%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL684+1.001 : TPTP v8.1.2. Released v4.0.0.
% 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 : n025.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 08:20:12 EDT 2023

% Result   : Theorem 0.19s 0.37s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL684+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % 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 : n025.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 : Thu Aug 24 19:35:06 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.37  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.37  
% 0.19/0.37  % SZS status Theorem
% 0.19/0.37  
% 0.19/0.37  % SZS output start Proof
% 0.19/0.37  Take the following subset of the input axioms:
% 0.19/0.37    fof(main, conjecture, ~?[X]: ~(~![Y]: (~r1(X, Y) | ![X2]: (~r1(Y, X2) | ~(p201(X2) & p101(X2)))) | ~(p201(X) & p101(X)))).
% 0.19/0.37    fof(reflexivity, axiom, ![X2]: r1(X2, X2)).
% 0.19/0.37  
% 0.19/0.37  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.37  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.37  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.37    fresh(y, y, x1...xn) = u
% 0.19/0.37    C => fresh(s, t, x1...xn) = v
% 0.19/0.37  where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.37  variables of u and v.
% 0.19/0.37  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.37  input problem has no model of domain size 1).
% 0.19/0.37  
% 0.19/0.37  The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.37  
% 0.19/0.37  Axiom 1 (main): p201(x) = true2.
% 0.19/0.37  Axiom 2 (main_1): p101(x) = true2.
% 0.19/0.37  Axiom 3 (reflexivity): r1(X, X) = true2.
% 0.19/0.37  
% 0.19/0.37  Goal 1 (main_2): tuple(r1(X, Y), r1(x, X), p201(Y), p101(Y)) = tuple(true2, true2, true2, true2).
% 0.19/0.37  The goal is true when:
% 0.19/0.37    X = x
% 0.19/0.37    Y = x
% 0.19/0.37  
% 0.19/0.37  Proof:
% 0.19/0.37    tuple(r1(x, x), r1(x, x), p201(x), p101(x))
% 0.19/0.37  = { by axiom 1 (main) }
% 0.19/0.37    tuple(r1(x, x), r1(x, x), true2, p101(x))
% 0.19/0.37  = { by axiom 2 (main_1) }
% 0.19/0.37    tuple(r1(x, x), r1(x, x), true2, true2)
% 0.19/0.37  = { by axiom 3 (reflexivity) }
% 0.19/0.37    tuple(true2, r1(x, x), true2, true2)
% 0.19/0.37  = { by axiom 3 (reflexivity) }
% 0.19/0.37    tuple(true2, true2, true2, true2)
% 0.19/0.37  % SZS output end Proof
% 0.19/0.37  
% 0.19/0.37  RESULT: Theorem (the conjecture is true).
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