0.03/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.14/0.34	% Computer : n016.cluster.edu
0.14/0.34	% Model    : x86_64 x86_64
0.14/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.34	% Memory   : 8042.1875MB
0.14/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.14/0.34	% CPULimit : 960
0.14/0.34	% WCLimit  : 120
0.14/0.34	% DateTime : Tue Aug  9 03:27:27 EDT 2022
0.14/0.34	% CPUTime  : 
0.20/0.40	% SZS status Unsatisfiable
0.20/0.40	
0.20/0.40	% SZS output start Proof
0.20/0.40	Axiom 1 (n_definition): apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z).
0.20/0.40	Axiom 2 (b_definition): apply(X, apply(Y, Z)) = apply(apply(apply(b, X), Y), Z).
0.20/0.40	
0.20/0.40	Goal 1 (prove_fixed_point): X = apply(combinator, X).
0.20/0.40	The goal is true when:
0.20/0.40	  X = apply(apply(apply(n, apply(b, apply(b, combinator))), X), apply(n, apply(b, apply(b, combinator))))
0.20/0.40	
0.20/0.40	Proof:
0.20/0.40	  apply(apply(apply(n, apply(b, apply(b, combinator))), X), apply(n, apply(b, apply(b, combinator))))
0.20/0.40	= { by axiom 1 (n_definition) }
0.20/0.40	  apply(apply(apply(apply(b, apply(b, combinator)), apply(n, apply(b, apply(b, combinator)))), X), apply(n, apply(b, apply(b, combinator))))
0.20/0.40	= { by axiom 2 (b_definition) R->L }
0.20/0.40	  apply(apply(apply(b, combinator), apply(apply(n, apply(b, apply(b, combinator))), X)), apply(n, apply(b, apply(b, combinator))))
0.20/0.40	= { by axiom 2 (b_definition) R->L }
0.20/0.40	  apply(combinator, apply(apply(apply(n, apply(b, apply(b, combinator))), X), apply(n, apply(b, apply(b, combinator)))))
0.20/0.40	% SZS output end Proof
0.20/0.40	
0.20/0.40	RESULT: Unsatisfiable (the axioms are contradictory).
0.20/0.40	EOF