%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET024-4 : TPTP v8.1.2. Released v1.0.0.
% 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 : n014.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 15:30:41 EDT 2023

% Result   : Unsatisfiable 0.16s 0.74s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET024-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.32  % Computer : n014.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Sat Aug 26 08:59:47 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.16/0.74  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.16/0.74  
% 0.16/0.74  % SZS status Unsatisfiable
% 0.16/0.74  
% 0.16/0.74  % SZS output start Proof
% 0.16/0.74  Take the following subset of the input axioms:
% 0.16/0.74    fof(a_little_set, hypothesis, little_set(a)).
% 0.16/0.74    fof(non_ordered_pair2, axiom, ![X, Y, U]: (member(U, non_ordered_pair(X, Y)) | (~little_set(U) | U!=X))).
% 0.16/0.74    fof(prove_membership_of_singleton_set, negated_conjecture, ~member(a, singleton_set(a))).
% 0.16/0.74    fof(singleton_set, axiom, ![X2]: singleton_set(X2)=non_ordered_pair(X2, X2)).
% 0.16/0.74  
% 0.16/0.74  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.74  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.74  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.74    fresh(y, y, x1...xn) = u
% 0.16/0.74    C => fresh(s, t, x1...xn) = v
% 0.16/0.74  where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.74  variables of u and v.
% 0.16/0.74  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.74  input problem has no model of domain size 1).
% 0.16/0.74  
% 0.16/0.74  The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.74  
% 0.16/0.74  Axiom 1 (a_little_set): little_set(a) = true2.
% 0.16/0.74  Axiom 2 (singleton_set): singleton_set(X) = non_ordered_pair(X, X).
% 0.16/0.74  Axiom 3 (non_ordered_pair2): fresh53(X, X, Y, Z) = true2.
% 0.16/0.74  Axiom 4 (non_ordered_pair2): fresh53(little_set(X), true2, X, Y) = member(X, non_ordered_pair(X, Y)).
% 0.16/0.74  
% 0.16/0.74  Goal 1 (prove_membership_of_singleton_set): member(a, singleton_set(a)) = true2.
% 0.16/0.74  Proof:
% 0.16/0.74    member(a, singleton_set(a))
% 0.16/0.74  = { by axiom 2 (singleton_set) }
% 0.16/0.74    member(a, non_ordered_pair(a, a))
% 0.16/0.74  = { by axiom 4 (non_ordered_pair2) R->L }
% 0.16/0.74    fresh53(little_set(a), true2, a, a)
% 0.16/0.74  = { by axiom 1 (a_little_set) }
% 0.16/0.74    fresh53(true2, true2, a, a)
% 0.16/0.74  = { by axiom 3 (non_ordered_pair2) }
% 0.16/0.74    true2
% 0.16/0.74  % SZS output end Proof
% 0.16/0.74  
% 0.16/0.74  RESULT: Unsatisfiable (the axioms are contradictory).
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