%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU887^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:02:35 PM UTC 2025 % Result : Theorem 3.66s 3.83s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU887^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n001.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 06:20:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.66/3.83 SZS status Theorem for theBenchmark.p % 3.66/3.83 SZS output start Proof for theBenchmark.p % 3.66/3.83 Clause #0 (by assumption #[]): Eq % 3.66/3.83 (Not % 3.66/3.83 (∀ (F : b → a) (G : c → b) (S : c → Prop) (Xx : a), % 3.66/3.83 (Exists fun Xt => And (S Xt) (Eq Xx (F (G Xt)))) → % 3.66/3.83 Exists fun Xt => And (Exists fun Xt0 => And (S Xt0) (Eq Xt (G Xt0))) (Eq Xx (F Xt)))) % 3.66/3.83 True % 3.66/3.83 Clause #1 (by clausification #[0]): Eq % 3.66/3.83 (∀ (F : b → a) (G : c → b) (S : c → Prop) (Xx : a), % 3.66/3.83 (Exists fun Xt => And (S Xt) (Eq Xx (F (G Xt)))) → % 3.66/3.83 Exists fun Xt => And (Exists fun Xt0 => And (S Xt0) (Eq Xt (G Xt0))) (Eq Xx (F Xt))) % 3.66/3.83 False % 3.66/3.83 Clause #2 (by clausification #[1]): ∀ (a_1 : b → a), % 3.66/3.83 Eq % 3.66/3.83 (Not % 3.66/3.83 (∀ (G : c → b) (S : c → Prop) (Xx : a), % 3.66/3.83 (Exists fun Xt => And (S Xt) (Eq Xx (skS.0 0 a_1 (G Xt)))) → % 3.66/3.83 Exists fun Xt => And (Exists fun Xt0 => And (S Xt0) (Eq Xt (G Xt0))) (Eq Xx (skS.0 0 a_1 Xt)))) % 3.66/3.83 True % 3.66/3.83 Clause #3 (by clausification #[2]): ∀ (a_1 : b → a), % 3.66/3.83 Eq % 3.66/3.83 (∀ (G : c → b) (S : c → Prop) (Xx : a), % 3.66/3.83 (Exists fun Xt => And (S Xt) (Eq Xx (skS.0 0 a_1 (G Xt)))) → % 3.66/3.83 Exists fun Xt => And (Exists fun Xt0 => And (S Xt0) (Eq Xt (G Xt0))) (Eq Xx (skS.0 0 a_1 Xt))) % 3.66/3.83 False % 3.66/3.83 Clause #4 (by clausification #[3]): ∀ (a_1 : b → a) (a_2 : c → b), % 3.66/3.83 Eq % 3.66/3.83 (Not % 3.66/3.83 (∀ (S : c → Prop) (Xx : a), % 3.66/3.83 (Exists fun Xt => And (S Xt) (Eq Xx (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xt)))) → % 3.66/3.83 Exists fun Xt => And (Exists fun Xt0 => And (S Xt0) (Eq Xt (skS.0 1 a_1 a_2 Xt0))) (Eq Xx (skS.0 0 a_1 Xt)))) % 3.66/3.83 True % 3.66/3.83 Clause #5 (by clausification #[4]): ∀ (a_1 : b → a) (a_2 : c → b), % 3.66/3.83 Eq % 3.66/3.83 (∀ (S : c → Prop) (Xx : a), % 3.66/3.83 (Exists fun Xt => And (S Xt) (Eq Xx (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xt)))) → % 3.66/3.83 Exists fun Xt => And (Exists fun Xt0 => And (S Xt0) (Eq Xt (skS.0 1 a_1 a_2 Xt0))) (Eq Xx (skS.0 0 a_1 Xt))) % 3.66/3.83 False % 3.66/3.83 Clause #6 (by clausification #[5]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop), % 3.66/3.83 Eq % 3.66/3.83 (Not % 3.66/3.83 (∀ (Xx : a), % 3.66/3.83 (Exists fun Xt => And (skS.0 2 a_1 a_2 a_3 Xt) (Eq Xx (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xt)))) → % 3.66/3.83 Exists fun Xt => % 3.66/3.83 And (Exists fun Xt0 => And (skS.0 2 a_1 a_2 a_3 Xt0) (Eq Xt (skS.0 1 a_1 a_2 Xt0))) % 3.66/3.83 (Eq Xx (skS.0 0 a_1 Xt)))) % 3.66/3.83 True % 3.66/3.83 Clause #7 (by clausification #[6]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop), % 3.66/3.83 Eq % 3.66/3.83 (∀ (Xx : a), % 3.66/3.83 (Exists fun Xt => And (skS.0 2 a_1 a_2 a_3 Xt) (Eq Xx (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xt)))) → % 3.66/3.83 Exists fun Xt => % 3.66/3.83 And (Exists fun Xt0 => And (skS.0 2 a_1 a_2 a_3 Xt0) (Eq Xt (skS.0 1 a_1 a_2 Xt0))) (Eq Xx (skS.0 0 a_1 Xt))) % 3.66/3.83 False % 3.66/3.83 Clause #8 (by clausification #[7]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a), % 3.66/3.83 Eq % 3.66/3.83 (Not % 3.66/3.83 ((Exists fun Xt => % 3.66/3.83 And (skS.0 2 a_1 a_2 a_3 Xt) (Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xt)))) → % 3.66/3.83 Exists fun Xt => % 3.66/3.83 And (Exists fun Xt0 => And (skS.0 2 a_1 a_2 a_3 Xt0) (Eq Xt (skS.0 1 a_1 a_2 Xt0))) % 3.66/3.83 (Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 Xt)))) % 3.66/3.83 True % 3.66/3.83 Clause #9 (by clausification #[8]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a), % 3.66/3.83 Eq % 3.66/3.83 ((Exists fun Xt => And (skS.0 2 a_1 a_2 a_3 Xt) (Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xt)))) → % 3.66/3.83 Exists fun Xt => % 3.66/3.83 And (Exists fun Xt0 => And (skS.0 2 a_1 a_2 a_3 Xt0) (Eq Xt (skS.0 1 a_1 a_2 Xt0))) % 3.66/3.83 (Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 Xt))) % 3.66/3.83 False % 3.66/3.83 Clause #10 (by clausification #[9]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a), % 3.66/3.83 Eq (Exists fun Xt => And (skS.0 2 a_1 a_2 a_3 Xt) (Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 (skS.0 1 a_1 a_2 Xt)))) % 3.66/3.83 True % 3.66/3.83 Clause #11 (by clausification #[9]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a), % 3.66/3.83 Eq % 3.66/3.83 (Exists fun Xt => % 3.66/3.83 And (Exists fun Xt0 => And (skS.0 2 a_1 a_2 a_3 Xt0) (Eq Xt (skS.0 1 a_1 a_2 Xt0))) % 3.66/3.83 (Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 Xt))) % 3.66/3.83 False % 3.66/3.83 Clause #12 (by clausification #[10]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : c), % 3.68/3.85 Eq % 3.68/3.85 (And (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) % 3.68/3.85 (Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5))))) % 3.68/3.85 True % 3.68/3.85 Clause #13 (by clausification #[12]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : c), % 3.68/3.85 Eq (Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5)))) True % 3.68/3.85 Clause #14 (by clausification #[12]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : c), % 3.68/3.85 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) True % 3.68/3.85 Clause #15 (by clausification #[13]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : c), % 3.68/3.85 Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4 a_5))) % 3.68/3.85 Clause #16 (by clausification #[11]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : b) (a_5 : a), % 3.68/3.85 Eq % 3.68/3.85 (And (Exists fun Xt0 => And (skS.0 2 a_1 a_2 a_3 Xt0) (Eq a_4 (skS.0 1 a_1 a_2 Xt0))) % 3.68/3.85 (Eq (skS.0 3 a_1 a_2 a_3 a_5) (skS.0 0 a_1 a_4))) % 3.68/3.85 False % 3.68/3.85 Clause #17 (by clausification #[16]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : b) (a_5 : a), % 3.68/3.85 Or (Eq (Exists fun Xt0 => And (skS.0 2 a_1 a_2 a_3 Xt0) (Eq a_4 (skS.0 1 a_1 a_2 Xt0))) False) % 3.68/3.85 (Eq (Eq (skS.0 3 a_1 a_2 a_3 a_5) (skS.0 0 a_1 a_4)) False) % 3.68/3.85 Clause #18 (by clausification #[17]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : b) (a_6 : c), % 3.68/3.85 Or (Eq (Eq (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 a_5)) False) % 3.68/3.85 (Eq (And (skS.0 2 a_1 a_2 a_3 a_6) (Eq a_5 (skS.0 1 a_1 a_2 a_6))) False) % 3.68/3.85 Clause #19 (by clausification #[18]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : c) (a_5 : b) (a_6 : a), % 3.68/3.85 Or (Eq (And (skS.0 2 a_1 a_2 a_3 a_4) (Eq a_5 (skS.0 1 a_1 a_2 a_4))) False) % 3.68/3.85 (Ne (skS.0 3 a_1 a_2 a_3 a_6) (skS.0 0 a_1 a_5)) % 3.68/3.85 Clause #20 (by clausification #[19]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : b) (a_6 : c), % 3.68/3.85 Or (Ne (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 a_5)) % 3.68/3.85 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_6) False) (Eq (Eq a_5 (skS.0 1 a_1 a_2 a_6)) False)) % 3.68/3.85 Clause #21 (by clausification #[20]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : b) (a_6 : c), % 3.68/3.85 Or (Ne (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 a_5)) % 3.68/3.85 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_6) False) (Ne a_5 (skS.0 1 a_1 a_2 a_6))) % 3.68/3.85 Clause #22 (by destructive equality resolution #[21]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : c), % 3.68/3.85 Or (Ne (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 0 a_1 (skS.0 1 a_1 a_2 a_5))) (Eq (skS.0 2 a_1 a_2 a_3 a_5) False) % 3.68/3.85 Clause #23 (by superposition #[22, 15]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : c → Prop) (a_6 : a) (a_7 : c), % 3.68/3.85 Or (Ne (skS.0 3 a_1 a_2 a_3 a_4) (skS.0 3 a_1 a_2 a_5 a_6)) % 3.68/3.85 (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_5 a_6 a_7)) False) % 3.68/3.85 Clause #24 (by equality resolution #[23]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : c), % 3.68/3.85 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 (fun x => a_3 x) a_4 a_5)) False % 3.68/3.85 Clause #25 (by betaEtaReduce #[24]): ∀ (a_1 : b → a) (a_2 : c → b) (a_3 : c → Prop) (a_4 : a) (a_5 : c), % 3.68/3.85 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5)) False % 3.68/3.85 Clause #26 (by superposition #[25, 14]): Eq False True % 3.68/3.85 Clause #27 (by clausification #[26]): False % 3.68/3.85 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------