TSTP Solution File: SYO223^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO223^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 04:21:54 EDT 2023
% Result : Theorem 4.77s 5.00s
% Output : Proof 4.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO223^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 00:02:56 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.77/5.00 SZS status Theorem for theBenchmark.p
% 4.77/5.00 SZS output start Proof for theBenchmark.p
% 4.77/5.00 Clause #0 (by assumption #[]): Eq
% 4.77/5.00 (Not
% 4.77/5.00 (And (∀ (X : Iota), cUNIQUE X → ∀ (Z : Iota), Eq X Z) (cUNIQUE cS) →
% 4.77/5.00 Exists fun Xan => And (Eq (Xan cP) (cLIKE cP cS)) (Eq (Xan cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)))))
% 4.77/5.00 True
% 4.77/5.00 Clause #1 (by clausification #[0]): Eq
% 4.77/5.00 (And (∀ (X : Iota), cUNIQUE X → ∀ (Z : Iota), Eq X Z) (cUNIQUE cS) →
% 4.77/5.00 Exists fun Xan => And (Eq (Xan cP) (cLIKE cP cS)) (Eq (Xan cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))))
% 4.77/5.00 False
% 4.77/5.00 Clause #2 (by clausification #[1]): Eq (And (∀ (X : Iota), cUNIQUE X → ∀ (Z : Iota), Eq X Z) (cUNIQUE cS)) True
% 4.77/5.00 Clause #3 (by clausification #[1]): Eq (Exists fun Xan => And (Eq (Xan cP) (cLIKE cP cS)) (Eq (Xan cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))))
% 4.77/5.00 False
% 4.77/5.00 Clause #4 (by clausification #[2]): Eq (cUNIQUE cS) True
% 4.77/5.00 Clause #5 (by clausification #[2]): Eq (∀ (X : Iota), cUNIQUE X → ∀ (Z : Iota), Eq X Z) True
% 4.77/5.00 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (cUNIQUE a → ∀ (Z : Iota), Eq a Z) True
% 4.77/5.00 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (cUNIQUE a) False) (Eq (∀ (Z : Iota), Eq a Z) True)
% 4.77/5.00 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cUNIQUE a) False) (Eq (Eq a a_1) True)
% 4.77/5.00 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cUNIQUE a) False) (Eq a a_1)
% 4.77/5.00 Clause #10 (by superposition #[9, 4]): ∀ (a : Iota), Or (Eq cS a) (Eq False True)
% 4.77/5.00 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq cS a
% 4.77/5.00 Clause #12 (by superposition #[11, 4]): ∀ (a : Iota), Eq (cUNIQUE a) True
% 4.77/5.00 Clause #13 (by superposition #[11, 11]): ∀ (a a_1 : Iota), Eq a a_1
% 4.77/5.00 Clause #14 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (And (Eq (a cP) (cLIKE cP cS)) (Eq (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)))) False
% 4.77/5.00 Clause #15 (by clausification #[14]): ∀ (a : Iota → Prop),
% 4.77/5.00 Or (Eq (Eq (a cP) (cLIKE cP cS)) False) (Eq (Eq (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))) False)
% 4.77/5.00 Clause #16 (by clausification #[15]): ∀ (a : Iota → Prop), Or (Eq (Eq (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))) False) (Ne (a cP) (cLIKE cP cS))
% 4.77/5.00 Clause #17 (by clausification #[16]): ∀ (a : Iota → Prop), Or (Ne (a cP) (cLIKE cP cS)) (Ne (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)))
% 4.77/5.00 Clause #18 (by clausification #[17]): ∀ (a : Iota → Prop),
% 4.77/5.00 Or (Ne (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))) (Or (Eq (a cP) False) (Eq (cLIKE cP cS) False))
% 4.77/5.00 Clause #19 (by clausification #[17]): ∀ (a : Iota → Prop),
% 4.77/5.00 Or (Ne (a cJ) (Exists fun X => And (cUNIQUE X) (cLIKE cJ X))) (Or (Eq (a cP) True) (Eq (cLIKE cP cS) True))
% 4.77/5.00 Clause #20 (by clausification #[18]): ∀ (a : Iota → Prop),
% 4.77/5.00 Or (Eq (a cP) False)
% 4.77/5.00 (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Eq (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)) False)))
% 4.77/5.00 Clause #22 (by clausification #[20]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.77/5.00 Or (Eq (a cP) False)
% 4.77/5.00 (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Eq (And (cUNIQUE a_1) (cLIKE cJ a_1)) False)))
% 4.77/5.00 Clause #23 (by clausification #[22]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.77/5.00 Or (Eq (a cP) False)
% 4.77/5.00 (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Or (Eq (cUNIQUE a_1) False) (Eq (cLIKE cJ a_1) False))))
% 4.77/5.00 Clause #24 (by forward demodulation #[23, 12]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.77/5.00 Or (Eq (a cP) False)
% 4.77/5.00 (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Or (Eq True False) (Eq (cLIKE cJ a_1) False))))
% 4.77/5.00 Clause #25 (by clausification #[24]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.77/5.00 Or (Eq (a cP) False) (Or (Eq (cLIKE cP cS) False) (Or (Eq (a cJ) False) (Eq (cLIKE cJ a_1) False)))
% 4.77/5.00 Clause #26 (by superposition #[25, 12]): ∀ (a : Iota → Iota) (a_1 : Iota),
% 4.77/5.00 Or (Eq (cLIKE cP cS) False)
% 4.77/5.00 (Or (Eq ((fun x => cUNIQUE (a x)) cJ) False) (Or (Eq (cLIKE cJ a_1) False) (Eq False True)))
% 4.77/5.00 Clause #65 (by clausification #[19]): ∀ (a : Iota → Prop),
% 4.77/5.00 Or (Eq (a cP) True)
% 4.77/5.00 (Or (Eq (cLIKE cP cS) True) (Or (Eq (a cJ) True) (Eq (Exists fun X => And (cUNIQUE X) (cLIKE cJ X)) True)))
% 4.85/5.03 Clause #114 (by betaEtaReduce #[26]): ∀ (a : Iota → Iota) (a_1 : Iota),
% 4.85/5.03 Or (Eq (cLIKE cP cS) False) (Or (Eq (cUNIQUE (a cJ)) False) (Or (Eq (cLIKE cJ a_1) False) (Eq False True)))
% 4.85/5.03 Clause #115 (by clausification #[114]): ∀ (a : Iota → Iota) (a_1 : Iota), Or (Eq (cLIKE cP cS) False) (Or (Eq (cUNIQUE (a cJ)) False) (Eq (cLIKE cJ a_1) False))
% 4.85/5.03 Clause #304 (by clausification #[65]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.85/5.03 Or (Eq (a cP) True)
% 4.85/5.03 (Or (Eq (cLIKE cP cS) True) (Or (Eq (a cJ) True) (Eq (And (cUNIQUE (skS.0 1 a_1)) (cLIKE cJ (skS.0 1 a_1))) True)))
% 4.85/5.03 Clause #305 (by clausification #[304]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.85/5.03 Or (Eq (a cP) True) (Or (Eq (cLIKE cP cS) True) (Or (Eq (a cJ) True) (Eq (cLIKE cJ (skS.0 1 a_1)) True)))
% 4.85/5.03 Clause #347 (by superposition #[305, 13]): ∀ (a : Iota → Prop) (a_1 : Iota),
% 4.85/5.03 Or (Eq (a cP) True) (Or (Eq (cLIKE cP cS) True) (Or (Eq (a cJ) True) (Eq (cLIKE cJ a_1) True)))
% 4.85/5.03 Clause #433 (by equality factoring #[347]): ∀ (a : Iota) (a_1 : Prop),
% 4.85/5.03 Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Ne True True) (Eq ((fun x => a_1) cP) True)))
% 4.85/5.03 Clause #503 (by betaEtaReduce #[433]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Ne True True) (Eq a_1 True)))
% 4.85/5.03 Clause #504 (by clausification #[503]): ∀ (a : Iota) (a_1 : Prop),
% 4.85/5.03 Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Eq a_1 True) (Or (Eq True False) (Eq True False))))
% 4.85/5.03 Clause #506 (by clausification #[504]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Eq a_1 True) (Eq True False)))
% 4.85/5.03 Clause #507 (by clausification #[506]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Eq a_1 True))
% 4.85/5.03 Clause #522 (by equality factoring #[507]): ∀ (a : Iota), Or (Eq (cLIKE cP cS) True) (Or (Ne True True) (Eq (cLIKE cJ a) True))
% 4.85/5.03 Clause #554 (by clausification #[522]): ∀ (a : Iota), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Or (Eq True False) (Eq True False)))
% 4.85/5.03 Clause #556 (by clausification #[554]): ∀ (a : Iota), Or (Eq (cLIKE cP cS) True) (Or (Eq (cLIKE cJ a) True) (Eq True False))
% 4.85/5.03 Clause #557 (by clausification #[556]): ∀ (a : Iota), Or (Eq (cLIKE cP cS) True) (Eq (cLIKE cJ a) True)
% 4.85/5.03 Clause #564 (by superposition #[557, 13]): ∀ (a a_1 : Iota), Or (Eq (cLIKE cP cS) True) (Eq (cLIKE a a_1) True)
% 4.85/5.03 Clause #584 (by equality factoring #[564]): Or (Ne True True) (Eq (cLIKE cP cS) True)
% 4.85/5.03 Clause #603 (by clausification #[584]): Or (Eq (cLIKE cP cS) True) (Or (Eq True False) (Eq True False))
% 4.85/5.03 Clause #605 (by clausification #[603]): Or (Eq (cLIKE cP cS) True) (Eq True False)
% 4.85/5.03 Clause #606 (by clausification #[605]): Eq (cLIKE cP cS) True
% 4.85/5.03 Clause #610 (by backward demodulation #[606, 115]): ∀ (a : Iota → Iota) (a_1 : Iota), Or (Eq True False) (Or (Eq (cUNIQUE (a cJ)) False) (Eq (cLIKE cJ a_1) False))
% 4.85/5.03 Clause #618 (by superposition #[606, 13]): ∀ (a : Iota), Eq (cLIKE a cS) True
% 4.85/5.03 Clause #623 (by superposition #[618, 13]): ∀ (a a_1 : Iota), Eq (cLIKE a a_1) True
% 4.85/5.03 Clause #632 (by clausification #[610]): ∀ (a : Iota → Iota) (a_1 : Iota), Or (Eq (cUNIQUE (a cJ)) False) (Eq (cLIKE cJ a_1) False)
% 4.85/5.03 Clause #633 (by superposition #[632, 12]): ∀ (a : Iota), Or (Eq (cLIKE cJ a) False) (Eq False True)
% 4.85/5.03 Clause #641 (by clausification #[633]): ∀ (a : Iota), Eq (cLIKE cJ a) False
% 4.85/5.03 Clause #642 (by superposition #[641, 623]): Eq False True
% 4.85/5.03 Clause #644 (by clausification #[642]): False
% 4.85/5.03 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------