%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GEO020-3 : 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 : n029.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 23:26:52 EDT 2023

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : GEO020-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Aug 29 23:39:12 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.42  Command-line arguments: --no-flatten-goal
% 0.20/0.42  
% 0.20/0.42  % SZS status Unsatisfiable
% 0.20/0.42  
% 0.20/0.42  % SZS output start Proof
% 0.20/0.42  Take the following subset of the input axioms:
% 0.20/0.42    fof(d2, axiom, ![X, V, W, U]: (~equidistant(U, V, W, X) | equidistant(W, X, U, V))).
% 0.20/0.42    fof(d3, axiom, ![V2, X2, W2, U2]: (~equidistant(U2, V2, W2, X2) | equidistant(V2, U2, W2, X2))).
% 0.20/0.42    fof(prove_symmetry, negated_conjecture, ~equidistant(x, w, u, v)).
% 0.20/0.43    fof(u_to_v_equals_w_to_x, hypothesis, equidistant(u, v, w, x)).
% 0.20/0.43  
% 0.20/0.43  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.43  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.43  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.43    fresh(y, y, x1...xn) = u
% 0.20/0.43    C => fresh(s, t, x1...xn) = v
% 0.20/0.43  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.43  variables of u and v.
% 0.20/0.43  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.43  input problem has no model of domain size 1).
% 0.20/0.43  
% 0.20/0.43  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.43  
% 0.20/0.43  Axiom 1 (u_to_v_equals_w_to_x): equidistant(u, v, w, x) = true.
% 0.20/0.43  Axiom 2 (d2): fresh10(X, X, Y, Z, W, V) = true.
% 0.20/0.43  Axiom 3 (d3): fresh9(X, X, Y, Z, W, V) = true.
% 0.20/0.43  Axiom 4 (d2): fresh10(equidistant(X, Y, Z, W), true, X, Y, Z, W) = equidistant(Z, W, X, Y).
% 0.20/0.43  Axiom 5 (d3): fresh9(equidistant(X, Y, Z, W), true, X, Y, Z, W) = equidistant(Y, X, Z, W).
% 0.20/0.43  
% 0.20/0.43  Goal 1 (prove_symmetry): equidistant(x, w, u, v) = true.
% 0.20/0.43  Proof:
% 0.20/0.43    equidistant(x, w, u, v)
% 0.20/0.43  = { by axiom 5 (d3) R->L }
% 0.20/0.43    fresh9(equidistant(w, x, u, v), true, w, x, u, v)
% 0.20/0.43  = { by axiom 4 (d2) R->L }
% 0.20/0.43    fresh9(fresh10(equidistant(u, v, w, x), true, u, v, w, x), true, w, x, u, v)
% 0.20/0.43  = { by axiom 1 (u_to_v_equals_w_to_x) }
% 0.20/0.43    fresh9(fresh10(true, true, u, v, w, x), true, w, x, u, v)
% 0.20/0.43  = { by axiom 2 (d2) }
% 0.20/0.43    fresh9(true, true, w, x, u, v)
% 0.20/0.43  = { by axiom 3 (d3) }
% 0.20/0.43    true
% 0.20/0.43  % SZS output end Proof
% 0.20/0.43  
% 0.20/0.43  RESULT: Unsatisfiable (the axioms are contradictory).
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