TSTP Solution File: SEU932^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU932^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 : Thu Aug 31 16:44:20 EDT 2023
% Result : Theorem 3.64s 3.79s
% Output : Proof 3.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU932^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 18:46:11 EDT 2023
% 0.14/0.34 % CPUTime :
% 3.64/3.79 SZS status Theorem for theBenchmark.p
% 3.64/3.79 SZS output start Proof for theBenchmark.p
% 3.64/3.79 Clause #0 (by assumption #[]): Eq
% 3.64/3.79 (Not
% 3.64/3.79 (∀ (Xf : Iota → Iota),
% 3.64/3.79 (Exists fun Xg =>
% 3.64/3.79 And (Eq (fun Xx => Xf (Xg Xx)) fun Xx => Xg (Xf Xx))
% 3.64/3.79 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx))) →
% 3.64/3.79 Exists fun Xy => Eq (Xf Xy) Xy))
% 3.64/3.79 True
% 3.64/3.79 Clause #1 (by clausification #[0]): Eq
% 3.64/3.79 (∀ (Xf : Iota → Iota),
% 3.64/3.79 (Exists fun Xg =>
% 3.64/3.79 And (Eq (fun Xx => Xf (Xg Xx)) fun Xx => Xg (Xf Xx))
% 3.64/3.79 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx))) →
% 3.64/3.79 Exists fun Xy => Eq (Xf Xy) Xy)
% 3.64/3.79 False
% 3.64/3.79 Clause #2 (by clausification #[1]): ∀ (a : Iota → Iota),
% 3.64/3.79 Eq
% 3.64/3.79 (Not
% 3.64/3.79 ((Exists fun Xg =>
% 3.64/3.79 And (Eq (fun Xx => skS.0 0 a (Xg Xx)) fun Xx => Xg (skS.0 0 a Xx))
% 3.64/3.79 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx))) →
% 3.64/3.79 Exists fun Xy => Eq (skS.0 0 a Xy) Xy))
% 3.64/3.79 True
% 3.64/3.79 Clause #3 (by clausification #[2]): ∀ (a : Iota → Iota),
% 3.64/3.79 Eq
% 3.64/3.79 ((Exists fun Xg =>
% 3.64/3.79 And (Eq (fun Xx => skS.0 0 a (Xg Xx)) fun Xx => Xg (skS.0 0 a Xx))
% 3.64/3.79 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx))) →
% 3.64/3.79 Exists fun Xy => Eq (skS.0 0 a Xy) Xy)
% 3.64/3.79 False
% 3.64/3.79 Clause #4 (by clausification #[3]): ∀ (a : Iota → Iota),
% 3.64/3.79 Eq
% 3.64/3.79 (Exists fun Xg =>
% 3.64/3.79 And (Eq (fun Xx => skS.0 0 a (Xg Xx)) fun Xx => Xg (skS.0 0 a Xx))
% 3.64/3.79 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx)))
% 3.64/3.79 True
% 3.64/3.79 Clause #5 (by clausification #[3]): ∀ (a : Iota → Iota), Eq (Exists fun Xy => Eq (skS.0 0 a Xy) Xy) False
% 3.64/3.79 Clause #6 (by clausification #[4]): ∀ (a a_1 : Iota → Iota),
% 3.64/3.79 Eq
% 3.64/3.79 (And (Eq (fun Xx => skS.0 0 a (skS.0 1 a a_1 Xx)) fun Xx => skS.0 1 a a_1 (skS.0 0 a Xx))
% 3.64/3.79 (Exists fun Xx => And (Eq (skS.0 1 a a_1 Xx) Xx) (∀ (Xz : Iota), Eq (skS.0 1 a a_1 Xz) Xz → Eq Xz Xx)))
% 3.64/3.79 True
% 3.64/3.79 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota → Iota),
% 3.64/3.79 Eq (Exists fun Xx => And (Eq (skS.0 1 a a_1 Xx) Xx) (∀ (Xz : Iota), Eq (skS.0 1 a a_1 Xz) Xz → Eq Xz Xx)) True
% 3.64/3.79 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota → Iota), Eq (Eq (fun Xx => skS.0 0 a (skS.0 1 a a_1 Xx)) fun Xx => skS.0 1 a a_1 (skS.0 0 a Xx)) True
% 3.64/3.79 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota),
% 3.64/3.79 Eq
% 3.64/3.79 (And (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_2))
% 3.64/3.79 (∀ (Xz : Iota), Eq (skS.0 1 a a_1 Xz) Xz → Eq Xz (skS.0 2 a a_1 a_2)))
% 3.64/3.79 True
% 3.64/3.79 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Eq (∀ (Xz : Iota), Eq (skS.0 1 a a_1 Xz) Xz → Eq Xz (skS.0 2 a a_1 a_2)) True
% 3.64/3.79 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Eq (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_2)) True
% 3.64/3.79 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Eq (Eq (skS.0 1 a a_1 a_2) a_2 → Eq a_2 (skS.0 2 a a_1 a_3)) True
% 3.64/3.79 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota),
% 3.64/3.79 Or (Eq (Eq (skS.0 1 a a_1 a_2) a_2) False) (Eq (Eq a_2 (skS.0 2 a a_1 a_3)) True)
% 3.64/3.79 Clause #14 (by clausification #[13]): ∀ (a : Iota) (a_1 a_2 : Iota → Iota) (a_3 : Iota), Or (Eq (Eq a (skS.0 2 a_1 a_2 a_3)) True) (Ne (skS.0 1 a_1 a_2 a) a)
% 3.64/3.79 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Or (Ne (skS.0 1 a a_1 a_2) a_2) (Eq a_2 (skS.0 2 a a_1 a_3))
% 3.64/3.79 Clause #16 (by clausification #[5]): ∀ (a : Iota → Iota) (a_1 : Iota), Eq (Eq (skS.0 0 a a_1) a_1) False
% 3.64/3.79 Clause #17 (by clausification #[16]): ∀ (a : Iota → Iota) (a_1 : Iota), Ne (skS.0 0 a a_1) a_1
% 3.64/3.79 Clause #18 (by clausification #[11]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_2)
% 3.64/3.79 Clause #19 (by superposition #[18, 15]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota),
% 3.64/3.79 Or (Ne (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_2)) (Eq (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_3))
% 3.64/3.79 Clause #20 (by clausification #[8]): ∀ (a a_1 : Iota → Iota), Eq (fun Xx => skS.0 0 a (skS.0 1 a a_1 Xx)) fun Xx => skS.0 1 a a_1 (skS.0 0 a Xx)
% 3.64/3.80 Clause #21 (by argument congruence #[20]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota),
% 3.64/3.80 Eq ((fun Xx => skS.0 0 a (skS.0 1 a a_1 Xx)) a_2) ((fun Xx => skS.0 1 a a_1 (skS.0 0 a Xx)) a_2)
% 3.64/3.80 Clause #23 (by betaEtaReduce #[21]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Eq (skS.0 0 a (skS.0 1 a a_1 a_2)) (skS.0 1 a a_1 (skS.0 0 a a_2))
% 3.64/3.80 Clause #24 (by superposition #[23, 15]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota),
% 3.64/3.80 Or (Ne (skS.0 0 a (skS.0 1 a a_1 a_2)) (skS.0 0 a a_2)) (Eq (skS.0 0 a a_2) (skS.0 2 a a_1 a_3))
% 3.64/3.80 Clause #25 (by eliminate resolved literals #[19]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Eq (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_3)
% 3.64/3.80 Clause #26 (by superposition #[24, 18]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota),
% 3.64/3.80 Or (Ne (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 0 a (skS.0 2 a a_1 a_2)))
% 3.64/3.80 (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_3))
% 3.64/3.80 Clause #29 (by eliminate resolved literals #[26]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_3)
% 3.64/3.80 Clause #30 (by superposition #[29, 17]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Ne (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_3)
% 3.64/3.80 Clause #36 (by forward contextual literal cutting #[30, 25]): False
% 3.64/3.80 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------