↑ Up

Duper---1.0.THM-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz 
%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : COM012+1 : TPTP v9.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n001.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 Oct  3 07:45:47 PM UTC 2025

% Result   : Theorem 3.97s 4.17s
% Output   : Proof 4.06s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : COM012+1 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.13  % Command    : duper %s
% 0.13/0.34  % Computer : n001.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Oct  2 15:53:53 EDT 2025
% 0.13/0.35  % CPUTime    : 
% 3.97/4.17  SZS status Theorem for theBenchmark.p
% 3.97/4.17  SZS output start Proof for theBenchmark.p
% 3.97/4.17  Clause #6 (by assumption #[]): Eq
% 3.97/4.17    (∀ (W0 W1 W2 W3 : Iota),
% 3.97/4.17      And (And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2)) (aElement0 W3) →
% 3.97/4.17        And (sdtmndtplgtdt0 W0 W1 W2) (sdtmndtplgtdt0 W2 W1 W3) → sdtmndtplgtdt0 W0 W1 W3)
% 3.97/4.17    True
% 3.97/4.17  Clause #7 (by assumption #[]): Eq
% 3.97/4.17    (∀ (W0 W1 W2 : Iota),
% 3.97/4.17      And (And (aElement0 W0) (aRewritingSystem0 W1)) (aElement0 W2) →
% 3.97/4.17        Iff (sdtmndtasgtdt0 W0 W1 W2) (Or (Eq W0 W2) (sdtmndtplgtdt0 W0 W1 W2)))
% 3.97/4.17    True
% 3.97/4.17  Clause #8 (by assumption #[]): Eq (And (And (And (aElement0 xx) (aRewritingSystem0 xR)) (aElement0 xy)) (aElement0 xz)) True
% 3.97/4.17  Clause #9 (by assumption #[]): Eq (Not (And (sdtmndtasgtdt0 xx xR xy) (sdtmndtasgtdt0 xy xR xz) → sdtmndtasgtdt0 xx xR xz)) True
% 3.97/4.17  Clause #19 (by clausification #[9]): Eq (And (sdtmndtasgtdt0 xx xR xy) (sdtmndtasgtdt0 xy xR xz) → sdtmndtasgtdt0 xx xR xz) False
% 3.97/4.17  Clause #20 (by clausification #[19]): Eq (And (sdtmndtasgtdt0 xx xR xy) (sdtmndtasgtdt0 xy xR xz)) True
% 3.97/4.17  Clause #21 (by clausification #[19]): Eq (sdtmndtasgtdt0 xx xR xz) False
% 3.97/4.17  Clause #22 (by clausification #[20]): Eq (sdtmndtasgtdt0 xy xR xz) True
% 3.97/4.17  Clause #23 (by clausification #[20]): Eq (sdtmndtasgtdt0 xx xR xy) True
% 3.97/4.17  Clause #37 (by clausification #[6]): ∀ (a : Iota),
% 3.97/4.17    Eq
% 3.97/4.17      (∀ (W1 W2 W3 : Iota),
% 3.97/4.17        And (And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2)) (aElement0 W3) →
% 3.97/4.17          And (sdtmndtplgtdt0 a W1 W2) (sdtmndtplgtdt0 W2 W1 W3) → sdtmndtplgtdt0 a W1 W3)
% 3.97/4.17      True
% 3.97/4.17  Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 3.97/4.17    Eq
% 3.97/4.17      (∀ (W2 W3 : Iota),
% 3.97/4.17        And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2)) (aElement0 W3) →
% 3.97/4.17          And (sdtmndtplgtdt0 a a_1 W2) (sdtmndtplgtdt0 W2 a_1 W3) → sdtmndtplgtdt0 a a_1 W3)
% 3.97/4.17      True
% 3.97/4.17  Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.17    Eq
% 3.97/4.17      (∀ (W3 : Iota),
% 3.97/4.17        And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 W3) →
% 3.97/4.17          And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 W3) → sdtmndtplgtdt0 a a_1 W3)
% 3.97/4.17      True
% 3.97/4.17  Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.17    Eq
% 3.97/4.17      (And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 a_3) →
% 3.97/4.17        And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3)
% 3.97/4.17      True
% 3.97/4.17  Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.17    Or (Eq (And (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) (aElement0 a_3)) False)
% 3.97/4.17      (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3) True)
% 3.97/4.17  Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.17    Or (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3) → sdtmndtplgtdt0 a a_1 a_3) True)
% 3.97/4.17      (Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False) (Eq (aElement0 a_3) False))
% 3.97/4.17  Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.17    Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False)
% 3.97/4.17      (Or (Eq (aElement0 a_3) False)
% 3.97/4.17        (Or (Eq (And (sdtmndtplgtdt0 a a_1 a_2) (sdtmndtplgtdt0 a_2 a_1 a_3)) False)
% 3.97/4.17          (Eq (sdtmndtplgtdt0 a a_1 a_3) True)))
% 3.97/4.17  Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.17    Or (Eq (aElement0 a) False)
% 3.97/4.17      (Or (Eq (And (sdtmndtplgtdt0 a_1 a_2 a_3) (sdtmndtplgtdt0 a_3 a_2 a)) False)
% 3.97/4.17        (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)
% 3.97/4.17          (Or (Eq (And (aElement0 a_1) (aRewritingSystem0 a_2)) False) (Eq (aElement0 a_3) False))))
% 3.97/4.17  Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.17    Or (Eq (aElement0 a) False)
% 3.97/4.17      (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)
% 3.97/4.17        (Or (Eq (And (aElement0 a_1) (aRewritingSystem0 a_2)) False)
% 3.97/4.17          (Or (Eq (aElement0 a_3) False)
% 3.97/4.17            (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a_3) False) (Eq (sdtmndtplgtdt0 a_3 a_2 a) False)))))
% 3.97/4.17  Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.17    Or (Eq (aElement0 a) False)
% 3.97/4.17      (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)
% 3.97/4.17        (Or (Eq (aElement0 a_3) False)
% 3.97/4.19          (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a_3) False)
% 3.97/4.19            (Or (Eq (sdtmndtplgtdt0 a_3 a_2 a) False)
% 3.97/4.19              (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))))
% 3.97/4.19  Clause #47 (by clausification #[8]): Eq (aElement0 xz) True
% 3.97/4.19  Clause #48 (by clausification #[8]): Eq (And (And (aElement0 xx) (aRewritingSystem0 xR)) (aElement0 xy)) True
% 3.97/4.19  Clause #50 (by superposition #[47, 46]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.19    Or (Eq True False)
% 3.97/4.19      (Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 3.97/4.19        (Or (Eq (aElement0 a_2) False)
% 3.97/4.19          (Or (Eq (sdtmndtplgtdt0 a a_1 a_2) False)
% 3.97/4.19            (Or (Eq (sdtmndtplgtdt0 a_2 a_1 xz) False)
% 3.97/4.19              (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))))))
% 3.97/4.19  Clause #51 (by clausification #[48]): Eq (aElement0 xy) True
% 3.97/4.19  Clause #52 (by clausification #[48]): Eq (And (aElement0 xx) (aRewritingSystem0 xR)) True
% 3.97/4.19  Clause #70 (by clausification #[52]): Eq (aRewritingSystem0 xR) True
% 3.97/4.19  Clause #71 (by clausification #[52]): Eq (aElement0 xx) True
% 3.97/4.19  Clause #80 (by clausification #[7]): ∀ (a : Iota),
% 3.97/4.19    Eq
% 3.97/4.19      (∀ (W1 W2 : Iota),
% 3.97/4.19        And (And (aElement0 a) (aRewritingSystem0 W1)) (aElement0 W2) →
% 3.97/4.19          Iff (sdtmndtasgtdt0 a W1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a W1 W2)))
% 3.97/4.19      True
% 3.97/4.19  Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota),
% 3.97/4.19    Eq
% 3.97/4.19      (∀ (W2 : Iota),
% 3.97/4.19        And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 W2) →
% 3.97/4.19          Iff (sdtmndtasgtdt0 a a_1 W2) (Or (Eq a W2) (sdtmndtplgtdt0 a a_1 W2)))
% 3.97/4.19      True
% 3.97/4.19  Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.19    Eq
% 3.97/4.19      (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2) →
% 3.97/4.19        Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)))
% 3.97/4.19      True
% 3.97/4.19  Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.19    Or (Eq (And (And (aElement0 a) (aRewritingSystem0 a_1)) (aElement0 a_2)) False)
% 3.97/4.19      (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 3.97/4.19  Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.19    Or (Eq (Iff (sdtmndtasgtdt0 a a_1 a_2) (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2))) True)
% 3.97/4.19      (Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False) (Eq (aElement0 a_2) False))
% 3.97/4.19  Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.19    Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False)
% 3.97/4.19      (Or (Eq (aElement0 a_2) False)
% 3.97/4.19        (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) True) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) False)))
% 3.97/4.19  Clause #86 (by clausification #[84]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.19    Or (Eq (And (aElement0 a) (aRewritingSystem0 a_1)) False)
% 3.97/4.19      (Or (Eq (aElement0 a_2) False)
% 3.97/4.19        (Or (Eq (sdtmndtasgtdt0 a a_1 a_2) False) (Eq (Or (Eq a a_2) (sdtmndtplgtdt0 a a_1 a_2)) True)))
% 3.97/4.19  Clause #87 (by clausification #[85]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.19    Or (Eq (aElement0 a) False)
% 3.97/4.19      (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 3.97/4.19        (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) False)
% 3.97/4.19          (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))
% 3.97/4.19  Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.19    Or (Eq (aElement0 a) False)
% 3.97/4.19      (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) True)
% 3.97/4.19        (Or (Eq (aElement0 a_1) False) (Or (Eq (aRewritingSystem0 a_2) False) (Eq (sdtmndtplgtdt0 a_1 a_2 a) False))))
% 3.97/4.19  Clause #90 (by superposition #[88, 47]): ∀ (a a_1 : Iota),
% 3.97/4.19    Or (Eq (sdtmndtasgtdt0 a a_1 xz) True)
% 3.97/4.19      (Or (Eq (aElement0 a) False)
% 3.97/4.19        (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xz) False) (Eq False True))))
% 3.97/4.19  Clause #97 (by clausification #[90]): ∀ (a a_1 : Iota),
% 3.97/4.19    Or (Eq (sdtmndtasgtdt0 a a_1 xz) True)
% 3.97/4.19      (Or (Eq (aElement0 a) False) (Or (Eq (aRewritingSystem0 a_1) False) (Eq (sdtmndtplgtdt0 a a_1 xz) False)))
% 3.97/4.19  Clause #100 (by superposition #[97, 71]): ∀ (a : Iota),
% 3.97/4.19    Or (Eq (sdtmndtasgtdt0 xx a xz) True)
% 3.97/4.19      (Or (Eq (aRewritingSystem0 a) False) (Or (Eq (sdtmndtplgtdt0 xx a xz) False) (Eq False True)))
% 3.97/4.19  Clause #101 (by clausification #[100]): ∀ (a : Iota),
% 3.97/4.19    Or (Eq (sdtmndtasgtdt0 xx a xz) True) (Or (Eq (aRewritingSystem0 a) False) (Eq (sdtmndtplgtdt0 xx a xz) False))
% 3.97/4.19  Clause #102 (by superposition #[101, 70]): Or (Eq (sdtmndtasgtdt0 xx xR xz) True) (Or (Eq (sdtmndtplgtdt0 xx xR xz) False) (Eq False True))
% 3.97/4.21  Clause #103 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.21    Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 3.97/4.21      (Or (Eq (aElement0 a_2) False)
% 3.97/4.21        (Or (Eq (sdtmndtplgtdt0 a a_1 a_2) False)
% 3.97/4.21          (Or (Eq (sdtmndtplgtdt0 a_2 a_1 xz) False) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False)))))
% 3.97/4.21  Clause #105 (by superposition #[103, 51]): ∀ (a a_1 : Iota),
% 3.97/4.21    Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 3.97/4.21      (Or (Eq (sdtmndtplgtdt0 a a_1 xy) False)
% 3.97/4.21        (Or (Eq (sdtmndtplgtdt0 xy a_1 xz) False)
% 3.97/4.21          (Or (Eq (aElement0 a) False) (Or (Eq (aRewritingSystem0 a_1) False) (Eq False True)))))
% 3.97/4.21  Clause #107 (by clausification #[102]): Or (Eq (sdtmndtasgtdt0 xx xR xz) True) (Eq (sdtmndtplgtdt0 xx xR xz) False)
% 3.97/4.21  Clause #210 (by clausification #[86]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.21    Or (Eq (aElement0 a) False)
% 3.97/4.21      (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 3.97/4.21        (Or (Eq (Or (Eq a_1 a) (sdtmndtplgtdt0 a_1 a_2 a)) True)
% 3.97/4.21          (Or (Eq (aElement0 a_1) False) (Eq (aRewritingSystem0 a_2) False))))
% 3.97/4.21  Clause #211 (by clausification #[210]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.21    Or (Eq (aElement0 a) False)
% 3.97/4.21      (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 3.97/4.21        (Or (Eq (aElement0 a_1) False)
% 3.97/4.21          (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (Eq a_1 a) True) (Eq (sdtmndtplgtdt0 a_1 a_2 a) True)))))
% 3.97/4.21  Clause #212 (by clausification #[211]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.21    Or (Eq (aElement0 a) False)
% 3.97/4.21      (Or (Eq (sdtmndtasgtdt0 a_1 a_2 a) False)
% 3.97/4.21        (Or (Eq (aElement0 a_1) False)
% 3.97/4.21          (Or (Eq (aRewritingSystem0 a_2) False) (Or (Eq (sdtmndtplgtdt0 a_1 a_2 a) True) (Eq a_1 a)))))
% 3.97/4.21  Clause #213 (by superposition #[212, 47]): ∀ (a a_1 : Iota),
% 3.97/4.21    Or (Eq (sdtmndtasgtdt0 a a_1 xz) False)
% 3.97/4.21      (Or (Eq (aElement0 a) False)
% 3.97/4.21        (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xz) True) (Or (Eq a xz) (Eq False True)))))
% 3.97/4.21  Clause #214 (by superposition #[212, 51]): ∀ (a a_1 : Iota),
% 3.97/4.21    Or (Eq (sdtmndtasgtdt0 a a_1 xy) False)
% 3.97/4.21      (Or (Eq (aElement0 a) False)
% 3.97/4.21        (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xy) True) (Or (Eq a xy) (Eq False True)))))
% 3.97/4.21  Clause #235 (by clausification #[214]): ∀ (a a_1 : Iota),
% 3.97/4.21    Or (Eq (sdtmndtasgtdt0 a a_1 xy) False)
% 3.97/4.21      (Or (Eq (aElement0 a) False)
% 3.97/4.21        (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xy) True) (Eq a xy))))
% 3.97/4.21  Clause #236 (by superposition #[235, 23]): Or (Eq (aElement0 xx) False)
% 3.97/4.21    (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Or (Eq xx xy) (Eq False True))))
% 3.97/4.21  Clause #238 (by clausification #[105]): ∀ (a a_1 : Iota),
% 3.97/4.21    Or (Eq (sdtmndtplgtdt0 a a_1 xz) True)
% 3.97/4.21      (Or (Eq (sdtmndtplgtdt0 a a_1 xy) False)
% 3.97/4.21        (Or (Eq (sdtmndtplgtdt0 xy a_1 xz) False) (Or (Eq (aElement0 a) False) (Eq (aRewritingSystem0 a_1) False))))
% 3.97/4.21  Clause #240 (by clausification #[236]): Or (Eq (aElement0 xx) False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)))
% 3.97/4.21  Clause #241 (by forward demodulation #[240, 71]): Or (Eq True False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)))
% 3.97/4.21  Clause #242 (by clausification #[241]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy))
% 3.97/4.21  Clause #243 (by forward demodulation #[242, 70]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy))
% 3.97/4.21  Clause #244 (by clausification #[243]): Or (Eq (sdtmndtplgtdt0 xx xR xy) True) (Eq xx xy)
% 3.97/4.21  Clause #245 (by superposition #[244, 238]): Or (Eq xx xy)
% 3.97/4.21    (Or (Eq (sdtmndtplgtdt0 xx xR xz) True)
% 3.97/4.21      (Or (Eq True False)
% 3.97/4.21        (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False)))))
% 3.97/4.21  Clause #246 (by clausification #[245]): Or (Eq xx xy)
% 3.97/4.21    (Or (Eq (sdtmndtplgtdt0 xx xR xz) True)
% 3.97/4.21      (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq (aElement0 xx) False) (Eq (aRewritingSystem0 xR) False))))
% 3.97/4.21  Clause #247 (by forward demodulation #[246, 71]): Or (Eq xx xy)
% 3.97/4.21    (Or (Eq (sdtmndtplgtdt0 xx xR xz) True)
% 3.97/4.21      (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Or (Eq True False) (Eq (aRewritingSystem0 xR) False))))
% 4.06/4.23  Clause #248 (by clausification #[247]): Or (Eq xx xy)
% 4.06/4.23    (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Eq (aRewritingSystem0 xR) False)))
% 4.06/4.23  Clause #249 (by forward demodulation #[248, 70]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) (Or (Eq (sdtmndtplgtdt0 xy xR xz) False) (Eq True False)))
% 4.06/4.23  Clause #250 (by clausification #[249]): Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) (Eq (sdtmndtplgtdt0 xy xR xz) False))
% 4.06/4.23  Clause #251 (by clausification #[213]): ∀ (a a_1 : Iota),
% 4.06/4.23    Or (Eq (sdtmndtasgtdt0 a a_1 xz) False)
% 4.06/4.23      (Or (Eq (aElement0 a) False)
% 4.06/4.23        (Or (Eq (aRewritingSystem0 a_1) False) (Or (Eq (sdtmndtplgtdt0 a a_1 xz) True) (Eq a xz))))
% 4.06/4.23  Clause #252 (by superposition #[251, 22]): Or (Eq (aElement0 xy) False)
% 4.06/4.23    (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Or (Eq xy xz) (Eq False True))))
% 4.06/4.23  Clause #256 (by clausification #[252]): Or (Eq (aElement0 xy) False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz)))
% 4.06/4.23  Clause #257 (by forward demodulation #[256, 51]): Or (Eq True False) (Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz)))
% 4.06/4.23  Clause #258 (by clausification #[257]): Or (Eq (aRewritingSystem0 xR) False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz))
% 4.06/4.23  Clause #259 (by forward demodulation #[258, 70]): Or (Eq True False) (Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz))
% 4.06/4.23  Clause #260 (by clausification #[259]): Or (Eq (sdtmndtplgtdt0 xy xR xz) True) (Eq xy xz)
% 4.06/4.23  Clause #261 (by superposition #[260, 250]): Or (Eq xy xz) (Or (Eq xx xy) (Or (Eq (sdtmndtplgtdt0 xx xR xz) True) (Eq True False)))
% 4.06/4.23  Clause #262 (by clausification #[261]): Or (Eq xy xz) (Or (Eq xx xy) (Eq (sdtmndtplgtdt0 xx xR xz) True))
% 4.06/4.23  Clause #263 (by superposition #[262, 107]): Or (Eq xy xz) (Or (Eq xx xy) (Or (Eq (sdtmndtasgtdt0 xx xR xz) True) (Eq True False)))
% 4.06/4.23  Clause #264 (by clausification #[263]): Or (Eq xy xz) (Or (Eq xx xy) (Eq (sdtmndtasgtdt0 xx xR xz) True))
% 4.06/4.23  Clause #265 (by superposition #[264, 21]): Or (Eq xy xz) (Or (Eq xx xy) (Eq True False))
% 4.06/4.23  Clause #267 (by clausification #[265]): Or (Eq xy xz) (Eq xx xy)
% 4.06/4.23  Clause #269 (by superposition #[267, 21]): Or (Eq xx xy) (Eq (sdtmndtasgtdt0 xx xR xy) False)
% 4.06/4.23  Clause #283 (by superposition #[269, 23]): Or (Eq xx xy) (Eq False True)
% 4.06/4.23  Clause #284 (by clausification #[283]): Eq xx xy
% 4.06/4.23  Clause #285 (by backward demodulation #[284, 22]): Eq (sdtmndtasgtdt0 xx xR xz) True
% 4.06/4.23  Clause #317 (by superposition #[285, 21]): Eq True False
% 4.06/4.23  Clause #320 (by clausification #[317]): False
% 4.06/4.23  SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------