%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET063-7 : 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 : n004.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 15:30:59 EDT 2023

% Result   : Unsatisfiable 0.20s 0.52s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET063-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.35  % Computer : n004.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Sat Aug 26 13:28:08 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.20/0.52  Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.52  
% 0.20/0.52  % SZS status Unsatisfiable
% 0.20/0.52  
% 0.20/0.52  % SZS output start Proof
% 0.20/0.52  Take the following subset of the input axioms:
% 0.20/0.52    fof(null_class_is_subclass, axiom, ![X]: subclass(null_class, X)).
% 0.20/0.52    fof(prove_corollary_of_null_class_is_subclass_1, negated_conjecture, subclass(x, null_class)).
% 0.20/0.52    fof(prove_corollary_of_null_class_is_subclass_2, negated_conjecture, x!=null_class).
% 0.20/0.52    fof(subclass_implies_equal, axiom, ![Y, X2]: (~subclass(X2, Y) | (~subclass(Y, X2) | X2=Y))).
% 0.20/0.52  
% 0.20/0.52  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.52  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.52  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.52    fresh(y, y, x1...xn) = u
% 0.20/0.52    C => fresh(s, t, x1...xn) = v
% 0.20/0.52  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.52  variables of u and v.
% 0.20/0.52  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.52  input problem has no model of domain size 1).
% 0.20/0.52  
% 0.20/0.52  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.52  
% 0.20/0.52  Axiom 1 (prove_corollary_of_null_class_is_subclass_1): subclass(x, null_class) = true2.
% 0.20/0.52  Axiom 2 (null_class_is_subclass): subclass(null_class, X) = true2.
% 0.20/0.52  Axiom 3 (subclass_implies_equal): fresh6(X, X, Y, Z) = Y.
% 0.20/0.52  Axiom 4 (subclass_implies_equal): fresh5(X, X, Y, Z) = Z.
% 0.20/0.52  Axiom 5 (subclass_implies_equal): fresh6(subclass(X, Y), true2, Y, X) = fresh5(subclass(Y, X), true2, Y, X).
% 0.20/0.52  
% 0.20/0.52  Goal 1 (prove_corollary_of_null_class_is_subclass_2): x = null_class.
% 0.20/0.52  Proof:
% 0.20/0.52    x
% 0.20/0.52  = { by axiom 3 (subclass_implies_equal) R->L }
% 0.20/0.52    fresh6(true2, true2, x, null_class)
% 0.20/0.52  = { by axiom 2 (null_class_is_subclass) R->L }
% 0.20/0.52    fresh6(subclass(null_class, x), true2, x, null_class)
% 0.20/0.52  = { by axiom 5 (subclass_implies_equal) }
% 0.20/0.52    fresh5(subclass(x, null_class), true2, x, null_class)
% 0.20/0.52  = { by axiom 1 (prove_corollary_of_null_class_is_subclass_1) }
% 0.20/0.52    fresh5(true2, true2, x, null_class)
% 0.20/0.52  = { by axiom 4 (subclass_implies_equal) }
% 0.20/0.52    null_class
% 0.20/0.52  % SZS output end Proof
% 0.20/0.52  
% 0.20/0.52  RESULT: Unsatisfiable (the axioms are contradictory).
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