0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% 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 : n023.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 : 960
0.12/0.33	% WCLimit  : 120
0.12/0.33	% DateTime : Tue Aug  9 02:40:58 EDT 2022
0.12/0.33	% CPUTime  : 
0.12/0.37	% SZS status Unsatisfiable
0.12/0.37	
0.12/0.37	% SZS output start Proof
0.12/0.37	Axiom 1 (w_definition): apply(apply(w, X), Y) = apply(apply(X, Y), Y).
0.12/0.37	Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
0.12/0.37	
0.12/0.37	Goal 1 (prove_fixed_point): X = apply(combinator, X).
0.12/0.37	The goal is true when:
0.12/0.37	  X = apply(apply(w, apply(b, combinator)), apply(w, apply(b, combinator)))
0.12/0.37	
0.12/0.37	Proof:
0.12/0.37	  apply(apply(w, apply(b, combinator)), apply(w, apply(b, combinator)))
0.12/0.37	= { by axiom 1 (w_definition) }
0.12/0.37	  apply(apply(apply(b, combinator), apply(w, apply(b, combinator))), apply(w, apply(b, combinator)))
0.12/0.37	= { by axiom 2 (b_definition) }
0.12/0.37	  apply(combinator, apply(apply(w, apply(b, combinator)), apply(w, apply(b, combinator))))
0.12/0.37	% SZS output end Proof
0.12/0.37	
0.12/0.37	RESULT: Unsatisfiable (the axioms are contradictory).
0.12/0.38	EOF