0.06/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% 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 : n026.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 : 960
0.11/0.33	% WCLimit  : 120
0.11/0.33	% DateTime : Tue Aug  9 03:55:49 EDT 2022
0.11/0.33	% CPUTime  : 
0.18/0.60	% SZS status Unsatisfiable
0.18/0.60	
0.18/0.60	% SZS output start Proof
0.18/0.60	Axiom 1 (k_definition): X = apply(apply(k, X), Y).
1.95/0.60	Axiom 2 (s_definition): apply(apply(X, Y), apply(Z, Y)) = apply(apply(apply(s, X), Z), Y).
1.95/0.60	
1.95/0.60	Goal 1 (prove_fixed_point): X = apply(combinator, X).
1.95/0.60	The goal is true when:
1.95/0.60	  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))))
1.95/0.60	
1.95/0.60	Proof:
1.95/0.60	  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))))
1.95/0.60	= { by axiom 2 (s_definition) R->L }
1.95/0.60	  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)))))
1.95/0.60	= { by axiom 1 (k_definition) R->L }
1.95/0.60	  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)))
1.95/0.60	= { by axiom 2 (s_definition) R->L }
1.95/0.60	  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))))
1.95/0.60	= { by axiom 2 (s_definition) R->L }
1.95/0.60	  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)))))
1.95/0.60	= { by axiom 1 (k_definition) R->L }
1.95/0.60	  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)))))
1.95/0.60	% SZS output end Proof
1.95/0.60	
1.95/0.60	RESULT: Unsatisfiable (the axioms are contradictory).
1.95/0.61	EOF