0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.32	% Computer   : n026.cluster.edu
0.13/0.32	% Model      : x86_64 x86_64
0.13/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.32	% Memory     : 8042.1875MB
0.13/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.32	% CPULimit   : 1200
0.13/0.32	% WCLimit    : 120
0.13/0.32	% DateTime   : Tue Jul 13 15:34:59 EDT 2021
0.13/0.33	% CPUTime    : 
9.19/1.51	% SZS status Unsatisfiable
9.19/1.51	
9.19/1.52	% SZS output start Proof
9.19/1.52	Axiom 1 (l2_definition): apply(X, apply(Y, Y)) = apply(apply(l2, Y), X).
9.19/1.52	Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
9.19/1.52	
9.19/1.52	Goal 1 (prove_fixed_point): apply(combinator, X) = X.
9.19/1.52	The goal is true when:
9.19/1.52	  X = apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(l2, apply(apply(b, apply(b, combinator)), l2)))
9.19/1.52	
9.19/1.52	Proof:
9.19/1.52	  apply(combinator, apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(l2, apply(apply(b, apply(b, combinator)), l2))))
9.19/1.52	= { by axiom 1 (l2_definition) R->L }
9.19/1.52	  apply(combinator, apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(apply(apply(b, apply(b, combinator)), l2), apply(apply(b, apply(b, combinator)), l2))))
9.19/1.52	= { by axiom 2 (b_definition) R->L }
9.19/1.52	  apply(apply(apply(b, combinator), apply(l2, apply(apply(b, apply(b, combinator)), l2))), apply(apply(apply(b, apply(b, combinator)), l2), apply(apply(b, apply(b, combinator)), l2)))
9.19/1.52	= { by axiom 1 (l2_definition) }
9.19/1.52	  apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(apply(b, combinator), apply(l2, apply(apply(b, apply(b, combinator)), l2))))
9.19/1.52	= { by axiom 2 (b_definition) R->L }
9.19/1.52	  apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(apply(apply(b, apply(b, combinator)), l2), apply(apply(b, apply(b, combinator)), l2)))
9.19/1.52	= { by axiom 1 (l2_definition) }
9.19/1.52	  apply(apply(l2, apply(apply(b, apply(b, combinator)), l2)), apply(l2, apply(apply(b, apply(b, combinator)), l2)))
9.19/1.52	% SZS output end Proof
9.19/1.52	
9.19/1.52	RESULT: Unsatisfiable (the axioms are contradictory).
9.19/1.52	EOF