%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN318+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 : 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 : Fri Sep  1 03:34:03 EDT 2023

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN318+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35  % CPULimit : 300
% 0.20/0.35  % WCLimit  : 300
% 0.20/0.35  % DateTime : Sat Aug 26 19:06:29 EDT 2023
% 0.20/0.35  % CPUTime  : 
% 0.20/0.39  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.39  
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  Take the following subset of the input axioms:
% 0.20/0.39    fof(church_46_2_4, conjecture, ?[Y]: (![X]: (big_f(X) => (big_f(Y) => big_g(X))) => (p => ![X2]: (big_f(X2) => big_g(Y))))).
% 0.20/0.39  
% 0.20/0.39  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.39  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.39  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.39    fresh(y, y, x1...xn) = u
% 0.20/0.39    C => fresh(s, t, x1...xn) = v
% 0.20/0.39  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.39  variables of u and v.
% 0.20/0.39  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.39  input problem has no model of domain size 1).
% 0.20/0.39  
% 0.20/0.39  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.39  
% 0.20/0.39  Axiom 1 (church_46_2_4): big_f(x) = true2.
% 0.20/0.39  Axiom 2 (church_46_2_4_2): fresh2(X, X, Y) = true2.
% 0.20/0.39  Axiom 3 (church_46_2_4_2): fresh(X, X, Y, Z) = big_g(Z).
% 0.20/0.39  Axiom 4 (church_46_2_4_2): fresh(big_f(X), true2, Y, X) = fresh2(big_f(Y), true2, X).
% 0.20/0.39  
% 0.20/0.39  Goal 1 (church_46_2_4_3): big_g(X) = true2.
% 0.20/0.39  The goal is true when:
% 0.20/0.39    X = x
% 0.20/0.39  
% 0.20/0.39  Proof:
% 0.20/0.39    big_g(x)
% 0.20/0.39  = { by axiom 3 (church_46_2_4_2) R->L }
% 0.20/0.39    fresh(true2, true2, x, x)
% 0.20/0.39  = { by axiom 1 (church_46_2_4) R->L }
% 0.20/0.39    fresh(big_f(x), true2, x, x)
% 0.20/0.39  = { by axiom 4 (church_46_2_4_2) }
% 0.20/0.39    fresh2(big_f(x), true2, x)
% 0.20/0.39  = { by axiom 1 (church_46_2_4) }
% 0.20/0.39    fresh2(true2, true2, x)
% 0.20/0.39  = { by axiom 2 (church_46_2_4_2) }
% 0.20/0.39    true2
% 0.20/0.39  % SZS output end Proof
% 0.20/0.39  
% 0.20/0.39  RESULT: Theorem (the conjecture is true).
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