%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN368+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 : n006.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 03:34:20 EDT 2023

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN368+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.13  % 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 : n006.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 : Sat Aug 26 18:31:22 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.36  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.12/0.36  
% 0.12/0.36  % SZS status Theorem
% 0.12/0.36  
% 0.12/0.36  % SZS output start Proof
% 0.12/0.36  Take the following subset of the input axioms:
% 0.12/0.36    fof(x2119, conjecture, ?[Y]: ![X]: (big_p(Y) => big_p(X))).
% 0.12/0.36  
% 0.12/0.36  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.12/0.36  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.12/0.36  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.12/0.36    fresh(y, y, x1...xn) = u
% 0.12/0.36    C => fresh(s, t, x1...xn) = v
% 0.12/0.36  where fresh is a fresh function symbol and x1..xn are the free
% 0.12/0.36  variables of u and v.
% 0.12/0.36  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.12/0.36  input problem has no model of domain size 1).
% 0.12/0.36  
% 0.12/0.36  The encoding turns the above axioms into the following unit equations and goals:
% 0.12/0.36  
% 0.12/0.36  Axiom 1 (x2119): big_p(X) = true.
% 0.12/0.36  
% 0.12/0.36  Goal 1 (x2119_1): big_p(x) = true.
% 0.12/0.36  Proof:
% 0.12/0.36    big_p(x)
% 0.12/0.36  = { by axiom 1 (x2119) }
% 0.12/0.36    true
% 0.12/0.36  % SZS output end Proof
% 0.12/0.36  
% 0.12/0.36  RESULT: Theorem (the conjecture is true).
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