%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL161-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n015.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 08:17:42 EDT 2023

% Result   : Unsatisfiable 0.14s 0.40s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL161-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n015.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 : Fri Aug 25 06:07:51 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.40  Command-line arguments: --ground-connectedness --complete-subsets
% 0.14/0.40  
% 0.14/0.40  % SZS status Unsatisfiable
% 0.14/0.40  
% 0.20/0.40  % SZS output start Proof
% 0.20/0.40  Axiom 1 (and_star_commutativity): and_star(X, Y) = and_star(Y, X).
% 0.20/0.40  Axiom 2 (axiom_4): and_star(X, truth) = X.
% 0.20/0.40  Axiom 3 (axiom_3): xor(X, X) = falsehood.
% 0.20/0.40  Axiom 4 (xor_commutativity): xor(X, Y) = xor(Y, X).
% 0.20/0.40  Axiom 5 (axiom_2): xor(X, falsehood) = X.
% 0.20/0.40  Axiom 6 (axiom_1): not(X) = xor(X, truth).
% 0.20/0.40  Axiom 7 (axiom_7): xor(X, xor(truth, Y)) = xor(xor(X, truth), Y).
% 0.20/0.40  Axiom 8 (implies_definition): implies(X, Y) = xor(truth, and_star(X, xor(truth, Y))).
% 0.20/0.40  
% 0.20/0.40  Lemma 9: xor(truth, X) = not(X).
% 0.20/0.40  Proof:
% 0.20/0.40    xor(truth, X)
% 0.20/0.40  = { by axiom 4 (xor_commutativity) R->L }
% 0.20/0.40    xor(X, truth)
% 0.20/0.40  = { by axiom 6 (axiom_1) R->L }
% 0.20/0.40    not(X)
% 0.20/0.40  
% 0.20/0.40  Goal 1 (prove_wajsberg_axiom): implies(truth, x) = x.
% 0.20/0.40  Proof:
% 0.20/0.40    implies(truth, x)
% 0.20/0.40  = { by axiom 8 (implies_definition) }
% 0.20/0.40    xor(truth, and_star(truth, xor(truth, x)))
% 0.20/0.40  = { by axiom 1 (and_star_commutativity) R->L }
% 0.20/0.40    xor(truth, and_star(xor(truth, x), truth))
% 0.20/0.40  = { by axiom 2 (axiom_4) }
% 0.20/0.40    xor(truth, xor(truth, x))
% 0.20/0.40  = { by lemma 9 }
% 0.20/0.40    not(xor(truth, x))
% 0.20/0.40  = { by lemma 9 }
% 0.20/0.40    not(not(x))
% 0.20/0.40  = { by axiom 6 (axiom_1) }
% 0.20/0.40    xor(not(x), truth)
% 0.20/0.40  = { by axiom 6 (axiom_1) }
% 0.20/0.40    xor(xor(x, truth), truth)
% 0.20/0.40  = { by axiom 7 (axiom_7) R->L }
% 0.20/0.40    xor(x, xor(truth, truth))
% 0.20/0.40  = { by axiom 3 (axiom_3) }
% 0.20/0.40    xor(x, falsehood)
% 0.20/0.40  = { by axiom 5 (axiom_2) }
% 0.20/0.40    x
% 0.20/0.40  % SZS output end Proof
% 0.20/0.40  
% 0.20/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
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