%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO381^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 08:08:58 PM UTC 2025 % Result : Theorem 3.54s 3.70s % Output : Proof 3.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO381^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n024.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 12:54:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.54/3.70 SZS status Theorem for theBenchmark.p % 3.54/3.70 SZS output start Proof for theBenchmark.p % 3.54/3.70 Clause #0 (by assumption #[]): Eq (Not (Exists fun Xx => Iff (Exists fun Xz => ∀ (Xy : Iota), cR Xz Xy) (∀ (Xw : Iota), cR Xx Xw))) True % 3.54/3.70 Clause #1 (by clausification #[0]): Eq (Exists fun Xx => Iff (Exists fun Xz => ∀ (Xy : Iota), cR Xz Xy) (∀ (Xw : Iota), cR Xx Xw)) False % 3.54/3.70 Clause #2 (by clausification #[1]): ∀ (a : Iota), Eq (Iff (Exists fun Xz => ∀ (Xy : Iota), cR Xz Xy) (∀ (Xw : Iota), cR a Xw)) False % 3.54/3.70 Clause #3 (by clausification #[2]): ∀ (a : Iota), Or (Eq (Exists fun Xz => ∀ (Xy : Iota), cR Xz Xy) False) (Eq (∀ (Xw : Iota), cR a Xw) False) % 3.54/3.70 Clause #4 (by clausification #[2]): ∀ (a : Iota), Or (Eq (Exists fun Xz => ∀ (Xy : Iota), cR Xz Xy) True) (Eq (∀ (Xw : Iota), cR a Xw) True) % 3.54/3.70 Clause #5 (by clausification #[3]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xw : Iota), cR a Xw) False) (Eq (∀ (Xy : Iota), cR a_1 Xy) False) % 3.54/3.70 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (Xy : Iota), cR a Xy) False) (Eq (Not (cR a_1 (skS.0 0 a_1 a_2))) True) % 3.54/3.70 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Not (cR a (skS.0 0 a a_1))) True) (Eq (Not (cR a_2 (skS.0 1 a_2 a_3))) True) % 3.54/3.70 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Not (cR a (skS.0 1 a a_1))) True) (Eq (cR a_2 (skS.0 0 a_2 a_3)) False) % 3.54/3.70 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cR a (skS.0 0 a a_1)) False) (Eq (cR a_2 (skS.0 1 a_2 a_3)) False) % 3.54/3.70 Clause #10 (by clausification #[4]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xw : Iota), cR a Xw) True) (Eq (∀ (Xy : Iota), cR (skS.0 2 a_1) Xy) True) % 3.54/3.70 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (Xy : Iota), cR (skS.0 2 a) Xy) True) (Eq (cR a_1 a_2) True) % 3.54/3.70 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cR a a_1) True) (Eq (cR (skS.0 2 a_2) a_3) True) % 3.54/3.70 Clause #15 (by equality factoring #[12]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (cR (skS.0 2 a) a_1) True) % 3.54/3.70 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 2 a) a_1) True) (Or (Eq True False) (Eq True False)) % 3.54/3.70 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 2 a) a_1) True) (Eq True False) % 3.54/3.70 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (cR (skS.0 2 a) a_1) True % 3.54/3.70 Clause #20 (by superposition #[19, 9]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cR a (skS.0 1 a a_1)) False) % 3.54/3.70 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (cR a (skS.0 1 a a_1)) False % 3.54/3.70 Clause #22 (by superposition #[21, 19]): Eq False True % 3.54/3.70 Clause #24 (by clausification #[22]): False % 3.54/3.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------