%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SYN346+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 : n017.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 03:34:13 EDT 2023

% Result   : Theorem 0.13s 0.53s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.20  % Problem  : SYN346+1 : TPTP v8.1.2. Released v2.0.0.
% 0.02/0.21  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.08/0.43  % Computer : n017.cluster.edu
% 0.08/0.43  % Model    : x86_64 x86_64
% 0.08/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.43  % Memory   : 8042.1875MB
% 0.08/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.43  % CPULimit : 300
% 0.08/0.43  % WCLimit  : 300
% 0.08/0.43  % DateTime : Sat Aug 26 19:33:56 EDT 2023
% 0.08/0.45  % CPUTime  : 
% 0.13/0.53  Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.13/0.53  
% 0.13/0.53  % SZS status Theorem
% 0.13/0.55  
% 0.13/0.55  % SZS output start Proof
% 0.13/0.55  Take the following subset of the input axioms:
% 0.13/0.55    fof(church_46_17_2, conjecture, ![X1, X2]: ?[Y1, Y2]: ![Z1, Z2]: (big_f(X2, Z1) => (big_f(Y1, Z2) => ((big_f(Y1, Z1) & big_f(Y2, Z1)) | (big_f(X2, Z2) & big_f(Y2, Z2)))))).
% 0.13/0.55  
% 0.13/0.55  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.55  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.55  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.55    fresh(y, y, x1...xn) = u
% 0.13/0.55    C => fresh(s, t, x1...xn) = v
% 0.13/0.55  where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.55  variables of u and v.
% 0.13/0.55  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.55  input problem has no model of domain size 1).
% 0.13/0.55  
% 0.13/0.55  The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.55  
% 0.13/0.55  Axiom 1 (church_46_17_2_1): big_f(x2, z1(X, Y)) = true2.
% 0.13/0.55  
% 0.13/0.55  Goal 1 (church_46_17_2_2): tuple(big_f(X, z1(X, Y)), big_f(Y, z1(X, Y))) = tuple(true2, true2).
% 0.13/0.55  The goal is true when:
% 0.13/0.55    X = x2
% 0.13/0.55    Y = x2
% 0.13/0.55  
% 0.13/0.55  Proof:
% 0.13/0.55    tuple(big_f(x2, z1(x2, x2)), big_f(x2, z1(x2, x2)))
% 0.13/0.55  = { by axiom 1 (church_46_17_2_1) }
% 0.13/0.55    tuple(true2, big_f(x2, z1(x2, x2)))
% 0.13/0.55  = { by axiom 1 (church_46_17_2_1) }
% 0.13/0.55    tuple(true2, true2)
% 0.13/0.55  % SZS output end Proof
% 0.13/0.55  
% 0.13/0.55  RESULT: Theorem (the conjecture is true).
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