%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL455+1 : TPTP v8.1.2. Released 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 : n020.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 08:19:04 EDT 2023

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

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : LCL455+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n020.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 18:47:30 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.47  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.47  
% 0.19/0.47  % SZS status Theorem
% 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(hilbert_or_2, axiom, or_2).
% 0.19/0.47    fof(or_2, axiom, or_2 <=> ![X, Y]: is_a_theorem(implies(Y, or(X, Y)))).
% 0.19/0.47    fof(principia_r2, conjecture, r2).
% 0.19/0.47    fof(r2, axiom, r2 <=> ![P, Q]: is_a_theorem(implies(Q, or(P, Q)))).
% 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 (hilbert_or_2): or_2 = true.
% 0.19/0.47  Axiom 2 (r2): fresh11(X, X) = true.
% 0.19/0.47  Axiom 3 (or_2_1): fresh16(X, X, Y, Z) = true.
% 0.19/0.47  Axiom 4 (or_2_1): fresh16(or_2, true, X, Y) = is_a_theorem(implies(Y, or(X, Y))).
% 0.19/0.47  Axiom 5 (r2): fresh11(is_a_theorem(implies(q4, or(p4, q4))), true) = r2.
% 0.19/0.47  
% 0.19/0.47  Goal 1 (principia_r2): r2 = true.
% 0.19/0.47  Proof:
% 0.19/0.47    r2
% 0.19/0.47  = { by axiom 5 (r2) R->L }
% 0.19/0.47    fresh11(is_a_theorem(implies(q4, or(p4, q4))), true)
% 0.19/0.47  = { by axiom 4 (or_2_1) R->L }
% 0.19/0.47    fresh11(fresh16(or_2, true, p4, q4), true)
% 0.19/0.47  = { by axiom 1 (hilbert_or_2) }
% 0.19/0.47    fresh11(fresh16(true, true, p4, q4), true)
% 0.19/0.47  = { by axiom 3 (or_2_1) }
% 0.19/0.47    fresh11(true, true)
% 0.19/0.47  = { by axiom 2 (r2) }
% 0.19/0.47    true
% 0.19/0.47  % SZS output end Proof
% 0.19/0.47  
% 0.19/0.47  RESULT: Theorem (the conjecture is true).
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