0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% 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   : n003.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   : 1200
0.12/0.33	% WCLimit    : 120
0.12/0.33	% DateTime   : Tue Jul 13 13:19:54 EDT 2021
0.12/0.33	% CPUTime    : 
0.18/0.41	% SZS status Unsatisfiable
0.18/0.41	
0.18/0.41	% SZS output start Proof
0.18/0.41	Axiom 1 (l_definition): apply(X, apply(Y, Y)) = apply(apply(l, X), Y).
0.18/0.41	Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
0.18/0.41	
0.18/0.41	Goal 1 (prove_fixed_point): apply(X, f(X)) = apply(f(X), apply(X, f(X))).
0.18/0.41	The goal is true when:
0.18/0.41	  X = apply(apply(s, l), l)
0.18/0.41	
0.18/0.41	Proof:
0.18/0.41	  apply(apply(apply(s, l), l), f(apply(apply(s, l), l)))
0.18/0.41	= { by axiom 2 (s_definition) }
0.18/0.41	  apply(apply(l, f(apply(apply(s, l), l))), apply(l, f(apply(apply(s, l), l))))
0.18/0.41	= { by axiom 1 (l_definition) R->L }
0.18/0.41	  apply(f(apply(apply(s, l), l)), apply(apply(l, f(apply(apply(s, l), l))), apply(l, f(apply(apply(s, l), l)))))
0.18/0.41	= { by axiom 2 (s_definition) R->L }
0.18/0.41	  apply(f(apply(apply(s, l), l)), apply(apply(apply(s, l), l), f(apply(apply(s, l), l))))
0.18/0.41	% SZS output end Proof
0.18/0.41	
0.18/0.41	RESULT: Unsatisfiable (the axioms are contradictory).
0.18/0.42	EOF