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 : n010.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 04:13:50 EDT 2022
0.12/0.33	% CPUTime  : 
2.82/0.74	% SZS status Unsatisfiable
2.82/0.74	
2.82/0.75	% SZS output start Proof
2.82/0.75	Axiom 1 (m_definition): apply(X, X) = apply(m, X).
2.82/0.75	Axiom 2 (t_definition): apply(apply(t, X), Y) = apply(Y, X).
2.82/0.75	Axiom 3 (b_definition): apply(X, apply(Y, Z)) = apply(apply(apply(b, X), Y), Z).
2.82/0.75	
2.82/0.75	Goal 1 (prove_fixed_point): apply(X, f(X)) = apply(f(X), apply(X, f(X))).
2.82/0.75	The goal is true when:
2.82/0.75	  X = apply(apply(b, apply(apply(b, m), apply(t, m))), b)
2.82/0.75	
2.82/0.75	Proof:
2.82/0.75	  apply(apply(apply(b, apply(apply(b, m), apply(t, m))), b), f(apply(apply(b, apply(apply(b, m), apply(t, m))), b)))
2.82/0.75	= { by axiom 3 (b_definition) R->L }
2.82/0.75	  apply(apply(apply(b, m), apply(t, m)), apply(b, f(apply(apply(b, apply(apply(b, m), apply(t, m))), b))))
2.82/0.75	= { by axiom 3 (b_definition) R->L }
2.82/0.75	  apply(m, apply(apply(t, m), apply(b, f(apply(apply(b, apply(apply(b, m), apply(t, m))), b)))))
2.82/0.75	= { by axiom 2 (t_definition) }
2.82/0.75	  apply(m, apply(apply(b, f(apply(apply(b, apply(apply(b, m), apply(t, m))), b))), m))
2.82/0.75	= { by axiom 1 (m_definition) R->L }
2.82/0.75	  apply(apply(apply(b, f(apply(apply(b, apply(apply(b, m), apply(t, m))), b))), m), apply(apply(b, f(apply(apply(b, apply(apply(b, m), apply(t, m))), b))), m))
2.82/0.75	= { by axiom 3 (b_definition) R->L }
2.82/0.75	  apply(f(apply(apply(b, apply(apply(b, m), apply(t, m))), b)), apply(m, apply(apply(b, f(apply(apply(b, apply(apply(b, m), apply(t, m))), b))), m)))
2.82/0.75	= { by axiom 2 (t_definition) R->L }
2.82/0.75	  apply(f(apply(apply(b, apply(apply(b, m), apply(t, m))), b)), apply(m, apply(apply(t, m), apply(b, f(apply(apply(b, apply(apply(b, m), apply(t, m))), b))))))
2.82/0.75	= { by axiom 3 (b_definition) }
2.82/0.75	  apply(f(apply(apply(b, apply(apply(b, m), apply(t, m))), b)), apply(apply(apply(b, m), apply(t, m)), apply(b, f(apply(apply(b, apply(apply(b, m), apply(t, m))), b)))))
2.82/0.75	= { by axiom 3 (b_definition) }
2.82/0.75	  apply(f(apply(apply(b, apply(apply(b, m), apply(t, m))), b)), apply(apply(apply(b, apply(apply(b, m), apply(t, m))), b), f(apply(apply(b, apply(apply(b, m), apply(t, m))), b))))
2.82/0.75	% SZS output end Proof
2.82/0.75	
2.82/0.75	RESULT: Unsatisfiable (the axioms are contradictory).
2.82/0.75	EOF