0.03/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.35	% Computer : n005.cluster.edu
0.13/0.35	% Model    : x86_64 x86_64
0.13/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory   : 8042.1875MB
0.13/0.35	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit : 960
0.13/0.35	% WCLimit  : 120
0.13/0.35	% DateTime : Tue Aug  9 03:20:04 EDT 2022
0.13/0.35	% CPUTime  : 
0.20/0.43	% SZS status Unsatisfiable
0.20/0.43	
0.20/0.44	% SZS output start Proof
0.20/0.44	Axiom 1 (w1_definition): apply(apply(X, Y), Y) = apply(apply(w1, Y), X).
0.20/0.44	Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
0.20/0.44	
0.20/0.44	Goal 1 (prove_fixed_point): X = apply(combinator, X).
0.20/0.44	The goal is true when:
0.20/0.44	  X = apply(apply(w1, apply(apply(b, apply(b, combinator)), w1)), apply(apply(b, apply(b, combinator)), w1))
0.20/0.44	
0.20/0.44	Proof:
0.20/0.44	  apply(apply(w1, apply(apply(b, apply(b, combinator)), w1)), apply(apply(b, apply(b, combinator)), w1))
0.20/0.44	= { by axiom 1 (w1_definition) R->L }
0.20/0.44	  apply(apply(apply(apply(b, apply(b, combinator)), w1), apply(apply(b, apply(b, combinator)), w1)), apply(apply(b, apply(b, combinator)), w1))
0.20/0.44	= { by axiom 2 (b_definition) }
0.20/0.44	  apply(apply(apply(b, combinator), apply(w1, apply(apply(b, apply(b, combinator)), w1))), apply(apply(b, apply(b, combinator)), w1))
0.20/0.44	= { by axiom 2 (b_definition) }
0.20/0.44	  apply(combinator, apply(apply(w1, apply(apply(b, apply(b, combinator)), w1)), apply(apply(b, apply(b, combinator)), w1)))
0.20/0.44	% SZS output end Proof
0.20/0.44	
0.20/0.44	RESULT: Unsatisfiable (the axioms are contradictory).
0.20/0.44	EOF