TSTP Solution File: SYO112^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO112^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n009.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 04:21:33 EDT 2023
% Result : Theorem 8.01s 8.31s
% Output : Proof 8.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO112^5 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.11 % Command : duper %s
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 05:36:50 EDT 2023
% 0.11/0.32 % CPUTime :
% 8.01/8.31 SZS status Theorem for theBenchmark.p
% 8.01/8.31 SZS output start Proof for theBenchmark.p
% 8.01/8.31 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), Iff (cP X) (Exists fun Y => cP Y)) (Iff (∀ (X : Iota), cP X) (Exists fun Y => cP Y)))) True
% 8.01/8.31 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (∀ (X : Iota), Iff (cP X) (Exists cP)) (Iff (∀ (X : Iota), cP X) (Exists cP)))) True
% 8.01/8.31 Clause #2 (by clausification #[1]): Eq (Iff (∀ (X : Iota), Iff (cP X) (Exists cP)) (Iff (∀ (X : Iota), cP X) (Exists cP))) False
% 8.01/8.31 Clause #3 (by clausification #[2]): Or (Eq (∀ (X : Iota), Iff (cP X) (Exists cP)) False) (Eq (Iff (∀ (X : Iota), cP X) (Exists cP)) False)
% 8.01/8.31 Clause #4 (by clausification #[2]): Or (Eq (∀ (X : Iota), Iff (cP X) (Exists cP)) True) (Eq (Iff (∀ (X : Iota), cP X) (Exists cP)) True)
% 8.01/8.31 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq (Iff (∀ (X : Iota), cP X) (Exists cP)) False) (Eq (Not (Iff (cP (skS.0 0 a)) (Exists cP))) True)
% 8.01/8.31 Clause #6 (by clausification #[5]): ∀ (a : Iota),
% 8.01/8.31 Or (Eq (Not (Iff (cP (skS.0 0 a)) (Exists cP))) True) (Or (Eq (∀ (X : Iota), cP X) False) (Eq (Exists cP) False))
% 8.01/8.31 Clause #7 (by clausification #[5]): ∀ (a : Iota),
% 8.01/8.31 Or (Eq (Not (Iff (cP (skS.0 0 a)) (Exists cP))) True) (Or (Eq (∀ (X : Iota), cP X) True) (Eq (Exists cP) True))
% 8.01/8.31 Clause #8 (by clausification #[6]): ∀ (a : Iota),
% 8.01/8.31 Or (Eq (∀ (X : Iota), cP X) False) (Or (Eq (Exists cP) False) (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False))
% 8.01/8.31 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota),
% 8.01/8.31 Or (Eq (Exists cP) False) (Or (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False) (Eq (Not (cP (skS.0 1 a_1))) True))
% 8.01/8.31 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.31 Or (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False) (Or (Eq (Not (cP (skS.0 1 a_1))) True) (Eq (cP a_2) False))
% 8.01/8.31 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.31 Or (Eq (Not (cP (skS.0 1 a))) True) (Or (Eq (cP a_1) False) (Or (Eq (cP (skS.0 0 a_2)) False) (Eq (Exists cP) False)))
% 8.01/8.31 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.31 Or (Eq (cP a) False) (Or (Eq (cP (skS.0 0 a_1)) False) (Or (Eq (Exists cP) False) (Eq (cP (skS.0 1 a_2)) False)))
% 8.01/8.31 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.01/8.31 Or (Eq (cP a) False) (Or (Eq (cP (skS.0 0 a_1)) False) (Or (Eq (cP (skS.0 1 a_2)) False) (Eq (cP a_3) False)))
% 8.01/8.31 Clause #15 (by clausification #[4]): ∀ (a : Iota), Or (Eq (Iff (∀ (X : Iota), cP X) (Exists cP)) True) (Eq (Iff (cP a) (Exists cP)) True)
% 8.01/8.31 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (Iff (cP a) (Exists cP)) True) (Or (Eq (∀ (X : Iota), cP X) True) (Eq (Exists cP) False))
% 8.01/8.31 Clause #18 (by clausification #[16]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), cP X) True) (Or (Eq (Exists cP) False) (Or (Eq (cP a) True) (Eq (Exists cP) False)))
% 8.01/8.31 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (Exists cP) False) (Or (Eq (cP a) True) (Or (Eq (Exists cP) False) (Eq (cP a_1) True)))
% 8.01/8.31 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (Exists cP) False) (Or (Eq (cP a_1) True) (Eq (cP a_2) False)))
% 8.01/8.31 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) False) (Eq (cP a_3) False)))
% 8.01/8.31 Clause #36 (by clausification #[7]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), cP X) True) (Or (Eq (Exists cP) True) (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False))
% 8.01/8.31 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (Exists cP) True) (Or (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False) (Eq (cP a_1) True))
% 8.01/8.31 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.31 Or (Eq (Iff (cP (skS.0 0 a)) (Exists cP)) False) (Or (Eq (cP a_1) True) (Eq (cP (skS.0 8 a_2)) True))
% 8.01/8.31 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.31 Or (Eq (cP a) True) (Or (Eq (cP (skS.0 8 a_1)) True) (Or (Eq (cP (skS.0 0 a_2)) True) (Eq (Exists cP) True)))
% 8.01/8.31 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.01/8.31 Or (Eq (cP a) True) (Or (Eq (cP (skS.0 8 a_1)) True) (Or (Eq (cP (skS.0 0 a_2)) True) (Eq (cP (skS.0 9 a_3)) True)))
% 8.01/8.31 Clause #53 (by equality factoring #[42]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True) (Or (Eq (cP (skS.0 0 a_1)) True) (Or (Ne True True) (Eq (cP (skS.0 9 a_2)) True)))
% 8.01/8.37 Clause #56 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True)
% 8.01/8.37 (Or (Eq (cP (skS.0 0 a_1)) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Eq True False) (Eq True False))))
% 8.01/8.37 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True) (Or (Eq (cP (skS.0 0 a_1)) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Eq True False)))
% 8.01/8.37 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 8 a)) True) (Or (Eq (cP (skS.0 0 a_1)) True) (Eq (cP (skS.0 9 a_2)) True))
% 8.01/8.37 Clause #63 (by superposition #[59, 22]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True)
% 8.01/8.37 (Or (Eq (cP (skS.0 9 a_1)) True)
% 8.01/8.37 (Or (Eq (cP a_2) True) (Or (Eq (cP a_3) True) (Or (Eq True False) (Eq (cP a_4) False)))))
% 8.01/8.37 Clause #75 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True)
% 8.01/8.37 (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Eq (cP a_2) True) (Or (Eq (cP a_3) True) (Eq (cP a_4) False))))
% 8.01/8.37 Clause #77 (by superposition #[75, 59]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True)
% 8.01/8.37 (Or (Eq (cP (skS.0 9 a_1)) True)
% 8.01/8.37 (Or (Eq (cP a_2) True)
% 8.01/8.37 (Or (Eq (cP a_3) True) (Or (Eq (cP (skS.0 8 a_4)) True) (Or (Eq False True) (Eq (cP (skS.0 9 a_5)) True))))))
% 8.01/8.37 Clause #98 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True)
% 8.01/8.37 (Or (Eq (cP (skS.0 9 a_1)) True)
% 8.01/8.37 (Or (Eq (cP a_2) True) (Or (Eq (cP a_3) True) (Or (Eq (cP (skS.0 8 a_4)) True) (Eq (cP (skS.0 9 a_5)) True)))))
% 8.01/8.37 Clause #127 (by equality factoring #[98]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True)
% 8.01/8.37 (Or (Eq (cP a_1) True)
% 8.01/8.37 (Or (Eq (cP a_2) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Or (Ne True True) (Eq (cP (skS.0 9 a_4)) True)))))
% 8.01/8.37 Clause #131 (by clausification #[127]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True)
% 8.01/8.37 (Or (Eq (cP a_1) True)
% 8.01/8.37 (Or (Eq (cP a_2) True)
% 8.01/8.37 (Or (Eq (cP (skS.0 8 a_3)) True) (Or (Eq (cP (skS.0 9 a_4)) True) (Or (Eq True False) (Eq True False))))))
% 8.01/8.37 Clause #133 (by clausification #[131]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True)
% 8.01/8.37 (Or (Eq (cP a_1) True)
% 8.01/8.37 (Or (Eq (cP a_2) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Or (Eq (cP (skS.0 9 a_4)) True) (Eq True False)))))
% 8.01/8.37 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.01/8.37 Or (Eq (cP (skS.0 8 a)) True)
% 8.01/8.37 (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Eq (cP (skS.0 9 a_4)) True))))
% 8.01/8.37 Clause #156 (by equality factoring #[134]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.01/8.37 Or (Eq (cP a) True)
% 8.01/8.37 (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Ne True True) (Eq (cP (skS.0 8 a_3)) True))))
% 8.01/8.37 Clause #160 (by clausification #[156]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.01/8.37 Or (Eq (cP a) True)
% 8.01/8.37 (Or (Eq (cP a_1) True)
% 8.01/8.37 (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Or (Eq True False) (Eq True False)))))
% 8.01/8.37 Clause #162 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.01/8.37 Or (Eq (cP a) True)
% 8.01/8.37 (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Eq (cP (skS.0 8 a_3)) True) (Eq True False))))
% 8.01/8.37 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.01/8.37 Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Eq (cP (skS.0 8 a_3)) True)))
% 8.01/8.37 Clause #181 (by equality factoring #[163]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.37 Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Ne True True) (Eq (cP (skS.0 8 a_2)) True)))
% 8.01/8.37 Clause #182 (by clausification #[181]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.37 Or (Eq (cP a) True)
% 8.01/8.37 (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Eq (cP (skS.0 8 a_2)) True) (Or (Eq True False) (Eq True False))))
% 8.01/8.37 Clause #184 (by clausification #[182]): ∀ (a a_1 a_2 : Iota),
% 8.01/8.37 Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Eq (cP (skS.0 8 a_2)) True) (Eq True False)))
% 8.01/8.37 Clause #185 (by clausification #[184]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Eq (cP (skS.0 8 a_2)) True))
% 8.17/8.43 Clause #202 (by equality factoring #[185]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 9 a)) True) (Or (Ne True True) (Eq (cP (skS.0 8 a_1)) True))
% 8.17/8.43 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP (skS.0 8 a_1)) True) (Or (Eq True False) (Eq True False)))
% 8.17/8.43 Clause #205 (by clausification #[203]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP (skS.0 8 a_1)) True) (Eq True False))
% 8.17/8.43 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 9 a)) True) (Eq (cP (skS.0 8 a_1)) True)
% 8.17/8.43 Clause #212 (by superposition #[206, 22]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.17/8.43 Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq True False) (Eq (cP a_3) False))))
% 8.17/8.43 Clause #223 (by clausification #[212]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.17/8.43 Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Eq (cP a_3) False)))
% 8.17/8.43 Clause #225 (by superposition #[223, 206]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.17/8.43 Or (Eq (cP (skS.0 9 a)) True)
% 8.17/8.43 (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq (cP (skS.0 9 a_3)) True) (Eq False True))))
% 8.17/8.43 Clause #267 (by clausification #[225]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.17/8.43 Or (Eq (cP (skS.0 9 a)) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Eq (cP (skS.0 9 a_3)) True)))
% 8.17/8.43 Clause #279 (by equality factoring #[267]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Ne True True) (Eq (cP (skS.0 9 a_2)) True)))
% 8.17/8.43 Clause #282 (by clausification #[279]): ∀ (a a_1 a_2 : Iota),
% 8.17/8.43 Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Or (Eq True False) (Eq True False))))
% 8.17/8.43 Clause #284 (by clausification #[282]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP (skS.0 9 a_2)) True) (Eq True False)))
% 8.17/8.43 Clause #285 (by clausification #[284]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Eq (cP (skS.0 9 a_2)) True))
% 8.17/8.43 Clause #293 (by equality factoring #[285]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Ne True True) (Eq (cP (skS.0 9 a_1)) True))
% 8.17/8.43 Clause #295 (by clausification #[293]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Or (Eq True False) (Eq True False)))
% 8.17/8.43 Clause #297 (by clausification #[295]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cP (skS.0 9 a_1)) True) (Eq True False))
% 8.17/8.43 Clause #298 (by clausification #[297]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cP (skS.0 9 a_1)) True)
% 8.17/8.43 Clause #305 (by equality factoring #[298]): ∀ (a : Iota), Or (Ne True True) (Eq (cP (skS.0 9 a)) True)
% 8.17/8.43 Clause #306 (by clausification #[305]): ∀ (a : Iota), Or (Eq (cP (skS.0 9 a)) True) (Or (Eq True False) (Eq True False))
% 8.17/8.43 Clause #308 (by clausification #[306]): ∀ (a : Iota), Or (Eq (cP (skS.0 9 a)) True) (Eq True False)
% 8.17/8.43 Clause #309 (by clausification #[308]): ∀ (a : Iota), Eq (cP (skS.0 9 a)) True
% 8.17/8.43 Clause #310 (by superposition #[309, 14]): ∀ (a a_1 a_2 : Iota),
% 8.17/8.43 Or (Eq True False) (Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1)) False) (Eq (cP a_2) False)))
% 8.17/8.43 Clause #311 (by superposition #[309, 22]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Or (Eq True False) (Eq (cP a_2) False)))
% 8.17/8.43 Clause #313 (by clausification #[311]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Eq (cP a_2) False))
% 8.17/8.43 Clause #314 (by superposition #[313, 309]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cP a_1) True) (Eq False True))
% 8.17/8.43 Clause #315 (by clausification #[314]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cP a_1) True)
% 8.17/8.43 Clause #316 (by equality factoring #[315]): ∀ (a : Iota), Or (Ne True True) (Eq (cP a) True)
% 8.17/8.43 Clause #317 (by clausification #[316]): ∀ (a : Iota), Or (Eq (cP a) True) (Or (Eq True False) (Eq True False))
% 8.17/8.43 Clause #319 (by clausification #[317]): ∀ (a : Iota), Or (Eq (cP a) True) (Eq True False)
% 8.17/8.43 Clause #320 (by clausification #[319]): ∀ (a : Iota), Eq (cP a) True
% 8.17/8.43 Clause #333 (by clausification #[310]): ∀ (a a_1 a_2 : Iota), Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1)) False) (Eq (cP a_2) False))
% 8.17/8.43 Clause #334 (by superposition #[333, 320]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 1 a)) False) (Or (Eq (cP a_1) False) (Eq False True))
% 8.17/8.43 Clause #335 (by clausification #[334]): ∀ (a a_1 : Iota), Or (Eq (cP (skS.0 1 a)) False) (Eq (cP a_1) False)
% 8.17/8.43 Clause #336 (by superposition #[335, 320]): ∀ (a : Iota), Or (Eq (cP a) False) (Eq False True)
% 8.17/8.43 Clause #337 (by clausification #[336]): ∀ (a : Iota), Eq (cP a) False
% 8.17/8.43 Clause #338 (by superposition #[337, 320]): Eq False True
% 8.17/8.43 Clause #339 (by clausification #[338]): False
% 8.17/8.43 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------