%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GEO065-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n003.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 23:27:10 EDT 2023

% Result   : Unsatisfiable 0.21s 0.56s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GEO065-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Tue Aug 29 21:28:11 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.56  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.56  
% 0.21/0.56  % SZS status Unsatisfiable
% 0.21/0.56  
% 0.21/0.56  % SZS output start Proof
% 0.21/0.56  Take the following subset of the input axioms:
% 0.21/0.56    fof(colinearity2, axiom, ![X, Y, Z]: (~between(Y, Z, X) | colinear(X, Y, Z))).
% 0.21/0.56    fof(prove_uvw_colinear, negated_conjecture, ~colinear(u, v, w)).
% 0.21/0.56    fof(t1, axiom, ![V, W, U]: (~between(U, V, W) | between(W, V, U))).
% 0.21/0.56    fof(w_between_u_and_v, hypothesis, between(u, w, v)).
% 0.21/0.56  
% 0.21/0.56  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.56  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.56  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.56    fresh(y, y, x1...xn) = u
% 0.21/0.56    C => fresh(s, t, x1...xn) = v
% 0.21/0.56  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.56  variables of u and v.
% 0.21/0.56  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.56  input problem has no model of domain size 1).
% 0.21/0.56  
% 0.21/0.56  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.56  
% 0.21/0.57  Axiom 1 (w_between_u_and_v): between(u, w, v) = true2.
% 0.21/0.57  Axiom 2 (colinearity2): fresh39(X, X, Y, Z, W) = true2.
% 0.21/0.57  Axiom 3 (t1): fresh15(X, X, Y, Z, W) = true2.
% 0.21/0.57  Axiom 4 (colinearity2): fresh39(between(X, Y, Z), true2, X, Y, Z) = colinear(Z, X, Y).
% 0.21/0.57  Axiom 5 (t1): fresh15(between(X, Y, Z), true2, X, Y, Z) = between(Z, Y, X).
% 0.21/0.57  
% 0.21/0.57  Goal 1 (prove_uvw_colinear): colinear(u, v, w) = true2.
% 0.21/0.57  Proof:
% 0.21/0.57    colinear(u, v, w)
% 0.21/0.57  = { by axiom 4 (colinearity2) R->L }
% 0.21/0.57    fresh39(between(v, w, u), true2, v, w, u)
% 0.21/0.57  = { by axiom 5 (t1) R->L }
% 0.21/0.57    fresh39(fresh15(between(u, w, v), true2, u, w, v), true2, v, w, u)
% 0.21/0.57  = { by axiom 1 (w_between_u_and_v) }
% 0.21/0.57    fresh39(fresh15(true2, true2, u, w, v), true2, v, w, u)
% 0.21/0.57  = { by axiom 3 (t1) }
% 0.21/0.57    fresh39(true2, true2, v, w, u)
% 0.21/0.57  = { by axiom 2 (colinearity2) }
% 0.21/0.57    true2
% 0.21/0.57  % SZS output end Proof
% 0.21/0.57  
% 0.21/0.57  RESULT: Unsatisfiable (the axioms are contradictory).
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