0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.33	% Computer   : n027.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 180
0.13/0.33	% DateTime   : Thu Aug 29 11:52:09 EDT 2019
0.13/0.33	% CPUTime    : 
31.78/31.96	% SZS status Theorem
31.78/31.96	
31.78/31.96	% SZS output start Proof
31.78/31.96	Take the following subset of the input axioms:
31.78/31.97	  fof(aA2, axiom, ![Y, Z, X, V, Z2, V2]: (~s_e(X, Y, Z2, V2) | (s_e(Z, V, Z2, V2) | ~s_e(X, Y, Z, V)))).
31.78/31.97	  fof(aSatz10_12b, axiom, ![Xb, Xa, Xc, Xa1]: (~s_r(Xa1, Xb, Xc) | (~s_e(Xa, Xb, Xa1, Xb) | (s_e(Xa, Xc, Xa1, Xc) | ~s_r(Xa, Xb, Xc))))).
31.78/31.97	  fof(aSatz10_12c, conjecture, ![Xb, Xa, Xc, Xa1, Xc1]: (s_e(Xa, Xc, Xa1, Xc1) | (Xc1=Xc | (midpoint(Xc, Xc1)!=Xb | (~s_e(Xb, Xc, Xb, Xc1) | (~s_e(Xa, Xb, Xa1, Xb) | (~s_r(Xa1, Xb, Xc1) | ~s_r(Xa, Xb, Xc)))))))).
31.78/31.97	  fof(aSatz2_2, axiom, ![Xb, Xa, Xc, Xd]: (s_e(Xc, Xd, Xa, Xb) | ~s_e(Xa, Xb, Xc, Xd))).
31.78/31.97	  fof(aSatz7_6, axiom, ![Xa, Xp, Xq]: (~s_m(Xp, Xa, Xq) | Xq=s(Xa, Xp))).
31.78/31.97	  fof(aSatz7_7, axiom, ![Xa, Xp]: s(Xa, s(Xa, Xp))=Xp).
31.78/31.97	  fof(aSatz8_22, axiom, ![Xb, Xa]: s_m(Xa, midpoint(Xa, Xb), Xb)).
31.78/31.97	  fof(aSatz8_4, axiom, ![Xb, Xa, Xc]: (~s_r(Xa, Xb, Xc) | s_r(Xa, Xb, s(Xb, Xc)))).
31.78/31.97	  fof(d_Defn8_1, axiom, ![Xb, Xa, Xc]: ((s_e(Xa, Xc, Xa, s(Xb, Xc)) | ~s_r(Xa, Xb, Xc)) & (~s_e(Xa, Xc, Xa, s(Xb, Xc)) | s_r(Xa, Xb, Xc)))).
31.78/31.97	
31.78/31.97	Now clausify the problem and encode Horn clauses using encoding 3 of
31.78/31.97	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
31.78/31.97	We repeatedly replace C & s=t => u=v by the two clauses:
31.78/31.97	  fresh(y, y, x1...xn) = u
31.78/31.97	  C => fresh(s, t, x1...xn) = v
31.78/31.97	where fresh is a fresh function symbol and x1..xn are the free
31.78/31.97	variables of u and v.
31.78/31.97	A predicate p(X) is encoded as p(X)=true (this is sound, because the
31.78/31.97	input problem has no model of domain size 1).
31.78/31.97	
31.78/31.97	The encoding turns the above axioms into the following unit equations and goals:
31.78/31.97	
31.78/31.97	Axiom 1 (aA2): fresh183(X, X, Y, Z, W, V, U, T) = s_e(W, V, U, T).
31.78/31.97	Axiom 2 (aA2): fresh184(X, X, Y, Z, W, V) = true2.
31.78/31.97	Axiom 3 (aSatz10_12b): fresh174(X, X, Y, Z, W, V) = s_e(Y, W, V, W).
31.78/31.97	Axiom 4 (aSatz10_12b): fresh282(X, X, Y, Z, W) = true2.
31.78/31.97	Axiom 5 (aSatz10_12b): fresh281(X, X, Y, Z, W, V) = fresh282(s_e(Y, Z, V, Z), true2, Y, W, V).
31.78/31.97	Axiom 6 (aSatz2_2): fresh172(X, X, Y, Z, W, V) = true2.
31.78/31.97	Axiom 7 (aSatz7_6): fresh16(X, X, Y, Z, W) = W.
31.78/31.97	Axiom 8 (aSatz8_4): fresh92(X, X, Y, Z, W) = true2.
31.78/31.97	Axiom 9 (d_Defn8_1_1): fresh35(X, X, Y, Z, W) = true2.
31.78/31.97	Axiom 10 (aA2): fresh183(s_e(X, Y, Z, W), true2, X, Y, V, U, Z, W) = fresh184(s_e(X, Y, V, U), true2, V, U, Z, W).
31.78/31.97	Axiom 11 (aSatz10_12b): fresh281(s_r(X, Y, Z), true2, W, Y, Z, X) = fresh174(s_r(W, Y, Z), true2, W, Y, Z, X).
31.78/31.97	Axiom 12 (aSatz8_4): fresh92(s_r(X, Y, Z), true2, X, Y, Z) = s_r(X, Y, s(Y, Z)).
31.78/31.97	Axiom 13 (aSatz7_7): s(X, s(X, Y)) = Y.
31.78/31.97	Axiom 14 (aSatz8_22): s_m(X, midpoint(X, Y), Y) = true2.
31.78/31.97	Axiom 15 (aSatz7_6): fresh16(s_m(X, Y, Z), true2, X, Y, Z) = s(Y, X).
31.78/31.97	Axiom 16 (aSatz2_2): fresh172(s_e(X, Y, Z, W), true2, X, Y, Z, W) = s_e(Z, W, X, Y).
31.78/31.97	Axiom 17 (d_Defn8_1_1): fresh35(s_r(X, Y, Z), true2, X, Y, Z) = s_e(X, Z, X, s(Y, Z)).
31.78/31.97	Axiom 18 (aSatz10_12c): midpoint(sK4_aSatz10_12c_Xc, sK2_aSatz10_12c_Xc1) = sK5_aSatz10_12c_Xb.
31.78/31.97	Axiom 19 (aSatz10_12c_2): s_e(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb) = true2.
31.78/31.97	Axiom 20 (aSatz10_12c_3): s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1) = true2.
31.78/31.97	Axiom 21 (aSatz10_12c_4): s_r(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) = true2.
31.78/31.97	
31.78/31.97	Lemma 22: s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) = sK2_aSatz10_12c_Xc1.
31.78/31.97	Proof:
31.78/31.97	  s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc)
31.78/31.97	= { by axiom 15 (aSatz7_6) }
31.78/31.97	  fresh16(s_m(sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1), true2, sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 18 (aSatz10_12c) }
31.78/31.97	  fresh16(s_m(sK4_aSatz10_12c_Xc, midpoint(sK4_aSatz10_12c_Xc, sK2_aSatz10_12c_Xc1), sK2_aSatz10_12c_Xc1), true2, sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 14 (aSatz8_22) }
31.78/31.97	  fresh16(true2, true2, sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 7 (aSatz7_6) }
31.78/31.97	  sK2_aSatz10_12c_Xc1
31.78/31.97	
31.78/31.97	Lemma 23: s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) = true2.
31.78/31.97	Proof:
31.78/31.97	  s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc)
31.78/31.97	= { by axiom 13 (aSatz7_7) }
31.78/31.97	  s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, s(sK5_aSatz10_12c_Xb, s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc)))
31.78/31.97	= { by lemma 22 }
31.78/31.97	  s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, s(sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1))
31.78/31.97	= { by axiom 12 (aSatz8_4) }
31.78/31.97	  fresh92(s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1), true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 20 (aSatz10_12c_3) }
31.78/31.97	  fresh92(true2, true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 8 (aSatz8_4) }
31.78/31.97	  true2
31.78/31.97	
31.78/31.97	Goal 1 (aSatz10_12c_6): s_e(sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) = true2.
31.78/31.97	Proof:
31.78/31.97	  s_e(sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 1 (aA2) }
31.78/31.97	  fresh183(true2, true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 9 (d_Defn8_1_1) }
31.78/31.97	  fresh183(fresh35(true2, true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by lemma 23 }
31.78/31.97	  fresh183(fresh35(s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 17 (d_Defn8_1_1) }
31.78/31.97	  fresh183(s_e(sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc)), true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by lemma 22 }
31.78/31.97	  fresh183(s_e(sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1), true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 10 (aA2) }
31.78/31.97	  fresh184(s_e(sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 16 (aSatz2_2) }
31.78/31.97	  fresh184(fresh172(s_e(sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 3 (aSatz10_12b) }
31.78/31.97	  fresh184(fresh172(fresh174(true2, true2, sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 21 (aSatz10_12c_4) }
31.78/31.97	  fresh184(fresh172(fresh174(s_r(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 11 (aSatz10_12b) }
31.78/31.97	  fresh184(fresh172(fresh281(s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by lemma 23 }
31.78/31.97	  fresh184(fresh172(fresh281(true2, true2, sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 5 (aSatz10_12b) }
31.78/31.97	  fresh184(fresh172(fresh282(s_e(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 19 (aSatz10_12c_2) }
31.78/31.97	  fresh184(fresh172(fresh282(true2, true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 4 (aSatz10_12b) }
31.78/31.97	  fresh184(fresh172(true2, true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 6 (aSatz2_2) }
31.78/31.97	  fresh184(true2, true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
31.78/31.97	= { by axiom 2 (aA2) }
31.78/31.97	  true2
31.78/31.97	% SZS output end Proof
31.78/31.97	
31.78/31.97	RESULT: Theorem (the conjecture is true).
31.78/31.99	EOF