0.00/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.11/0.32	% Computer : n005.cluster.edu
0.11/0.32	% Model    : x86_64 x86_64
0.11/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory   : 8042.1875MB
0.11/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit : 960
0.11/0.33	% WCLimit  : 120
0.11/0.33	% DateTime : Tue Aug  9 03:29:34 EDT 2022
0.11/0.33	% CPUTime  : 
7.12/1.27	% SZS status Unsatisfiable
7.12/1.27	
7.12/1.27	% SZS output start Proof
7.12/1.27	Axiom 1 (l2_definition): apply(apply(l2, X), Y) = apply(Y, apply(X, X)).
7.12/1.27	Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
7.12/1.27	
7.12/1.27	Goal 1 (prove_fixed_point): apply(combinator, X) = X.
7.12/1.27	The goal is true when:
7.12/1.27	  X = apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(l2, apply(apply(b, apply(b, combinator)), l2)))
7.12/1.27	
7.12/1.27	Proof:
7.12/1.27	  apply(combinator, apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(l2, apply(apply(b, apply(b, combinator)), l2))))
7.12/1.27	= { by axiom 1 (l2_definition) }
7.12/1.27	  apply(combinator, apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(apply(apply(b, apply(b, combinator)), l2), apply(apply(b, apply(b, combinator)), l2))))
7.12/1.27	= { by axiom 2 (b_definition) R->L }
7.12/1.27	  apply(apply(apply(b, combinator), apply(l2, apply(apply(b, apply(b, combinator)), l2))), apply(apply(apply(b, apply(b, combinator)), l2), apply(apply(b, apply(b, combinator)), l2)))
7.12/1.27	= { by axiom 1 (l2_definition) R->L }
7.12/1.27	  apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(apply(b, combinator), apply(l2, apply(apply(b, apply(b, combinator)), l2))))
7.12/1.27	= { by axiom 2 (b_definition) R->L }
7.12/1.27	  apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(apply(apply(b, apply(b, combinator)), l2), apply(apply(b, apply(b, combinator)), l2)))
7.12/1.27	= { by axiom 1 (l2_definition) R->L }
7.12/1.27	  apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(l2, apply(apply(b, apply(b, combinator)), l2)))
7.12/1.27	% SZS output end Proof
7.12/1.27	
7.12/1.27	RESULT: Unsatisfiable (the axioms are contradictory).
7.12/1.28	EOF