%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN365^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:07:30 PM UTC 2025 % Result : Theorem 172.28s 172.55s % Output : Proof 172.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SYN365^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.11 % Command : duper %s % 0.10/0.32 % Computer : n018.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Thu Oct 2 15:30:53 EDT 2025 % 0.10/0.32 % CPUTime : % 172.28/172.55 SZS status Theorem for theBenchmark.p % 172.28/172.55 SZS output start Proof for theBenchmark.p % 172.28/172.55 Clause #0 (by assumption #[]): Eq % 172.28/172.55 (Not % 172.28/172.55 (And (∀ (Xx : Iota), Exists fun Xy => cP Xx → And (cR Xx (g (h Xy))) (cP Xy)) % 172.28/172.55 (∀ (Xw : Iota), cP Xw → And (cP (g Xw)) (cP (h Xw))) → % 172.28/172.55 ∀ (Xx : Iota), cP Xx → Exists fun Xy => And (cR Xx Xy) (cP Xy))) % 172.28/172.55 True % 172.28/172.55 Clause #1 (by clausification #[0]): Eq % 172.28/172.55 (And (∀ (Xx : Iota), Exists fun Xy => cP Xx → And (cR Xx (g (h Xy))) (cP Xy)) % 172.28/172.55 (∀ (Xw : Iota), cP Xw → And (cP (g Xw)) (cP (h Xw))) → % 172.28/172.55 ∀ (Xx : Iota), cP Xx → Exists fun Xy => And (cR Xx Xy) (cP Xy)) % 172.28/172.55 False % 172.28/172.55 Clause #2 (by clausification #[1]): Eq % 172.28/172.55 (And (∀ (Xx : Iota), Exists fun Xy => cP Xx → And (cR Xx (g (h Xy))) (cP Xy)) % 172.28/172.55 (∀ (Xw : Iota), cP Xw → And (cP (g Xw)) (cP (h Xw)))) % 172.28/172.55 True % 172.28/172.55 Clause #3 (by clausification #[1]): Eq (∀ (Xx : Iota), cP Xx → Exists fun Xy => And (cR Xx Xy) (cP Xy)) False % 172.28/172.55 Clause #4 (by clausification #[2]): Eq (∀ (Xw : Iota), cP Xw → And (cP (g Xw)) (cP (h Xw))) True % 172.28/172.55 Clause #5 (by clausification #[2]): Eq (∀ (Xx : Iota), Exists fun Xy => cP Xx → And (cR Xx (g (h Xy))) (cP Xy)) True % 172.28/172.55 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (cP a → And (cP (g a)) (cP (h a))) True % 172.28/172.55 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (And (cP (g a)) (cP (h a))) True) % 172.28/172.55 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (cP (h a)) True) % 172.28/172.55 Clause #9 (by clausification #[7]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq (cP (g a)) True) % 172.28/172.55 Clause #10 (by clausification #[3]): ∀ (a : Iota), Eq (Not (cP (skS.0 0 a) → Exists fun Xy => And (cR (skS.0 0 a) Xy) (cP Xy))) True % 172.28/172.55 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (cP (skS.0 0 a) → Exists fun Xy => And (cR (skS.0 0 a) Xy) (cP Xy)) False % 172.28/172.55 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (cP (skS.0 0 a)) True % 172.28/172.55 Clause #13 (by clausification #[11]): ∀ (a : Iota), Eq (Exists fun Xy => And (cR (skS.0 0 a) Xy) (cP Xy)) False % 172.28/172.55 Clause #22 (by clausification #[5]): ∀ (a : Iota), Eq (Exists fun Xy => cP a → And (cR a (g (h Xy))) (cP Xy)) True % 172.28/172.55 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (cP a → And (cR a (g (h (skS.0 1 a a_1)))) (cP (skS.0 1 a a_1))) True % 172.28/172.55 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (And (cR a (g (h (skS.0 1 a a_1)))) (cP (skS.0 1 a a_1))) True) % 172.28/172.55 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (cP (skS.0 1 a a_1)) True) % 172.28/172.55 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (cP a) False) (Eq (cR a (g (h (skS.0 1 a a_1)))) True) % 172.28/172.55 Clause #27 (by superposition #[25, 12]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 1 (skS.0 0 a) a_1)) True) (Eq False True) % 172.28/172.55 Clause #50 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (And (cR (skS.0 0 a) a_1) (cP a_1)) False % 172.28/172.55 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 0 a) a_1) False) (Eq (cP a_1) False) % 172.28/172.55 Clause #72 (by superposition #[26, 12]): ∀ (a a_1 : Iota), Or (Eq (cR (skS.0 0 a) (g (h (skS.0 1 (skS.0 0 a) a_1)))) True) (Eq False True) % 172.28/172.55 Clause #110 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (cP (skS.0 1 (skS.0 0 a) a_1)) True % 172.28/172.55 Clause #111 (by superposition #[110, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cP (h (skS.0 1 (skS.0 0 a) a_1))) True) % 172.28/172.55 Clause #500 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (cR (skS.0 0 a) (g (h (skS.0 1 (skS.0 0 a) a_1)))) True % 172.28/172.55 Clause #501 (by superposition #[500, 51]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cP (g (h (skS.0 1 (skS.0 0 a) a_1)))) False) % 172.28/172.55 Clause #1119 (by clausification #[111]): ∀ (a a_1 : Iota), Eq (cP (h (skS.0 1 (skS.0 0 a) a_1))) True % 172.28/172.55 Clause #1121 (by superposition #[1119, 9]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cP (g (h (skS.0 1 (skS.0 0 a) a_1)))) True) % 172.28/172.55 Clause #4262 (by clausification #[501]): ∀ (a a_1 : Iota), Eq (cP (g (h (skS.0 1 (skS.0 0 a) a_1)))) False % 172.28/172.55 Clause #4674 (by clausification #[1121]): ∀ (a a_1 : Iota), Eq (cP (g (h (skS.0 1 (skS.0 0 a) a_1)))) True % 172.28/172.55 Clause #4675 (by superposition #[4674, 4262]): Eq True False % 172.28/172.59 Clause #4685 (by clausification #[4675]): False % 172.28/172.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------