%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV060^5 : 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 08:02:48 PM UTC 2025 % Result : Theorem 4.02s 4.20s % Output : Proof 4.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV060^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.14/0.34 % Computer : n024.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 01:12:38 EDT 2025 % 0.14/0.35 % CPUTime : % 4.02/4.20 SZS status Theorem for theBenchmark.p % 4.02/4.20 SZS output start Proof for theBenchmark.p % 4.02/4.20 Clause #0 (by assumption #[]): Eq % 4.02/4.20 (Not % 4.02/4.20 (∀ (Xx : b) (Xy : a) (Xs Xk : b → a → Prop), % 4.02/4.20 And (∀ (Xx_0 : b) (Xy_9 : a), Xk Xx_0 Xy_9 → Or (Xs Xx_0 Xy_9) (And (Eq Xx_0 Xx) (Eq Xy_9 Xy))) (Not (Xk Xx Xy)) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), Xk Xx0 Xy0 → Xs Xx0 Xy0)) % 4.02/4.20 True % 4.02/4.20 Clause #1 (by clausification #[0]): Eq % 4.02/4.20 (∀ (Xx : b) (Xy : a) (Xs Xk : b → a → Prop), % 4.02/4.20 And (∀ (Xx_0 : b) (Xy_9 : a), Xk Xx_0 Xy_9 → Or (Xs Xx_0 Xy_9) (And (Eq Xx_0 Xx) (Eq Xy_9 Xy))) (Not (Xk Xx Xy)) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), Xk Xx0 Xy0 → Xs Xx0 Xy0) % 4.02/4.20 False % 4.02/4.20 Clause #2 (by clausification #[1]): ∀ (a_1 : b), % 4.02/4.20 Eq % 4.02/4.20 (Not % 4.02/4.20 (∀ (Xy : a) (Xs Xk : b → a → Prop), % 4.02/4.20 And (∀ (Xx_0 : b) (Xy_9 : a), Xk Xx_0 Xy_9 → Or (Xs Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 Xy))) % 4.02/4.20 (Not (Xk (skS.0 0 a_1) Xy)) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), Xk Xx0 Xy0 → Xs Xx0 Xy0)) % 4.02/4.20 True % 4.02/4.20 Clause #3 (by clausification #[2]): ∀ (a_1 : b), % 4.02/4.20 Eq % 4.02/4.20 (∀ (Xy : a) (Xs Xk : b → a → Prop), % 4.02/4.20 And (∀ (Xx_0 : b) (Xy_9 : a), Xk Xx_0 Xy_9 → Or (Xs Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 Xy))) % 4.02/4.20 (Not (Xk (skS.0 0 a_1) Xy)) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), Xk Xx0 Xy0 → Xs Xx0 Xy0) % 4.02/4.20 False % 4.02/4.20 Clause #4 (by clausification #[3]): ∀ (a_1 : b) (a_2 : a), % 4.02/4.20 Eq % 4.02/4.20 (Not % 4.02/4.20 (∀ (Xs Xk : b → a → Prop), % 4.02/4.20 And % 4.02/4.20 (∀ (Xx_0 : b) (Xy_9 : a), % 4.02/4.20 Xk Xx_0 Xy_9 → Or (Xs Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 (skS.0 1 a_1 a_2)))) % 4.02/4.20 (Not (Xk (skS.0 0 a_1) (skS.0 1 a_1 a_2))) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), Xk Xx0 Xy0 → Xs Xx0 Xy0)) % 4.02/4.20 True % 4.02/4.20 Clause #5 (by clausification #[4]): ∀ (a_1 : b) (a_2 : a), % 4.02/4.20 Eq % 4.02/4.20 (∀ (Xs Xk : b → a → Prop), % 4.02/4.20 And % 4.02/4.20 (∀ (Xx_0 : b) (Xy_9 : a), % 4.02/4.20 Xk Xx_0 Xy_9 → Or (Xs Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 (skS.0 1 a_1 a_2)))) % 4.02/4.20 (Not (Xk (skS.0 0 a_1) (skS.0 1 a_1 a_2))) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), Xk Xx0 Xy0 → Xs Xx0 Xy0) % 4.02/4.20 False % 4.02/4.20 Clause #6 (by clausification #[5]): ∀ (a_1 : b) (a_2 : a) (a_3 : b → a → Prop), % 4.02/4.20 Eq % 4.02/4.20 (Not % 4.02/4.20 (∀ (Xk : b → a → Prop), % 4.02/4.20 And % 4.02/4.20 (∀ (Xx_0 : b) (Xy_9 : a), % 4.02/4.20 Xk Xx_0 Xy_9 → % 4.02/4.20 Or (skS.0 2 a_1 a_2 a_3 Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 (skS.0 1 a_1 a_2)))) % 4.02/4.20 (Not (Xk (skS.0 0 a_1) (skS.0 1 a_1 a_2))) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), Xk Xx0 Xy0 → skS.0 2 a_1 a_2 a_3 Xx0 Xy0)) % 4.02/4.20 True % 4.02/4.20 Clause #7 (by clausification #[6]): ∀ (a_1 : b) (a_2 : a) (a_3 : b → a → Prop), % 4.02/4.20 Eq % 4.02/4.20 (∀ (Xk : b → a → Prop), % 4.02/4.20 And % 4.02/4.20 (∀ (Xx_0 : b) (Xy_9 : a), % 4.02/4.20 Xk Xx_0 Xy_9 → Or (skS.0 2 a_1 a_2 a_3 Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 (skS.0 1 a_1 a_2)))) % 4.02/4.20 (Not (Xk (skS.0 0 a_1) (skS.0 1 a_1 a_2))) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), Xk Xx0 Xy0 → skS.0 2 a_1 a_2 a_3 Xx0 Xy0) % 4.02/4.20 False % 4.02/4.20 Clause #8 (by clausification #[7]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), % 4.02/4.20 Eq % 4.02/4.20 (Not % 4.02/4.20 (And % 4.02/4.20 (∀ (Xx_0 : b) (Xy_9 : a), % 4.02/4.20 skS.0 3 a_1 a_2 a_3 a_4 Xx_0 Xy_9 → % 4.02/4.20 Or (skS.0 2 a_1 a_2 a_3 Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 (skS.0 1 a_1 a_2)))) % 4.02/4.20 (Not (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1) (skS.0 1 a_1 a_2))) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), skS.0 3 a_1 a_2 a_3 a_4 Xx0 Xy0 → skS.0 2 a_1 a_2 a_3 Xx0 Xy0)) % 4.02/4.20 True % 4.02/4.20 Clause #9 (by clausification #[8]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), % 4.02/4.20 Eq % 4.02/4.20 (And % 4.02/4.20 (∀ (Xx_0 : b) (Xy_9 : a), % 4.02/4.20 skS.0 3 a_1 a_2 a_3 a_4 Xx_0 Xy_9 → % 4.02/4.20 Or (skS.0 2 a_1 a_2 a_3 Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 (skS.0 1 a_1 a_2)))) % 4.02/4.20 (Not (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1) (skS.0 1 a_1 a_2))) → % 4.02/4.20 ∀ (Xx0 : b) (Xy0 : a), skS.0 3 a_1 a_2 a_3 a_4 Xx0 Xy0 → skS.0 2 a_1 a_2 a_3 Xx0 Xy0) % 4.02/4.20 False % 4.02/4.20 Clause #10 (by clausification #[9]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), % 4.02/4.22 Eq % 4.02/4.22 (And % 4.02/4.22 (∀ (Xx_0 : b) (Xy_9 : a), % 4.02/4.22 skS.0 3 a_1 a_2 a_3 a_4 Xx_0 Xy_9 → % 4.02/4.22 Or (skS.0 2 a_1 a_2 a_3 Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 (skS.0 1 a_1 a_2)))) % 4.02/4.22 (Not (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1) (skS.0 1 a_1 a_2)))) % 4.02/4.22 True % 4.02/4.22 Clause #11 (by clausification #[9]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), % 4.02/4.22 Eq (∀ (Xx0 : b) (Xy0 : a), skS.0 3 a_1 a_2 a_3 a_4 Xx0 Xy0 → skS.0 2 a_1 a_2 a_3 Xx0 Xy0) False % 4.02/4.22 Clause #12 (by clausification #[10]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), Eq (Not (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1) (skS.0 1 a_1 a_2))) True % 4.02/4.22 Clause #13 (by clausification #[10]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), % 4.02/4.22 Eq % 4.02/4.22 (∀ (Xx_0 : b) (Xy_9 : a), % 4.02/4.22 skS.0 3 a_1 a_2 a_3 a_4 Xx_0 Xy_9 → % 4.02/4.22 Or (skS.0 2 a_1 a_2 a_3 Xx_0 Xy_9) (And (Eq Xx_0 (skS.0 0 a_1)) (Eq Xy_9 (skS.0 1 a_1 a_2)))) % 4.02/4.22 True % 4.02/4.22 Clause #14 (by clausification #[12]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1) (skS.0 1 a_1 a_2)) False % 4.02/4.22 Clause #15 (by clausification #[11]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 4.02/4.22 Eq % 4.02/4.22 (Not % 4.02/4.22 (∀ (Xy0 : a), % 4.02/4.22 skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy0 → % 4.02/4.22 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy0)) % 4.02/4.22 True % 4.02/4.22 Clause #16 (by clausification #[15]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 4.02/4.22 Eq % 4.02/4.22 (∀ (Xy0 : a), % 4.02/4.22 skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy0 → skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy0) % 4.02/4.22 False % 4.02/4.22 Clause #17 (by clausification #[16]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.22 Eq % 4.02/4.22 (Not % 4.02/4.22 (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) → % 4.02/4.22 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6))) % 4.02/4.22 True % 4.02/4.22 Clause #18 (by clausification #[17]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.22 Eq % 4.02/4.22 (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) → % 4.02/4.22 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) % 4.02/4.22 False % 4.02/4.22 Clause #19 (by clausification #[18]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.22 Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True % 4.02/4.22 Clause #20 (by clausification #[18]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.22 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) False % 4.02/4.22 Clause #21 (by clausification #[13]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 4.02/4.22 Eq % 4.02/4.22 (∀ (Xy_9 : a), % 4.02/4.22 skS.0 3 a_1 a_2 a_3 a_4 a_5 Xy_9 → % 4.02/4.22 Or (skS.0 2 a_1 a_2 a_3 a_5 Xy_9) (And (Eq a_5 (skS.0 0 a_1)) (Eq Xy_9 (skS.0 1 a_1 a_2)))) % 4.02/4.22 True % 4.02/4.22 Clause #22 (by clausification #[21]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.22 Eq % 4.02/4.22 (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6 → % 4.02/4.22 Or (skS.0 2 a_1 a_2 a_3 a_5 a_6) (And (Eq a_5 (skS.0 0 a_1)) (Eq a_6 (skS.0 1 a_1 a_2)))) % 4.02/4.22 True % 4.02/4.22 Clause #23 (by clausification #[22]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.22 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 4.02/4.22 (Eq (Or (skS.0 2 a_1 a_2 a_3 a_5 a_6) (And (Eq a_5 (skS.0 0 a_1)) (Eq a_6 (skS.0 1 a_1 a_2)))) True) % 4.02/4.22 Clause #24 (by clausification #[23]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.22 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 4.02/4.22 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq (And (Eq a_5 (skS.0 0 a_1)) (Eq a_6 (skS.0 1 a_1 a_2))) True)) % 4.02/4.22 Clause #25 (by clausification #[24]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.22 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 4.02/4.22 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq (Eq a_6 (skS.0 1 a_1 a_2)) True)) % 4.02/4.22 Clause #26 (by clausification #[24]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.25 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 4.02/4.25 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq (Eq a_5 (skS.0 0 a_1)) True)) % 4.02/4.25 Clause #27 (by clausification #[25]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.25 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) % 4.02/4.25 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq a_6 (skS.0 1 a_1 a_2))) % 4.02/4.25 Clause #28 (by superposition #[27, 19]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.25 Or % 4.02/4.25 (Eq (skS.0 2 a_1 a_2 (fun x x_1 => a_3 x x_1) (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True) % 4.02/4.25 (Or (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) (Eq False True)) % 4.02/4.25 Clause #29 (by clausification #[26]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.25 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq a_5 (skS.0 0 a_1))) % 4.02/4.25 Clause #31 (by betaEtaReduce #[28]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.25 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True) % 4.02/4.25 (Or (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) (Eq False True)) % 4.02/4.25 Clause #32 (by clausification #[31]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.25 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True) % 4.02/4.25 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) % 4.02/4.25 Clause #33 (by superposition #[32, 20]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.25 Or (Eq (skS.0 5 a_1 a_2 (fun x x_1 => a_3 x x_1) (fun x x_1 => a_4 x x_1) a_5 a_6) (skS.0 1 a_1 a_2)) (Eq True False) % 4.02/4.25 Clause #34 (by betaEtaReduce #[33]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.25 Or (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) (Eq True False) % 4.02/4.25 Clause #35 (by clausification #[34]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a), % 4.02/4.25 Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2) % 4.02/4.25 Clause #36 (by backward demodulation #[35, 19]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 4.02/4.25 Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) True % 4.02/4.25 Clause #37 (by backward demodulation #[35, 20]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 4.02/4.25 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) False % 4.02/4.25 Clause #39 (by superposition #[36, 29]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 4.02/4.25 Or (Eq True False) % 4.02/4.25 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) True) % 4.02/4.25 (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1))) % 4.02/4.25 Clause #40 (by clausification #[39]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 4.02/4.25 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) True) % 4.02/4.25 (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) % 4.02/4.25 Clause #41 (by superposition #[40, 37]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 4.02/4.25 Or (Eq (skS.0 4 a_1 a_2 (fun x x_1 => a_3 x x_1) (fun x x_1 => a_4 x x_1) a_5) (skS.0 0 a_1)) (Eq True False) % 4.02/4.25 Clause #42 (by betaEtaReduce #[41]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), % 4.02/4.25 Or (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq True False) % 4.02/4.25 Clause #43 (by clausification #[42]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1) % 4.02/4.25 Clause #45 (by backward demodulation #[43, 36]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True % 4.02/4.25 Clause #49 (by superposition #[45, 14]): Eq True False % 4.02/4.25 Clause #50 (by clausification #[49]): False % 4.02/4.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------