%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GEO056-3 : 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 : 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 23:27:07 EDT 2023

% Result   : Unsatisfiable 0.23s 0.44s
% Output   : Proof 0.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GEO056-3 : 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
% 0.15/0.37  % Computer : n004.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Tue Aug 29 22:26:07 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.23/0.44  Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.23/0.44  
% 0.23/0.44  % SZS status Unsatisfiable
% 0.23/0.44  
% 0.23/0.44  % SZS output start Proof
% 0.23/0.44  Take the following subset of the input axioms:
% 0.23/0.44    fof(e1, axiom, ![V, W, U]: V=extension(U, V, W, W)).
% 0.23/0.44    fof(prove_v_equals_reflection, negated_conjecture, v!=reflection(u, v)).
% 0.23/0.44    fof(reflection, axiom, ![V2, U2]: reflection(U2, V2)=extension(U2, V2, U2, V2)).
% 0.23/0.44    fof(u_equals_v, hypothesis, u=v).
% 0.23/0.44  
% 0.23/0.44  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.23/0.44  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.23/0.44  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.23/0.44    fresh(y, y, x1...xn) = u
% 0.23/0.44    C => fresh(s, t, x1...xn) = v
% 0.23/0.44  where fresh is a fresh function symbol and x1..xn are the free
% 0.23/0.44  variables of u and v.
% 0.23/0.44  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.23/0.44  input problem has no model of domain size 1).
% 0.23/0.44  
% 0.23/0.44  The encoding turns the above axioms into the following unit equations and goals:
% 0.23/0.44  
% 0.23/0.44  Axiom 1 (u_equals_v): u = v.
% 0.23/0.44  Axiom 2 (reflection): reflection(X, Y) = extension(X, Y, X, Y).
% 0.23/0.44  Axiom 3 (e1): X = extension(Y, X, Z, Z).
% 0.23/0.44  
% 0.23/0.44  Goal 1 (prove_v_equals_reflection): v = reflection(u, v).
% 0.23/0.44  Proof:
% 0.23/0.44    v
% 0.23/0.44  = { by axiom 3 (e1) }
% 0.23/0.44    extension(v, v, v, v)
% 0.23/0.44  = { by axiom 2 (reflection) R->L }
% 0.23/0.44    reflection(v, v)
% 0.23/0.44  = { by axiom 1 (u_equals_v) R->L }
% 0.23/0.44    reflection(u, v)
% 0.23/0.44  % SZS output end Proof
% 0.23/0.44  
% 0.23/0.44  RESULT: Unsatisfiable (the axioms are contradictory).
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