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
0.12/0.33	% Computer   : n016.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1200
0.12/0.33	% WCLimit    : 120
0.12/0.33	% DateTime   : Tue Jul 13 10:55:23 EDT 2021
0.12/0.33	% CPUTime    : 
77.29/10.20	% SZS status Theorem
77.29/10.20	
77.29/10.20	% SZS output start Proof
77.29/10.20	Take the following subset of the input axioms:
77.29/10.21	  fof(ax1_1123, axiom, ![SPECMT, GENLMT]: ((mtvisible(SPECMT) & genlmt(SPECMT, GENLMT)) => mtvisible(GENLMT))).
77.29/10.21	  fof(ax1_139, axiom, ![ARG1, ARG2]: (tptptypes_6_818(ARG1, ARG2) <= tptptypes_7_819(ARG1, ARG2))).
77.29/10.21	  fof(ax1_178, axiom, tptptypes_9_824(f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886) <= mtvisible(c_tptp_member2668_mt)).
77.29/10.21	  fof(ax1_271, axiom, ![ARG1, ARG2]: (tptptypes_7_819(ARG1, ARG2) <= tptptypes_8_823(ARG1, ARG2))).
77.29/10.21	  fof(ax1_350, axiom, genlmt(c_tptp_spindlecollectormt, c_tptp_member2668_mt)).
77.29/10.21	  fof(ax1_416, axiom, ![ARG1, ARG2]: (tptptypes_5_802(ARG1, ARG2) <= tptptypes_6_818(ARG1, ARG2))).
77.29/10.21	  fof(ax1_427, axiom, ![ARG1, ARG2]: (tptptypes_8_823(ARG1, ARG2) <= tptptypes_9_824(ARG1, ARG2))).
77.29/10.21	  fof(query120, conjecture, mtvisible(c_tptp_spindlecollectormt) => tptptypes_5_802(f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)).
77.29/10.21	
77.29/10.21	Now clausify the problem and encode Horn clauses using encoding 3 of
77.29/10.21	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
77.29/10.21	We repeatedly replace C & s=t => u=v by the two clauses:
77.29/10.21	  fresh(y, y, x1...xn) = u
77.29/10.21	  C => fresh(s, t, x1...xn) = v
77.29/10.21	where fresh is a fresh function symbol and x1..xn are the free
77.29/10.21	variables of u and v.
77.29/10.21	A predicate p(X) is encoded as p(X)=true (this is sound, because the
77.29/10.21	input problem has no model of domain size 1).
77.29/10.21	
77.29/10.21	The encoding turns the above axioms into the following unit equations and goals:
77.29/10.21	
77.29/10.21	Axiom 1 (query120): mtvisible(c_tptp_spindlecollectormt) = true2.
77.29/10.21	Axiom 2 (ax1_350): genlmt(c_tptp_spindlecollectormt, c_tptp_member2668_mt) = true2.
77.29/10.21	Axiom 3 (ax1_178): fresh642(X, X) = true2.
77.29/10.21	Axiom 4 (ax1_1123): fresh680(X, X, Y) = true2.
77.29/10.21	Axiom 5 (ax1_1123): fresh681(X, X, Y, Z) = mtvisible(Z).
77.29/10.21	Axiom 6 (ax1_139): fresh660(X, X, Y, Z) = true2.
77.29/10.21	Axiom 7 (ax1_271): fresh596(X, X, Y, Z) = true2.
77.29/10.21	Axiom 8 (ax1_416): fresh527(X, X, Y, Z) = true2.
77.29/10.21	Axiom 9 (ax1_427): fresh521(X, X, Y, Z) = true2.
77.29/10.21	Axiom 10 (ax1_178): fresh642(mtvisible(c_tptp_member2668_mt), true2) = tptptypes_9_824(f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886).
77.29/10.21	Axiom 11 (ax1_1123): fresh681(mtvisible(X), true2, X, Y) = fresh680(genlmt(X, Y), true2, Y).
77.29/10.21	Axiom 12 (ax1_139): fresh660(tptptypes_7_819(X, Y), true2, X, Y) = tptptypes_6_818(X, Y).
77.29/10.21	Axiom 13 (ax1_271): fresh596(tptptypes_8_823(X, Y), true2, X, Y) = tptptypes_7_819(X, Y).
77.29/10.21	Axiom 14 (ax1_416): fresh527(tptptypes_6_818(X, Y), true2, X, Y) = tptptypes_5_802(X, Y).
77.29/10.21	Axiom 15 (ax1_427): fresh521(tptptypes_9_824(X, Y), true2, X, Y) = tptptypes_8_823(X, Y).
77.29/10.21	
77.29/10.21	Goal 1 (query120_1): tptptypes_5_802(f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886) = true2.
77.29/10.21	Proof:
77.29/10.21	  tptptypes_5_802(f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 14 (ax1_416) R->L }
77.29/10.21	  fresh527(tptptypes_6_818(f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 12 (ax1_139) R->L }
77.29/10.21	  fresh527(fresh660(tptptypes_7_819(f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 13 (ax1_271) R->L }
77.29/10.21	  fresh527(fresh660(fresh596(tptptypes_8_823(f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 15 (ax1_427) R->L }
77.29/10.21	  fresh527(fresh660(fresh596(fresh521(tptptypes_9_824(f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 10 (ax1_178) R->L }
77.29/10.21	  fresh527(fresh660(fresh596(fresh521(fresh642(mtvisible(c_tptp_member2668_mt), true2), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 5 (ax1_1123) R->L }
77.29/10.21	  fresh527(fresh660(fresh596(fresh521(fresh642(fresh681(true2, true2, c_tptp_spindlecollectormt, c_tptp_member2668_mt), true2), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 1 (query120) R->L }
77.29/10.21	  fresh527(fresh660(fresh596(fresh521(fresh642(fresh681(mtvisible(c_tptp_spindlecollectormt), true2, c_tptp_spindlecollectormt, c_tptp_member2668_mt), true2), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 11 (ax1_1123) }
77.29/10.21	  fresh527(fresh660(fresh596(fresh521(fresh642(fresh680(genlmt(c_tptp_spindlecollectormt, c_tptp_member2668_mt), true2, c_tptp_member2668_mt), true2), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 2 (ax1_350) }
77.29/10.21	  fresh527(fresh660(fresh596(fresh521(fresh642(fresh680(true2, true2, c_tptp_member2668_mt), true2), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 4 (ax1_1123) }
77.29/10.21	  fresh527(fresh660(fresh596(fresh521(fresh642(true2, true2), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 3 (ax1_178) }
77.29/10.21	  fresh527(fresh660(fresh596(fresh521(true2, true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 9 (ax1_427) }
77.29/10.21	  fresh527(fresh660(fresh596(true2, true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 7 (ax1_271) }
77.29/10.21	  fresh527(fresh660(true2, true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886), true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 6 (ax1_139) }
77.29/10.21	  fresh527(true2, true2, f_subcollectionofwithrelationfromtypefn(c_orientationvector, c_orientation, c_partiallytangible), c_tptpcol_16_8886)
77.29/10.21	= { by axiom 8 (ax1_416) }
77.29/10.21	  true2
77.29/10.21	% SZS output end Proof
77.29/10.21	
77.29/10.21	RESULT: Theorem (the conjecture is true).
77.29/10.24	EOF