%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN327+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 : n022.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 03:34:06 EDT 2023

% Result   : Theorem 0.22s 0.38s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SYN327+1 : TPTP v8.1.2. Released v2.0.0.
% 0.08/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35  % Computer : n022.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sat Aug 26 20:50:10 EDT 2023
% 0.21/0.35  % CPUTime  : 
% 0.22/0.38  Command-line arguments: --ground-connectedness --complete-subsets
% 0.22/0.38  
% 0.22/0.38  % SZS status Theorem
% 0.22/0.38  
% 0.22/0.38  % SZS output start Proof
% 0.22/0.38  Take the following subset of the input axioms:
% 0.22/0.38    fof(church_46_12_2, conjecture, ![X]: ?[Y]: ![Z]: (big_f(Y, X) => ((big_f(X, Z) => big_f(X, Y)) & (big_f(X, Y) => (~big_f(X, Z) => (big_f(Y, X) & big_f(Z, Y))))))).
% 0.22/0.38  
% 0.22/0.39  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.39  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.39  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.39    fresh(y, y, x1...xn) = u
% 0.22/0.39    C => fresh(s, t, x1...xn) = v
% 0.22/0.39  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.39  variables of u and v.
% 0.22/0.39  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.39  input problem has no model of domain size 1).
% 0.22/0.39  
% 0.22/0.39  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.39  
% 0.22/0.39  Axiom 1 (church_46_12_2): big_f(X, x) = true2.
% 0.22/0.39  
% 0.22/0.39  Goal 1 (church_46_12_2_2): tuple(big_f(X, x), big_f(x, X), big_f(z(X), X)) = tuple(true2, true2, true2).
% 0.22/0.39  The goal is true when:
% 0.22/0.39    X = x
% 0.22/0.39  
% 0.22/0.39  Proof:
% 0.22/0.39    tuple(big_f(x, x), big_f(x, x), big_f(z(x), x))
% 0.22/0.39  = { by axiom 1 (church_46_12_2) }
% 0.22/0.39    tuple(true2, big_f(x, x), big_f(z(x), x))
% 0.22/0.39  = { by axiom 1 (church_46_12_2) }
% 0.22/0.39    tuple(true2, true2, big_f(z(x), x))
% 0.22/0.39  = { by axiom 1 (church_46_12_2) }
% 0.22/0.39    tuple(true2, true2, true2)
% 0.22/0.39  % SZS output end Proof
% 0.22/0.39  
% 0.22/0.39  RESULT: Theorem (the conjecture is true).
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