%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET913+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 : n027.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 15:33:43 EDT 2023

% Result   : Theorem 0.19s 0.37s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET913+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sat Aug 26 10:02:34 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.37  Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.37  
% 0.19/0.37  % SZS status Theorem
% 0.19/0.37  
% 0.19/0.37  % SZS output start Proof
% 0.19/0.37  Take the following subset of the input axioms:
% 0.19/0.37    fof(antisymmetry_r2_hidden, axiom, ![A, B]: (in(A, B) => ~in(B, A))).
% 0.19/0.37    fof(l25_zfmisc_1, axiom, ![A2, B2]: ~(disjoint(singleton(A2), B2) & in(A2, B2))).
% 0.19/0.37    fof(t54_zfmisc_1, conjecture, ![A2, B2]: ~(disjoint(singleton(A2), B2) & in(A2, B2))).
% 0.19/0.37  
% 0.19/0.37  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.37  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.37  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.37    fresh(y, y, x1...xn) = u
% 0.19/0.37    C => fresh(s, t, x1...xn) = v
% 0.19/0.37  where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.37  variables of u and v.
% 0.19/0.37  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.37  input problem has no model of domain size 1).
% 0.19/0.37  
% 0.19/0.37  The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.37  
% 0.19/0.37  Axiom 1 (t54_zfmisc_1_1): in(a, b) = true2.
% 0.19/0.37  Axiom 2 (t54_zfmisc_1): disjoint(singleton(a), b) = true2.
% 0.19/0.37  
% 0.19/0.37  Goal 1 (l25_zfmisc_1): tuple(disjoint(singleton(X), Y), in(X, Y)) = tuple(true2, true2).
% 0.19/0.37  The goal is true when:
% 0.19/0.37    X = a
% 0.19/0.37    Y = b
% 0.19/0.37  
% 0.19/0.37  Proof:
% 0.19/0.37    tuple(disjoint(singleton(a), b), in(a, b))
% 0.19/0.37  = { by axiom 1 (t54_zfmisc_1_1) }
% 0.19/0.37    tuple(disjoint(singleton(a), b), true2)
% 0.19/0.37  = { by axiom 2 (t54_zfmisc_1) }
% 0.19/0.37    tuple(true2, true2)
% 0.19/0.37  % SZS output end Proof
% 0.19/0.37  
% 0.19/0.37  RESULT: Theorem (the conjecture is true).
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