TSTP Solution File: MGT003+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT003+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 : n002.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 09:16:55 EDT 2023
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT003+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.13 % 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 : n002.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 06:35:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.42 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.42
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 Take the following subset of the input axioms:
% 0.19/0.44 fof(mp4, axiom, ![X, T1, T2]: (reorganization_free(X, T1, T2) => (reorganization_free(X, T1, T1) & reorganization_free(X, T2, T2)))).
% 0.19/0.44 fof(mp5, axiom, ![T, X2]: (organization(X2, T) => ?[I]: inertia(X2, I, T))).
% 0.19/0.44 fof(t1_FOL, hypothesis, ![Y, I1, I2, P1, P2, X2, T1_2, T2_2]: ((organization(X2, T1_2) & (organization(Y, T2_2) & (reorganization_free(X2, T1_2, T1_2) & (reorganization_free(Y, T2_2, T2_2) & (inertia(X2, I1, T1_2) & (inertia(Y, I2, T2_2) & (survival_chance(X2, P1, T1_2) & (survival_chance(Y, P2, T2_2) & greater(I2, I1))))))))) => greater(P2, P1))).
% 0.19/0.44 fof(t2_FOL, hypothesis, ![X2, T1_2, T2_2, I1_2, I2_2]: ((organization(X2, T1_2) & (organization(X2, T2_2) & (reorganization_free(X2, T1_2, T2_2) & (inertia(X2, I1_2, T1_2) & (inertia(X2, I2_2, T2_2) & greater(T2_2, T1_2)))))) => greater(I2_2, I1_2))).
% 0.19/0.44 fof(t3_FOL, conjecture, ![X2, T1_2, T2_2, P1_2, P2_2]: ((organization(X2, T1_2) & (organization(X2, T2_2) & (reorganization_free(X2, T1_2, T2_2) & (survival_chance(X2, P1_2, T1_2) & (survival_chance(X2, P2_2, T2_2) & greater(T2_2, T1_2)))))) => greater(P2_2, P1_2))).
% 0.19/0.44
% 0.19/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.44 fresh(y, y, x1...xn) = u
% 0.19/0.44 C => fresh(s, t, x1...xn) = v
% 0.19/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.44 variables of u and v.
% 0.19/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.44 input problem has no model of domain size 1).
% 0.19/0.44
% 0.19/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.44
% 0.19/0.44 Axiom 1 (t3_FOL_5): greater(t2, t1) = true.
% 0.19/0.44 Axiom 2 (t3_FOL_1): organization(x, t1) = true.
% 0.19/0.44 Axiom 3 (t3_FOL_2): organization(x, t2) = true.
% 0.19/0.44 Axiom 4 (t3_FOL_3): survival_chance(x, p1, t1) = true.
% 0.19/0.44 Axiom 5 (t3_FOL_4): survival_chance(x, p2, t2) = true.
% 0.19/0.44 Axiom 6 (t3_FOL): reorganization_free(x, t1, t2) = true.
% 0.19/0.44 Axiom 7 (mp5): fresh(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 8 (t1_FOL): fresh18(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 9 (t2_FOL): fresh9(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 10 (mp4_1): fresh3(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 11 (mp4): fresh2(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 12 (mp5): fresh(organization(X, Y), true, X, Y) = inertia(X, i(X, Y), Y).
% 0.19/0.44 Axiom 13 (t1_FOL): fresh16(X, X, Y, Z, W, V) = greater(W, Z).
% 0.19/0.44 Axiom 14 (t2_FOL): fresh8(X, X, Y, Z, W, V, U) = fresh9(reorganization_free(Y, V, U), true, Z, W).
% 0.19/0.44 Axiom 15 (t2_FOL): fresh7(X, X, Y, Z, W, V, U) = greater(W, Z).
% 0.19/0.44 Axiom 16 (mp4_1): fresh3(reorganization_free(X, Y, Z), true, X, Z) = reorganization_free(X, Z, Z).
% 0.19/0.44 Axiom 17 (mp4): fresh2(reorganization_free(X, Y, Z), true, X, Y) = reorganization_free(X, Y, Y).
% 0.19/0.44 Axiom 18 (t1_FOL): fresh17(X, X, Y, Z, W, V, U, T) = fresh18(reorganization_free(Y, T, T), true, V, U).
% 0.19/0.44 Axiom 19 (t1_FOL): fresh15(X, X, Y, Z, W, V, U, T) = fresh16(reorganization_free(Z, W, W), true, Y, V, U, T).
% 0.19/0.44 Axiom 20 (t2_FOL): fresh5(X, X, Y, Z, W, V, U) = fresh8(organization(Y, U), true, Y, Z, W, V, U).
% 0.19/0.44 Axiom 21 (t2_FOL): fresh6(X, X, Y, Z, W, V, U) = fresh7(organization(Y, V), true, Y, Z, W, V, U).
% 0.19/0.44 Axiom 22 (t1_FOL): fresh14(X, X, Y, Z, W, V, U, T) = fresh17(organization(Y, T), true, Y, Z, W, V, U, T).
% 0.19/0.44 Axiom 23 (t1_FOL): fresh13(X, X, Y, Z, W, V, U, T, S) = fresh15(organization(Z, W), true, Y, Z, W, U, T, S).
% 0.19/0.44 Axiom 24 (t2_FOL): fresh4(X, X, Y, Z, W, V, U) = fresh6(inertia(Y, Z, V), true, Y, Z, W, V, U).
% 0.19/0.44 Axiom 25 (t2_FOL): fresh4(greater(X, Y), true, Z, W, V, Y, X) = fresh5(inertia(Z, V, X), true, Z, W, V, Y, X).
% 0.19/0.44 Axiom 26 (t1_FOL): fresh12(X, X, Y, Z, W, V, U, T, S, X2) = fresh14(inertia(Y, V, X2), true, Y, Z, W, T, S, X2).
% 0.19/0.44 Axiom 27 (t1_FOL): fresh11(X, X, Y, Z, W, V, U, T, S, X2) = fresh13(inertia(Z, U, W), true, Y, Z, W, V, T, S, X2).
% 0.19/0.44 Axiom 28 (t1_FOL): fresh10(X, X, Y, Z, W, V, U, T, S, X2) = fresh12(survival_chance(Y, T, X2), true, Y, Z, W, V, U, T, S, X2).
% 0.19/0.44 Axiom 29 (t1_FOL): fresh10(greater(X, Y), true, Z, W, V, Y, X, U, T, S) = fresh11(survival_chance(W, T, V), true, Z, W, V, Y, X, U, T, S).
% 0.19/0.44
% 0.19/0.44 Lemma 30: inertia(x, i(x, t1), t1) = true.
% 0.19/0.44 Proof:
% 0.19/0.44 inertia(x, i(x, t1), t1)
% 0.19/0.44 = { by axiom 12 (mp5) R->L }
% 0.19/0.44 fresh(organization(x, t1), true, x, t1)
% 0.19/0.44 = { by axiom 2 (t3_FOL_1) }
% 0.19/0.44 fresh(true, true, x, t1)
% 0.19/0.44 = { by axiom 7 (mp5) }
% 0.19/0.44 true
% 0.19/0.44
% 0.19/0.44 Lemma 31: inertia(x, i(x, t2), t2) = true.
% 0.19/0.44 Proof:
% 0.19/0.44 inertia(x, i(x, t2), t2)
% 0.19/0.44 = { by axiom 12 (mp5) R->L }
% 0.19/0.44 fresh(organization(x, t2), true, x, t2)
% 0.19/0.44 = { by axiom 3 (t3_FOL_2) }
% 0.19/0.44 fresh(true, true, x, t2)
% 0.19/0.44 = { by axiom 7 (mp5) }
% 0.19/0.44 true
% 0.19/0.44
% 0.19/0.44 Goal 1 (t3_FOL_6): greater(p2, p1) = true.
% 0.19/0.44 Proof:
% 0.19/0.44 greater(p2, p1)
% 0.19/0.44 = { by axiom 13 (t1_FOL) R->L }
% 0.19/0.44 fresh16(true, true, x, p1, p2, t1)
% 0.19/0.44 = { by axiom 10 (mp4_1) R->L }
% 0.19/0.44 fresh16(fresh3(true, true, x, t2), true, x, p1, p2, t1)
% 0.19/0.44 = { by axiom 6 (t3_FOL) R->L }
% 0.19/0.44 fresh16(fresh3(reorganization_free(x, t1, t2), true, x, t2), true, x, p1, p2, t1)
% 0.19/0.44 = { by axiom 16 (mp4_1) }
% 0.19/0.44 fresh16(reorganization_free(x, t2, t2), true, x, p1, p2, t1)
% 0.19/0.44 = { by axiom 19 (t1_FOL) R->L }
% 0.19/0.44 fresh15(true, true, x, x, t2, p1, p2, t1)
% 0.19/0.44 = { by axiom 3 (t3_FOL_2) R->L }
% 0.19/0.44 fresh15(organization(x, t2), true, x, x, t2, p1, p2, t1)
% 0.19/0.44 = { by axiom 23 (t1_FOL) R->L }
% 0.19/0.44 fresh13(true, true, x, x, t2, i(x, t1), p1, p2, t1)
% 0.19/0.44 = { by lemma 31 R->L }
% 0.19/0.44 fresh13(inertia(x, i(x, t2), t2), true, x, x, t2, i(x, t1), p1, p2, t1)
% 0.19/0.44 = { by axiom 27 (t1_FOL) R->L }
% 0.19/0.44 fresh11(true, true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 5 (t3_FOL_4) R->L }
% 0.19/0.44 fresh11(survival_chance(x, p2, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 29 (t1_FOL) R->L }
% 0.19/0.44 fresh10(greater(i(x, t2), i(x, t1)), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 15 (t2_FOL) R->L }
% 0.19/0.44 fresh10(fresh7(true, true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 2 (t3_FOL_1) R->L }
% 0.19/0.44 fresh10(fresh7(organization(x, t1), true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 21 (t2_FOL) R->L }
% 0.19/0.44 fresh10(fresh6(true, true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by lemma 30 R->L }
% 0.19/0.44 fresh10(fresh6(inertia(x, i(x, t1), t1), true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 24 (t2_FOL) R->L }
% 0.19/0.44 fresh10(fresh4(true, true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 1 (t3_FOL_5) R->L }
% 0.19/0.44 fresh10(fresh4(greater(t2, t1), true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 25 (t2_FOL) }
% 0.19/0.44 fresh10(fresh5(inertia(x, i(x, t2), t2), true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by lemma 31 }
% 0.19/0.44 fresh10(fresh5(true, true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 20 (t2_FOL) }
% 0.19/0.44 fresh10(fresh8(organization(x, t2), true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 3 (t3_FOL_2) }
% 0.19/0.44 fresh10(fresh8(true, true, x, i(x, t1), i(x, t2), t1, t2), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 14 (t2_FOL) }
% 0.19/0.44 fresh10(fresh9(reorganization_free(x, t1, t2), true, i(x, t1), i(x, t2)), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 6 (t3_FOL) }
% 0.19/0.44 fresh10(fresh9(true, true, i(x, t1), i(x, t2)), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 9 (t2_FOL) }
% 0.19/0.44 fresh10(true, true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 28 (t1_FOL) }
% 0.19/0.44 fresh12(survival_chance(x, p1, t1), true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 4 (t3_FOL_3) }
% 0.19/0.44 fresh12(true, true, x, x, t2, i(x, t1), i(x, t2), p1, p2, t1)
% 0.19/0.44 = { by axiom 26 (t1_FOL) }
% 0.19/0.44 fresh14(inertia(x, i(x, t1), t1), true, x, x, t2, p1, p2, t1)
% 0.19/0.44 = { by lemma 30 }
% 0.19/0.44 fresh14(true, true, x, x, t2, p1, p2, t1)
% 0.19/0.44 = { by axiom 22 (t1_FOL) }
% 0.19/0.44 fresh17(organization(x, t1), true, x, x, t2, p1, p2, t1)
% 0.19/0.44 = { by axiom 2 (t3_FOL_1) }
% 0.19/0.44 fresh17(true, true, x, x, t2, p1, p2, t1)
% 0.19/0.44 = { by axiom 18 (t1_FOL) }
% 0.19/0.44 fresh18(reorganization_free(x, t1, t1), true, p1, p2)
% 0.19/0.44 = { by axiom 17 (mp4) R->L }
% 0.19/0.44 fresh18(fresh2(reorganization_free(x, t1, t2), true, x, t1), true, p1, p2)
% 0.19/0.44 = { by axiom 6 (t3_FOL) }
% 0.19/0.44 fresh18(fresh2(true, true, x, t1), true, p1, p2)
% 0.19/0.44 = { by axiom 11 (mp4) }
% 0.19/0.44 fresh18(true, true, p1, p2)
% 0.19/0.44 = { by axiom 8 (t1_FOL) }
% 0.19/0.44 true
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44
% 0.19/0.44 RESULT: Theorem (the conjecture is true).
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