TSTP Solution File: COM018+4 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : COM018+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 18:38:09 EDT 2023
% Result : Theorem 238.54s 238.94s
% Output : Proof 238.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 12:46:49 EDT 2023
% 0.14/0.34 % CPUTime :
% 238.54/238.94 SZS status Theorem for theBenchmark.p
% 238.54/238.94 SZS output start Proof for theBenchmark.p
% 238.54/238.94 Clause #13 (by assumption #[]): Eq
% 238.54/238.94 (∀ (W0 : Iota),
% 238.54/238.94 And (aRewritingSystem0 W0) (isTerminating0 W0) →
% 238.54/238.94 ∀ (W1 : Iota), aElement0 W1 → Exists fun W2 => aNormalFormOfIn0 W2 W1 W0)
% 238.54/238.94 True
% 238.54/238.94 Clause #14 (by assumption #[]): Eq (aRewritingSystem0 xR) True
% 238.54/238.94 Clause #15 (by assumption #[]): Eq
% 238.54/238.94 (And
% 238.54/238.94 (And
% 238.54/238.94 (And
% 238.54/238.94 (∀ (W0 W1 W2 : Iota),
% 238.54/238.94 And (And (And (And (aElement0 W0) (aElement0 W1)) (aElement0 W2)) (aReductOfIn0 W1 W0 xR))
% 238.54/238.94 (aReductOfIn0 W2 W0 xR) →
% 238.54/238.94 Exists fun W3 =>
% 238.54/238.94 And
% 238.54/238.94 (And
% 238.54/238.94 (And
% 238.54/238.94 (And (aElement0 W3)
% 238.54/238.94 (Or (Eq W1 W3)
% 238.54/238.94 (And
% 238.54/238.94 (Or (aReductOfIn0 W3 W1 xR)
% 238.54/238.94 (Exists fun W4 =>
% 238.54/238.94 And (And (aElement0 W4) (aReductOfIn0 W4 W1 xR)) (sdtmndtplgtdt0 W4 xR W3)))
% 238.54/238.94 (sdtmndtplgtdt0 W1 xR W3))))
% 238.54/238.94 (sdtmndtasgtdt0 W1 xR W3))
% 238.54/238.94 (Or (Eq W2 W3)
% 238.54/238.94 (And
% 238.54/238.94 (Or (aReductOfIn0 W3 W2 xR)
% 238.54/238.94 (Exists fun W4 => And (And (aElement0 W4) (aReductOfIn0 W4 W2 xR)) (sdtmndtplgtdt0 W4 xR W3)))
% 238.54/238.94 (sdtmndtplgtdt0 W2 xR W3))))
% 238.54/238.94 (sdtmndtasgtdt0 W2 xR W3))
% 238.54/238.94 (isLocallyConfluent0 xR))
% 238.54/238.94 (∀ (W0 W1 : Iota),
% 238.54/238.94 And (aElement0 W0) (aElement0 W1) →
% 238.54/238.94 Or
% 238.54/238.94 (Or (aReductOfIn0 W1 W0 xR)
% 238.54/238.94 (Exists fun W2 => And (And (aElement0 W2) (aReductOfIn0 W2 W0 xR)) (sdtmndtplgtdt0 W2 xR W1)))
% 238.54/238.94 (sdtmndtplgtdt0 W0 xR W1) →
% 238.54/238.94 iLess0 W1 W0))
% 238.54/238.94 (isTerminating0 xR))
% 238.54/238.94 True
% 238.54/238.94 Clause #21 (by assumption #[]): Eq
% 238.54/238.94 (And
% 238.54/238.94 (And
% 238.54/238.94 (And
% 238.54/238.94 (And (aElement0 xw)
% 238.54/238.94 (Or (Eq xu xw)
% 238.54/238.94 (And
% 238.54/238.94 (Or (aReductOfIn0 xw xu xR)
% 238.54/238.94 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xu xR)) (sdtmndtplgtdt0 W0 xR xw)))
% 238.54/238.94 (sdtmndtplgtdt0 xu xR xw))))
% 238.54/238.94 (sdtmndtasgtdt0 xu xR xw))
% 238.54/238.94 (Or (Eq xv xw)
% 238.54/238.94 (And
% 238.54/238.94 (Or (aReductOfIn0 xw xv xR)
% 238.54/238.94 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xv xR)) (sdtmndtplgtdt0 W0 xR xw)))
% 238.54/238.94 (sdtmndtplgtdt0 xv xR xw))))
% 238.54/238.94 (sdtmndtasgtdt0 xv xR xw))
% 238.54/238.94 True
% 238.54/238.94 Clause #22 (by assumption #[]): Eq
% 238.54/238.94 (Not
% 238.54/238.94 (Exists fun W0 =>
% 238.54/238.94 Or
% 238.54/238.94 (And
% 238.54/238.94 (And (aElement0 W0)
% 238.54/238.94 (Or
% 238.54/238.94 (Or
% 238.54/238.94 (Or (Or (Eq xw W0) (aReductOfIn0 W0 xw xR))
% 238.54/238.94 (Exists fun W1 => And (And (aElement0 W1) (aReductOfIn0 W1 xw xR)) (sdtmndtplgtdt0 W1 xR W0)))
% 238.54/238.94 (sdtmndtplgtdt0 xw xR W0))
% 238.54/238.94 (sdtmndtasgtdt0 xw xR W0)))
% 238.54/238.94 (Not (Exists fun W1 => aReductOfIn0 W1 W0 xR)))
% 238.54/238.94 (aNormalFormOfIn0 W0 xw xR)))
% 238.54/238.94 True
% 238.54/238.94 Clause #94 (by clausification #[13]): ∀ (a : Iota),
% 238.54/238.94 Eq
% 238.54/238.94 (And (aRewritingSystem0 a) (isTerminating0 a) →
% 238.54/238.94 ∀ (W1 : Iota), aElement0 W1 → Exists fun W2 => aNormalFormOfIn0 W2 W1 a)
% 238.54/238.94 True
% 238.54/238.94 Clause #95 (by clausification #[94]): ∀ (a : Iota),
% 238.54/238.94 Or (Eq (And (aRewritingSystem0 a) (isTerminating0 a)) False)
% 238.54/238.94 (Eq (∀ (W1 : Iota), aElement0 W1 → Exists fun W2 => aNormalFormOfIn0 W2 W1 a) True)
% 238.54/238.94 Clause #96 (by clausification #[95]): ∀ (a : Iota),
% 238.54/238.94 Or (Eq (∀ (W1 : Iota), aElement0 W1 → Exists fun W2 => aNormalFormOfIn0 W2 W1 a) True)
% 238.54/238.94 (Or (Eq (aRewritingSystem0 a) False) (Eq (isTerminating0 a) False))
% 238.54/238.94 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota),
% 238.54/238.94 Or (Eq (aRewritingSystem0 a) False)
% 238.54/238.94 (Or (Eq (isTerminating0 a) False) (Eq (aElement0 a_1 → Exists fun W2 => aNormalFormOfIn0 W2 a_1 a) True))
% 238.54/238.94 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota),
% 238.54/238.94 Or (Eq (aRewritingSystem0 a) False)
% 238.54/238.94 (Or (Eq (isTerminating0 a) False)
% 238.54/238.94 (Or (Eq (aElement0 a_1) False) (Eq (Exists fun W2 => aNormalFormOfIn0 W2 a_1 a) True)))
% 238.54/238.94 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota),
% 238.54/238.94 Or (Eq (aRewritingSystem0 a) False)
% 238.54/238.94 (Or (Eq (isTerminating0 a) False)
% 238.91/239.17 (Or (Eq (aElement0 a_1) False) (Eq (aNormalFormOfIn0 (skS.0 0 a_1 a a_2) a_1 a) True)))
% 238.91/239.17 Clause #100 (by superposition #[99, 14]): ∀ (a a_1 : Iota),
% 238.91/239.17 Or (Eq (isTerminating0 xR) False)
% 238.91/239.17 (Or (Eq (aElement0 a) False) (Or (Eq (aNormalFormOfIn0 (skS.0 0 a xR a_1) a xR) True) (Eq False True)))
% 238.91/239.17 Clause #230 (by clausification #[15]): Eq (isTerminating0 xR) True
% 238.91/239.17 Clause #303 (by clausification #[21]): Eq
% 238.91/239.17 (And
% 238.91/239.17 (And
% 238.91/239.17 (And (aElement0 xw)
% 238.91/239.17 (Or (Eq xu xw)
% 238.91/239.17 (And
% 238.91/239.17 (Or (aReductOfIn0 xw xu xR)
% 238.91/239.17 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xu xR)) (sdtmndtplgtdt0 W0 xR xw)))
% 238.91/239.17 (sdtmndtplgtdt0 xu xR xw))))
% 238.91/239.17 (sdtmndtasgtdt0 xu xR xw))
% 238.91/239.17 (Or (Eq xv xw)
% 238.91/239.17 (And
% 238.91/239.17 (Or (aReductOfIn0 xw xv xR)
% 238.91/239.17 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xv xR)) (sdtmndtplgtdt0 W0 xR xw)))
% 238.91/239.17 (sdtmndtplgtdt0 xv xR xw))))
% 238.91/239.17 True
% 238.91/239.17 Clause #314 (by clausification #[22]): Eq
% 238.91/239.17 (Exists fun W0 =>
% 238.91/239.17 Or
% 238.91/239.17 (And
% 238.91/239.17 (And (aElement0 W0)
% 238.91/239.17 (Or
% 238.91/239.17 (Or
% 238.91/239.17 (Or (Or (Eq xw W0) (aReductOfIn0 W0 xw xR))
% 238.91/239.17 (Exists fun W1 => And (And (aElement0 W1) (aReductOfIn0 W1 xw xR)) (sdtmndtplgtdt0 W1 xR W0)))
% 238.91/239.17 (sdtmndtplgtdt0 xw xR W0))
% 238.91/239.17 (sdtmndtasgtdt0 xw xR W0)))
% 238.91/239.17 (Not (Exists fun W1 => aReductOfIn0 W1 W0 xR)))
% 238.91/239.17 (aNormalFormOfIn0 W0 xw xR))
% 238.91/239.17 False
% 238.91/239.17 Clause #315 (by clausification #[314]): ∀ (a : Iota),
% 238.91/239.17 Eq
% 238.91/239.17 (Or
% 238.91/239.17 (And
% 238.91/239.17 (And (aElement0 a)
% 238.91/239.17 (Or
% 238.91/239.17 (Or
% 238.91/239.17 (Or (Or (Eq xw a) (aReductOfIn0 a xw xR))
% 238.91/239.17 (Exists fun W1 => And (And (aElement0 W1) (aReductOfIn0 W1 xw xR)) (sdtmndtplgtdt0 W1 xR a)))
% 238.91/239.17 (sdtmndtplgtdt0 xw xR a))
% 238.91/239.17 (sdtmndtasgtdt0 xw xR a)))
% 238.91/239.17 (Not (Exists fun W1 => aReductOfIn0 W1 a xR)))
% 238.91/239.17 (aNormalFormOfIn0 a xw xR))
% 238.91/239.17 False
% 238.91/239.17 Clause #316 (by clausification #[315]): ∀ (a : Iota), Eq (aNormalFormOfIn0 a xw xR) False
% 238.91/239.17 Clause #386 (by clausification #[100]): ∀ (a a_1 : Iota),
% 238.91/239.17 Or (Eq (isTerminating0 xR) False) (Or (Eq (aElement0 a) False) (Eq (aNormalFormOfIn0 (skS.0 0 a xR a_1) a xR) True))
% 238.91/239.17 Clause #387 (by forward demodulation #[386, 230]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (aElement0 a) False) (Eq (aNormalFormOfIn0 (skS.0 0 a xR a_1) a xR) True))
% 238.91/239.17 Clause #388 (by clausification #[387]): ∀ (a a_1 : Iota), Or (Eq (aElement0 a) False) (Eq (aNormalFormOfIn0 (skS.0 0 a xR a_1) a xR) True)
% 238.91/239.17 Clause #1261 (by clausification #[303]): Eq
% 238.91/239.17 (And
% 238.91/239.17 (And (aElement0 xw)
% 238.91/239.17 (Or (Eq xu xw)
% 238.91/239.17 (And
% 238.91/239.17 (Or (aReductOfIn0 xw xu xR)
% 238.91/239.17 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xu xR)) (sdtmndtplgtdt0 W0 xR xw)))
% 238.91/239.17 (sdtmndtplgtdt0 xu xR xw))))
% 238.91/239.17 (sdtmndtasgtdt0 xu xR xw))
% 238.91/239.17 True
% 238.91/239.17 Clause #10045 (by clausification #[1261]): Eq
% 238.91/239.17 (And (aElement0 xw)
% 238.91/239.17 (Or (Eq xu xw)
% 238.91/239.17 (And
% 238.91/239.17 (Or (aReductOfIn0 xw xu xR)
% 238.91/239.17 (Exists fun W0 => And (And (aElement0 W0) (aReductOfIn0 W0 xu xR)) (sdtmndtplgtdt0 W0 xR xw)))
% 238.91/239.17 (sdtmndtplgtdt0 xu xR xw))))
% 238.91/239.17 True
% 238.91/239.17 Clause #11667 (by clausification #[10045]): Eq (aElement0 xw) True
% 238.91/239.17 Clause #11695 (by superposition #[11667, 388]): ∀ (a : Iota), Or (Eq True False) (Eq (aNormalFormOfIn0 (skS.0 0 xw xR a) xw xR) True)
% 238.91/239.17 Clause #12187 (by clausification #[11695]): ∀ (a : Iota), Eq (aNormalFormOfIn0 (skS.0 0 xw xR a) xw xR) True
% 238.91/239.17 Clause #12188 (by superposition #[12187, 316]): Eq True False
% 238.91/239.17 Clause #12189 (by clausification #[12188]): False
% 238.91/239.17 SZS output end Proof for theBenchmark.p
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