%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SEU143+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n023.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 17:51:11 EDT 2023

% Result   : Theorem 0.13s 0.39s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SEU143+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 00:51:12 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.39  Command-line arguments: --ground-connectedness --complete-subsets
% 0.13/0.39  
% 0.13/0.39  % SZS status Theorem
% 0.13/0.39  
% 0.13/0.39  % SZS output start Proof
% 0.13/0.39  Take the following subset of the input axioms:
% 0.13/0.40    fof(antisymmetry_r2_hidden, axiom, ![A, B]: (in(A, B) => ~in(B, A))).
% 0.13/0.40    fof(d1_tarski, axiom, ![A2, B2]: (B2=singleton(A2) <=> ![C]: (in(C, B2) <=> C=A2))).
% 0.13/0.40    fof(d1_xboole_0, axiom, ![A3]: (A3=empty_set <=> ![B2]: ~in(B2, A3))).
% 0.13/0.40    fof(l1_zfmisc_1, conjecture, ![A3]: singleton(A3)!=empty_set).
% 0.13/0.40  
% 0.13/0.40  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.40  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.40  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.40    fresh(y, y, x1...xn) = u
% 0.13/0.40    C => fresh(s, t, x1...xn) = v
% 0.13/0.40  where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.40  variables of u and v.
% 0.13/0.40  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.40  input problem has no model of domain size 1).
% 0.13/0.40  
% 0.13/0.40  The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.40  
% 0.13/0.40  Axiom 1 (l1_zfmisc_1): singleton(a3) = empty_set.
% 0.13/0.40  Axiom 2 (d1_tarski_2): fresh5(X, X, Y, Z) = true2.
% 0.13/0.40  Axiom 3 (d1_tarski_2): fresh5(X, singleton(Y), Y, X) = in(Y, X).
% 0.13/0.40  
% 0.13/0.40  Goal 1 (d1_xboole_0_1): tuple2(X, in(Y, X)) = tuple2(empty_set, true2).
% 0.13/0.40  The goal is true when:
% 0.13/0.40    X = empty_set
% 0.13/0.40    Y = a3
% 0.13/0.40  
% 0.13/0.40  Proof:
% 0.13/0.40    tuple2(empty_set, in(a3, empty_set))
% 0.13/0.40  = { by axiom 1 (l1_zfmisc_1) R->L }
% 0.13/0.40    tuple2(empty_set, in(a3, singleton(a3)))
% 0.13/0.40  = { by axiom 3 (d1_tarski_2) R->L }
% 0.13/0.40    tuple2(empty_set, fresh5(singleton(a3), singleton(a3), a3, singleton(a3)))
% 0.13/0.40  = { by axiom 2 (d1_tarski_2) }
% 0.13/0.40    tuple2(empty_set, true2)
% 0.13/0.40  % SZS output end Proof
% 0.13/0.40  
% 0.13/0.40  RESULT: Theorem (the conjecture is true).
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