TSTP Solution File: NUM852+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUM852+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 : n015.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 11:58:39 EDT 2023
% Result : Theorem 0.20s 0.50s
% 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 : NUM852+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 : n015.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 17:40:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.50
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 Take the following subset of the input axioms:
% 0.20/0.51 fof('ass(cond(189, 0), 0)', axiom, ![Vd295, Vd296]: greater(vplus(Vd295, Vd296), Vd295)).
% 0.20/0.51 fof('ass(cond(270, 0), 0)', axiom, ![Vd418, Vd419]: vmul(Vd418, Vd419)=vmul(Vd419, Vd418)).
% 0.20/0.51 fof('ass(cond(281, 0), 0)', axiom, ![Vd432, Vd433, Vd434]: vmul(Vd432, vplus(Vd433, Vd434))=vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))).
% 0.20/0.51 fof('ass(cond(302, 0), 2)', axiom, ![Vd470, Vd471]: (greater(Vd470, Vd471) => vmul(Vd470, vd469)=vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469))).
% 0.20/0.51 fof('holds(conseq_conjunct1(conseq(304)), 483, 0)', axiom, greater(vd481, vd480)).
% 0.20/0.51 fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)', conjecture, greater(vmul(vd481, vd469), vmul(vd480, vd469))).
% 0.20/0.51
% 0.20/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.51 fresh(y, y, x1...xn) = u
% 0.20/0.51 C => fresh(s, t, x1...xn) = v
% 0.20/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.51 variables of u and v.
% 0.20/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.51 input problem has no model of domain size 1).
% 0.20/0.51
% 0.20/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.51
% 0.20/0.51 Axiom 1 (ass(cond(270, 0), 0)): vmul(X, Y) = vmul(Y, X).
% 0.20/0.51 Axiom 2 (holds(conseq_conjunct1(conseq(304)), 483, 0)): greater(vd481, vd480) = true2.
% 0.20/0.51 Axiom 3 (ass(cond(302, 0), 2)): fresh24(X, X, Y, Z) = vmul(Y, vd469).
% 0.20/0.51 Axiom 4 (ass(cond(189, 0), 0)): greater(vplus(X, Y), X) = true2.
% 0.20/0.51 Axiom 5 (ass(cond(302, 0), 2)): fresh24(greater(X, Y), true2, X, Y) = vmul(vplus(Y, vskolem9(X, Y)), vd469).
% 0.20/0.51 Axiom 6 (ass(cond(281, 0), 0)): vmul(X, vplus(Y, Z)) = vplus(vmul(X, Y), vmul(X, Z)).
% 0.20/0.51
% 0.20/0.51 Goal 1 (holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)): greater(vmul(vd481, vd469), vmul(vd480, vd469)) = true2.
% 0.20/0.51 Proof:
% 0.20/0.51 greater(vmul(vd481, vd469), vmul(vd480, vd469))
% 0.20/0.51 = { by axiom 1 (ass(cond(270, 0), 0)) R->L }
% 0.20/0.51 greater(vmul(vd481, vd469), vmul(vd469, vd480))
% 0.20/0.51 = { by axiom 3 (ass(cond(302, 0), 2)) R->L }
% 0.20/0.51 greater(fresh24(true2, true2, vd481, vd480), vmul(vd469, vd480))
% 0.20/0.51 = { by axiom 2 (holds(conseq_conjunct1(conseq(304)), 483, 0)) R->L }
% 0.20/0.51 greater(fresh24(greater(vd481, vd480), true2, vd481, vd480), vmul(vd469, vd480))
% 0.20/0.51 = { by axiom 5 (ass(cond(302, 0), 2)) }
% 0.20/0.51 greater(vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469), vmul(vd469, vd480))
% 0.20/0.51 = { by axiom 1 (ass(cond(270, 0), 0)) }
% 0.20/0.51 greater(vmul(vd469, vplus(vd480, vskolem9(vd481, vd480))), vmul(vd469, vd480))
% 0.20/0.51 = { by axiom 6 (ass(cond(281, 0), 0)) }
% 0.20/0.51 greater(vplus(vmul(vd469, vd480), vmul(vd469, vskolem9(vd481, vd480))), vmul(vd469, vd480))
% 0.20/0.51 = { by axiom 4 (ass(cond(189, 0), 0)) }
% 0.20/0.51 true2
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51
% 0.20/0.51 RESULT: Theorem (the conjecture is true).
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