0.00/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.11	% 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   : n007.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
0.11/0.32	% CPULimit   : 1200
0.11/0.32	% WCLimit    : 120
0.11/0.32	% DateTime   : Tue Jul 13 14:33:19 EDT 2021
0.11/0.32	% CPUTime    : 
0.17/0.36	% SZS status Unsatisfiable
0.17/0.36	
0.17/0.36	% SZS output start Proof
0.17/0.36	Axiom 1 (i_definition): apply(i, X) = X.
0.17/0.36	Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
0.17/0.37	Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
0.17/0.37	
0.17/0.37	Goal 1 (prove_fixed_point): X = apply(fixed_pt, X).
0.17/0.37	The goal is true when:
0.17/0.37	  X = apply(apply(apply(s, apply(b, fixed_pt)), i), apply(apply(s, apply(b, fixed_pt)), i))
0.17/0.37	
0.17/0.37	Proof:
0.17/0.37	  apply(apply(apply(s, apply(b, fixed_pt)), i), apply(apply(s, apply(b, fixed_pt)), i))
0.17/0.37	= { by axiom 2 (s_definition) }
0.17/0.37	  apply(apply(apply(b, fixed_pt), apply(apply(s, apply(b, fixed_pt)), i)), apply(i, apply(apply(s, apply(b, fixed_pt)), i)))
0.17/0.37	= { by axiom 3 (b_definition) }
0.17/0.37	  apply(fixed_pt, apply(apply(apply(s, apply(b, fixed_pt)), i), apply(i, apply(apply(s, apply(b, fixed_pt)), i))))
0.17/0.37	= { by axiom 1 (i_definition) }
0.17/0.37	  apply(fixed_pt, apply(apply(apply(s, apply(b, fixed_pt)), i), apply(apply(s, apply(b, fixed_pt)), i)))
0.17/0.37	% SZS output end Proof
0.17/0.37	
0.17/0.37	RESULT: Unsatisfiable (the axioms are contradictory).
0.17/0.37	EOF