0.10/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.11	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.11/0.32	% Computer   : n020.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   : 1200
0.11/0.32	% WCLimit    : 120
0.11/0.32	% DateTime   : Wed Jul 14 14:09:20 EDT 2021
0.11/0.32	% CPUTime    : 
0.17/0.46	% SZS status Theorem
0.17/0.46	
0.17/0.47	% SZS output start Proof
0.17/0.47	Take the following subset of the input axioms:
0.17/0.47	  fof(ax55, axiom, ![U, V, W, X, Y]: i(triple(U, insert_slb(V, pair(X, Y)), W))=insert_pq(i(triple(U, V, W)), X)).
0.17/0.47	  fof(l2_co, conjecture, ![U]: (![V, W, X, Y]: i(triple(V, U, X))=i(triple(W, U, Y)) => ![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)))).
0.17/0.47	
0.17/0.47	Now clausify the problem and encode Horn clauses using encoding 3 of
0.17/0.47	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.17/0.47	We repeatedly replace C & s=t => u=v by the two clauses:
0.17/0.47	  fresh(y, y, x1...xn) = u
0.17/0.47	  C => fresh(s, t, x1...xn) = v
0.17/0.47	where fresh is a fresh function symbol and x1..xn are the free
0.17/0.47	variables of u and v.
0.17/0.47	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.17/0.47	input problem has no model of domain size 1).
0.17/0.47	
0.17/0.47	The encoding turns the above axioms into the following unit equations and goals:
0.17/0.47	
0.17/0.47	Axiom 1 (l2_co): i(triple(X, u, Y)) = i(triple(Z, u, W)).
0.17/0.47	Axiom 2 (ax55): i(triple(X, insert_slb(Y, pair(Z, W)), V)) = insert_pq(i(triple(X, Y, V)), Z).
0.17/0.47	
0.17/0.47	Goal 1 (l2_co_1): i(triple(z, insert_slb(u, pair(x4, x5)), x2)) = i(triple(x1, insert_slb(u, pair(x4, x5)), x3)).
0.17/0.47	Proof:
0.17/0.47	  i(triple(z, insert_slb(u, pair(x4, x5)), x2))
0.17/0.47	= { by axiom 2 (ax55) }
0.17/0.47	  insert_pq(i(triple(z, u, x2)), x4)
0.17/0.47	= { by axiom 1 (l2_co) R->L }
0.17/0.47	  insert_pq(i(triple(x1, u, x3)), x4)
0.17/0.47	= { by axiom 2 (ax55) R->L }
0.17/0.47	  i(triple(x1, insert_slb(u, pair(x4, x5)), x3))
0.17/0.47	% SZS output end Proof
0.17/0.47	
0.17/0.47	RESULT: Theorem (the conjecture is true).
0.17/0.47	EOF