%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM802^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 : Fri Oct 3 07:57:23 PM UTC 2025 % Result : Theorem 3.56s 3.71s % Output : Proof 3.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : NUM802^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n014.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 08:45:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.56/3.71 SZS status Theorem for theBenchmark.p % 3.56/3.71 SZS output start Proof for theBenchmark.p % 3.56/3.71 Clause #0 (by assumption #[]): Eq % 3.56/3.71 (Not % 3.56/3.71 (c_less_ c_2 c0 → % 3.56/3.71 (∀ (Xu Xv : Iota), c_less_ Xu c0 → Ne Xu (absval Xv)) → % 3.56/3.71 Exists fun A => And (∀ (Xy : Iota), Not (A (absval Xy))) (A c_2))) % 3.56/3.71 True % 3.56/3.71 Clause #1 (by clausification #[0]): Eq % 3.56/3.71 (c_less_ c_2 c0 → % 3.56/3.71 (∀ (Xu Xv : Iota), c_less_ Xu c0 → Ne Xu (absval Xv)) → % 3.56/3.71 Exists fun A => And (∀ (Xy : Iota), Not (A (absval Xy))) (A c_2)) % 3.56/3.71 False % 3.56/3.71 Clause #2 (by clausification #[1]): Eq (c_less_ c_2 c0) True % 3.56/3.71 Clause #3 (by clausification #[1]): Eq % 3.56/3.71 ((∀ (Xu Xv : Iota), c_less_ Xu c0 → Ne Xu (absval Xv)) → % 3.56/3.71 Exists fun A => And (∀ (Xy : Iota), Not (A (absval Xy))) (A c_2)) % 3.56/3.71 False % 3.56/3.71 Clause #4 (by clausification #[3]): Eq (∀ (Xu Xv : Iota), c_less_ Xu c0 → Ne Xu (absval Xv)) True % 3.56/3.71 Clause #5 (by clausification #[3]): Eq (Exists fun A => And (∀ (Xy : Iota), Not (A (absval Xy))) (A c_2)) False % 3.56/3.71 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Xv : Iota), c_less_ a c0 → Ne a (absval Xv)) True % 3.56/3.71 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (c_less_ a c0 → Ne a (absval a_1)) True % 3.56/3.71 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (c_less_ a c0) False) (Eq (Ne a (absval a_1)) True) % 3.56/3.71 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (c_less_ a c0) False) (Ne a (absval a_1)) % 3.56/3.71 Clause #10 (by destructive equality resolution #[9]): ∀ (a : Iota), Eq (c_less_ (absval a) c0) False % 3.56/3.71 Clause #11 (by clausification #[5]): ∀ (a : Iota → Prop), Eq (And (∀ (Xy : Iota), Not (a (absval Xy))) (a c_2)) False % 3.56/3.71 Clause #12 (by clausification #[11]): ∀ (a : Iota → Prop), Or (Eq (∀ (Xy : Iota), Not (a (absval Xy))) False) (Eq (a c_2) False) % 3.56/3.71 Clause #13 (by clausification #[12]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a c_2) False) (Eq (Not (Not (a (absval (skS.0 0 a a_1))))) True) % 3.56/3.71 Clause #14 (by clausification #[13]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a c_2) False) (Eq (Not (a (absval (skS.0 0 a a_1)))) False) % 3.56/3.71 Clause #15 (by clausification #[14]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a c_2) False) (Eq (a (absval (skS.0 0 a a_1))) True) % 3.56/3.71 Clause #24 (by superposition #[15, 2]): ∀ (a : Iota), Or (Eq ((fun x => c_less_ x c0) (absval (skS.0 0 (fun x => c_less_ x c0) a))) True) (Eq False True) % 3.56/3.71 Clause #29 (by betaEtaReduce #[24]): ∀ (a : Iota), Or (Eq (c_less_ (absval (skS.0 0 (fun x => c_less_ x c0) a)) c0) True) (Eq False True) % 3.56/3.71 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (c_less_ (absval (skS.0 0 (fun x => c_less_ x c0) a)) c0) True % 3.56/3.71 Clause #31 (by superposition #[30, 10]): Eq True False % 3.56/3.71 Clause #38 (by clausification #[31]): False % 3.56/3.71 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------