%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL134-1 : 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 : n027.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 0.20s 0.38s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL134-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n027.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 : Thu Aug 24 19:56:32 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.38  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.38  
% 0.20/0.38  % SZS status Unsatisfiable
% 0.20/0.38  
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  Axiom 1 (wajsberg_1): implies(truth, X) = X.
% 0.20/0.39  Axiom 2 (wajsberg_3): implies(implies(X, Y), Y) = implies(implies(Y, X), X).
% 0.20/0.39  Axiom 3 (wajsberg_2): implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth.
% 0.20/0.39  
% 0.20/0.39  Lemma 4: implies(X, implies(implies(X, Y), Y)) = truth.
% 0.20/0.39  Proof:
% 0.20/0.39    implies(X, implies(implies(X, Y), Y))
% 0.20/0.39  = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.39    implies(X, implies(implies(X, Y), implies(truth, Y)))
% 0.20/0.39  = { by axiom 1 (wajsberg_1) R->L }
% 0.20/0.39    implies(implies(truth, X), implies(implies(X, Y), implies(truth, Y)))
% 0.20/0.39  = { by axiom 3 (wajsberg_2) }
% 0.20/0.39    truth
% 0.20/0.39  
% 0.20/0.39  Goal 1 (prove_wajsberg_lemma): implies(x, truth) = truth.
% 0.20/0.39  Proof:
% 0.20/0.39    implies(x, truth)
% 0.20/0.39  = { by lemma 4 R->L }
% 0.20/0.39    implies(x, implies(truth, implies(implies(truth, x), x)))
% 0.20/0.39  = { by axiom 1 (wajsberg_1) }
% 0.20/0.39    implies(x, implies(implies(truth, x), x))
% 0.20/0.39  = { by axiom 2 (wajsberg_3) }
% 0.20/0.39    implies(x, implies(implies(x, truth), truth))
% 0.20/0.39  = { by lemma 4 }
% 0.20/0.39    truth
% 0.20/0.39  % SZS output end Proof
% 0.20/0.39  
% 0.20/0.39  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------