TSTP Solution File: NUM855+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM855+1 : 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 : n014.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 11:58:40 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM855+1 : 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 : n014.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 14:31:32 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.65 Command-line arguments: --flatten
% 0.20/0.65
% 0.20/0.65 % SZS status Theorem
% 0.20/0.65
% 0.20/0.66 % SZS output start Proof
% 0.20/0.66 Take the following subset of the input axioms:
% 0.20/0.66 fof('ass(cond(140, 0), 0)', axiom, ![Vd208, Vd209]: (greater(Vd208, Vd209) => less(Vd209, Vd208))).
% 0.20/0.66 fof('ass(cond(189, 0), 0)', axiom, ![Vd295, Vd296]: greater(vplus(Vd295, Vd296), Vd295)).
% 0.20/0.66 fof('ass(cond(270, 0), 0)', axiom, ![Vd418, Vd419]: vmul(Vd418, Vd419)=vmul(Vd419, Vd418)).
% 0.20/0.66 fof('ass(cond(33, 0), 0)', axiom, ![Vd46, Vd47, Vd48]: vplus(vplus(Vd46, Vd47), Vd48)=vplus(Vd46, vplus(Vd47, Vd48))).
% 0.20/0.66 fof('ass(cond(61, 0), 0)', axiom, ![Vd78, Vd79]: vplus(Vd79, Vd78)=vplus(Vd78, Vd79)).
% 0.20/0.66 fof('def(cond(conseq(axiom(3)), 12), 1)', axiom, ![Vd198, Vd199]: (less(Vd199, Vd198) <=> ?[Vd201]: Vd198=vplus(Vd199, Vd201))).
% 0.20/0.66 fof('holds(conjunct1(314), 510, 0)', axiom, greater(vd508, vd509)).
% 0.20/0.66 fof('holds(conjunct1(315), 514, 0)', axiom, greater(vmul(vd508, vd511), vmul(vd509, vd511))).
% 0.20/0.66 fof('holds(conjunct2(315), 515, 1)', axiom, greater(vmul(vd511, vd509), vmul(vd512, vd509))).
% 0.20/0.66 fof('holds(conseq_conjunct2(315), 516, 0)', conjecture, greater(vmul(vd508, vd511), vmul(vd509, vd512))).
% 0.20/0.66
% 0.20/0.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.66 fresh(y, y, x1...xn) = u
% 0.20/0.66 C => fresh(s, t, x1...xn) = v
% 0.20/0.66 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.66 variables of u and v.
% 0.20/0.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.66 input problem has no model of domain size 1).
% 0.20/0.66
% 0.20/0.66 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.66
% 0.20/0.66 Axiom 1 (holds(conjunct1(314), 510, 0)): greater(vd508, vd509) = true2.
% 0.20/0.66 Axiom 2 (ass(cond(270, 0), 0)): vmul(X, Y) = vmul(Y, X).
% 0.20/0.66 Axiom 3 (ass(cond(61, 0), 0)): vplus(X, Y) = vplus(Y, X).
% 0.20/0.66 Axiom 4 (ass(cond(140, 0), 0)): fresh40(X, X, Y, Z) = true2.
% 0.20/0.66 Axiom 5 (def(cond(conseq(axiom(3)), 12), 1)_1): fresh7(X, X, Y, Z) = Y.
% 0.20/0.66 Axiom 6 (ass(cond(189, 0), 0)): greater(vplus(X, Y), X) = true2.
% 0.20/0.66 Axiom 7 (ass(cond(33, 0), 0)): vplus(vplus(X, Y), Z) = vplus(X, vplus(Y, Z)).
% 0.20/0.66 Axiom 8 (ass(cond(140, 0), 0)): fresh40(greater(X, Y), true2, X, Y) = less(Y, X).
% 0.20/0.66 Axiom 9 (def(cond(conseq(axiom(3)), 12), 1)_1): fresh7(less(X, Y), true2, Y, X) = vplus(X, vd201(Y, X)).
% 0.20/0.66 Axiom 10 (holds(conjunct1(315), 514, 0)): greater(vmul(vd508, vd511), vmul(vd509, vd511)) = true2.
% 0.20/0.66 Axiom 11 (holds(conjunct2(315), 515, 1)): greater(vmul(vd511, vd509), vmul(vd512, vd509)) = true2.
% 0.20/0.66
% 0.20/0.66 Lemma 12: fresh40(X, X, Y, Z) = greater(vd508, vd509).
% 0.20/0.66 Proof:
% 0.20/0.66 fresh40(X, X, Y, Z)
% 0.20/0.66 = { by axiom 4 (ass(cond(140, 0), 0)) }
% 0.20/0.66 true2
% 0.20/0.66 = { by axiom 1 (holds(conjunct1(314), 510, 0)) R->L }
% 0.20/0.66 greater(vd508, vd509)
% 0.20/0.66
% 0.20/0.66 Lemma 13: greater(vmul(vd508, vd511), vmul(vd509, vd511)) = greater(vd508, vd509).
% 0.20/0.66 Proof:
% 0.20/0.66 greater(vmul(vd508, vd511), vmul(vd509, vd511))
% 0.20/0.66 = { by axiom 10 (holds(conjunct1(315), 514, 0)) }
% 0.20/0.66 true2
% 0.20/0.66 = { by axiom 1 (holds(conjunct1(314), 510, 0)) R->L }
% 0.20/0.66 greater(vd508, vd509)
% 0.20/0.66
% 0.20/0.66 Lemma 14: fresh40(greater(X, Y), greater(vd508, vd509), X, Y) = less(Y, X).
% 0.20/0.66 Proof:
% 0.20/0.66 fresh40(greater(X, Y), greater(vd508, vd509), X, Y)
% 0.20/0.66 = { by axiom 1 (holds(conjunct1(314), 510, 0)) }
% 0.20/0.66 fresh40(greater(X, Y), true2, X, Y)
% 0.20/0.66 = { by axiom 8 (ass(cond(140, 0), 0)) }
% 0.20/0.66 less(Y, X)
% 0.20/0.66
% 0.20/0.66 Lemma 15: fresh7(less(X, Y), greater(vd508, vd509), Y, X) = vplus(X, vd201(Y, X)).
% 0.20/0.66 Proof:
% 0.20/0.66 fresh7(less(X, Y), greater(vd508, vd509), Y, X)
% 0.20/0.66 = { by axiom 1 (holds(conjunct1(314), 510, 0)) }
% 0.20/0.66 fresh7(less(X, Y), true2, Y, X)
% 0.20/0.66 = { by axiom 9 (def(cond(conseq(axiom(3)), 12), 1)_1) }
% 0.20/0.66 vplus(X, vd201(Y, X))
% 0.20/0.66
% 0.20/0.66 Goal 1 (holds(conseq_conjunct2(315), 516, 0)): greater(vmul(vd508, vd511), vmul(vd509, vd512)) = true2.
% 0.20/0.66 Proof:
% 0.20/0.66 greater(vmul(vd508, vd511), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 5 (def(cond(conseq(axiom(3)), 12), 1)_1) R->L }
% 0.20/0.66 greater(fresh7(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vmul(vd508, vd511), vmul(vd509, vd511)), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 13 }
% 0.20/0.66 greater(fresh7(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vd508, vd509), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 13 }
% 0.20/0.66 greater(fresh7(greater(vd508, vd509), greater(vd508, vd509), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 12 R->L }
% 0.20/0.66 greater(fresh7(fresh40(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vmul(vd508, vd511), vmul(vd509, vd511)), vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd508, vd509), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 13 }
% 0.20/0.66 greater(fresh7(fresh40(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vd508, vd509), vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd508, vd509), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 2 (ass(cond(270, 0), 0)) }
% 0.20/0.66 greater(fresh7(fresh40(greater(vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd508, vd509), vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd508, vd509), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 14 }
% 0.20/0.66 greater(fresh7(less(vmul(vd511, vd509), vmul(vd508, vd511)), greater(vd508, vd509), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 greater(vplus(vmul(vd511, vd509), vd201(vmul(vd508, vd511), vmul(vd511, vd509))), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 3 (ass(cond(61, 0), 0)) R->L }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd511, vd509)), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 5 (def(cond(conseq(axiom(3)), 12), 1)_1) R->L }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vmul(vd508, vd511), vmul(vd509, vd511)), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 13 }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 13 }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(greater(vd508, vd509), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 12 R->L }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(fresh40(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vmul(vd508, vd511), vmul(vd509, vd511)), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 13 }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(fresh40(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 13 }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(fresh40(greater(vd508, vd509), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 1 (holds(conjunct1(314), 510, 0)) }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(fresh40(true2, greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 11 (holds(conjunct2(315), 515, 1)) R->L }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(fresh40(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 2 (ass(cond(270, 0), 0)) R->L }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(fresh40(greater(vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 14 }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh7(less(vmul(vd509, vd512), vmul(vd511, vd509)), greater(vd508, vd509), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
% 0.20/0.66 = { by lemma 15 }
% 0.20/0.66 greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), vplus(vmul(vd509, vd512), vd201(vmul(vd511, vd509), vmul(vd509, vd512)))), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 3 (ass(cond(61, 0), 0)) R->L }
% 0.20/0.66 greater(vplus(vplus(vmul(vd509, vd512), vd201(vmul(vd511, vd509), vmul(vd509, vd512))), vd201(vmul(vd508, vd511), vmul(vd511, vd509))), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 7 (ass(cond(33, 0), 0)) }
% 0.20/0.66 greater(vplus(vmul(vd509, vd512), vplus(vd201(vmul(vd511, vd509), vmul(vd509, vd512)), vd201(vmul(vd508, vd511), vmul(vd511, vd509)))), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 3 (ass(cond(61, 0), 0)) }
% 0.20/0.66 greater(vplus(vmul(vd509, vd512), vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), vd201(vmul(vd511, vd509), vmul(vd509, vd512)))), vmul(vd509, vd512))
% 0.20/0.66 = { by axiom 6 (ass(cond(189, 0), 0)) }
% 0.20/0.66 true2
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66
% 0.20/0.66 RESULT: Theorem (the conjecture is true).
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