @t24 () (_ @t7 @t22)) % 0.31/0.55 (define @t25 () (lambda @t8 @t24)) % 0.31/0.55 (define @t26 () (_ @t7 @t24)) % 0.31/0.55 (define @t27 () (lambda @t8 @t26)) % 0.31/0.55 (define @t28 () (lambda @t8 (_ @t7 @t26))) % 0.31/0.55 (define @t29 () (_ @t1 @t7)) % 0.31/0.55 (define @t30 () (_ @t29 @t6)) % 0.31/0.55 (define @t31 () (lambda (@list @t1 @t7 @t6) (_ @t7 @t30))) % 0.31/0.55 (define @t32 () (@var "M" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 0.31/0.55 (define @t33 () (@list @t32 @t1 @t7 @t6)) % 0.31/0.55 (define @t34 () (lambda @t33 (_ (_ @t32 @t7) @t30))) % 0.31/0.55 (define @t35 () (lambda @t33 (_ (_ @t32 @t29) @t6))) % 0.31/0.55 (define @t36 () (_ @t7 @t6)) % 0.31/0.55 (define @t37 () (lambda @t8 @t36)) % 0.31/0.55 (define @t38 () (not (= @t37 @t37))) % 0.31/0.55 (define @t39 () (not (= @t1 @t37))) % 0.31/0.55 (define @t40 () (or @t39 @t39)) % 0.31/0.55 (define @t41 () (@var "BOUND_VARIABLE_7559" $$unsorted)) % 0.31/0.55 (define @t42 () (_ @t7 @t41)) % 0.31/0.55 (define @t43 () (@list @t41)) % 0.31/0.55 (define @t44 () (lambda @t43 @t42)) % 0.31/0.55 (define @t45 () (_ @t1 @t44 @t6)) % 0.31/0.55 (define @t46 () (lambda @t8 @t45)) % 0.31/0.55 (define @t47 () (= @t37 @t46)) % 0.31/0.55 (define @t48 () (not @t47)) % 0.31/0.55 (define @t49 () (_ @t7 @t41)) % 0.31/0.55 (define @t50 () (lambda @t43 @t49)) % 0.31/0.55 (define @t51 () (_ (_ @t1 @t50) @t6)) % 0.31/0.55 (define @t52 () (lambda @t8 @t51)) % 0.31/0.55 (define @t53 () (= @t11 @t52)) % 0.31/0.55 (define @t54 () (not @t53)) % 0.31/0.55 (define @t55 () (forall @t3 @t54)) % 0.31/0.55 (define @t56 () (not @t55)) % 0.31/0.55 (define @t57 () (lambda (@list @t6) @t10)) % 0.31/0.55 (define @t58 () (_ @t11 @t7)) % 0.31/0.55 (define @t59 () (lambda @t8 (_ (_ @t1 @t58) @t6))) % 0.31/0.55 (define @t60 () (@var "BOUND_VARIABLE_7533" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 0.31/0.55 (define @t61 () (_ @t60 @t7)) % 0.31/0.55 (define @t62 () (lambda (@list @t60 @t7 @t6) (_ (_ @t1 @t61) @t6))) % 0.31/0.55 (define @t63 () (= (_ (_ @t35 @t1) @t11) @t11)) % 0.31/0.55 (define @t64 () (exists @t3 @t63)) % 0.31/0.55 (assume @p1 @t5) % 0.31/0.55 (assume @p2 true) % 0.31/0.55 (step @p3 (= tptp.zero @t9) :rule refl :args (@t9)) % 0.31/0.55 (step @p4 (= tptp.one @t11) :rule refl :args (@t11)) % 0.31/0.55 (step @p5 (= tptp.two @t13) :rule refl :args (@t13)) % 0.31/0.55 (step @p6 (= tptp.three @t15) :rule refl :args (@t15)) % 0.31/0.55 (step @p7 (= tptp.four @t17) :rule refl :args (@t17)) % 0.31/0.55 (step @p8 (= tptp.five @t19) :rule refl :args (@t19)) % 0.31/0.55 (step @p9 (= tptp.six @t21) :rule refl :args (@t21)) % 0.31/0.55 (step @p10 (= tptp.seven @t23) :rule refl :args (@t23)) % 0.31/0.55 (step @p11 (= tptp.eight @t25) :rule refl :args (@t25)) % 0.31/0.55 (step @p12 (= tptp.nine @t27) :rule refl :args (@t27)) % 0.31/0.55 (step @p13 (= tptp.ten @t28) :rule refl :args (@t28)) % 0.31/0.55 (step @p14 (= tptp.succ @t31) :rule refl :args (@t31)) % 0.31/0.55 (step @p15 (= tptp.plus @t34) :rule refl :args (@t34)) % 0.31/0.55 (step @p16 (= tptp.mult @t35) :rule refl :args (@t35)) % 0.31/0.55 (step @p17 :rule evaluate :args ((not true))) % 0.31/0.55 (step @p18 :rule evaluate :args ((not false))) % 0.31/0.55 (step @p19 :rule eq-refl :args (@t37)) % 0.31/0.55 (step @p20 :rule cong :premises (@p19) :args (@t38)) % 0.31/0.55 (step @p21 :rule trans :premises (@p20 @p17)) % 0.31/0.55 (step @p22 :rule quant-var-elim-eq :args ((= (forall @t3 @t40) @t38))) % 0.31/0.55 (step @p23 :rule aci_norm :args ((= @t39 @t40))) % 0.31/0.55 (step @p24 :rule cong :premises (@p23) :args ((forall @t3 @t39))) % 0.31/0.55 (step @p25 :rule trans :premises (@p24 @p22)) % 0.31/0.55 (step @p26 :rule trans :premises (@p25 @p21)) % 0.31/0.55 (step @p27 :rule eq-symm :args (@t37 @t1)) % 0.31/0.55 (step @p28 :rule lambda-elim :args ((= (lambda @t8 (_ @t1 @t7 @t6)) @t1))) % 0.31/0.55 (step @p29 :rule refl :args (@t6)) % 0.31/0.55 (step @p30 :rule lambda-elim :args ((= @t44 @t7))) % 0.31/0.55 (step @p31 :rule cong :premises (@p30 @p29) :args (@t45)) % 0.31/0.55 (step @p32 :rule cong :premises (@p31) :args (@t46)) % 0.31/0.55 (step @p33 :rule trans :premises (@p32 @p28)) % 0.31/0.55 (step @p34 :rule refl :args (@t37)) % 0.31/0.55 (step @p35 :rule cong :premises (@p34 @p33) :args (@t47)) % 0.31/0.55 (step @p36 :rule trans :premises (@p35 @p27)) % 0.31/0.55 (step @p37 :rule cong :premises (@p36) :args (@t48)) % 0.31/0.55 (step @p38 :rule cong :premises (@p37) :args ((forall @t3 @t48))) % 0.31/0.55 (step @p39 :rule trans :premises (@p38 @p26)) % 0.31/0.55 (step @p40 :rule refl :args ((_ @t1 @t50 @t6))) % 0.31/0.55 (step @p41 :rule refl :args (@t6)) % 0.31/0.55 (step @p42 :rule refl :args (@t42)) % 0.31/0.55 (step @p43 :rule cong :premises (@p42) :args (@t44)) % 0.31/0.55 (step @p44 :rule cong :premises (@p43 @p41) :args (@t45)) % 0.31/0.55 (step @p45 :rule trans :premises (@p44 @p40)) % 0.31/0.55 (step @p46 :rule refl :args (@t1)) % 0.31/0.55 (step @p47 :rule ho_cong :premises (@p46 @p43)) % 0.31/0.55 (step @p48 :rule ho_cong :premises (@p47 @p41)) % 0.31/0.55 (step @p49 :rule cong :premises (@p48 @p45) :args ((= (_ (_ @t1 @t44) @t6) @t45))) % 0.31/0.55 (step @p50 :rule symm :premises (@p49)) % 0.31/0.55 (step @p51 :rule refl :args (@t51)) % 0.31/0.55 (step @p52 :rule eq_resolve :premises (@p51 @p50)) % 0.31/0.55 (step @p53 :rule refl :args (@t49)) % 0.31/0.55 (step @p54 :rule cong :premises (@p53 @p42) :args ((= @t49 @t42))) % 0.31/0.55 (step @p55 :rule symm :premises (@p54)) % 0.31/0.55 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.31/0.55 (step @p57 :rule cong :premises (@p56) :args (@t50)) % 0.31/0.55 (step @p58 :rule ho_cong :premises (@p46 @p57)) % 0.31/0.55 (step @p59 :rule ho_cong :premises (@p58 @p41)) % 0.31/0.55 (step @p60 :rule trans :premises (@p59 @p52)) % 0.31/0.55 (step @p61 :rule cong :premises (@p60) :args (@t52)) % 0.31/0.55 (step @p62 :rule refl :args (@t36)) % 0.31/0.55 (step @p63 :rule refl :args (@t10)) % 0.31/0.55 (step @p64 :rule cong :premises (@p63 @p62) :args ((= @t10 @t36))) % 0.31/0.55 (step @p65 :rule symm :premises (@p64)) % 0.31/0.55 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.31/0.55 (step @p67 :rule cong :premises (@p66) :args (@t11)) % 0.31/0.55 (step @p68 :rule cong :premises (@p67 @p61) :args (@t53)) % 0.31/0.55 (step @p69 :rule cong :premises (@p68) :args (@t54)) % 0.31/0.55 (step @p70 :rule cong :premises (@p69) :args (@t55)) % 0.31/0.55 (step @p71 :rule trans :premises (@p70 @p39)) % 0.31/0.55 (step @p72 :rule cong :premises (@p71) :args (@t56)) % 0.31/0.55 (step @p73 :rule trans :premises (@p72 @p18)) % 0.31/0.55 (step @p74 :rule exists-elim :args ((= (exists @t3 @t53) @t56))) % 0.31/0.55 (step @p75 :rule trans :premises (@p74 @p73)) % 0.31/0.55 (step @p76 :rule eq-symm :args (@t52 @t11)) % 0.31/0.55 (step @p77 :rule refl :args (@t11)) % 0.31/0.55 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.31/0.55 ; trust TRUST_THEORY_REWRITE % 0.31/0.55 (step @p78 :rule trust :premises () :args ((= (lambda @t8 (_ (_ @t1 @t57) @t6)) @t52))) % 0.31/0.55 (step @p79 :rule beta-reduce :args ((= @t58 @t57))) % 0.31/0.55 (step @p80 :rule refl :args (@t1)) % 0.31/0.55 (step @p81 :rule ho_cong :premises (@p80 @p79)) % 0.31/0.55 (step @p82 :rule ho_cong :premises (@p81 @p29)) % 0.31/0.55 (step @p83 :rule cong :premises (@p82) :args (@t59)) % 0.31/0.55 (step @p84 :rule trans :premises (@p83 @p78)) % 0.31/0.55 (step @p85 :rule beta-reduce :args ((= (_ @t62 @t11) @t59))) % 0.31/0.55 (step @p86 :rule trans :premises (@p85 @p84)) % 0.31/0.55 (step @p87 :rule beta-reduce :args ((= (_ (lambda (@list @t32 @t60 @t7 @t6) (_ (_ @t32 @t61) @t6)) @t1) @t62))) % 0.31/0.55 (step @p88 :rule alpha_equiv :args (@t35 (@list @t1) (@list @t60))) % 0.31/0.55 (step @p89 :rule ho_cong :premises (@p88 @p46)) % 0.31/0.55 (step @p90 :rule trans :premises (@p89 @p87)) % 0.31/0.55 (step @p91 :rule ho_cong :premises (@p90 @p77)) % 0.31/0.55 (step @p92 :rule trans :premises (@p91 @p86)) % 0.31/0.55 (step @p93 :rule cong :premises (@p92 @p77) :args (@t63)) % 0.31/0.55 (step @p94 :rule trans :premises (@p93 @p76)) % 0.31/0.55 (step @p95 :rule cong :premises (@p94) :args (@t64)) % 0.31/0.55 (step @p96 :rule trans :premises (@p95 @p75)) % 0.31/0.55 (step @p97 :rule cong :premises (@p96) :args ((not @t64))) % 0.31/0.55 (step @p98 :rule trans :premises (@p97 @p17)) % 0.31/0.55 (step @p99 :rule ho_cong :premises (@p16 @p80)) % 0.31/0.55 (step @p100 :rule ho_cong :premises (@p99 @p4)) % 0.31/0.55 (step @p101 :rule cong :premises (@p100 @p4) :args (@t2)) % 0.31/0.55 (step @p102 :rule cong :premises (@p101) :args (@t4)) % 0.31/0.55 (step @p103 :rule cong :premises (@p102) :args (@t5)) % 0.31/0.55 (step @p104 :rule trans :premises (@p103 @p98)) % 0.31/0.55 (step @p105 false :rule eq_resolve :premises (@p1 @p104)) % 0.31/0.55 ) % 0.31/0.55 % SZS output end Proof % 0.31/0.55 % cvc5 exiting %------------------------------------------------------------------------------