%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : COL064-11 : TPTP v8.1.2. Bugfixed v1.2.0.
% 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 : Wed Aug 30 18:31:55 EDT 2023

% Result   : Unsatisfiable 0.10s 0.33s
% Output   : Proof 0.10s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : COL064-11 : TPTP v8.1.2. Bugfixed v1.2.0.
% 0.00/0.10  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.30  % Computer : n027.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
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sun Aug 27 05:32:20 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.10/0.33  Command-line arguments: --no-flatten-goal
% 0.10/0.33  
% 0.10/0.33  % SZS status Unsatisfiable
% 0.10/0.33  
% 0.10/0.34  % SZS output start Proof
% 0.10/0.34  Axiom 1 (t_definition): apply(apply(t, X), Y) = apply(Y, X).
% 0.10/0.34  Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.10/0.34  
% 0.10/0.34  Goal 1 (prove_v_combinator): apply(apply(apply(apply(apply(b, apply(apply(b, apply(apply(b, apply(t, apply(apply(b, b), t))), b)), t)), t), x), y), z) = apply(apply(z, x), y).
% 0.10/0.34  Proof:
% 0.10/0.34    apply(apply(apply(apply(apply(b, apply(apply(b, apply(apply(b, apply(t, apply(apply(b, b), t))), b)), t)), t), x), y), z)
% 0.10/0.34  = { by axiom 2 (b_definition) }
% 0.10/0.34    apply(apply(apply(apply(apply(b, apply(apply(b, apply(t, apply(apply(b, b), t))), b)), t), apply(t, x)), y), z)
% 0.10/0.34  = { by axiom 2 (b_definition) }
% 0.10/0.34    apply(apply(apply(apply(apply(b, apply(t, apply(apply(b, b), t))), b), apply(t, apply(t, x))), y), z)
% 0.10/0.34  = { by axiom 2 (b_definition) }
% 0.10/0.34    apply(apply(apply(apply(t, apply(apply(b, b), t)), apply(b, apply(t, apply(t, x)))), y), z)
% 0.10/0.34  = { by axiom 1 (t_definition) }
% 0.10/0.34    apply(apply(apply(apply(b, apply(t, apply(t, x))), apply(apply(b, b), t)), y), z)
% 0.10/0.34  = { by axiom 2 (b_definition) }
% 0.10/0.34    apply(apply(apply(t, apply(t, x)), apply(apply(apply(b, b), t), y)), z)
% 0.10/0.34  = { by axiom 2 (b_definition) }
% 0.10/0.34    apply(apply(apply(t, apply(t, x)), apply(b, apply(t, y))), z)
% 0.10/0.34  = { by axiom 1 (t_definition) }
% 0.10/0.34    apply(apply(apply(b, apply(t, y)), apply(t, x)), z)
% 0.10/0.34  = { by axiom 2 (b_definition) }
% 0.10/0.34    apply(apply(t, y), apply(apply(t, x), z))
% 0.10/0.34  = { by axiom 1 (t_definition) }
% 0.10/0.34    apply(apply(t, y), apply(z, x))
% 0.10/0.34  = { by axiom 1 (t_definition) }
% 0.10/0.34    apply(apply(z, x), y)
% 0.10/0.34  % SZS output end Proof
% 0.10/0.34  
% 0.10/0.34  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------