TSTP Solution File: SYN924+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN924+1 : TPTP v8.1.2. Released v3.1.0.
% 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 02:13:17 EDT 2023
% Result : Theorem 4.48s 4.68s
% Output : Proof 4.56s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN924+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : duper %s
% 0.19/0.35 % Computer : n027.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Sat Aug 26 17:53:05 EDT 2023
% 0.19/0.35 % CPUTime :
% 4.48/4.68 SZS status Theorem for theBenchmark.p
% 4.48/4.68 SZS output start Proof for theBenchmark.p
% 4.48/4.68 Clause #0 (by assumption #[]): Eq (Not (Iff (Exists fun X => Or (p X) (q X)) (Or (Exists fun X => p X) (Exists fun X => q X)))) True
% 4.48/4.68 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Exists fun X => Or (p X) (q X)) (Or (Exists p) (Exists q)))) True
% 4.48/4.68 Clause #2 (by clausification #[1]): Eq (Iff (Exists fun X => Or (p X) (q X)) (Or (Exists p) (Exists q))) False
% 4.48/4.68 Clause #3 (by clausification #[2]): Or (Eq (Exists fun X => Or (p X) (q X)) False) (Eq (Or (Exists p) (Exists q)) False)
% 4.48/4.68 Clause #4 (by clausification #[2]): Or (Eq (Exists fun X => Or (p X) (q X)) True) (Eq (Or (Exists p) (Exists q)) True)
% 4.48/4.68 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq (Or (Exists p) (Exists q)) False) (Eq (Or (p a) (q a)) False)
% 4.48/4.68 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (Or (p a) (q a)) False) (Eq (Exists q) False)
% 4.48/4.68 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq (Or (p a) (q a)) False) (Eq (Exists p) False)
% 4.48/4.68 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq (Exists q) False) (Eq (q a) False)
% 4.48/4.68 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (q a) False) (Eq (q a_1) False)
% 4.48/4.68 Clause #13 (by clausification #[7]): ∀ (a : Iota), Or (Eq (Exists p) False) (Eq (p a) False)
% 4.48/4.68 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (p a) False) (Eq (p a_1) False)
% 4.48/4.68 Clause #16 (by clausification #[4]): ∀ (a : Iota), Or (Eq (Or (Exists p) (Exists q)) True) (Eq (Or (p (skS.0 0 a)) (q (skS.0 0 a))) True)
% 4.48/4.68 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (Or (p (skS.0 0 a)) (q (skS.0 0 a))) True) (Or (Eq (Exists p) True) (Eq (Exists q) True))
% 4.48/4.68 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (Exists p) True) (Or (Eq (Exists q) True) (Or (Eq (p (skS.0 0 a)) True) (Eq (q (skS.0 0 a)) True)))
% 4.48/4.68 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota),
% 4.48/4.68 Or (Eq (Exists q) True) (Or (Eq (p (skS.0 0 a)) True) (Or (Eq (q (skS.0 0 a)) True) (Eq (p (skS.0 1 a_1)) True)))
% 4.48/4.68 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 4.48/4.68 Or (Eq (p (skS.0 0 a)) True)
% 4.48/4.68 (Or (Eq (q (skS.0 0 a)) True) (Or (Eq (p (skS.0 1 a_1)) True) (Eq (q (skS.0 2 a_2)) True)))
% 4.48/4.68 Clause #22 (by superposition #[20, 15]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.48/4.68 Or (Eq (q (skS.0 0 a)) True)
% 4.48/4.68 (Or (Eq (p (skS.0 1 a_1)) True) (Or (Eq (q (skS.0 2 a_2)) True) (Or (Eq True False) (Eq (p a_3) False))))
% 4.48/4.68 Clause #28 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.48/4.68 Or (Eq (q (skS.0 0 a)) True) (Or (Eq (p (skS.0 1 a_1)) True) (Or (Eq (q (skS.0 2 a_2)) True) (Eq (p a_3) False)))
% 4.48/4.68 Clause #29 (by superposition #[28, 20]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.48/4.68 Or (Eq (q (skS.0 0 a)) True)
% 4.48/4.68 (Or (Eq (p (skS.0 1 a_1)) True)
% 4.48/4.68 (Or (Eq (q (skS.0 2 a_2)) True)
% 4.48/4.68 (Or (Eq False True)
% 4.48/4.68 (Or (Eq (q (skS.0 0 a_3)) True) (Or (Eq (p (skS.0 1 a_4)) True) (Eq (q (skS.0 2 a_5)) True))))))
% 4.48/4.68 Clause #41 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.48/4.68 Or (Eq (q (skS.0 0 a)) True)
% 4.48/4.68 (Or (Eq (p (skS.0 1 a_1)) True)
% 4.48/4.68 (Or (Eq (q (skS.0 2 a_2)) True)
% 4.48/4.68 (Or (Eq (q (skS.0 0 a_3)) True) (Or (Eq (p (skS.0 1 a_4)) True) (Eq (q (skS.0 2 a_5)) True)))))
% 4.48/4.68 Clause #68 (by equality factoring #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.48/4.68 Or (Eq (q (skS.0 0 a)) True)
% 4.48/4.68 (Or (Eq (p (skS.0 1 a_1)) True)
% 4.48/4.68 (Or (Eq (q (skS.0 0 a_2)) True) (Or (Eq (p (skS.0 1 a_3)) True) (Or (Ne True True) (Eq (q (skS.0 2 a_4)) True)))))
% 4.48/4.68 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.48/4.68 Or (Eq (q (skS.0 0 a)) True)
% 4.48/4.68 (Or (Eq (p (skS.0 1 a_1)) True)
% 4.48/4.68 (Or (Eq (q (skS.0 0 a_2)) True)
% 4.48/4.68 (Or (Eq (p (skS.0 1 a_3)) True) (Or (Eq (q (skS.0 2 a_4)) True) (Or (Eq True False) (Eq True False))))))
% 4.48/4.68 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.48/4.68 Or (Eq (q (skS.0 0 a)) True)
% 4.48/4.68 (Or (Eq (p (skS.0 1 a_1)) True)
% 4.48/4.68 (Or (Eq (q (skS.0 0 a_2)) True)
% 4.48/4.68 (Or (Eq (p (skS.0 1 a_3)) True) (Or (Eq (q (skS.0 2 a_4)) True) (Eq True False)))))
% 4.48/4.68 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.48/4.68 Or (Eq (q (skS.0 0 a)) True)
% 4.56/4.71 (Or (Eq (p (skS.0 1 a_1)) True)
% 4.56/4.71 (Or (Eq (q (skS.0 0 a_2)) True) (Or (Eq (p (skS.0 1 a_3)) True) (Eq (q (skS.0 2 a_4)) True))))
% 4.56/4.71 Clause #94 (by equality factoring #[72]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 0 a)) True)
% 4.56/4.71 (Or (Eq (q (skS.0 0 a_1)) True) (Or (Eq (q (skS.0 2 a_2)) True) (Or (Ne True True) (Eq (p (skS.0 1 a_3)) True))))
% 4.56/4.71 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 0 a)) True)
% 4.56/4.71 (Or (Eq (q (skS.0 0 a_1)) True)
% 4.56/4.71 (Or (Eq (q (skS.0 2 a_2)) True) (Or (Eq (p (skS.0 1 a_3)) True) (Or (Eq True False) (Eq True False)))))
% 4.56/4.71 Clause #97 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 0 a)) True)
% 4.56/4.71 (Or (Eq (q (skS.0 0 a_1)) True) (Or (Eq (q (skS.0 2 a_2)) True) (Or (Eq (p (skS.0 1 a_3)) True) (Eq True False))))
% 4.56/4.71 Clause #98 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 0 a)) True)
% 4.56/4.71 (Or (Eq (q (skS.0 0 a_1)) True) (Or (Eq (q (skS.0 2 a_2)) True) (Eq (p (skS.0 1 a_3)) True)))
% 4.56/4.71 Clause #111 (by equality factoring #[98]): ∀ (a a_1 a_2 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 2 a)) True) (Or (Eq (p (skS.0 1 a_1)) True) (Or (Ne True True) (Eq (q (skS.0 0 a_2)) True)))
% 4.56/4.71 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 2 a)) True)
% 4.56/4.71 (Or (Eq (p (skS.0 1 a_1)) True) (Or (Eq (q (skS.0 0 a_2)) True) (Or (Eq True False) (Eq True False))))
% 4.56/4.71 Clause #114 (by clausification #[112]): ∀ (a a_1 a_2 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 2 a)) True) (Or (Eq (p (skS.0 1 a_1)) True) (Or (Eq (q (skS.0 0 a_2)) True) (Eq True False)))
% 4.56/4.71 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 2 a)) True) (Or (Eq (p (skS.0 1 a_1)) True) (Eq (q (skS.0 0 a_2)) True))
% 4.56/4.71 Clause #120 (by superposition #[115, 15]): ∀ (a a_1 a_2 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 2 a)) True) (Or (Eq (q (skS.0 0 a_1)) True) (Or (Eq True False) (Eq (p a_2) False)))
% 4.56/4.71 Clause #143 (by clausification #[120]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 2 a)) True) (Or (Eq (q (skS.0 0 a_1)) True) (Eq (p a_2) False))
% 4.56/4.71 Clause #144 (by superposition #[143, 115]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 2 a)) True)
% 4.56/4.71 (Or (Eq (q (skS.0 0 a_1)) True) (Or (Eq (q (skS.0 2 a_2)) True) (Or (Eq False True) (Eq (q (skS.0 0 a_3)) True))))
% 4.56/4.71 Clause #181 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 2 a)) True)
% 4.56/4.71 (Or (Eq (q (skS.0 0 a_1)) True) (Or (Eq (q (skS.0 2 a_2)) True) (Eq (q (skS.0 0 a_3)) True)))
% 4.56/4.71 Clause #199 (by equality factoring #[181]): ∀ (a a_1 a_2 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 2 a)) True) (Or (Eq (q (skS.0 2 a_1)) True) (Or (Ne True True) (Eq (q (skS.0 0 a_2)) True)))
% 4.56/4.71 Clause #200 (by clausification #[199]): ∀ (a a_1 a_2 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 2 a)) True)
% 4.56/4.71 (Or (Eq (q (skS.0 2 a_1)) True) (Or (Eq (q (skS.0 0 a_2)) True) (Or (Eq True False) (Eq True False))))
% 4.56/4.71 Clause #202 (by clausification #[200]): ∀ (a a_1 a_2 : Iota),
% 4.56/4.71 Or (Eq (q (skS.0 2 a)) True) (Or (Eq (q (skS.0 2 a_1)) True) (Or (Eq (q (skS.0 0 a_2)) True) (Eq True False)))
% 4.56/4.71 Clause #203 (by clausification #[202]): ∀ (a a_1 a_2 : Iota), Or (Eq (q (skS.0 2 a)) True) (Or (Eq (q (skS.0 2 a_1)) True) (Eq (q (skS.0 0 a_2)) True))
% 4.56/4.71 Clause #211 (by equality factoring #[203]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 0 a)) True) (Or (Ne True True) (Eq (q (skS.0 2 a_1)) True))
% 4.56/4.71 Clause #212 (by clausification #[211]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 0 a)) True) (Or (Eq (q (skS.0 2 a_1)) True) (Or (Eq True False) (Eq True False)))
% 4.56/4.71 Clause #214 (by clausification #[212]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 0 a)) True) (Or (Eq (q (skS.0 2 a_1)) True) (Eq True False))
% 4.56/4.71 Clause #215 (by clausification #[214]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 0 a)) True) (Eq (q (skS.0 2 a_1)) True)
% 4.56/4.71 Clause #218 (by superposition #[215, 10]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 0 a)) True) (Or (Eq True False) (Eq (q a_1) False))
% 4.56/4.71 Clause #221 (by clausification #[218]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 0 a)) True) (Eq (q a_1) False)
% 4.56/4.71 Clause #223 (by superposition #[221, 215]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 0 a)) True) (Or (Eq (q (skS.0 0 a_1)) True) (Eq False True))
% 4.56/4.72 Clause #228 (by clausification #[223]): ∀ (a a_1 : Iota), Or (Eq (q (skS.0 0 a)) True) (Eq (q (skS.0 0 a_1)) True)
% 4.56/4.72 Clause #230 (by equality factoring #[228]): ∀ (a : Iota), Or (Ne True True) (Eq (q (skS.0 0 a)) True)
% 4.56/4.72 Clause #231 (by clausification #[230]): ∀ (a : Iota), Or (Eq (q (skS.0 0 a)) True) (Or (Eq True False) (Eq True False))
% 4.56/4.72 Clause #233 (by clausification #[231]): ∀ (a : Iota), Or (Eq (q (skS.0 0 a)) True) (Eq True False)
% 4.56/4.72 Clause #234 (by clausification #[233]): ∀ (a : Iota), Eq (q (skS.0 0 a)) True
% 4.56/4.72 Clause #235 (by superposition #[234, 10]): ∀ (a : Iota), Or (Eq True False) (Eq (q a) False)
% 4.56/4.72 Clause #237 (by clausification #[235]): ∀ (a : Iota), Eq (q a) False
% 4.56/4.72 Clause #238 (by superposition #[237, 234]): Eq False True
% 4.56/4.72 Clause #239 (by clausification #[238]): False
% 4.56/4.72 SZS output end Proof for theBenchmark.p
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