0.00/0.04	% 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
0.03/0.23	% Computer   : n007.star.cs.uiowa.edu
0.03/0.23	% Model      : x86_64 x86_64
0.03/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.23	% Memory     : 32218.625MB
0.03/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.23	% CPULimit   : 300
0.03/0.23	% DateTime   : Sat Jul 14 05:23:39 CDT 2018
0.03/0.23	% CPUTime    : 
112.34/112.56	% SZS status Theorem
112.34/112.56	
112.34/112.56	% SZS output start Proof
112.34/112.56	Take the following subset of the input axioms:
112.34/112.56	  fof(aA2, axiom,
112.34/112.56	      ![Y, Z, X, V, Z2, V2]:
112.34/112.56	        (~s_e(X, Y, Z, V) | (~s_e(X, Y, Z2, V2) | s_e(Z, V, Z2, V2)))).
112.34/112.56	  fof(aSatz10_12b, axiom,
112.34/112.56	      ![Xb, Xa, Xc, Xa1]:
112.34/112.56	        (~s_r(Xa, Xb, Xc)
112.34/112.56	           | (~s_e(Xa, Xb, Xa1, Xb)
112.34/112.56	                | (s_e(Xa, Xc, Xa1, Xc) | ~s_r(Xa1, Xb, Xc))))).
112.34/112.56	  fof(aSatz10_12c, conjecture,
112.34/112.56	      ![Xb, Xa, Xc, Xa1, Xc1]:
112.34/112.56	        (~s_r(Xa1, Xb, Xc1)
112.34/112.56	           | (~s_e(Xa, Xb, Xa1, Xb)
112.34/112.56	                | (~s_e(Xb, Xc, Xb, Xc1)
112.34/112.56	                     | (Xb!=midpoint(Xc, Xc1)
112.34/112.56	                          | (Xc=Xc1 | (s_e(Xa, Xc, Xa1, Xc1) | ~s_r(Xa, Xb, Xc)))))))).
112.34/112.56	  fof(aSatz2_2, axiom,
112.34/112.56	      ![Xb, Xa, Xc, Xd]: (~s_e(Xa, Xb, Xc, Xd) | s_e(Xc, Xd, Xa, Xb))).
112.34/112.56	  fof(aSatz7_6, axiom,
112.34/112.56	      ![Xp, Xa, Xq]: (~s_m(Xp, Xa, Xq) | Xq=s(Xa, Xp))).
112.34/112.56	  fof(aSatz7_7, axiom, ![Xp, Xa]: s(Xa, s(Xa, Xp))=Xp).
112.34/112.56	  fof(aSatz8_22, axiom, ![Xb, Xa]: s_m(Xa, midpoint(Xa, Xb), Xb)).
112.34/112.56	  fof(aSatz8_4, axiom,
112.34/112.56	      ![Xb, Xa, Xc]: (~s_r(Xa, Xb, Xc) | s_r(Xa, Xb, s(Xb, Xc)))).
112.34/112.56	  fof(d_Defn8_1, axiom,
112.34/112.56	      ![Xb, Xa, Xc]:
112.34/112.56	        ((s_e(Xa, Xc, Xa, s(Xb, Xc)) | ~s_r(Xa, Xb, Xc))
112.34/112.56	           & (s_r(Xa, Xb, Xc) | ~s_e(Xa, Xc, Xa, s(Xb, Xc))))).
112.34/112.56	
112.34/112.56	Now clausify the problem and encode Horn clauses using encoding 3 of
112.34/112.56	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
112.34/112.56	We repeatedly replace C & s=t => u=v by the two clauses:
112.34/112.56	  $$fresh(y, y, x1...xn) = u
112.34/112.56	  C => $$fresh(s, t, x1...xn) = v
112.34/112.56	where $$fresh is a fresh function symbol and x1..xn are the free
112.34/112.56	variables of u and v.
112.34/112.56	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
112.34/112.56	input problem has no model of domain size 1).
112.34/112.56	
112.34/112.56	The encoding turns the above axioms into the following unit equations and goals:
112.34/112.56	
112.34/112.56	Axiom 1 (aA2): $$fresh188(X, X, Y, Z, W, V, U, T) = s_e(W, V, U, T).
112.34/112.56	Axiom 2 (aA2): $$fresh187(X, X, Y, Z, W, V) = $$true2.
112.34/112.56	Axiom 15 (aSatz10_12b): $$fresh178(X, X, Y, Z, W, V) = s_e(Y, W, V, W).
112.34/112.56	Axiom 16 (aSatz10_12b): $$fresh214(X, X, Y, Z, W) = $$true2.
112.34/112.56	Axiom 17 (aSatz10_12b): $$fresh215(X, X, Y, Z, W, V) = $$fresh214(s_e(Y, Z, V, Z), $$true2, Y, W, V).
112.34/112.56	Axiom 28 (aSatz2_2): $$fresh174(X, X, Y, Z, W, V) = $$true2.
112.34/112.56	Axiom 130 (aSatz7_6): $$fresh22(X, X, Y, Z, W) = W.
112.34/112.56	Axiom 177 (aSatz8_4): $$fresh93(X, X, Y, Z, W) = $$true2.
112.34/112.56	Axiom 278 (d_Defn8_1_1): $$fresh35(X, X, Y, Z, W) = $$true2.
112.34/112.56	Axiom 290 (aA2): $$fresh188(s_e(X, Y, Z, W), $$true2, X, Y, V, U, Z, W) = $$fresh187(s_e(X, Y, V, U), $$true2, V, U, Z, W).
112.34/112.56	Axiom 297 (aSatz8_4): $$fresh93(s_r(X, Y, Z), $$true2, X, Y, Z) = s_r(X, Y, s(Y, Z)).
112.34/112.56	Axiom 307 (aSatz8_22): s_m(X, midpoint(X, Y), Y) = $$true2.
112.34/112.56	Axiom 320 (d_Defn8_1_1): $$fresh35(s_r(X, Y, Z), $$true2, X, Y, Z) = s_e(X, Z, X, s(Y, Z)).
112.34/112.56	Axiom 329 (aSatz7_6): $$fresh22(s_m(X, Y, Z), $$true2, X, Y, Z) = s(Y, X).
112.34/112.56	Axiom 361 (aSatz7_7): s(X, s(X, Y)) = Y.
112.34/112.56	Axiom 406 (aSatz10_12b): $$fresh215(s_r(X, Y, Z), $$true2, W, Y, Z, X) = $$fresh178(s_r(W, Y, Z), $$true2, W, Y, Z, X).
112.34/112.56	Axiom 456 (aSatz2_2): $$fresh174(s_e(X, Y, Z, W), $$true2, X, Y, Z, W) = s_e(Z, W, X, Y).
112.34/112.56	Axiom 464 (aSatz10_12c): sK5_aSatz10_12c_Xb = midpoint(sK4_aSatz10_12c_Xc, sK2_aSatz10_12c_Xc1).
112.34/112.56	Axiom 466 (aSatz10_12c_2): s_e(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb) = $$true2.
112.34/112.56	Axiom 467 (aSatz10_12c_3): s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1) = $$true2.
112.34/112.56	Axiom 468 (aSatz10_12c_4): s_r(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) = $$true2.
112.34/112.56	
112.34/112.56	Lemma 469: s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) = sK2_aSatz10_12c_Xc1.
112.34/112.56	Proof:
112.34/112.56	  s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc)
112.34/112.56	= { by axiom 329 (aSatz7_6) }
112.34/112.56	  $$fresh22(s_m(sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1), $$true2, sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
112.34/112.56	= { by axiom 464 (aSatz10_12c) }
112.34/112.56	  $$fresh22(s_m(sK4_aSatz10_12c_Xc, midpoint(sK4_aSatz10_12c_Xc, sK2_aSatz10_12c_Xc1), sK2_aSatz10_12c_Xc1), $$true2, sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
112.34/112.56	= { by axiom 307 (aSatz8_22) }
112.34/112.56	  $$fresh22($$true2, $$true2, sK4_aSatz10_12c_Xc, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
112.34/112.56	= { by axiom 130 (aSatz7_6) }
112.34/112.57	  sK2_aSatz10_12c_Xc1
112.34/112.57	
112.34/112.57	Lemma 470: s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc) = $$true2.
112.34/112.57	Proof:
112.34/112.57	  s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc)
112.34/112.57	= { by axiom 361 (aSatz7_7) }
112.34/112.57	  s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, s(sK5_aSatz10_12c_Xb, s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc)))
112.34/112.57	= { by lemma 469 }
112.34/112.57	  s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, s(sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1))
112.34/112.57	= { by axiom 297 (aSatz8_4) }
112.34/112.57	  $$fresh93(s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1), $$true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 467 (aSatz10_12c_3) }
112.34/112.57	  $$fresh93($$true2, $$true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 177 (aSatz8_4) }
112.34/112.57	  $$true2
112.34/112.57	
112.34/112.57	Goal 1 (aSatz10_12c_6): s_e(sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1) = $$true2.
112.34/112.57	Proof:
112.34/112.57	  s_e(sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 1 (aA2) }
112.34/112.57	  $$fresh188($$true2, $$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)
112.34/112.57	= { by axiom 278 (d_Defn8_1_1) }
112.34/112.57	  $$fresh188($$fresh35($$true2, $$true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), $$true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by lemma 470 }
112.34/112.57	  $$fresh188($$fresh35(s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), $$true2, sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), $$true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 320 (d_Defn8_1_1) }
112.34/112.57	  $$fresh188(s_e(sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, s(sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc)), $$true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by lemma 469 }
112.34/112.57	  $$fresh188(s_e(sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1), $$true2, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 290 (aA2) }
112.34/112.57	  $$fresh187(s_e(sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc), $$true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 456 (aSatz2_2) }
112.34/112.57	  $$fresh187($$fresh174(s_e(sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), $$true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), $$true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 15 (aSatz10_12b) }
112.34/112.57	  $$fresh187($$fresh174($$fresh178($$true2, $$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)
112.34/112.57	= { by axiom 468 (aSatz10_12c_4) }
112.34/112.57	  $$fresh187($$fresh174($$fresh178(s_r(sK1_aSatz10_12c_Xa, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), $$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)
112.34/112.57	= { by axiom 406 (aSatz10_12b) }
112.34/112.57	  $$fresh187($$fresh174($$fresh215(s_r(sK3_aSatz10_12c_Xa1, sK5_aSatz10_12c_Xb, sK4_aSatz10_12c_Xc), $$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)
112.34/112.57	= { by lemma 470 }
112.34/112.57	  $$fresh187($$fresh174($$fresh215($$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), $$true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 17 (aSatz10_12b) }
112.34/112.57	  $$fresh187($$fresh174($$fresh214(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), $$true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 466 (aSatz10_12c_2) }
112.34/112.57	  $$fresh187($$fresh174($$fresh214($$true2, $$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)
112.34/112.57	= { by axiom 16 (aSatz10_12b) }
112.34/112.57	  $$fresh187($$fresh174($$true2, $$true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK4_aSatz10_12c_Xc), $$true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 28 (aSatz2_2) }
112.34/112.57	  $$fresh187($$true2, $$true2, sK1_aSatz10_12c_Xa, sK4_aSatz10_12c_Xc, sK3_aSatz10_12c_Xa1, sK2_aSatz10_12c_Xc1)
112.34/112.57	= { by axiom 2 (aA2) }
112.34/112.57	  $$true2
112.34/112.57	% SZS output end Proof
112.34/112.57	
112.34/112.57	RESULT: Theorem (the conjecture is true).
112.34/112.60	EOF