%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET046^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 07:59:29 PM UTC 2025 % Result : Theorem 4.89s 5.09s % Output : Proof 4.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET046^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.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 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 14:11:23 EDT 2025 % 0.13/0.35 % CPUTime : % 4.89/5.09 SZS status Theorem for theBenchmark.p % 4.89/5.09 SZS output start Proof for theBenchmark.p % 4.89/5.09 Clause #0 (by assumption #[]): Eq % 4.89/5.09 (Not % 4.89/5.09 (Not % 4.89/5.09 (Exists fun Xy => % 4.89/5.09 ∀ (Xx : Iota), % 4.89/5.09 And (cF Xx Xy → Not (Exists fun Xz => And (cF Xx Xz) (cF Xz Xx))) % 4.89/5.09 (Not (Exists fun Xz => And (cF Xx Xz) (cF Xz Xx)) → cF Xx Xy)))) % 4.89/5.09 True % 4.89/5.09 Clause #1 (by clausification #[0]): Eq % 4.89/5.09 (Not % 4.89/5.09 (Exists fun Xy => % 4.89/5.09 ∀ (Xx : Iota), % 4.89/5.09 And (cF Xx Xy → Not (Exists fun Xz => And (cF Xx Xz) (cF Xz Xx))) % 4.89/5.09 (Not (Exists fun Xz => And (cF Xx Xz) (cF Xz Xx)) → cF Xx Xy))) % 4.89/5.09 False % 4.89/5.09 Clause #2 (by clausification #[1]): Eq % 4.89/5.09 (Exists fun Xy => % 4.89/5.09 ∀ (Xx : Iota), % 4.89/5.09 And (cF Xx Xy → Not (Exists fun Xz => And (cF Xx Xz) (cF Xz Xx))) % 4.89/5.09 (Not (Exists fun Xz => And (cF Xx Xz) (cF Xz Xx)) → cF Xx Xy)) % 4.89/5.09 True % 4.89/5.09 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 4.89/5.09 Eq % 4.89/5.09 (∀ (Xx : Iota), % 4.89/5.09 And (cF Xx (skS.0 0 a) → Not (Exists fun Xz => And (cF Xx Xz) (cF Xz Xx))) % 4.89/5.09 (Not (Exists fun Xz => And (cF Xx Xz) (cF Xz Xx)) → cF Xx (skS.0 0 a))) % 4.89/5.09 True % 4.89/5.09 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 4.89/5.09 Eq % 4.89/5.09 (And (cF a (skS.0 0 a_1) → Not (Exists fun Xz => And (cF a Xz) (cF Xz a))) % 4.89/5.09 (Not (Exists fun Xz => And (cF a Xz) (cF Xz a)) → cF a (skS.0 0 a_1))) % 4.89/5.09 True % 4.89/5.09 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (Not (Exists fun Xz => And (cF a Xz) (cF Xz a)) → cF a (skS.0 0 a_1)) True % 4.89/5.09 Clause #6 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (cF a (skS.0 0 a_1) → Not (Exists fun Xz => And (cF a Xz) (cF Xz a))) True % 4.89/5.09 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (Not (Exists fun Xz => And (cF a Xz) (cF Xz a))) False) (Eq (cF a (skS.0 0 a_1)) True) % 4.89/5.09 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cF a (skS.0 0 a_1)) True) (Eq (Exists fun Xz => And (cF a Xz) (cF Xz a)) True) % 4.89/5.09 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a (skS.0 0 a_1)) True) (Eq (And (cF a (skS.0 1 a a_2)) (cF (skS.0 1 a a_2) a)) True) % 4.89/5.09 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a (skS.0 0 a_1)) True) (Eq (cF (skS.0 1 a a_2) a) True) % 4.89/5.09 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a (skS.0 0 a_1)) True) (Eq (cF a (skS.0 1 a a_2)) True) % 4.89/5.09 Clause #12 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (cF a (skS.0 0 a_1)) False) (Eq (Not (Exists fun Xz => And (cF a Xz) (cF Xz a))) True) % 4.89/5.09 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (cF a (skS.0 0 a_1)) False) (Eq (Exists fun Xz => And (cF a Xz) (cF Xz a)) False) % 4.89/5.09 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a (skS.0 0 a_1)) False) (Eq (And (cF a a_2) (cF a_2 a)) False) % 4.89/5.09 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a (skS.0 0 a_1)) False) (Or (Eq (cF a a_2) False) (Eq (cF a_2 a) False)) % 4.89/5.09 Clause #17 (by superposition #[15, 10]): ∀ (a a_1 a_2 a_3 : Iota), % 4.89/5.09 Or (Eq (cF (skS.0 1 (skS.0 0 a) a_1) a_2) False) % 4.89/5.09 (Or (Eq (cF a_2 (skS.0 1 (skS.0 0 a) a_1)) False) (Or (Eq (cF (skS.0 0 a) (skS.0 0 a_3)) True) (Eq False True))) % 4.89/5.09 Clause #29 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota), % 4.89/5.09 Or (Eq (cF (skS.0 1 (skS.0 0 a) a_1) a_2) False) % 4.89/5.09 (Or (Eq (cF a_2 (skS.0 1 (skS.0 0 a) a_1)) False) (Eq (cF (skS.0 0 a) (skS.0 0 a_3)) True)) % 4.89/5.09 Clause #33 (by superposition #[29, 10]): ∀ (a a_1 a_2 a_3 : Iota), % 4.89/5.09 Or (Eq (cF (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) False) % 4.89/5.09 (Or (Eq (cF (skS.0 0 a) (skS.0 0 a_2)) True) (Or (Eq (cF (skS.0 0 a) (skS.0 0 a_3)) True) (Eq False True))) % 4.89/5.09 Clause #218 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), % 4.89/5.09 Or (Eq (cF (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) False) % 4.89/5.09 (Or (Eq (cF (skS.0 0 a) (skS.0 0 a_2)) True) (Eq (cF (skS.0 0 a) (skS.0 0 a_3)) True)) % 4.89/5.09 Clause #219 (by superposition #[218, 11]): ∀ (a a_1 a_2 a_3 : Iota), % 4.89/5.09 Or (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True) % 4.89/5.09 (Or (Eq (cF (skS.0 0 a) (skS.0 0 a_2)) True) (Or (Eq (cF (skS.0 0 a) (skS.0 0 a_3)) True) (Eq False True))) % 4.89/5.09 Clause #220 (by clausification #[219]): ∀ (a a_1 a_2 a_3 : Iota), % 4.89/5.09 Or (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True) % 4.94/5.10 (Or (Eq (cF (skS.0 0 a) (skS.0 0 a_2)) True) (Eq (cF (skS.0 0 a) (skS.0 0 a_3)) True)) % 4.94/5.10 Clause #234 (by equality factoring #[220]): ∀ (a a_1 a_2 : Iota), % 4.94/5.10 Or (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True) (Or (Ne True True) (Eq (cF (skS.0 0 a) (skS.0 0 a_2)) True)) % 4.94/5.10 Clause #235 (by clausification #[234]): ∀ (a a_1 a_2 : Iota), % 4.94/5.10 Or (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True) % 4.94/5.10 (Or (Eq (cF (skS.0 0 a) (skS.0 0 a_2)) True) (Or (Eq True False) (Eq True False))) % 4.94/5.10 Clause #237 (by clausification #[235]): ∀ (a a_1 a_2 : Iota), % 4.94/5.10 Or (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True) (Or (Eq (cF (skS.0 0 a) (skS.0 0 a_2)) True) (Eq True False)) % 4.94/5.10 Clause #238 (by clausification #[237]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True) (Eq (cF (skS.0 0 a) (skS.0 0 a_2)) True) % 4.94/5.10 Clause #252 (by equality factoring #[238]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True) % 4.94/5.10 Clause #253 (by clausification #[252]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True) (Or (Eq True False) (Eq True False)) % 4.94/5.10 Clause #255 (by clausification #[253]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True) (Eq True False) % 4.94/5.10 Clause #256 (by clausification #[255]): ∀ (a a_1 : Iota), Eq (cF (skS.0 0 a) (skS.0 0 a_1)) True % 4.94/5.10 Clause #257 (by superposition #[256, 15]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cF (skS.0 0 a) a_1) False) (Eq (cF a_1 (skS.0 0 a)) False)) % 4.94/5.10 Clause #270 (by clausification #[257]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 0 a) a_1) False) (Eq (cF a_1 (skS.0 0 a)) False) % 4.94/5.10 Clause #271 (by superposition #[270, 256]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 0 a) (skS.0 0 a_1)) False) (Eq False True) % 4.94/5.10 Clause #301 (by clausification #[271]): ∀ (a a_1 : Iota), Eq (cF (skS.0 0 a) (skS.0 0 a_1)) False % 4.94/5.10 Clause #302 (by superposition #[301, 256]): Eq False True % 4.94/5.10 Clause #307 (by clausification #[302]): False % 4.94/5.10 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------