0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.34	% Computer : n025.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit : 960
0.13/0.34	% WCLimit  : 120
0.13/0.34	% DateTime : Tue Aug  9 03:01:11 EDT 2022
0.13/0.34	% CPUTime  : 
0.19/0.39	% SZS status Unsatisfiable
0.19/0.39	
0.19/0.40	% SZS output start Proof
0.19/0.40	Axiom 1 (i_definition): X = apply(i, X).
0.19/0.40	Axiom 2 (b_definition): apply(X, apply(Y, Z)) = apply(apply(apply(b, X), Y), Z).
0.19/0.40	Axiom 3 (s_definition): apply(apply(X, Y), apply(Z, Y)) = apply(apply(apply(s, X), Z), Y).
0.19/0.40	
0.19/0.40	Goal 1 (prove_fixed_point): apply(fixed_pt, X) = X.
0.19/0.40	The goal is true when:
0.19/0.40	  X = apply(apply(apply(s, apply(b, fixed_pt)), i), apply(apply(s, apply(b, fixed_pt)), i))
0.19/0.40	
0.19/0.40	Proof:
0.19/0.40	  apply(fixed_pt, apply(apply(apply(s, apply(b, fixed_pt)), i), apply(apply(s, apply(b, fixed_pt)), i)))
0.19/0.40	= { by axiom 1 (i_definition) }
0.19/0.40	  apply(fixed_pt, apply(apply(apply(s, apply(b, fixed_pt)), i), apply(i, apply(apply(s, apply(b, fixed_pt)), i))))
0.19/0.40	= { by axiom 2 (b_definition) }
0.19/0.40	  apply(apply(apply(b, fixed_pt), apply(apply(s, apply(b, fixed_pt)), i)), apply(i, apply(apply(s, apply(b, fixed_pt)), i)))
0.19/0.40	= { by axiom 3 (s_definition) }
0.19/0.40	  apply(apply(apply(s, apply(b, fixed_pt)), i), apply(apply(s, apply(b, fixed_pt)), i))
0.19/0.40	% SZS output end Proof
0.19/0.40	
0.19/0.40	RESULT: Unsatisfiable (the axioms are contradictory).
0.19/0.40	EOF