%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP176-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% 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 01:14:17 EDT 2023

% Result   : Unsatisfiable 0.20s 0.48s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP176-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13  % Command    : toma --casc %s
% 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   : Mon Aug 28 23:19:40 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.48  % SZS status Unsatisfiable
% 0.20/0.48  % SZS output start Proof
% 0.20/0.48  original problem:
% 0.20/0.48  axioms:
% 0.20/0.48  multiply(identity(), X) = X
% 0.20/0.48  multiply(inverse(X), X) = identity()
% 0.20/0.48  multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.20/0.48  greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.20/0.48  least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.20/0.48  greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.20/0.48  least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.20/0.48  least_upper_bound(X, X) = X
% 0.20/0.48  greatest_lower_bound(X, X) = X
% 0.20/0.48  least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.20/0.48  greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.20/0.48  multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.20/0.48  multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.20/0.48  multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.20/0.48  multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.20/0.48  goal:
% 0.20/0.48  multiply(c(), multiply(least_upper_bound(a(), b()), d())) != least_upper_bound(multiply(c(), multiply(a(), d())), multiply(c(), multiply(b(), d())))
% 0.20/0.48  To show the unsatisfiability of the original goal,
% 0.20/0.48  it suffices to show that multiply(c(), multiply(least_upper_bound(a(), b()), d())) = least_upper_bound(multiply(c(), multiply(a(), d())), multiply(c(), multiply(b(), d()))) (skolemized goal) is valid under the axioms.
% 0.20/0.48  Here is an equational proof:
% 0.20/0.48  11: multiply(X0, least_upper_bound(X1, X2)) = least_upper_bound(multiply(X0, X1), multiply(X0, X2)).
% 0.20/0.48  Proof: Axiom.
% 0.20/0.48  
% 0.20/0.48  13: multiply(least_upper_bound(X1, X2), X0) = least_upper_bound(multiply(X1, X0), multiply(X2, X0)).
% 0.20/0.48  Proof: Axiom.
% 0.20/0.48  
% 0.20/0.48  15: multiply(c(), multiply(least_upper_bound(a(), b()), d())) = least_upper_bound(multiply(c(), multiply(a(), d())), multiply(c(), multiply(b(), d()))).
% 0.20/0.48  Proof: Rewrite lhs with equations []
% 0.20/0.48                 rhs with equations [11,13].
% 0.20/0.48  
% 0.20/0.48  % SZS output end Proof
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