%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : COM018+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 07:45:48 PM UTC 2025 % Result : Theorem 4.92s 5.15s % Output : Proof 4.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COM018+1 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.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 15:56:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.92/5.15 SZS status Theorem for theBenchmark.p % 4.92/5.15 SZS output start Proof for theBenchmark.p % 4.92/5.15 Clause #13 (by assumption #[]): Eq % 4.92/5.15 (∀ (W0 : Iota), % 4.92/5.15 And (aRewritingSystem0 W0) (isTerminating0 W0) → % 4.92/5.15 ∀ (W1 : Iota), aElement0 W1 → Exists fun W2 => aNormalFormOfIn0 W2 W1 W0) % 4.92/5.15 True % 4.92/5.15 Clause #14 (by assumption #[]): Eq (aRewritingSystem0 xR) True % 4.92/5.15 Clause #15 (by assumption #[]): Eq (And (isLocallyConfluent0 xR) (isTerminating0 xR)) True % 4.92/5.15 Clause #21 (by assumption #[]): Eq (And (And (aElement0 xw) (sdtmndtasgtdt0 xu xR xw)) (sdtmndtasgtdt0 xv xR xw)) True % 4.92/5.15 Clause #22 (by assumption #[]): Eq (Not (Exists fun W0 => aNormalFormOfIn0 W0 xw xR)) True % 4.92/5.15 Clause #32 (by clausification #[15]): Eq (isTerminating0 xR) True % 4.92/5.15 Clause #70 (by clausification #[22]): Eq (Exists fun W0 => aNormalFormOfIn0 W0 xw xR) False % 4.92/5.15 Clause #71 (by clausification #[70]): ∀ (a : Iota), Eq (aNormalFormOfIn0 a xw xR) False % 4.92/5.15 Clause #113 (by clausification #[13]): ∀ (a : Iota), % 4.92/5.15 Eq % 4.92/5.15 (And (aRewritingSystem0 a) (isTerminating0 a) → % 4.92/5.15 ∀ (W1 : Iota), aElement0 W1 → Exists fun W2 => aNormalFormOfIn0 W2 W1 a) % 4.92/5.15 True % 4.92/5.15 Clause #114 (by clausification #[113]): ∀ (a : Iota), % 4.92/5.15 Or (Eq (And (aRewritingSystem0 a) (isTerminating0 a)) False) % 4.92/5.15 (Eq (∀ (W1 : Iota), aElement0 W1 → Exists fun W2 => aNormalFormOfIn0 W2 W1 a) True) % 4.92/5.15 Clause #115 (by clausification #[114]): ∀ (a : Iota), % 4.92/5.15 Or (Eq (∀ (W1 : Iota), aElement0 W1 → Exists fun W2 => aNormalFormOfIn0 W2 W1 a) True) % 4.92/5.15 (Or (Eq (aRewritingSystem0 a) False) (Eq (isTerminating0 a) False)) % 4.92/5.15 Clause #116 (by clausification #[115]): ∀ (a a_1 : Iota), % 4.92/5.15 Or (Eq (aRewritingSystem0 a) False) % 4.92/5.15 (Or (Eq (isTerminating0 a) False) (Eq (aElement0 a_1 → Exists fun W2 => aNormalFormOfIn0 W2 a_1 a) True)) % 4.92/5.15 Clause #117 (by clausification #[116]): ∀ (a a_1 : Iota), % 4.92/5.15 Or (Eq (aRewritingSystem0 a) False) % 4.92/5.15 (Or (Eq (isTerminating0 a) False) % 4.92/5.15 (Or (Eq (aElement0 a_1) False) (Eq (Exists fun W2 => aNormalFormOfIn0 W2 a_1 a) True))) % 4.92/5.15 Clause #118 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), % 4.92/5.15 Or (Eq (aRewritingSystem0 a) False) % 4.92/5.15 (Or (Eq (isTerminating0 a) False) % 4.92/5.15 (Or (Eq (aElement0 a_1) False) (Eq (aNormalFormOfIn0 (skS.0 0 a_1 a a_2) a_1 a) True))) % 4.92/5.15 Clause #119 (by superposition #[118, 14]): ∀ (a a_1 : Iota), % 4.92/5.15 Or (Eq (isTerminating0 xR) False) % 4.92/5.15 (Or (Eq (aElement0 a) False) (Or (Eq (aNormalFormOfIn0 (skS.0 0 a xR a_1) a xR) True) (Eq False True))) % 4.92/5.15 Clause #121 (by clausification #[21]): Eq (And (aElement0 xw) (sdtmndtasgtdt0 xu xR xw)) True % 4.92/5.15 Clause #123 (by clausification #[121]): Eq (aElement0 xw) True % 4.92/5.15 Clause #518 (by clausification #[119]): ∀ (a a_1 : Iota), % 4.92/5.15 Or (Eq (isTerminating0 xR) False) (Or (Eq (aElement0 a) False) (Eq (aNormalFormOfIn0 (skS.0 0 a xR a_1) a xR) True)) % 4.92/5.15 Clause #519 (by forward demodulation #[518, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (aElement0 a) False) (Eq (aNormalFormOfIn0 (skS.0 0 a xR a_1) a xR) True)) % 4.92/5.15 Clause #520 (by clausification #[519]): ∀ (a a_1 : Iota), Or (Eq (aElement0 a) False) (Eq (aNormalFormOfIn0 (skS.0 0 a xR a_1) a xR) True) % 4.92/5.15 Clause #524 (by superposition #[520, 123]): ∀ (a : Iota), Or (Eq (aNormalFormOfIn0 (skS.0 0 xw xR a) xw xR) True) (Eq False True) % 4.92/5.15 Clause #641 (by clausification #[524]): ∀ (a : Iota), Eq (aNormalFormOfIn0 (skS.0 0 xw xR a) xw xR) True % 4.92/5.15 Clause #642 (by superposition #[641, 71]): Eq True False % 4.92/5.15 Clause #643 (by clausification #[642]): False % 4.92/5.15 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------