%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SWV148+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 : n005.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 23:02:45 EDT 2023

% Result   : Theorem 0.22s 0.60s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14  % Problem  : SWV148+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.14/0.15  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36  % Computer : n005.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 05:37:38 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.22/0.60  Command-line arguments: --no-flatten-goal
% 0.22/0.60  
% 0.22/0.60  % SZS status Theorem
% 0.22/0.60  
% 0.22/0.60  % SZS output start Proof
% 0.22/0.60  Take the following subset of the input axioms:
% 0.22/0.60    fof(gauss_array_0018, conjecture, ~leq(tptp_float_0_001, tptp_float_0_001) => leq(s_best7, n3)).
% 0.22/0.60    fof(reflexivity_leq, axiom, ![X]: leq(X, X)).
% 0.22/0.60  
% 0.22/0.60  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.60  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.60  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.60    fresh(y, y, x1...xn) = u
% 0.22/0.60    C => fresh(s, t, x1...xn) = v
% 0.22/0.60  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.60  variables of u and v.
% 0.22/0.60  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.60  input problem has no model of domain size 1).
% 0.22/0.60  
% 0.22/0.60  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.60  
% 0.22/0.60  Axiom 1 (reflexivity_leq): leq(X, X) = true3.
% 0.22/0.60  
% 0.22/0.60  Goal 1 (gauss_array_0018): leq(tptp_float_0_001, tptp_float_0_001) = true3.
% 0.22/0.60  Proof:
% 0.22/0.60    leq(tptp_float_0_001, tptp_float_0_001)
% 0.22/0.60  = { by axiom 1 (reflexivity_leq) }
% 0.22/0.60    true3
% 0.22/0.60  % SZS output end Proof
% 0.22/0.60  
% 0.22/0.60  RESULT: Theorem (the conjecture is true).
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