%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWV011-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n010.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 : Thu Aug 31 23:02:11 EDT 2023

% Result   : Unsatisfiable 0.22s 0.40s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWV011-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Tue Aug 29 08:26:48 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.40  Command-line arguments: --no-flatten-goal
% 0.22/0.40  
% 0.22/0.40  % SZS status Unsatisfiable
% 0.22/0.40  
% 0.22/0.40  % SZS output start Proof
% 0.22/0.40  Take the following subset of the input axioms:
% 0.22/0.40    fof(ax1_11, axiom, b_holds(key(generate_key(an_a_nonce), a))).
% 0.22/0.40    fof(ax3_13, axiom, a_holds(key(generate_key(an_a_nonce), b))).
% 0.22/0.40    fof(co1_17, negated_conjecture, ![A]: (~a_holds(key(A, b)) | ~b_holds(key(A, a)))).
% 0.22/0.40  
% 0.22/0.40  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.40  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.40  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.40    fresh(y, y, x1...xn) = u
% 0.22/0.40    C => fresh(s, t, x1...xn) = v
% 0.22/0.40  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.40  variables of u and v.
% 0.22/0.40  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.40  input problem has no model of domain size 1).
% 0.22/0.40  
% 0.22/0.40  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.40  
% 0.22/0.40  Axiom 1 (ax1_11): b_holds(key(generate_key(an_a_nonce), a)) = true2.
% 0.22/0.40  Axiom 2 (ax3_13): a_holds(key(generate_key(an_a_nonce), b)) = true2.
% 0.22/0.40  
% 0.22/0.40  Goal 1 (co1_17): tuple(b_holds(key(X, a)), a_holds(key(X, b))) = tuple(true2, true2).
% 0.22/0.40  The goal is true when:
% 0.22/0.40    X = generate_key(an_a_nonce)
% 0.22/0.40  
% 0.22/0.40  Proof:
% 0.22/0.40    tuple(b_holds(key(generate_key(an_a_nonce), a)), a_holds(key(generate_key(an_a_nonce), b)))
% 0.22/0.40  = { by axiom 1 (ax1_11) }
% 0.22/0.40    tuple(true2, a_holds(key(generate_key(an_a_nonce), b)))
% 0.22/0.40  = { by axiom 2 (ax3_13) }
% 0.22/0.40    tuple(true2, true2)
% 0.22/0.40  % SZS output end Proof
% 0.22/0.40  
% 0.22/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
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