0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.34	% Computer   : n010.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 180
0.12/0.34	% DateTime   : Thu Aug 29 11:18:06 EDT 2019
0.12/0.34	% CPUTime    : 
2.06/2.28	% SZS status Theorem
2.06/2.28	
2.06/2.28	% SZS output start Proof
2.06/2.28	Take the following subset of the input axioms:
2.06/2.28	  fof(aSatz7_15a, axiom, ![Xa, Xp, Xq, Xr]: (~s_t(Xp, Xq, Xr) | s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))).
2.06/2.28	  fof(aSatz7_15b, conjecture, ![Xa, Xp, Xq, Xr]: (s_t(Xp, Xq, Xr) | ~s_t(s(Xa, Xp), s(Xa, Xq), s(Xa, Xr)))).
2.06/2.28	  fof(aSatz7_7, axiom, ![Xa, Xp]: s(Xa, s(Xa, Xp))=Xp).
2.06/2.28	
2.06/2.28	Now clausify the problem and encode Horn clauses using encoding 3 of
2.06/2.28	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
2.06/2.28	We repeatedly replace C & s=t => u=v by the two clauses:
2.06/2.28	  fresh(y, y, x1...xn) = u
2.06/2.28	  C => fresh(s, t, x1...xn) = v
2.06/2.28	where fresh is a fresh function symbol and x1..xn are the free
2.06/2.28	variables of u and v.
2.06/2.28	A predicate p(X) is encoded as p(X)=true (this is sound, because the
2.06/2.28	input problem has no model of domain size 1).
2.06/2.28	
2.06/2.28	The encoding turns the above axioms into the following unit equations and goals:
2.06/2.28	
2.06/2.28	Axiom 1 (aSatz7_15a): fresh57(X, X, Y, Z, W, V) = true2.
2.06/2.28	Axiom 2 (aSatz7_15a): fresh57(s_t(X, Y, Z), true2, X, Y, Z, W) = s_t(s(W, X), s(W, Y), s(W, Z)).
2.06/2.28	Axiom 3 (aSatz7_7): s(X, s(X, Y)) = Y.
2.06/2.28	Axiom 4 (aSatz7_15b): s_t(s(sK1_aSatz7_15b_Xa, sK4_aSatz7_15b_Xp), s(sK1_aSatz7_15b_Xa, sK3_aSatz7_15b_Xq), s(sK1_aSatz7_15b_Xa, sK2_aSatz7_15b_Xr)) = true2.
2.06/2.28	
2.06/2.28	Goal 1 (aSatz7_15b_1): s_t(sK4_aSatz7_15b_Xp, sK3_aSatz7_15b_Xq, sK2_aSatz7_15b_Xr) = true2.
2.06/2.28	Proof:
2.06/2.28	  s_t(sK4_aSatz7_15b_Xp, sK3_aSatz7_15b_Xq, sK2_aSatz7_15b_Xr)
2.06/2.28	= { by axiom 3 (aSatz7_7) }
2.06/2.28	  s_t(s(sK1_aSatz7_15b_Xa, s(sK1_aSatz7_15b_Xa, sK4_aSatz7_15b_Xp)), sK3_aSatz7_15b_Xq, sK2_aSatz7_15b_Xr)
2.06/2.28	= { by axiom 3 (aSatz7_7) }
2.06/2.28	  s_t(s(sK1_aSatz7_15b_Xa, s(sK1_aSatz7_15b_Xa, sK4_aSatz7_15b_Xp)), s(sK1_aSatz7_15b_Xa, s(sK1_aSatz7_15b_Xa, sK3_aSatz7_15b_Xq)), sK2_aSatz7_15b_Xr)
2.06/2.28	= { by axiom 3 (aSatz7_7) }
2.06/2.28	  s_t(s(sK1_aSatz7_15b_Xa, s(sK1_aSatz7_15b_Xa, sK4_aSatz7_15b_Xp)), s(sK1_aSatz7_15b_Xa, s(sK1_aSatz7_15b_Xa, sK3_aSatz7_15b_Xq)), s(sK1_aSatz7_15b_Xa, s(sK1_aSatz7_15b_Xa, sK2_aSatz7_15b_Xr)))
2.06/2.28	= { by axiom 2 (aSatz7_15a) }
2.06/2.28	  fresh57(s_t(s(sK1_aSatz7_15b_Xa, sK4_aSatz7_15b_Xp), s(sK1_aSatz7_15b_Xa, sK3_aSatz7_15b_Xq), s(sK1_aSatz7_15b_Xa, sK2_aSatz7_15b_Xr)), true2, s(sK1_aSatz7_15b_Xa, sK4_aSatz7_15b_Xp), s(sK1_aSatz7_15b_Xa, sK3_aSatz7_15b_Xq), s(sK1_aSatz7_15b_Xa, sK2_aSatz7_15b_Xr), sK1_aSatz7_15b_Xa)
2.06/2.28	= { by axiom 4 (aSatz7_15b) }
2.06/2.28	  fresh57(true2, true2, s(sK1_aSatz7_15b_Xa, sK4_aSatz7_15b_Xp), s(sK1_aSatz7_15b_Xa, sK3_aSatz7_15b_Xq), s(sK1_aSatz7_15b_Xa, sK2_aSatz7_15b_Xr), sK1_aSatz7_15b_Xa)
2.06/2.28	= { by axiom 1 (aSatz7_15a) }
2.06/2.28	  true2
2.06/2.28	% SZS output end Proof
2.06/2.28	
2.06/2.28	RESULT: Theorem (the conjecture is true).
2.13/2.29	EOF