%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GEO039-3 : 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 23:27:00 EDT 2023

% Result   : Unsatisfiable 0.20s 0.46s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GEO039-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14  % 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 21:54:27 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.46  Command-line arguments: --no-flatten-goal
% 0.20/0.46  
% 0.20/0.46  % SZS status Unsatisfiable
% 0.20/0.46  
% 0.20/0.46  % SZS output start Proof
% 0.20/0.46  Take the following subset of the input axioms:
% 0.20/0.46    fof(identity_for_betweeness, axiom, ![X, Y]: (~between(X, Y, X) | X=Y)).
% 0.20/0.46    fof(prove_corollary, negated_conjecture, ~between(v, w, x)).
% 0.20/0.46    fof(t3, axiom, ![V, U]: between(U, V, V)).
% 0.20/0.46    fof(u_is_x, hypothesis, u=x).
% 0.20/0.46    fof(w_between_u_and_x, hypothesis, between(u, w, x)).
% 0.20/0.46  
% 0.20/0.46  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.46  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.46  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.46    fresh(y, y, x1...xn) = u
% 0.20/0.46    C => fresh(s, t, x1...xn) = v
% 0.20/0.46  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.46  variables of u and v.
% 0.20/0.46  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.46  input problem has no model of domain size 1).
% 0.20/0.46  
% 0.20/0.46  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.46  
% 0.20/0.46  Axiom 1 (u_is_x): u = x.
% 0.20/0.46  Axiom 2 (t3): between(X, Y, Y) = true.
% 0.20/0.46  Axiom 3 (w_between_u_and_x): between(u, w, x) = true.
% 0.20/0.46  Axiom 4 (identity_for_betweeness): fresh3(X, X, Y, Z) = Z.
% 0.20/0.46  Axiom 5 (identity_for_betweeness): fresh3(between(X, Y, X), true, X, Y) = X.
% 0.20/0.46  
% 0.20/0.46  Goal 1 (prove_corollary): between(v, w, x) = true.
% 0.20/0.46  Proof:
% 0.20/0.47    between(v, w, x)
% 0.20/0.47  = { by axiom 1 (u_is_x) R->L }
% 0.20/0.47    between(v, w, u)
% 0.20/0.47  = { by axiom 4 (identity_for_betweeness) R->L }
% 0.20/0.47    between(v, fresh3(true, true, u, w), u)
% 0.20/0.47  = { by axiom 3 (w_between_u_and_x) R->L }
% 0.20/0.47    between(v, fresh3(between(u, w, x), true, u, w), u)
% 0.20/0.47  = { by axiom 1 (u_is_x) R->L }
% 0.20/0.47    between(v, fresh3(between(u, w, u), true, u, w), u)
% 0.20/0.47  = { by axiom 5 (identity_for_betweeness) }
% 0.20/0.47    between(v, u, u)
% 0.20/0.47  = { by axiom 2 (t3) }
% 0.20/0.47    true
% 0.20/0.47  % SZS output end Proof
% 0.20/0.47  
% 0.20/0.47  RESULT: Unsatisfiable (the axioms are contradictory).
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