%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : HWV011-2 : 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 : n008.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 02:31:33 EDT 2023

% Result   : Unsatisfiable 0.19s 0.47s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : HWV011-2 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34  % Computer : n008.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Tue Aug 29 17:09:02 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.19/0.47  Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.47  
% 0.19/0.47  % SZS status Unsatisfiable
% 0.19/0.47  
% 0.19/0.47  % SZS output start Proof
% 0.19/0.47  Take the following subset of the input axioms:
% 0.19/0.47    fof(axiom_5, axiom, ![T_0]: fwork_DOTfifo_DOTrtl_DOTlevel_(T_0)=fwork_DOTfifo_DOTrtl_DOTint__level_(T_0)).
% 0.19/0.47    fof(axiom_7, axiom, ![T_2]: (~p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(T_2)) | fwork_DOTfifo_DOTrtl_DOTint__level_(T_2)=fwork_DOTfifo_DOTrtl_DOTfifo__length_)).
% 0.19/0.47    fof(quest_1, negated_conjecture, fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)!=fwork_DOTfifo_DOTrtl_DOTfifo__length_).
% 0.19/0.47    fof(quest_2, negated_conjecture, p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206))).
% 0.19/0.47  
% 0.19/0.47  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.47  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.47  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.47    fresh(y, y, x1...xn) = u
% 0.19/0.47    C => fresh(s, t, x1...xn) = v
% 0.19/0.47  where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.47  variables of u and v.
% 0.19/0.47  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.47  input problem has no model of domain size 1).
% 0.19/0.47  
% 0.19/0.47  The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.47  
% 0.19/0.47  Axiom 1 (axiom_5): fwork_DOTfifo_DOTrtl_DOTlevel_(X) = fwork_DOTfifo_DOTrtl_DOTint__level_(X).
% 0.19/0.47  Axiom 2 (quest_2): p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206)) = true2.
% 0.19/0.47  Axiom 3 (axiom_7): fresh12(X, X, Y) = fwork_DOTfifo_DOTrtl_DOTfifo__length_.
% 0.19/0.47  Axiom 4 (axiom_7): fresh12(p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(X)), true2, X) = fwork_DOTfifo_DOTrtl_DOTint__level_(X).
% 0.19/0.47  
% 0.19/0.47  Goal 1 (quest_1): fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_.
% 0.19/0.47  Proof:
% 0.19/0.47    fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)
% 0.19/0.47  = { by axiom 1 (axiom_5) }
% 0.19/0.47    fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)
% 0.19/0.47  = { by axiom 4 (axiom_7) R->L }
% 0.19/0.47    fresh12(p__pred_(fwork_DOTfifo_DOTrtl_DOTfull_(t_206)), true2, t_206)
% 0.19/0.47  = { by axiom 2 (quest_2) }
% 0.19/0.47    fresh12(true2, true2, t_206)
% 0.19/0.47  = { by axiom 3 (axiom_7) }
% 0.19/0.47    fwork_DOTfifo_DOTrtl_DOTfifo__length_
% 0.19/0.47  % SZS output end Proof
% 0.19/0.47  
% 0.19/0.47  RESULT: Unsatisfiable (the axioms are contradictory).
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