%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET025-3 : 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 : 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 15:30:42 EDT 2023

% Result   : Unsatisfiable 3.49s 0.82s
% Output   : Proof 3.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10  % Problem  : SET025-3 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.11  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.31  % Computer : n023.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Sat Aug 26 12:35:26 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 3.49/0.82  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 3.49/0.82  
% 3.49/0.82  % SZS status Unsatisfiable
% 3.49/0.82  
% 3.49/0.82  % SZS output start Proof
% 3.49/0.82  Take the following subset of the input axioms:
% 3.49/0.83    fof(non_ordered_pair4, axiom, ![X, Y]: little_set(non_ordered_pair(X, Y))).
% 3.49/0.83    fof(ordered_pair, axiom, ![X2, Y2]: ordered_pair(X2, Y2)=non_ordered_pair(singleton_set(X2), non_ordered_pair(X2, Y2))).
% 3.49/0.83    fof(prove_ordered_pairs_are_small, negated_conjecture, ~little_set(ordered_pair(a, b))).
% 3.49/0.83  
% 3.49/0.83  Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.49/0.83  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.49/0.83  We repeatedly replace C & s=t => u=v by the two clauses:
% 3.49/0.83    fresh(y, y, x1...xn) = u
% 3.49/0.83    C => fresh(s, t, x1...xn) = v
% 3.49/0.83  where fresh is a fresh function symbol and x1..xn are the free
% 3.49/0.83  variables of u and v.
% 3.49/0.83  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.49/0.83  input problem has no model of domain size 1).
% 3.49/0.83  
% 3.49/0.83  The encoding turns the above axioms into the following unit equations and goals:
% 3.49/0.83  
% 3.49/0.83  Axiom 1 (non_ordered_pair4): little_set(non_ordered_pair(X, Y)) = true2.
% 3.49/0.83  Axiom 2 (ordered_pair): ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y)).
% 3.49/0.83  
% 3.49/0.83  Goal 1 (prove_ordered_pairs_are_small): little_set(ordered_pair(a, b)) = true2.
% 3.49/0.83  Proof:
% 3.49/0.83    little_set(ordered_pair(a, b))
% 3.49/0.83  = { by axiom 2 (ordered_pair) }
% 3.49/0.83    little_set(non_ordered_pair(singleton_set(a), non_ordered_pair(a, b)))
% 3.49/0.83  = { by axiom 1 (non_ordered_pair4) }
% 3.49/0.83    true2
% 3.49/0.83  % SZS output end Proof
% 3.49/0.83  
% 3.49/0.83  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------