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Duper---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : GEO237+3 : TPTP v9.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n007.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 07:48:19 PM UTC 2025

% Result   : Theorem 26.55s 26.80s
% Output   : Proof 26.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : GEO237+3 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.13  % Command    : duper %s
% 0.13/0.34  % Computer : n007.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   : Fri Oct  3 12:44:23 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 26.55/26.80  SZS status Theorem for theBenchmark.p
% 26.55/26.80  SZS output start Proof for theBenchmark.p
% 26.55/26.80  Clause #7 (by assumption #[]): Eq
% 26.55/26.80    (∀ (A B L : Iota),
% 26.55/26.80      Iff (divides_points L A B)
% 26.55/26.80        (Or (And (left_apart_point A L) (right_apart_point B L)) (And (right_apart_point A L) (left_apart_point B L))))
% 26.55/26.80    True
% 26.55/26.80  Clause #19 (by assumption #[]): Eq (∀ (A L : Iota), Not (Or (left_apart_point A L) (left_apart_point A (reverse_line L)))) True
% 26.55/26.80  Clause #36 (by assumption #[]): Eq
% 26.55/26.80    (Not
% 26.55/26.80      (∀ (A B C L : Iota),
% 26.55/26.80        apart_point_and_line C L → divides_points L A B → Or (divides_points L A C) (divides_points L B C)))
% 26.55/26.80    True
% 26.55/26.80  Clause #132 (by clausification #[7]): ∀ (a : Iota),
% 26.55/26.80    Eq
% 26.55/26.80      (∀ (B L : Iota),
% 26.55/26.80        Iff (divides_points L a B)
% 26.55/26.80          (Or (And (left_apart_point a L) (right_apart_point B L)) (And (right_apart_point a L) (left_apart_point B L))))
% 26.55/26.80      True
% 26.55/26.80  Clause #133 (by clausification #[132]): ∀ (a a_1 : Iota),
% 26.55/26.80    Eq
% 26.55/26.80      (∀ (L : Iota),
% 26.55/26.80        Iff (divides_points L a a_1)
% 26.55/26.80          (Or (And (left_apart_point a L) (right_apart_point a_1 L))
% 26.55/26.80            (And (right_apart_point a L) (left_apart_point a_1 L))))
% 26.55/26.80      True
% 26.55/26.80  Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 : Iota),
% 26.55/26.80    Eq
% 26.55/26.80      (Iff (divides_points a a_1 a_2)
% 26.55/26.80        (Or (And (left_apart_point a_1 a) (right_apart_point a_2 a))
% 26.55/26.80          (And (right_apart_point a_1 a) (left_apart_point a_2 a))))
% 26.55/26.80      True
% 26.55/26.80  Clause #136 (by clausification #[134]): ∀ (a a_1 a_2 : Iota),
% 26.55/26.80    Or (Eq (divides_points a a_1 a_2) False)
% 26.55/26.80      (Eq
% 26.55/26.80        (Or (And (left_apart_point a_1 a) (right_apart_point a_2 a))
% 26.55/26.80          (And (right_apart_point a_1 a) (left_apart_point a_2 a)))
% 26.55/26.80        True)
% 26.55/26.80  Clause #163 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (L : Iota), Not (Or (left_apart_point a L) (left_apart_point a (reverse_line L)))) True
% 26.55/26.80  Clause #164 (by clausification #[163]): ∀ (a a_1 : Iota), Eq (Not (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1)))) True
% 26.55/26.80  Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Eq (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1))) False
% 26.55/26.80  Clause #167 (by clausification #[165]): ∀ (a a_1 : Iota), Eq (left_apart_point a a_1) False
% 26.55/26.80  Clause #361 (by clausification #[36]): Eq
% 26.55/26.80    (∀ (A B C L : Iota),
% 26.55/26.80      apart_point_and_line C L → divides_points L A B → Or (divides_points L A C) (divides_points L B C))
% 26.55/26.80    False
% 26.55/26.80  Clause #362 (by clausification #[361]): ∀ (a : Iota),
% 26.55/26.80    Eq
% 26.55/26.80      (Not
% 26.55/26.80        (∀ (B C L : Iota),
% 26.55/26.80          apart_point_and_line C L →
% 26.55/26.80            divides_points L (skS.0 0 a) B → Or (divides_points L (skS.0 0 a) C) (divides_points L B C)))
% 26.55/26.80      True
% 26.55/26.80  Clause #363 (by clausification #[362]): ∀ (a : Iota),
% 26.55/26.80    Eq
% 26.55/26.80      (∀ (B C L : Iota),
% 26.55/26.80        apart_point_and_line C L →
% 26.55/26.80          divides_points L (skS.0 0 a) B → Or (divides_points L (skS.0 0 a) C) (divides_points L B C))
% 26.55/26.80      False
% 26.55/26.80  Clause #364 (by clausification #[363]): ∀ (a a_1 : Iota),
% 26.55/26.80    Eq
% 26.55/26.80      (Not
% 26.55/26.80        (∀ (C L : Iota),
% 26.55/26.80          apart_point_and_line C L →
% 26.55/26.80            divides_points L (skS.0 0 a) (skS.0 1 a a_1) →
% 26.55/26.80              Or (divides_points L (skS.0 0 a) C) (divides_points L (skS.0 1 a a_1) C)))
% 26.55/26.80      True
% 26.55/26.80  Clause #365 (by clausification #[364]): ∀ (a a_1 : Iota),
% 26.55/26.80    Eq
% 26.55/26.80      (∀ (C L : Iota),
% 26.55/26.80        apart_point_and_line C L →
% 26.55/26.80          divides_points L (skS.0 0 a) (skS.0 1 a a_1) →
% 26.55/26.80            Or (divides_points L (skS.0 0 a) C) (divides_points L (skS.0 1 a a_1) C))
% 26.55/26.80      False
% 26.55/26.80  Clause #366 (by clausification #[365]): ∀ (a a_1 a_2 : Iota),
% 26.55/26.80    Eq
% 26.55/26.80      (Not
% 26.55/26.80        (∀ (L : Iota),
% 26.55/26.80          apart_point_and_line (skS.0 2 a a_1 a_2) L →
% 26.55/26.80            divides_points L (skS.0 0 a) (skS.0 1 a a_1) →
% 26.55/26.80              Or (divides_points L (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 26.55/26.80                (divides_points L (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 26.55/26.80      True
% 26.55/26.80  Clause #367 (by clausification #[366]): ∀ (a a_1 a_2 : Iota),
% 26.55/26.80    Eq
% 26.55/26.80      (∀ (L : Iota),
% 26.55/26.80        apart_point_and_line (skS.0 2 a a_1 a_2) L →
% 26.55/26.80          divides_points L (skS.0 0 a) (skS.0 1 a a_1) →
% 26.55/26.80            Or (divides_points L (skS.0 0 a) (skS.0 2 a a_1 a_2)) (divides_points L (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 26.55/26.80      False
% 26.55/26.80  Clause #368 (by clausification #[367]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.64/26.87    Eq
% 26.64/26.87      (Not
% 26.64/26.87        (apart_point_and_line (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) →
% 26.64/26.87          divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 1 a a_1) →
% 26.64/26.87            Or (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 26.64/26.87              (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 26.64/26.87      True
% 26.64/26.87  Clause #369 (by clausification #[368]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.64/26.87    Eq
% 26.64/26.87      (apart_point_and_line (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) →
% 26.64/26.87        divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 1 a a_1) →
% 26.64/26.87          Or (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 26.64/26.87            (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 26.64/26.87      False
% 26.64/26.87  Clause #371 (by clausification #[369]): ∀ (a a_1 a_2 a_3 : Iota),
% 26.64/26.87    Eq
% 26.64/26.87      (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 1 a a_1) →
% 26.64/26.87        Or (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 26.64/26.87          (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 26.64/26.87      False
% 26.64/26.87  Clause #489 (by clausification #[136]): ∀ (a a_1 a_2 : Iota),
% 26.64/26.87    Or (Eq (divides_points a a_1 a_2) False)
% 26.64/26.87      (Or (Eq (And (left_apart_point a_1 a) (right_apart_point a_2 a)) True)
% 26.64/26.87        (Eq (And (right_apart_point a_1 a) (left_apart_point a_2 a)) True))
% 26.64/26.87  Clause #491 (by clausification #[489]): ∀ (a a_1 a_2 : Iota),
% 26.64/26.87    Or (Eq (divides_points a a_1 a_2) False)
% 26.64/26.87      (Or (Eq (And (right_apart_point a_1 a) (left_apart_point a_2 a)) True) (Eq (left_apart_point a_1 a) True))
% 26.64/26.87  Clause #3293 (by clausification #[371]): ∀ (a a_1 a_2 a_3 : Iota), Eq (divides_points (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) (skS.0 1 a a_1)) True
% 26.64/26.87  Clause #8493 (by clausification #[491]): ∀ (a a_1 a_2 : Iota),
% 26.64/26.87    Or (Eq (divides_points a a_1 a_2) False) (Or (Eq (left_apart_point a_1 a) True) (Eq (left_apart_point a_2 a) True))
% 26.64/26.87  Clause #8495 (by forward demodulation #[8493, 167]): ∀ (a a_1 a_2 : Iota), Or (Eq (divides_points a a_1 a_2) False) (Or (Eq False True) (Eq (left_apart_point a_2 a) True))
% 26.64/26.87  Clause #8496 (by clausification #[8495]): ∀ (a a_1 a_2 : Iota), Or (Eq (divides_points a a_1 a_2) False) (Eq (left_apart_point a_2 a) True)
% 26.64/26.87  Clause #8497 (by forward demodulation #[8496, 167]): ∀ (a a_1 a_2 : Iota), Or (Eq (divides_points a a_1 a_2) False) (Eq False True)
% 26.64/26.87  Clause #8498 (by clausification #[8497]): ∀ (a a_1 a_2 : Iota), Eq (divides_points a a_1 a_2) False
% 26.64/26.87  Clause #8499 (by superposition #[8498, 3293]): Eq False True
% 26.64/26.87  Clause #8500 (by clausification #[8499]): False
% 26.64/26.87  SZS output end Proof for theBenchmark.p
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