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   : n007.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   : Wed Jul 14 13:57:35 EDT 2021
0.19/0.34	% CPUTime    : 
3.76/0.85	% SZS status Theorem
3.76/0.85	
3.76/0.85	% SZS output start Proof
3.76/0.85	Take the following subset of the input axioms:
3.76/0.85	  fof(cl5_nebula_init_0046, conjecture, ![D, E]: ((leq(n0, D) & (leq(E, n4) & (leq(D, n135299) & leq(n0, E)))) => (gt(pv10, D) => a_select3(q_init, D, E)=init)) <= (leq(pv10, n135299) & (![A]: ((leq(n0, A) & leq(A, pred(pv10))) => ![B]: (a_select3(q_init, A, B)=init <= (leq(n0, B) & leq(B, n4)))) & (![C]: ((leq(C, n4) & leq(n0, C)) => init=a_select3(center_init, C, n0)) & leq(n0, pv10))))).
3.76/0.85	  fof(leq_gt_pred, axiom, ![X, Y]: (gt(Y, X) <=> leq(X, pred(Y)))).
3.76/0.85	
3.76/0.86	Now clausify the problem and encode Horn clauses using encoding 3 of
3.76/0.86	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
3.76/0.86	We repeatedly replace C & s=t => u=v by the two clauses:
3.76/0.86	  fresh(y, y, x1...xn) = u
3.76/0.86	  C => fresh(s, t, x1...xn) = v
3.76/0.86	where fresh is a fresh function symbol and x1..xn are the free
3.76/0.86	variables of u and v.
3.76/0.86	A predicate p(X) is encoded as p(X)=true (this is sound, because the
3.76/0.86	input problem has no model of domain size 1).
3.76/0.86	
3.76/0.86	The encoding turns the above axioms into the following unit equations and goals:
3.76/0.86	
3.76/0.86	Axiom 1 (cl5_nebula_init_0046_2): leq(n0, d) = true3.
3.76/0.86	Axiom 2 (cl5_nebula_init_0046_1): leq(n0, e) = true3.
3.76/0.86	Axiom 3 (cl5_nebula_init_0046_4): leq(e, n4) = true3.
3.76/0.86	Axiom 4 (cl5_nebula_init_0046_6): gt(pv10, d) = true3.
3.76/0.86	Axiom 5 (cl5_nebula_init_0046_8): fresh46(X, X, Y, Z) = a_select3(q_init, Y, Z).
3.76/0.86	Axiom 6 (cl5_nebula_init_0046_8): fresh43(X, X, Y, Z) = init.
3.76/0.86	Axiom 7 (leq_gt_pred_1): fresh34(X, X, Y, Z) = true3.
3.76/0.86	Axiom 8 (cl5_nebula_init_0046_8): fresh45(X, X, Y, Z) = fresh46(leq(Z, n4), true3, Y, Z).
3.76/0.86	Axiom 9 (cl5_nebula_init_0046_8): fresh44(X, X, Y, Z) = fresh45(leq(n0, Y), true3, Y, Z).
3.76/0.86	Axiom 10 (leq_gt_pred_1): fresh34(gt(X, Y), true3, Y, X) = leq(Y, pred(X)).
3.76/0.86	Axiom 11 (cl5_nebula_init_0046_8): fresh44(leq(n0, X), true3, Y, X) = fresh43(leq(Y, pred(pv10)), true3, Y, X).
3.76/0.86	
3.76/0.86	Goal 1 (cl5_nebula_init_0046_7): a_select3(q_init, d, e) = init.
3.76/0.86	Proof:
3.76/0.86	  a_select3(q_init, d, e)
3.76/0.86	= { by axiom 5 (cl5_nebula_init_0046_8) R->L }
3.76/0.86	  fresh46(true3, true3, d, e)
3.76/0.86	= { by axiom 3 (cl5_nebula_init_0046_4) R->L }
3.76/0.86	  fresh46(leq(e, n4), true3, d, e)
3.76/0.86	= { by axiom 8 (cl5_nebula_init_0046_8) R->L }
3.76/0.86	  fresh45(true3, true3, d, e)
3.76/0.86	= { by axiom 1 (cl5_nebula_init_0046_2) R->L }
3.76/0.86	  fresh45(leq(n0, d), true3, d, e)
3.76/0.86	= { by axiom 9 (cl5_nebula_init_0046_8) R->L }
3.76/0.86	  fresh44(true3, true3, d, e)
3.76/0.86	= { by axiom 2 (cl5_nebula_init_0046_1) R->L }
3.76/0.86	  fresh44(leq(n0, e), true3, d, e)
3.76/0.86	= { by axiom 11 (cl5_nebula_init_0046_8) }
3.76/0.86	  fresh43(leq(d, pred(pv10)), true3, d, e)
3.76/0.86	= { by axiom 10 (leq_gt_pred_1) R->L }
3.76/0.86	  fresh43(fresh34(gt(pv10, d), true3, d, pv10), true3, d, e)
3.76/0.86	= { by axiom 4 (cl5_nebula_init_0046_6) }
3.76/0.86	  fresh43(fresh34(true3, true3, d, pv10), true3, d, e)
3.76/0.86	= { by axiom 7 (leq_gt_pred_1) }
3.76/0.86	  fresh43(true3, true3, d, e)
3.76/0.86	= { by axiom 6 (cl5_nebula_init_0046_8) }
3.76/0.86	  init
3.76/0.86	% SZS output end Proof
3.76/0.86	
3.76/0.86	RESULT: Theorem (the conjecture is true).
3.76/0.86	EOF