0.04/0.13	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.13	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.35	% Computer : n003.cluster.edu
0.13/0.35	% Model    : x86_64 x86_64
0.13/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory   : 8042.1875MB
0.13/0.35	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit : 960
0.13/0.35	% WCLimit  : 120
0.13/0.35	% DateTime : Tue Aug  9 03:17:21 EDT 2022
0.13/0.35	% CPUTime  : 
0.19/0.38	% SZS status Unsatisfiable
0.19/0.38	
0.19/0.39	% SZS output start Proof
0.19/0.39	Axiom 1 (m_definition): apply(m, X) = apply(X, X).
0.19/0.39	Axiom 2 (q_definition): apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z)).
0.19/0.39	
0.19/0.39	Goal 1 (prove_fixed_point): apply(f(X), apply(X, f(X))) = apply(X, f(X)).
0.19/0.39	The goal is true when:
0.19/0.39	  X = apply(apply(q, apply(q, m)), m)
0.19/0.39	
0.19/0.39	Proof:
0.19/0.39	  apply(f(apply(apply(q, apply(q, m)), m)), apply(apply(apply(q, apply(q, m)), m), f(apply(apply(q, apply(q, m)), m))))
0.19/0.39	= { by axiom 2 (q_definition) }
0.19/0.39	  apply(f(apply(apply(q, apply(q, m)), m)), apply(m, apply(apply(q, m), f(apply(apply(q, apply(q, m)), m)))))
0.19/0.39	= { by axiom 2 (q_definition) R->L }
0.19/0.39	  apply(apply(apply(q, m), f(apply(apply(q, apply(q, m)), m))), apply(apply(q, m), f(apply(apply(q, apply(q, m)), m))))
0.19/0.39	= { by axiom 1 (m_definition) R->L }
0.19/0.39	  apply(m, apply(apply(q, m), f(apply(apply(q, apply(q, m)), m))))
0.19/0.39	= { by axiom 2 (q_definition) R->L }
0.19/0.39	  apply(apply(apply(q, apply(q, m)), m), f(apply(apply(q, apply(q, m)), m)))
0.19/0.39	% SZS output end Proof
0.19/0.39	
0.19/0.39	RESULT: Unsatisfiable (the axioms are contradictory).
0.19/0.39	EOF