%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GEO055-3 : 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 : n026.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 0.21s 0.46s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GEO055-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % 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 : n026.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 23:30:21 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.46  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.46  
% 0.21/0.46  % SZS status Unsatisfiable
% 0.21/0.46  
% 0.21/0.46  % SZS output start Proof
% 0.21/0.46  Take the following subset of the input axioms:
% 0.21/0.46    fof(prove_equidistance, negated_conjecture, ~equidistant(v, reflection(u, v), u, v)).
% 0.21/0.46    fof(reflection, axiom, ![V, U]: reflection(U, V)=extension(U, V, U, V)).
% 0.21/0.46    fof(segment_construction2, axiom, ![X, Y, V2, W]: equidistant(Y, extension(X, Y, W, V2), W, V2)).
% 0.21/0.46  
% 0.21/0.46  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.46  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.46  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.46    fresh(y, y, x1...xn) = u
% 0.21/0.46    C => fresh(s, t, x1...xn) = v
% 0.21/0.46  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.46  variables of u and v.
% 0.21/0.46  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.46  input problem has no model of domain size 1).
% 0.21/0.46  
% 0.21/0.46  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.46  
% 0.21/0.46  Axiom 1 (reflection): reflection(X, Y) = extension(X, Y, X, Y).
% 0.21/0.46  Axiom 2 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 0.21/0.46  
% 0.21/0.46  Goal 1 (prove_equidistance): equidistant(v, reflection(u, v), u, v) = true.
% 0.21/0.46  Proof:
% 0.21/0.46    equidistant(v, reflection(u, v), u, v)
% 0.21/0.46  = { by axiom 1 (reflection) }
% 0.21/0.46    equidistant(v, extension(u, v, u, v), u, v)
% 0.21/0.46  = { by axiom 2 (segment_construction2) }
% 0.21/0.46    true
% 0.21/0.46  % SZS output end Proof
% 0.21/0.46  
% 0.21/0.46  RESULT: Unsatisfiable (the axioms are contradictory).
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