%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN953+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n023.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 03:36:38 EDT 2023

% Result   : Theorem 0.16s 0.33s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SYN953+1 : TPTP v8.1.2. Released v3.1.0.
% 0.05/0.10  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.31  % Computer : n023.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sat Aug 26 21:39:56 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.16/0.33  Command-line arguments: --no-flatten-goal
% 0.16/0.33  
% 0.16/0.33  % SZS status Theorem
% 0.16/0.33  
% 0.16/0.33  % SZS output start Proof
% 0.16/0.33  Take the following subset of the input axioms:
% 0.16/0.34    fof(prove_this, conjecture, ![X]: (p(X) => q(X)) => (![X2]: p(X2) => ![X2]: q(X2))).
% 0.16/0.34  
% 0.16/0.34  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.34  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.34  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.34    fresh(y, y, x1...xn) = u
% 0.16/0.34    C => fresh(s, t, x1...xn) = v
% 0.16/0.34  where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.34  variables of u and v.
% 0.16/0.34  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.34  input problem has no model of domain size 1).
% 0.16/0.34  
% 0.16/0.34  The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.34  
% 0.16/0.34  Axiom 1 (prove_this): p(X) = true.
% 0.16/0.34  Axiom 2 (prove_this_1): fresh(X, X, Y) = true.
% 0.16/0.34  Axiom 3 (prove_this_1): fresh(p(X), true, X) = q(X).
% 0.16/0.34  
% 0.16/0.34  Goal 1 (prove_this_2): q(x) = true.
% 0.16/0.34  Proof:
% 0.16/0.34    q(x)
% 0.16/0.34  = { by axiom 3 (prove_this_1) R->L }
% 0.16/0.34    fresh(p(x), true, x)
% 0.16/0.34  = { by axiom 1 (prove_this) }
% 0.16/0.34    fresh(true, true, x)
% 0.16/0.34  = { by axiom 2 (prove_this_1) }
% 0.16/0.34    true
% 0.16/0.34  % SZS output end Proof
% 0.16/0.34  
% 0.16/0.34  RESULT: Theorem (the conjecture is true).
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