%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GRP001^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 07:48:59 PM UTC 2025 % Result : Theorem 4.93s 5.16s % Output : Proof 4.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP001^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.14/0.35 % Computer : n013.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 17:43:53 EDT 2025 % 0.14/0.35 % CPUTime : % 4.93/5.16 SZS status Theorem for theBenchmark.p % 4.93/5.16 SZS output start Proof for theBenchmark.p % 4.93/5.16 Clause #0 (by assumption #[]): Eq % 4.93/5.16 (Not % 4.93/5.16 (And (And (And (∀ (Xx : Iota), Eq (cP e Xx) Xx) (∀ (Xy : Iota), Eq (cP Xy e) Xy)) (∀ (Xz : Iota), Eq (cP Xz Xz) e)) % 4.93/5.16 (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) → % 4.93/5.16 ∀ (Xa Xb : Iota), Eq (cP Xa Xb) (cP Xb Xa))) % 4.93/5.16 True % 4.93/5.16 Clause #1 (by clausification #[0]): Eq % 4.93/5.16 (And (And (And (∀ (Xx : Iota), Eq (cP e Xx) Xx) (∀ (Xy : Iota), Eq (cP Xy e) Xy)) (∀ (Xz : Iota), Eq (cP Xz Xz) e)) % 4.93/5.16 (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) → % 4.93/5.16 ∀ (Xa Xb : Iota), Eq (cP Xa Xb) (cP Xb Xa)) % 4.93/5.16 False % 4.93/5.16 Clause #2 (by clausification #[1]): Eq % 4.93/5.16 (And (And (And (∀ (Xx : Iota), Eq (cP e Xx) Xx) (∀ (Xy : Iota), Eq (cP Xy e) Xy)) (∀ (Xz : Iota), Eq (cP Xz Xz) e)) % 4.93/5.16 (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz)))) % 4.93/5.16 True % 4.93/5.16 Clause #3 (by clausification #[1]): Eq (∀ (Xa Xb : Iota), Eq (cP Xa Xb) (cP Xb Xa)) False % 4.93/5.16 Clause #4 (by clausification #[2]): Eq (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) True % 4.93/5.16 Clause #5 (by clausification #[2]): Eq (And (And (∀ (Xx : Iota), Eq (cP e Xx) Xx) (∀ (Xy : Iota), Eq (cP Xy e) Xy)) (∀ (Xz : Iota), Eq (cP Xz Xz) e)) True % 4.93/5.16 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), Eq (cP (cP a Xy) Xz) (cP a (cP Xy Xz))) True % 4.93/5.16 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), Eq (cP (cP a a_1) Xz) (cP a (cP a_1 Xz))) True % 4.93/5.16 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Eq (Eq (cP (cP a a_1) a_2) (cP a (cP a_1 a_2))) True % 4.93/5.16 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Eq (cP (cP a a_1) a_2) (cP a (cP a_1 a_2)) % 4.93/5.16 Clause #10 (by superposition #[9, 9]): ∀ (a a_1 a_2 a_3 : Iota), Eq (cP (cP a (cP a_1 a_2)) a_3) (cP (cP a a_1) (cP a_2 a_3)) % 4.93/5.16 Clause #11 (by clausification #[3]): ∀ (a : Iota), Eq (Not (∀ (Xb : Iota), Eq (cP (skS.0 0 a) Xb) (cP Xb (skS.0 0 a)))) True % 4.93/5.16 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Xb : Iota), Eq (cP (skS.0 0 a) Xb) (cP Xb (skS.0 0 a))) False % 4.93/5.16 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Not (Eq (cP (skS.0 0 a) (skS.0 1 a a_1)) (cP (skS.0 1 a a_1) (skS.0 0 a)))) True % 4.93/5.16 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Eq (cP (skS.0 0 a) (skS.0 1 a a_1)) (cP (skS.0 1 a a_1) (skS.0 0 a))) False % 4.93/5.16 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Ne (cP (skS.0 0 a) (skS.0 1 a a_1)) (cP (skS.0 1 a a_1) (skS.0 0 a)) % 4.93/5.16 Clause #16 (by forward demodulation #[10, 9]): ∀ (a a_1 a_2 a_3 : Iota), Eq (cP (cP a (cP a_1 a_2)) a_3) (cP a (cP a_1 (cP a_2 a_3))) % 4.93/5.16 Clause #39 (by clausification #[5]): Eq (∀ (Xz : Iota), Eq (cP Xz Xz) e) True % 4.93/5.16 Clause #40 (by clausification #[5]): Eq (And (∀ (Xx : Iota), Eq (cP e Xx) Xx) (∀ (Xy : Iota), Eq (cP Xy e) Xy)) True % 4.93/5.16 Clause #41 (by clausification #[39]): ∀ (a : Iota), Eq (Eq (cP a a) e) True % 4.93/5.16 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (cP a a) e % 4.93/5.16 Clause #46 (by superposition #[42, 9]): ∀ (a a_1 : Iota), Eq e (cP a (cP a_1 (cP a a_1))) % 4.93/5.16 Clause #49 (by superposition #[42, 9]): ∀ (a a_1 : Iota), Eq (cP e a) (cP a_1 (cP a_1 a)) % 4.93/5.16 Clause #63 (by superposition #[49, 42]): ∀ (a : Iota), Eq (cP e a) (cP a e) % 4.93/5.16 Clause #870 (by clausification #[40]): Eq (∀ (Xy : Iota), Eq (cP Xy e) Xy) True % 4.93/5.16 Clause #872 (by clausification #[870]): ∀ (a : Iota), Eq (Eq (cP a e) a) True % 4.93/5.16 Clause #873 (by clausification #[872]): ∀ (a : Iota), Eq (cP a e) a % 4.93/5.16 Clause #874 (by backward demodulation #[873, 63]): ∀ (a : Iota), Eq (cP e a) a % 4.93/5.16 Clause #897 (by backward demodulation #[874, 49]): ∀ (a a_1 : Iota), Eq a (cP a_1 (cP a_1 a)) % 4.93/5.16 Clause #951 (by superposition #[897, 16]): ∀ (a a_1 a_2 a_3 : Iota), Eq a (cP (cP a_1 (cP a_2 a_3)) (cP a_1 (cP a_2 (cP a_3 a)))) % 4.93/5.16 Clause #1052 (by superposition #[951, 46]): ∀ (a a_1 : Iota), Eq a (cP (cP a_1 (cP a a_1)) e) % 4.93/5.16 Clause #1106 (by superposition #[1052, 873]): ∀ (a a_1 : Iota), Eq a (cP a_1 (cP a a_1)) % 4.93/5.16 Clause #1172 (by superposition #[1106, 897]): ∀ (a a_1 : Iota), Eq (cP a a_1) (cP a_1 a) % 4.93/5.17 Clause #1291 (by backward contextual literal cutting #[1172, 15]): False % 4.93/5.17 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------