0.06/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% 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 : n006.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 02:25:29 EDT 2022
0.12/0.33	% CPUTime  : 
0.12/0.38	% SZS status Unsatisfiable
0.12/0.38	
0.12/0.38	% SZS output start Proof
0.12/0.38	Axiom 1 (m_definition): apply(m, X) = apply(X, X).
0.12/0.38	Axiom 2 (l_definition): apply(apply(l, X), Y) = apply(X, apply(Y, Y)).
0.12/0.38	Axiom 3 (b_definition): apply(X, apply(Y, Z)) = apply(apply(apply(b, X), Y), Z).
0.12/0.38	
0.12/0.38	Goal 1 (prove_fixed_point): apply(f(X), apply(X, f(X))) = apply(X, f(X)).
0.12/0.38	The goal is true when:
0.12/0.38	  X = apply(apply(b, m), l)
0.12/0.38	
0.12/0.38	Proof:
0.12/0.38	  apply(f(apply(apply(b, m), l)), apply(apply(apply(b, m), l), f(apply(apply(b, m), l))))
0.12/0.38	= { by axiom 3 (b_definition) R->L }
0.12/0.38	  apply(f(apply(apply(b, m), l)), apply(m, apply(l, f(apply(apply(b, m), l)))))
0.12/0.38	= { by axiom 1 (m_definition) }
0.12/0.38	  apply(f(apply(apply(b, m), l)), apply(apply(l, f(apply(apply(b, m), l))), apply(l, f(apply(apply(b, m), l)))))
0.12/0.38	= { by axiom 2 (l_definition) R->L }
0.12/0.38	  apply(apply(l, f(apply(apply(b, m), l))), apply(l, f(apply(apply(b, m), l))))
0.12/0.38	= { by axiom 1 (m_definition) R->L }
0.12/0.38	  apply(m, apply(l, f(apply(apply(b, m), l))))
0.12/0.38	= { by axiom 3 (b_definition) }
0.12/0.38	  apply(apply(apply(b, m), l), f(apply(apply(b, m), l)))
0.12/0.38	% SZS output end Proof
0.12/0.38	
0.12/0.38	RESULT: Unsatisfiable (the axioms are contradictory).
0.12/0.38	EOF