%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV175^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:02:54 PM UTC 2025 % Result : Theorem 31.19s 31.37s % Output : Proof 31.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEV175^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n013.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 01:06:08 EDT 2025 % 0.13/0.34 % CPUTime : % 31.19/31.37 SZS status Theorem for theBenchmark.p % 31.19/31.37 SZS output start Proof for theBenchmark.p % 31.19/31.37 Clause #0 (by assumption #[]): Eq % 31.19/31.37 (Not % 31.19/31.37 (∀ (Xh : (Iota → Prop) → Iota), % 31.19/31.37 Exists fun Xt => % 31.19/31.37 And (Not (Xt (Xh Xt))) (Eq (Xh fun Xz => Exists fun Xt0 => And (Not (Xt0 (Xh Xt0))) (Eq Xz (Xh Xt0))) (Xh Xt)))) % 31.19/31.37 True % 31.19/31.37 Clause #1 (by clausification #[0]): Eq % 31.19/31.37 (∀ (Xh : (Iota → Prop) → Iota), % 31.19/31.37 Exists fun Xt => % 31.19/31.37 And (Not (Xt (Xh Xt))) (Eq (Xh fun Xz => Exists fun Xt0 => And (Not (Xt0 (Xh Xt0))) (Eq Xz (Xh Xt0))) (Xh Xt))) % 31.19/31.37 False % 31.19/31.37 Clause #2 (by clausification #[1]): ∀ (a : (Iota → Prop) → Iota), % 31.19/31.37 Eq % 31.19/31.37 (Not % 31.19/31.37 (Exists fun Xt => % 31.19/31.37 And (Not (Xt (skS.0 0 a Xt))) % 31.19/31.37 (Eq (skS.0 0 a fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a Xt0))) (Eq Xz (skS.0 0 a Xt0))) % 31.19/31.37 (skS.0 0 a Xt)))) % 31.19/31.37 True % 31.19/31.37 Clause #3 (by clausification #[2]): ∀ (a : (Iota → Prop) → Iota), % 31.19/31.37 Eq % 31.19/31.37 (Exists fun Xt => % 31.19/31.37 And (Not (Xt (skS.0 0 a Xt))) % 31.19/31.37 (Eq (skS.0 0 a fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a Xt0))) (Eq Xz (skS.0 0 a Xt0))) % 31.19/31.37 (skS.0 0 a Xt))) % 31.19/31.37 False % 31.19/31.37 Clause #4 (by clausification #[3]): ∀ (a : Iota → Prop) (a_1 : (Iota → Prop) → Iota), % 31.19/31.37 Eq % 31.19/31.37 (And (Not (a (skS.0 0 a_1 a))) % 31.19/31.37 (Eq (skS.0 0 a_1 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_1 Xt0))) (Eq Xz (skS.0 0 a_1 Xt0))) % 31.19/31.37 (skS.0 0 a_1 a))) % 31.19/31.37 False % 31.19/31.37 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop) (a_1 : (Iota → Prop) → Iota), % 31.19/31.37 Or (Eq (Not (a (skS.0 0 a_1 a))) False) % 31.19/31.37 (Eq % 31.19/31.37 (Eq (skS.0 0 a_1 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_1 Xt0))) (Eq Xz (skS.0 0 a_1 Xt0))) % 31.19/31.37 (skS.0 0 a_1 a)) % 31.19/31.37 False) % 31.19/31.37 Clause #6 (by clausification #[5]): ∀ (a : (Iota → Prop) → Iota) (a_1 : Iota → Prop), % 31.19/31.37 Or % 31.19/31.37 (Eq % 31.19/31.37 (Eq (skS.0 0 a fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a Xt0))) (Eq Xz (skS.0 0 a Xt0))) % 31.19/31.37 (skS.0 0 a a_1)) % 31.19/31.37 False) % 31.19/31.37 (Eq (a_1 (skS.0 0 a a_1)) True) % 31.19/31.37 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 : (Iota → Prop) → Iota), % 31.19/31.37 Or (Eq (a (skS.0 0 a_1 a)) True) % 31.19/31.37 (Ne (skS.0 0 a_1 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_1 Xt0))) (Eq Xz (skS.0 0 a_1 Xt0))) % 31.19/31.37 (skS.0 0 a_1 a)) % 31.19/31.37 Clause #8 (by equality resolution #[7]): ∀ (a : (Iota → Prop) → Iota), % 31.19/31.37 Eq % 31.19/31.37 ((fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a Xt0))) (Eq Xz (skS.0 0 a Xt0))) % 31.19/31.37 (skS.0 0 a fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a Xt0))) (Eq Xz (skS.0 0 a Xt0)))) % 31.19/31.37 True % 31.19/31.37 Clause #9 (by betaEtaReduce #[8]): ∀ (a : (Iota → Prop) → Iota), % 31.19/31.37 Eq % 31.19/31.37 (Exists fun Xt0 => % 31.19/31.37 And (Not (Xt0 (skS.0 0 a Xt0))) % 31.19/31.37 (Eq (skS.0 0 a fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a Xt0))) (Eq Xz (skS.0 0 a Xt0))) % 31.19/31.37 (skS.0 0 a Xt0))) % 31.19/31.37 True % 31.19/31.37 Clause #10 (by clausification #[9]): ∀ (a : (Iota → Prop) → Iota) (a_1 : Iota → Prop), % 31.19/31.37 Eq % 31.19/31.37 (And (Not (skS.0 1 a a_1 (skS.0 0 a (skS.0 1 a a_1)))) % 31.19/31.37 (Eq (skS.0 0 a fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a Xt0))) (Eq Xz (skS.0 0 a Xt0))) % 31.19/31.37 (skS.0 0 a (skS.0 1 a a_1)))) % 31.19/31.37 True % 31.19/31.37 Clause #11 (by clausification #[10]): ∀ (a : (Iota → Prop) → Iota) (a_1 : Iota → Prop), % 31.19/31.37 Eq % 31.19/31.37 (Eq (skS.0 0 a fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a Xt0))) (Eq Xz (skS.0 0 a Xt0))) % 31.19/31.37 (skS.0 0 a (skS.0 1 a a_1))) % 31.19/31.37 True % 31.19/31.37 Clause #13 (by clausification #[11]): ∀ (a : (Iota → Prop) → Iota) (a_1 : Iota → Prop), % 31.19/31.37 Eq (skS.0 0 a fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a Xt0))) (Eq Xz (skS.0 0 a Xt0))) % 31.19/31.37 (skS.0 0 a (skS.0 1 a a_1)) % 31.19/31.37 Clause #15 (by fluidSup #[13, 7]): ∀ (a : Iota → Prop) (a_1 : Iota → (Iota → Prop) → Iota) (a_2 : (Iota → Prop) → Iota) (a_3 : Iota → Prop), % 31.19/31.37 Or % 31.19/31.37 (Eq % 31.19/31.37 (a % 31.19/31.37 (skS.0 0 % 31.19/31.37 (fun x => % 31.19/31.37 a_1 (skS.0 0 a_2 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_2 Xt0))) (Eq Xz (skS.0 0 a_2 Xt0))) x) % 31.19/31.37 a)) % 31.19/31.37 True) % 31.19/31.37 (Ne % 31.19/31.37 (skS.0 0 (a_1 (skS.0 0 a_2 (skS.0 1 a_2 a_3))) fun Xz => % 31.19/31.37 Exists fun Xt0 => % 31.19/31.37 And % 31.19/31.37 (Not % 31.19/31.37 (Xt0 % 31.19/31.40 (skS.0 0 % 31.19/31.40 (fun x => % 31.19/31.40 a_1 % 31.19/31.40 (skS.0 0 a_2 fun Xz => % 31.19/31.40 Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_2 Xt0))) (Eq Xz (skS.0 0 a_2 Xt0))) % 31.19/31.40 x) % 31.19/31.40 Xt0))) % 31.19/31.40 (Eq Xz % 31.19/31.40 (skS.0 0 % 31.19/31.40 (fun x => % 31.19/31.40 a_1 % 31.19/31.40 (skS.0 0 a_2 fun Xz => % 31.19/31.40 Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_2 Xt0))) (Eq Xz (skS.0 0 a_2 Xt0))) % 31.19/31.40 x) % 31.19/31.40 Xt0))) % 31.19/31.40 (skS.0 0 % 31.19/31.40 (fun x => % 31.19/31.40 a_1 (skS.0 0 a_2 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_2 Xt0))) (Eq Xz (skS.0 0 a_2 Xt0))) x) % 31.19/31.40 a)) % 31.19/31.40 Clause #67 (by betaEtaReduce #[15]): ∀ (a : Iota → Prop) (a_1 : Iota → (Iota → Prop) → Iota) (a_2 : (Iota → Prop) → Iota) (a_3 : Iota → Prop), % 31.19/31.40 Or % 31.19/31.40 (Eq % 31.19/31.40 (a % 31.19/31.40 (skS.0 0 % 31.19/31.40 (a_1 (skS.0 0 a_2 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_2 Xt0))) (Eq Xz (skS.0 0 a_2 Xt0)))) % 31.19/31.40 a)) % 31.19/31.40 True) % 31.19/31.40 (Ne % 31.19/31.40 (skS.0 0 (a_1 (skS.0 0 a_2 (skS.0 1 a_2 a_3))) fun Xz => % 31.19/31.40 Exists fun Xt0 => % 31.19/31.40 And % 31.19/31.40 (Not % 31.19/31.40 (Xt0 % 31.19/31.40 (skS.0 0 % 31.19/31.40 (a_1 % 31.19/31.40 (skS.0 0 a_2 fun Xz => % 31.19/31.40 Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_2 Xt0))) (Eq Xz (skS.0 0 a_2 Xt0)))) % 31.19/31.40 Xt0))) % 31.19/31.40 (Eq Xz % 31.19/31.40 (skS.0 0 % 31.19/31.40 (a_1 % 31.19/31.40 (skS.0 0 a_2 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_2 Xt0))) (Eq Xz (skS.0 0 a_2 Xt0)))) % 31.19/31.40 Xt0))) % 31.19/31.40 (skS.0 0 % 31.19/31.40 (a_1 (skS.0 0 a_2 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_2 Xt0))) (Eq Xz (skS.0 0 a_2 Xt0)))) a)) % 31.19/31.40 Clause #68 (by equality resolution #[67]): ∀ (a : Iota) (a_1 : (Iota → Prop) → Iota), % 31.19/31.40 Eq % 31.19/31.40 ((fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 (fun x => a) Xt0))) (Eq Xz (skS.0 0 (fun x => a) Xt0))) % 31.19/31.40 (skS.0 0 % 31.19/31.40 ((fun _ x => a) % 31.19/31.40 (skS.0 0 a_1 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 a_1 Xt0))) (Eq Xz (skS.0 0 a_1 Xt0)))) % 31.19/31.40 fun Xz => Exists fun Xt0 => And (Not (Xt0 (skS.0 0 (fun x => a) Xt0))) (Eq Xz (skS.0 0 (fun x => a) Xt0)))) % 31.19/31.40 True % 31.19/31.40 Clause #253 (by betaEtaReduce #[68]): ∀ (a : Iota), % 31.19/31.40 Eq % 31.19/31.40 (Exists fun Xt0 => % 31.19/31.40 And (Not (Xt0 (skS.0 0 (fun x => a) Xt0))) % 31.19/31.40 (Eq % 31.19/31.40 (skS.0 0 (fun x => a) fun Xz => % 31.19/31.40 Exists fun Xt0 => And (Not (Xt0 (skS.0 0 (fun x => a) Xt0))) (Eq Xz (skS.0 0 (fun x => a) Xt0))) % 31.19/31.40 (skS.0 0 (fun x => a) Xt0))) % 31.19/31.40 True % 31.19/31.40 Clause #254 (by clausification #[253]): ∀ (a : Iota) (a_1 : Iota → Prop), % 31.19/31.40 Eq % 31.19/31.40 (And (Not (skS.0 2 a a_1 (skS.0 0 (fun x => a) (skS.0 2 a a_1)))) % 31.19/31.40 (Eq % 31.19/31.40 (skS.0 0 (fun x => a) fun Xz => % 31.19/31.40 Exists fun Xt0 => And (Not (Xt0 (skS.0 0 (fun x => a) Xt0))) (Eq Xz (skS.0 0 (fun x => a) Xt0))) % 31.19/31.40 (skS.0 0 (fun x => a) (skS.0 2 a a_1)))) % 31.19/31.40 True % 31.19/31.40 Clause #255 (by clausification #[254]): ∀ (a : Iota) (a_1 : Iota → Prop), % 31.19/31.40 Eq % 31.19/31.40 (Eq % 31.19/31.40 (skS.0 0 (fun x => a) fun Xz => % 31.19/31.40 Exists fun Xt0 => And (Not (Xt0 (skS.0 0 (fun x => a) Xt0))) (Eq Xz (skS.0 0 (fun x => a) Xt0))) % 31.19/31.40 (skS.0 0 (fun x => a) (skS.0 2 a a_1))) % 31.19/31.40 True % 31.19/31.40 Clause #256 (by clausification #[254]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (Not (skS.0 2 a a_1 (skS.0 0 (fun x => a) (skS.0 2 a a_1)))) True % 31.19/31.40 Clause #257 (by clausification #[255]): ∀ (a : Iota) (a_1 : Iota → Prop), % 31.19/31.40 Eq % 31.19/31.40 (skS.0 0 (fun x => a) fun Xz => % 31.19/31.40 Exists fun Xt0 => And (Not (Xt0 (skS.0 0 (fun x => a) Xt0))) (Eq Xz (skS.0 0 (fun x => a) Xt0))) % 31.19/31.40 (skS.0 0 (fun x => a) (skS.0 2 a a_1)) % 31.19/31.40 Clause #259 (by superposition #[257, 257]): ∀ (a : Iota) (a_1 a_2 : Iota → Prop), Eq (skS.0 0 (fun x => a) (skS.0 2 a a_1)) (skS.0 0 (fun x => a) (skS.0 2 a a_2)) % 31.19/31.40 Clause #357 (by clausification #[256]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (skS.0 2 a a_1 (skS.0 0 (fun x => a) (skS.0 2 a a_1))) False % 31.19/31.40 Clause #521 (by superposition #[259, 7]): ∀ (a : Iota) (a_1 a_2 : Iota → Prop), % 31.19/31.40 Or (Eq (skS.0 2 a a_1 (skS.0 0 (fun x => a) (skS.0 2 a a_2))) True) % 31.44/31.63 (Ne % 31.44/31.63 (skS.0 0 (fun x => a) fun Xz => % 31.44/31.63 Exists fun Xt0 => And (Not (Xt0 (skS.0 0 (fun x => a) Xt0))) (Eq Xz (skS.0 0 (fun x => a) Xt0))) % 31.44/31.63 (skS.0 0 (fun x => a) (skS.0 2 a a_2))) % 31.44/31.63 Clause #4143 (by superposition #[521, 257]): ∀ (a : Iota) (a_1 a_2 a_3 : Iota → Prop), % 31.44/31.63 Or (Eq (skS.0 2 a a_1 (skS.0 0 (fun x => a) (skS.0 2 a a_2))) True) % 31.44/31.63 (Ne (skS.0 0 (fun x => a) (skS.0 2 a a_3)) (skS.0 0 (fun x => a) (skS.0 2 a a_2))) % 31.44/31.63 Clause #4205 (by equality resolution #[4143]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Prop), Eq (skS.0 2 a a_1 (skS.0 0 (fun x => a) (skS.0 2 a fun x => a_2))) True % 31.44/31.63 Clause #4556 (by fluidLoobHoist #[4205]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Prop), % 31.44/31.63 Or (Eq (skS.0 2 a a_1 (skS.0 0 (fun x => a) (skS.0 2 a fun x => True))) True) (Eq a_2 False) % 31.44/31.63 Clause #4792 (by falseElim #[4556]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (skS.0 2 a a_1 (skS.0 0 (fun x => a) (skS.0 2 a fun x => True))) True % 31.44/31.63 Clause #4793 (by superposition #[4792, 357]): Eq True False % 31.44/31.63 Clause #4977 (by clausification #[4793]): False % 31.44/31.63 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------