%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 : Tue May 5 06:59:12 PM UTC 2026 % Result : Theorem 4.15s 4.32s % Output : Proof 4.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : duper %s % 0.16/0.34 % Computer : n011.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue May 5 12:33:17 EDT 2026 % 0.16/0.35 % CPUTime : % 4.15/4.32 SZS status Theorem for theBenchmark.p % 4.15/4.32 SZS output start Proof for theBenchmark.p % 4.15/4.32 Clause #25 (by assumption #[]): Eq (∀ (E : Iota), Iff (nf (lam E)) (nf E)) True % 4.15/4.32 Clause #26 (by assumption #[]): Eq (∀ (X4 : Iota), nf (var X4)) True % 4.15/4.32 Clause #28 (by assumption #[]): Eq (∀ (Z Xs : Iota), Eq (index (cons Z Xs) zero) (just Z)) True % 4.15/4.32 Clause #32 (by assumption #[]): Eq (∀ (X E Tx2 T1 : Iota), Iff (tc X (lam E) (arr Tx2 T1)) (tc (cons Tx2 X) E T1)) True % 4.15/4.32 Clause #34 (by assumption #[]): Eq (∀ (X Z X3 Tx3 : Iota), Eq (index X X3) (just Tx3) → Iff (tc X (var X3) Z) (Eq Tx3 Z)) True % 4.15/4.32 Clause #35 (by assumption #[]): Eq (Not (Exists fun E => And (nf E) (tc nil E (arr a (arr b b))))) True % 4.15/4.32 Clause #36 (by clausification #[26]): ∀ (a : Iota), Eq (nf (var a)) True % 4.15/4.32 Clause #49 (by clausification #[25]): ∀ (a : Iota), Eq (Iff (nf (lam a)) (nf a)) True % 4.15/4.32 Clause #50 (by clausification #[49]): ∀ (a : Iota), Or (Eq (nf (lam a)) True) (Eq (nf a) False) % 4.15/4.32 Clause #52 (by superposition #[50, 36]): ∀ (a : Iota), Or (Eq (nf (lam (var a))) True) (Eq False True) % 4.15/4.32 Clause #53 (by clausification #[52]): ∀ (a : Iota), Eq (nf (lam (var a))) True % 4.15/4.32 Clause #54 (by superposition #[53, 50]): ∀ (a : Iota), Or (Eq (nf (lam (lam (var a)))) True) (Eq True False) % 4.15/4.32 Clause #59 (by clausification #[54]): ∀ (a : Iota), Eq (nf (lam (lam (var a)))) True % 4.15/4.32 Clause #138 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Xs : Iota), Eq (index (cons a Xs) zero) (just a)) True % 4.15/4.32 Clause #139 (by clausification #[138]): ∀ (a a_1 : Iota), Eq (Eq (index (cons a a_1) zero) (just a)) True % 4.15/4.32 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), Eq (index (cons a a_1) zero) (just a) % 4.15/4.32 Clause #191 (by clausification #[35]): Eq (Exists fun E => And (nf E) (tc nil E (arr a (arr b b)))) False % 4.15/4.32 Clause #192 (by clausification #[191]): ∀ (a_1 : Iota), Eq (And (nf a_1) (tc nil a_1 (arr a (arr b b)))) False % 4.15/4.32 Clause #193 (by clausification #[192]): ∀ (a_1 : Iota), Or (Eq (nf a_1) False) (Eq (tc nil a_1 (arr a (arr b b))) False) % 4.15/4.32 Clause #196 (by superposition #[193, 59]): ∀ (a_1 : Iota), Or (Eq (tc nil (lam (lam (var a_1))) (arr a (arr b b))) False) (Eq False True) % 4.15/4.32 Clause #205 (by clausification #[32]): ∀ (a : Iota), Eq (∀ (E Tx2 T1 : Iota), Iff (tc a (lam E) (arr Tx2 T1)) (tc (cons Tx2 a) E T1)) True % 4.15/4.32 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), Eq (∀ (Tx2 T1 : Iota), Iff (tc a (lam a_1) (arr Tx2 T1)) (tc (cons Tx2 a) a_1 T1)) True % 4.15/4.32 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 : Iota), Eq (∀ (T1 : Iota), Iff (tc a (lam a_1) (arr a_2 T1)) (tc (cons a_2 a) a_1 T1)) True % 4.15/4.32 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Iff (tc a (lam a_1) (arr a_2 a_3)) (tc (cons a_2 a) a_1 a_3)) True % 4.15/4.32 Clause #209 (by clausification #[208]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (tc a (lam a_1) (arr a_2 a_3)) True) (Eq (tc (cons a_2 a) a_1 a_3) False) % 4.15/4.32 Clause #212 (by clausification #[196]): ∀ (a_1 : Iota), Eq (tc nil (lam (lam (var a_1))) (arr a (arr b b))) False % 4.15/4.32 Clause #215 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (Z X3 Tx3 : Iota), Eq (index a X3) (just Tx3) → Iff (tc a (var X3) Z) (Eq Tx3 Z)) True % 4.15/4.32 Clause #216 (by clausification #[215]): ∀ (a a_1 : Iota), Eq (∀ (X3 Tx3 : Iota), Eq (index a X3) (just Tx3) → Iff (tc a (var X3) a_1) (Eq Tx3 a_1)) True % 4.15/4.32 Clause #217 (by clausification #[216]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Tx3 : Iota), Eq (index a a_1) (just Tx3) → Iff (tc a (var a_1) a_2) (Eq Tx3 a_2)) True % 4.15/4.32 Clause #218 (by clausification #[217]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Eq (index a a_1) (just a_2) → Iff (tc a (var a_1) a_3) (Eq a_2 a_3)) True % 4.15/4.32 Clause #219 (by clausification #[218]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Eq (index a a_1) (just a_2)) False) (Eq (Iff (tc a (var a_1) a_3) (Eq a_2 a_3)) True) % 4.15/4.32 Clause #220 (by clausification #[219]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Iff (tc a (var a_1) a_2) (Eq a_3 a_2)) True) (Ne (index a a_1) (just a_3)) % 4.15/4.32 Clause #221 (by clausification #[220]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (index a a_1) (just a_2)) (Or (Eq (tc a (var a_1) a_3) True) (Eq (Eq a_2 a_3) False)) % 4.15/4.32 Clause #223 (by clausification #[221]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (index a a_1) (just a_2)) (Or (Eq (tc a (var a_1) a_3) True) (Ne a_2 a_3)) % 4.15/4.32 Clause #224 (by destructive equality resolution #[223]): ∀ (a a_1 a_2 : Iota), Or (Ne (index a a_1) (just a_2)) (Eq (tc a (var a_1) a_2) True) % 4.15/4.32 Clause #225 (by superposition #[224, 140]): ∀ (a a_1 a_2 : Iota), Or (Ne (just a) (just a_1)) (Eq (tc (cons a a_2) (var zero) a_1) True) % 4.15/4.32 Clause #228 (by equality resolution #[225]): ∀ (a a_1 : Iota), Eq (tc (cons a a_1) (var zero) a) True % 4.15/4.32 Clause #230 (by superposition #[228, 209]): ∀ (a a_1 : Iota), Or (Eq (tc a (lam (var zero)) (arr a_1 a_1)) True) (Eq True False) % 4.15/4.32 Clause #231 (by clausification #[230]): ∀ (a a_1 : Iota), Eq (tc a (lam (var zero)) (arr a_1 a_1)) True % 4.15/4.32 Clause #235 (by superposition #[231, 209]): ∀ (a a_1 a_2 : Iota), Or (Eq (tc a (lam (lam (var zero))) (arr a_1 (arr a_2 a_2))) True) (Eq True False) % 4.15/4.32 Clause #238 (by clausification #[235]): ∀ (a a_1 a_2 : Iota), Eq (tc a (lam (lam (var zero))) (arr a_1 (arr a_2 a_2))) True % 4.15/4.32 Clause #239 (by superposition #[238, 212]): Eq True False % 4.15/4.32 Clause #244 (by clausification #[239]): False % 4.15/4.32 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------