%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : COL001-2 : 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 : n001.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 18:31:30 EDT 2023

% Result   : Unsatisfiable 0.13s 0.40s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : COL001-2 : 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
% 0.13/0.35  % Computer : n001.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 05:15:17 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.40  Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.13/0.40  
% 0.13/0.40  % SZS status Unsatisfiable
% 0.13/0.40  
% 0.13/0.40  % SZS output start Proof
% 0.13/0.40  Axiom 1 (i_definition): apply(i, X) = X.
% 0.13/0.40  Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
% 0.13/0.40  Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.13/0.40  
% 0.13/0.40  Goal 1 (prove_fixed_point): X = apply(combinator, X).
% 0.13/0.40  The goal is true when:
% 0.13/0.40    X = apply(apply(apply(s, apply(b, combinator)), i), apply(apply(s, apply(b, combinator)), i))
% 0.13/0.40  
% 0.13/0.40  Proof:
% 0.13/0.40    apply(apply(apply(s, apply(b, combinator)), i), apply(apply(s, apply(b, combinator)), i))
% 0.13/0.40  = { by axiom 2 (s_definition) }
% 0.13/0.40    apply(apply(apply(b, combinator), apply(apply(s, apply(b, combinator)), i)), apply(i, apply(apply(s, apply(b, combinator)), i)))
% 0.13/0.40  = { by axiom 1 (i_definition) }
% 0.13/0.40    apply(apply(apply(b, combinator), apply(apply(s, apply(b, combinator)), i)), apply(apply(s, apply(b, combinator)), i))
% 0.13/0.40  = { by axiom 3 (b_definition) }
% 0.13/0.40    apply(combinator, apply(apply(apply(s, apply(b, combinator)), i), apply(apply(s, apply(b, combinator)), i)))
% 0.13/0.40  % SZS output end Proof
% 0.13/0.40  
% 0.13/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------