TSTP Solution File: MGT017+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT017+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n016.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 09:17:01 EDT 2023
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT017+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:43:59 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 Take the following subset of the input axioms:
% 0.19/0.53 fof(a13_FOL, hypothesis, ![X, Y, C, I1, I2, Rt, Ta, Tb, Tc]: ((organization(X, Ta) & (organization(Y, Ta) & (organization(Y, Tc) & (class(X, C, Ta) & (class(Y, C, Ta) & (reorganization(X, Ta, Tb) & (reorganization(Y, Ta, Tc) & (reorganization_type(X, Rt, Ta) & (reorganization_type(Y, Rt, Ta) & (inertia(X, I1, Ta) & (inertia(Y, I2, Ta) & greater(I2, I1)))))))))))) => greater(Tc, Tb))).
% 0.19/0.53 fof(a5_FOL, hypothesis, ![S1, S2, T1, T2, X2, Y2, C2, I1_2, I2_2]: ((organization(X2, T1) & (organization(Y2, T2) & (class(X2, C2, T1) & (class(Y2, C2, T2) & (size(X2, S1, T1) & (size(Y2, S2, T2) & (inertia(X2, I1_2, T1) & (inertia(Y2, I2_2, T2) & greater(S2, S1))))))))) => greater(I2_2, I1_2))).
% 0.19/0.53 fof(mp5, axiom, ![T, X2]: (organization(X2, T) => ?[I]: inertia(X2, I, T))).
% 0.19/0.53 fof(t17_FOL, conjecture, ![X2, Y2, C2, S1_2, S2_2, Rt2, Ta2, Tb2, Tc2]: ((organization(X2, Ta2) & (organization(Y2, Ta2) & (organization(Y2, Tc2) & (class(X2, C2, Ta2) & (class(Y2, C2, Ta2) & (reorganization(X2, Ta2, Tb2) & (reorganization(Y2, Ta2, Tc2) & (reorganization_type(X2, Rt2, Ta2) & (reorganization_type(Y2, Rt2, Ta2) & (size(X2, S1_2, Ta2) & (size(Y2, S2_2, Ta2) & greater(S2_2, S1_2)))))))))))) => greater(Tc2, Tb2))).
% 0.19/0.53
% 0.19/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.53 fresh(y, y, x1...xn) = u
% 0.19/0.53 C => fresh(s, t, x1...xn) = v
% 0.19/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.53 variables of u and v.
% 0.19/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.53 input problem has no model of domain size 1).
% 0.19/0.53
% 0.19/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.53
% 0.19/0.53 Axiom 1 (t17_FOL_7): greater(s2, s1) = true.
% 0.19/0.53 Axiom 2 (t17_FOL): organization(x, ta) = true.
% 0.19/0.53 Axiom 3 (t17_FOL_2): organization(y, tc) = true.
% 0.19/0.53 Axiom 4 (t17_FOL_1): organization(y, ta) = true.
% 0.19/0.53 Axiom 5 (t17_FOL_5): size(x, s1, ta) = true.
% 0.19/0.53 Axiom 6 (t17_FOL_6): size(y, s2, ta) = true.
% 0.19/0.53 Axiom 7 (t17_FOL_8): reorganization(x, ta, tb) = true.
% 0.19/0.53 Axiom 8 (t17_FOL_9): reorganization(y, ta, tc) = true.
% 0.19/0.53 Axiom 9 (t17_FOL_10): reorganization_type(x, rt, ta) = true.
% 0.19/0.53 Axiom 10 (t17_FOL_11): reorganization_type(y, rt, ta) = true.
% 0.19/0.53 Axiom 11 (t17_FOL_3): class(x, c, ta) = true.
% 0.19/0.53 Axiom 12 (t17_FOL_4): class(y, c, ta) = true.
% 0.19/0.53 Axiom 13 (mp5): fresh(X, X, Y, Z) = true.
% 0.19/0.53 Axiom 14 (a5_FOL): fresh22(X, X, Y, Z) = true.
% 0.19/0.53 Axiom 15 (a13_FOL): fresh13(X, X, Y, Z) = true.
% 0.19/0.53 Axiom 16 (mp5): fresh(organization(X, Y), true, X, Y) = inertia(X, i(X, Y), Y).
% 0.19/0.53 Axiom 17 (a5_FOL): fresh20(X, X, Y, Z, W, V) = greater(W, Z).
% 0.19/0.53 Axiom 18 (a13_FOL): fresh11(X, X, Y, Z, W, V) = greater(V, W).
% 0.19/0.53 Axiom 19 (a13_FOL): fresh12(X, X, Y, Z, W, V, U) = fresh13(organization(Y, W), true, V, U).
% 0.19/0.53 Axiom 20 (a5_FOL): fresh21(X, X, Y, Z, W, V, U, T) = fresh22(organization(Y, T), true, W, V).
% 0.19/0.53 Axiom 21 (a5_FOL): fresh19(X, X, Y, Z, W, V, U, T) = fresh20(organization(Z, U), true, Y, W, V, T).
% 0.19/0.53 Axiom 22 (a13_FOL): fresh10(X, X, Y, Z, W, V, U) = fresh11(organization(Z, W), true, Y, W, V, U).
% 0.19/0.53 Axiom 23 (a13_FOL): fresh9(X, X, Y, Z, W, V, U, T) = fresh12(organization(Z, T), true, Y, Z, V, U, T).
% 0.19/0.53 Axiom 24 (a13_FOL): fresh8(X, X, Y, Z, W, V, U, T, S) = fresh10(inertia(Y, W, U), true, Y, Z, U, T, S).
% 0.19/0.53 Axiom 25 (a5_FOL): fresh18(X, X, Y, Z, W, V, U, T) = fresh21(inertia(Y, W, T), true, Y, Z, W, V, U, T).
% 0.19/0.53 Axiom 26 (a5_FOL): fresh17(X, X, Y, Z, W, V, U, T, S) = fresh19(inertia(Z, U, T), true, Y, Z, V, U, T, S).
% 0.19/0.53 Axiom 27 (a5_FOL): fresh16(X, X, Y, Z, W, V, U, T, S) = fresh18(class(Y, W, S), true, Y, Z, V, U, T, S).
% 0.19/0.53 Axiom 28 (a13_FOL): fresh7(X, X, Y, Z, W, V, U, T, S, X2) = fresh9(inertia(Z, U, T), true, Y, Z, V, T, S, X2).
% 0.19/0.53 Axiom 29 (a5_FOL): fresh15(X, X, Y, Z, W, V, U, T, S, X2) = fresh17(class(Z, W, S), true, Y, Z, W, U, T, S, X2).
% 0.19/0.53 Axiom 30 (a5_FOL): fresh14(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh16(size(Y, V, Y2), true, Y, Z, W, T, S, X2, Y2).
% 0.19/0.53 Axiom 31 (a13_FOL): fresh6(X, X, Y, Z, W, V, U, T, S, X2) = fresh8(class(Y, W, T), true, Y, Z, V, U, T, S, X2).
% 0.19/0.53 Axiom 32 (a13_FOL): fresh5(X, X, Y, Z, W, V, U, T, S, X2) = fresh6(greater(U, V), true, Y, Z, W, V, U, T, S, X2).
% 0.19/0.53 Axiom 33 (a5_FOL): fresh14(greater(X, Y), true, Z, W, V, Y, X, U, T, S, X2) = fresh15(size(W, X, S), true, Z, W, V, Y, U, T, S, X2).
% 0.19/0.53 Axiom 34 (a13_FOL): fresh4(X, X, Y, Z, W, V, U, T, S, X2) = fresh7(class(Z, W, T), true, Y, Z, W, V, U, T, S, X2).
% 0.19/0.53 Axiom 35 (a13_FOL): fresh3(X, X, Y, Z, W, V, U, T, S, X2) = fresh5(reorganization(Y, T, S), true, Y, Z, W, V, U, T, S, X2).
% 0.19/0.53 Axiom 36 (a13_FOL): fresh2(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh4(reorganization(Z, S, Y2), true, Y, Z, V, U, T, S, X2, Y2).
% 0.19/0.53 Axiom 37 (a13_FOL): fresh2(reorganization_type(X, Y, Z), true, W, X, Y, V, U, T, Z, S, X2) = fresh3(reorganization_type(W, Y, Z), true, W, X, V, U, T, Z, S, X2).
% 0.19/0.53
% 0.19/0.53 Lemma 38: inertia(x, i(x, ta), ta) = true.
% 0.19/0.53 Proof:
% 0.19/0.53 inertia(x, i(x, ta), ta)
% 0.19/0.53 = { by axiom 16 (mp5) R->L }
% 0.19/0.53 fresh(organization(x, ta), true, x, ta)
% 0.19/0.53 = { by axiom 2 (t17_FOL) }
% 0.19/0.53 fresh(true, true, x, ta)
% 0.19/0.53 = { by axiom 13 (mp5) }
% 0.19/0.53 true
% 0.19/0.53
% 0.19/0.53 Lemma 39: inertia(y, i(y, ta), ta) = true.
% 0.19/0.53 Proof:
% 0.19/0.53 inertia(y, i(y, ta), ta)
% 0.19/0.53 = { by axiom 16 (mp5) R->L }
% 0.19/0.53 fresh(organization(y, ta), true, y, ta)
% 0.19/0.53 = { by axiom 4 (t17_FOL_1) }
% 0.19/0.53 fresh(true, true, y, ta)
% 0.19/0.53 = { by axiom 13 (mp5) }
% 0.19/0.53 true
% 0.19/0.53
% 0.19/0.53 Goal 1 (t17_FOL_12): greater(tc, tb) = true.
% 0.19/0.53 Proof:
% 0.19/0.53 greater(tc, tb)
% 0.19/0.53 = { by axiom 18 (a13_FOL) R->L }
% 0.19/0.53 fresh11(true, true, x, ta, tb, tc)
% 0.19/0.53 = { by axiom 4 (t17_FOL_1) R->L }
% 0.19/0.53 fresh11(organization(y, ta), true, x, ta, tb, tc)
% 0.19/0.53 = { by axiom 22 (a13_FOL) R->L }
% 0.19/0.53 fresh10(true, true, x, y, ta, tb, tc)
% 0.19/0.53 = { by lemma 38 R->L }
% 0.19/0.53 fresh10(inertia(x, i(x, ta), ta), true, x, y, ta, tb, tc)
% 0.19/0.53 = { by axiom 24 (a13_FOL) R->L }
% 0.19/0.53 fresh8(true, true, x, y, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 11 (t17_FOL_3) R->L }
% 0.19/0.53 fresh8(class(x, c, ta), true, x, y, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 31 (a13_FOL) R->L }
% 0.19/0.53 fresh6(true, true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 14 (a5_FOL) R->L }
% 0.19/0.53 fresh6(fresh22(true, true, i(x, ta), i(y, ta)), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 2 (t17_FOL) R->L }
% 0.19/0.53 fresh6(fresh22(organization(x, ta), true, i(x, ta), i(y, ta)), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 20 (a5_FOL) R->L }
% 0.19/0.53 fresh6(fresh21(true, true, x, y, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by lemma 38 R->L }
% 0.19/0.53 fresh6(fresh21(inertia(x, i(x, ta), ta), true, x, y, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 25 (a5_FOL) R->L }
% 0.19/0.53 fresh6(fresh18(true, true, x, y, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 11 (t17_FOL_3) R->L }
% 0.19/0.53 fresh6(fresh18(class(x, c, ta), true, x, y, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 27 (a5_FOL) R->L }
% 0.19/0.53 fresh6(fresh16(true, true, x, y, c, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 5 (t17_FOL_5) R->L }
% 0.19/0.53 fresh6(fresh16(size(x, s1, ta), true, x, y, c, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 30 (a5_FOL) R->L }
% 0.19/0.53 fresh6(fresh14(true, true, x, y, c, s1, s2, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 1 (t17_FOL_7) R->L }
% 0.19/0.53 fresh6(fresh14(greater(s2, s1), true, x, y, c, s1, s2, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 33 (a5_FOL) }
% 0.19/0.53 fresh6(fresh15(size(y, s2, ta), true, x, y, c, s1, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 6 (t17_FOL_6) }
% 0.19/0.53 fresh6(fresh15(true, true, x, y, c, s1, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 29 (a5_FOL) }
% 0.19/0.53 fresh6(fresh17(class(y, c, ta), true, x, y, c, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 12 (t17_FOL_4) }
% 0.19/0.53 fresh6(fresh17(true, true, x, y, c, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 26 (a5_FOL) }
% 0.19/0.53 fresh6(fresh19(inertia(y, i(y, ta), ta), true, x, y, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by lemma 39 }
% 0.19/0.53 fresh6(fresh19(true, true, x, y, i(x, ta), i(y, ta), ta, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 21 (a5_FOL) }
% 0.19/0.53 fresh6(fresh20(organization(y, ta), true, x, i(x, ta), i(y, ta), ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 4 (t17_FOL_1) }
% 0.19/0.53 fresh6(fresh20(true, true, x, i(x, ta), i(y, ta), ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 17 (a5_FOL) }
% 0.19/0.53 fresh6(greater(i(y, ta), i(x, ta)), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 32 (a13_FOL) R->L }
% 0.19/0.53 fresh5(true, true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 7 (t17_FOL_8) R->L }
% 0.19/0.53 fresh5(reorganization(x, ta, tb), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 35 (a13_FOL) R->L }
% 0.19/0.53 fresh3(true, true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 9 (t17_FOL_10) R->L }
% 0.19/0.53 fresh3(reorganization_type(x, rt, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 37 (a13_FOL) R->L }
% 0.19/0.53 fresh2(reorganization_type(y, rt, ta), true, x, y, rt, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 10 (t17_FOL_11) }
% 0.19/0.53 fresh2(true, true, x, y, rt, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 36 (a13_FOL) }
% 0.19/0.53 fresh4(reorganization(y, ta, tc), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 8 (t17_FOL_9) }
% 0.19/0.53 fresh4(true, true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 34 (a13_FOL) }
% 0.19/0.53 fresh7(class(y, c, ta), true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 12 (t17_FOL_4) }
% 0.19/0.53 fresh7(true, true, x, y, c, i(x, ta), i(y, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 28 (a13_FOL) }
% 0.19/0.53 fresh9(inertia(y, i(y, ta), ta), true, x, y, i(x, ta), ta, tb, tc)
% 0.19/0.53 = { by lemma 39 }
% 0.19/0.53 fresh9(true, true, x, y, i(x, ta), ta, tb, tc)
% 0.19/0.53 = { by axiom 23 (a13_FOL) }
% 0.19/0.53 fresh12(organization(y, tc), true, x, y, ta, tb, tc)
% 0.19/0.53 = { by axiom 3 (t17_FOL_2) }
% 0.19/0.53 fresh12(true, true, x, y, ta, tb, tc)
% 0.19/0.53 = { by axiom 19 (a13_FOL) }
% 0.19/0.53 fresh13(organization(x, ta), true, tb, tc)
% 0.19/0.53 = { by axiom 2 (t17_FOL) }
% 0.19/0.53 fresh13(true, true, tb, tc)
% 0.19/0.53 = { by axiom 15 (a13_FOL) }
% 0.19/0.53 true
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53
% 0.19/0.53 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------