TSTP Solution File: MGT008+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT008+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 : n024.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 09:16:57 EDT 2023
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT008+1 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.13 % 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 : n024.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 : Mon Aug 28 06:06:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.44 Command-line arguments: --no-flatten-goal
% 0.20/0.44
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 Take the following subset of the input axioms:
% 0.20/0.48 fof(a5_FOL, hypothesis, ![X, Y, C, S1, S2, I1, I2, T1, T2]: ((organization(X, T1) & (organization(Y, T2) & (class(X, C, T1) & (class(Y, C, T2) & (size(X, S1, T1) & (size(Y, S2, T2) & (inertia(X, I1, T1) & (inertia(Y, I2, T2) & greater(S2, S1))))))))) => greater(I2, I1))).
% 0.20/0.48 fof(mp5, axiom, ![T, X2]: (organization(X2, T) => ?[I]: inertia(X2, I, T))).
% 0.20/0.48 fof(t1_FOL, hypothesis, ![P1, P2, X2, Y2, T1_2, T2_2, I1_2, I2_2]: ((organization(X2, T1_2) & (organization(Y2, T2_2) & (reorganization_free(X2, T1_2, T1_2) & (reorganization_free(Y2, T2_2, T2_2) & (inertia(X2, I1_2, T1_2) & (inertia(Y2, I2_2, T2_2) & (survival_chance(X2, P1, T1_2) & (survival_chance(Y2, P2, T2_2) & greater(I2_2, I1_2))))))))) => greater(P2, P1))).
% 0.20/0.48 fof(t8_FOL, conjecture, ![X2, Y2, C2, S1_2, S2_2, T1_2, T2_2, P1_2, P2_2]: ((organization(X2, T1_2) & (organization(Y2, T2_2) & (reorganization_free(X2, T1_2, T1_2) & (reorganization_free(Y2, T2_2, T2_2) & (class(X2, C2, T1_2) & (class(Y2, C2, T2_2) & (survival_chance(X2, P1_2, T1_2) & (survival_chance(Y2, P2_2, T2_2) & (size(X2, S1_2, T1_2) & (size(Y2, S2_2, T2_2) & greater(S2_2, S1_2))))))))))) => greater(P2_2, P1_2))).
% 0.20/0.48
% 0.20/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.48 fresh(y, y, x1...xn) = u
% 0.20/0.48 C => fresh(s, t, x1...xn) = v
% 0.20/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.48 variables of u and v.
% 0.20/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.48 input problem has no model of domain size 1).
% 0.20/0.48
% 0.20/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.48
% 0.20/0.48 Axiom 1 (t8_FOL_6): greater(s2, s1) = true.
% 0.20/0.48 Axiom 2 (t8_FOL): organization(x, t1) = true.
% 0.20/0.48 Axiom 3 (t8_FOL_1): organization(y, t2) = true.
% 0.20/0.48 Axiom 4 (t8_FOL_2): class(x, c, t1) = true.
% 0.20/0.48 Axiom 5 (t8_FOL_3): class(y, c, t2) = true.
% 0.20/0.48 Axiom 6 (t8_FOL_4): size(x, s1, t1) = true.
% 0.20/0.48 Axiom 7 (t8_FOL_5): size(y, s2, t2) = true.
% 0.20/0.48 Axiom 8 (t8_FOL_7): reorganization_free(x, t1, t1) = true.
% 0.20/0.48 Axiom 9 (t8_FOL_8): reorganization_free(y, t2, t2) = true.
% 0.20/0.48 Axiom 10 (t8_FOL_9): survival_chance(x, p1, t1) = true.
% 0.20/0.48 Axiom 11 (t8_FOL_10): survival_chance(y, p2, t2) = true.
% 0.20/0.48 Axiom 12 (mp5): fresh(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 13 (a5_FOL): fresh19(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 14 (t1_FOL): fresh10(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 15 (mp5): fresh(organization(X, Y), true, X, Y) = inertia(X, i(X, Y), Y).
% 0.20/0.48 Axiom 16 (a5_FOL): fresh17(X, X, Y, Z, W, V) = greater(W, Z).
% 0.20/0.48 Axiom 17 (t1_FOL): fresh8(X, X, Y, Z, W, V) = greater(W, Z).
% 0.20/0.48 Axiom 18 (a5_FOL): fresh18(X, X, Y, Z, W, V, U, T) = fresh19(organization(Y, T), true, W, V).
% 0.20/0.49 Axiom 19 (a5_FOL): fresh16(X, X, Y, Z, W, V, U, T) = fresh17(organization(Z, U), true, Y, W, V, T).
% 0.20/0.49 Axiom 20 (t1_FOL): fresh9(X, X, Y, Z, W, V, U, T) = fresh10(organization(Y, T), true, V, U).
% 0.20/0.49 Axiom 21 (t1_FOL): fresh7(X, X, Y, Z, W, V, U, T, S) = fresh8(organization(Z, W), true, Y, U, T, S).
% 0.20/0.49 Axiom 22 (a5_FOL): fresh15(X, X, Y, Z, W, V, U, T) = fresh18(inertia(Y, W, T), true, Y, Z, W, V, U, T).
% 0.20/0.49 Axiom 23 (a5_FOL): fresh14(X, X, Y, Z, W, V, U, T, S) = fresh16(inertia(Z, U, T), true, Y, Z, V, U, T, S).
% 0.20/0.49 Axiom 24 (a5_FOL): fresh13(X, X, Y, Z, W, V, U, T, S) = fresh15(class(Y, W, S), true, Y, Z, V, U, T, S).
% 0.20/0.49 Axiom 25 (t1_FOL): fresh6(X, X, Y, Z, W, V, U, T, S, X2) = fresh9(inertia(Y, V, X2), true, Y, Z, W, T, S, X2).
% 0.20/0.49 Axiom 26 (a5_FOL): fresh12(X, X, Y, Z, W, V, U, T, S, X2) = fresh14(class(Z, W, S), true, Y, Z, W, U, T, S, X2).
% 0.20/0.49 Axiom 27 (a5_FOL): fresh11(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh13(size(Y, V, Y2), true, Y, Z, W, T, S, X2, Y2).
% 0.20/0.49 Axiom 28 (t1_FOL): fresh5(X, X, Y, Z, W, V, U, T, S, X2) = fresh7(inertia(Z, U, W), true, Y, Z, W, V, T, S, X2).
% 0.20/0.49 Axiom 29 (t1_FOL): fresh4(X, X, Y, Z, W, V, U, T, S, X2) = fresh6(greater(U, V), true, Y, Z, W, V, U, T, S, X2).
% 0.20/0.49 Axiom 30 (a5_FOL): fresh11(greater(X, Y), true, Z, W, V, Y, X, U, T, S, X2) = fresh12(size(W, X, S), true, Z, W, V, Y, U, T, S, X2).
% 0.20/0.49 Axiom 31 (t1_FOL): fresh3(X, X, Y, Z, W, V, U, T, S, X2) = fresh5(reorganization_free(Y, X2, X2), true, Y, Z, W, V, U, T, S, X2).
% 0.20/0.49 Axiom 32 (t1_FOL): fresh2(X, X, Y, Z, W, V, U, T, S, X2) = fresh4(reorganization_free(Z, W, W), true, Y, Z, W, V, U, T, S, X2).
% 0.20/0.49 Axiom 33 (t1_FOL): fresh2(survival_chance(X, Y, Z), true, W, X, Z, V, U, T, Y, S) = fresh3(survival_chance(W, T, S), true, W, X, Z, V, U, T, Y, S).
% 0.20/0.49
% 0.20/0.49 Lemma 34: inertia(x, i(x, t1), t1) = true.
% 0.20/0.49 Proof:
% 0.20/0.49 inertia(x, i(x, t1), t1)
% 0.20/0.49 = { by axiom 15 (mp5) R->L }
% 0.20/0.49 fresh(organization(x, t1), true, x, t1)
% 0.20/0.49 = { by axiom 2 (t8_FOL) }
% 0.20/0.49 fresh(true, true, x, t1)
% 0.20/0.49 = { by axiom 12 (mp5) }
% 0.20/0.49 true
% 0.20/0.49
% 0.20/0.49 Lemma 35: inertia(y, i(y, t2), t2) = true.
% 0.20/0.49 Proof:
% 0.20/0.49 inertia(y, i(y, t2), t2)
% 0.20/0.49 = { by axiom 15 (mp5) R->L }
% 0.20/0.49 fresh(organization(y, t2), true, y, t2)
% 0.20/0.49 = { by axiom 3 (t8_FOL_1) }
% 0.20/0.49 fresh(true, true, y, t2)
% 0.20/0.49 = { by axiom 12 (mp5) }
% 0.20/0.49 true
% 0.20/0.49
% 0.20/0.49 Goal 1 (t8_FOL_11): greater(p2, p1) = true.
% 0.20/0.49 Proof:
% 0.20/0.49 greater(p2, p1)
% 0.20/0.49 = { by axiom 17 (t1_FOL) R->L }
% 0.20/0.49 fresh8(true, true, x, p1, p2, t1)
% 0.20/0.49 = { by axiom 3 (t8_FOL_1) R->L }
% 0.20/0.49 fresh8(organization(y, t2), true, x, p1, p2, t1)
% 0.20/0.49 = { by axiom 21 (t1_FOL) R->L }
% 0.20/0.49 fresh7(true, true, x, y, t2, i(x, t1), p1, p2, t1)
% 0.20/0.49 = { by lemma 35 R->L }
% 0.20/0.49 fresh7(inertia(y, i(y, t2), t2), true, x, y, t2, i(x, t1), p1, p2, t1)
% 0.20/0.49 = { by axiom 28 (t1_FOL) R->L }
% 0.20/0.49 fresh5(true, true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 8 (t8_FOL_7) R->L }
% 0.20/0.49 fresh5(reorganization_free(x, t1, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 31 (t1_FOL) R->L }
% 0.20/0.49 fresh3(true, true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 10 (t8_FOL_9) R->L }
% 0.20/0.49 fresh3(survival_chance(x, p1, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 33 (t1_FOL) R->L }
% 0.20/0.49 fresh2(survival_chance(y, p2, t2), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 11 (t8_FOL_10) }
% 0.20/0.49 fresh2(true, true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 32 (t1_FOL) }
% 0.20/0.49 fresh4(reorganization_free(y, t2, t2), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 9 (t8_FOL_8) }
% 0.20/0.49 fresh4(true, true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 29 (t1_FOL) }
% 0.20/0.49 fresh6(greater(i(y, t2), i(x, t1)), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 16 (a5_FOL) R->L }
% 0.20/0.49 fresh6(fresh17(true, true, x, i(x, t1), i(y, t2), t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 3 (t8_FOL_1) R->L }
% 0.20/0.49 fresh6(fresh17(organization(y, t2), true, x, i(x, t1), i(y, t2), t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 19 (a5_FOL) R->L }
% 0.20/0.49 fresh6(fresh16(true, true, x, y, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by lemma 35 R->L }
% 0.20/0.49 fresh6(fresh16(inertia(y, i(y, t2), t2), true, x, y, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 23 (a5_FOL) R->L }
% 0.20/0.49 fresh6(fresh14(true, true, x, y, c, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 5 (t8_FOL_3) R->L }
% 0.20/0.49 fresh6(fresh14(class(y, c, t2), true, x, y, c, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 26 (a5_FOL) R->L }
% 0.20/0.49 fresh6(fresh12(true, true, x, y, c, s1, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 7 (t8_FOL_5) R->L }
% 0.20/0.49 fresh6(fresh12(size(y, s2, t2), true, x, y, c, s1, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 30 (a5_FOL) R->L }
% 0.20/0.49 fresh6(fresh11(greater(s2, s1), true, x, y, c, s1, s2, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 1 (t8_FOL_6) }
% 0.20/0.49 fresh6(fresh11(true, true, x, y, c, s1, s2, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 27 (a5_FOL) }
% 0.20/0.49 fresh6(fresh13(size(x, s1, t1), true, x, y, c, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 6 (t8_FOL_4) }
% 0.20/0.49 fresh6(fresh13(true, true, x, y, c, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 24 (a5_FOL) }
% 0.20/0.49 fresh6(fresh15(class(x, c, t1), true, x, y, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 4 (t8_FOL_2) }
% 0.20/0.49 fresh6(fresh15(true, true, x, y, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 22 (a5_FOL) }
% 0.20/0.49 fresh6(fresh18(inertia(x, i(x, t1), t1), true, x, y, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by lemma 34 }
% 0.20/0.49 fresh6(fresh18(true, true, x, y, i(x, t1), i(y, t2), t2, t1), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 18 (a5_FOL) }
% 0.20/0.49 fresh6(fresh19(organization(x, t1), true, i(x, t1), i(y, t2)), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 2 (t8_FOL) }
% 0.20/0.49 fresh6(fresh19(true, true, i(x, t1), i(y, t2)), true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 13 (a5_FOL) }
% 0.20/0.49 fresh6(true, true, x, y, t2, i(x, t1), i(y, t2), p1, p2, t1)
% 0.20/0.49 = { by axiom 25 (t1_FOL) }
% 0.20/0.49 fresh9(inertia(x, i(x, t1), t1), true, x, y, t2, p1, p2, t1)
% 0.20/0.49 = { by lemma 34 }
% 0.20/0.49 fresh9(true, true, x, y, t2, p1, p2, t1)
% 0.20/0.49 = { by axiom 20 (t1_FOL) }
% 0.20/0.49 fresh10(organization(x, t1), true, p1, p2)
% 0.20/0.49 = { by axiom 2 (t8_FOL) }
% 0.20/0.49 fresh10(true, true, p1, p2)
% 0.20/0.49 = { by axiom 14 (t1_FOL) }
% 0.20/0.49 true
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49
% 0.20/0.49 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------