%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : LCL132-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n032.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 08:13:54 EDT 2023

% Result   : Unsatisfiable 0.15s 0.54s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : LCL132-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11  % Command    : toma --casc %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Fri Aug 25 04:50:42 EDT 2023
% 0.10/0.30  % CPUTime    : 
% 0.15/0.54  % SZS status Unsatisfiable
% 0.15/0.54  % SZS output start Proof
% 0.15/0.54  original problem:
% 0.15/0.54  axioms:
% 0.15/0.54  implies(truth(), X) = X
% 0.15/0.54  implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth()
% 0.15/0.54  implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 0.15/0.54  implies(implies(not(X), not(Y)), implies(Y, X)) = truth()
% 0.15/0.54  goal:
% 0.15/0.54  implies(x(), x()) != truth()
% 0.15/0.54  To show the unsatisfiability of the original goal,
% 0.15/0.54  it suffices to show that implies(x(), x()) = truth() (skolemized goal) is valid under the axioms.
% 0.15/0.54  Here is an equational proof:
% 0.15/0.54  0: implies(truth(), X0) = X0.
% 0.15/0.54  Proof: Axiom.
% 0.15/0.54  
% 0.15/0.54  1: implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))) = truth().
% 0.15/0.54  Proof: Axiom.
% 0.15/0.54  
% 0.15/0.54  2: implies(implies(X0, X1), X1) = implies(implies(X1, X0), X0).
% 0.15/0.54  Proof: Axiom.
% 0.15/0.54  
% 0.15/0.54  4: implies(implies(X2, truth()), truth()) = implies(X2, X2).
% 0.15/0.54  Proof: A critical pair between equations 2 and 0.
% 0.15/0.54  
% 0.15/0.54  8: truth() = implies(implies(X0, truth()), implies(X3, implies(X0, X3))).
% 0.15/0.54  Proof: A critical pair between equations 1 and 0.
% 0.15/0.54  
% 0.15/0.54  10: truth() = implies(implies(implies(implies(X3, X5), X5), X3), truth()).
% 0.15/0.54  Proof: A critical pair between equations 1 and 1.
% 0.15/0.54  
% 0.15/0.54  13: implies(implies(X3, implies(X2, X3)), implies(X2, X3)) = implies(implies(implies(X3, X2), X2), X3).
% 0.15/0.54  Proof: A critical pair between equations 2 and 2.
% 0.15/0.54  
% 0.15/0.54  16: truth() = implies(implies(implies(X3, implies(X5, X3)), implies(X5, X3)), truth()).
% 0.15/0.54  Proof: Rewrite equation 10,
% 0.15/0.54                 lhs with equations []
% 0.15/0.54                 rhs with equations [13].
% 0.15/0.54  
% 0.15/0.54  28: truth() = implies(implies(truth(), implies(truth(), implies(X6, truth()))), truth()).
% 0.15/0.54  Proof: A critical pair between equations 16 and 8.
% 0.15/0.54  
% 0.15/0.54  31: truth() = implies(X6, X6).
% 0.15/0.54  Proof: Rewrite equation 28,
% 0.15/0.54                 lhs with equations []
% 0.15/0.54                 rhs with equations [0,0,4].
% 0.15/0.54  
% 0.15/0.54  35: implies(x(), x()) = truth().
% 0.15/0.54  Proof: Rewrite lhs with equations [31]
% 0.15/0.54                 rhs with equations [].
% 0.15/0.54  
% 0.15/0.54  % SZS output end Proof
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