%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM416^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.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 0.45s 0.63s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM416^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n006.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 11:17:04 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.45/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.63 % SZS status Theorem % 0.45/0.63 % SZS output start Proof % 0.45/0.63 ( % 0.45/0.63 (declare-sort $$unsorted 0) % 0.45/0.63 (define tptp.zero () (let ((_let_1 (@var "Y" $$unsorted))) (lambda (@list (@var "X" (-> $$unsorted $$unsorted)) _let_1) _let_1))) % 0.45/0.63 (define tptp.one () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.45/0.63 (define tptp.two () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 _let_1)))))) % 0.45/0.63 (define tptp.three () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))) % 0.45/0.63 (define tptp.four () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))) % 0.45/0.63 (define tptp.five () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))) % 0.45/0.63 (define tptp.six () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.45/0.63 (define tptp.seven () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))) % 0.45/0.63 (define tptp.eight () (let ((_let_1 (@var "Y" $$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)))))))))))) % 0.45/0.63 (define tptp.nine () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))))) % 0.45/0.63 (define tptp.ten () (let ((_let_1 (@var "Y" $$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)))))))))))))) % 0.45/0.63 (define tptp.succ () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (lambda (@list _let_3 _let_2 _let_1) (_ _let_2 (_ (_ _let_3 _let_2) _let_1))))))) % 0.45/0.63 (define tptp.plus () (let ((_let_1 (@var "Y" $$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)))))))) % 0.45/0.63 (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 $$unsorted)))) (lambda (@list _let_4 _let_3 _let_2 _let_1) (_ (_ _let_4 (_ _let_3 _let_2)) _let_1))))))) % 0.45/0.63 (define @t1 () (_ tptp.mult tptp.ten)) % 0.45/0.63 (define @t2 () (= (_ @t1 (_ @t1 tptp.ten)) (_ (_ tptp.mult (_ (_ tptp.plus tptp.ten) tptp.ten)) (_ (_ tptp.mult tptp.five) tptp.ten)))) % 0.45/0.63 (define @t3 () (not @t2)) % 0.45/0.63 (define @t4 () (@var "Y" $$unsorted)) % 0.45/0.63 (define @t5 () (@var "X" (-> $$unsorted $$unsorted))) % 0.45/0.63 (define @t6 () (@list @t5 @t4)) % 0.45/0.63 (define @t7 () (lambda @t6 @t4)) % 0.45/0.63 (define @t8 () (_ @t5 @t4)) % 0.45/0.63 (define @t9 () (lambda @t6 @t8)) % 0.45/0.63 (define @t10 () (_ @t5 @t8)) % 0.45/0.63 (define @t11 () (lambda @t6 @t10)) % 0.45/0.63 (define @t12 () (_ @t5 @t10)) % 0.45/0.63 (define @t13 () (lambda @t6 @t12)) % 0.45/0.63 (define @t14 () (_ @t5 @t12)) % 0.45/0.63 (define @t15 () (lambda @t6 @t14)) % 0.45/0.63 (define @t16 () (_ @t5 @t14)) % 0.45/0.63 (define @t17 () (lambda @t6 @t16)) % 0.45/0.63 (define @t18 () (_ @t5 @t16)) % 0.45/0.63 (define @t19 () (lambda @t6 @t18)) % 0.45/0.63 (define @t20 () (_ @t5 @t18)) % 0.45/0.63 (define @t21 () (lambda @t6 @t20)) % 0.45/0.63 (define @t22 () (_ @t5 @t20)) % 0.45/0.63 (define @t23 () (lambda @t6 @t22)) % 0.45/0.63 (define @t24 () (_ @t5 @t22)) % 0.45/0.63 (define @t25 () (lambda @t6 @t24)) % 0.45/0.63 (define @t26 () (_ @t5 @t24)) % 0.45/0.63 (define @t27 () (lambda @t6 @t26)) % 0.45/0.63 (define @t28 () (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 0.45/0.63 (define @t29 () (_ @t28 @t5)) % 0.45/0.63 (define @t30 () (_ @t29 @t4)) % 0.45/0.63 (define @t31 () (_ @t5 @t30)) % 0.45/0.63 (define @t32 () (@list @t28 @t5 @t4)) % 0.45/0.63 (define @t33 () (lambda @t32 @t31)) % 0.45/0.63 (define @t34 () (@var "M" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 0.45/0.63 (define @t35 () (@list @t34 @t28 @t5 @t4)) % 0.45/0.63 (define @t36 () (lambda @t35 (_ (_ @t34 @t5) @t30))) % 0.45/0.63 (define @t37 () (lambda @t35 (_ (_ @t34 @t29) @t4))) % 0.45/0.63 (define @t38 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t26))))))))))) % 0.45/0.63 (define @t39 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t38))))))))))) % 0.45/0.63 (define @t40 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t39))))))))))) % 0.45/0.63 (define @t41 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t40))))))))))) % 0.45/0.63 (define @t42 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t41))))))))))) % 0.45/0.63 (define @t43 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t42))))))))))) % 0.45/0.63 (define @t44 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t43))))))))))) % 0.45/0.63 (define @t45 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t44))))))))))) % 0.45/0.63 (define @t46 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t45))))))))))) % 0.45/0.63 (define @t47 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t46))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t48 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t47))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t49 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t48))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t50 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t49))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t51 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t50))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t52 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t51))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t53 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t52))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t54 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t53))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t55 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t54))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t56 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t55))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t57 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t56))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t58 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t57))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t59 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t58))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t60 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t59))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t61 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t60))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t62 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t61))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t63 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t62))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t64 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t63))))))))))))))))))))))))))))))))))))))))))))))))))) % 0.45/0.63 (define @t65 () (@list @t4)) % 0.45/0.63 (define @t66 () (lambda @t65 @t41)) % 0.45/0.63 (define @t67 () (lambda @t6 @t41)) % 0.45/0.63 (define @t68 () (_ @t67 @t5)) % 0.45/0.63 (define @t69 () (lambda @t6 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 (_ @t68 @t4)))))))))))))))))))))) % 0.45/0.63 (define @t70 () (_ @t29 (_ @t29 (_ @t29 (_ @t29 @t30))))) % 0.45/0.63 (define @t71 () (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 @t70)))))) % 0.45/0.63 (define @t72 () (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 @t71))))))))))) % 0.45/0.63 (define @t73 () (lambda @t65 @t26)) % 0.45/0.63 (define @t74 () (_ @t27 @t5)) % 0.45/0.63 (define @t75 () (_ @t74 @t4)) % 0.45/0.63 (define @t76 () (_ @t74 (_ @t74 (_ @t74 (_ @t74 @t75))))) % 0.45/0.63 (define @t77 () (lambda @t6 @t76)) % 0.45/0.63 (define @t78 () (lambda @t65 @t70)) % 0.45/0.63 (define @t79 () (_ @t17 @t29)) % 0.45/0.63 (define @t80 () (lambda @t32 (_ @t79 @t4))) % 0.45/0.63 (define @t81 () (_ @t37 @t17)) % 0.45/0.63 (define @t82 () (lambda @t65 @t72)) % 0.45/0.63 (define @t83 () (lambda @t6 @t38)) % 0.45/0.63 (define @t84 () (_ @t83 @t29)) % 0.45/0.63 (define @t85 () (lambda @t32 (_ @t84 @t4))) % 0.45/0.63 (define @t86 () (lambda @t6 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t75)))))))))))) % 0.45/0.63 (define @t87 () (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 (_ @t5 @t31)))))))))) % 0.45/0.63 (define @t88 () (lambda @t32 (_ @t74 @t30))) % 0.45/0.63 (define @t89 () (_ @t36 @t27)) % 0.45/0.63 (define @t90 () (lambda @t65 @t46)) % 0.45/0.63 (define @t91 () (lambda @t6 @t46)) % 0.45/0.63 (define @t92 () (_ @t91 @t5)) % 0.45/0.63 (define @t93 () (lambda @t6 (_ @t92 (_ @t92 (_ @t92 (_ @t92 (_ @t92 (_ @t92 (_ @t92 (_ @t92 (_ @t92 (_ @t92 @t4)))))))))))) % 0.45/0.63 (define @t94 () (lambda @t32 @t71)) % 0.45/0.63 (define @t95 () (lambda @t6 (_ @t74 (_ @t74 (_ @t74 (_ @t74 (_ @t74 @t76))))))) % 0.45/0.63 (define @t96 () (lambda @t65 @t71)) % 0.45/0.63 (define @t97 () (_ @t27 @t29)) % 0.45/0.63 (define @t98 () (lambda @t32 (_ @t97 @t4))) % 0.45/0.63 (define @t99 () (_ @t37 @t27)) % 0.45/0.63 (define @t100 () (= (_ @t99 (_ @t99 @t27)) (_ (_ @t37 (_ @t89 @t27)) (_ @t81 @t27)))) % 0.45/0.63 (assume @p1 @t3) % 0.45/0.63 (assume @p2 true) % 0.45/0.63 (step @p3 (= tptp.zero @t7) :rule refl :args (@t7)) % 0.45/0.63 (step @p4 (= tptp.one @t9) :rule refl :args (@t9)) % 0.45/0.63 (step @p5 (= tptp.two @t11) :rule refl :args (@t11)) % 0.45/0.63 (step @p6 (= tptp.three @t13) :rule refl :args (@t13)) % 0.45/0.63 (step @p7 (= tptp.four @t15) :rule refl :args (@t15)) % 0.45/0.63 (step @p8 (= tptp.five @t17) :rule refl :args (@t17)) % 0.45/0.63 (step @p9 (= tptp.six @t19) :rule refl :args (@t19)) % 0.45/0.63 (step @p10 (= tptp.seven 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:rule ho_cong :premises (@p158 @p164)) % 0.45/0.63 (step @p166 :rule trans :premises (@p165 @p154)) % 0.45/0.63 (step @p167 :rule ho_cong :premises (@p158 @p166)) % 0.45/0.63 (step @p168 :rule trans :premises (@p167 @p153)) % 0.45/0.63 (step @p169 :rule ho_cong :premises (@p158 @p168)) % 0.45/0.63 (step @p170 :rule trans :premises (@p169 @p152)) % 0.45/0.63 (step @p171 :rule ho_cong :premises (@p158 @p170)) % 0.45/0.63 (step @p172 :rule trans :premises (@p171 @p151)) % 0.45/0.63 (step @p173 :rule ho_cong :premises (@p158 @p172)) % 0.45/0.63 (step @p174 :rule trans :premises (@p173 @p150)) % 0.45/0.63 (step @p175 :rule ho_cong :premises (@p158 @p174)) % 0.45/0.63 (step @p176 :rule trans :premises (@p175 @p149)) % 0.45/0.63 (step @p177 :rule ho_cong :premises (@p158 @p176)) % 0.45/0.63 (step @p178 :rule trans :premises (@p177 @p148)) % 0.45/0.63 (step @p179 :rule cong :premises (@p178) :args (@t93)) % 0.45/0.63 (step @p180 :rule beta-reduce :args ((= (_ @t94 @t91) @t93))) % 0.45/0.63 (step @p181 :rule trans :premises (@p180 @p179)) % 0.45/0.63 (step @p182 :rule beta-reduce :args ((= (_ @t73 @t45) @t46))) % 0.45/0.63 (step @p183 :rule beta-reduce :args ((= (_ @t73 @t44) @t45))) % 0.45/0.63 (step @p184 :rule beta-reduce :args ((= (_ @t73 @t43) @t44))) % 0.45/0.63 (step @p185 :rule beta-reduce :args ((= (_ @t73 @t42) @t43))) % 0.45/0.63 (step @p186 :rule beta-reduce :args ((= (_ @t73 @t41) @t42))) % 0.45/0.63 (step @p187 :rule ho_cong :premises (@p89 @p99)) % 0.45/0.63 (step @p188 :rule trans :premises (@p187 @p186)) % 0.45/0.63 (step @p189 :rule ho_cong :premises (@p89 @p188)) % 0.45/0.63 (step @p190 :rule trans :premises (@p189 @p185)) % 0.45/0.63 (step @p191 :rule ho_cong :premises (@p89 @p190)) % 0.45/0.63 (step @p192 :rule trans :premises (@p191 @p184)) % 0.45/0.63 (step @p193 :rule ho_cong :premises (@p89 @p192)) % 0.45/0.63 (step @p194 :rule trans :premises (@p193 @p183)) % 0.45/0.63 (step @p195 :rule ho_cong :premises (@p89 @p194)) % 0.45/0.63 (step @p196 :rule trans :premises (@p195 @p182)) % 0.45/0.63 (step @p197 :rule cong :premises (@p196) :args (@t95)) % 0.45/0.63 (step @p198 :rule beta-reduce :args ((= (_ @t94 @t27) @t95))) % 0.45/0.63 (step @p199 :rule trans :premises (@p198 @p197)) % 0.45/0.63 (step @p200 :rule beta-reduce :args ((= (_ @t96 @t4) @t71))) % 0.45/0.63 (step @p201 :rule beta-reduce :args ((= @t97 @t96))) % 0.45/0.63 (step @p202 :rule ho_cong :premises (@p201 @p39)) % 0.45/0.63 (step @p203 :rule trans :premises (@p202 @p200)) % 0.45/0.63 (step @p204 :rule cong :premises (@p203) :args (@t98)) % 0.45/0.63 (step @p205 :rule beta-reduce :args ((= @t99 @t98))) % 0.45/0.63 (step @p206 :rule trans :premises (@p205 @p204)) % 0.45/0.63 (step @p207 :rule ho_cong :premises (@p206 @p103)) % 0.45/0.63 (step @p208 :rule trans :premises (@p207 @p199)) % 0.45/0.63 (step @p209 :rule ho_cong :premises (@p206 @p208)) % 0.45/0.63 (step @p210 :rule trans :premises (@p209 @p181)) % 0.45/0.63 (step @p211 :rule cong :premises (@p210 @p147) :args (@t100)) % 0.45/0.63 (step @p212 :rule trans :premises (@p211 @p18)) % 0.45/0.63 (step @p213 :rule cong :premises (@p212) :args ((not @t100))) % 0.45/0.63 (step @p214 :rule trans :premises (@p213 @p17)) % 0.45/0.63 (step @p215 :rule ho_cong :premises (@p16 @p8)) % 0.45/0.63 (step @p216 :rule ho_cong :premises (@p215 @p13)) % 0.45/0.63 (step @p217 :rule ho_cong :premises (@p15 @p13)) % 0.45/0.63 (step @p218 :rule ho_cong :premises (@p217 @p13)) % 0.45/0.63 (step @p219 :rule ho_cong :premises (@p16 @p218)) % 0.45/0.63 (step @p220 :rule ho_cong :premises (@p219 @p216)) % 0.45/0.63 (step @p221 :rule ho_cong :premises (@p16 @p13)) % 0.45/0.63 (step @p222 :rule ho_cong :premises (@p221 @p13)) % 0.45/0.63 (step @p223 :rule ho_cong :premises (@p221 @p222)) % 0.45/0.63 (step @p224 :rule cong :premises (@p223 @p220) :args (@t2)) % 0.45/0.63 (step @p225 :rule cong :premises (@p224) :args (@t3)) % 0.45/0.63 (step @p226 :rule trans :premises (@p225 @p214)) % 0.45/0.63 (step @p227 false :rule eq_resolve :premises (@p1 @p226)) % 0.45/0.63 ) % 0.45/0.63 % SZS output end Proof % 0.45/0.63 % cvc5 exiting %------------------------------------------------------------------------------