%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : HWV030-2 : TPTP v8.1.2. Released v2.5.0.
% 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 : n024.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 02:31:39 EDT 2023

% Result   : Unsatisfiable 0.18s 0.51s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : HWV030-2 : TPTP v8.1.2. Released v2.5.0.
% 0.10/0.12  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Aug 29 15:27:37 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.51  Command-line arguments: --no-flatten-goal
% 0.18/0.51  
% 0.18/0.51  % SZS status Unsatisfiable
% 0.18/0.51  
% 0.18/0.51  % SZS output start Proof
% 0.18/0.51  Take the following subset of the input axioms:
% 0.18/0.51    fof(axiom_11, axiom, ![T_5]: (fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(T_5, n1))=n0 | ~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5)))).
% 0.18/0.51    fof(quest_1, negated_conjecture, p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))).
% 0.18/0.51    fof(quest_2, negated_conjecture, p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206, n1)))).
% 0.18/0.51    fof(quest_3, negated_conjecture, ~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)).
% 0.18/0.51  
% 0.18/0.51  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.51  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.51  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.51    fresh(y, y, x1...xn) = u
% 0.18/0.51    C => fresh(s, t, x1...xn) = v
% 0.18/0.51  where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.51  variables of u and v.
% 0.18/0.51  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.51  input problem has no model of domain size 1).
% 0.18/0.51  
% 0.18/0.51  The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.51  
% 0.18/0.51  Axiom 1 (quest_1): p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) = true2.
% 0.18/0.51  Axiom 2 (axiom_11): fresh31(X, X, Y) = n0.
% 0.18/0.51  Axiom 3 (axiom_11): fresh31(p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(X)), true2, X) = fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(X, n1)).
% 0.18/0.51  Axiom 4 (quest_2): p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206, n1))) = true2.
% 0.18/0.51  
% 0.18/0.51  Goal 1 (quest_3): p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0) = true2.
% 0.18/0.51  Proof:
% 0.18/0.51    p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)
% 0.18/0.51  = { by axiom 2 (axiom_11) R->L }
% 0.18/0.51    p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fresh31(true2, true2, t_206))
% 0.18/0.51  = { by axiom 1 (quest_1) R->L }
% 0.18/0.51    p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fresh31(p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)), true2, t_206))
% 0.18/0.51  = { by axiom 3 (axiom_11) }
% 0.18/0.51    p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTwr__level_(f_ADD_(t_206, n1)))
% 0.18/0.51  = { by axiom 4 (quest_2) }
% 0.18/0.51    true2
% 0.18/0.51  % SZS output end Proof
% 0.18/0.51  
% 0.18/0.51  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------