0.08/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.13	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.33	% Computer : n025.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 1440
0.12/0.33	% WCLimit  : 180
0.12/0.33	% DateTime : Mon Jul  3 04:05:23 EDT 2023
0.12/0.33	% CPUTime  : 
0.12/0.39	% SZS status Unsatisfiable
0.12/0.39	
0.18/0.39	% SZS output start Proof
0.18/0.39	Axiom 1 (n_definition): apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z).
0.18/0.40	Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
0.18/0.40	
0.18/0.40	Goal 1 (prove_fixed_point): apply(combinator, X) = X.
0.18/0.40	The goal is true when:
0.18/0.40	  X = apply(apply(apply(n, apply(b, apply(b, combinator))), X), apply(n, apply(b, apply(b, combinator))))
0.18/0.40	
0.18/0.40	Proof:
0.18/0.40	  apply(combinator, apply(apply(apply(n, apply(b, apply(b, combinator))), X), apply(n, apply(b, apply(b, combinator)))))
0.18/0.40	= { by axiom 2 (b_definition) R->L }
0.18/0.40	  apply(apply(apply(b, combinator), apply(apply(n, apply(b, apply(b, combinator))), X)), apply(n, apply(b, apply(b, combinator))))
0.18/0.40	= { by axiom 2 (b_definition) R->L }
0.18/0.40	  apply(apply(apply(apply(b, apply(b, combinator)), apply(n, apply(b, apply(b, combinator)))), X), apply(n, apply(b, apply(b, combinator))))
0.18/0.40	= { by axiom 1 (n_definition) R->L }
0.18/0.40	  apply(apply(apply(n, apply(b, apply(b, combinator))), X), apply(n, apply(b, apply(b, combinator))))
0.18/0.40	% SZS output end Proof
0.18/0.40	
0.18/0.40	RESULT: Unsatisfiable (the axioms are contradictory).
0.18/0.40	EOF