%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV096^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 4.82s 5.01s % Output : Proof 4.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEV096^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n018.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 01:00:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.82/5.01 SZS status Theorem for theBenchmark.p % 4.82/5.01 SZS output start Proof for theBenchmark.p % 4.82/5.01 Clause #0 (by assumption #[]): Eq % 4.82/5.01 (Not % 4.82/5.01 (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx) → % 4.82/5.01 And % 4.82/5.01 (And (∀ (Xx : a), Exists fun Xy => f Xx Xy) % 4.82/5.01 (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) % 4.82/5.01 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) → % 4.82/5.01 ∀ (Xy : b), Exists fun Xx => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z)))) % 4.82/5.01 True % 4.82/5.01 Clause #1 (by betaEtaReduce #[0]): Eq % 4.82/5.01 (Not % 4.82/5.01 (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx) → % 4.82/5.01 And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) % 4.82/5.01 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) → % 4.82/5.01 ∀ (Xy : b), Exists fun Xx => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z)))) % 4.82/5.01 True % 4.82/5.01 Clause #2 (by clausification #[1]): Eq % 4.82/5.01 (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx) → % 4.82/5.01 And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) % 4.82/5.01 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) → % 4.82/5.01 ∀ (Xy : b), Exists fun Xx => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z))) % 4.82/5.01 False % 4.82/5.01 Clause #3 (by clausification #[2]): Eq (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx)) True % 4.82/5.01 Clause #4 (by clausification #[2]): Eq % 4.82/5.01 (And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2)) % 4.82/5.01 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) → % 4.82/5.01 ∀ (Xy : b), Exists fun Xx => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z))) % 4.82/5.01 False % 4.82/5.01 Clause #5 (by clausification #[3]): Eq (∀ (Xx : a), cR Xx Xx) True % 4.82/5.01 Clause #7 (by clausification #[5]): ∀ (a : a), Eq (cR a a) True % 4.82/5.01 Clause #17 (by clausification #[4]): Eq (∀ (Xy : b), Exists fun Xx => ∀ (Xw : a), Or (f Xx Xy) (And (Not (f Xw Xy)) (cR Xx z))) False % 4.82/5.01 Clause #25 (by clausification #[17]): ∀ (a_1 : b), % 4.82/5.01 Eq (Not (Exists fun Xx => ∀ (Xw : a), Or (f Xx (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR Xx z)))) True % 4.82/5.01 Clause #26 (by clausification #[25]): ∀ (a_1 : b), Eq (Exists fun Xx => ∀ (Xw : a), Or (f Xx (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR Xx z))) False % 4.82/5.01 Clause #27 (by clausification #[26]): ∀ (a_1 : a) (a_2 : b), Eq (∀ (Xw : a), Or (f a_1 (skS.0 0 a_2)) (And (Not (f Xw (skS.0 0 a_2))) (cR a_1 z))) False % 4.82/5.01 Clause #28 (by clausification #[27]): ∀ (a_1 : a) (a_2 : b) (a_3 : a), % 4.82/5.01 Eq (Not (Or (f a_1 (skS.0 0 a_2)) (And (Not (f (skS.0 1 a_1 a_2 a_3) (skS.0 0 a_2))) (cR a_1 z)))) True % 4.82/5.01 Clause #29 (by clausification #[28]): ∀ (a_1 : a) (a_2 : b) (a_3 : a), % 4.82/5.01 Eq (Or (f a_1 (skS.0 0 a_2)) (And (Not (f (skS.0 1 a_1 a_2 a_3) (skS.0 0 a_2))) (cR a_1 z))) False % 4.82/5.01 Clause #30 (by clausification #[29]): ∀ (a_1 : a) (a_2 : b) (a_3 : a), Eq (And (Not (f (skS.0 1 a_1 a_2 a_3) (skS.0 0 a_2))) (cR a_1 z)) False % 4.82/5.01 Clause #31 (by clausification #[29]): ∀ (a : a) (a_1 : b), Eq (f a (skS.0 0 a_1)) False % 4.82/5.01 Clause #32 (by clausification #[30]): ∀ (a_1 : a) (a_2 : b) (a_3 : a), Or (Eq (Not (f (skS.0 1 a_1 a_2 a_3) (skS.0 0 a_2))) False) (Eq (cR a_1 z) False) % 4.82/5.01 Clause #33 (by clausification #[32]): ∀ (a_1 : a) (a_2 : b) (a_3 : a), Or (Eq (cR a_1 z) False) (Eq (f (skS.0 1 a_1 a_2 a_3) (skS.0 0 a_2)) True) % 4.82/5.01 Clause #34 (by superposition #[33, 7]): ∀ (a_1 : b) (a_2 : a), Or (Eq (f (skS.0 1 z a_1 a_2) (skS.0 0 a_1)) True) (Eq False True) % 4.82/5.01 Clause #49 (by clausification #[34]): ∀ (a_1 : b) (a_2 : a), Eq (f (skS.0 1 z a_1 a_2) (skS.0 0 a_1)) True % 4.82/5.01 Clause #50 (by superposition #[49, 31]): Eq True False % 4.82/5.01 Clause #54 (by clausification #[50]): False % 4.82/5.01 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------