TSTP Solution File: SYO371^5 by Duper---1.0
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% File : Duper---1.0
% Problem : SYO371^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n027.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 04:22:17 EDT 2023
% Result : Theorem 3.73s 3.95s
% Output : Proof 3.80s
% 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 : SYO371^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.16/0.35 % Computer : n027.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sat Aug 26 05:32:04 EDT 2023
% 0.16/0.35 % CPUTime :
% 3.73/3.95 SZS status Theorem for theBenchmark.p
% 3.73/3.95 SZS output start Proof for theBenchmark.p
% 3.73/3.95 Clause #0 (by assumption #[]): Eq (Not ((∀ (R : Prop → Prop), R cP → R cQ) → Iff cP cQ)) True
% 3.73/3.95 Clause #1 (by clausification #[0]): Eq ((∀ (R : Prop → Prop), R cP → R cQ) → Iff cP cQ) False
% 3.73/3.95 Clause #2 (by clausification #[1]): Eq (∀ (R : Prop → Prop), R cP → R cQ) True
% 3.73/3.95 Clause #3 (by clausification #[1]): Eq (Iff cP cQ) False
% 3.73/3.95 Clause #4 (by clausification #[2]): ∀ (a : Prop → Prop), Eq (a cP → a cQ) True
% 3.73/3.95 Clause #5 (by clausification #[4]): ∀ (a : Prop → Prop), Or (Eq (a cP) False) (Eq (a cQ) True)
% 3.73/3.95 Clause #6 (by identity loobHoist #[5]): ∀ (a : Prop → Prop), Or (Eq (a cQ) True) (Or (Eq (a True) False) (Eq cP False))
% 3.73/3.95 Clause #7 (by identity boolHoist #[5]): ∀ (a : Prop → Prop), Or (Eq (a cQ) True) (Or (Eq (a False) False) (Eq cP True))
% 3.73/3.95 Clause #9 (by identity boolHoist #[6]): ∀ (a : Prop → Prop), Or (Eq (a True) False) (Or (Eq cP False) (Or (Eq (a False) True) (Eq cQ True)))
% 3.73/3.95 Clause #10 (by clausification #[3]): Or (Eq cP False) (Eq cQ False)
% 3.73/3.95 Clause #11 (by clausification #[3]): Or (Eq cP True) (Eq cQ True)
% 3.73/3.95 Clause #12 (by identity loobHoist #[7]): ∀ (a : Prop → Prop), Or (Eq (a False) False) (Or (Eq cP True) (Or (Eq (a True) True) (Eq cQ False)))
% 3.73/3.95 Clause #16 (by neHoist #[12]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP True)
% 3.73/3.95 (Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) True) True)
% 3.73/3.95 (Or (Eq cQ False) (Or (Eq True False) (Eq (a_1 False) (a_2 False)))))
% 3.73/3.95 Clause #22 (by neHoist #[9]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP False)
% 3.73/3.95 (Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) False) True)
% 3.73/3.95 (Or (Eq cQ True) (Or (Eq True False) (Eq (a_1 True) (a_2 True)))))
% 3.73/3.95 Clause #52 (by betaEtaReduce #[16]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP True)
% 3.73/3.95 (Or (Eq (Ne (a_1 True) (a_2 True)) True) (Or (Eq cQ False) (Or (Eq True False) (Eq (a_1 False) (a_2 False)))))
% 3.73/3.95 Clause #53 (by clausification #[52]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP True) (Or (Eq cQ False) (Or (Eq True False) (Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True)))))
% 3.73/3.95 Clause #54 (by clausification #[53]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP True) (Or (Eq cQ False) (Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True))))
% 3.73/3.95 Clause #55 (by superposition #[54, 11]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP True) (Or (Eq (a_1 False) (a_2 False)) (Or (Ne (a_1 True) (a_2 True)) (Or (Eq cP True) (Eq False True))))
% 3.73/3.95 Clause #60 (by clausification #[55]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP True) (Or (Eq (a_1 False) (a_2 False)) (Or (Ne (a_1 True) (a_2 True)) (Eq cP True)))
% 3.73/3.95 Clause #61 (by eliminate duplicate literals #[60]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP True) (Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True)))
% 3.73/3.95 Clause #62 (by equality resolution #[61]): Or (Eq cP True) (Eq ((fun x => x) False) ((fun x => True) False))
% 3.73/3.95 Clause #69 (by betaEtaReduce #[62]): Or (Eq cP True) (Eq False True)
% 3.73/3.95 Clause #70 (by clausification #[69]): Eq cP True
% 3.73/3.95 Clause #71 (by backward demodulation #[70, 10]): Or (Eq True False) (Eq cQ False)
% 3.73/3.95 Clause #85 (by clausification #[71]): Eq cQ False
% 3.73/3.95 Clause #112 (by betaEtaReduce #[22]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP False)
% 3.73/3.95 (Or (Eq (Ne (a_1 False) (a_2 False)) True) (Or (Eq cQ True) (Or (Eq True False) (Eq (a_1 True) (a_2 True)))))
% 3.73/3.95 Clause #113 (by clausification #[112]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP False) (Or (Eq cQ True) (Or (Eq True False) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False)))))
% 3.73/3.95 Clause #114 (by clausification #[113]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.73/3.95 Or (Eq cP False) (Or (Eq cQ True) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False))))
% 3.80/3.96 Clause #115 (by forward demodulation #[114, 70]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.80/3.96 Or (Eq True False) (Or (Eq cQ True) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False))))
% 3.80/3.96 Clause #116 (by clausification #[115]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x),
% 3.80/3.96 Or (Eq cQ True) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False)))
% 3.80/3.96 Clause #117 (by equality resolution #[116]): Or (Eq cQ True) (Eq ((fun x => x) True) ((fun x => False) True))
% 3.80/3.96 Clause #124 (by betaEtaReduce #[117]): Or (Eq cQ True) (Eq True False)
% 3.80/3.96 Clause #125 (by clausification #[124]): Eq cQ True
% 3.80/3.96 Clause #126 (by superposition #[125, 85]): Eq True False
% 3.80/3.96 Clause #129 (by clausification #[126]): False
% 3.80/3.96 SZS output end Proof for theBenchmark.p
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