%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN364^5 : TPTP v9.2.0. Released v4.0.0. % 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 08:07:30 PM UTC 2025 % Result : Theorem 5.74s 5.94s % Output : Proof 5.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SYN364^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.11 % Command : duper %s % 0.11/0.31 % Computer : n020.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Thu Oct 2 15:39:53 EDT 2025 % 0.11/0.32 % CPUTime : % 5.74/5.94 SZS status Theorem for theBenchmark.p % 5.74/5.94 SZS output start Proof for theBenchmark.p % 5.74/5.94 Clause #0 (by assumption #[]): Eq % 5.74/5.94 (Not % 5.74/5.94 (And % 5.74/5.94 (And (∀ (Xx : Iota), (Exists fun Xy => cP Xx Xy) → ∀ (Xz : Iota), cP Xz Xz) % 5.74/5.94 (∀ (Xu : Iota), Exists fun Xv => Or (cP Xu Xv) (And (cM Xu) (cQ (f Xu Xv))))) % 5.74/5.94 (∀ (Xw : Iota), cQ Xw → Not (cM (g Xw))) → % 5.74/5.94 ∀ (Xu : Iota), Exists fun Xv => And (cP (g Xu) Xv) (cP Xu Xu))) % 5.74/5.94 True % 5.74/5.94 Clause #1 (by betaEtaReduce #[0]): Eq % 5.74/5.94 (Not % 5.74/5.94 (And % 5.74/5.94 (And (∀ (Xx : Iota), Exists (cP Xx) → ∀ (Xz : Iota), cP Xz Xz) % 5.74/5.94 (∀ (Xu : Iota), Exists fun Xv => Or (cP Xu Xv) (And (cM Xu) (cQ (f Xu Xv))))) % 5.74/5.94 (∀ (Xw : Iota), cQ Xw → Not (cM (g Xw))) → % 5.74/5.94 ∀ (Xu : Iota), Exists fun Xv => And (cP (g Xu) Xv) (cP Xu Xu))) % 5.74/5.94 True % 5.74/5.94 Clause #2 (by clausification #[1]): Eq % 5.74/5.94 (And % 5.74/5.94 (And (∀ (Xx : Iota), Exists (cP Xx) → ∀ (Xz : Iota), cP Xz Xz) % 5.74/5.94 (∀ (Xu : Iota), Exists fun Xv => Or (cP Xu Xv) (And (cM Xu) (cQ (f Xu Xv))))) % 5.74/5.94 (∀ (Xw : Iota), cQ Xw → Not (cM (g Xw))) → % 5.74/5.94 ∀ (Xu : Iota), Exists fun Xv => And (cP (g Xu) Xv) (cP Xu Xu)) % 5.74/5.94 False % 5.74/5.94 Clause #3 (by clausification #[2]): Eq % 5.74/5.94 (And % 5.74/5.94 (And (∀ (Xx : Iota), Exists (cP Xx) → ∀ (Xz : Iota), cP Xz Xz) % 5.74/5.94 (∀ (Xu : Iota), Exists fun Xv => Or (cP Xu Xv) (And (cM Xu) (cQ (f Xu Xv))))) % 5.74/5.94 (∀ (Xw : Iota), cQ Xw → Not (cM (g Xw)))) % 5.74/5.94 True % 5.74/5.94 Clause #4 (by clausification #[2]): Eq (∀ (Xu : Iota), Exists fun Xv => And (cP (g Xu) Xv) (cP Xu Xu)) False % 5.74/5.94 Clause #5 (by clausification #[3]): Eq (∀ (Xw : Iota), cQ Xw → Not (cM (g Xw))) True % 5.74/5.94 Clause #6 (by clausification #[3]): Eq % 5.74/5.94 (And (∀ (Xx : Iota), Exists (cP Xx) → ∀ (Xz : Iota), cP Xz Xz) % 5.74/5.94 (∀ (Xu : Iota), Exists fun Xv => Or (cP Xu Xv) (And (cM Xu) (cQ (f Xu Xv))))) % 5.74/5.94 True % 5.74/5.94 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (cQ a → Not (cM (g a))) True % 5.74/5.94 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (cQ a) False) (Eq (Not (cM (g a))) True) % 5.74/5.94 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (cQ a) False) (Eq (cM (g a)) False) % 5.74/5.94 Clause #10 (by clausification #[4]): ∀ (a : Iota), Eq (Not (Exists fun Xv => And (cP (g (skS.0 0 a)) Xv) (cP (skS.0 0 a) (skS.0 0 a)))) True % 5.74/5.94 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Exists fun Xv => And (cP (g (skS.0 0 a)) Xv) (cP (skS.0 0 a) (skS.0 0 a))) False % 5.74/5.94 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (And (cP (g (skS.0 0 a)) a_1) (cP (skS.0 0 a) (skS.0 0 a))) False % 5.74/5.94 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (cP (g (skS.0 0 a)) a_1) False) (Eq (cP (skS.0 0 a) (skS.0 0 a)) False) % 5.74/5.94 Clause #14 (by clausification #[6]): Eq (∀ (Xu : Iota), Exists fun Xv => Or (cP Xu Xv) (And (cM Xu) (cQ (f Xu Xv)))) True % 5.74/5.94 Clause #15 (by clausification #[6]): Eq (∀ (Xx : Iota), Exists (cP Xx) → ∀ (Xz : Iota), cP Xz Xz) True % 5.74/5.94 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (Exists fun Xv => Or (cP a Xv) (And (cM a) (cQ (f a Xv)))) True % 5.74/5.94 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Or (cP a (skS.0 1 a a_1)) (And (cM a) (cQ (f a (skS.0 1 a a_1))))) True % 5.74/5.94 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (cP a (skS.0 1 a a_1)) True) (Eq (And (cM a) (cQ (f a (skS.0 1 a a_1)))) True) % 5.74/5.94 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (cP a (skS.0 1 a a_1)) True) (Eq (cQ (f a (skS.0 1 a a_1))) True) % 5.74/5.94 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (cP a (skS.0 1 a a_1)) True) (Eq (cM a) True) % 5.74/5.94 Clause #21 (by superposition #[19, 9]): ∀ (a a_1 : Iota), Or (Eq (cP a (skS.0 1 a a_1)) True) (Or (Eq True False) (Eq (cM (g (f a (skS.0 1 a a_1)))) False)) % 5.74/5.94 Clause #22 (by clausification #[15]): ∀ (a : Iota), Eq (Exists (cP a) → ∀ (Xz : Iota), cP Xz Xz) True % 5.74/5.94 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (Exists (cP a)) False) (Eq (∀ (Xz : Iota), cP Xz Xz) True) % 5.74/5.94 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xz : Iota), cP Xz Xz) True) (Eq (cP a a_1) False) % 5.74/5.94 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a_1) False) (Eq (cP a_2 a_2) True) % 5.74/5.96 Clause #27 (by superposition #[20, 25]): ∀ (a a_1 : Iota), Or (Eq (cP a a) True) (Or (Eq False True) (Eq (cM a_1) True)) % 5.74/5.96 Clause #28 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (cP a (skS.0 1 a a_1)) True) (Eq (cM (g (f a (skS.0 1 a a_1)))) False) % 5.74/5.96 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (cP a a) True) (Eq (cM a_1) True) % 5.74/5.96 Clause #32 (by superposition #[29, 28]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a) True) (Or (Eq (cP a_1 (skS.0 1 a_1 a_2)) True) (Eq True False)) % 5.74/5.96 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a a) True) (Eq (cP a_1 (skS.0 1 a_1 a_2)) True) % 5.74/5.96 Clause #38 (by superposition #[34, 25]): ∀ (a a_1 : Iota), Or (Eq (cP a a) True) (Or (Eq True False) (Eq (cP a_1 a_1) True)) % 5.74/5.96 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (cP a a) True) (Eq (cP a_1 a_1) True) % 5.74/5.96 Clause #40 (by equality factoring #[39]): ∀ (a : Iota), Or (Ne True True) (Eq (cP a a) True) % 5.74/5.96 Clause #41 (by clausification #[40]): ∀ (a : Iota), Or (Eq (cP a a) True) (Or (Eq True False) (Eq True False)) % 5.74/5.96 Clause #43 (by clausification #[41]): ∀ (a : Iota), Or (Eq (cP a a) True) (Eq True False) % 5.74/5.96 Clause #44 (by clausification #[43]): ∀ (a : Iota), Eq (cP a a) True % 5.74/5.96 Clause #45 (by superposition #[44, 13]): ∀ (a : Iota), Or (Eq True False) (Eq (cP (skS.0 0 a) (skS.0 0 a)) False) % 5.74/5.96 Clause #50 (by clausification #[45]): ∀ (a : Iota), Eq (cP (skS.0 0 a) (skS.0 0 a)) False % 5.74/5.96 Clause #51 (by superposition #[50, 44]): Eq False True % 5.74/5.96 Clause #52 (by clausification #[51]): False % 5.74/5.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------