TSTP Solution File: NUM857+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM857+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:58:41 EDT 2023
% Result : Theorem 67.14s 8.95s
% Output : Proof 67.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM857+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n022.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 : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 12:48:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 67.14/8.95 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 67.14/8.95
% 67.14/8.95 % SZS status Theorem
% 67.14/8.95
% 67.26/8.96 % SZS output start Proof
% 67.26/8.96 Take the following subset of the input axioms:
% 67.26/8.96 fof('ass(cond(140, 0), 0)', axiom, ![Vd208, Vd209]: (greater(Vd208, Vd209) => less(Vd209, Vd208))).
% 67.26/8.96 fof('ass(cond(163, 0), 0)', axiom, ![Vd258, Vd259]: (leq(Vd258, Vd259) => geq(Vd259, Vd258))).
% 67.26/8.96 fof('ass(cond(189, 0), 0)', axiom, ![Vd295, Vd296]: greater(vplus(Vd295, Vd296), Vd295)).
% 67.26/8.96 fof('ass(cond(241, 0), 0)', axiom, ![Vd386, Vd387]: (less(Vd386, vplus(Vd387, v1)) => leq(Vd386, Vd387))).
% 67.26/8.96 fof('ass(cond(270, 0), 0)', axiom, ![Vd418, Vd419]: vmul(Vd418, Vd419)=vmul(Vd419, Vd418)).
% 67.26/8.96 fof('ass(cond(290, 0), 0)', axiom, ![Vd444, Vd445, Vd446]: vmul(vmul(Vd444, Vd445), Vd446)=vmul(Vd444, vmul(Vd445, Vd446))).
% 67.26/8.96 fof('ass(cond(318, 0), 0)', axiom, ![Vd517, Vd518, Vd519, Vd520]: (((greater(Vd519, Vd520) & geq(Vd517, Vd518)) | (geq(Vd519, Vd520) & greater(Vd517, Vd518))) => greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))).
% 67.26/8.96 fof('ass(cond(conjunct1(307), 0), 0)', axiom, ![Vd486, Vd487, Vd488]: (greater(vmul(Vd486, Vd487), vmul(Vd488, Vd487)) => greater(Vd486, Vd488))).
% 67.26/8.96 fof('holds(conjunct1(antec(323)), 528, 0)', axiom, geq(vd526, vd527)).
% 67.26/8.96 fof('holds(conjunct2(antec(323)), 531, 0)', axiom, geq(vd529, vd530)).
% 67.26/8.96 fof('holds(conseq(323), 532, 0)', conjecture, geq(vmul(vd526, vd529), vmul(vd527, vd530))).
% 67.26/8.97 fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))', axiom, ![Vd42, Vd43]: (vplus(Vd42, vsucc(Vd43))=vsucc(vplus(Vd42, Vd43)) & vplus(Vd42, v1)=vsucc(Vd42))).
% 67.26/8.97
% 67.26/8.97 Now clausify the problem and encode Horn clauses using encoding 3 of
% 67.26/8.97 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 67.26/8.97 We repeatedly replace C & s=t => u=v by the two clauses:
% 67.26/8.97 fresh(y, y, x1...xn) = u
% 67.26/8.97 C => fresh(s, t, x1...xn) = v
% 67.26/8.97 where fresh is a fresh function symbol and x1..xn are the free
% 67.26/8.97 variables of u and v.
% 67.26/8.97 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 67.26/8.97 input problem has no model of domain size 1).
% 67.26/8.97
% 67.26/8.97 The encoding turns the above axioms into the following unit equations and goals:
% 67.26/8.97
% 67.26/8.97 Axiom 1 (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))_1): vplus(X, v1) = vsucc(X).
% 67.26/8.97 Axiom 2 (ass(cond(270, 0), 0)): vmul(X, Y) = vmul(Y, X).
% 67.26/8.97 Axiom 3 (holds(conjunct1(antec(323)), 528, 0)): geq(vd526, vd527) = true2.
% 67.26/8.97 Axiom 4 (holds(conjunct2(antec(323)), 531, 0)): geq(vd529, vd530) = true2.
% 67.26/8.97 Axiom 5 (ass(cond(290, 0), 0)): vmul(vmul(X, Y), Z) = vmul(X, vmul(Y, Z)).
% 67.26/8.97 Axiom 6 (ass(cond(189, 0), 0)): greater(vplus(X, Y), X) = true2.
% 67.26/8.97 Axiom 7 (ass(cond(140, 0), 0)): fresh46(X, X, Y, Z) = true2.
% 67.26/8.97 Axiom 8 (ass(cond(163, 0), 0)): fresh44(X, X, Y, Z) = true2.
% 67.26/8.97 Axiom 9 (ass(cond(241, 0), 0)): fresh34(X, X, Y, Z) = true2.
% 67.26/8.97 Axiom 10 (ass(cond(conjunct1(307), 0), 0)): fresh25(X, X, Y, Z) = true2.
% 67.26/8.97 Axiom 11 (ass(cond(140, 0), 0)): fresh46(greater(X, Y), true2, X, Y) = less(Y, X).
% 67.26/8.97 Axiom 12 (ass(cond(163, 0), 0)): fresh44(leq(X, Y), true2, X, Y) = geq(Y, X).
% 67.26/8.97 Axiom 13 (ass(cond(318, 0), 0)): fresh29(X, X, Y, Z, W, V) = greater(vmul(Y, W), vmul(Z, V)).
% 67.26/8.97 Axiom 14 (ass(cond(318, 0), 0)): fresh28(X, X, Y, Z, W, V) = true2.
% 67.26/8.97 Axiom 15 (ass(cond(318, 0), 0)_1): fresh27(X, X, Y, Z, W, V) = greater(vmul(Y, W), vmul(Z, V)).
% 67.26/8.97 Axiom 16 (ass(cond(318, 0), 0)_1): fresh26(X, X, Y, Z, W, V) = true2.
% 67.26/8.97 Axiom 17 (ass(cond(241, 0), 0)): fresh34(less(X, vplus(Y, v1)), true2, X, Y) = leq(X, Y).
% 67.26/8.97 Axiom 18 (ass(cond(318, 0), 0)): fresh29(greater(X, Y), true2, Z, W, X, Y) = fresh28(geq(Z, W), true2, Z, W, X, Y).
% 67.26/8.97 Axiom 19 (ass(cond(318, 0), 0)_1): fresh27(greater(X, Y), true2, X, Y, Z, W) = fresh26(geq(Z, W), true2, X, Y, Z, W).
% 67.26/8.97 Axiom 20 (ass(cond(conjunct1(307), 0), 0)): fresh25(greater(vmul(X, Y), vmul(Z, Y)), true2, X, Z) = greater(X, Z).
% 67.26/8.97
% 67.26/8.97 Goal 1 (holds(conseq(323), 532, 0)): geq(vmul(vd526, vd529), vmul(vd527, vd530)) = true2.
% 67.26/8.97 Proof:
% 67.26/8.97 geq(vmul(vd526, vd529), vmul(vd527, vd530))
% 67.26/8.97 = { by axiom 12 (ass(cond(163, 0), 0)) R->L }
% 67.26/8.97 fresh44(leq(vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 17 (ass(cond(241, 0), 0)) R->L }
% 67.26/8.97 fresh44(fresh34(less(vmul(vd527, vd530), vplus(vmul(vd526, vd529), v1)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 1 (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))_1) }
% 67.26/8.97 fresh44(fresh34(less(vmul(vd527, vd530), vsucc(vmul(vd526, vd529))), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 11 (ass(cond(140, 0), 0)) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(greater(vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 20 (ass(cond(conjunct1(307), 0), 0)) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(greater(vmul(vsucc(vmul(vd526, vd529)), vmul(vd526, vd529)), vmul(vmul(vd527, vd530), vmul(vd526, vd529))), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 2 (ass(cond(270, 0), 0)) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(greater(vmul(vmul(vd526, vd529), vsucc(vmul(vd526, vd529))), vmul(vmul(vd527, vd530), vmul(vd526, vd529))), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 2 (ass(cond(270, 0), 0)) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(greater(vmul(vmul(vd526, vd529), vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vmul(vd527, vd530))), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 2 (ass(cond(270, 0), 0)) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(greater(vmul(vsucc(vmul(vd526, vd529)), vmul(vd526, vd529)), vmul(vmul(vd526, vd529), vmul(vd527, vd530))), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 5 (ass(cond(290, 0), 0)) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(greater(vmul(vsucc(vmul(vd526, vd529)), vmul(vd526, vd529)), vmul(vmul(vmul(vd526, vd529), vd527), vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 2 (ass(cond(270, 0), 0)) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(greater(vmul(vmul(vd526, vd529), vsucc(vmul(vd526, vd529))), vmul(vmul(vmul(vd526, vd529), vd527), vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 5 (ass(cond(290, 0), 0)) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(greater(vmul(vd526, vmul(vd529, vsucc(vmul(vd526, vd529)))), vmul(vmul(vmul(vd526, vd529), vd527), vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 2 (ass(cond(270, 0), 0)) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(greater(vmul(vd526, vmul(vsucc(vmul(vd526, vd529)), vd529)), vmul(vmul(vmul(vd526, vd529), vd527), vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 5 (ass(cond(290, 0), 0)) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(greater(vmul(vmul(vd526, vsucc(vmul(vd526, vd529))), vd529), vmul(vmul(vmul(vd526, vd529), vd527), vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 15 (ass(cond(318, 0), 0)_1) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh27(true2, true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 14 (ass(cond(318, 0), 0)) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh27(fresh28(true2, true2, vd526, vd527, vsucc(vmul(vd526, vd529)), vmul(vd526, vd529)), true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 3 (holds(conjunct1(antec(323)), 528, 0)) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh27(fresh28(geq(vd526, vd527), true2, vd526, vd527, vsucc(vmul(vd526, vd529)), vmul(vd526, vd529)), true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 18 (ass(cond(318, 0), 0)) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh27(fresh29(greater(vsucc(vmul(vd526, vd529)), vmul(vd526, vd529)), true2, vd526, vd527, vsucc(vmul(vd526, vd529)), vmul(vd526, vd529)), true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 1 (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))_1) R->L }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh27(fresh29(greater(vplus(vmul(vd526, vd529), v1), vmul(vd526, vd529)), true2, vd526, vd527, vsucc(vmul(vd526, vd529)), vmul(vd526, vd529)), true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 6 (ass(cond(189, 0), 0)) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh27(fresh29(true2, true2, vd526, vd527, vsucc(vmul(vd526, vd529)), vmul(vd526, vd529)), true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 13 (ass(cond(318, 0), 0)) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh27(greater(vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vd527, vmul(vd526, vd529))), true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 2 (ass(cond(270, 0), 0)) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh27(greater(vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527)), true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 19 (ass(cond(318, 0), 0)_1) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh26(geq(vd529, vd530), true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 4 (holds(conjunct2(antec(323)), 531, 0)) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(fresh26(true2, true2, vmul(vd526, vsucc(vmul(vd526, vd529))), vmul(vmul(vd526, vd529), vd527), vd529, vd530), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 16 (ass(cond(318, 0), 0)_1) }
% 67.26/8.97 fresh44(fresh34(fresh46(fresh25(true2, true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 10 (ass(cond(conjunct1(307), 0), 0)) }
% 67.26/8.97 fresh44(fresh34(fresh46(true2, true2, vsucc(vmul(vd526, vd529)), vmul(vd527, vd530)), true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 7 (ass(cond(140, 0), 0)) }
% 67.26/8.97 fresh44(fresh34(true2, true2, vmul(vd527, vd530), vmul(vd526, vd529)), true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 9 (ass(cond(241, 0), 0)) }
% 67.26/8.97 fresh44(true2, true2, vmul(vd527, vd530), vmul(vd526, vd529))
% 67.26/8.97 = { by axiom 8 (ass(cond(163, 0), 0)) }
% 67.26/8.97 true2
% 67.26/8.97 % SZS output end Proof
% 67.26/8.97
% 67.26/8.97 RESULT: Theorem (the conjecture is true).
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