%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV394^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:03:08 PM UTC 2025 % Result : Theorem 3.66s 3.84s % Output : Proof 3.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SEV394^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.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 % 0.19/0.34 % CPULimit : 300 % 0.19/0.34 % WCLimit : 300 % 0.19/0.34 % DateTime : Fri Oct 3 01:11:53 EDT 2025 % 0.19/0.34 % CPUTime : % 3.66/3.84 SZS status Theorem for theBenchmark.p % 3.66/3.84 SZS output start Proof for theBenchmark.p % 3.66/3.84 Clause #0 (by assumption #[]): Eq % 3.66/3.84 (Not % 3.66/3.84 (∀ (Xw Xy Xz : a → Prop), % 3.66/3.84 And (∀ (Xx : a), And (Xw Xx) (Not (Xz Xx)) → Xy Xx) (Eq (fun Xx => And (Xz Xx) (Not (Xy Xx))) fun Xx => False) → % 3.66/3.84 ∀ (Xx : a), Xw Xx → Xy Xx)) % 3.66/3.84 True % 3.66/3.84 Clause #1 (by clausification #[0]): Eq % 3.66/3.84 (∀ (Xw Xy Xz : a → Prop), % 3.66/3.84 And (∀ (Xx : a), And (Xw Xx) (Not (Xz Xx)) → Xy Xx) (Eq (fun Xx => And (Xz Xx) (Not (Xy Xx))) fun Xx => False) → % 3.66/3.84 ∀ (Xx : a), Xw Xx → Xy Xx) % 3.66/3.84 False % 3.66/3.84 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop), % 3.66/3.84 Eq % 3.66/3.84 (Not % 3.66/3.84 (∀ (Xy Xz : a → Prop), % 3.66/3.84 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Xz Xx)) → Xy Xx) % 3.66/3.84 (Eq (fun Xx => And (Xz Xx) (Not (Xy Xx))) fun Xx => False) → % 3.66/3.84 ∀ (Xx : a), skS.0 0 a_1 Xx → Xy Xx)) % 3.66/3.84 True % 3.66/3.84 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop), % 3.66/3.84 Eq % 3.66/3.84 (∀ (Xy Xz : a → Prop), % 3.66/3.84 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Xz Xx)) → Xy Xx) % 3.66/3.84 (Eq (fun Xx => And (Xz Xx) (Not (Xy Xx))) fun Xx => False) → % 3.66/3.84 ∀ (Xx : a), skS.0 0 a_1 Xx → Xy Xx) % 3.66/3.84 False % 3.66/3.84 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop), % 3.66/3.84 Eq % 3.66/3.84 (Not % 3.66/3.84 (∀ (Xz : a → Prop), % 3.66/3.84 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Xz Xx)) → skS.0 1 a_1 a_2 Xx) % 3.66/3.84 (Eq (fun Xx => And (Xz Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) → % 3.66/3.84 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)) % 3.66/3.84 True % 3.66/3.84 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop), % 3.66/3.84 Eq % 3.66/3.84 (∀ (Xz : a → Prop), % 3.66/3.84 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Xz Xx)) → skS.0 1 a_1 a_2 Xx) % 3.66/3.84 (Eq (fun Xx => And (Xz Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) → % 3.66/3.84 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 3.66/3.84 False % 3.66/3.84 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.66/3.84 Eq % 3.66/3.84 (Not % 3.66/3.84 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx) % 3.66/3.84 (Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) → % 3.66/3.84 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)) % 3.66/3.84 True % 3.66/3.84 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.66/3.84 Eq % 3.66/3.84 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx) % 3.66/3.84 (Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) → % 3.66/3.84 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) % 3.66/3.84 False % 3.66/3.84 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.66/3.84 Eq % 3.66/3.84 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx) % 3.66/3.84 (Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False)) % 3.66/3.84 True % 3.66/3.84 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) False % 3.66/3.84 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.66/3.84 Eq (Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False) True % 3.66/3.84 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), % 3.66/3.84 Eq (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx) True % 3.66/3.84 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) fun Xx => False % 3.66/3.84 Clause #13 (by argument congruence #[12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.66/3.84 Eq ((fun Xx => And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 1 a_1 a_2 Xx))) a_4) ((fun Xx => False) a_4) % 3.66/3.84 Clause #14 (by clausification #[9]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), % 3.66/3.84 Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3))) True % 3.66/3.84 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False % 3.66/3.84 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True % 3.66/3.86 Clause #17 (by clausification #[15]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False % 3.66/3.86 Clause #18 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 3.66/3.86 Eq (And (skS.0 0 a_1 a_2) (Not (skS.0 2 a_1 a_3 a_4 a_2)) → skS.0 1 a_1 a_3 a_2) True % 3.66/3.86 Clause #19 (by clausification #[18]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), % 3.66/3.86 Or (Eq (And (skS.0 0 a_1 a_2) (Not (skS.0 2 a_1 a_3 a_4 a_2))) False) (Eq (skS.0 1 a_1 a_3 a_2) True) % 3.66/3.86 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 3.66/3.86 Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 0 a_1 a_3) False) (Eq (Not (skS.0 2 a_1 a_2 a_4 a_3)) False)) % 3.66/3.86 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop), % 3.66/3.86 Or (Eq (skS.0 1 a_1 a_2 a_3) True) (Or (Eq (skS.0 0 a_1 a_3) False) (Eq (skS.0 2 a_1 a_2 a_4 a_3) True)) % 3.66/3.86 Clause #22 (by superposition #[21, 16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 3.66/3.86 Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 a_1 a_3 a_4)) True) % 3.66/3.86 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) (Eq False True)) % 3.66/3.86 Clause #23 (by betaEtaReduce #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (And (skS.0 2 a_1 a_2 a_3 a_4) (Not (skS.0 1 a_1 a_2 a_4))) False % 3.66/3.86 Clause #24 (by clausification #[23]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) False) (Eq (Not (skS.0 1 a_1 a_2 a_4)) False) % 3.66/3.86 Clause #25 (by clausification #[24]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 2 a_1 a_2 a_3 a_4) False) (Eq (skS.0 1 a_1 a_2 a_4) True) % 3.66/3.86 Clause #26 (by betaEtaReduce #[22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 3.66/3.86 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 3.66/3.86 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) (Eq False True)) % 3.66/3.86 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop), % 3.66/3.86 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) % 3.66/3.86 Clause #28 (by superposition #[27, 25]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.66/3.86 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 (fun x => a_1 x) a_3 a_4)) True) % 3.66/3.86 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)) % 3.66/3.86 Clause #29 (by betaEtaReduce #[28]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.66/3.86 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 3.66/3.86 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)) % 3.66/3.86 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), % 3.66/3.86 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) % 3.66/3.86 Clause #31 (by eliminate duplicate literals #[30]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True % 3.66/3.86 Clause #33 (by superposition #[31, 17]): Eq True False % 3.66/3.86 Clause #34 (by clausification #[33]): False % 3.66/3.86 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------