TSTP Solution File: COM016+4 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : COM016+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 : Wed Aug 30 18:38:08 EDT 2023
% Result : Theorem 11.59s 11.84s
% Output : Proof 11.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : COM016+4 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.12 % Command : duper %s
% 0.11/0.32 % Computer : n010.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 : Tue Aug 29 12:44:04 EDT 2023
% 0.11/0.32 % CPUTime :
% 11.59/11.84 SZS status Theorem for theBenchmark.p
% 11.59/11.84 SZS output start Proof for theBenchmark.p
% 11.59/11.84 Clause #7 (by assumption #[]): Eq
% 11.59/11.84 (∀ (W0 W1 W2 : Iota),
% 11.59/11.84 And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2) →
% 11.59/11.84 Iff (sdtmndtasgtdt0 W0 W1 W2) (Or (Eq W0 W2) (sdtmndtplgtdt0 W0 W1 W2)))
% 11.59/11.84 True
% 11.59/11.84 Clause #14 (by assumption #[]): Eq (aRewritingSystem0 xR) True
% 11.59/11.84 Clause #16 (by assumption #[]): Eq (And (And (aElement0 xa) (aElement0 xb)) (aElement0 xc)) True
% 11.59/11.84 Clause #18 (by assumption #[]): Eq
% 11.59/11.84 (And
% 11.59/11.84 (And
% 11.59/11.84 (And
% 11.59/11.84 (Or (aReductOfIn0 xb xa xR)
% 11.59/11.84 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtplgtdt0 W0 xR xb)))
% 11.59/11.84 (sdtmndtplgtdt0 xa xR xb))
% 11.59/11.84 (Or (aReductOfIn0 xc xa xR)
% 11.59/11.84 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtplgtdt0 W0 xR xc))))
% 11.59/11.84 (sdtmndtplgtdt0 xa xR xc))
% 11.59/11.84 True
% 11.59/11.84 Clause #19 (by assumption #[]): Eq
% 11.59/11.84 (Not
% 11.59/11.84 (Exists fun W0 =>
% 11.59/11.84 And (And (aElement0 W0) (aReductOfIn0 W0 xa xR))
% 11.59/11.84 (Or
% 11.59/11.84 (Or
% 11.59/11.84 (Or (Or (Eq W0 xb) (aReductOfIn0 xb W0 xR))
% 11.59/11.84 (Exists fun W1 => And (And (aElement0 W1) (aReductOfIn0 W1 W0 xR)) (sdtmndtplgtdt0 W1 xR xb)))
% 11.59/11.84 (sdtmndtplgtdt0 W0 xR xb))
% 11.59/11.84 (sdtmndtasgtdt0 W0 xR xb))))
% 11.59/11.84 True
% 11.59/11.84 Clause #43 (by clausification #[16]): Eq (And (aElement0 xa) (aElement0 xb)) True
% 11.59/11.84 Clause #45 (by clausification #[43]): Eq (aElement0 xb) True
% 11.59/11.84 Clause #104 (by clausification #[7]): ∀ (a : Iota),
% 11.59/11.84 Eq
% 11.59/11.84 (∀ (W1 W2 : Iota),
% 11.59/11.84 And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2) →
% 11.59/11.84 Iff (sdtmndtasgtdt0 a W1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a W1 W2)))
% 11.59/11.84 True
% 11.59/11.84 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota),
% 11.59/11.84 Eq
% 11.59/11.84 (∀ (W2 : Iota),
% 11.59/11.84 And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2) →
% 11.59/11.84 Iff (sdtmndtasgtdt0 a a_1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a a_1 W2)))
% 11.59/11.84 True
% 11.59/11.84 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota),
% 11.59/11.84 Eq
% 11.59/11.84 (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2) →
% 11.59/11.84 Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)))
% 11.59/11.84 True
% 11.59/11.84 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota),
% 11.59/11.84 Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False)
% 11.59/11.84 (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 11.59/11.84 Clause #108 (by clausification #[107]): ∀ (a a_1 a_2 : Iota),
% 11.59/11.84 Or (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 11.59/11.84 (Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) (Eq (aElement0 a_2) False))
% 11.59/11.84 Clause #109 (by clausification #[108]): ∀ (a a_1 a_2 : Iota),
% 11.59/11.84 Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False)
% 11.59/11.84 (Or (Eq (aElement0 a_2) False)
% 11.59/11.84 (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) True) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) False)))
% 11.59/11.84 Clause #111 (by clausification #[109]): ∀ (a a_1 a_2 : Iota),
% 11.59/11.84 Or (Eq (aElement0 a) False)
% 11.59/11.84 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 11.59/11.84 (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) False)
% 11.59/11.84 (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))
% 11.59/11.84 Clause #113 (by clausification #[111]): ∀ (a a_1 a_2 : Iota),
% 11.59/11.84 Or (Eq (aElement0 a) False)
% 11.59/11.84 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 11.59/11.84 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Eq (Eq a_1 a) False))))
% 11.59/11.84 Clause #262 (by clausification #[18]): Eq
% 11.59/11.84 (And
% 11.59/11.84 (And
% 11.59/11.84 (Or (aReductOfIn0 xb xa xR)
% 11.59/11.84 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtplgtdt0 W0 xR xb)))
% 11.59/11.84 (sdtmndtplgtdt0 xa xR xb))
% 11.59/11.84 (Or (aReductOfIn0 xc xa xR)
% 11.59/11.84 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtplgtdt0 W0 xR xc))))
% 11.59/11.84 True
% 11.59/11.84 Clause #265 (by clausification #[113]): ∀ (a a_1 a_2 : Iota),
% 11.59/11.84 Or (Eq (aElement0 a) False)
% 11.59/11.84 (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 11.59/11.84 (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Ne a_1 a))))
% 11.59/11.84 Clause #266 (by destructive equality resolution #[265]): ∀ (a a_1 : Iota),
% 11.59/11.84 Or (Eq (aElement0 a) False)
% 11.69/11.86 (Or (Eq (sdtmndtasgtdt0 a a_1 a) True) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False)))
% 11.69/11.86 Clause #267 (by eliminate duplicate literals #[266]): ∀ (a a_1 : Iota), Or (Eq (aElement0 a) False) (Or (Eq (sdtmndtasgtdt0 a a_1 a) True) (Eq (aRewritingSystem0 a_1) False))
% 11.69/11.86 Clause #269 (by superposition #[267, 45]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xb a xb) True) (Or (Eq (aRewritingSystem0 a) False) (Eq False True))
% 11.69/11.86 Clause #274 (by clausification #[269]): ∀ (a : Iota), Or (Eq (sdtmndtasgtdt0 xb a xb) True) (Eq (aRewritingSystem0 a) False)
% 11.69/11.86 Clause #275 (by superposition #[274, 14]): Or (Eq (sdtmndtasgtdt0 xb xR xb) True) (Eq False True)
% 11.69/11.86 Clause #276 (by clausification #[19]): Eq
% 11.69/11.86 (Exists fun W0 =>
% 11.69/11.86 And (And (aElement0 W0) (aReductOfIn0 W0 xa xR))
% 11.69/11.86 (Or
% 11.69/11.86 (Or
% 11.69/11.86 (Or (Or (Eq W0 xb) (aReductOfIn0 xb W0 xR))
% 11.69/11.86 (Exists fun W1 => And (And (aElement0 W1) (aReductOfIn0 W1 W0 xR)) (sdtmndtplgtdt0 W1 xR xb)))
% 11.69/11.86 (sdtmndtplgtdt0 W0 xR xb))
% 11.69/11.86 (sdtmndtasgtdt0 W0 xR xb)))
% 11.69/11.86 False
% 11.69/11.86 Clause #277 (by clausification #[276]): ∀ (a : Iota),
% 11.69/11.86 Eq
% 11.69/11.86 (And (And (aElement0 a) (aReductOfIn0 a xa xR))
% 11.69/11.86 (Or
% 11.69/11.86 (Or
% 11.69/11.86 (Or (Or (Eq a xb) (aReductOfIn0 xb a xR))
% 11.69/11.86 (Exists fun W1 => And (And (aElement0 W1) (aReductOfIn0 W1 a xR)) (sdtmndtplgtdt0 W1 xR xb)))
% 11.69/11.86 (sdtmndtplgtdt0 a xR xb))
% 11.69/11.86 (sdtmndtasgtdt0 a xR xb)))
% 11.69/11.86 False
% 11.69/11.86 Clause #278 (by clausification #[277]): ∀ (a : Iota),
% 11.69/11.86 Or (Eq (And (aElement0 a) (aReductOfIn0 a xa xR)) False)
% 11.69/11.86 (Eq
% 11.69/11.86 (Or
% 11.69/11.86 (Or
% 11.69/11.86 (Or (Or (Eq a xb) (aReductOfIn0 xb a xR))
% 11.69/11.86 (Exists fun W1 => And (And (aElement0 W1) (aReductOfIn0 W1 a xR)) (sdtmndtplgtdt0 W1 xR xb)))
% 11.69/11.86 (sdtmndtplgtdt0 a xR xb))
% 11.69/11.86 (sdtmndtasgtdt0 a xR xb))
% 11.69/11.86 False)
% 11.69/11.86 Clause #279 (by clausification #[278]): ∀ (a : Iota),
% 11.69/11.86 Or
% 11.69/11.86 (Eq
% 11.69/11.86 (Or
% 11.69/11.86 (Or
% 11.69/11.86 (Or (Or (Eq a xb) (aReductOfIn0 xb a xR))
% 11.69/11.86 (Exists fun W1 => And (And (aElement0 W1) (aReductOfIn0 W1 a xR)) (sdtmndtplgtdt0 W1 xR xb)))
% 11.69/11.86 (sdtmndtplgtdt0 a xR xb))
% 11.69/11.86 (sdtmndtasgtdt0 a xR xb))
% 11.69/11.86 False)
% 11.69/11.86 (Or (Eq (aElement0 a) False) (Eq (aReductOfIn0 a xa xR) False))
% 11.69/11.86 Clause #280 (by clausification #[279]): ∀ (a : Iota), Or (Eq (aElement0 a) False) (Or (Eq (aReductOfIn0 a xa xR) False) (Eq (sdtmndtasgtdt0 a xR xb) False))
% 11.69/11.86 Clause #281 (by clausification #[279]): ∀ (a : Iota),
% 11.69/11.86 Or (Eq (aElement0 a) False)
% 11.69/11.86 (Or (Eq (aReductOfIn0 a xa xR) False)
% 11.69/11.86 (Eq
% 11.69/11.86 (Or
% 11.69/11.86 (Or (Or (Eq a xb) (aReductOfIn0 xb a xR))
% 11.69/11.86 (Exists fun W1 => And (And (aElement0 W1) (aReductOfIn0 W1 a xR)) (sdtmndtplgtdt0 W1 xR xb)))
% 11.69/11.86 (sdtmndtplgtdt0 a xR xb))
% 11.69/11.86 False))
% 11.69/11.86 Clause #283 (by superposition #[280, 45]): Or (Eq (aReductOfIn0 xb xa xR) False) (Or (Eq (sdtmndtasgtdt0 xb xR xb) False) (Eq False True))
% 11.69/11.86 Clause #285 (by clausification #[275]): Eq (sdtmndtasgtdt0 xb xR xb) True
% 11.69/11.86 Clause #289 (by clausification #[283]): Or (Eq (aReductOfIn0 xb xa xR) False) (Eq (sdtmndtasgtdt0 xb xR xb) False)
% 11.69/11.86 Clause #1082 (by clausification #[262]): Eq
% 11.69/11.86 (And
% 11.69/11.86 (Or (aReductOfIn0 xb xa xR)
% 11.69/11.86 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtplgtdt0 W0 xR xb)))
% 11.69/11.86 (sdtmndtplgtdt0 xa xR xb))
% 11.69/11.86 True
% 11.69/11.86 Clause #1134 (by clausification #[281]): ∀ (a : Iota), Or (Eq (aElement0 a) False) (Or (Eq (aReductOfIn0 a xa xR) False) (Eq (sdtmndtplgtdt0 a xR xb) False))
% 11.69/11.86 Clause #1179 (by clausification #[1082]): Eq
% 11.69/11.86 (Or (aReductOfIn0 xb xa xR)
% 11.69/11.86 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtplgtdt0 W0 xR xb)))
% 11.69/11.86 True
% 11.69/11.86 Clause #1269 (by clausification #[1179]): Or (Eq (aReductOfIn0 xb xa xR) True)
% 11.69/11.86 (Eq (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xa xR)) (sdtmndtplgtdt0 W0 xR xb)) True)
% 11.69/11.86 Clause #1270 (by clausification #[1269]): ∀ (a : Iota),
% 11.69/11.86 Or (Eq (aReductOfIn0 xb xa xR) True)
% 11.69/11.86 (Eq (And (And (aElement0 (skS.0 16 a)) (aReductOfIn0 (skS.0 16 a) xa xR)) (sdtmndtplgtdt0 (skS.0 16 a) xR xb)) True)
% 11.69/11.86 Clause #1271 (by clausification #[1270]): ∀ (a : Iota), Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (sdtmndtplgtdt0 (skS.0 16 a) xR xb) True)
% 11.69/11.89 Clause #1272 (by clausification #[1270]): ∀ (a : Iota),
% 11.69/11.89 Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (And (aElement0 (skS.0 16 a)) (aReductOfIn0 (skS.0 16 a) xa xR)) True)
% 11.69/11.89 Clause #1278 (by clausification #[1272]): ∀ (a : Iota), Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aReductOfIn0 (skS.0 16 a) xa xR) True)
% 11.69/11.89 Clause #1279 (by clausification #[1272]): ∀ (a : Iota), Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aElement0 (skS.0 16 a)) True)
% 11.69/11.89 Clause #1318 (by superposition #[1279, 1134]): ∀ (a : Iota),
% 11.69/11.89 Or (Eq (aReductOfIn0 xb xa xR) True)
% 11.69/11.89 (Or (Eq True False)
% 11.69/11.89 (Or (Eq (aReductOfIn0 (skS.0 16 a) xa xR) False) (Eq (sdtmndtplgtdt0 (skS.0 16 a) xR xb) False)))
% 11.69/11.89 Clause #1420 (by clausification #[1318]): ∀ (a : Iota),
% 11.69/11.89 Or (Eq (aReductOfIn0 xb xa xR) True)
% 11.69/11.89 (Or (Eq (aReductOfIn0 (skS.0 16 a) xa xR) False) (Eq (sdtmndtplgtdt0 (skS.0 16 a) xR xb) False))
% 11.69/11.89 Clause #1421 (by superposition #[1420, 1278]): ∀ (a : Iota),
% 11.69/11.89 Or (Eq (aReductOfIn0 xb xa xR) True)
% 11.69/11.89 (Or (Eq (sdtmndtplgtdt0 (skS.0 16 a) xR xb) False) (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq False True)))
% 11.69/11.89 Clause #1422 (by clausification #[1421]): ∀ (a : Iota),
% 11.69/11.89 Or (Eq (aReductOfIn0 xb xa xR) True)
% 11.69/11.89 (Or (Eq (sdtmndtplgtdt0 (skS.0 16 a) xR xb) False) (Eq (aReductOfIn0 xb xa xR) True))
% 11.69/11.89 Clause #1423 (by eliminate duplicate literals #[1422]): ∀ (a : Iota), Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (sdtmndtplgtdt0 (skS.0 16 a) xR xb) False)
% 11.69/11.89 Clause #1424 (by superposition #[1423, 1271]): Or (Eq (aReductOfIn0 xb xa xR) True) (Or (Eq (aReductOfIn0 xb xa xR) True) (Eq False True))
% 11.69/11.89 Clause #1425 (by clausification #[1424]): Or (Eq (aReductOfIn0 xb xa xR) True) (Eq (aReductOfIn0 xb xa xR) True)
% 11.69/11.89 Clause #1426 (by eliminate duplicate literals #[1425]): Eq (aReductOfIn0 xb xa xR) True
% 11.69/11.89 Clause #1427 (by backward demodulation #[1426, 289]): Or (Eq True False) (Eq (sdtmndtasgtdt0 xb xR xb) False)
% 11.69/11.89 Clause #1460 (by clausification #[1427]): Eq (sdtmndtasgtdt0 xb xR xb) False
% 11.69/11.89 Clause #1461 (by superposition #[1460, 285]): Eq False True
% 11.69/11.89 Clause #1462 (by clausification #[1461]): False
% 11.69/11.89 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------