0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn
0.02/0.23	% Computer   : n174.star.cs.uiowa.edu
0.02/0.23	% Model      : x86_64 x86_64
0.02/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.23	% Memory     : 32218.625MB
0.02/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.23	% CPULimit   : 300
0.02/0.23	% DateTime   : Sat Jul 14 04:30:55 CDT 2018
0.02/0.23	% CPUTime    : 
203.45/203.73	% SZS status Theorem
203.45/203.73	
203.45/203.73	% SZS output start Proof
203.45/203.73	Take the following subset of the input axioms:
203.45/203.74	  fof(ax2_1376, axiom,
203.45/203.74	      mtvisible(c_tptpgeo_member5_mt)
203.45/203.74	        => borderson(c_georegion_l4_x56_y47, c_georegion_l4_x57_y47)).
203.45/203.74	  fof(ax2_2388, axiom,
203.45/203.74	      genlmt(c_tptpgeo_spindlecollectormt, c_tptpgeo_member5_mt)).
203.45/203.74	  fof(ax2_7642, axiom,
203.45/203.74	      ![X, Y]: (borderson(Y, X) <= borderson(X, Y))).
203.45/203.74	  fof(ax2_7997, axiom,
203.45/203.74	      ![SPECMT, GENLMT]:
203.45/203.74	        ((genlmt(SPECMT, GENLMT) & mtvisible(SPECMT))
203.45/203.74	           => mtvisible(GENLMT))).
203.45/203.74	  fof(query159, conjecture,
203.45/203.74	      mtvisible(c_tptpgeo_spindlecollectormt)
203.45/203.74	        => borderson(c_georegion_l4_x57_y47, c_georegion_l4_x56_y47)).
203.45/203.74	
203.45/203.74	Now clausify the problem and encode Horn clauses using encoding 3 of
203.45/203.74	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
203.45/203.74	We repeatedly replace C & s=t => u=v by the two clauses:
203.45/203.74	  $$fresh(y, y, x1...xn) = u
203.45/203.74	  C => $$fresh(s, t, x1...xn) = v
203.45/203.74	where $$fresh is a fresh function symbol and x1..xn are the free
203.45/203.74	variables of u and v.
203.45/203.74	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
203.45/203.74	input problem has no model of domain size 1).
203.45/203.74	
203.45/203.74	The encoding turns the above axioms into the following unit equations and goals:
203.45/203.74	
203.45/203.74	Axiom 180 (ax2_1376): $$fresh4724(X, X) = $$true2.
203.45/203.74	Axiom 4573 (ax2_7642): $$fresh403(X, X, Y, Z) = $$true2.
203.45/203.74	Axiom 4866 (ax2_7997): $$fresh110(X, X, Y, Z) = mtvisible(Z).
203.45/203.74	Axiom 4867 (ax2_7997): $$fresh109(X, X, Y) = $$true2.
203.45/203.74	Axiom 5128 (ax2_2388): genlmt(c_tptpgeo_spindlecollectormt, c_tptpgeo_member5_mt) = $$true2.
203.45/203.74	Axiom 5725 (ax2_7997): $$fresh110(genlmt(X, Y), $$true2, X, Y) = $$fresh109(mtvisible(X), $$true2, Y).
203.45/203.74	Axiom 7025 (ax2_1376): $$fresh4724(mtvisible(c_tptpgeo_member5_mt), $$true2) = borderson(c_georegion_l4_x56_y47, c_georegion_l4_x57_y47).
203.45/203.74	Axiom 9730 (ax2_7642): $$fresh403(borderson(X, Y), $$true2, X, Y) = borderson(Y, X).
203.45/203.74	Axiom 12917 (query159): mtvisible(c_tptpgeo_spindlecollectormt) = $$true2.
203.45/203.74	
203.45/203.74	Goal 1 (query159_1): borderson(c_georegion_l4_x57_y47, c_georegion_l4_x56_y47) = $$true2.
203.45/203.74	Proof:
203.45/203.74	  borderson(c_georegion_l4_x57_y47, c_georegion_l4_x56_y47)
203.45/203.74	= { by axiom 9730 (ax2_7642) }
203.45/203.74	  $$fresh403(borderson(c_georegion_l4_x56_y47, c_georegion_l4_x57_y47), $$true2, c_georegion_l4_x56_y47, c_georegion_l4_x57_y47)
203.45/203.74	= { by axiom 7025 (ax2_1376) }
203.45/203.74	  $$fresh403($$fresh4724(mtvisible(c_tptpgeo_member5_mt), $$true2), $$true2, c_georegion_l4_x56_y47, c_georegion_l4_x57_y47)
203.45/203.74	= { by axiom 4866 (ax2_7997) }
203.45/203.74	  $$fresh403($$fresh4724($$fresh110($$true2, $$true2, c_tptpgeo_spindlecollectormt, c_tptpgeo_member5_mt), $$true2), $$true2, c_georegion_l4_x56_y47, c_georegion_l4_x57_y47)
203.45/203.74	= { by axiom 5128 (ax2_2388) }
203.45/203.74	  $$fresh403($$fresh4724($$fresh110(genlmt(c_tptpgeo_spindlecollectormt, c_tptpgeo_member5_mt), $$true2, c_tptpgeo_spindlecollectormt, c_tptpgeo_member5_mt), $$true2), $$true2, c_georegion_l4_x56_y47, c_georegion_l4_x57_y47)
203.45/203.74	= { by axiom 5725 (ax2_7997) }
203.45/203.74	  $$fresh403($$fresh4724($$fresh109(mtvisible(c_tptpgeo_spindlecollectormt), $$true2, c_tptpgeo_member5_mt), $$true2), $$true2, c_georegion_l4_x56_y47, c_georegion_l4_x57_y47)
203.45/203.74	= { by axiom 12917 (query159) }
203.45/203.74	  $$fresh403($$fresh4724($$fresh109($$true2, $$true2, c_tptpgeo_member5_mt), $$true2), $$true2, c_georegion_l4_x56_y47, c_georegion_l4_x57_y47)
203.45/203.74	= { by axiom 4867 (ax2_7997) }
203.45/203.74	  $$fresh403($$fresh4724($$true2, $$true2), $$true2, c_georegion_l4_x56_y47, c_georegion_l4_x57_y47)
203.45/203.74	= { by axiom 180 (ax2_1376) }
203.45/203.74	  $$fresh403($$true2, $$true2, c_georegion_l4_x56_y47, c_georegion_l4_x57_y47)
203.45/203.74	= { by axiom 4573 (ax2_7642) }
203.45/203.74	  $$true2
203.45/203.74	% SZS output end Proof
203.45/203.74	
203.45/203.74	RESULT: Theorem (the conjecture is true).
203.66/203.90	EOF