TSTP Solution File: SET638^5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET638^5 : TPTP v8.1.2. 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 : Thu Aug 31 14:47:13 EDT 2023
% Result : Theorem 3.90s 4.11s
% Output : Proof 3.90s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET638^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : duper %s
% 0.14/0.37 % Computer : n020.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sat Aug 26 08:48:44 EDT 2023
% 0.14/0.37 % CPUTime :
% 3.90/4.11 SZS status Theorem for theBenchmark.p
% 3.90/4.11 SZS output start Proof for theBenchmark.p
% 3.90/4.11 Clause #0 (by assumption #[]): Eq
% 3.90/4.11 (Not
% 3.90/4.11 (∀ (X Y Z : a → Prop),
% 3.90/4.11 And (∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx)) (Eq (fun Xx => And (X Xx) (Z Xx)) fun Xx => False) →
% 3.90/4.11 ∀ (Xx : a), X Xx → Y Xx))
% 3.90/4.11 True
% 3.90/4.11 Clause #1 (by clausification #[0]): Eq
% 3.90/4.11 (∀ (X Y Z : a → Prop),
% 3.90/4.11 And (∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx)) (Eq (fun Xx => And (X Xx) (Z Xx)) fun Xx => False) →
% 3.90/4.11 ∀ (Xx : a), X Xx → Y Xx)
% 3.90/4.11 False
% 3.90/4.11 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop),
% 3.90/4.11 Eq
% 3.90/4.11 (Not
% 3.90/4.11 (∀ (Y Z : a → Prop),
% 3.90/4.11 And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx))
% 3.90/4.11 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) fun Xx => False) →
% 3.90/4.11 ∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx))
% 3.90/4.11 True
% 3.90/4.11 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop),
% 3.90/4.11 Eq
% 3.90/4.11 (∀ (Y Z : a → Prop),
% 3.90/4.11 And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx)) (Eq (fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) fun Xx => False) →
% 3.90/4.11 ∀ (Xx : a), skS.0 0 a_1 Xx → Y Xx)
% 3.90/4.11 False
% 3.90/4.11 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop),
% 3.90/4.11 Eq
% 3.90/4.11 (Not
% 3.90/4.11 (∀ (Z : a → Prop),
% 3.90/4.11 And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx))
% 3.90/4.11 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) fun Xx => False) →
% 3.90/4.11 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx))
% 3.90/4.11 True
% 3.90/4.11 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop),
% 3.90/4.11 Eq
% 3.90/4.11 (∀ (Z : a → Prop),
% 3.90/4.11 And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx))
% 3.90/4.11 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) fun Xx => False) →
% 3.90/4.11 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 3.90/4.11 False
% 3.90/4.11 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.90/4.11 Eq
% 3.90/4.11 (Not
% 3.90/4.11 (And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))
% 3.90/4.11 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False) →
% 3.90/4.11 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx))
% 3.90/4.11 True
% 3.90/4.11 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.90/4.11 Eq
% 3.90/4.11 (And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))
% 3.90/4.11 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False) →
% 3.90/4.11 ∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 3.90/4.11 False
% 3.90/4.11 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 3.90/4.11 Eq
% 3.90/4.11 (And (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx))
% 3.90/4.11 (Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False))
% 3.90/4.11 True
% 3.90/4.11 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) False
% 3.90/4.11 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False) True
% 3.90/4.11 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) True
% 3.90/4.11 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) fun Xx => False
% 3.90/4.11 Clause #13 (by argument congruence #[12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.90/4.11 Eq ((fun Xx => And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) a_4) ((fun Xx => False) a_4)
% 3.90/4.11 Clause #14 (by clausification #[9]): ∀ (a_1 a_2 : a → Prop) (a_3 : a),
% 3.90/4.11 Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3))) True
% 3.90/4.11 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False
% 3.90/4.11 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True
% 3.90/4.11 Clause #17 (by clausification #[15]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False
% 3.90/4.11 Clause #18 (by betaEtaReduce #[13]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Eq (And (skS.0 0 a_1 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) False
% 3.90/4.13 Clause #19 (by clausification #[18]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Or (Eq (skS.0 0 a_1 a_2) False) (Eq (skS.0 2 a_1 a_3 a_4 a_2) False)
% 3.90/4.13 Clause #20 (by superposition #[19, 16]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 3.90/4.13 Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_3 (skS.0 3 a_1 a_4 a_5)) False) (Eq False True)
% 3.90/4.13 Clause #21 (by betaEtaReduce #[20]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5)) False) (Eq False True)
% 3.90/4.13 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5)) False
% 3.90/4.13 Clause #23 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop),
% 3.90/4.13 Eq (skS.0 0 a_1 a_2 → Or (skS.0 1 a_1 a_3 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) True
% 3.90/4.13 Clause #24 (by clausification #[23]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop),
% 3.90/4.13 Or (Eq (skS.0 0 a_1 a_2) False) (Eq (Or (skS.0 1 a_1 a_3 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) True)
% 3.90/4.13 Clause #25 (by clausification #[24]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop),
% 3.90/4.13 Or (Eq (skS.0 0 a_1 a_2) False) (Or (Eq (skS.0 1 a_1 a_3 a_2) True) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True))
% 3.90/4.13 Clause #26 (by superposition #[25, 16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.90/4.13 Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 3.90/4.13 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) (Eq False True))
% 3.90/4.13 Clause #27 (by betaEtaReduce #[26]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.90/4.13 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 3.90/4.13 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True) (Eq False True))
% 3.90/4.13 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 3.90/4.13 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_3 a_4)) True)
% 3.90/4.13 Clause #29 (by superposition #[28, 22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 3.90/4.13 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 (fun x => a_1 x) (fun x => a_3 x) a_4)) True)
% 3.90/4.13 (Eq True False)
% 3.90/4.13 Clause #30 (by betaEtaReduce #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq True False)
% 3.90/4.13 Clause #31 (by clausification #[30]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True
% 3.90/4.13 Clause #33 (by superposition #[31, 17]): Eq True False
% 3.90/4.13 Clause #35 (by clausification #[33]): False
% 3.90/4.13 SZS output end Proof for theBenchmark.p
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