%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN074+1 : TPTP v9.2.0. Released v2.0.0. % 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 08:07:08 PM UTC 2025 % Result : Theorem 7.74s 7.94s % Output : Proof 7.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN074+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.13 % Command : duper %s % 0.14/0.35 % Computer : n004.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 15:46:53 EDT 2025 % 0.14/0.35 % CPUTime : % 7.74/7.94 SZS status Theorem for theBenchmark.p % 7.74/7.94 SZS output start Proof for theBenchmark.p % 7.74/7.94 Clause #0 (by assumption #[]): Eq (Exists fun Z => Exists fun W => ∀ (X Y : Iota), Iff (big_f X Y) (And (Eq X Z) (Eq Y W))) True % 7.74/7.94 Clause #1 (by assumption #[]): Eq (Not (Exists fun Z => ∀ (X : Iota), Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f X Y) (Eq Y W)) (Eq X Z))) True % 7.74/7.94 Clause #2 (by clausification #[0]): ∀ (a : Iota), Eq (Exists fun W => ∀ (X Y : Iota), Iff (big_f X Y) (And (Eq X (skS.0 0 a)) (Eq Y W))) True % 7.74/7.94 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), Eq (∀ (X Y : Iota), Iff (big_f X Y) (And (Eq X (skS.0 0 a)) (Eq Y (skS.0 1 a a_1)))) True % 7.74/7.94 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Y : Iota), Iff (big_f a Y) (And (Eq a (skS.0 0 a_1)) (Eq Y (skS.0 1 a_1 a_2)))) True % 7.74/7.94 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Iff (big_f a a_1) (And (Eq a (skS.0 0 a_2)) (Eq a_1 (skS.0 1 a_2 a_3)))) True % 7.74/7.94 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) True) (Eq (And (Eq a (skS.0 0 a_2)) (Eq a_1 (skS.0 1 a_2 a_3))) False) % 7.74/7.94 Clause #7 (by clausification #[5]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) False) (Eq (And (Eq a (skS.0 0 a_2)) (Eq a_1 (skS.0 1 a_2 a_3))) True) % 7.74/7.94 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), % 7.74/7.94 Or (Eq (big_f a a_1) True) (Or (Eq (Eq a (skS.0 0 a_2)) False) (Eq (Eq a_1 (skS.0 1 a_2 a_3)) False)) % 7.74/7.94 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq (Eq a_1 (skS.0 1 a_2 a_3)) False) (Ne a (skS.0 0 a_2))) % 7.74/7.94 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) True) (Or (Ne a (skS.0 0 a_2)) (Ne a_1 (skS.0 1 a_2 a_3))) % 7.74/7.94 Clause #11 (by destructive equality resolution #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a) a_1) True) (Ne a_1 (skS.0 1 a a_2)) % 7.74/7.94 Clause #12 (by destructive equality resolution #[11]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True % 7.74/7.94 Clause #13 (by clausification #[1]): Eq (Exists fun Z => ∀ (X : Iota), Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f X Y) (Eq Y W)) (Eq X Z)) False % 7.74/7.94 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (X : Iota), Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f X Y) (Eq Y W)) (Eq X a)) False % 7.74/7.94 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), % 7.74/7.94 Eq (Not (Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y W)) (Eq (skS.0 2 a a_1) a))) True % 7.74/7.94 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 7.74/7.94 Eq (Iff (Exists fun W => ∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y W)) (Eq (skS.0 2 a a_1) a)) False % 7.74/7.94 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 7.74/7.94 Or (Eq (Exists fun W => ∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y W)) False) (Eq (Eq (skS.0 2 a a_1) a) False) % 7.74/7.94 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), % 7.74/7.94 Or (Eq (Exists fun W => ∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y W)) True) (Eq (Eq (skS.0 2 a a_1) a) True) % 7.74/7.94 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 7.74/7.94 Or (Eq (Eq (skS.0 2 a a_1) a) False) (Eq (∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y a_2)) False) % 7.74/7.94 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y a_2)) False) (Ne (skS.0 2 a a_1) a) % 7.74/7.94 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota), % 7.74/7.94 Or (Ne (skS.0 2 a a_1) a) % 7.74/7.94 (Eq (Not (Iff (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) (Eq (skS.0 3 a a_1 a_2 a_3) a_2))) True) % 7.74/7.94 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), % 7.74/7.94 Or (Ne (skS.0 2 a a_1) a) % 7.74/7.94 (Eq (Iff (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) (Eq (skS.0 3 a a_1 a_2 a_3) a_2)) False) % 7.74/7.94 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), % 7.74/7.94 Or (Ne (skS.0 2 a a_1) a) % 7.74/7.94 (Or (Eq (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) False) (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_2) False)) % 7.74/7.94 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), % 7.74/7.94 Or (Ne (skS.0 2 a a_1) a) % 7.74/7.94 (Or (Eq (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) True) (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_2) True)) % 7.80/7.96 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Ne (skS.0 2 a a_1) a) % 7.80/7.96 (Or (Eq (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) False) (Ne (skS.0 3 a a_1 a_2 a_3) a_2)) % 7.80/7.96 Clause #26 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) False) (Eq (Eq a_1 (skS.0 1 a_2 a_3)) True) % 7.80/7.96 Clause #27 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (Eq a (skS.0 0 a_2)) True) % 7.80/7.96 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a a_1) False) (Eq a_1 (skS.0 1 a_2 a_3)) % 7.80/7.96 Clause #29 (by superposition #[28, 12]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 1 a a_1) (skS.0 1 a_2 a_3)) (Eq False True) % 7.80/7.96 Clause #30 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq a (skS.0 0 a_2)) % 7.80/7.96 Clause #31 (by superposition #[30, 12]): ∀ (a a_1 : Iota), Or (Eq (skS.0 0 a) (skS.0 0 a_1)) (Eq False True) % 7.80/7.96 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (skS.0 0 a_1) % 7.80/7.96 Clause #33 (by superposition #[32, 12]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) True % 7.80/7.96 Clause #34 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 7.80/7.96 Or (Eq (Eq (skS.0 2 a a_1) a) True) (Eq (∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y (skS.0 4 a a_1 a_2))) True) % 7.80/7.96 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 7.80/7.96 Or (Eq (∀ (Y : Iota), Iff (big_f (skS.0 2 a a_1) Y) (Eq Y (skS.0 4 a a_1 a_2))) True) (Eq (skS.0 2 a a_1) a) % 7.80/7.96 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Eq (skS.0 2 a a_1) a) (Eq (Iff (big_f (skS.0 2 a a_1) a_2) (Eq a_2 (skS.0 4 a a_1 a_3))) True) % 7.80/7.96 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Eq (skS.0 2 a a_1) a) (Or (Eq (big_f (skS.0 2 a a_1) a_2) True) (Eq (Eq a_2 (skS.0 4 a a_1 a_3)) False)) % 7.80/7.96 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Eq (skS.0 2 a a_1) a) (Or (Eq (big_f (skS.0 2 a a_1) a_2) True) (Ne a_2 (skS.0 4 a a_1 a_3))) % 7.80/7.96 Clause #40 (by destructive equality resolution #[39]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 2 a a_1) a) (Eq (big_f (skS.0 2 a a_1) (skS.0 4 a a_1 a_2)) True) % 7.80/7.96 Clause #43 (by superposition #[40, 30]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 2 a a_1) a) (Or (Eq True False) (Eq (skS.0 2 a a_1) (skS.0 0 a_2))) % 7.80/7.96 Clause #46 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 1 a a_1) (skS.0 1 a_2 a_3) % 7.80/7.96 Clause #47 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 2 a a_1) a) (Eq (skS.0 2 a a_1) (skS.0 0 a_2)) % 7.80/7.96 Clause #56 (by equality factoring #[47]): ∀ (a a_1 a_2 : Iota), Or (Ne (skS.0 0 a) a_1) (Eq (skS.0 2 a_1 a_2) a_1) % 7.80/7.96 Clause #57 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Ne (skS.0 2 a a_1) a) % 7.80/7.96 (Or (Eq (big_f (skS.0 2 a a_1) (skS.0 3 a a_1 a_2 a_3)) True) (Eq (skS.0 3 a a_1 a_2 a_3) a_2)) % 7.80/7.96 Clause #59 (by destructive equality resolution #[56]): ∀ (a a_1 : Iota), Eq (skS.0 2 (skS.0 0 a) a_1) (skS.0 0 a) % 7.80/7.96 Clause #60 (by superposition #[59, 25]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Ne (skS.0 0 a) (skS.0 0 a)) % 7.80/7.96 (Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) False) (Ne (skS.0 3 (skS.0 0 a) a_1 a_2 a_3) a_2)) % 7.80/7.96 Clause #61 (by superposition #[59, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Ne (skS.0 0 a) (skS.0 0 a)) % 7.80/7.96 (Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) True) (Eq (skS.0 3 (skS.0 0 a) a_1 a_2 a_3) a_2)) % 7.80/7.96 Clause #233 (by eliminate resolved literals #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) False) (Ne (skS.0 3 (skS.0 0 a) a_1 a_2 a_3) a_2) % 7.80/7.96 Clause #255 (by eliminate resolved literals #[61]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) True) (Eq (skS.0 3 (skS.0 0 a) a_1 a_2 a_3) a_2) % 7.80/7.96 Clause #263 (by superposition #[255, 233]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) True) % 7.80/7.96 (Or (Eq (big_f (skS.0 0 a) a_2) False) (Ne a_2 a_2)) % 7.80/7.96 Clause #737 (by eliminate resolved literals #[263]): ∀ (a a_1 a_2 a_3 : Iota), % 7.80/7.96 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 a_2 a_3)) True) (Eq (big_f (skS.0 0 a) a_2) False) % 7.82/7.97 Clause #738 (by superposition #[737, 33]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.82/7.97 Or (Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 (skS.0 1 a_2 a_3) a_4)) True) (Eq False True) % 7.82/7.97 Clause #743 (by clausification #[738]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_f (skS.0 0 a) (skS.0 3 (skS.0 0 a) a_1 (skS.0 1 a_2 a_3) a_4)) True % 7.82/7.97 Clause #750 (by superposition #[743, 28]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 7.82/7.97 Or (Eq True False) (Eq (skS.0 3 (skS.0 0 a) a_1 (skS.0 1 a_2 a_3) a_4) (skS.0 1 a_5 a_6)) % 7.82/7.97 Clause #760 (by clausification #[750]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), Eq (skS.0 3 (skS.0 0 a) a_1 (skS.0 1 a_2 a_3) a_4) (skS.0 1 a_5 a_6) % 7.82/7.97 Clause #764 (by superposition #[760, 233]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.82/7.97 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) False) (Ne (skS.0 1 a_1 a_2) (skS.0 1 a_3 a_4)) % 7.82/7.97 Clause #778 (by forward contextual literal cutting #[764, 46]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) False % 7.82/7.97 Clause #779 (by superposition #[778, 33]): Eq False True % 7.82/7.97 Clause #781 (by clausification #[779]): False % 7.82/7.97 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------