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   : n064.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 05:34:25 CDT 2018
0.03/0.24	% CPUTime    : 
2.82/3.05	% SZS status Theorem
2.82/3.05	
2.82/3.05	% SZS output start Proof
2.82/3.05	Take the following subset of the input axioms:
2.82/3.08	  fof(aSatz7_10a, axiom, ![Xa, Xp]: (Xa=Xp | Xp!=s(Xa, Xp))).
2.82/3.08	  fof(aSatz7_15a, axiom,
2.82/3.08	      ![Xa, Xp, Xq, Xr]:
2.82/3.08	        (s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)) | ~s_t(Xp, Xq, Xr))).
2.82/3.08	  fof(aSatz7_16a, axiom,
2.82/3.08	      ![Xa, Xp, Xq, Xr, Xcs]:
2.82/3.08	        (s_e(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr), s(Xa, Xcs))
2.82/3.08	           | ~s_e(Xp, Xq, Xr, Xcs))).
2.82/3.08	  fof(aSatz7_17, axiom,
2.82/3.08	      ![Xb, Xa, Xp, Xq]:
2.82/3.08	        (~s_m(Xp, Xb, Xq) | (Xb=Xa | ~s_m(Xp, Xa, Xq)))).
2.82/3.09	  fof(aSatz7_19, conjecture,
2.82/3.09	      ![Xb, Xa, Xp]: (s(Xa, s(Xb, Xp))!=s(Xb, s(Xa, Xp)) | Xb=Xa)).
2.82/3.09	  fof(aSatz7_4a, axiom, ![Xa, Xp]: s_m(Xp, Xa, s(Xa, Xp))).
2.82/3.09	  fof(aSatz7_7, axiom, ![Xa, Xp]: Xp=s(Xa, s(Xa, Xp))).
2.82/3.09	  fof(d_Defn7_1, axiom,
2.82/3.09	      ![Xb, Xa, Xm]:
2.82/3.09	        ((s_e(Xm, Xa, Xm, Xb) | ~s_m(Xa, Xm, Xb))
2.82/3.09	           & ((~s_e(Xm, Xa, Xm, Xb) | (s_m(Xa, Xm, Xb) | ~s_t(Xa, Xm, Xb)))
2.82/3.09	                & (s_t(Xa, Xm, Xb) | ~s_m(Xa, Xm, Xb))))).
2.82/3.09	
2.82/3.09	Now clausify the problem and encode Horn clauses using encoding 3 of
2.82/3.09	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
2.82/3.09	We repeatedly replace C & s=t => u=v by the two clauses:
2.82/3.09	  $$fresh(y, y, x1...xn) = u
2.82/3.09	  C => $$fresh(s, t, x1...xn) = v
2.82/3.09	where $$fresh is a fresh function symbol and x1..xn are the free
2.82/3.09	variables of u and v.
2.82/3.09	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
2.82/3.09	input problem has no model of domain size 1).
2.82/3.09	
2.82/3.09	The encoding turns the above axioms into the following unit equations and goals:
2.82/3.09	
2.82/3.09	Axiom 100 (aSatz7_10a): $$fresh4(X, X, Y, Z) = Z.
2.82/3.09	Axiom 101 (aSatz7_15a): $$fresh63(X, X, Y, Z, W, V) = $$true2.
2.82/3.09	Axiom 103 (aSatz7_16a): $$fresh61(X, X, Y, Z, W, V, U) = $$true2.
2.82/3.09	Axiom 105 (aSatz7_17): $$fresh16(X, X, Y, Z) = Y.
2.82/3.09	Axiom 106 (aSatz7_17): $$fresh17(X, X, Y, Z, W, V) = V.
2.82/3.09	Axiom 161 (d_Defn7_1): $$fresh31(X, X, Y, Z, W) = s_m(Y, Z, W).
2.82/3.09	Axiom 162 (d_Defn7_1): $$fresh30(X, X, Y, Z, W) = $$true2.
2.82/3.09	Axiom 163 (d_Defn7_1_1): $$fresh29(X, X, Y, Z, W) = $$true2.
2.82/3.09	Axiom 164 (d_Defn7_1_2): $$fresh28(X, X, Y, Z, W) = $$true2.
2.82/3.09	Axiom 209 (aSatz7_4a): s_m(X, Y, s(Y, X)) = $$true2.
2.82/3.09	Axiom 228 (aSatz7_17): $$fresh17(s_m(X, Y, Z), $$true2, X, W, Z, Y) = $$fresh16(s_m(X, W, Z), $$true2, W, Y).
2.82/3.09	Axiom 244 (aSatz7_10a): $$fresh4(X, s(Y, X), Y, X) = Y.
2.82/3.09	Axiom 255 (aSatz7_7): X = s(Y, s(Y, X)).
2.82/3.09	Axiom 282 (aSatz7_16a): $$fresh61(s_e(X, Y, Z, W), $$true2, X, Y, Z, W, V) = s_e(s(V, X), s(V, Y), s(V, Z), s(V, W)).
2.82/3.09	Axiom 292 (aSatz7_15a): $$fresh63(s_t(X, Y, Z), $$true2, X, Y, Z, W) = s_t(s(W, X), s(W, Y), s(W, Z)).
2.82/3.09	Axiom 293 (d_Defn7_1_2): $$fresh28(s_m(X, Y, Z), $$true2, X, Y, Z) = s_t(X, Y, Z).
2.82/3.09	Axiom 294 (d_Defn7_1_1): $$fresh29(s_m(X, Y, Z), $$true2, X, Y, Z) = s_e(Y, X, Y, Z).
2.82/3.09	Axiom 295 (d_Defn7_1): $$fresh31(s_t(X, Y, Z), $$true2, X, Y, Z) = $$fresh30(s_e(Y, X, Y, Z), $$true2, X, Y, Z).
2.82/3.09	Axiom 301 (aSatz7_19): s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)) = s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)).
2.82/3.09	
2.82/3.09	Lemma 302: s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp))) = s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp).
2.82/3.09	Proof:
2.82/3.09	  s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)))
2.82/3.09	= { by axiom 301 (aSatz7_19) }
2.82/3.09	  s(sK2_aSatz7_19_Xb, s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)))
2.82/3.09	= { by axiom 255 (aSatz7_7) }
2.92/3.12	  s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)
2.92/3.12	
2.92/3.12	Goal 1 (aSatz7_19_1): sK2_aSatz7_19_Xb = sK3_aSatz7_19_Xa.
2.92/3.12	Proof:
2.92/3.12	  sK2_aSatz7_19_Xb
2.92/3.12	= { by axiom 244 (aSatz7_10a) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 105 (aSatz7_17) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$true2, $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 162 (d_Defn7_1) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh30($$true2, $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 103 (aSatz7_16a) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh30($$fresh61($$true2, $$true2, sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), sK2_aSatz7_19_Xb), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 163 (d_Defn7_1_1) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh30($$fresh61($$fresh29($$true2, $$true2, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp))), $$true2, sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), sK2_aSatz7_19_Xb), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 209 (aSatz7_4a) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh30($$fresh61($$fresh29(s_m(s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp))), $$true2, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp))), $$true2, sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), sK2_aSatz7_19_Xb), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 294 (d_Defn7_1_1) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh30($$fresh61(s_e(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp))), $$true2, sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), sK2_aSatz7_19_Xb), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 282 (aSatz7_16a) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh30(s_e(s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK2_aSatz7_19_Xb, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)))), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 255 (aSatz7_7) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh30(s_e(s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)))), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by lemma 302 }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh30(s_e(s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 295 (d_Defn7_1) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh31(s_t(sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 255 (aSatz7_7) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh31(s_t(s(sK2_aSatz7_19_Xb, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by lemma 302 }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh31(s_t(s(sK2_aSatz7_19_Xb, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)))), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 292 (aSatz7_15a) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh31($$fresh63(s_t(s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp))), $$true2, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), sK2_aSatz7_19_Xb), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 293 (d_Defn7_1_2) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh31($$fresh63($$fresh28(s_m(s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp))), $$true2, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp))), $$true2, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), sK2_aSatz7_19_Xb), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 209 (aSatz7_4a) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh31($$fresh63($$fresh28($$true2, $$true2, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp))), $$true2, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), sK2_aSatz7_19_Xb), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 164 (d_Defn7_1_2) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh31($$fresh63($$true2, $$true2, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)), sK2_aSatz7_19_Xb), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 101 (aSatz7_15a) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16($$fresh31($$true2, $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 161 (d_Defn7_1) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh16(s_m(sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 228 (aSatz7_17) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh17(s_m(sK1_aSatz7_19_Xp, sK3_aSatz7_19_Xa, s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)), $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 209 (aSatz7_4a) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, $$fresh17($$true2, $$true2, sK1_aSatz7_19_Xp, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp), sK3_aSatz7_19_Xa), sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 106 (aSatz7_17) }
2.92/3.12	  $$fresh4(sK3_aSatz7_19_Xa, sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
2.92/3.12	= { by axiom 100 (aSatz7_10a) }
2.92/3.12	  sK3_aSatz7_19_Xa
2.92/3.12	% SZS output end Proof
2.92/3.12	
2.92/3.12	RESULT: Theorem (the conjecture is true).
2.92/3.12	EOF