0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n003.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 180
0.12/0.34	% DateTime   : Thu Aug 29 12:48:32 EDT 2019
0.12/0.34	% CPUTime    : 
0.58/0.74	% SZS status Theorem
0.58/0.74	
0.58/0.74	% SZS output start Proof
0.58/0.74	Take the following subset of the input axioms:
0.58/0.74	  fof('ass(cond(140, 0), 0)', axiom, ![Vd208, Vd209]: (less(Vd209, Vd208) <= greater(Vd208, Vd209))).
0.58/0.74	  fof('ass(cond(147, 0), 0)', axiom, ![Vd226, Vd227]: (less(Vd226, Vd227) => greater(Vd227, Vd226))).
0.58/0.74	  fof('ass(cond(189, 0), 0)', axiom, ![Vd295, Vd296]: greater(vplus(Vd295, Vd296), Vd295)).
0.58/0.74	  fof('ass(cond(33, 0), 0)', axiom, ![Vd46, Vd47, Vd48]: vplus(vplus(Vd46, Vd47), Vd48)=vplus(Vd46, vplus(Vd47, Vd48))).
0.58/0.74	  fof('ass(cond(61, 0), 0)', axiom, ![Vd78, Vd79]: vplus(Vd79, Vd78)=vplus(Vd78, Vd79)).
0.58/0.74	  fof('def(cond(conseq(axiom(3)), 11), 1)', axiom, ![Vd193, Vd194]: (?[Vd196]: vplus(Vd193, Vd196)=Vd194 <=> greater(Vd194, Vd193))).
0.58/0.74	  fof('holds(213, 351, 2)', axiom, vplus(vd345, vd348)=vplus(vd348, vd345)).
0.58/0.74	  fof('holds(214, 352, 0)', conjecture, greater(vplus(vd344, vd347), vplus(vd345, vd348))).
0.58/0.74	  fof('holds(conjunct1(211), 346, 0)', axiom, greater(vd344, vd345)).
0.58/0.74	  fof('holds(conjunct2(211), 349, 0)', axiom, greater(vd347, vd348)).
0.58/0.74	
0.58/0.74	Now clausify the problem and encode Horn clauses using encoding 3 of
0.58/0.74	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.58/0.74	We repeatedly replace C & s=t => u=v by the two clauses:
0.58/0.74	  fresh(y, y, x1...xn) = u
0.58/0.74	  C => fresh(s, t, x1...xn) = v
0.58/0.74	where fresh is a fresh function symbol and x1..xn are the free
0.58/0.74	variables of u and v.
0.58/0.74	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.58/0.74	input problem has no model of domain size 1).
0.58/0.74	
0.58/0.74	The encoding turns the above axioms into the following unit equations and goals:
0.58/0.74	
0.58/0.74	Axiom 1 (ass(cond(140, 0), 0)): fresh8(X, X, Y, Z) = true2.
0.58/0.74	Axiom 2 (ass(cond(147, 0), 0)): fresh9(X, X, Y, Z) = true2.
0.58/0.74	Axiom 3 (def(cond(conseq(axiom(3)), 11), 1)_1): fresh2(X, X, Y, Z) = Z.
0.58/0.74	Axiom 4 (def(cond(conseq(axiom(3)), 11), 1)_1): fresh2(greater(X, Y), true2, Y, X) = vplus(Y, sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(Y, X)).
0.58/0.74	Axiom 5 (holds(213, 351, 2)): vplus(vd345, vd348) = vplus(vd348, vd345).
0.58/0.74	Axiom 6 (holds(conjunct1(211), 346, 0)): greater(vd344, vd345) = true2.
0.58/0.74	Axiom 7 (ass(cond(189, 0), 0)): greater(vplus(X, Y), X) = true2.
0.58/0.74	Axiom 8 (ass(cond(33, 0), 0)): vplus(vplus(X, Y), Z) = vplus(X, vplus(Y, Z)).
0.58/0.74	Axiom 9 (ass(cond(61, 0), 0)): vplus(X, Y) = vplus(Y, X).
0.58/0.74	Axiom 10 (holds(conjunct2(211), 349, 0)): greater(vd347, vd348) = true2.
0.58/0.74	Axiom 11 (ass(cond(147, 0), 0)): fresh9(less(X, Y), true2, X, Y) = greater(Y, X).
0.58/0.75	Axiom 12 (ass(cond(140, 0), 0)): fresh8(greater(X, Y), true2, X, Y) = less(Y, X).
0.58/0.75	
0.58/0.75	Goal 1 (holds(214, 352, 0)): greater(vplus(vd344, vd347), vplus(vd345, vd348)) = true2.
0.58/0.75	Proof:
0.58/0.75	  greater(vplus(vd344, vd347), vplus(vd345, vd348))
0.58/0.75	= { by axiom 9 (ass(cond(61, 0), 0)) }
0.58/0.75	  greater(vplus(vd347, vd344), vplus(vd345, vd348))
0.58/0.75	= { by axiom 11 (ass(cond(147, 0), 0)) }
0.58/0.75	  fresh9(less(vplus(vd345, vd348), vplus(vd347, vd344)), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 5 (holds(213, 351, 2)) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vd347, vd344)), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 3 (def(cond(conseq(axiom(3)), 11), 1)_1) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(fresh2(true2, true2, vd348, vd347), vd344)), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 10 (holds(conjunct2(211), 349, 0)) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(fresh2(greater(vd347, vd348), true2, vd348, vd347), vd344)), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 4 (def(cond(conseq(axiom(3)), 11), 1)_1) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vplus(vd348, sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347)), vd344)), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 8 (ass(cond(33, 0), 0)) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vd348, vplus(sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347), vd344))), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 9 (ass(cond(61, 0), 0)) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vd348, vplus(vd344, sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347)))), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 3 (def(cond(conseq(axiom(3)), 11), 1)_1) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vd348, vplus(fresh2(true2, true2, vd345, vd344), sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347)))), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 6 (holds(conjunct1(211), 346, 0)) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vd348, vplus(fresh2(greater(vd344, vd345), true2, vd345, vd344), sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347)))), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 4 (def(cond(conseq(axiom(3)), 11), 1)_1) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vd348, vplus(vplus(vd345, sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd345, vd344)), sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347)))), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 8 (ass(cond(33, 0), 0)) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vd348, vplus(vd345, vplus(sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd345, vd344), sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347))))), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 9 (ass(cond(61, 0), 0)) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vd348, vplus(vd345, vplus(sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347), sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd345, vd344))))), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 8 (ass(cond(33, 0), 0)) }
0.58/0.75	  fresh9(less(vplus(vd348, vd345), vplus(vplus(vd348, vd345), vplus(sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347), sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd345, vd344)))), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 12 (ass(cond(140, 0), 0)) }
0.58/0.75	  fresh9(fresh8(greater(vplus(vplus(vd348, vd345), vplus(sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347), sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd345, vd344))), vplus(vd348, vd345)), true2, vplus(vplus(vd348, vd345), vplus(sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347), sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd345, vd344))), vplus(vd348, vd345)), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 7 (ass(cond(189, 0), 0)) }
0.58/0.75	  fresh9(fresh8(true2, true2, vplus(vplus(vd348, vd345), vplus(sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd348, vd347), sK1_def(cond(conseq(axiom(3)), 11), 1)_Vd196(vd345, vd344))), vplus(vd348, vd345)), true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 1 (ass(cond(140, 0), 0)) }
0.58/0.75	  fresh9(true2, true2, vplus(vd345, vd348), vplus(vd347, vd344))
0.58/0.75	= { by axiom 2 (ass(cond(147, 0), 0)) }
0.58/0.75	  true2
0.58/0.75	% SZS output end Proof
0.58/0.75	
0.58/0.75	RESULT: Theorem (the conjecture is true).
0.58/0.75	EOF