%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GEO002-3 : 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 : n019.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 0.19s 0.45s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO002-3 : 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
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Aug 29 22:51:57 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.45  
% 0.19/0.45  % SZS status Unsatisfiable
% 0.19/0.45  
% 0.19/0.45  % SZS output start Proof
% 0.19/0.45  Take the following subset of the input axioms:
% 0.19/0.45    fof(prove_a_between_a_and_b, negated_conjecture, ~between(a, a, b)).
% 0.19/0.45    fof(t1, axiom, ![V, W, U]: (~between(U, V, W) | between(W, V, U))).
% 0.19/0.45    fof(t3, axiom, ![V2, U2]: between(U2, V2, V2)).
% 0.19/0.45  
% 0.19/0.45  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.45  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.45  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.45    fresh(y, y, x1...xn) = u
% 0.19/0.45    C => fresh(s, t, x1...xn) = v
% 0.19/0.45  where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.45  variables of u and v.
% 0.19/0.45  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.45  input problem has no model of domain size 1).
% 0.19/0.45  
% 0.19/0.45  The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.46  
% 0.19/0.46  Axiom 1 (t3): between(X, Y, Y) = true.
% 0.19/0.46  Axiom 2 (t1): fresh6(X, X, Y, Z, W) = true.
% 0.19/0.46  Axiom 3 (t1): fresh6(between(X, Y, Z), true, X, Y, Z) = between(Z, Y, X).
% 0.19/0.46  
% 0.19/0.46  Goal 1 (prove_a_between_a_and_b): between(a, a, b) = true.
% 0.19/0.46  Proof:
% 0.19/0.46    between(a, a, b)
% 0.19/0.46  = { by axiom 3 (t1) R->L }
% 0.19/0.46    fresh6(between(b, a, a), true, b, a, a)
% 0.19/0.46  = { by axiom 1 (t3) }
% 0.19/0.46    fresh6(true, true, b, a, a)
% 0.19/0.46  = { by axiom 2 (t1) }
% 0.19/0.46    true
% 0.19/0.46  % SZS output end Proof
% 0.19/0.46  
% 0.19/0.46  RESULT: Unsatisfiable (the axioms are contradictory).
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