0.07/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.11/0.33	% Computer   : n014.cluster.edu
0.11/0.33	% Model      : x86_64 x86_64
0.11/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory     : 8042.1875MB
0.11/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit   : 1200
0.11/0.33	% WCLimit    : 120
0.11/0.33	% DateTime   : Tue Jul 13 15:21:49 EDT 2021
0.11/0.33	% CPUTime    : 
1.77/0.60	% SZS status Unsatisfiable
1.77/0.60	
1.77/0.61	% SZS output start Proof
1.77/0.61	Axiom 1 (k_definition): apply(apply(k, X), Y) = X.
1.77/0.61	Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
1.77/0.61	
1.77/0.61	Goal 1 (prove_fixed_point): X = apply(combinator, X).
1.77/0.61	The goal is true when:
1.77/0.61	  X = apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))))
1.77/0.61	
1.77/0.61	Proof:
1.77/0.61	  apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))))
1.77/0.61	= { by axiom 2 (s_definition) }
1.77/0.61	  apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(k, apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))), apply(X, apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))))
1.77/0.61	= { by axiom 1 (k_definition) }
1.77/0.61	  apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))
1.77/0.61	= { by axiom 2 (s_definition) }
1.77/0.61	  apply(apply(apply(s, apply(k, combinator)), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X))))
1.77/0.61	= { by axiom 2 (s_definition) }
1.77/0.61	  apply(apply(apply(k, combinator), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))), apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))))
1.77/0.61	= { by axiom 1 (k_definition) }
1.77/0.61	  apply(combinator, apply(apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)), apply(apply(apply(s, k), X), apply(apply(s, apply(s, apply(k, combinator))), apply(apply(s, k), X)))))
1.77/0.61	% SZS output end Proof
1.77/0.61	
1.77/0.61	RESULT: Unsatisfiable (the axioms are contradictory).
1.77/0.61	EOF