0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.14/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.14/0.34	% Computer   : n026.cluster.edu
0.14/0.34	% Model      : x86_64 x86_64
0.14/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.34	% Memory     : 8042.1875MB
0.14/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.34	% CPULimit   : 960
0.14/0.34	% WCLimit    : 120
0.14/0.34	% DateTime   : Thu Jul  2 06:44:09 EDT 2020
0.14/0.34	% CPUTime    : 
0.20/0.42	% SZS status Theorem
0.20/0.42	
0.20/0.42	% SZS output start Proof
0.20/0.42	Take the following subset of the input axioms:
0.20/0.42	  fof(thm_2Ebinary__ieee_2Efloat__to__real__negate, axiom, ![A_27a, V0x_2E0, A_27b]: s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0)))))=s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a, A_27b), V0x_2E0)))))).
0.20/0.42	  fof(thm_2Ebinary__ieee_2Eneg__ulp, conjecture, ![A_27t, A_27w]: s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))=s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))))).
0.20/0.42	  fof(thm_2Ebinary__ieee_2Eulp, axiom, ![A_27t, A_27w]: s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))=s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t, A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t, A_27w)), c_2Ebool_2Ethe__value_2E0)))))).
0.20/0.42	
0.20/0.42	Now clausify the problem and encode Horn clauses using encoding 3 of
0.20/0.42	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.20/0.42	We repeatedly replace C & s=t => u=v by the two clauses:
0.20/0.42	  fresh(y, y, x1...xn) = u
0.20/0.42	  C => fresh(s, t, x1...xn) = v
0.20/0.42	where fresh is a fresh function symbol and x1..xn are the free
0.20/0.42	variables of u and v.
0.20/0.42	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.20/0.42	input problem has no model of domain size 1).
0.20/0.42	
0.20/0.42	The encoding turns the above axioms into the following unit equations and goals:
0.20/0.42	
0.20/0.42	Axiom 1 (thm_2Ebinary__ieee_2Efloat__to__real__negate): s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(X, Y), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(X, Y), Z))))) = s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(X, Y), Z))))).
0.20/0.42	Axiom 2 (thm_2Ebinary__ieee_2Eulp): s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X, Y)), c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(X, Y), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X, Y)), c_2Ebool_2Ethe__value_2E0))))).
0.20/0.42	
0.20/0.43	Goal 1 (thm_2Ebinary__ieee_2Eneg__ulp): s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w)), c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w)), c_2Ebool_2Ethe__value_2E0))))))).
0.20/0.43	Proof:
0.20/0.43	  s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w)), c_2Ebool_2Ethe__value_2E0)))))
0.20/0.43	= { by axiom 2 (thm_2Ebinary__ieee_2Eulp) }
0.20/0.43	  s(tyop_2Erealax_2Ereal, c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w)), c_2Ebool_2Ethe__value_2E0)))))))
0.20/0.43	= { by axiom 1 (thm_2Ebinary__ieee_2Efloat__to__real__negate) }
0.20/0.43	  s(tyop_2Erealax_2Ereal, c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w), c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w), c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK2_thm_2Ebinary__ieee_2Eneg__ulp_A_27t, sK1_thm_2Ebinary__ieee_2Eneg__ulp_A_27w)), c_2Ebool_2Ethe__value_2E0)))))))
0.20/0.43	% SZS output end Proof
0.20/0.43	
0.20/0.43	RESULT: Theorem (the conjecture is true).
0.20/0.43	EOF