0.00/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.16/5.34	% Computer : n028.cluster.edu
0.16/5.34	% Model    : x86_64 x86_64
0.16/5.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.16/5.34	% Memory   : 8042.1875MB
0.16/5.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.16/5.34	% CPULimit : 960
0.16/5.34	% WCLimit  : 120
0.16/5.34	% DateTime : Tue Aug  9 03:28:40 EDT 2022
0.16/5.34	% CPUTime  : 
0.19/5.41	% SZS status Unsatisfiable
0.19/5.41	
0.19/5.42	% SZS output start Proof
0.19/5.42	Axiom 1 (w1_definition): apply(apply(X, Y), Y) = apply(apply(w1, Y), X).
0.19/5.42	Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
0.19/5.42	
0.19/5.42	Goal 1 (prove_fixed_point): X = apply(combinator, X).
0.19/5.42	The goal is true when:
0.19/5.42	  X = apply(apply(w1, apply(apply(b, apply(b, combinator)), w1)), apply(apply(b, apply(b, combinator)), w1))
0.19/5.42	
0.19/5.42	Proof:
0.19/5.42	  apply(apply(w1, apply(apply(b, apply(b, combinator)), w1)), apply(apply(b, apply(b, combinator)), w1))
0.19/5.42	= { by axiom 1 (w1_definition) R->L }
0.19/5.42	  apply(apply(apply(apply(b, apply(b, combinator)), w1), apply(apply(b, apply(b, combinator)), w1)), apply(apply(b, apply(b, combinator)), w1))
0.19/5.42	= { by axiom 2 (b_definition) }
0.19/5.42	  apply(apply(apply(b, combinator), apply(w1, apply(apply(b, apply(b, combinator)), w1))), apply(apply(b, apply(b, combinator)), w1))
0.19/5.42	= { by axiom 2 (b_definition) }
0.19/5.42	  apply(combinator, apply(apply(w1, apply(apply(b, apply(b, combinator)), w1)), apply(apply(b, apply(b, combinator)), w1)))
0.19/5.42	% SZS output end Proof
0.19/5.42	
0.19/5.42	RESULT: Unsatisfiable (the axioms are contradictory).
0.19/5.42	EOF