TSTP Solution File: SEV131^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV131^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 19:24:19 EDT 2023
% Result : Theorem 3.42s 3.58s
% Output : Proof 3.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEV131^5 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n023.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 Aug 24 02:21:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.42/3.58 SZS status Theorem for theBenchmark.p
% 3.42/3.58 SZS output start Proof for theBenchmark.p
% 3.42/3.58 Clause #0 (by assumption #[]): Eq
% 3.42/3.58 (Not
% 3.42/3.58 (∀ (Xr : a → a → Prop) (Xx Xy : a),
% 3.42/3.58 Xr Xx Xy → ∀ (Xx0 : a → Prop), (∀ (Xy0 Xz : a), And (Xr Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 Xx → Xx0 Xy))
% 3.42/3.58 True
% 3.42/3.58 Clause #1 (by clausification #[0]): Eq
% 3.42/3.58 (∀ (Xr : a → a → Prop) (Xx Xy : a),
% 3.42/3.58 Xr Xx Xy → ∀ (Xx0 : a → Prop), (∀ (Xy0 Xz : a), And (Xr Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 Xx → Xx0 Xy)
% 3.42/3.58 False
% 3.42/3.58 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a → Prop),
% 3.42/3.58 Eq
% 3.42/3.58 (Not
% 3.42/3.58 (∀ (Xx Xy : a),
% 3.42/3.58 skS.0 0 a_1 Xx Xy →
% 3.42/3.58 ∀ (Xx0 : a → Prop), (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 Xx → Xx0 Xy))
% 3.42/3.58 True
% 3.42/3.58 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a → Prop),
% 3.42/3.58 Eq
% 3.42/3.58 (∀ (Xx Xy : a),
% 3.42/3.58 skS.0 0 a_1 Xx Xy →
% 3.42/3.58 ∀ (Xx0 : a → Prop), (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 Xx → Xx0 Xy)
% 3.42/3.58 False
% 3.42/3.58 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a → Prop) (a_2 : a),
% 3.42/3.58 Eq
% 3.42/3.58 (Not
% 3.42/3.58 (∀ (Xy : a),
% 3.42/3.58 skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy →
% 3.42/3.58 ∀ (Xx0 : a → Prop),
% 3.42/3.58 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 (skS.0 1 a_1 a_2) → Xx0 Xy))
% 3.42/3.58 True
% 3.42/3.58 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a → Prop) (a_2 : a),
% 3.42/3.58 Eq
% 3.42/3.58 (∀ (Xy : a),
% 3.42/3.58 skS.0 0 a_1 (skS.0 1 a_1 a_2) Xy →
% 3.42/3.58 ∀ (Xx0 : a → Prop),
% 3.42/3.58 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 (skS.0 1 a_1 a_2) → Xx0 Xy)
% 3.42/3.58 False
% 3.42/3.58 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a),
% 3.42/3.58 Eq
% 3.42/3.58 (Not
% 3.42/3.58 (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) →
% 3.42/3.58 ∀ (Xx0 : a → Prop),
% 3.42/3.58 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) →
% 3.42/3.58 Xx0 (skS.0 1 a_1 a_2) → Xx0 (skS.0 2 a_1 a_2 a_3)))
% 3.42/3.58 True
% 3.42/3.58 Clause #7 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a),
% 3.42/3.58 Eq
% 3.42/3.58 (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3) →
% 3.42/3.58 ∀ (Xx0 : a → Prop),
% 3.42/3.58 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) →
% 3.42/3.58 Xx0 (skS.0 1 a_1 a_2) → Xx0 (skS.0 2 a_1 a_2 a_3))
% 3.42/3.58 False
% 3.42/3.58 Clause #8 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)) True
% 3.42/3.58 Clause #9 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a),
% 3.42/3.58 Eq
% 3.42/3.58 (∀ (Xx0 : a → Prop),
% 3.42/3.58 (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (Xx0 Xy0) → Xx0 Xz) → Xx0 (skS.0 1 a_1 a_2) → Xx0 (skS.0 2 a_1 a_2 a_3))
% 3.42/3.58 False
% 3.42/3.58 Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop),
% 3.42/3.58 Eq
% 3.42/3.58 (Not
% 3.42/3.58 ((∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (skS.0 3 a_1 a_2 a_3 a_4 Xy0) → skS.0 3 a_1 a_2 a_3 a_4 Xz) →
% 3.42/3.58 skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_2) → skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3)))
% 3.42/3.58 True
% 3.42/3.58 Clause #11 (by clausification #[10]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop),
% 3.42/3.58 Eq
% 3.42/3.58 ((∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (skS.0 3 a_1 a_2 a_3 a_4 Xy0) → skS.0 3 a_1 a_2 a_3 a_4 Xz) →
% 3.42/3.58 skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_2) → skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3))
% 3.42/3.58 False
% 3.42/3.58 Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop),
% 3.42/3.58 Eq (∀ (Xy0 Xz : a), And (skS.0 0 a_1 Xy0 Xz) (skS.0 3 a_1 a_2 a_3 a_4 Xy0) → skS.0 3 a_1 a_2 a_3 a_4 Xz) True
% 3.42/3.58 Clause #13 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop),
% 3.42/3.58 Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_2) → skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3)) False
% 3.42/3.58 Clause #14 (by clausification #[12]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a) (a_5 : a → Prop),
% 3.42/3.58 Eq (∀ (Xz : a), And (skS.0 0 a_1 a_2 Xz) (skS.0 3 a_1 a_3 a_4 a_5 a_2) → skS.0 3 a_1 a_3 a_4 a_5 Xz) True
% 3.42/3.58 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 a_5 : a) (a_6 : a → Prop),
% 3.42/3.59 Eq (And (skS.0 0 a_1 a_2 a_3) (skS.0 3 a_1 a_4 a_5 a_6 a_2) → skS.0 3 a_1 a_4 a_5 a_6 a_3) True
% 3.42/3.59 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 a_5 : a) (a_6 : a → Prop),
% 3.42/3.59 Or (Eq (And (skS.0 0 a_1 a_2 a_3) (skS.0 3 a_1 a_4 a_5 a_6 a_2)) False) (Eq (skS.0 3 a_1 a_4 a_5 a_6 a_3) True)
% 3.42/3.59 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 3.42/3.59 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5) True)
% 3.42/3.59 (Or (Eq (skS.0 0 a_1 a_6 a_5) False) (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_6) False))
% 3.42/3.59 Clause #18 (by superposition #[17, 8]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 3.42/3.59 Or (Eq (skS.0 3 (fun x x_1 => a_1 x x_1) a_2 a_3 a_4 (skS.0 2 a_1 a_5 a_6)) True)
% 3.42/3.59 (Or (Eq (skS.0 3 (fun x x_1 => a_1 x x_1) a_2 a_3 a_4 (skS.0 1 a_1 a_5)) False) (Eq False True))
% 3.42/3.59 Clause #19 (by clausification #[13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_2)) True
% 3.42/3.59 Clause #20 (by clausification #[13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_3)) False
% 3.42/3.59 Clause #21 (by betaEtaReduce #[18]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 3.42/3.59 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_5 a_6)) True)
% 3.42/3.59 (Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_5)) False) (Eq False True))
% 3.42/3.59 Clause #22 (by clausification #[21]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 3.42/3.59 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_5 a_6)) True) (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 1 a_1 a_5)) False)
% 3.42/3.59 Clause #23 (by superposition #[22, 19]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 3.42/3.59 Or (Eq (skS.0 3 (fun x x_1 => a_1 x x_1) a_2 a_3 (fun x => a_4 x) (skS.0 2 (fun x x_1 => a_1 x x_1) a_2 a_5)) True)
% 3.42/3.59 (Eq False True)
% 3.42/3.59 Clause #24 (by betaEtaReduce #[23]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 3.42/3.59 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_5)) True) (Eq False True)
% 3.42/3.59 Clause #25 (by clausification #[24]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a), Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 2 a_1 a_2 a_5)) True
% 3.42/3.59 Clause #26 (by superposition #[25, 20]): Eq True False
% 3.42/3.59 Clause #27 (by clausification #[26]): False
% 3.42/3.59 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------