%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV097^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 08:02:50 PM UTC 2025 % Result : Theorem 3.75s 3.91s % Output : Proof 3.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEV097^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n012.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 01:22:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.75/3.91 SZS status Theorem for theBenchmark.p % 3.75/3.91 SZS output start Proof for theBenchmark.p % 3.75/3.91 Clause #0 (by assumption #[]): Eq % 3.75/3.91 (Not % 3.75/3.91 (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx) → % 3.75/3.91 And % 3.75/3.91 (And (∀ (Xx : a), Exists fun Xy => f Xx Xy) % 3.75/3.91 (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) % 3.75/3.91 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) → % 3.75/3.91 ∀ (Xx : a), Exists fun Xy => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z)))) % 3.75/3.91 True % 3.75/3.91 Clause #1 (by betaEtaReduce #[0]): Eq % 3.75/3.91 (Not % 3.75/3.91 (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx) → % 3.75/3.91 And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) % 3.75/3.91 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) → % 3.75/3.91 ∀ (Xx : a), Exists fun Xy => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z)))) % 3.75/3.91 True % 3.75/3.91 Clause #2 (by clausification #[1]): Eq % 3.75/3.91 (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx) → % 3.75/3.91 And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) % 3.75/3.91 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) → % 3.75/3.91 ∀ (Xx : a), Exists fun Xy => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z))) % 3.75/3.91 False % 3.75/3.91 Clause #4 (by clausification #[2]): Eq % 3.75/3.91 (And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) % 3.75/3.91 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) → % 3.75/3.91 ∀ (Xx : a), Exists fun Xy => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z))) % 3.75/3.91 False % 3.75/3.91 Clause #16 (by clausification #[4]): Eq % 3.75/3.91 (And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) % 3.75/3.91 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2)) % 3.75/3.91 True % 3.75/3.91 Clause #17 (by clausification #[4]): Eq (∀ (Xx : a), Exists fun Xy => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z))) False % 3.75/3.91 Clause #19 (by clausification #[16]): Eq (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) True % 3.75/3.91 Clause #25 (by clausification #[17]): ∀ (a_1 : a), % 3.75/3.91 Eq (Not (Exists fun Xy => ∀ (Xw : a), Or (f (skS.0 0 a_1) Xy) (And (Not (f Xw Xy)) (cR (skS.0 0 a_1) z)))) True % 3.75/3.91 Clause #26 (by clausification #[25]): ∀ (a_1 : a), Eq (Exists fun Xy => ∀ (Xw : a), Or (f (skS.0 0 a_1) Xy) (And (Not (f Xw Xy)) (cR (skS.0 0 a_1) z))) False % 3.75/3.91 Clause #27 (by clausification #[26]): ∀ (a_1 : a) (a_2 : b), Eq (∀ (Xw : a), Or (f (skS.0 0 a_1) a_2) (And (Not (f Xw a_2)) (cR (skS.0 0 a_1) z))) False % 3.75/3.91 Clause #28 (by clausification #[27]): ∀ (a_1 : a) (a_2 : b) (a_3 : a), % 3.75/3.91 Eq (Not (Or (f (skS.0 0 a_1) a_2) (And (Not (f (skS.0 1 a_1 a_2 a_3) a_2)) (cR (skS.0 0 a_1) z)))) True % 3.75/3.91 Clause #29 (by clausification #[28]): ∀ (a_1 : a) (a_2 : b) (a_3 : a), % 3.75/3.91 Eq (Or (f (skS.0 0 a_1) a_2) (And (Not (f (skS.0 1 a_1 a_2 a_3) a_2)) (cR (skS.0 0 a_1) z))) False % 3.75/3.91 Clause #31 (by clausification #[29]): ∀ (a_1 : a) (a_2 : b), Eq (f (skS.0 0 a_1) a_2) False % 3.75/3.91 Clause #35 (by clausification #[19]): Eq (∀ (Xx : a), Exists (f Xx)) True % 3.75/3.91 Clause #41 (by clausification #[35]): ∀ (a : a), Eq (Exists (f a)) True % 3.75/3.91 Clause #42 (by clausification #[41]): ∀ (a_1 : a) (a_2 : b), Eq (f a_1 (skS.0 2 a_1 a_2)) True % 3.75/3.91 Clause #43 (by superposition #[42, 31]): Eq True False % 3.75/3.91 Clause #46 (by clausification #[43]): False % 3.75/3.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------