%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET061+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n025.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 15:30:57 EDT 2023

% Result   : Theorem 0.19s 0.51s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET061+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n025.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 13:13:38 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.51  Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.51  
% 0.19/0.51  % SZS status Theorem
% 0.19/0.51  
% 0.19/0.51  % SZS output start Proof
% 0.19/0.51  Take the following subset of the input axioms:
% 0.19/0.51    fof(complement, axiom, ![X, Z]: (member(Z, complement(X)) <=> (member(Z, universal_class) & ~member(Z, X)))).
% 0.19/0.51    fof(disjoint_defn, axiom, ![Y, X2]: (disjoint(X2, Y) <=> ![U]: ~(member(U, X2) & member(U, Y)))).
% 0.19/0.51    fof(domain_of, axiom, ![X2, Z2]: (member(Z2, domain_of(X2)) <=> (member(Z2, universal_class) & restrict(X2, singleton(Z2), universal_class)!=null_class))).
% 0.19/0.51    fof(existence_of_null_class, conjecture, ?[X2]: ![Z2]: ~member(Z2, X2)).
% 0.19/0.51    fof(null_class_defn, axiom, ![X2]: ~member(X2, null_class)).
% 0.19/0.51  
% 0.19/0.51  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.51  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.51  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.51    fresh(y, y, x1...xn) = u
% 0.19/0.51    C => fresh(s, t, x1...xn) = v
% 0.19/0.51  where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.51  variables of u and v.
% 0.19/0.51  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.51  input problem has no model of domain size 1).
% 0.19/0.51  
% 0.19/0.51  The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.51  
% 0.19/0.51  Axiom 1 (existence_of_null_class): member(z(X), X) = true2.
% 0.19/0.51  
% 0.19/0.51  Goal 1 (null_class_defn): member(X, null_class) = true2.
% 0.19/0.51  The goal is true when:
% 0.19/0.51    X = z(null_class)
% 0.19/0.51  
% 0.19/0.51  Proof:
% 0.19/0.51    member(z(null_class), null_class)
% 0.19/0.51  = { by axiom 1 (existence_of_null_class) }
% 0.19/0.51    true2
% 0.19/0.51  % SZS output end Proof
% 0.19/0.51  
% 0.19/0.51  RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------