TSTP Solution File: SYO299^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO299^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 04:22:05 EDT 2023
% Result : Theorem 3.53s 3.77s
% Output : Proof 3.53s
% 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 : SYO299^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 01:28:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.53/3.77 SZS status Theorem for theBenchmark.p
% 3.53/3.77 SZS output start Proof for theBenchmark.p
% 3.53/3.77 Clause #0 (by assumption #[]): Eq (Not (∀ (P Q R : Prop), Exists fun S => Iff (Iff P Q) R → Iff P (Iff Q S))) True
% 3.53/3.77 Clause #1 (by clausification #[0]): Eq (∀ (P Q R : Prop), Exists fun S => Iff (Iff P Q) R → Iff P (Iff Q S)) False
% 3.53/3.77 Clause #2 (by clausification #[1]): ∀ (a : Prop), Eq (Not (∀ (Q R : Prop), Exists fun S => Iff (Iff (skS.0 0 a) Q) R → Iff (skS.0 0 a) (Iff Q S))) True
% 3.53/3.77 Clause #3 (by clausification #[2]): ∀ (a : Prop), Eq (∀ (Q R : Prop), Exists fun S => Iff (Iff (skS.0 0 a) Q) R → Iff (skS.0 0 a) (Iff Q S)) False
% 3.53/3.77 Clause #4 (by clausification #[3]): ∀ (a a_1 : Prop),
% 3.53/3.77 Eq
% 3.53/3.77 (Not
% 3.53/3.77 (∀ (R : Prop), Exists fun S => Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) R → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) S)))
% 3.53/3.77 True
% 3.53/3.77 Clause #5 (by clausification #[4]): ∀ (a a_1 : Prop),
% 3.53/3.77 Eq (∀ (R : Prop), Exists fun S => Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) R → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) S))
% 3.53/3.77 False
% 3.53/3.77 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.77 Eq
% 3.53/3.77 (Not
% 3.53/3.77 (Exists fun S =>
% 3.53/3.77 Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) S)))
% 3.53/3.77 True
% 3.53/3.77 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.77 Eq
% 3.53/3.77 (Exists fun S =>
% 3.53/3.77 Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) S))
% 3.53/3.77 False
% 3.53/3.77 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Prop),
% 3.53/3.77 Eq (Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) a_3)) False
% 3.53/3.77 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Prop), Eq (Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) a_2)) False
% 3.53/3.77 Clause #31 (by clausification #[10]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) False) (Eq (Iff (skS.0 1 a a_1) a_2) False)
% 3.53/3.77 Clause #32 (by clausification #[10]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) True) (Eq (Iff (skS.0 1 a a_1) a_2) True)
% 3.53/3.77 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a a_1) False) (Eq a_2 False))
% 3.53/3.77 Clause #34 (by clausification #[31]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a a_1) True) (Eq a_2 True))
% 3.53/3.77 Clause #35 (by identity loobHoist #[33]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq a_2 False) (Or (Eq (skS.0 0 True) False) (Eq a False)))
% 3.53/3.77 Clause #37 (by identity loobHoist #[35]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.77 Or (Eq a False) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a_1 True) False) (Eq a_2 False))))
% 3.53/3.77 Clause #39 (by identity loobHoist #[37]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.77 Or (Eq a False)
% 3.53/3.77 (Or (Eq (skS.0 0 True) False)
% 3.53/3.77 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 True True) False) (Eq a_1 False)))))
% 3.53/3.77 Clause #41 (by eliminate duplicate literals #[39]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.77 Or (Eq a False) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) False))))
% 3.53/3.77 Clause #42 (by falseElim #[41]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False)))
% 3.53/3.77 Clause #43 (by identity loobHoist #[34]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq a_2 True) (Or (Eq (skS.0 0 True) False) (Eq a False)))
% 3.53/3.77 Clause #45 (by identity loobHoist #[43]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.77 Or (Eq a True) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a_1 True) True) (Eq a_2 False))))
% 3.53/3.77 Clause #47 (by identity loobHoist #[45]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.77 Or (Eq a True)
% 3.53/3.77 (Or (Eq (skS.0 0 True) False)
% 3.53/3.77 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 True True) True) (Eq a_1 False)))))
% 3.53/3.77 Clause #49 (by eliminate duplicate literals #[47]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.77 Or (Eq a True) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) True))))
% 3.53/3.77 Clause #50 (by clausification #[32]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) True) (Or (Eq (skS.0 1 a a_1) True) (Eq a_2 False))
% 3.53/3.77 Clause #51 (by clausification #[32]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) True) (Or (Eq (skS.0 1 a a_1) False) (Eq a_2 True))
% 3.53/3.79 Clause #52 (by identity loobHoist #[50]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq a_2 False) (Or (Eq (skS.0 0 True) True) (Eq a False)))
% 3.53/3.79 Clause #54 (by identity loobHoist #[52]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.79 Or (Eq a False) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a_1 True) True) (Eq a_2 False))))
% 3.53/3.79 Clause #56 (by identity loobHoist #[54]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.79 Or (Eq a False)
% 3.53/3.79 (Or (Eq (skS.0 0 True) True)
% 3.53/3.79 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 True True) True) (Eq a_1 False)))))
% 3.53/3.79 Clause #58 (by eliminate duplicate literals #[56]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.79 Or (Eq a False) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) True))))
% 3.53/3.79 Clause #59 (by falseElim #[58]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) True)))
% 3.53/3.79 Clause #60 (by identity loobHoist #[51]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq a_2 True) (Or (Eq (skS.0 0 True) True) (Eq a False)))
% 3.53/3.79 Clause #62 (by identity loobHoist #[60]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.79 Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a_1 True) False) (Eq a_2 False))))
% 3.53/3.79 Clause #64 (by identity loobHoist #[62]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.79 Or (Eq a True)
% 3.53/3.79 (Or (Eq (skS.0 0 True) True)
% 3.53/3.79 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 True True) False) (Eq a_1 False)))))
% 3.53/3.79 Clause #66 (by eliminate duplicate literals #[64]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.79 Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) False))))
% 3.53/3.79 Clause #67 (by falseElim #[66]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False)))
% 3.53/3.79 Clause #90 (by falseElim #[67]): ∀ (a : Prop), Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) False))
% 3.53/3.79 Clause #111 (by falseElim #[59]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Eq (skS.0 1 True True) True))
% 3.53/3.79 Clause #112 (by falseElim #[111]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) True)
% 3.53/3.79 Clause #113 (by superposition #[112, 90]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Eq True False)))
% 3.53/3.79 Clause #114 (by clausification #[113]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a True) (Eq (skS.0 0 True) True))
% 3.53/3.79 Clause #115 (by eliminate duplicate literals #[114]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Eq a True)
% 3.53/3.79 Clause #118 (by equality factoring #[115]): Or (Ne True True) (Eq (skS.0 0 True) True)
% 3.53/3.79 Clause #120 (by clausification #[118]): Or (Eq (skS.0 0 True) True) (Or (Eq True False) (Eq True False))
% 3.53/3.79 Clause #122 (by clausification #[120]): Or (Eq (skS.0 0 True) True) (Eq True False)
% 3.53/3.79 Clause #123 (by clausification #[122]): Eq (skS.0 0 True) True
% 3.53/3.79 Clause #124 (by backward demodulation #[123, 49]): ∀ (a a_1 a_2 : Prop),
% 3.53/3.79 Or (Eq a True) (Or (Eq True False) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) True))))
% 3.53/3.79 Clause #125 (by backward demodulation #[123, 42]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False)))
% 3.53/3.79 Clause #130 (by clausification #[125]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False))
% 3.53/3.79 Clause #132 (by falseElim #[130]): ∀ (a : Prop), Or (Eq a False) (Eq (skS.0 1 True True) False)
% 3.53/3.79 Clause #134 (by falseElim #[132]): Eq (skS.0 1 True True) False
% 3.53/3.79 Clause #143 (by clausification #[124]): ∀ (a a_1 a_2 : Prop), Or (Eq a True) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) True)))
% 3.53/3.79 Clause #145 (by falseElim #[143]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq a_1 False) (Eq (skS.0 1 True True) True))
% 3.53/3.79 Clause #147 (by falseElim #[145]): ∀ (a : Prop), Or (Eq a True) (Eq (skS.0 1 True True) True)
% 3.53/3.79 Clause #149 (by superposition #[147, 134]): ∀ (a : Prop), Or (Eq a True) (Eq True False)
% 3.53/3.79 Clause #152 (by clausification #[149]): ∀ (a : Prop), Eq a True
% 3.53/3.79 Clause #154 (by falseElim #[152]): False
% 3.53/3.79 SZS output end Proof for theBenchmark.p
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