%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO267^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:08:49 PM UTC 2025 % Result : Theorem 4.10s 4.31s % Output : Proof 4.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYO267^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.15/0.36 % Computer : n021.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 14:36:08 EDT 2025 % 0.15/0.36 % CPUTime : % 4.10/4.31 SZS status Theorem for theBenchmark.p % 4.10/4.31 SZS output start Proof for theBenchmark.p % 4.10/4.31 Clause #0 (by assumption #[]): Eq % 4.10/4.31 (Not % 4.10/4.31 (∀ (P : Iota → Prop), % 4.10/4.31 Exists fun M => ∀ (G H : Iota → Iota), And (M G) (M H) → And (M fun Z => G (H Z)) (∀ (Y : Iota), P Y → P (G Y)))) % 4.10/4.31 True % 4.10/4.31 Clause #1 (by clausification #[0]): Eq % 4.10/4.31 (∀ (P : Iota → Prop), % 4.10/4.31 Exists fun M => ∀ (G H : Iota → Iota), And (M G) (M H) → And (M fun Z => G (H Z)) (∀ (Y : Iota), P Y → P (G Y))) % 4.10/4.31 False % 4.10/4.31 Clause #2 (by clausification #[1]): ∀ (a : Iota → Prop), % 4.10/4.31 Eq % 4.10/4.31 (Not % 4.10/4.31 (Exists fun M => % 4.10/4.31 ∀ (G H : Iota → Iota), % 4.10/4.31 And (M G) (M H) → And (M fun Z => G (H Z)) (∀ (Y : Iota), skS.0 0 a Y → skS.0 0 a (G Y)))) % 4.10/4.31 True % 4.10/4.31 Clause #3 (by clausification #[2]): ∀ (a : Iota → Prop), % 4.10/4.31 Eq % 4.10/4.31 (Exists fun M => % 4.10/4.31 ∀ (G H : Iota → Iota), And (M G) (M H) → And (M fun Z => G (H Z)) (∀ (Y : Iota), skS.0 0 a Y → skS.0 0 a (G Y))) % 4.10/4.31 False % 4.10/4.31 Clause #4 (by clausification #[3]): ∀ (a : (Iota → Iota) → Prop) (a_1 : Iota → Prop), % 4.10/4.31 Eq % 4.10/4.31 (∀ (G H : Iota → Iota), % 4.10/4.31 And (a G) (a H) → And (a fun Z => G (H Z)) (∀ (Y : Iota), skS.0 0 a_1 Y → skS.0 0 a_1 (G Y))) % 4.10/4.31 False % 4.10/4.31 Clause #5 (by clausification #[4]): ∀ (a : (Iota → Iota) → Prop) (a_1 : Iota → Prop) (a_2 : Iota → Iota), % 4.10/4.31 Eq % 4.10/4.31 (Not % 4.10/4.31 (∀ (H : Iota → Iota), % 4.10/4.31 And (a (skS.0 1 a a_1 a_2)) (a H) → % 4.10/4.31 And (a fun Z => skS.0 1 a a_1 a_2 (H Z)) (∀ (Y : Iota), skS.0 0 a_1 Y → skS.0 0 a_1 (skS.0 1 a a_1 a_2 Y)))) % 4.10/4.31 True % 4.10/4.31 Clause #6 (by clausification #[5]): ∀ (a : (Iota → Iota) → Prop) (a_1 : Iota → Prop) (a_2 : Iota → Iota), % 4.10/4.31 Eq % 4.10/4.31 (∀ (H : Iota → Iota), % 4.10/4.31 And (a (skS.0 1 a a_1 a_2)) (a H) → % 4.10/4.31 And (a fun Z => skS.0 1 a a_1 a_2 (H Z)) (∀ (Y : Iota), skS.0 0 a_1 Y → skS.0 0 a_1 (skS.0 1 a a_1 a_2 Y))) % 4.10/4.31 False % 4.10/4.31 Clause #7 (by clausification #[6]): ∀ (a : (Iota → Iota) → Prop) (a_1 : Iota → Prop) (a_2 a_3 : Iota → Iota), % 4.10/4.31 Eq % 4.10/4.31 (Not % 4.10/4.31 (And (a (skS.0 1 a a_1 a_2)) (a (skS.0 2 a a_1 a_2 a_3)) → % 4.10/4.31 And (a fun Z => skS.0 1 a a_1 a_2 (skS.0 2 a a_1 a_2 a_3 Z)) % 4.10/4.31 (∀ (Y : Iota), skS.0 0 a_1 Y → skS.0 0 a_1 (skS.0 1 a a_1 a_2 Y)))) % 4.10/4.31 True % 4.10/4.31 Clause #8 (by clausification #[7]): ∀ (a : (Iota → Iota) → Prop) (a_1 : Iota → Prop) (a_2 a_3 : Iota → Iota), % 4.10/4.31 Eq % 4.10/4.31 (And (a (skS.0 1 a a_1 a_2)) (a (skS.0 2 a a_1 a_2 a_3)) → % 4.10/4.31 And (a fun Z => skS.0 1 a a_1 a_2 (skS.0 2 a a_1 a_2 a_3 Z)) % 4.10/4.31 (∀ (Y : Iota), skS.0 0 a_1 Y → skS.0 0 a_1 (skS.0 1 a a_1 a_2 Y))) % 4.10/4.31 False % 4.10/4.31 Clause #9 (by clausification #[8]): ∀ (a : (Iota → Iota) → Prop) (a_1 : Iota → Prop) (a_2 a_3 : Iota → Iota), % 4.10/4.31 Eq (And (a (skS.0 1 a a_1 a_2)) (a (skS.0 2 a a_1 a_2 a_3))) True % 4.10/4.31 Clause #11 (by clausification #[9]): ∀ (a : (Iota → Iota) → Prop) (a_1 : Iota → Prop) (a_2 a_3 : Iota → Iota), Eq (a (skS.0 2 a a_1 a_2 a_3)) True % 4.10/4.31 Clause #16 (by fluidSup #[11, 11]): ∀ (a : Prop), Eq ((fun _ => a) True) True % 4.10/4.31 Clause #25 (by betaEtaReduce #[16]): ∀ (a : Prop), Eq a True % 4.10/4.31 Clause #26 (by falseElim #[25]): False % 4.10/4.31 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------