%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU664^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:02:10 PM UTC 2025 % Result : Theorem 9.06s 9.28s % Output : Proof 9.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SEU664^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.14 % Command : duper %s % 0.14/0.36 % Computer : n017.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 06:04:23 EDT 2025 % 0.14/0.36 % CPUTime : % 9.06/9.28 SZS status Theorem for theBenchmark.p % 9.06/9.28 SZS output start Proof for theBenchmark.p % 9.06/9.28 Clause #0 (by assumption #[]): Eq % 9.06/9.28 (Eq cartprodmempair1 % 9.06/9.28 (∀ (A B Xu : Iota), % 9.06/9.28 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))) % 9.06/9.28 True % 9.06/9.28 Clause #1 (by assumption #[]): Eq (Eq cartprodfstpairEq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (kfst (kpair Xx Xy)) Xx)) True % 9.06/9.28 Clause #2 (by assumption #[]): Eq (Eq cartprodsndpairEq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy)) True % 9.06/9.28 Clause #3 (by assumption #[]): Eq % 9.06/9.28 (Not % 9.06/9.28 (cartprodmempair1 → % 9.06/9.28 cartprodfstpairEq → % 9.06/9.28 cartprodsndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu)) % 9.06/9.28 True % 9.06/9.28 Clause #4 (by clausification #[3]): Eq % 9.06/9.28 (cartprodmempair1 → % 9.06/9.28 cartprodfstpairEq → cartprodsndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) % 9.06/9.28 False % 9.06/9.28 Clause #5 (by clausification #[4]): Eq cartprodmempair1 True % 9.06/9.28 Clause #6 (by clausification #[4]): Eq (cartprodfstpairEq → cartprodsndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) % 9.06/9.28 False % 9.06/9.28 Clause #7 (by clausification #[6]): Eq cartprodfstpairEq True % 9.06/9.28 Clause #8 (by clausification #[6]): Eq (cartprodsndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) False % 9.06/9.28 Clause #9 (by clausification #[8]): Eq cartprodsndpairEq True % 9.06/9.28 Clause #10 (by clausification #[8]): Eq (∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) False % 9.06/9.28 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Not (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu)) True % 9.06/9.28 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) False % 9.06/9.28 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 9.06/9.28 Eq (Not (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu)) True % 9.06/9.28 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 9.06/9.28 Eq (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) False % 9.06/9.28 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 9.06/9.28 Eq % 9.06/9.28 (Not % 9.06/9.28 (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → % 9.06/9.28 Eq (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2))) (skS.0 2 a a_1 a_2))) % 9.06/9.28 True % 9.06/9.28 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), % 9.06/9.28 Eq % 9.06/9.28 (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → % 9.06/9.28 Eq (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2))) (skS.0 2 a a_1 a_2)) % 9.06/9.28 False % 9.06/9.28 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1))) True % 9.06/9.28 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (Eq (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2))) (skS.0 2 a a_1 a_2)) False % 9.06/9.28 Clause #19 (by clausification #[1]): Eq cartprodfstpairEq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (kfst (kpair Xx Xy)) Xx) % 9.06/9.28 Clause #20 (by forward demodulation #[19, 7]): Eq True (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (kfst (kpair Xx Xy)) Xx) % 9.06/9.28 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy B → Eq (kfst (kpair Xx Xy)) Xx) True % 9.06/9.28 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a_1 → Eq (kfst (kpair Xx Xy)) Xx) True % 9.06/9.28 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → ∀ (Xy : Iota), in Xy a_2 → Eq (kfst (kpair a Xy)) a) True % 9.06/9.28 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (∀ (Xy : Iota), in Xy a_2 → Eq (kfst (kpair a Xy)) a) True) % 9.06/9.28 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Eq (in a_2 a_3 → Eq (kfst (kpair a a_2)) a) True) % 9.06/9.31 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 a_3) False) (Eq (Eq (kfst (kpair a a_2)) a) True)) % 9.06/9.31 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 a_3) False) (Eq (kfst (kpair a a_2)) a)) % 9.06/9.31 Clause #29 (by clausification #[0]): Eq cartprodmempair1 % 9.06/9.31 (∀ (A B Xu : Iota), % 9.06/9.31 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 9.06/9.31 Clause #30 (by forward demodulation #[29, 5]): Eq True % 9.06/9.31 (∀ (A B Xu : Iota), % 9.06/9.31 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 9.06/9.31 Clause #31 (by clausification #[30]): ∀ (a : Iota), % 9.06/9.31 Eq % 9.06/9.31 (∀ (B Xu : Iota), % 9.06/9.31 in Xu (cartprod a B) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 9.06/9.31 True % 9.06/9.31 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 9.06/9.31 Eq % 9.06/9.31 (∀ (Xu : Iota), % 9.06/9.31 in Xu (cartprod a a_1) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy a_1) (Eq Xu (kpair Xx Xy)))) % 9.06/9.31 True % 9.06/9.31 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 9.06/9.31 Eq % 9.06/9.31 (in a (cartprod a_1 a_2) → Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) % 9.06/9.31 True % 9.06/9.31 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 9.06/9.31 Or (Eq (in a (cartprod a_1 a_2)) False) % 9.06/9.31 (Eq (Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) True) % 9.06/9.31 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), % 9.06/9.31 Or (Eq (in a (cartprod a_1 a_2)) False) % 9.06/9.31 (Eq % 9.06/9.31 (And (in (skS.0 3 a_1 a_2 a a_3) a_1) % 9.06/9.31 (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy)))) % 9.06/9.31 True) % 9.06/9.31 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 9.06/9.31 Or (Eq (in a (cartprod a_1 a_2)) False) % 9.06/9.31 (Eq (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy))) True) % 9.06/9.31 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (in (skS.0 3 a_1 a_2 a a_3) a_1) True) % 9.06/9.31 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 9.06/9.31 Or (Eq (in a (cartprod a_1 a_2)) False) % 9.06/9.31 (Eq (And (in (skS.0 4 a_2 a a_1 a_3 a_4) a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) (skS.0 4 a_2 a a_1 a_3 a_4)))) % 9.06/9.31 True) % 9.06/9.31 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 9.06/9.31 Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) (skS.0 4 a_2 a a_1 a_3 a_4))) True) % 9.06/9.31 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (in (skS.0 4 a_2 a a_1 a_3 a_4) a_2) True) % 9.06/9.31 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 9.06/9.31 Or (Eq (in a (cartprod a_1 a_2)) False) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) (skS.0 4 a_2 a a_1 a_3 a_4))) % 9.06/9.31 Clause #42 (by superposition #[41, 17]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 9.06/9.31 Or % 9.06/9.31 (Eq (skS.0 2 a a_1 a_2) % 9.06/9.31 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 9.06/9.31 (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4))) % 9.06/9.31 (Eq False True) % 9.06/9.31 Clause #43 (by clausification #[2]): Eq cartprodsndpairEq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy) % 9.06/9.31 Clause #44 (by forward demodulation #[43, 9]): Eq True (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy) % 9.06/9.31 Clause #45 (by clausification #[44]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy) True % 9.06/9.31 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a_1 → Eq (ksnd (kpair Xx Xy)) Xy) True % 9.06/9.31 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → ∀ (Xy : Iota), in Xy a_2 → Eq (ksnd (kpair a Xy)) Xy) True % 9.06/9.31 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (∀ (Xy : Iota), in Xy a_2 → Eq (ksnd (kpair a Xy)) Xy) True) % 9.15/9.34 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Eq (in a_2 a_3 → Eq (ksnd (kpair a a_2)) a_2) True) % 9.15/9.34 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 a_3) False) (Eq (Eq (ksnd (kpair a a_2)) a_2) True)) % 9.15/9.34 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 a_3) False) (Eq (ksnd (kpair a a_2)) a_2)) % 9.15/9.34 Clause #55 (by superposition #[37, 17]): ∀ (a a_1 a_2 a_3 : Iota), % 9.15/9.34 Or (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) (skS.0 0 a)) True) (Eq False True) % 9.15/9.34 Clause #56 (by superposition #[40, 17]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 9.15/9.34 Or (Eq (in (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4) (skS.0 1 a a_1)) True) (Eq False True) % 9.15/9.34 Clause #59 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Ne (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2))) (skS.0 2 a a_1 a_2) % 9.15/9.34 Clause #62 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) (skS.0 0 a)) True % 9.15/9.34 Clause #63 (by superposition #[62, 27]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 9.15/9.34 Or (Eq True False) % 9.15/9.34 (Or (Eq (in a a_1) False) % 9.15/9.34 (Eq (kfst (kpair (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) a)) % 9.15/9.34 (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5))) % 9.15/9.34 Clause #64 (by superposition #[62, 51]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 9.15/9.34 Or (Eq True False) % 9.15/9.34 (Or (Eq (in a a_1) False) % 9.15/9.34 (Eq (ksnd (kpair (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) a)) a)) % 9.15/9.34 Clause #67 (by clausification #[64]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 9.15/9.34 Or (Eq (in a a_1) False) (Eq (ksnd (kpair (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) a)) a) % 9.15/9.34 Clause #70 (by clausification #[56]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 9.15/9.34 Eq (in (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4) (skS.0 1 a a_1)) True % 9.15/9.34 Clause #75 (by superposition #[70, 67]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 9.15/9.34 Or (Eq True False) % 9.15/9.34 (Eq % 9.15/9.34 (ksnd % 9.15/9.34 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 9.15/9.34 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8))) % 9.15/9.34 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8)) % 9.15/9.34 Clause #76 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 9.15/9.34 Eq (skS.0 2 a a_1 a_2) % 9.15/9.34 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 9.15/9.34 (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4)) % 9.15/9.34 Clause #85 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 9.15/9.34 Or (Eq (in a a_1) False) % 9.15/9.34 (Eq (kfst (kpair (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) a)) % 9.15/9.34 (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5)) % 9.15/9.34 Clause #88 (by superposition #[85, 70]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 9.15/9.34 Or % 9.15/9.34 (Eq % 9.15/9.34 (kfst % 9.15/9.34 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 9.15/9.34 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8))) % 9.15/9.34 (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)) % 9.15/9.34 (Eq False True) % 9.15/9.34 Clause #100 (by clausification #[88]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 9.15/9.34 Eq % 9.15/9.34 (kfst % 9.15/9.34 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 9.15/9.34 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8))) % 9.15/9.34 (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 9.15/9.34 Clause #101 (by superposition #[100, 76]): ∀ (a a_1 a_2 a_3 : Iota), Eq (kfst (skS.0 2 a a_1 a_2)) (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 9.15/9.34 Clause #104 (by backward demodulation #[101, 76]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 9.15/9.34 Eq (skS.0 2 a a_1 a_2) % 9.15/9.34 (kpair (kfst (skS.0 2 a a_1 a_2)) (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4)) % 9.15/9.34 Clause #116 (by clausification #[75]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 9.15/9.34 Eq % 9.15/9.34 (ksnd % 9.15/9.34 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 9.15/9.35 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8))) % 9.15/9.35 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8) % 9.15/9.35 Clause #117 (by forward demodulation #[116, 101]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 9.15/9.35 Eq (ksnd (kpair (kfst (skS.0 2 a a_1 a_2)) (skS.0 4 (skS.0 1 a_3 a_4) (skS.0 2 a_3 a_4 a_5) (skS.0 0 a_3) a_6 a_7))) % 9.15/9.35 (skS.0 4 (skS.0 1 a_3 a_4) (skS.0 2 a_3 a_4 a_5) (skS.0 0 a_3) a_6 a_7) % 9.15/9.35 Clause #136 (by superposition #[104, 117]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 9.15/9.35 Eq (ksnd (skS.0 2 a a_1 a_2)) (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4) % 9.15/9.35 Clause #148 (by backward demodulation #[136, 104]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 2 a a_1 a_2) (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2))) % 9.15/9.35 Clause #164 (by forward contextual literal cutting #[148, 59]): False % 9.15/9.35 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------