0.11/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.14/0.35	% Computer   : n026.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 960
0.14/0.35	% WCLimit    : 120
0.14/0.35	% DateTime   : Thu Jul  2 08:41:39 EDT 2020
0.14/0.35	% CPUTime    : 
32.00/4.39	% SZS status Theorem
32.00/4.39	
32.00/4.39	% SZS output start Proof
32.00/4.39	Take the following subset of the input axioms:
32.00/4.39	  fof(thm_2Ebool_2EEQ__CLAUSES, axiom, ![V0t_2E0]: ((s(tyop_2Emin_2Ebool, V0t_2E0)=s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0) <=> p(s(tyop_2Emin_2Ebool, V0t_2E0))) & ((~p(s(tyop_2Emin_2Ebool, V0t_2E0)) <=> s(tyop_2Emin_2Ebool, V0t_2E0)=s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0)) & ((s(tyop_2Emin_2Ebool, V0t_2E0)=s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) <=> ~p(s(tyop_2Emin_2Ebool, V0t_2E0))) & (s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)=s(tyop_2Emin_2Ebool, V0t_2E0) <=> p(s(tyop_2Emin_2Ebool, V0t_2E0))))))).
32.00/4.39	  fof(thm_2Ebool_2ETRUTH, axiom, p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0))).
32.00/4.39	  fof(thm_2Einteger_2EINT__DIVIDES__NEG, axiom, ![V1q_2E0, V0p_2E0]: (s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, V0p_2E0))), s(tyop_2Einteger_2Eint, V1q_2E0)))=s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, V0p_2E0), s(tyop_2Einteger_2Eint, V1q_2E0))) & s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, V0p_2E0), s(tyop_2Einteger_2Eint, V1q_2E0)))=s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, V0p_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, V1q_2E0))))))).
32.00/4.39	  fof(thm_2Einteger_2EINT__DIVIDES__RADD, axiom, ![V1q_2E0, V0p_2E0, V2r_2E0]: (p(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, V0p_2E0), s(tyop_2Einteger_2Eint, V1q_2E0)))) => s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, V0p_2E0), s(tyop_2Einteger_2Eint, V2r_2E0)))=s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, V0p_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint, V2r_2E0), s(tyop_2Einteger_2Eint, V1q_2E0))))))).
32.00/4.39	  fof(thm_2Einteger_2EINT__DIVIDES__RSUB, conjecture, ![V1q_2E0, V0p_2E0, V2r_2E0]: (p(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, V0p_2E0), s(tyop_2Einteger_2Eint, V1q_2E0)))) => s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, V0p_2E0), s(tyop_2Einteger_2Eint, V2r_2E0)))=s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, V0p_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint, V2r_2E0), s(tyop_2Einteger_2Eint, V1q_2E0))))))).
32.00/4.39	  fof(thm_2Einteger_2Eint__sub, axiom, ![V0x_2E0, V1y_2E0]: s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint, V0x_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, V1y_2E0)))))=s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint, V0x_2E0), s(tyop_2Einteger_2Eint, V1y_2E0)))).
32.00/4.39	
32.00/4.39	Now clausify the problem and encode Horn clauses using encoding 3 of
32.00/4.39	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
32.00/4.39	We repeatedly replace C & s=t => u=v by the two clauses:
32.00/4.39	  fresh(y, y, x1...xn) = u
32.00/4.39	  C => fresh(s, t, x1...xn) = v
32.00/4.39	where fresh is a fresh function symbol and x1..xn are the free
32.00/4.39	variables of u and v.
32.00/4.39	A predicate p(X) is encoded as p(X)=true (this is sound, because the
32.00/4.39	input problem has no model of domain size 1).
32.00/4.39	
32.00/4.39	The encoding turns the above axioms into the following unit equations and goals:
32.00/4.39	
32.00/4.39	Axiom 1 (thm_2Ebool_2EEQ__CLAUSES_7): fresh58(X, X, Y) = s(tyop_2Emin_2Ebool, Y).
32.00/4.39	Axiom 2 (thm_2Einteger_2EINT__DIVIDES__RADD): fresh41(X, X, Y, Z, W) = s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, Y), s(tyop_2Einteger_2Eint, W))).
32.00/4.39	Axiom 3 (thm_2Ebool_2EEQ__CLAUSES_7): fresh58(p(s(tyop_2Emin_2Ebool, X)), true2, X) = s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0).
32.00/4.39	Axiom 4 (thm_2Einteger_2Eint__sub): s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint, X), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, Y))))) = s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint, X), s(tyop_2Einteger_2Eint, Y))).
32.00/4.39	Axiom 5 (thm_2Einteger_2EINT__DIVIDES__NEG_1): s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, X), s(tyop_2Einteger_2Eint, Y))) = s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, X), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, Y))))).
32.00/4.39	Axiom 6 (thm_2Ebool_2ETRUTH): p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)) = true2.
32.00/4.39	Axiom 7 (thm_2Einteger_2EINT__DIVIDES__RADD): fresh41(p(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, X), s(tyop_2Einteger_2Eint, Y)))), true2, X, Y, Z) = s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, X), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint, Z), s(tyop_2Einteger_2Eint, Y))))).
32.00/4.39	Axiom 8 (thm_2Einteger_2EINT__DIVIDES__RSUB): p(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)))) = true2.
32.00/4.39	
32.00/4.39	Goal 1 (thm_2Einteger_2EINT__DIVIDES__RSUB_1): s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0))) = s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint, sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0), s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0))))).
32.00/4.39	Proof:
32.00/4.39	  s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0)))
32.00/4.39	= { by axiom 2 (thm_2Einteger_2EINT__DIVIDES__RADD) }
32.00/4.39	  fresh41(?, ?, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0, ?, sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0)
32.00/4.39	= { by axiom 2 (thm_2Einteger_2EINT__DIVIDES__RADD) }
32.00/4.39	  s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0)))
32.00/4.39	= { by axiom 2 (thm_2Einteger_2EINT__DIVIDES__RADD) }
32.00/4.39	  fresh41(true2, true2, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)), sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0)
32.00/4.39	= { by axiom 6 (thm_2Ebool_2ETRUTH) }
32.00/4.39	  fresh41(p(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0)), true2, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)), sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0)
32.00/4.39	= { by axiom 3 (thm_2Ebool_2EEQ__CLAUSES_7) }
32.00/4.39	  fresh41(p(fresh58(p(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)))), true2, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)))), true2, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)), sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0)
32.00/4.39	= { by axiom 8 (thm_2Einteger_2EINT__DIVIDES__RSUB) }
32.00/4.39	  fresh41(p(fresh58(true2, true2, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)))), true2, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)), sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0)
32.00/4.39	= { by axiom 1 (thm_2Ebool_2EEQ__CLAUSES_7) }
32.00/4.39	  fresh41(p(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)))), true2, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)), sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0)
32.00/4.39	= { by axiom 5 (thm_2Einteger_2EINT__DIVIDES__NEG_1) }
32.00/4.39	  fresh41(p(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)))))), true2, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)), sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0)
32.00/4.39	= { by axiom 7 (thm_2Einteger_2EINT__DIVIDES__RADD) }
32.00/4.39	  s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__add_2E2(s(tyop_2Einteger_2Eint, sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)))))))
32.00/4.39	= { by axiom 4 (thm_2Einteger_2Eint__sub) }
32.00/4.39	  s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__divides_2E2(s(tyop_2Einteger_2Eint, sK6_thm_2Einteger_2EINT__DIVIDES__RSUB_V0p_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__sub_2E2(s(tyop_2Einteger_2Eint, sK4_thm_2Einteger_2EINT__DIVIDES__RSUB_V2r_2E0), s(tyop_2Einteger_2Eint, sK5_thm_2Einteger_2EINT__DIVIDES__RSUB_V1q_2E0)))))
32.00/4.39	% SZS output end Proof
32.00/4.39	
32.00/4.39	RESULT: Theorem (the conjecture is true).
32.00/4.41	EOF