0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.11/0.32	% Computer   : n024.cluster.edu
0.11/0.32	% Model      : x86_64 x86_64
0.11/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory     : 8042.1875MB
0.11/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 960
0.11/0.32	% WCLimit    : 120
0.11/0.32	% DateTime   : Thu Jul  2 08:47:26 EDT 2020
0.11/0.32	% CPUTime    : 
12.52/1.95	% SZS status Theorem
12.52/1.95	
12.52/1.95	% SZS output start Proof
12.52/1.95	Take the following subset of the input axioms:
13.12/2.00	  fof(aSatz7_10a, axiom, ![Xa, Xp]: (s(Xa, Xp)!=Xp | Xa=Xp)).
13.12/2.00	  fof(aSatz7_15a, axiom, ![Xa, Xp, Xr, Xq]: (s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)) | ~s_t(Xp, Xq, Xr))).
13.12/2.00	  fof(aSatz7_16a, axiom, ![Xa, Xp, Xr, Xq, Xcs]: (s_e(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr), s(Xa, Xcs)) | ~s_e(Xp, Xq, Xr, Xcs))).
13.12/2.00	  fof(aSatz7_17, axiom, ![Xa, Xp, Xb, Xq]: (Xb=Xa | (~s_m(Xp, Xb, Xq) | ~s_m(Xp, Xa, Xq)))).
13.12/2.00	  fof(aSatz7_19, conjecture, ![Xa, Xp, Xb]: (Xb=Xa | s(Xb, s(Xa, Xp))!=s(Xa, s(Xb, Xp)))).
13.12/2.00	  fof(aSatz7_4a, axiom, ![Xa, Xp]: s_m(Xp, Xa, s(Xa, Xp))).
13.12/2.00	  fof(aSatz7_7, axiom, ![Xa, Xp]: Xp=s(Xa, s(Xa, Xp))).
13.12/2.00	  fof(d_Defn7_1, axiom, ![Xa, Xb, Xm]: ((s_t(Xa, Xm, Xb) | ~s_m(Xa, Xm, Xb)) & ((~s_e(Xm, Xa, Xm, Xb) | (s_m(Xa, Xm, Xb) | ~s_t(Xa, Xm, Xb))) & (s_e(Xm, Xa, Xm, Xb) | ~s_m(Xa, Xm, Xb))))).
13.12/2.00	
13.12/2.00	Now clausify the problem and encode Horn clauses using encoding 3 of
13.12/2.00	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
13.12/2.00	We repeatedly replace C & s=t => u=v by the two clauses:
13.12/2.00	  fresh(y, y, x1...xn) = u
13.12/2.00	  C => fresh(s, t, x1...xn) = v
13.12/2.00	where fresh is a fresh function symbol and x1..xn are the free
13.12/2.00	variables of u and v.
13.12/2.00	A predicate p(X) is encoded as p(X)=true (this is sound, because the
13.12/2.00	input problem has no model of domain size 1).
13.12/2.00	
13.12/2.00	The encoding turns the above axioms into the following unit equations and goals:
13.12/2.00	
13.12/2.00	Axiom 1 (aSatz7_10a): fresh4(X, X, Y, Z) = Z.
13.12/2.00	Axiom 2 (aSatz7_15a): fresh63(X, X, Y, Z, W, V) = true2.
13.12/2.00	Axiom 3 (aSatz7_16a): fresh61(X, X, Y, Z, W, V, U) = true2.
13.12/2.00	Axiom 4 (aSatz7_17): fresh18(X, X, Y, Z) = Y.
13.12/2.00	Axiom 5 (aSatz7_17): fresh19(X, X, Y, Z, W, V) = V.
13.12/2.00	Axiom 6 (d_Defn7_1): fresh30(X, X, Y, Z, W) = s_m(Y, Z, W).
13.12/2.00	Axiom 7 (d_Defn7_1): fresh29(X, X, Y, Z, W) = true2.
13.12/2.00	Axiom 8 (d_Defn7_1_1): fresh28(X, X, Y, Z, W) = true2.
13.12/2.00	Axiom 9 (d_Defn7_1_2): fresh27(X, X, Y, Z, W) = true2.
13.12/2.00	Axiom 10 (aSatz7_17): fresh19(s_m(X, Y, Z), true2, X, W, Z, Y) = fresh18(s_m(X, W, Z), true2, W, Y).
13.12/2.00	Axiom 11 (aSatz7_4a): s_m(X, Y, s(Y, X)) = true2.
13.12/2.00	Axiom 12 (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)).
13.12/2.00	Axiom 13 (d_Defn7_1_2): fresh27(s_m(X, Y, Z), true2, X, Y, Z) = s_e(Y, X, Y, Z).
13.12/2.00	Axiom 14 (d_Defn7_1_1): fresh28(s_m(X, Y, Z), true2, X, Y, Z) = s_t(X, Y, Z).
13.12/2.00	Axiom 15 (d_Defn7_1): fresh30(s_e(X, Y, X, Z), true2, Y, X, Z) = fresh29(s_t(Y, X, Z), true2, Y, X, Z).
13.12/2.00	Axiom 16 (aSatz7_15a): fresh63(s_t(X, Y, Z), true2, X, Y, Z, W) = s_t(s(W, X), s(W, Y), s(W, Z)).
13.12/2.00	Axiom 17 (aSatz7_7): X = s(Y, s(Y, X)).
13.12/2.00	Axiom 18 (aSatz7_10a): fresh4(s(X, Y), Y, X, Y) = X.
13.12/2.00	Axiom 19 (aSatz7_19): s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)) = s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)).
13.12/2.00	
13.12/2.00	Lemma 20: 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).
13.12/2.00	Proof:
13.12/2.00	  s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, s(sK2_aSatz7_19_Xb, sK1_aSatz7_19_Xp)))
13.12/2.00	= { by axiom 19 (aSatz7_19) }
13.12/2.00	  s(sK2_aSatz7_19_Xb, s(sK2_aSatz7_19_Xb, s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)))
13.12/2.00	= { by axiom 17 (aSatz7_7) }
13.12/2.05	  s(sK3_aSatz7_19_Xa, sK1_aSatz7_19_Xp)
13.12/2.05	
13.12/2.05	Goal 1 (aSatz7_19_1): sK2_aSatz7_19_Xb = sK3_aSatz7_19_Xa.
13.12/2.05	Proof:
13.12/2.05	  sK2_aSatz7_19_Xb
13.12/2.05	= { by axiom 18 (aSatz7_10a) }
13.12/2.05	  fresh4(s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 4 (aSatz7_17) }
13.12/2.05	  fresh4(fresh18(true2, true2, s(sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 7 (d_Defn7_1) }
13.12/2.05	  fresh4(fresh18(fresh29(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 2 (aSatz7_15a) }
13.12/2.05	  fresh4(fresh18(fresh29(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 8 (d_Defn7_1_1) }
13.12/2.05	  fresh4(fresh18(fresh29(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 11 (aSatz7_4a) }
13.12/2.05	  fresh4(fresh18(fresh29(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 14 (d_Defn7_1_1) }
13.12/2.05	  fresh4(fresh18(fresh29(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 16 (aSatz7_15a) }
13.12/2.05	  fresh4(fresh18(fresh29(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 17 (aSatz7_7) }
13.12/2.05	  fresh4(fresh18(fresh29(s_t(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by lemma 20 }
13.12/2.05	  fresh4(fresh18(fresh29(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 15 (d_Defn7_1) }
13.12/2.05	  fresh4(fresh18(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 17 (aSatz7_7) }
13.12/2.05	  fresh4(fresh18(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(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by lemma 20 }
13.12/2.05	  fresh4(fresh18(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 12 (aSatz7_16a) }
13.12/2.05	  fresh4(fresh18(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 13 (d_Defn7_1_2) }
13.12/2.05	  fresh4(fresh18(fresh30(fresh61(fresh27(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 11 (aSatz7_4a) }
13.12/2.05	  fresh4(fresh18(fresh30(fresh61(fresh27(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 9 (d_Defn7_1_2) }
13.12/2.05	  fresh4(fresh18(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 3 (aSatz7_16a) }
13.12/2.05	  fresh4(fresh18(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 6 (d_Defn7_1) }
13.12/2.05	  fresh4(fresh18(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 10 (aSatz7_17) }
13.12/2.05	  fresh4(fresh19(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 11 (aSatz7_4a) }
13.12/2.05	  fresh4(fresh19(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), sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 5 (aSatz7_17) }
13.12/2.05	  fresh4(sK3_aSatz7_19_Xa, sK3_aSatz7_19_Xa, sK2_aSatz7_19_Xb, sK3_aSatz7_19_Xa)
13.12/2.05	= { by axiom 1 (aSatz7_10a) }
13.12/2.05	  sK3_aSatz7_19_Xa
13.12/2.05	% SZS output end Proof
13.12/2.05	
13.12/2.05	RESULT: Theorem (the conjecture is true).
13.12/2.07	EOF