%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV059^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:02:48 PM UTC 2025 % Result : Theorem 5.65s 5.89s % Output : Proof 5.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SEV059^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.11 % Command : duper %s % 0.10/0.32 % Computer : n002.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 : Fri Oct 3 01:23:08 EDT 2025 % 0.10/0.32 % CPUTime : % 5.65/5.89 SZS status Theorem for theBenchmark.p % 5.65/5.89 SZS output start Proof for theBenchmark.p % 5.65/5.89 Clause #0 (by assumption #[]): Eq % 5.65/5.89 (Not % 5.65/5.89 (And % 5.65/5.89 (And (∀ (Xx Xy Xz : a), And (c_less_ Xx Xy) (c_less_ Xy Xz) → c_less_ Xx Xz) % 5.65/5.89 (∀ (X : b), c_less_ (cA X) (cA (cF X)))) % 5.65/5.89 (Eq cG fun Z => cF (cF Z)) → % 5.65/5.89 ∀ (Y : b), c_less_ (cA Y) (cA (cG Y)))) % 5.65/5.89 True % 5.65/5.89 Clause #1 (by clausification #[0]): Eq % 5.65/5.89 (And % 5.65/5.89 (And (∀ (Xx Xy Xz : a), And (c_less_ Xx Xy) (c_less_ Xy Xz) → c_less_ Xx Xz) % 5.65/5.89 (∀ (X : b), c_less_ (cA X) (cA (cF X)))) % 5.65/5.89 (Eq cG fun Z => cF (cF Z)) → % 5.65/5.89 ∀ (Y : b), c_less_ (cA Y) (cA (cG Y))) % 5.65/5.89 False % 5.65/5.89 Clause #2 (by clausification #[1]): Eq % 5.65/5.89 (And % 5.65/5.89 (And (∀ (Xx Xy Xz : a), And (c_less_ Xx Xy) (c_less_ Xy Xz) → c_less_ Xx Xz) % 5.65/5.89 (∀ (X : b), c_less_ (cA X) (cA (cF X)))) % 5.65/5.89 (Eq cG fun Z => cF (cF Z))) % 5.65/5.89 True % 5.65/5.89 Clause #3 (by clausification #[1]): Eq (∀ (Y : b), c_less_ (cA Y) (cA (cG Y))) False % 5.65/5.89 Clause #4 (by clausification #[2]): Eq (Eq cG fun Z => cF (cF Z)) True % 5.65/5.89 Clause #5 (by clausification #[2]): Eq (And (∀ (Xx Xy Xz : a), And (c_less_ Xx Xy) (c_less_ Xy Xz) → c_less_ Xx Xz) (∀ (X : b), c_less_ (cA X) (cA (cF X)))) % 5.65/5.89 True % 5.65/5.89 Clause #6 (by clausification #[4]): Eq cG fun Z => cF (cF Z) % 5.65/5.89 Clause #7 (by argument congruence #[6]): ∀ (a : b), Eq (cG a) ((fun Z => cF (cF Z)) a) % 5.65/5.89 Clause #8 (by betaEtaReduce #[7]): ∀ (a : b), Eq (cG a) (cF (cF a)) % 5.65/5.89 Clause #12 (by clausification #[3]): ∀ (a : b), Eq (Not (c_less_ (cA (skS.0 0 a)) (cA (cG (skS.0 0 a))))) True % 5.65/5.89 Clause #13 (by clausification #[12]): ∀ (a : b), Eq (c_less_ (cA (skS.0 0 a)) (cA (cG (skS.0 0 a)))) False % 5.65/5.89 Clause #14 (by clausification #[5]): Eq (∀ (X : b), c_less_ (cA X) (cA (cF X))) True % 5.65/5.89 Clause #15 (by clausification #[5]): Eq (∀ (Xx Xy Xz : a), And (c_less_ Xx Xy) (c_less_ Xy Xz) → c_less_ Xx Xz) True % 5.65/5.89 Clause #16 (by clausification #[14]): ∀ (a : b), Eq (c_less_ (cA a) (cA (cF a))) True % 5.65/5.89 Clause #17 (by superposition #[16, 8]): ∀ (a : b), Eq (c_less_ (cA (cF a)) (cA (cG a))) True % 5.65/5.89 Clause #20 (by clausification #[15]): ∀ (a_1 : a), Eq (∀ (Xy Xz : a), And (c_less_ a_1 Xy) (c_less_ Xy Xz) → c_less_ a_1 Xz) True % 5.65/5.89 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 : a), Eq (∀ (Xz : a), And (c_less_ a_1 a_2) (c_less_ a_2 Xz) → c_less_ a_1 Xz) True % 5.65/5.89 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a : a), Eq (And (c_less_ a_1 a_2) (c_less_ a_2 a) → c_less_ a_1 a) True % 5.65/5.89 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 a : a), Or (Eq (And (c_less_ a_1 a_2) (c_less_ a_2 a)) False) (Eq (c_less_ a_1 a) True) % 5.65/5.89 Clause #24 (by clausification #[23]): ∀ (a_1 a_2 a : a), Or (Eq (c_less_ a_1 a_2) True) (Or (Eq (c_less_ a_1 a) False) (Eq (c_less_ a a_2) False)) % 5.65/5.89 Clause #25 (by superposition #[24, 16]): ∀ (a_1 : b) (a : a), Or (Eq (c_less_ (cA a_1) a) True) (Or (Eq (c_less_ (cA (cF a_1)) a) False) (Eq False True)) % 5.65/5.89 Clause #28 (by clausification #[25]): ∀ (a_1 : b) (a : a), Or (Eq (c_less_ (cA a_1) a) True) (Eq (c_less_ (cA (cF a_1)) a) False) % 5.65/5.89 Clause #30 (by superposition #[28, 17]): ∀ (a : b), Or (Eq (c_less_ (cA a) (cA (cG a))) True) (Eq False True) % 5.65/5.89 Clause #34 (by clausification #[30]): ∀ (a : b), Eq (c_less_ (cA a) (cA (cG a))) True % 5.65/5.89 Clause #35 (by superposition #[34, 13]): Eq True False % 5.65/5.89 Clause #40 (by clausification #[35]): False % 5.65/5.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------