%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GEO003-2 : 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 : n004.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 23:26:43 EDT 2023

% Result   : Unsatisfiable 0.22s 0.44s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GEO003-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.15  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.37  % Computer : n004.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Tue Aug 29 19:50:52 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 0.22/0.44  Command-line arguments: --no-flatten-goal
% 0.22/0.44  
% 0.22/0.44  % SZS status Unsatisfiable
% 0.22/0.45  
% 0.22/0.45  % SZS output start Proof
% 0.22/0.45  Take the following subset of the input axioms:
% 0.22/0.45    fof(identity_for_equidistance, axiom, ![X, Y, Z]: (~equidistant(X, Y, Z, Z) | X=Y)).
% 0.22/0.45    fof(prove_b_between_a_and_b, negated_conjecture, ~between(a, b, b)).
% 0.22/0.45    fof(segment_construction1, axiom, ![V, W, X2, Y2]: between(X2, Y2, extension(X2, Y2, W, V))).
% 0.22/0.45    fof(segment_construction2, axiom, ![V2, X2, Y2, W2]: equidistant(Y2, extension(X2, Y2, W2, V2), W2, V2)).
% 0.22/0.45  
% 0.22/0.45  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.45  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.45  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.45    fresh(y, y, x1...xn) = u
% 0.22/0.45    C => fresh(s, t, x1...xn) = v
% 0.22/0.45  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.45  variables of u and v.
% 0.22/0.45  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.45  input problem has no model of domain size 1).
% 0.22/0.45  
% 0.22/0.45  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.45  
% 0.22/0.45  Axiom 1 (identity_for_equidistance): fresh(X, X, Y, Z) = Z.
% 0.22/0.45  Axiom 2 (segment_construction1): between(X, Y, extension(X, Y, Z, W)) = true.
% 0.22/0.45  Axiom 3 (identity_for_equidistance): fresh(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 0.22/0.45  Axiom 4 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 0.22/0.45  
% 0.22/0.45  Goal 1 (prove_b_between_a_and_b): between(a, b, b) = true.
% 0.22/0.45  Proof:
% 0.22/0.45    between(a, b, b)
% 0.22/0.45  = { by axiom 3 (identity_for_equidistance) R->L }
% 0.22/0.45    between(a, b, fresh(equidistant(b, extension(a, b, X, X), X, X), true, b, extension(a, b, X, X)))
% 0.22/0.45  = { by axiom 4 (segment_construction2) }
% 0.22/0.45    between(a, b, fresh(true, true, b, extension(a, b, X, X)))
% 0.22/0.45  = { by axiom 1 (identity_for_equidistance) }
% 0.22/0.45    between(a, b, extension(a, b, X, X))
% 0.22/0.45  = { by axiom 2 (segment_construction1) }
% 0.22/0.45    true
% 0.22/0.45  % SZS output end Proof
% 0.22/0.45  
% 0.22/0.45  RESULT: Unsatisfiable (the axioms are contradictory).
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