%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL133-1 : 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 : n023.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 08:17:36 EDT 2023

% Result   : Unsatisfiable 0.12s 0.37s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : LCL133-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.12  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Aug 25 05:48:42 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.37  Command-line arguments: --no-flatten-goal
% 0.12/0.37  
% 0.12/0.37  % SZS status Unsatisfiable
% 0.12/0.37  
% 0.12/0.37  % SZS output start Proof
% 0.12/0.37  Axiom 1 (lemma_antecedent): implies(X, Y) = implies(Y, X).
% 0.12/0.37  Axiom 2 (wajsberg_1): implies(truth, X) = X.
% 0.12/0.37  Axiom 3 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.12/0.37  Axiom 4 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.12/0.37  
% 0.12/0.37  Lemma 5: implies(X, X) = X.
% 0.12/0.37  Proof:
% 0.12/0.37    implies(X, X)
% 0.12/0.37  = { by axiom 2 (wajsberg_1) R->L }
% 0.12/0.37    implies(X, implies(truth, X))
% 0.12/0.37  = { by axiom 1 (lemma_antecedent) R->L }
% 0.12/0.37    implies(implies(truth, X), X)
% 0.12/0.37  = { by axiom 3 (wajsberg_3) R->L }
% 0.12/0.37    implies(implies(X, truth), truth)
% 0.12/0.37  = { by axiom 1 (lemma_antecedent) }
% 0.12/0.37    implies(truth, implies(X, truth))
% 0.12/0.37  = { by axiom 1 (lemma_antecedent) R->L }
% 0.12/0.37    implies(truth, implies(truth, X))
% 0.12/0.37  = { by axiom 2 (wajsberg_1) }
% 0.12/0.37    implies(truth, X)
% 0.12/0.37  = { by axiom 2 (wajsberg_1) }
% 0.12/0.37    X
% 0.12/0.37  
% 0.12/0.37  Lemma 6: implies(X, implies(X, Y)) = truth.
% 0.12/0.37  Proof:
% 0.12/0.37    implies(X, implies(X, Y))
% 0.12/0.37  = { by lemma 5 R->L }
% 0.12/0.37    implies(X, implies(implies(X, Y), implies(X, Y)))
% 0.12/0.37  = { by lemma 5 R->L }
% 0.12/0.37    implies(implies(X, X), implies(implies(X, Y), implies(X, Y)))
% 0.12/0.37  = { by axiom 4 (wajsberg_2) }
% 0.12/0.37    truth
% 0.12/0.37  
% 0.12/0.37  Goal 1 (prove_wajsberg_lemma): x = y.
% 0.12/0.37  Proof:
% 0.12/0.37    x
% 0.12/0.37  = { by axiom 2 (wajsberg_1) R->L }
% 0.12/0.37    implies(truth, x)
% 0.12/0.37  = { by axiom 2 (wajsberg_1) R->L }
% 0.12/0.37    implies(truth, implies(truth, x))
% 0.12/0.37  = { by lemma 6 }
% 0.12/0.37    truth
% 0.12/0.37  = { by lemma 6 R->L }
% 0.12/0.37    implies(truth, implies(truth, y))
% 0.12/0.37  = { by axiom 2 (wajsberg_1) }
% 0.12/0.37    implies(truth, y)
% 0.12/0.37  = { by axiom 2 (wajsberg_1) }
% 0.12/0.37    y
% 0.12/0.37  % SZS output end Proof
% 0.12/0.37  
% 0.12/0.37  RESULT: Unsatisfiable (the axioms are contradictory).
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