0.02/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.12	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.11/0.33	% Computer : n027.cluster.edu
0.11/0.33	% Model    : x86_64 x86_64
0.11/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory   : 8042.1875MB
0.11/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit : 960
0.11/0.33	% WCLimit  : 120
0.11/0.33	% DateTime : Tue Aug  9 03:52:06 EDT 2022
0.11/0.33	% CPUTime  : 
0.17/0.41	% SZS status Unsatisfiable
0.17/0.41	
0.17/0.41	% SZS output start Proof
0.17/0.41	Axiom 1 (b_definition): apply(X, apply(Y, Z)) = apply(apply(apply(b, X), Y), Z).
0.17/0.41	Axiom 2 (n_definition): apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z).
0.17/0.41	
0.17/0.41	Goal 1 (prove_fixed_point): apply(X, f(X)) = apply(f(X), apply(X, f(X))).
0.17/0.41	The goal is true when:
0.17/0.41	  X = apply(apply(apply(n, apply(b, apply(b, apply(n, b)))), X), apply(n, apply(b, apply(b, apply(n, b)))))
0.17/0.41	
0.17/0.41	Proof:
0.17/0.41	  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)))))))
0.17/0.41	= { by axiom 2 (n_definition) }
0.17/0.41	  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)))))))
0.17/0.41	= { by axiom 1 (b_definition) R->L }
0.17/0.41	  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)))))))
0.17/0.41	= { by axiom 1 (b_definition) R->L }
0.17/0.41	  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)))))))
0.17/0.41	= { by axiom 2 (n_definition) }
0.17/0.41	  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)))))))
0.17/0.41	= { by axiom 1 (b_definition) R->L }
0.17/0.41	  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))))))))
0.17/0.41	% SZS output end Proof
0.17/0.41	
0.17/0.41	RESULT: Unsatisfiable (the axioms are contradictory).
0.17/0.42	EOF