%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : COL035-1 : 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 : n020.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 18:31:43 EDT 2023

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : COL035-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.14  % 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 : n020.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 : Sun Aug 27 04:33:14 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.42  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.42  
% 0.20/0.42  % SZS status Unsatisfiable
% 0.20/0.42  
% 0.20/0.42  % SZS output start Proof
% 0.20/0.42  Axiom 1 (l_definition): apply(apply(l, X), Y) = apply(X, apply(Y, Y)).
% 0.20/0.42  Axiom 2 (w_definition): apply(apply(w, X), Y) = apply(apply(X, Y), Y).
% 0.20/0.42  Axiom 3 (q_definition): apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z)).
% 0.20/0.42  
% 0.20/0.42  Goal 1 (prove_fixed_point): apply(X, f(X)) = apply(f(X), apply(X, f(X))).
% 0.20/0.42  The goal is true when:
% 0.20/0.42    X = apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w)))
% 0.20/0.42  
% 0.20/0.42  Proof:
% 0.20/0.42    apply(apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w))), f(apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w)))))
% 0.20/0.42  = { by axiom 1 (l_definition) }
% 0.20/0.42    apply(apply(apply(apply(q, q), w), apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w)))), f(apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w)))))
% 0.20/0.42  = { by axiom 3 (q_definition) }
% 0.20/0.42    apply(apply(w, apply(q, apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w))))), f(apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w)))))
% 0.20/0.42  = { by axiom 2 (w_definition) }
% 0.20/0.42    apply(apply(apply(q, apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w)))), f(apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w))))), f(apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w)))))
% 0.20/0.42  = { by axiom 3 (q_definition) }
% 0.20/0.42    apply(f(apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w)))), apply(apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w))), f(apply(apply(l, apply(apply(q, q), w)), apply(l, apply(apply(q, q), w))))))
% 0.20/0.42  % SZS output end Proof
% 0.20/0.42  
% 0.20/0.42  RESULT: Unsatisfiable (the axioms are contradictory).
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