%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM531+2 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 07:56:40 PM UTC 2025 % Result : Theorem 5.21s 5.42s % Output : Proof 5.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.09 % Problem : NUM531+2 : TPTP v9.2.0. Released v4.0.0. % 0.02/0.10 % Command : duper %s % 0.09/0.31 % Computer : n009.cluster.edu % 0.09/0.31 % Model : x86_64 x86_64 % 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.31 % Memory : 8042.1875MB % 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.31 % CPULimit : 300 % 0.09/0.31 % WCLimit : 300 % 0.09/0.31 % DateTime : Fri Oct 3 07:46:38 EDT 2025 % 0.09/0.31 % CPUTime : % 5.21/5.42 SZS status Theorem for theBenchmark.p % 5.21/5.42 SZS output start Proof for theBenchmark.p % 5.21/5.42 Clause #5 (by assumption #[]): Eq (isFinite0 slcrc0) True % 5.21/5.42 Clause #7 (by assumption #[]): Eq (∀ (W0 : Iota), And (aSet0 W0) (isCountable0 W0) → Not (isFinite0 W0)) True % 5.21/5.42 Clause #8 (by assumption #[]): Eq % 5.21/5.42 (Not % 5.21/5.42 (∀ (W0 : Iota), % 5.21/5.42 And (aSet0 W0) (isCountable0 W0) → Not (And (Not (Exists fun W1 => aElementOf0 W1 W0)) (Eq W0 slcrc0)))) % 5.21/5.42 True % 5.21/5.42 Clause #23 (by clausification #[7]): ∀ (a : Iota), Eq (And (aSet0 a) (isCountable0 a) → Not (isFinite0 a)) True % 5.21/5.42 Clause #24 (by clausification #[23]): ∀ (a : Iota), Or (Eq (And (aSet0 a) (isCountable0 a)) False) (Eq (Not (isFinite0 a)) True) % 5.21/5.42 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (Not (isFinite0 a)) True) (Or (Eq (aSet0 a) False) (Eq (isCountable0 a) False)) % 5.21/5.42 Clause #26 (by clausification #[25]): ∀ (a : Iota), Or (Eq (aSet0 a) False) (Or (Eq (isCountable0 a) False) (Eq (isFinite0 a) False)) % 5.21/5.42 Clause #46 (by clausification #[8]): Eq % 5.21/5.42 (∀ (W0 : Iota), % 5.21/5.42 And (aSet0 W0) (isCountable0 W0) → Not (And (Not (Exists fun W1 => aElementOf0 W1 W0)) (Eq W0 slcrc0))) % 5.21/5.42 False % 5.21/5.42 Clause #47 (by clausification #[46]): ∀ (a : Iota), % 5.21/5.42 Eq % 5.21/5.42 (Not % 5.21/5.42 (And (aSet0 (skS.0 1 a)) (isCountable0 (skS.0 1 a)) → % 5.21/5.42 Not (And (Not (Exists fun W1 => aElementOf0 W1 (skS.0 1 a))) (Eq (skS.0 1 a) slcrc0)))) % 5.21/5.42 True % 5.21/5.42 Clause #48 (by clausification #[47]): ∀ (a : Iota), % 5.21/5.42 Eq % 5.21/5.42 (And (aSet0 (skS.0 1 a)) (isCountable0 (skS.0 1 a)) → % 5.21/5.42 Not (And (Not (Exists fun W1 => aElementOf0 W1 (skS.0 1 a))) (Eq (skS.0 1 a) slcrc0))) % 5.21/5.42 False % 5.21/5.42 Clause #49 (by clausification #[48]): ∀ (a : Iota), Eq (And (aSet0 (skS.0 1 a)) (isCountable0 (skS.0 1 a))) True % 5.21/5.42 Clause #50 (by clausification #[48]): ∀ (a : Iota), Eq (Not (And (Not (Exists fun W1 => aElementOf0 W1 (skS.0 1 a))) (Eq (skS.0 1 a) slcrc0))) False % 5.21/5.42 Clause #51 (by clausification #[49]): ∀ (a : Iota), Eq (isCountable0 (skS.0 1 a)) True % 5.21/5.42 Clause #52 (by clausification #[49]): ∀ (a : Iota), Eq (aSet0 (skS.0 1 a)) True % 5.21/5.42 Clause #54 (by superposition #[52, 26]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (isCountable0 (skS.0 1 a)) False) (Eq (isFinite0 (skS.0 1 a)) False)) % 5.21/5.42 Clause #58 (by clausification #[54]): ∀ (a : Iota), Or (Eq (isCountable0 (skS.0 1 a)) False) (Eq (isFinite0 (skS.0 1 a)) False) % 5.21/5.42 Clause #59 (by superposition #[58, 51]): ∀ (a : Iota), Or (Eq (isFinite0 (skS.0 1 a)) False) (Eq False True) % 5.21/5.42 Clause #60 (by clausification #[59]): ∀ (a : Iota), Eq (isFinite0 (skS.0 1 a)) False % 5.21/5.42 Clause #62 (by clausification #[50]): ∀ (a : Iota), Eq (And (Not (Exists fun W1 => aElementOf0 W1 (skS.0 1 a))) (Eq (skS.0 1 a) slcrc0)) True % 5.21/5.42 Clause #63 (by clausification #[62]): ∀ (a : Iota), Eq (Eq (skS.0 1 a) slcrc0) True % 5.21/5.42 Clause #65 (by clausification #[63]): ∀ (a : Iota), Eq (skS.0 1 a) slcrc0 % 5.21/5.42 Clause #67 (by backward demodulation #[65, 60]): Eq (isFinite0 slcrc0) False % 5.21/5.42 Clause #68 (by superposition #[67, 5]): Eq False True % 5.21/5.42 Clause #69 (by clausification #[68]): False % 5.21/5.42 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------