%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN048+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n032.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 : Fri Sep  1 03:32:51 EDT 2023

% Result   : Theorem 0.07s 0.30s
% Output   : Proof 0.07s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SYN048+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.09  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.07/0.28  % Computer : n032.cluster.edu
% 0.07/0.28  % Model    : x86_64 x86_64
% 0.07/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28  % Memory   : 8042.1875MB
% 0.07/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28  % CPULimit : 300
% 0.07/0.28  % WCLimit  : 300
% 0.07/0.28  % DateTime : Sat Aug 26 21:22:14 EDT 2023
% 0.07/0.28  % CPUTime  : 
% 0.07/0.30  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.07/0.30  
% 0.07/0.30  % SZS status Theorem
% 0.07/0.30  
% 0.07/0.30  % SZS output start Proof
% 0.07/0.30  Take the following subset of the input axioms:
% 0.07/0.30    fof(pel18, conjecture, ?[Y]: ![X]: (big_f(Y) => big_f(X))).
% 0.07/0.30  
% 0.07/0.30  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.07/0.30  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.07/0.30  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.07/0.30    fresh(y, y, x1...xn) = u
% 0.07/0.30    C => fresh(s, t, x1...xn) = v
% 0.07/0.30  where fresh is a fresh function symbol and x1..xn are the free
% 0.07/0.30  variables of u and v.
% 0.07/0.30  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.07/0.30  input problem has no model of domain size 1).
% 0.07/0.30  
% 0.07/0.30  The encoding turns the above axioms into the following unit equations and goals:
% 0.07/0.30  
% 0.07/0.30  Axiom 1 (pel18): big_f(X) = true.
% 0.07/0.30  
% 0.07/0.30  Goal 1 (pel18_1): big_f(x) = true.
% 0.07/0.30  Proof:
% 0.07/0.30    big_f(x)
% 0.07/0.30  = { by axiom 1 (pel18) }
% 0.07/0.30    true
% 0.07/0.30  % SZS output end Proof
% 0.07/0.30  
% 0.07/0.30  RESULT: Theorem (the conjecture is true).
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