%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : COL075-2 : TPTP v8.1.2. Released 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 : n013.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 18:32:00 EDT 2023

% Result   : Unsatisfiable 0.21s 0.42s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : COL075-2 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14  % 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 : n013.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 04:49:02 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.42  Command-line arguments: --ground-connectedness --complete-subsets
% 0.21/0.42  
% 0.21/0.42  % SZS status Unsatisfiable
% 0.21/0.42  
% 0.21/0.42  % SZS output start Proof
% 0.21/0.42  Axiom 1 (k_definition): apply(apply(k, X), Y) = X.
% 0.21/0.42  Axiom 2 (abstraction): apply(apply(apply(abstraction, X), Y), Z) = apply(apply(X, apply(k, Z)), apply(Y, Z)).
% 0.21/0.42  
% 0.21/0.42  Goal 1 (prove_diagonal_combinator): apply(apply(X, b(X)), c(X)) = apply(b(X), b(X)).
% 0.21/0.42  The goal is true when:
% 0.21/0.42    X = apply(apply(abstraction, abstraction), k)
% 0.21/0.42  
% 0.21/0.42  Proof:
% 0.21/0.42    apply(apply(apply(apply(abstraction, abstraction), k), b(apply(apply(abstraction, abstraction), k))), c(apply(apply(abstraction, abstraction), k)))
% 0.21/0.42  = { by axiom 2 (abstraction) }
% 0.21/0.42    apply(apply(apply(abstraction, apply(k, b(apply(apply(abstraction, abstraction), k)))), apply(k, b(apply(apply(abstraction, abstraction), k)))), c(apply(apply(abstraction, abstraction), k)))
% 0.21/0.42  = { by axiom 2 (abstraction) }
% 0.21/0.42    apply(apply(apply(k, b(apply(apply(abstraction, abstraction), k))), apply(k, c(apply(apply(abstraction, abstraction), k)))), apply(apply(k, b(apply(apply(abstraction, abstraction), k))), c(apply(apply(abstraction, abstraction), k))))
% 0.21/0.42  = { by axiom 1 (k_definition) }
% 0.21/0.42    apply(apply(apply(k, b(apply(apply(abstraction, abstraction), k))), apply(k, c(apply(apply(abstraction, abstraction), k)))), b(apply(apply(abstraction, abstraction), k)))
% 0.21/0.42  = { by axiom 1 (k_definition) }
% 0.21/0.42    apply(b(apply(apply(abstraction, abstraction), k)), b(apply(apply(abstraction, abstraction), k)))
% 0.21/0.42  % SZS output end Proof
% 0.21/0.42  
% 0.21/0.42  RESULT: Unsatisfiable (the axioms are contradictory).
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