%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : CAT011-2 : 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 : n007.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 : Wed Aug 30 18:18:54 EDT 2023

% Result   : Unsatisfiable 0.20s 0.38s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : CAT011-2 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n007.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 : Sun Aug 27 00:47:27 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.38  Command-line arguments: --no-flatten-goal
% 0.20/0.38  
% 0.20/0.38  % SZS status Unsatisfiable
% 0.20/0.38  
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  Take the following subset of the input axioms:
% 0.20/0.39    fof(codomain_of_domain_is_domain, axiom, ![X]: codomain(domain(X))=domain(X)).
% 0.20/0.39    fof(domain_of_codomain_is_codomain, axiom, ![X2]: domain(codomain(X2))=codomain(X2)).
% 0.20/0.39    fof(prove_domain_is_idempotent, negated_conjecture, domain(domain(a))!=domain(a)).
% 0.20/0.39  
% 0.20/0.39  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.39  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.39  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.39    fresh(y, y, x1...xn) = u
% 0.20/0.39    C => fresh(s, t, x1...xn) = v
% 0.20/0.39  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.39  variables of u and v.
% 0.20/0.39  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.39  input problem has no model of domain size 1).
% 0.20/0.39  
% 0.20/0.39  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.39  
% 0.20/0.39  Axiom 1 (codomain_of_domain_is_domain): codomain(domain(X)) = domain(X).
% 0.20/0.39  Axiom 2 (domain_of_codomain_is_codomain): domain(codomain(X)) = codomain(X).
% 0.20/0.39  
% 0.20/0.39  Goal 1 (prove_domain_is_idempotent): domain(domain(a)) = domain(a).
% 0.20/0.39  Proof:
% 0.20/0.39    domain(domain(a))
% 0.20/0.39  = { by axiom 1 (codomain_of_domain_is_domain) R->L }
% 0.20/0.39    domain(codomain(domain(a)))
% 0.20/0.39  = { by axiom 2 (domain_of_codomain_is_codomain) }
% 0.20/0.39    codomain(domain(a))
% 0.20/0.39  = { by axiom 1 (codomain_of_domain_is_domain) }
% 0.20/0.39    domain(a)
% 0.20/0.39  % SZS output end Proof
% 0.20/0.39  
% 0.20/0.39  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------