%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN943+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:08:17 PM UTC 2025 % Result : Theorem 5.26s 5.45s % Output : Proof 5.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SYN943+1 : TPTP v9.2.0. Released v3.1.0. % 0.10/0.12 % Command : duper %s % 0.14/0.33 % Computer : n003.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Thu Oct 2 15:32:53 EDT 2025 % 0.14/0.34 % CPUTime : % 5.26/5.45 SZS status Theorem for theBenchmark.p % 5.26/5.45 SZS output start Proof for theBenchmark.p % 5.26/5.45 Clause #0 (by assumption #[]): Eq % 5.26/5.45 (Not % 5.26/5.45 (∀ (A : Iota), % 5.26/5.45 Exists fun X => % 5.26/5.45 Exists fun X2 => % 5.26/5.45 Exists fun X3 => % 5.26/5.45 Exists fun X4 => % 5.26/5.45 Exists fun Y => % 5.26/5.45 And (And (And (And (p A) (e A)) (e X → Or (g X) (s X (f X)))) (e X2 → Or (g X2) (c (f X2)))) % 5.26/5.45 (s A Y → p Y) → % 5.26/5.45 Or (And (p X3) (g X3)) (And (p X4) (c X4)))) % 5.26/5.45 True % 5.26/5.45 Clause #1 (by clausification #[0]): Eq % 5.26/5.45 (∀ (A : Iota), % 5.26/5.45 Exists fun X => % 5.26/5.45 Exists fun X2 => % 5.26/5.45 Exists fun X3 => % 5.26/5.45 Exists fun X4 => % 5.26/5.45 Exists fun Y => % 5.26/5.45 And (And (And (And (p A) (e A)) (e X → Or (g X) (s X (f X)))) (e X2 → Or (g X2) (c (f X2)))) % 5.26/5.45 (s A Y → p Y) → % 5.26/5.45 Or (And (p X3) (g X3)) (And (p X4) (c X4))) % 5.26/5.45 False % 5.26/5.45 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 5.26/5.45 Eq % 5.26/5.45 (Not % 5.26/5.45 (Exists fun X => % 5.26/5.45 Exists fun X2 => % 5.26/5.45 Exists fun X3 => % 5.26/5.45 Exists fun X4 => % 5.26/5.45 Exists fun Y => % 5.26/5.45 And % 5.26/5.45 (And (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e X → Or (g X) (s X (f X)))) % 5.26/5.45 (e X2 → Or (g X2) (c (f X2)))) % 5.26/5.45 (s (skS.0 0 a) Y → p Y) → % 5.26/5.45 Or (And (p X3) (g X3)) (And (p X4) (c X4)))) % 5.26/5.45 True % 5.26/5.45 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 5.26/5.45 Eq % 5.26/5.45 (Exists fun X => % 5.26/5.45 Exists fun X2 => % 5.26/5.45 Exists fun X3 => % 5.26/5.45 Exists fun X4 => % 5.26/5.45 Exists fun Y => % 5.26/5.45 And % 5.26/5.45 (And (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e X → Or (g X) (s X (f X)))) % 5.26/5.45 (e X2 → Or (g X2) (c (f X2)))) % 5.26/5.45 (s (skS.0 0 a) Y → p Y) → % 5.26/5.45 Or (And (p X3) (g X3)) (And (p X4) (c X4))) % 5.26/5.45 False % 5.26/5.45 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 5.26/5.45 Eq % 5.26/5.45 (Exists fun X2 => % 5.26/5.45 Exists fun X3 => % 5.26/5.45 Exists fun X4 => % 5.26/5.45 Exists fun Y => % 5.26/5.45 And % 5.26/5.45 (And (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e a_1 → Or (g a_1) (s a_1 (f a_1)))) % 5.26/5.45 (e X2 → Or (g X2) (c (f X2)))) % 5.26/5.45 (s (skS.0 0 a) Y → p Y) → % 5.26/5.45 Or (And (p X3) (g X3)) (And (p X4) (c X4))) % 5.26/5.45 False % 5.26/5.45 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 5.26/5.45 Eq % 5.26/5.45 (Exists fun X3 => % 5.26/5.45 Exists fun X4 => % 5.26/5.45 Exists fun Y => % 5.26/5.45 And % 5.26/5.45 (And (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e a_1 → Or (g a_1) (s a_1 (f a_1)))) % 5.26/5.45 (e a_2 → Or (g a_2) (c (f a_2)))) % 5.26/5.45 (s (skS.0 0 a) Y → p Y) → % 5.26/5.45 Or (And (p X3) (g X3)) (And (p X4) (c X4))) % 5.26/5.45 False % 5.26/5.45 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 a_3 : Iota), % 5.26/5.45 Eq % 5.26/5.45 (Exists fun X4 => % 5.26/5.45 Exists fun Y => % 5.26/5.45 And % 5.26/5.45 (And (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e a_1 → Or (g a_1) (s a_1 (f a_1)))) % 5.26/5.45 (e a_2 → Or (g a_2) (c (f a_2)))) % 5.26/5.45 (s (skS.0 0 a) Y → p Y) → % 5.26/5.45 Or (And (p a_3) (g a_3)) (And (p X4) (c X4))) % 5.26/5.45 False % 5.26/5.45 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.26/5.45 Eq % 5.26/5.45 (Exists fun Y => % 5.26/5.45 And % 5.26/5.45 (And (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e a_1 → Or (g a_1) (s a_1 (f a_1)))) % 5.26/5.45 (e a_2 → Or (g a_2) (c (f a_2)))) % 5.26/5.45 (s (skS.0 0 a) Y → p Y) → % 5.26/5.45 Or (And (p a_3) (g a_3)) (And (p a_4) (c a_4))) % 5.26/5.45 False % 5.26/5.45 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.26/5.45 Eq % 5.26/5.45 (And % 5.26/5.45 (And (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e a_1 → Or (g a_1) (s a_1 (f a_1)))) % 5.26/5.45 (e a_2 → Or (g a_2) (c (f a_2)))) % 5.26/5.45 (s (skS.0 0 a) a_3 → p a_3) → % 5.26/5.45 Or (And (p a_4) (g a_4)) (And (p a_5) (c a_5))) % 5.26/5.45 False % 5.26/5.45 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 5.26/5.45 Eq % 5.26/5.45 (And % 5.26/5.45 (And (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e a_1 → Or (g a_1) (s a_1 (f a_1)))) % 5.26/5.45 (e a_2 → Or (g a_2) (c (f a_2)))) % 5.26/5.45 (s (skS.0 0 a) a_3 → p a_3)) % 5.26/5.45 True % 5.26/5.45 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Or (And (p a) (g a)) (And (p a_1) (c a_1))) False % 5.32/5.50 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (s (skS.0 0 a) a_1 → p a_1) True % 5.32/5.50 Clause #12 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 5.32/5.50 Eq % 5.32/5.50 (And (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e a_1 → Or (g a_1) (s a_1 (f a_1)))) % 5.32/5.50 (e a_2 → Or (g a_2) (c (f a_2)))) % 5.32/5.50 True % 5.32/5.50 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (s (skS.0 0 a) a_1) False) (Eq (p a_1) True) % 5.32/5.50 Clause #14 (by clausification #[10]): ∀ (a : Iota), Eq (And (p a) (c a)) False % 5.32/5.50 Clause #15 (by clausification #[10]): ∀ (a : Iota), Eq (And (p a) (g a)) False % 5.32/5.50 Clause #16 (by clausification #[14]): ∀ (a : Iota), Or (Eq (p a) False) (Eq (c a) False) % 5.32/5.50 Clause #17 (by clausification #[15]): ∀ (a : Iota), Or (Eq (p a) False) (Eq (g a) False) % 5.32/5.50 Clause #18 (by clausification #[12]): ∀ (a : Iota), Eq (e a → Or (g a) (c (f a))) True % 5.32/5.50 Clause #19 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (And (And (p (skS.0 0 a)) (e (skS.0 0 a))) (e a_1 → Or (g a_1) (s a_1 (f a_1)))) True % 5.32/5.50 Clause #20 (by clausification #[18]): ∀ (a : Iota), Or (Eq (e a) False) (Eq (Or (g a) (c (f a))) True) % 5.32/5.50 Clause #21 (by clausification #[20]): ∀ (a : Iota), Or (Eq (e a) False) (Or (Eq (g a) True) (Eq (c (f a)) True)) % 5.32/5.50 Clause #22 (by clausification #[19]): ∀ (a : Iota), Eq (e a → Or (g a) (s a (f a))) True % 5.32/5.50 Clause #23 (by clausification #[19]): ∀ (a : Iota), Eq (And (p (skS.0 0 a)) (e (skS.0 0 a))) True % 5.32/5.50 Clause #24 (by clausification #[22]): ∀ (a : Iota), Or (Eq (e a) False) (Eq (Or (g a) (s a (f a))) True) % 5.32/5.50 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (e a) False) (Or (Eq (g a) True) (Eq (s a (f a)) True)) % 5.32/5.50 Clause #26 (by clausification #[23]): ∀ (a : Iota), Eq (e (skS.0 0 a)) True % 5.32/5.50 Clause #27 (by clausification #[23]): ∀ (a : Iota), Eq (p (skS.0 0 a)) True % 5.32/5.50 Clause #28 (by superposition #[26, 21]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (g (skS.0 0 a)) True) (Eq (c (f (skS.0 0 a))) True)) % 5.32/5.50 Clause #29 (by superposition #[26, 25]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (g (skS.0 0 a)) True) (Eq (s (skS.0 0 a) (f (skS.0 0 a))) True)) % 5.32/5.50 Clause #31 (by superposition #[27, 17]): ∀ (a : Iota), Or (Eq True False) (Eq (g (skS.0 0 a)) False) % 5.32/5.50 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (g (skS.0 0 a)) False % 5.32/5.50 Clause #34 (by clausification #[28]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) True) (Eq (c (f (skS.0 0 a))) True) % 5.32/5.50 Clause #35 (by forward demodulation #[34, 32]): ∀ (a : Iota), Or (Eq False True) (Eq (c (f (skS.0 0 a))) True) % 5.32/5.50 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (c (f (skS.0 0 a))) True % 5.32/5.50 Clause #37 (by clausification #[29]): ∀ (a : Iota), Or (Eq (g (skS.0 0 a)) True) (Eq (s (skS.0 0 a) (f (skS.0 0 a))) True) % 5.32/5.50 Clause #38 (by forward demodulation #[37, 32]): ∀ (a : Iota), Or (Eq False True) (Eq (s (skS.0 0 a) (f (skS.0 0 a))) True) % 5.32/5.50 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (s (skS.0 0 a) (f (skS.0 0 a))) True % 5.32/5.50 Clause #40 (by superposition #[39, 13]): ∀ (a : Iota), Or (Eq True False) (Eq (p (f (skS.0 0 a))) True) % 5.32/5.50 Clause #41 (by clausification #[40]): ∀ (a : Iota), Eq (p (f (skS.0 0 a))) True % 5.32/5.50 Clause #42 (by superposition #[41, 16]): ∀ (a : Iota), Or (Eq True False) (Eq (c (f (skS.0 0 a))) False) % 5.32/5.50 Clause #45 (by clausification #[42]): ∀ (a : Iota), Eq (c (f (skS.0 0 a))) False % 5.32/5.50 Clause #46 (by superposition #[45, 36]): Eq False True % 5.32/5.50 Clause #47 (by clausification #[46]): False % 5.32/5.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------