%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GEO054-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n009.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 23:27:06 EDT 2023

% Result   : Unsatisfiable 0.14s 0.43s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : GEO054-2 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36  % Computer : n009.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Tue Aug 29 19:14:35 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 0.14/0.43  Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.14/0.43  
% 0.14/0.43  % SZS status Unsatisfiable
% 0.14/0.43  
% 0.14/0.43  % SZS output start Proof
% 0.14/0.43  Take the following subset of the input axioms:
% 0.14/0.43    fof(prove_v_between_u_and_reflection, negated_conjecture, ~between(u, v, reflection(u, v))).
% 0.14/0.43    fof(reflection, axiom, ![V, U]: reflection(U, V)=extension(U, V, U, V)).
% 0.14/0.43    fof(segment_construction1, axiom, ![X, Y, V2, W]: between(X, Y, extension(X, Y, W, V2))).
% 0.14/0.43  
% 0.14/0.43  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.43  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.43  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.43    fresh(y, y, x1...xn) = u
% 0.14/0.43    C => fresh(s, t, x1...xn) = v
% 0.14/0.43  where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.43  variables of u and v.
% 0.14/0.43  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.43  input problem has no model of domain size 1).
% 0.14/0.43  
% 0.14/0.43  The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.43  
% 0.14/0.43  Axiom 1 (reflection): reflection(X, Y) = extension(X, Y, X, Y).
% 0.14/0.43  Axiom 2 (segment_construction1): between(X, Y, extension(X, Y, Z, W)) = true.
% 0.14/0.43  
% 0.14/0.43  Goal 1 (prove_v_between_u_and_reflection): between(u, v, reflection(u, v)) = true.
% 0.14/0.43  Proof:
% 0.14/0.43    between(u, v, reflection(u, v))
% 0.14/0.44  = { by axiom 1 (reflection) }
% 0.14/0.44    between(u, v, extension(u, v, u, v))
% 0.14/0.44  = { by axiom 2 (segment_construction1) }
% 0.14/0.44    true
% 0.14/0.44  % SZS output end Proof
% 0.14/0.44  
% 0.14/0.44  RESULT: Unsatisfiable (the axioms are contradictory).
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