%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET101-7 : 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 : n002.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 15:31:16 EDT 2023

% Result   : Unsatisfiable 0.21s 0.60s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET101-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 08:40:18 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.60  Command-line arguments: --no-flatten-goal
% 0.21/0.60  
% 0.21/0.60  % SZS status Unsatisfiable
% 0.21/0.60  
% 0.21/0.60  % SZS output start Proof
% 0.21/0.60  Take the following subset of the input axioms:
% 0.21/0.61    fof(commutativity_of_unordered_pair, axiom, ![X, Y]: unordered_pair(X, Y)=unordered_pair(Y, X)).
% 0.21/0.61    fof(corollary_1_to_singletons_are_sets, axiom, ![X2, Y2]: member(singleton(Y2), unordered_pair(X2, singleton(Y2)))).
% 0.21/0.61    fof(ordered_pair, axiom, ![X2, Y2]: unordered_pair(singleton(X2), unordered_pair(X2, singleton(Y2)))=ordered_pair(X2, Y2)).
% 0.21/0.61    fof(prove_singleton_member_of_ordered_pair_1, negated_conjecture, ~member(singleton(x), ordered_pair(x, y))).
% 0.21/0.61  
% 0.21/0.61  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.61  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.61  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.61    fresh(y, y, x1...xn) = u
% 0.21/0.61    C => fresh(s, t, x1...xn) = v
% 0.21/0.61  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.61  variables of u and v.
% 0.21/0.61  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.61  input problem has no model of domain size 1).
% 0.21/0.61  
% 0.21/0.61  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.61  
% 0.21/0.61  Axiom 1 (commutativity_of_unordered_pair): unordered_pair(X, Y) = unordered_pair(Y, X).
% 0.21/0.61  Axiom 2 (ordered_pair): unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y).
% 0.21/0.61  Axiom 3 (corollary_1_to_singletons_are_sets): member(singleton(X), unordered_pair(Y, singleton(X))) = true2.
% 0.21/0.61  
% 0.21/0.61  Goal 1 (prove_singleton_member_of_ordered_pair_1): member(singleton(x), ordered_pair(x, y)) = true2.
% 0.21/0.61  Proof:
% 0.21/0.61    member(singleton(x), ordered_pair(x, y))
% 0.21/0.61  = { by axiom 2 (ordered_pair) R->L }
% 0.21/0.61    member(singleton(x), unordered_pair(singleton(x), unordered_pair(x, singleton(y))))
% 0.21/0.61  = { by axiom 1 (commutativity_of_unordered_pair) R->L }
% 0.21/0.61    member(singleton(x), unordered_pair(unordered_pair(x, singleton(y)), singleton(x)))
% 0.21/0.61  = { by axiom 3 (corollary_1_to_singletons_are_sets) }
% 0.21/0.61    true2
% 0.21/0.61  % SZS output end Proof
% 0.21/0.61  
% 0.21/0.61  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------