%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUM387+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n031.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 : Thu Aug 31 11:56:07 EDT 2023

% Result   : Theorem 0.22s 0.44s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.16  % Problem  : NUM387+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.16  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.37  % Computer : n031.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Fri Aug 25 09:30:07 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.22/0.44  Command-line arguments: --no-flatten-goal
% 0.22/0.44  
% 0.22/0.44  % SZS status Theorem
% 0.22/0.44  
% 0.22/0.44  % SZS output start Proof
% 0.22/0.44  Take the following subset of the input axioms:
% 0.22/0.44    fof(antisymmetry_r2_hidden, axiom, ![A, B]: (in(A, B) => ~in(B, A))).
% 0.22/0.44    fof(fc1_ordinal1, axiom, ![A2]: ~empty(succ(A2))).
% 0.22/0.44    fof(t10_ordinal1, axiom, ![A2]: in(A2, succ(A2))).
% 0.22/0.44    fof(t14_ordinal1, conjecture, ![A2]: A2!=succ(A2)).
% 0.22/0.44    fof(t7_boole, axiom, ![A2, B2]: ~(in(A2, B2) & empty(B2))).
% 0.22/0.44  
% 0.22/0.44  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.44  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.45  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.45    fresh(y, y, x1...xn) = u
% 0.22/0.45    C => fresh(s, t, x1...xn) = v
% 0.22/0.45  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.45  variables of u and v.
% 0.22/0.45  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.45  input problem has no model of domain size 1).
% 0.22/0.45  
% 0.22/0.45  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.45  
% 0.22/0.45  Axiom 1 (t14_ordinal1): a = succ(a).
% 0.22/0.45  Axiom 2 (t10_ordinal1): in(X, succ(X)) = true2.
% 0.22/0.45  
% 0.22/0.45  Lemma 3: in(a, a) = true2.
% 0.22/0.45  Proof:
% 0.22/0.45    in(a, a)
% 0.22/0.45  = { by axiom 1 (t14_ordinal1) }
% 0.22/0.45    in(a, succ(a))
% 0.22/0.45  = { by axiom 2 (t10_ordinal1) }
% 0.22/0.45    true2
% 0.22/0.45  
% 0.22/0.45  Goal 1 (antisymmetry_r2_hidden): tuple(in(X, Y), in(Y, X)) = tuple(true2, true2).
% 0.22/0.45  The goal is true when:
% 0.22/0.45    X = a
% 0.22/0.45    Y = a
% 0.22/0.45  
% 0.22/0.45  Proof:
% 0.22/0.45    tuple(in(a, a), in(a, a))
% 0.22/0.45  = { by lemma 3 }
% 0.22/0.45    tuple(true2, in(a, a))
% 0.22/0.45  = { by lemma 3 }
% 0.22/0.45    tuple(true2, true2)
% 0.22/0.45  % SZS output end Proof
% 0.22/0.45  
% 0.22/0.45  RESULT: Theorem (the conjecture is true).
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