%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV494^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:03:14 PM UTC 2025 % Result : Theorem 3.49s 3.73s % Output : Proof 3.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV494^1 : TPTP v9.2.0. Released v7.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.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 00:58:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.49/3.73 SZS status Theorem for theBenchmark.p % 3.49/3.73 SZS output start Proof for theBenchmark.p % 3.49/3.73 Clause #0 (by assumption #[]): Eq % 3.49/3.73 (∀ (A : «type/nums/num»), % 3.49/3.73 Eq («const/arith/-» («const/nums/SUC» A) («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) A) % 3.49/3.73 True % 3.49/3.73 Clause #1 (by assumption #[]): Eq % 3.49/3.73 (∀ (A A0 : «type/nums/num»), % 3.49/3.73 «const/arith/<=» A A0 → % 3.49/3.73 Eq % 3.49/3.73 («const/sets/INSERT» «type/nums/num» A0 % 3.49/3.73 («const/iterate/..» A («const/arith/-» A0 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))))) % 3.49/3.73 («const/iterate/..» A A0)) % 3.49/3.73 True % 3.49/3.73 Clause #2 (by assumption #[]): Eq % 3.49/3.73 (Not % 3.49/3.73 (∀ (A A0 : «type/nums/num»), % 3.49/3.73 «const/arith/<=» A («const/nums/SUC» A0) → % 3.49/3.73 Eq («const/iterate/..» A («const/nums/SUC» A0)) % 3.49/3.73 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» A0) («const/iterate/..» A A0)))) % 3.49/3.73 True % 3.49/3.73 Clause #3 (by clausification #[0]): ∀ (a : «type/nums/num»), % 3.49/3.73 Eq (Eq («const/arith/-» («const/nums/SUC» a) («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) a) True % 3.49/3.73 Clause #4 (by clausification #[3]): ∀ (a : «type/nums/num»), % 3.49/3.73 Eq («const/arith/-» («const/nums/SUC» a) («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) a % 3.49/3.73 Clause #5 (by clausification #[2]): Eq % 3.49/3.73 (∀ (A A0 : «type/nums/num»), % 3.49/3.73 «const/arith/<=» A («const/nums/SUC» A0) → % 3.49/3.73 Eq («const/iterate/..» A («const/nums/SUC» A0)) % 3.49/3.73 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» A0) («const/iterate/..» A A0))) % 3.49/3.73 False % 3.49/3.73 Clause #6 (by clausification #[5]): ∀ (a : «type/nums/num»), % 3.49/3.73 Eq % 3.49/3.73 (Not % 3.49/3.73 (∀ (A0 : «type/nums/num»), % 3.49/3.73 «const/arith/<=» (skS.0 0 a) («const/nums/SUC» A0) → % 3.49/3.73 Eq («const/iterate/..» (skS.0 0 a) («const/nums/SUC» A0)) % 3.49/3.73 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» A0) («const/iterate/..» (skS.0 0 a) A0)))) % 3.49/3.73 True % 3.49/3.73 Clause #7 (by clausification #[6]): ∀ (a : «type/nums/num»), % 3.49/3.73 Eq % 3.49/3.73 (∀ (A0 : «type/nums/num»), % 3.49/3.73 «const/arith/<=» (skS.0 0 a) («const/nums/SUC» A0) → % 3.49/3.73 Eq («const/iterate/..» (skS.0 0 a) («const/nums/SUC» A0)) % 3.49/3.73 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» A0) («const/iterate/..» (skS.0 0 a) A0))) % 3.49/3.73 False % 3.49/3.73 Clause #8 (by clausification #[7]): ∀ (a a_1 : «type/nums/num»), % 3.49/3.73 Eq % 3.49/3.73 (Not % 3.49/3.73 («const/arith/<=» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1)) → % 3.49/3.73 Eq («const/iterate/..» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1))) % 3.49/3.73 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» (skS.0 1 a a_1)) % 3.49/3.73 («const/iterate/..» (skS.0 0 a) (skS.0 1 a a_1))))) % 3.49/3.73 True % 3.49/3.73 Clause #9 (by clausification #[8]): ∀ (a a_1 : «type/nums/num»), % 3.49/3.73 Eq % 3.49/3.73 («const/arith/<=» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1)) → % 3.49/3.73 Eq («const/iterate/..» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1))) % 3.49/3.73 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» (skS.0 1 a a_1)) % 3.49/3.73 («const/iterate/..» (skS.0 0 a) (skS.0 1 a a_1)))) % 3.49/3.73 False % 3.49/3.73 Clause #10 (by clausification #[9]): ∀ (a a_1 : «type/nums/num»), Eq («const/arith/<=» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1))) True % 3.49/3.73 Clause #11 (by clausification #[9]): ∀ (a a_1 : «type/nums/num»), % 3.49/3.73 Eq % 3.49/3.73 (Eq («const/iterate/..» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1))) % 3.49/3.73 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» (skS.0 1 a a_1)) % 3.49/3.73 («const/iterate/..» (skS.0 0 a) (skS.0 1 a a_1)))) % 3.49/3.73 False % 3.49/3.73 Clause #12 (by clausification #[1]): ∀ (a : «type/nums/num»), % 3.49/3.73 Eq % 3.49/3.73 (∀ (A0 : «type/nums/num»), % 3.49/3.73 «const/arith/<=» a A0 → % 3.49/3.73 Eq % 3.49/3.73 («const/sets/INSERT» «type/nums/num» A0 % 3.49/3.73 («const/iterate/..» a («const/arith/-» A0 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))))) % 3.49/3.73 («const/iterate/..» a A0)) % 3.49/3.73 True % 3.49/3.73 Clause #13 (by clausification #[12]): ∀ (a a_1 : «type/nums/num»), % 3.49/3.73 Eq % 3.49/3.73 («const/arith/<=» a a_1 → % 3.49/3.73 Eq % 3.49/3.73 («const/sets/INSERT» «type/nums/num» a_1 % 3.57/3.74 («const/iterate/..» a («const/arith/-» a_1 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))))) % 3.57/3.74 («const/iterate/..» a a_1)) % 3.57/3.74 True % 3.57/3.74 Clause #14 (by clausification #[13]): ∀ (a a_1 : «type/nums/num»), % 3.57/3.74 Or (Eq («const/arith/<=» a a_1) False) % 3.57/3.74 (Eq % 3.57/3.74 (Eq % 3.57/3.74 («const/sets/INSERT» «type/nums/num» a_1 % 3.57/3.74 («const/iterate/..» a («const/arith/-» a_1 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))))) % 3.57/3.74 («const/iterate/..» a a_1)) % 3.57/3.74 True) % 3.57/3.74 Clause #15 (by clausification #[14]): ∀ (a a_1 : «type/nums/num»), % 3.57/3.74 Or (Eq («const/arith/<=» a a_1) False) % 3.57/3.74 (Eq % 3.57/3.74 («const/sets/INSERT» «type/nums/num» a_1 % 3.57/3.74 («const/iterate/..» a («const/arith/-» a_1 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))))) % 3.57/3.74 («const/iterate/..» a a_1)) % 3.57/3.74 Clause #16 (by superposition #[15, 10]): ∀ (a a_1 : «type/nums/num»), % 3.57/3.74 Or % 3.57/3.74 (Eq % 3.57/3.74 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» (skS.0 1 a a_1)) % 3.57/3.74 («const/iterate/..» (skS.0 0 a) % 3.57/3.74 («const/arith/-» («const/nums/SUC» (skS.0 1 a a_1)) % 3.57/3.74 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))))) % 3.57/3.74 («const/iterate/..» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1)))) % 3.57/3.74 (Eq False True) % 3.57/3.74 Clause #17 (by clausification #[11]): ∀ (a a_1 : «type/nums/num»), % 3.57/3.74 Ne («const/iterate/..» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1))) % 3.57/3.74 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» (skS.0 1 a a_1)) % 3.57/3.74 («const/iterate/..» (skS.0 0 a) (skS.0 1 a a_1))) % 3.57/3.74 Clause #18 (by clausification #[16]): ∀ (a a_1 : «type/nums/num»), % 3.57/3.74 Eq % 3.57/3.74 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» (skS.0 1 a a_1)) % 3.57/3.74 («const/iterate/..» (skS.0 0 a) % 3.57/3.74 («const/arith/-» («const/nums/SUC» (skS.0 1 a a_1)) % 3.57/3.74 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))))) % 3.57/3.74 («const/iterate/..» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1))) % 3.57/3.74 Clause #19 (by forward demodulation #[18, 4]): ∀ (a a_1 : «type/nums/num»), % 3.57/3.74 Eq % 3.57/3.74 («const/sets/INSERT» «type/nums/num» («const/nums/SUC» (skS.0 1 a a_1)) % 3.57/3.74 («const/iterate/..» (skS.0 0 a) (skS.0 1 a a_1))) % 3.57/3.74 («const/iterate/..» (skS.0 0 a) («const/nums/SUC» (skS.0 1 a a_1))) % 3.57/3.74 Clause #20 (by forward contextual literal cutting #[19, 17]): False % 3.57/3.74 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------