%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET094-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : Thu Aug 31 15:31:13 EDT 2023

% Result   : Unsatisfiable 0.23s 0.61s
% Output   : Proof 0.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem  : SET094-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.15/0.16  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37  % Computer : n022.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Sat Aug 26 08:38:25 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.23/0.61  Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.23/0.61  
% 0.23/0.61  % SZS status Unsatisfiable
% 0.23/0.61  
% 0.23/0.61  % SZS output start Proof
% 0.23/0.61  Take the following subset of the input axioms:
% 0.23/0.61    fof(only_member_in_singleton, axiom, ![X, Y]: (~member(Y, singleton(X)) | Y=X)).
% 0.23/0.61    fof(prove_property_of_singletons1_1, negated_conjecture, singleton(member_of(x))=x).
% 0.23/0.61    fof(prove_property_of_singletons1_2, negated_conjecture, member(y, x)).
% 0.23/0.61    fof(prove_property_of_singletons1_3, negated_conjecture, member_of(x)!=y).
% 0.23/0.61  
% 0.23/0.61  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.23/0.61  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.23/0.61  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.23/0.61    fresh(y, y, x1...xn) = u
% 0.23/0.61    C => fresh(s, t, x1...xn) = v
% 0.23/0.61  where fresh is a fresh function symbol and x1..xn are the free
% 0.23/0.61  variables of u and v.
% 0.23/0.61  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.23/0.61  input problem has no model of domain size 1).
% 0.23/0.61  
% 0.23/0.61  The encoding turns the above axioms into the following unit equations and goals:
% 0.23/0.61  
% 0.23/0.61  Axiom 1 (prove_property_of_singletons1_2): member(y, x) = true2.
% 0.23/0.61  Axiom 2 (prove_property_of_singletons1_1): singleton(member_of(x)) = x.
% 0.23/0.61  Axiom 3 (only_member_in_singleton): fresh(X, X, Y, Z) = Z.
% 0.23/0.61  Axiom 4 (only_member_in_singleton): fresh(member(X, singleton(Y)), true2, X, Y) = X.
% 0.23/0.61  
% 0.23/0.61  Goal 1 (prove_property_of_singletons1_3): member_of(x) = y.
% 0.23/0.61  Proof:
% 0.23/0.61    member_of(x)
% 0.23/0.61  = { by axiom 3 (only_member_in_singleton) R->L }
% 0.23/0.62    fresh(true2, true2, y, member_of(x))
% 0.23/0.62  = { by axiom 1 (prove_property_of_singletons1_2) R->L }
% 0.23/0.62    fresh(member(y, x), true2, y, member_of(x))
% 0.23/0.62  = { by axiom 2 (prove_property_of_singletons1_1) R->L }
% 0.23/0.62    fresh(member(y, singleton(member_of(x))), true2, y, member_of(x))
% 0.23/0.62  = { by axiom 4 (only_member_in_singleton) }
% 0.23/0.62    y
% 0.23/0.62  % SZS output end Proof
% 0.23/0.62  
% 0.23/0.62  RESULT: Unsatisfiable (the axioms are contradictory).
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