%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN065+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:07:06 PM UTC 2025 % Result : Theorem 4.38s 4.56s % Output : Proof 4.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : SYN065+1 : TPTP v9.2.0. Released v2.0.0. % 0.09/0.16 % Command : duper %s % 0.16/0.36 % Computer : n007.cluster.edu % 0.16/0.36 % Model : x86_64 x86_64 % 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.36 % Memory : 8042.1875MB % 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.36 % CPULimit : 300 % 0.16/0.36 % WCLimit : 300 % 0.16/0.36 % DateTime : Thu Oct 2 15:04:53 EDT 2025 % 0.16/0.36 % CPUTime : % 4.38/4.56 SZS status Theorem for theBenchmark.p % 4.38/4.56 SZS output start Proof for theBenchmark.p % 4.38/4.56 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), Exists fun Y => big_f X Y) True % 4.38/4.56 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Exists fun Y => big_g X Y) True % 4.38/4.56 Clause #2 (by assumption #[]): Eq (∀ (X Y : Iota), Or (big_f X Y) (big_g X Y) → ∀ (Z : Iota), Or (big_f Y Z) (big_g Y Z) → big_h X Z) True % 4.38/4.56 Clause #3 (by assumption #[]): Eq (Not (∀ (X : Iota), Exists fun Y => big_h X Y)) True % 4.38/4.56 Clause #4 (by betaEtaReduce #[1]): Eq (∀ (X : Iota), Exists (big_g X)) True % 4.38/4.56 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Exists (big_g a)) True % 4.38/4.56 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (big_g a (skS.0 0 a a_1)) True % 4.38/4.56 Clause #7 (by betaEtaReduce #[0]): Eq (∀ (X : Iota), Exists (big_f X)) True % 4.38/4.56 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Exists (big_f a)) True % 4.38/4.56 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (big_f a (skS.0 1 a a_1)) True % 4.38/4.56 Clause #10 (by betaEtaReduce #[3]): Eq (Not (∀ (X : Iota), Exists (big_h X))) True % 4.38/4.56 Clause #11 (by clausification #[10]): Eq (∀ (X : Iota), Exists (big_h X)) False % 4.38/4.56 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (Not (Exists (big_h (skS.0 2 a)))) True % 4.38/4.56 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (Exists (big_h (skS.0 2 a))) False % 4.38/4.56 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (big_h (skS.0 2 a) a_1) False % 4.38/4.56 Clause #15 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (big_f a Y) (big_g a Y) → ∀ (Z : Iota), Or (big_f Y Z) (big_g Y Z) → big_h a Z) True % 4.38/4.56 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Or (big_f a a_1) (big_g a a_1) → ∀ (Z : Iota), Or (big_f a_1 Z) (big_g a_1 Z) → big_h a Z) True % 4.38/4.56 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 4.38/4.56 Or (Eq (Or (big_f a a_1) (big_g a a_1)) False) (Eq (∀ (Z : Iota), Or (big_f a_1 Z) (big_g a_1 Z) → big_h a Z) True) % 4.38/4.56 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (∀ (Z : Iota), Or (big_f a Z) (big_g a Z) → big_h a_1 Z) True) (Eq (big_g a_1 a) False) % 4.38/4.56 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) False) (Eq (Or (big_f a_1 a_2) (big_g a_1 a_2) → big_h a a_2) True) % 4.38/4.56 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 4.38/4.56 Or (Eq (big_g a a_1) False) (Or (Eq (Or (big_f a_1 a_2) (big_g a_1 a_2)) False) (Eq (big_h a a_2) True)) % 4.38/4.56 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) False) (Or (Eq (big_h a a_2) True) (Eq (big_f a_1 a_2) False)) % 4.38/4.56 Clause #30 (by superposition #[23, 6]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_h a a_1) True) (Or (Eq (big_f (skS.0 0 a a_2) a_1) False) (Eq False True)) % 4.38/4.56 Clause #32 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_h a a_1) True) (Eq (big_f (skS.0 0 a a_2) a_1) False) % 4.38/4.56 Clause #33 (by superposition #[32, 9]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_h a (skS.0 1 (skS.0 0 a a_1) a_2)) True) (Eq False True) % 4.38/4.56 Clause #40 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (big_h a (skS.0 1 (skS.0 0 a a_1) a_2)) True % 4.38/4.56 Clause #41 (by superposition #[40, 14]): Eq True False % 4.38/4.56 Clause #42 (by clausification #[41]): False % 4.38/4.56 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------