TSTP Solution File: SYO375^5 by Duper---1.0
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% File : Duper---1.0
% Problem : SYO375^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 Sep 1 04:22:18 EDT 2023
% Result : Theorem 3.63s 3.81s
% Output : Proof 3.63s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO375^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n004.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 : Sat Aug 26 06:05:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.63/3.81 SZS status Theorem for theBenchmark.p
% 3.63/3.81 SZS output start Proof for theBenchmark.p
% 3.63/3.81 Clause #0 (by assumption #[]): Eq (Not (∀ (X Y : Iota → Prop), (∀ (W : Iota), Iff (X W) (Y W)) → ∀ (Xx : Iota), Iff (X Xx) (Y Xx))) True
% 3.63/3.81 Clause #1 (by clausification #[0]): Eq (∀ (X Y : Iota → Prop), (∀ (W : Iota), Iff (X W) (Y W)) → ∀ (Xx : Iota), Iff (X Xx) (Y Xx)) False
% 3.63/3.81 Clause #2 (by clausification #[1]): ∀ (a : Iota → Prop),
% 3.63/3.81 Eq (Not (∀ (Y : Iota → Prop), (∀ (W : Iota), Iff (skS.0 0 a W) (Y W)) → ∀ (Xx : Iota), Iff (skS.0 0 a Xx) (Y Xx)))
% 3.63/3.81 True
% 3.63/3.81 Clause #3 (by clausification #[2]): ∀ (a : Iota → Prop),
% 3.63/3.81 Eq (∀ (Y : Iota → Prop), (∀ (W : Iota), Iff (skS.0 0 a W) (Y W)) → ∀ (Xx : Iota), Iff (skS.0 0 a Xx) (Y Xx)) False
% 3.63/3.81 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota → Prop),
% 3.63/3.81 Eq (Not ((∀ (W : Iota), Iff (skS.0 0 a W) (skS.0 1 a a_1 W)) → ∀ (Xx : Iota), Iff (skS.0 0 a Xx) (skS.0 1 a a_1 Xx)))
% 3.63/3.81 True
% 3.63/3.81 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota → Prop),
% 3.63/3.81 Eq ((∀ (W : Iota), Iff (skS.0 0 a W) (skS.0 1 a a_1 W)) → ∀ (Xx : Iota), Iff (skS.0 0 a Xx) (skS.0 1 a a_1 Xx)) False
% 3.63/3.81 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota → Prop), Eq (∀ (W : Iota), Iff (skS.0 0 a W) (skS.0 1 a a_1 W)) True
% 3.63/3.81 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota → Prop), Eq (∀ (Xx : Iota), Iff (skS.0 0 a Xx) (skS.0 1 a a_1 Xx)) False
% 3.63/3.81 Clause #8 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 : Iota) (a_2 : Iota → Prop), Eq (Iff (skS.0 0 a a_1) (skS.0 1 a a_2 a_1)) True
% 3.63/3.81 Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (skS.0 0 a a_1) True) (Eq (skS.0 1 a a_2 a_1) False)
% 3.63/3.81 Clause #10 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (skS.0 0 a a_1) False) (Eq (skS.0 1 a a_2 a_1) True)
% 3.63/3.81 Clause #11 (by clausification #[7]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota),
% 3.63/3.81 Eq (Not (Iff (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)))) True
% 3.63/3.81 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), Eq (Iff (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1 (skS.0 2 a a_1 a_2))) False
% 3.63/3.81 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota),
% 3.63/3.81 Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) False) (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) False)
% 3.63/3.81 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota),
% 3.63/3.81 Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) True)
% 3.63/3.81 Clause #15 (by superposition #[14, 9]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota),
% 3.63/3.81 Or (Eq (skS.0 0 (fun x => a x) (skS.0 2 (fun x => a x) (fun x => a_1 x) a_2)) True)
% 3.63/3.81 (Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Eq True False))
% 3.63/3.81 Clause #16 (by betaEtaReduce #[15]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota),
% 3.63/3.81 Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Eq True False))
% 3.63/3.81 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota),
% 3.63/3.81 Or (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True) (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True)
% 3.63/3.81 Clause #18 (by eliminate duplicate literals #[17]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) True
% 3.63/3.81 Clause #19 (by backward demodulation #[18, 13]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), Or (Eq True False) (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) False)
% 3.63/3.81 Clause #21 (by superposition #[18, 10]): ∀ (a a_1 a_2 : Iota → Prop) (a_3 : Iota), Or (Eq True False) (Eq (skS.0 1 a a_1 (skS.0 2 a a_2 a_3)) True)
% 3.63/3.81 Clause #22 (by clausification #[19]): ∀ (a a_1 : Iota → Prop) (a_2 : Iota), Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) False
% 3.63/3.81 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota → Prop) (a_3 : Iota), Eq (skS.0 1 a a_1 (skS.0 2 a a_2 a_3)) True
% 3.63/3.81 Clause #24 (by superposition #[23, 22]): Eq True False
% 3.63/3.81 Clause #26 (by clausification #[24]): False
% 3.63/3.81 SZS output end Proof for theBenchmark.p
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