%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP170-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n020.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 01:17:29 EDT 2023

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP170-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34  % Computer : n020.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 20:49:28 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.42  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.42  
% 0.19/0.42  % SZS status Unsatisfiable
% 0.19/0.42  
% 0.19/0.42  % SZS output start Proof
% 0.19/0.42  Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.19/0.42  Axiom 2 (p03c_1): least_upper_bound(a, b) = b.
% 0.19/0.42  Axiom 3 (p03c_2): least_upper_bound(c, d) = d.
% 0.19/0.42  Axiom 4 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.19/0.42  Axiom 5 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 0.19/0.42  Axiom 6 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.19/0.42  Axiom 7 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.19/0.42  
% 0.19/0.42  Goal 1 (prove_p03c): greatest_lower_bound(multiply(a, c), multiply(b, d)) = multiply(a, c).
% 0.19/0.42  Proof:
% 0.19/0.42    greatest_lower_bound(multiply(a, c), multiply(b, d))
% 0.19/0.42  = { by axiom 2 (p03c_1) R->L }
% 0.19/0.42    greatest_lower_bound(multiply(a, c), multiply(least_upper_bound(a, b), d))
% 0.19/0.42  = { by axiom 1 (symmetry_of_lub) R->L }
% 0.19/0.42    greatest_lower_bound(multiply(a, c), multiply(least_upper_bound(b, a), d))
% 0.19/0.42  = { by axiom 7 (monotony_lub2) }
% 0.19/0.42    greatest_lower_bound(multiply(a, c), least_upper_bound(multiply(b, d), multiply(a, d)))
% 0.19/0.42  = { by axiom 3 (p03c_2) R->L }
% 0.19/0.42    greatest_lower_bound(multiply(a, c), least_upper_bound(multiply(b, d), multiply(a, least_upper_bound(c, d))))
% 0.19/0.42  = { by axiom 6 (monotony_lub1) }
% 0.19/0.42    greatest_lower_bound(multiply(a, c), least_upper_bound(multiply(b, d), least_upper_bound(multiply(a, c), multiply(a, d))))
% 0.19/0.42  = { by axiom 1 (symmetry_of_lub) R->L }
% 0.19/0.42    greatest_lower_bound(multiply(a, c), least_upper_bound(multiply(b, d), least_upper_bound(multiply(a, d), multiply(a, c))))
% 0.19/0.42  = { by axiom 5 (associativity_of_lub) }
% 0.19/0.42    greatest_lower_bound(multiply(a, c), least_upper_bound(least_upper_bound(multiply(b, d), multiply(a, d)), multiply(a, c)))
% 0.19/0.42  = { by axiom 1 (symmetry_of_lub) R->L }
% 0.19/0.43    greatest_lower_bound(multiply(a, c), least_upper_bound(multiply(a, c), least_upper_bound(multiply(b, d), multiply(a, d))))
% 0.19/0.43  = { by axiom 4 (glb_absorbtion) }
% 0.19/0.43    multiply(a, c)
% 0.19/0.43  % SZS output end Proof
% 0.19/0.43  
% 0.19/0.43  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------