0.08/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.14/0.36	% Computer   : n025.cluster.edu
0.14/0.36	% Model      : x86_64 x86_64
0.14/0.36	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.36	% Memory     : 8042.1875MB
0.14/0.36	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.36	% CPULimit   : 960
0.14/0.36	% WCLimit    : 120
0.14/0.36	% DateTime   : Thu Jul  2 07:31:03 EDT 2020
0.14/0.36	% CPUTime    : 
0.22/0.45	% SZS status Theorem
0.22/0.45	
0.22/0.45	% SZS output start Proof
0.22/0.45	Take the following subset of the input axioms:
0.22/0.45	  fof(ax55, axiom, ![U, V, W, X, Y]: insert_pq(i(triple(U, V, W)), X)=i(triple(U, insert_slb(V, pair(X, Y)), W))).
0.22/0.45	  fof(l2_co, conjecture, ![U]: (![Z, X1, X2, X3, X4, X5]: i(triple(Z, insert_slb(U, pair(X4, X5)), X2))=i(triple(X1, insert_slb(U, pair(X4, X5)), X3)) <= ![V, W, X, Y]: i(triple(V, U, X))=i(triple(W, U, Y)))).
0.22/0.45	
0.22/0.45	Now clausify the problem and encode Horn clauses using encoding 3 of
0.22/0.45	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.22/0.45	We repeatedly replace C & s=t => u=v by the two clauses:
0.22/0.45	  fresh(y, y, x1...xn) = u
0.22/0.45	  C => fresh(s, t, x1...xn) = v
0.22/0.45	where fresh is a fresh function symbol and x1..xn are the free
0.22/0.45	variables of u and v.
0.22/0.45	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.22/0.45	input problem has no model of domain size 1).
0.22/0.45	
0.22/0.45	The encoding turns the above axioms into the following unit equations and goals:
0.22/0.45	
0.22/0.45	Axiom 1 (ax55): insert_pq(i(triple(X, Y, Z)), W) = i(triple(X, insert_slb(Y, pair(W, V)), Z)).
0.22/0.45	Axiom 2 (l2_co): i(triple(X, sK7_l2_co_U, Y)) = i(triple(Z, sK7_l2_co_U, W)).
0.22/0.45	
0.22/0.45	Lemma 3: i(triple(X, sK7_l2_co_U, Y)) = i(triple(?, sK7_l2_co_U, ?)).
0.22/0.45	Proof:
0.22/0.45	  i(triple(X, sK7_l2_co_U, Y))
0.22/0.45	= { by axiom 2 (l2_co) }
0.22/0.45	  i(triple(Z, sK7_l2_co_U, W))
0.22/0.45	= { by axiom 2 (l2_co) }
0.22/0.45	  i(triple(?, sK7_l2_co_U, ?))
0.22/0.45	
0.22/0.45	Goal 1 (l2_co_1): i(triple(sK6_l2_co_Z, insert_slb(sK7_l2_co_U, pair(sK2_l2_co_X4, sK1_l2_co_X5)), sK4_l2_co_X2)) = i(triple(sK5_l2_co_X1, insert_slb(sK7_l2_co_U, pair(sK2_l2_co_X4, sK1_l2_co_X5)), sK3_l2_co_X3)).
0.22/0.45	Proof:
0.22/0.45	  i(triple(sK6_l2_co_Z, insert_slb(sK7_l2_co_U, pair(sK2_l2_co_X4, sK1_l2_co_X5)), sK4_l2_co_X2))
0.22/0.45	= { by axiom 1 (ax55) }
0.22/0.45	  insert_pq(i(triple(sK6_l2_co_Z, sK7_l2_co_U, sK4_l2_co_X2)), sK2_l2_co_X4)
0.22/0.45	= { by lemma 3 }
0.22/0.46	  insert_pq(i(triple(?, sK7_l2_co_U, ?)), sK2_l2_co_X4)
0.22/0.46	= { by lemma 3 }
0.22/0.46	  insert_pq(i(triple(sK5_l2_co_X1, sK7_l2_co_U, sK3_l2_co_X3)), sK2_l2_co_X4)
0.22/0.46	= { by axiom 1 (ax55) }
0.22/0.46	  i(triple(sK5_l2_co_X1, insert_slb(sK7_l2_co_U, pair(sK2_l2_co_X4, sK1_l2_co_X5)), sK3_l2_co_X3))
0.22/0.46	% SZS output end Proof
0.22/0.46	
0.22/0.46	RESULT: Theorem (the conjecture is true).
0.22/0.46	EOF