%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN366+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 : n001.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 0.21s 0.39s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYN366+1 : TPTP v8.1.2. Released v2.0.0.
% 0.13/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n001.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 22:21:31 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.39  Command-line arguments: --no-flatten-goal
% 0.21/0.39  
% 0.21/0.39  % SZS status Theorem
% 0.21/0.39  
% 0.21/0.39  % SZS output start Proof
% 0.21/0.39  Take the following subset of the input axioms:
% 0.21/0.39    fof(x2117, conjecture, (![U, V]: (big_r(U, U) <=> big_r(U, V)) & ![W, Z]: (big_r(W, W) <=> big_r(Z, W))) => (?[X]: big_r(X, X) => ![Y]: big_r(Y, Y))).
% 0.21/0.39  
% 0.21/0.39  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.39  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.39  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.39    fresh(y, y, x1...xn) = u
% 0.21/0.39    C => fresh(s, t, x1...xn) = v
% 0.21/0.39  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.39  variables of u and v.
% 0.21/0.39  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.39  input problem has no model of domain size 1).
% 0.21/0.39  
% 0.21/0.39  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.39  
% 0.21/0.39  Axiom 1 (x2117): big_r(x, x) = true.
% 0.21/0.39  Axiom 2 (x2117_4): fresh(X, X, Y) = true.
% 0.21/0.39  Axiom 3 (x2117_1): fresh3(X, X, Y, Z) = true.
% 0.21/0.39  Axiom 4 (x2117_4): fresh(big_r(X, Y), true, Y) = big_r(Y, Y).
% 0.21/0.39  Axiom 5 (x2117_1): fresh3(big_r(X, X), true, X, Y) = big_r(X, Y).
% 0.21/0.39  
% 0.21/0.39  Goal 1 (x2117_5): big_r(y, y) = true.
% 0.21/0.39  Proof:
% 0.21/0.39    big_r(y, y)
% 0.21/0.39  = { by axiom 4 (x2117_4) R->L }
% 0.21/0.39    fresh(big_r(x, y), true, y)
% 0.21/0.39  = { by axiom 5 (x2117_1) R->L }
% 0.21/0.39    fresh(fresh3(big_r(x, x), true, x, y), true, y)
% 0.21/0.39  = { by axiom 1 (x2117) }
% 0.21/0.39    fresh(fresh3(true, true, x, y), true, y)
% 0.21/0.39  = { by axiom 3 (x2117_1) }
% 0.21/0.39    fresh(true, true, y)
% 0.21/0.39  = { by axiom 2 (x2117_4) }
% 0.21/0.39    true
% 0.21/0.39  % SZS output end Proof
% 0.21/0.39  
% 0.21/0.39  RESULT: Theorem (the conjecture is true).
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