%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUN067+2 : TPTP v9.2.0. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 07:57:48 PM UTC 2025 % Result : Theorem 3.34s 3.58s % Output : Proof 3.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : NUN067+2 : TPTP v9.2.0. Released v7.3.0. % 0.10/0.12 % Command : duper %s % 0.13/0.34 % Computer : n027.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 : Thu Oct 2 11:38:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.34/3.58 SZS status Theorem for theBenchmark.p % 3.34/3.58 SZS output start Proof for theBenchmark.p % 3.34/3.58 Clause #1 (by assumption #[]): Eq % 3.34/3.58 (∀ (X11 : Iota), % 3.34/3.58 Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 X11 X12)) (Ne X12 Y21)) (And (r2 X11 X12) (Eq X12 Y21))) % 3.34/3.58 True % 3.34/3.58 Clause #10 (by assumption #[]): Eq (∀ (X7 Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 Y10)) (Not (r2 X7 Y10))) True % 3.34/3.58 Clause #11 (by assumption #[]): Eq (Not (Exists fun Y1 => ∀ (Y2 : Iota), Or (Not (r1 Y2)) (Ne Y1 Y2))) True % 3.34/3.58 Clause #12 (by clausification #[11]): Eq (Exists fun Y1 => ∀ (Y2 : Iota), Or (Not (r1 Y2)) (Ne Y1 Y2)) False % 3.34/3.58 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (Y2 : Iota), Or (Not (r1 Y2)) (Ne a Y2)) False % 3.34/3.58 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Not (Or (Not (r1 (skS.0 0 a a_1))) (Ne a (skS.0 0 a a_1)))) True % 3.34/3.58 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Or (Not (r1 (skS.0 0 a a_1))) (Ne a (skS.0 0 a a_1))) False % 3.34/3.58 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Ne a (skS.0 0 a a_1)) False % 3.34/3.58 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Not (r1 (skS.0 0 a a_1))) False % 3.34/3.58 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Eq a (skS.0 0 a a_1) % 3.34/3.58 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (r1 (skS.0 0 a a_1)) True % 3.34/3.58 Clause #20 (by forward demodulation #[19, 18]): ∀ (a : Iota), Eq (r1 a) True % 3.34/3.58 Clause #21 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (Y10 : Iota), Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 Y10)) (Not (r2 a Y10))) True % 3.34/3.58 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (Or (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 a)) (Not (r2 a_1 a))) True % 3.34/3.58 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (∀ (Y20 : Iota), Or (Not (r1 Y20)) (Ne Y20 a)) True) (Eq (Not (r2 a_1 a)) True) % 3.34/3.58 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (Not (r2 a a_1)) True) (Eq (Or (Not (r1 a_2)) (Ne a_2 a_1)) True) % 3.34/3.58 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (Or (Not (r1 a)) (Ne a a_1)) True) (Eq (r2 a_2 a_1) False) % 3.34/3.58 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Not (r1 a_2)) True) (Eq (Ne a_2 a_1) True)) % 3.34/3.58 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (Ne a_2 a_1) True) (Eq (r1 a_2) False)) % 3.34/3.58 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) False) (Or (Eq (r1 a_2) False) (Ne a_2 a_1)) % 3.34/3.58 Clause #29 (by destructive equality resolution #[28]): ∀ (a a_1 : Iota), Or (Eq (r2 a a_1) False) (Eq (r1 a_1) False) % 3.34/3.58 Clause #30 (by forward demodulation #[29, 20]): ∀ (a a_1 : Iota), Or (Eq (r2 a a_1) False) (Eq True False) % 3.34/3.58 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (r2 a a_1) False % 3.34/3.58 Clause #62 (by clausification #[1]): ∀ (a : Iota), % 3.34/3.58 Eq (Exists fun Y21 => ∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 Y21)) (And (r2 a X12) (Eq X12 Y21))) True % 3.34/3.58 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 3.34/3.58 Eq (∀ (X12 : Iota), Or (And (Not (r2 a X12)) (Ne X12 (skS.0 4 a a_1))) (And (r2 a X12) (Eq X12 (skS.0 4 a a_1)))) True % 3.34/3.58 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 3.34/3.58 Eq (Or (And (Not (r2 a a_1)) (Ne a_1 (skS.0 4 a a_2))) (And (r2 a a_1) (Eq a_1 (skS.0 4 a a_2)))) True % 3.34/3.58 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 3.34/3.58 Or (Eq (And (Not (r2 a a_1)) (Ne a_1 (skS.0 4 a a_2))) True) (Eq (And (r2 a a_1) (Eq a_1 (skS.0 4 a a_2))) True) % 3.34/3.58 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (r2 a a_1) (Eq a_1 (skS.0 4 a a_2))) True) (Eq (Ne a_1 (skS.0 4 a a_2)) True) % 3.34/3.58 Clause #69 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Or (Eq (Ne a (skS.0 4 a_1 a_2)) True) (Eq (r2 a_1 a) True) % 3.34/3.58 Clause #73 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq (r2 a a_1) True) (Ne a_1 (skS.0 4 a a_2)) % 3.34/3.58 Clause #74 (by destructive equality resolution #[73]): ∀ (a a_1 : Iota), Eq (r2 a (skS.0 4 a a_1)) True % 3.34/3.58 Clause #75 (by superposition #[74, 31]): Eq True False % 3.34/3.58 Clause #88 (by clausification #[75]): False % 3.34/3.58 SZS output end Proof for theBenchmark.p 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