TSTP Solution File: MGT009-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT009-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n009.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 : Unsatisfiable 0.20s 0.47s
% 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
% 0.12/0.12 % Problem : MGT009-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n009.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 06:32:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 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(a3_FOL_3, hypothesis, ![B, C, D, E, F, G, H, A2]: (~organization(A2, B) | (~organization(C, D) | (~reorganization_free(A2, B, B) | (~reorganization_free(C, D, D) | (~reproducibility(A2, E, B) | (~reproducibility(C, F, D) | (~inertia(A2, G, B) | (~inertia(C, H, D) | (~greater(H, G) | greater(F, E))))))))))).
% 0.20/0.51 fof(a5_FOL_4, hypothesis, ![I, B2, A2_2, C2, D2, E2, F2, G2, H2]: (~organization(A2_2, B2) | (~organization(C2, D2) | (~class(A2_2, E2, B2) | (~class(C2, E2, D2) | (~size(A2_2, F2, B2) | (~size(C2, G2, D2) | (~inertia(A2_2, H2, B2) | (~inertia(C2, I, D2) | (~greater(G2, F2) | greater(I, H2))))))))))).
% 0.20/0.51 fof(mp5_1, axiom, ![B2, A2_2]: (~organization(A2_2, B2) | inertia(A2_2, sk1(B2, A2_2), B2))).
% 0.20/0.51 fof(t9_FOL_10, negated_conjecture, class(sk3, sk4, sk10)).
% 0.20/0.51 fof(t9_FOL_11, negated_conjecture, reproducibility(sk2, sk5, sk9)).
% 0.20/0.51 fof(t9_FOL_12, negated_conjecture, reproducibility(sk3, sk6, sk10)).
% 0.20/0.51 fof(t9_FOL_13, negated_conjecture, size(sk2, sk7, sk9)).
% 0.20/0.51 fof(t9_FOL_14, negated_conjecture, size(sk3, sk8, sk10)).
% 0.20/0.51 fof(t9_FOL_15, negated_conjecture, greater(sk8, sk7)).
% 0.20/0.51 fof(t9_FOL_16, negated_conjecture, ~greater(sk6, sk5)).
% 0.20/0.51 fof(t9_FOL_5, negated_conjecture, organization(sk2, sk9)).
% 0.20/0.51 fof(t9_FOL_6, negated_conjecture, organization(sk3, sk10)).
% 0.20/0.51 fof(t9_FOL_7, negated_conjecture, reorganization_free(sk2, sk9, sk9)).
% 0.20/0.51 fof(t9_FOL_8, negated_conjecture, reorganization_free(sk3, sk10, sk10)).
% 0.20/0.51 fof(t9_FOL_9, negated_conjecture, class(sk2, sk4, sk9)).
% 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 (t9_FOL_5): organization(sk2, sk9) = true.
% 0.20/0.51 Axiom 2 (t9_FOL_6): organization(sk3, sk10) = true.
% 0.20/0.51 Axiom 3 (t9_FOL_15): greater(sk8, sk7) = true.
% 0.20/0.51 Axiom 4 (t9_FOL_7): reorganization_free(sk2, sk9, sk9) = true.
% 0.20/0.51 Axiom 5 (t9_FOL_8): reorganization_free(sk3, sk10, sk10) = true.
% 0.20/0.51 Axiom 6 (t9_FOL_11): reproducibility(sk2, sk5, sk9) = true.
% 0.20/0.51 Axiom 7 (t9_FOL_12): reproducibility(sk3, sk6, sk10) = true.
% 0.20/0.51 Axiom 8 (t9_FOL_9): class(sk2, sk4, sk9) = true.
% 0.20/0.51 Axiom 9 (t9_FOL_10): class(sk3, sk4, sk10) = true.
% 0.20/0.51 Axiom 10 (t9_FOL_13): size(sk2, sk7, sk9) = true.
% 0.20/0.51 Axiom 11 (t9_FOL_14): size(sk3, sk8, sk10) = true.
% 0.20/0.51 Axiom 12 (mp5_1): fresh(X, X, Y, Z) = true.
% 0.20/0.51 Axiom 13 (a3_FOL_3): fresh19(X, X, Y, Z) = true.
% 0.20/0.51 Axiom 14 (a5_FOL_4): fresh10(X, X, Y, Z) = true.
% 0.20/0.51 Axiom 15 (mp5_1): fresh(organization(X, Y), true, X, Y) = inertia(X, sk1(Y, X), Y).
% 0.20/0.51 Axiom 16 (a3_FOL_3): fresh17(X, X, Y, Z, W, V) = greater(W, Z).
% 0.20/0.51 Axiom 17 (a5_FOL_4): fresh8(X, X, Y, Z, W, V) = greater(W, Z).
% 0.20/0.51 Axiom 18 (a3_FOL_3): fresh18(X, X, Y, Z, W, V, U, T) = fresh19(organization(Y, T), true, V, U).
% 0.20/0.51 Axiom 19 (a5_FOL_4): fresh9(X, X, Y, Z, W, V, U, T) = fresh10(organization(Y, T), true, V, U).
% 0.20/0.51 Axiom 20 (a5_FOL_4): fresh7(X, X, Y, Z, W, V, U, T) = fresh8(organization(Z, W), true, Y, V, U, T).
% 0.20/0.51 Axiom 21 (a3_FOL_3): fresh16(X, X, Y, Z, W, V, U, T, S) = fresh17(organization(Z, W), true, Y, V, U, S).
% 0.20/0.51 Axiom 22 (a5_FOL_4): fresh5(X, X, Y, Z, W, V, U, T, S, X2) = fresh6(greater(U, V), true, Y, Z, W, T, S, X2).
% 0.20/0.51 Axiom 23 (a3_FOL_3): fresh15(X, X, Y, Z, W, V, U, T, S, X2) = fresh18(inertia(Y, T, X2), true, Y, Z, W, V, U, X2).
% 0.20/0.51 Axiom 24 (a5_FOL_4): fresh6(X, X, Y, Z, W, V, U, T) = fresh9(inertia(Y, V, T), true, Y, Z, W, V, U, T).
% 0.20/0.51 Axiom 25 (a5_FOL_4): fresh4(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh7(inertia(Z, X2, W), true, Y, Z, W, S, X2, Y2).
% 0.20/0.51 Axiom 26 (a3_FOL_3): fresh14(X, X, Y, Z, W, V, U, T, S, X2) = fresh16(inertia(Z, S, W), true, Y, Z, W, V, U, T, X2).
% 0.20/0.51 Axiom 27 (a3_FOL_3): fresh13(X, X, Y, Z, W, V, U, T, S, X2) = fresh15(reorganization_free(Y, X2, X2), true, Y, Z, W, V, U, T, S, X2).
% 0.20/0.51 Axiom 28 (a3_FOL_3): fresh12(X, X, Y, Z, W, V, U, T, S, X2) = fresh14(reorganization_free(Z, W, W), true, Y, Z, W, V, U, T, S, X2).
% 0.20/0.51 Axiom 29 (a3_FOL_3): fresh11(X, X, Y, Z, W, V, U, T, S, X2) = fresh13(reproducibility(Y, V, X2), true, Y, Z, W, V, U, T, S, X2).
% 0.20/0.51 Axiom 30 (a3_FOL_3): fresh11(greater(X, Y), true, Z, W, V, U, T, Y, X, S) = fresh12(reproducibility(W, T, V), true, Z, W, V, U, T, Y, X, S).
% 0.20/0.51 Axiom 31 (a5_FOL_4): fresh3(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh5(class(Y, V, Y2), true, Y, Z, W, U, T, S, X2, Y2).
% 0.20/0.51 Axiom 32 (a5_FOL_4): fresh2(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh4(class(Z, V, W), true, Y, Z, W, V, U, T, S, X2, Y2).
% 0.20/0.51 Axiom 33 (a5_FOL_4): fresh2(size(X, Y, Z), true, W, X, Z, V, U, Y, T, S, X2) = fresh3(size(W, U, X2), true, W, X, Z, V, U, Y, T, S, X2).
% 0.20/0.51
% 0.20/0.51 Lemma 34: inertia(sk2, sk1(sk9, sk2), sk9) = true.
% 0.20/0.51 Proof:
% 0.20/0.51 inertia(sk2, sk1(sk9, sk2), sk9)
% 0.20/0.51 = { by axiom 15 (mp5_1) R->L }
% 0.20/0.51 fresh(organization(sk2, sk9), true, sk2, sk9)
% 0.20/0.51 = { by axiom 1 (t9_FOL_5) }
% 0.20/0.51 fresh(true, true, sk2, sk9)
% 0.20/0.51 = { by axiom 12 (mp5_1) }
% 0.20/0.51 true
% 0.20/0.51
% 0.20/0.51 Lemma 35: inertia(sk3, sk1(sk10, sk3), sk10) = true.
% 0.20/0.51 Proof:
% 0.20/0.51 inertia(sk3, sk1(sk10, sk3), sk10)
% 0.20/0.51 = { by axiom 15 (mp5_1) R->L }
% 0.20/0.51 fresh(organization(sk3, sk10), true, sk3, sk10)
% 0.20/0.51 = { by axiom 2 (t9_FOL_6) }
% 0.20/0.51 fresh(true, true, sk3, sk10)
% 0.20/0.51 = { by axiom 12 (mp5_1) }
% 0.20/0.52 true
% 0.20/0.52
% 0.20/0.52 Goal 1 (t9_FOL_16): greater(sk6, sk5) = true.
% 0.20/0.52 Proof:
% 0.20/0.52 greater(sk6, sk5)
% 0.20/0.52 = { by axiom 16 (a3_FOL_3) R->L }
% 0.20/0.52 fresh17(true, true, sk2, sk5, sk6, sk9)
% 0.20/0.52 = { by axiom 2 (t9_FOL_6) R->L }
% 0.20/0.52 fresh17(organization(sk3, sk10), true, sk2, sk5, sk6, sk9)
% 0.20/0.52 = { by axiom 21 (a3_FOL_3) R->L }
% 0.20/0.52 fresh16(true, true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk9)
% 0.20/0.52 = { by lemma 35 R->L }
% 0.20/0.52 fresh16(inertia(sk3, sk1(sk10, sk3), sk10), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk9)
% 0.20/0.52 = { by axiom 26 (a3_FOL_3) R->L }
% 0.20/0.52 fresh14(true, true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 5 (t9_FOL_8) R->L }
% 0.20/0.52 fresh14(reorganization_free(sk3, sk10, sk10), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 28 (a3_FOL_3) R->L }
% 0.20/0.52 fresh12(true, true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 7 (t9_FOL_12) R->L }
% 0.20/0.52 fresh12(reproducibility(sk3, sk6, sk10), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 30 (a3_FOL_3) R->L }
% 0.20/0.52 fresh11(greater(sk1(sk10, sk3), sk1(sk9, sk2)), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 17 (a5_FOL_4) R->L }
% 0.20/0.52 fresh11(fresh8(true, true, sk2, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 2 (t9_FOL_6) R->L }
% 0.20/0.52 fresh11(fresh8(organization(sk3, sk10), true, sk2, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 20 (a5_FOL_4) R->L }
% 0.20/0.52 fresh11(fresh7(true, true, sk2, sk3, sk10, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by lemma 35 R->L }
% 0.20/0.52 fresh11(fresh7(inertia(sk3, sk1(sk10, sk3), sk10), true, sk2, sk3, sk10, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 25 (a5_FOL_4) R->L }
% 0.20/0.52 fresh11(fresh4(true, true, sk2, sk3, sk10, sk4, sk7, sk8, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 9 (t9_FOL_10) R->L }
% 0.20/0.52 fresh11(fresh4(class(sk3, sk4, sk10), true, sk2, sk3, sk10, sk4, sk7, sk8, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 32 (a5_FOL_4) R->L }
% 0.20/0.52 fresh11(fresh2(true, true, sk2, sk3, sk10, sk4, sk7, sk8, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 11 (t9_FOL_14) R->L }
% 0.20/0.52 fresh11(fresh2(size(sk3, sk8, sk10), true, sk2, sk3, sk10, sk4, sk7, sk8, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 33 (a5_FOL_4) }
% 0.20/0.52 fresh11(fresh3(size(sk2, sk7, sk9), true, sk2, sk3, sk10, sk4, sk7, sk8, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 10 (t9_FOL_13) }
% 0.20/0.52 fresh11(fresh3(true, true, sk2, sk3, sk10, sk4, sk7, sk8, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 31 (a5_FOL_4) }
% 0.20/0.52 fresh11(fresh5(class(sk2, sk4, sk9), true, sk2, sk3, sk10, sk7, sk8, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 8 (t9_FOL_9) }
% 0.20/0.52 fresh11(fresh5(true, true, sk2, sk3, sk10, sk7, sk8, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 22 (a5_FOL_4) }
% 0.20/0.52 fresh11(fresh6(greater(sk8, sk7), true, sk2, sk3, sk10, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 3 (t9_FOL_15) }
% 0.20/0.52 fresh11(fresh6(true, true, sk2, sk3, sk10, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 24 (a5_FOL_4) }
% 0.20/0.52 fresh11(fresh9(inertia(sk2, sk1(sk9, sk2), sk9), true, sk2, sk3, sk10, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by lemma 34 }
% 0.20/0.52 fresh11(fresh9(true, true, sk2, sk3, sk10, sk1(sk9, sk2), sk1(sk10, sk3), sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 19 (a5_FOL_4) }
% 0.20/0.52 fresh11(fresh10(organization(sk2, sk9), true, sk1(sk9, sk2), sk1(sk10, sk3)), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 1 (t9_FOL_5) }
% 0.20/0.52 fresh11(fresh10(true, true, sk1(sk9, sk2), sk1(sk10, sk3)), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 14 (a5_FOL_4) }
% 0.20/0.52 fresh11(true, true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 29 (a3_FOL_3) }
% 0.20/0.52 fresh13(reproducibility(sk2, sk5, sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 6 (t9_FOL_11) }
% 0.20/0.52 fresh13(true, true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 27 (a3_FOL_3) }
% 0.20/0.52 fresh15(reorganization_free(sk2, sk9, sk9), true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 4 (t9_FOL_7) }
% 0.20/0.52 fresh15(true, true, sk2, sk3, sk10, sk5, sk6, sk1(sk9, sk2), sk1(sk10, sk3), sk9)
% 0.20/0.52 = { by axiom 23 (a3_FOL_3) }
% 0.20/0.52 fresh18(inertia(sk2, sk1(sk9, sk2), sk9), true, sk2, sk3, sk10, sk5, sk6, sk9)
% 0.20/0.52 = { by lemma 34 }
% 0.20/0.52 fresh18(true, true, sk2, sk3, sk10, sk5, sk6, sk9)
% 0.20/0.52 = { by axiom 18 (a3_FOL_3) }
% 0.20/0.52 fresh19(organization(sk2, sk9), true, sk5, sk6)
% 0.20/0.52 = { by axiom 1 (t9_FOL_5) }
% 0.20/0.52 fresh19(true, true, sk5, sk6)
% 0.20/0.52 = { by axiom 13 (a3_FOL_3) }
% 0.20/0.52 true
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52
% 0.20/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------