%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET084-7 : 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 : n011.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 15:31:09 EDT 2023

% Result   : Unsatisfiable 0.22s 0.59s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SET084-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sat Aug 26 11:47:09 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.59  Command-line arguments: --ground-connectedness --complete-subsets
% 0.22/0.59  
% 0.22/0.59  % SZS status Unsatisfiable
% 0.22/0.59  
% 0.22/0.59  % SZS output start Proof
% 0.22/0.59  Take the following subset of the input axioms:
% 0.22/0.59    fof(only_member_in_singleton, axiom, ![X, Y]: (~member(Y, singleton(X)) | Y=X)).
% 0.22/0.59    fof(prove_singleton_identified_by_element2_1, negated_conjecture, singleton(x)=singleton(y)).
% 0.22/0.59    fof(prove_singleton_identified_by_element2_2, negated_conjecture, member(y, universal_class)).
% 0.22/0.59    fof(prove_singleton_identified_by_element2_3, negated_conjecture, x!=y).
% 0.22/0.59    fof(set_in_its_singleton, axiom, ![X2]: (~member(X2, universal_class) | member(X2, singleton(X2)))).
% 0.22/0.59  
% 0.22/0.59  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.59  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.59  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.59    fresh(y, y, x1...xn) = u
% 0.22/0.59    C => fresh(s, t, x1...xn) = v
% 0.22/0.59  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.59  variables of u and v.
% 0.22/0.59  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.59  input problem has no model of domain size 1).
% 0.22/0.59  
% 0.22/0.59  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.59  
% 0.22/0.59  Axiom 1 (prove_singleton_identified_by_element2_1): singleton(x) = singleton(y).
% 0.22/0.59  Axiom 2 (prove_singleton_identified_by_element2_2): member(y, universal_class) = true2.
% 0.22/0.59  Axiom 3 (set_in_its_singleton): fresh25(X, X, Y) = true2.
% 0.22/0.59  Axiom 4 (only_member_in_singleton): fresh(X, X, Y, Z) = Z.
% 0.22/0.59  Axiom 5 (set_in_its_singleton): fresh25(member(X, universal_class), true2, X) = member(X, singleton(X)).
% 0.22/0.59  Axiom 6 (only_member_in_singleton): fresh(member(X, singleton(Y)), true2, X, Y) = X.
% 0.22/0.59  
% 0.22/0.59  Goal 1 (prove_singleton_identified_by_element2_3): x = y.
% 0.22/0.59  Proof:
% 0.22/0.59    x
% 0.22/0.59  = { by axiom 4 (only_member_in_singleton) R->L }
% 0.22/0.59    fresh(true2, true2, y, x)
% 0.22/0.59  = { by axiom 3 (set_in_its_singleton) R->L }
% 0.22/0.59    fresh(fresh25(true2, true2, y), true2, y, x)
% 0.22/0.59  = { by axiom 2 (prove_singleton_identified_by_element2_2) R->L }
% 0.22/0.59    fresh(fresh25(member(y, universal_class), true2, y), true2, y, x)
% 0.22/0.59  = { by axiom 5 (set_in_its_singleton) }
% 0.22/0.59    fresh(member(y, singleton(y)), true2, y, x)
% 0.22/0.59  = { by axiom 1 (prove_singleton_identified_by_element2_1) R->L }
% 0.22/0.59    fresh(member(y, singleton(x)), true2, y, x)
% 0.22/0.59  = { by axiom 6 (only_member_in_singleton) }
% 0.22/0.59    y
% 0.22/0.59  % SZS output end Proof
% 0.22/0.59  
% 0.22/0.59  RESULT: Unsatisfiable (the axioms are contradictory).
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