%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP146-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n029.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 01:14:08 EDT 2023

% Result   : Unsatisfiable 0.16s 0.46s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14  % Problem    : GRP146-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.14  % Command    : toma --casc %s
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 23:15:41 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.16/0.46  % SZS status Unsatisfiable
% 0.16/0.46  % SZS output start Proof
% 0.16/0.46  original problem:
% 0.16/0.46  axioms:
% 0.16/0.46  multiply(identity(), X) = X
% 0.16/0.46  multiply(inverse(X), X) = identity()
% 0.16/0.46  multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.16/0.46  greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.16/0.46  least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.16/0.46  greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.16/0.46  least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.16/0.46  least_upper_bound(X, X) = X
% 0.16/0.46  greatest_lower_bound(X, X) = X
% 0.16/0.46  least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.16/0.46  greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.16/0.46  multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.16/0.46  multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.16/0.46  multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.16/0.46  multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.16/0.46  least_upper_bound(a(), c()) = c()
% 0.16/0.46  least_upper_bound(b(), c()) = c()
% 0.16/0.46  goal:
% 0.16/0.46  least_upper_bound(least_upper_bound(a(), b()), c()) != c()
% 0.16/0.46  To show the unsatisfiability of the original goal,
% 0.16/0.46  it suffices to show that least_upper_bound(least_upper_bound(a(), b()), c()) = c() (skolemized goal) is valid under the axioms.
% 0.16/0.46  Here is an equational proof:
% 0.16/0.46  6: least_upper_bound(X0, least_upper_bound(X1, X2)) = least_upper_bound(least_upper_bound(X0, X1), X2).
% 0.16/0.46  Proof: Axiom.
% 0.16/0.46  
% 0.16/0.46  15: least_upper_bound(a(), c()) = c().
% 0.16/0.46  Proof: Axiom.
% 0.16/0.46  
% 0.16/0.46  16: least_upper_bound(b(), c()) = c().
% 0.16/0.46  Proof: Axiom.
% 0.16/0.46  
% 0.16/0.46  17: least_upper_bound(least_upper_bound(a(), b()), c()) = c().
% 0.16/0.46  Proof: Rewrite lhs with equations [6,16,15]
% 0.16/0.46                 rhs with equations [].
% 0.16/0.46  
% 0.16/0.46  % SZS output end Proof
%------------------------------------------------------------------------------