0.02/0.09	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.09	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.08/0.29	% Computer   : n014.cluster.edu
0.08/0.29	% Model      : x86_64 x86_64
0.08/0.29	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.08/0.29	% Memory     : 8042.1875MB
0.08/0.29	% OS         : Linux 3.10.0-693.el7.x86_64
0.08/0.29	% CPULimit   : 1200
0.08/0.29	% WCLimit    : 120
0.08/0.29	% DateTime   : Tue Jul 13 13:20:04 EDT 2021
0.08/0.29	% CPUTime    : 
0.14/0.35	% SZS status Unsatisfiable
0.14/0.35	
0.14/0.35	% SZS output start Proof
0.14/0.35	Axiom 1 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
0.14/0.35	Axiom 2 (n_definition): apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z).
0.14/0.35	
0.14/0.35	Goal 1 (prove_fixed_point): apply(X, f(X)) = apply(f(X), apply(X, f(X))).
0.14/0.35	The goal is true when:
0.14/0.35	  X = apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))
0.14/0.35	
0.14/0.35	Proof:
0.14/0.35	  apply(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b))))), f(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))))
0.14/0.35	= { by axiom 2 (n_definition) }
0.14/0.35	  apply(apply(apply(apply(apply(b, apply(b, apply(n, b))), apply(n, apply(b, apply(b, apply(n, b))))), X), apply(n, apply(b, apply(b, apply(n, b))))), f(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))))
0.14/0.35	= { by axiom 1 (b_definition) }
0.14/0.35	  apply(apply(apply(apply(b, apply(n, b)), apply(apply(n, apply(b, apply(b, apply(n, b)))), X)), apply(n, apply(b, apply(b, apply(n, b))))), f(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))))
0.14/0.35	= { by axiom 1 (b_definition) }
0.14/0.35	  apply(apply(apply(n, b), apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))), f(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))))
0.14/0.35	= { by axiom 2 (n_definition) }
0.14/0.35	  apply(apply(apply(b, f(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b))))))), apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))), f(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))))
0.14/0.35	= { by axiom 1 (b_definition) }
0.14/0.35	  apply(f(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))), apply(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b))))), f(apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b))))))))
0.14/0.35	% SZS output end Proof
0.14/0.35	
0.14/0.35	RESULT: Unsatisfiable (the axioms are contradictory).
0.14/0.36	EOF