%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LAT035-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n009.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 06:27:13 EDT 2023

% Result   : Unsatisfiable 0.22s 0.41s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : LAT035-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35  % Computer : n009.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug 24 07:35:36 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.22/0.41  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.41  
% 0.22/0.41  % SZS status Unsatisfiable
% 0.22/0.41  
% 0.22/0.41  % SZS output start Proof
% 0.22/0.41  Take the following subset of the input axioms:
% 0.22/0.41    fof(comp_join_hemimorphism, negated_conjecture, f(k(join(aa, bb)))!=join(f(k(aa)), f(k(bb))) | f(k(n0))!=n0).
% 0.22/0.41    fof(f_on_meet, axiom, ![U, V]: f(meet(U, V))=join(f(U), f(V))).
% 0.22/0.41    fof(f_on_top, axiom, f(n1)=n0).
% 0.22/0.41    fof(k_on_bottom, axiom, k(n0)=n1).
% 0.22/0.41    fof(k_on_join, axiom, ![U2, V2]: k(join(U2, V2))=meet(k(U2), k(V2))).
% 0.22/0.41  
% 0.22/0.41  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.41  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.41  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.41    fresh(y, y, x1...xn) = u
% 0.22/0.41    C => fresh(s, t, x1...xn) = v
% 0.22/0.41  where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.41  variables of u and v.
% 0.22/0.41  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.41  input problem has no model of domain size 1).
% 0.22/0.41  
% 0.22/0.41  The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.41  
% 0.22/0.41  Axiom 1 (f_on_top): f(n1) = n0.
% 0.22/0.41  Axiom 2 (k_on_bottom): k(n0) = n1.
% 0.22/0.41  Axiom 3 (k_on_join): k(join(X, Y)) = meet(k(X), k(Y)).
% 0.22/0.41  Axiom 4 (f_on_meet): f(meet(X, Y)) = join(f(X), f(Y)).
% 0.22/0.41  
% 0.22/0.41  Goal 1 (comp_join_hemimorphism): tuple(f(k(join(aa, bb))), f(k(n0))) = tuple(join(f(k(aa)), f(k(bb))), n0).
% 0.22/0.41  Proof:
% 0.22/0.41    tuple(f(k(join(aa, bb))), f(k(n0)))
% 0.22/0.41  = { by axiom 2 (k_on_bottom) }
% 0.22/0.41    tuple(f(k(join(aa, bb))), f(n1))
% 0.22/0.41  = { by axiom 1 (f_on_top) }
% 0.22/0.41    tuple(f(k(join(aa, bb))), n0)
% 0.22/0.41  = { by axiom 3 (k_on_join) }
% 0.22/0.41    tuple(f(meet(k(aa), k(bb))), n0)
% 0.22/0.41  = { by axiom 4 (f_on_meet) }
% 0.22/0.41    tuple(join(f(k(aa)), f(k(bb))), n0)
% 0.22/0.41  % SZS output end Proof
% 0.22/0.41  
% 0.22/0.41  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------