%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG202+1 : TPTP v9.2.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 07:44:06 PM UTC 2025 % Result : Theorem 11.24s 11.46s % Output : Proof 11.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG202+1 : TPTP v9.2.0. Released v2.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n012.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 : Fri Oct 3 09:40:23 EDT 2025 % 0.13/0.34 % CPUTime : % 11.24/11.46 SZS status Theorem for theBenchmark.p % 11.24/11.46 SZS output start Proof for theBenchmark.p % 11.24/11.46 Clause #1 (by assumption #[]): Eq (∀ (U : Iota), sorti2 U → ∀ (V : Iota), sorti2 V → sorti2 (op2 U V)) True % 11.24/11.46 Clause #2 (by assumption #[]): Eq (∀ (U : Iota), sorti1 U → Eq (op1 U U) U) True % 11.24/11.46 Clause #3 (by assumption #[]): Eq (Not (∀ (U : Iota), sorti2 U → Eq (op2 U U) U)) True % 11.24/11.46 Clause #4 (by assumption #[]): Eq % 11.24/11.46 (Not % 11.24/11.46 (And (∀ (U : Iota), sorti1 U → sorti2 (h U)) (∀ (V : Iota), sorti2 V → sorti1 (j V)) → % 11.24/11.46 Not % 11.24/11.46 (And % 11.24/11.46 (And % 11.24/11.46 (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X))) % 11.24/11.46 (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z)))) % 11.24/11.46 (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1)) % 11.24/11.46 (∀ (X2 : Iota), sorti1 X2 → Eq (j (h X2)) X2)))) % 11.24/11.46 True % 11.24/11.46 Clause #5 (by clausification #[2]): ∀ (a : Iota), Eq (sorti1 a → Eq (op1 a a) a) True % 11.24/11.46 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (sorti1 a) False) (Eq (Eq (op1 a a) a) True) % 11.24/11.46 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (sorti1 a) False) (Eq (op1 a a) a) % 11.24/11.46 Clause #8 (by clausification #[1]): ∀ (a : Iota), Eq (sorti2 a → ∀ (V : Iota), sorti2 V → sorti2 (op2 a V)) True % 11.24/11.46 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (sorti2 a) False) (Eq (∀ (V : Iota), sorti2 V → sorti2 (op2 a V)) True) % 11.24/11.46 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (sorti2 a) False) (Eq (sorti2 a_1 → sorti2 (op2 a a_1)) True) % 11.24/11.46 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (sorti2 a) False) (Or (Eq (sorti2 a_1) False) (Eq (sorti2 (op2 a a_1)) True)) % 11.24/11.46 Clause #16 (by clausification #[3]): Eq (∀ (U : Iota), sorti2 U → Eq (op2 U U) U) False % 11.24/11.46 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (Not (sorti2 (skS.0 0 a) → Eq (op2 (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a))) True % 11.24/11.46 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (sorti2 (skS.0 0 a) → Eq (op2 (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a)) False % 11.24/11.46 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (sorti2 (skS.0 0 a)) True % 11.24/11.46 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (Eq (op2 (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a)) False % 11.24/11.46 Clause #21 (by superposition #[19, 11]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (sorti2 a) False) (Eq (sorti2 (op2 (skS.0 0 a_1) a)) True)) % 11.24/11.46 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (sorti2 a) False) (Eq (sorti2 (op2 (skS.0 0 a_1) a)) True) % 11.24/11.46 Clause #23 (by superposition #[22, 19]): ∀ (a a_1 : Iota), Or (Eq (sorti2 (op2 (skS.0 0 a) (skS.0 0 a_1))) True) (Eq False True) % 11.24/11.46 Clause #24 (by clausification #[4]): Eq % 11.24/11.46 (And (∀ (U : Iota), sorti1 U → sorti2 (h U)) (∀ (V : Iota), sorti2 V → sorti1 (j V)) → % 11.24/11.46 Not % 11.24/11.46 (And % 11.24/11.46 (And % 11.24/11.46 (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X))) % 11.24/11.46 (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z)))) % 11.24/11.46 (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1)) % 11.24/11.46 (∀ (X2 : Iota), sorti1 X2 → Eq (j (h X2)) X2))) % 11.24/11.46 False % 11.24/11.46 Clause #25 (by clausification #[24]): Eq (And (∀ (U : Iota), sorti1 U → sorti2 (h U)) (∀ (V : Iota), sorti2 V → sorti1 (j V))) True % 11.24/11.46 Clause #26 (by clausification #[24]): Eq % 11.24/11.46 (Not % 11.24/11.46 (And % 11.24/11.46 (And % 11.24/11.46 (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X))) % 11.24/11.46 (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z)))) % 11.24/11.46 (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1)) % 11.24/11.46 (∀ (X2 : Iota), sorti1 X2 → Eq (j (h X2)) X2))) % 11.24/11.46 False % 11.24/11.46 Clause #27 (by clausification #[25]): Eq (∀ (V : Iota), sorti2 V → sorti1 (j V)) True % 11.24/11.46 Clause #29 (by clausification #[27]): ∀ (a : Iota), Eq (sorti2 a → sorti1 (j a)) True % 11.24/11.46 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (sorti2 a) False) (Eq (sorti1 (j a)) True) % 11.24/11.46 Clause #31 (by superposition #[30, 19]): ∀ (a : Iota), Or (Eq (sorti1 (j (skS.0 0 a))) True) (Eq False True) % 11.31/11.49 Clause #34 (by clausification #[31]): ∀ (a : Iota), Eq (sorti1 (j (skS.0 0 a))) True % 11.31/11.49 Clause #35 (by superposition #[34, 7]): ∀ (a : Iota), Or (Eq True False) (Eq (op1 (j (skS.0 0 a)) (j (skS.0 0 a))) (j (skS.0 0 a))) % 11.31/11.49 Clause #50 (by clausification #[20]): ∀ (a : Iota), Ne (op2 (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a) % 11.31/11.49 Clause #63 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (sorti2 (op2 (skS.0 0 a) (skS.0 0 a_1))) True % 11.31/11.49 Clause #72 (by clausification #[26]): Eq % 11.31/11.49 (And % 11.31/11.49 (And % 11.31/11.49 (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X))) % 11.31/11.49 (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z)))) % 11.31/11.49 (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1)) % 11.31/11.49 (∀ (X2 : Iota), sorti1 X2 → Eq (j (h X2)) X2)) % 11.31/11.49 True % 11.31/11.49 Clause #74 (by clausification #[72]): Eq % 11.31/11.49 (And % 11.31/11.49 (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X))) % 11.31/11.49 (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z)))) % 11.31/11.49 (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1)) % 11.31/11.49 True % 11.31/11.49 Clause #106 (by clausification #[35]): ∀ (a : Iota), Eq (op1 (j (skS.0 0 a)) (j (skS.0 0 a))) (j (skS.0 0 a)) % 11.31/11.49 Clause #408 (by clausification #[74]): Eq (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1) True % 11.31/11.49 Clause #409 (by clausification #[74]): Eq % 11.31/11.49 (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X))) % 11.31/11.49 (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z)))) % 11.31/11.49 True % 11.31/11.49 Clause #410 (by clausification #[408]): ∀ (a : Iota), Eq (sorti2 a → Eq (h (j a)) a) True % 11.31/11.49 Clause #411 (by clausification #[410]): ∀ (a : Iota), Or (Eq (sorti2 a) False) (Eq (Eq (h (j a)) a) True) % 11.31/11.49 Clause #412 (by clausification #[411]): ∀ (a : Iota), Or (Eq (sorti2 a) False) (Eq (h (j a)) a) % 11.31/11.49 Clause #413 (by superposition #[412, 19]): ∀ (a : Iota), Or (Eq (h (j (skS.0 0 a))) (skS.0 0 a)) (Eq False True) % 11.31/11.49 Clause #415 (by superposition #[412, 63]): ∀ (a a_1 : Iota), Or (Eq (h (j (op2 (skS.0 0 a) (skS.0 0 a_1)))) (op2 (skS.0 0 a) (skS.0 0 a_1))) (Eq False True) % 11.31/11.49 Clause #432 (by clausification #[413]): ∀ (a : Iota), Eq (h (j (skS.0 0 a))) (skS.0 0 a) % 11.31/11.49 Clause #1080 (by clausification #[415]): ∀ (a a_1 : Iota), Eq (h (j (op2 (skS.0 0 a) (skS.0 0 a_1)))) (op2 (skS.0 0 a) (skS.0 0 a_1)) % 11.31/11.49 Clause #1825 (by clausification #[409]): Eq (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z))) True % 11.31/11.49 Clause #1827 (by clausification #[1825]): ∀ (a : Iota), Eq (sorti2 a → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 a Z)) (op1 (j a) (j Z))) True % 11.31/11.49 Clause #1828 (by clausification #[1827]): ∀ (a : Iota), Or (Eq (sorti2 a) False) (Eq (∀ (Z : Iota), sorti2 Z → Eq (j (op2 a Z)) (op1 (j a) (j Z))) True) % 11.31/11.49 Clause #1829 (by clausification #[1828]): ∀ (a a_1 : Iota), Or (Eq (sorti2 a) False) (Eq (sorti2 a_1 → Eq (j (op2 a a_1)) (op1 (j a) (j a_1))) True) % 11.31/11.49 Clause #1830 (by clausification #[1829]): ∀ (a a_1 : Iota), % 11.31/11.49 Or (Eq (sorti2 a) False) (Or (Eq (sorti2 a_1) False) (Eq (Eq (j (op2 a a_1)) (op1 (j a) (j a_1))) True)) % 11.31/11.49 Clause #1831 (by clausification #[1830]): ∀ (a a_1 : Iota), Or (Eq (sorti2 a) False) (Or (Eq (sorti2 a_1) False) (Eq (j (op2 a a_1)) (op1 (j a) (j a_1)))) % 11.31/11.49 Clause #1832 (by superposition #[1831, 19]): ∀ (a a_1 : Iota), % 11.31/11.49 Or (Eq (sorti2 a) False) (Or (Eq (j (op2 (skS.0 0 a_1) a)) (op1 (j (skS.0 0 a_1)) (j a))) (Eq False True)) % 11.31/11.49 Clause #1909 (by clausification #[1832]): ∀ (a a_1 : Iota), Or (Eq (sorti2 a) False) (Eq (j (op2 (skS.0 0 a_1) a)) (op1 (j (skS.0 0 a_1)) (j a))) % 11.31/11.49 Clause #1910 (by superposition #[1909, 19]): ∀ (a a_1 : Iota), Or (Eq (j (op2 (skS.0 0 a) (skS.0 0 a_1))) (op1 (j (skS.0 0 a)) (j (skS.0 0 a_1)))) (Eq False True) % 11.31/11.49 Clause #1985 (by clausification #[1910]): ∀ (a a_1 : Iota), Eq (j (op2 (skS.0 0 a) (skS.0 0 a_1))) (op1 (j (skS.0 0 a)) (j (skS.0 0 a_1))) % 11.31/11.49 Clause #1988 (by superposition #[1985, 106]): ∀ (a : Iota), Eq (j (op2 (skS.0 0 a) (skS.0 0 a))) (j (skS.0 0 a)) % 11.31/11.50 Clause #1989 (by superposition #[1988, 1080]): ∀ (a : Iota), Eq (h (j (skS.0 0 a))) (op2 (skS.0 0 a) (skS.0 0 a)) % 11.31/11.50 Clause #1990 (by forward demodulation #[1989, 432]): ∀ (a : Iota), Eq (skS.0 0 a) (op2 (skS.0 0 a) (skS.0 0 a)) % 11.31/11.50 Clause #1991 (by forward contextual literal cutting #[1990, 50]): False % 11.31/11.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------