%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN381^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:07:33 PM UTC 2025 % Result : Theorem 3.53s 3.72s % Output : Proof 3.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN381^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.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 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 15:49:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.53/3.72 SZS status Theorem for theBenchmark.p % 3.53/3.72 SZS output start Proof for theBenchmark.p % 3.53/3.72 Clause #0 (by assumption #[]): Eq % 3.53/3.72 (Not % 3.53/3.72 (And (And (∀ (Xx : Iota), (Exists fun Xy => cQ Xx Xy) → cP Xx) (∀ (Xv : Iota), Exists fun Xu => cQ Xu Xv)) % 3.53/3.72 (∀ (Xw Xz : Iota), cQ Xw Xz → Or (cQ Xz Xw) (cQ Xz Xz)) → % 3.53/3.72 ∀ (Xz : Iota), cP Xz)) % 3.53/3.72 True % 3.53/3.72 Clause #1 (by betaEtaReduce #[0]): Eq % 3.53/3.72 (Not % 3.53/3.72 (And (And (∀ (Xx : Iota), Exists (cQ Xx) → cP Xx) (∀ (Xv : Iota), Exists fun Xu => cQ Xu Xv)) % 3.53/3.72 (∀ (Xw Xz : Iota), cQ Xw Xz → Or (cQ Xz Xw) (cQ Xz Xz)) → % 3.53/3.72 ∀ (Xz : Iota), cP Xz)) % 3.53/3.72 True % 3.53/3.72 Clause #2 (by clausification #[1]): Eq % 3.53/3.72 (And (And (∀ (Xx : Iota), Exists (cQ Xx) → cP Xx) (∀ (Xv : Iota), Exists fun Xu => cQ Xu Xv)) % 3.53/3.72 (∀ (Xw Xz : Iota), cQ Xw Xz → Or (cQ Xz Xw) (cQ Xz Xz)) → % 3.53/3.72 ∀ (Xz : Iota), cP Xz) % 3.53/3.72 False % 3.53/3.72 Clause #3 (by clausification #[2]): Eq % 3.53/3.72 (And (And (∀ (Xx : Iota), Exists (cQ Xx) → cP Xx) (∀ (Xv : Iota), Exists fun Xu => cQ Xu Xv)) % 3.53/3.72 (∀ (Xw Xz : Iota), cQ Xw Xz → Or (cQ Xz Xw) (cQ Xz Xz))) % 3.53/3.72 True % 3.53/3.72 Clause #4 (by clausification #[2]): Eq (∀ (Xz : Iota), cP Xz) False % 3.53/3.72 Clause #5 (by clausification #[3]): Eq (∀ (Xw Xz : Iota), cQ Xw Xz → Or (cQ Xz Xw) (cQ Xz Xz)) True % 3.53/3.72 Clause #6 (by clausification #[3]): Eq (And (∀ (Xx : Iota), Exists (cQ Xx) → cP Xx) (∀ (Xv : Iota), Exists fun Xu => cQ Xu Xv)) True % 3.53/3.72 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Xz : Iota), cQ a Xz → Or (cQ Xz a) (cQ Xz Xz)) True % 3.53/3.72 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (cQ a a_1 → Or (cQ a_1 a) (cQ a_1 a_1)) True % 3.53/3.72 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cQ a a_1) False) (Eq (Or (cQ a_1 a) (cQ a_1 a_1)) True) % 3.53/3.72 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (cQ a a_1) False) (Or (Eq (cQ a_1 a) True) (Eq (cQ a_1 a_1) True)) % 3.53/3.72 Clause #11 (by clausification #[4]): ∀ (a : Iota), Eq (Not (cP (skS.0 0 a))) True % 3.53/3.72 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (cP (skS.0 0 a)) False % 3.53/3.72 Clause #13 (by clausification #[6]): Eq (∀ (Xv : Iota), Exists fun Xu => cQ Xu Xv) True % 3.53/3.72 Clause #14 (by clausification #[6]): Eq (∀ (Xx : Iota), Exists (cQ Xx) → cP Xx) True % 3.53/3.72 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (Exists fun Xu => cQ Xu a) True % 3.53/3.72 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (cQ (skS.0 1 a a_1) a) True % 3.53/3.72 Clause #17 (by superposition #[16, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cQ a (skS.0 1 a a_1)) True) (Eq (cQ a a) True)) % 3.53/3.72 Clause #18 (by clausification #[14]): ∀ (a : Iota), Eq (Exists (cQ a) → cP a) True % 3.53/3.72 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (Exists (cQ a)) False) (Eq (cP a) True) % 3.53/3.72 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cQ a a_1) False) % 3.53/3.72 Clause #23 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (cQ a (skS.0 1 a a_1)) True) (Eq (cQ a a) True) % 3.53/3.72 Clause #25 (by superposition #[23, 20]): ∀ (a : Iota), Or (Eq (cQ a a) True) (Or (Eq (cP a) True) (Eq True False)) % 3.53/3.72 Clause #26 (by clausification #[25]): ∀ (a : Iota), Or (Eq (cQ a a) True) (Eq (cP a) True) % 3.53/3.72 Clause #27 (by superposition #[26, 20]): ∀ (a : Iota), Or (Eq (cP a) True) (Or (Eq (cP a) True) (Eq True False)) % 3.53/3.72 Clause #28 (by clausification #[27]): ∀ (a : Iota), Or (Eq (cP a) True) (Eq (cP a) True) % 3.53/3.72 Clause #29 (by eliminate duplicate literals #[28]): ∀ (a : Iota), Eq (cP a) True % 3.53/3.72 Clause #32 (by superposition #[29, 12]): Eq True False % 3.53/3.72 Clause #33 (by clausification #[32]): False % 3.53/3.72 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------