0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.34	% Computer   : n026.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   : 1200
0.12/0.34	% WCLimit    : 120
0.12/0.34	% DateTime   : Tue Jul 13 16:35:59 EDT 2021
0.12/0.34	% CPUTime    : 
6.57/1.18	% SZS status Theorem
6.57/1.18	
6.57/1.18	% SZS output start Proof
6.57/1.18	Take the following subset of the input axioms:
6.57/1.18	  fof(less_entry_point_neg_pos, axiom, ![X, Y, RDN_X, RDN_Y]: (less(X, Y) <= (rdn_translate(Y, rdn_pos(RDN_Y)) & rdn_translate(X, rdn_neg(RDN_X))))).
6.57/1.18	  fof(less_property, axiom, ![X, Y]: (less(X, Y) <=> (~less(Y, X) & Y!=X))).
6.57/1.18	  fof(rdn0, axiom, rdn_translate(n0, rdn_pos(rdnn(n0)))).
6.57/1.18	  fof(rdnn1, axiom, rdn_translate(nn1, rdn_neg(rdnn(n1)))).
6.57/1.18	  fof(something_less_n0, conjecture, ?[X]: less(X, n0)).
6.57/1.18	
6.57/1.18	Now clausify the problem and encode Horn clauses using encoding 3 of
6.57/1.18	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
6.57/1.18	We repeatedly replace C & s=t => u=v by the two clauses:
6.57/1.18	  fresh(y, y, x1...xn) = u
6.57/1.18	  C => fresh(s, t, x1...xn) = v
6.57/1.18	where fresh is a fresh function symbol and x1..xn are the free
6.57/1.18	variables of u and v.
6.57/1.18	A predicate p(X) is encoded as p(X)=true (this is sound, because the
6.57/1.18	input problem has no model of domain size 1).
6.57/1.18	
6.57/1.18	The encoding turns the above axioms into the following unit equations and goals:
6.57/1.18	
6.57/1.18	Axiom 1 (rdn0): rdn_translate(n0, rdn_pos(rdnn(n0))) = true2.
6.57/1.18	Axiom 2 (rdnn1): rdn_translate(nn1, rdn_neg(rdnn(n1))) = true2.
6.57/1.18	Axiom 3 (less_entry_point_neg_pos): fresh22(X, X, Y, Z) = true2.
6.57/1.18	Axiom 4 (less_entry_point_neg_pos): fresh23(X, X, Y, Z, W) = less(Y, Z).
6.57/1.18	Axiom 5 (less_entry_point_neg_pos): fresh23(rdn_translate(X, rdn_pos(Y)), true2, Z, X, W) = fresh22(rdn_translate(Z, rdn_neg(W)), true2, Z, X).
6.57/1.18	
6.57/1.18	Goal 1 (something_less_n0): less(X, n0) = true2.
6.57/1.18	The goal is true when:
6.57/1.18	  X = nn1
6.57/1.18	
6.57/1.18	Proof:
6.57/1.18	  less(nn1, n0)
6.57/1.18	= { by axiom 4 (less_entry_point_neg_pos) R->L }
6.57/1.18	  fresh23(true2, true2, nn1, n0, rdnn(n1))
6.57/1.18	= { by axiom 1 (rdn0) R->L }
6.57/1.18	  fresh23(rdn_translate(n0, rdn_pos(rdnn(n0))), true2, nn1, n0, rdnn(n1))
6.57/1.18	= { by axiom 5 (less_entry_point_neg_pos) }
6.57/1.18	  fresh22(rdn_translate(nn1, rdn_neg(rdnn(n1))), true2, nn1, n0)
6.57/1.18	= { by axiom 2 (rdnn1) }
6.57/1.18	  fresh22(true2, true2, nn1, n0)
6.57/1.18	= { by axiom 3 (less_entry_point_neg_pos) }
6.57/1.18	  true2
6.57/1.18	% SZS output end Proof
6.57/1.18	
6.57/1.18	RESULT: Theorem (the conjecture is true).
6.57/1.19	EOF