%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP182-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n012.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 01:14:19 EDT 2023

% Result   : Unsatisfiable 0.21s 0.45s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP182-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14  % Command    : toma --casc %s
% 0.14/0.35  % Computer : n012.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 21:57:09 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.45  % SZS status Unsatisfiable
% 0.21/0.45  % SZS output start Proof
% 0.21/0.45  original problem:
% 0.21/0.45  axioms:
% 0.21/0.45  multiply(identity(), X) = X
% 0.21/0.45  multiply(inverse(X), X) = identity()
% 0.21/0.45  multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.21/0.45  greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.21/0.45  least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.21/0.45  greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.21/0.45  least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.21/0.45  least_upper_bound(X, X) = X
% 0.21/0.45  greatest_lower_bound(X, X) = X
% 0.21/0.45  least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.21/0.45  greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.21/0.45  multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.21/0.45  multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.21/0.45  multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.21/0.45  multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.21/0.45  inverse(identity()) = identity()
% 0.21/0.45  inverse(inverse(X)) = X
% 0.21/0.45  inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X))
% 0.21/0.45  goal:
% 0.21/0.45  greatest_lower_bound(identity(), least_upper_bound(a(), identity())) != identity()
% 0.21/0.45  To show the unsatisfiability of the original goal,
% 0.21/0.45  it suffices to show that greatest_lower_bound(identity(), least_upper_bound(a(), identity())) = identity() (skolemized goal) is valid under the axioms.
% 0.21/0.45  Here is an equational proof:
% 0.21/0.45  4: least_upper_bound(X0, X1) = least_upper_bound(X1, X0).
% 0.21/0.45  Proof: Axiom.
% 0.21/0.45  
% 0.21/0.45  10: greatest_lower_bound(X0, least_upper_bound(X0, X1)) = X0.
% 0.21/0.45  Proof: Axiom.
% 0.21/0.45  
% 0.21/0.45  18: greatest_lower_bound(identity(), least_upper_bound(a(), identity())) = identity().
% 0.21/0.45  Proof: Rewrite lhs with equations [4,10]
% 0.21/0.45                 rhs with equations [].
% 0.21/0.45  
% 0.21/0.45  % SZS output end Proof
%------------------------------------------------------------------------------