TSTP Solution File: MGT003-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT003-1 : 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 : n001.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 : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT003-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 06:42:04 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.43 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.43
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 Take the following subset of the input axioms:
% 0.21/0.45 fof(mp4_1, axiom, ![B, C, A2]: (~reorganization_free(A2, B, C) | reorganization_free(A2, B, B))).
% 0.21/0.45 fof(mp4_2, axiom, ![B2, C2, A2_2]: (~reorganization_free(A2_2, B2, C2) | reorganization_free(A2_2, C2, C2))).
% 0.21/0.45 fof(mp5_3, axiom, ![B2, A2_2]: (~organization(A2_2, B2) | inertia(A2_2, sk1(B2, A2_2), B2))).
% 0.21/0.45 fof(t1_FOL_4, hypothesis, ![D, E, F, G, H, B2, C2, A2_2]: (~organization(A2_2, B2) | (~organization(C2, D) | (~reorganization_free(A2_2, B2, B2) | (~reorganization_free(C2, D, D) | (~inertia(A2_2, E, B2) | (~inertia(C2, F, D) | (~survival_chance(A2_2, G, B2) | (~survival_chance(C2, H, D) | (~greater(F, E) | greater(H, G))))))))))).
% 0.21/0.45 fof(t2_FOL_5, hypothesis, ![B2, C2, D2, E2, A2_2]: (~organization(A2_2, B2) | (~organization(A2_2, C2) | (~reorganization_free(A2_2, B2, C2) | (~inertia(A2_2, D2, B2) | (~inertia(A2_2, E2, C2) | (~greater(C2, B2) | greater(E2, D2)))))))).
% 0.21/0.45 fof(t3_FOL_10, negated_conjecture, survival_chance(sk2, sk4, sk6)).
% 0.21/0.45 fof(t3_FOL_11, negated_conjecture, greater(sk6, sk5)).
% 0.21/0.45 fof(t3_FOL_12, negated_conjecture, ~greater(sk4, sk3)).
% 0.21/0.45 fof(t3_FOL_6, negated_conjecture, organization(sk2, sk5)).
% 0.21/0.45 fof(t3_FOL_7, negated_conjecture, organization(sk2, sk6)).
% 0.21/0.45 fof(t3_FOL_8, negated_conjecture, reorganization_free(sk2, sk5, sk6)).
% 0.21/0.45 fof(t3_FOL_9, negated_conjecture, survival_chance(sk2, sk3, sk5)).
% 0.21/0.45
% 0.21/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.45 fresh(y, y, x1...xn) = u
% 0.21/0.45 C => fresh(s, t, x1...xn) = v
% 0.21/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.45 variables of u and v.
% 0.21/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.45 input problem has no model of domain size 1).
% 0.21/0.45
% 0.21/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.45
% 0.21/0.45 Axiom 1 (t3_FOL_11): greater(sk6, sk5) = true.
% 0.21/0.45 Axiom 2 (t3_FOL_6): organization(sk2, sk5) = true.
% 0.21/0.45 Axiom 3 (t3_FOL_7): organization(sk2, sk6) = true.
% 0.21/0.46 Axiom 4 (t3_FOL_9): survival_chance(sk2, sk3, sk5) = true.
% 0.21/0.46 Axiom 5 (t3_FOL_10): survival_chance(sk2, sk4, sk6) = true.
% 0.21/0.46 Axiom 6 (t3_FOL_8): reorganization_free(sk2, sk5, sk6) = true.
% 0.21/0.46 Axiom 7 (mp5_3): fresh(X, X, Y, Z) = true.
% 0.21/0.46 Axiom 8 (t1_FOL_4): fresh18(X, X, Y, Z) = true.
% 0.21/0.46 Axiom 9 (t2_FOL_5): fresh9(X, X, Y, Z) = true.
% 0.21/0.46 Axiom 10 (mp4_2): fresh3(X, X, Y, Z) = true.
% 0.21/0.46 Axiom 11 (mp4_1): fresh2(X, X, Y, Z) = true.
% 0.21/0.46 Axiom 12 (mp5_3): fresh(organization(X, Y), true, X, Y) = inertia(X, sk1(Y, X), Y).
% 0.21/0.46 Axiom 13 (t1_FOL_4): fresh16(X, X, Y, Z, W, V) = greater(W, Z).
% 0.21/0.46 Axiom 14 (t2_FOL_5): fresh8(X, X, Y, Z, W, V, U) = fresh9(reorganization_free(Y, Z, W), true, V, U).
% 0.21/0.46 Axiom 15 (t2_FOL_5): fresh7(X, X, Y, Z, W, V, U) = greater(U, V).
% 0.21/0.46 Axiom 16 (mp4_2): fresh3(reorganization_free(X, Y, Z), true, X, Z) = reorganization_free(X, Z, Z).
% 0.21/0.46 Axiom 17 (mp4_1): fresh2(reorganization_free(X, Y, Z), true, X, Y) = reorganization_free(X, Y, Y).
% 0.21/0.46 Axiom 18 (t1_FOL_4): fresh17(X, X, Y, Z, W, V, U, T) = fresh18(reorganization_free(Y, T, T), true, V, U).
% 0.21/0.46 Axiom 19 (t1_FOL_4): fresh15(X, X, Y, Z, W, V, U, T) = fresh16(reorganization_free(Z, W, W), true, Y, V, U, T).
% 0.21/0.46 Axiom 20 (t2_FOL_5): fresh5(X, X, Y, Z, W, V, U) = fresh8(organization(Y, W), true, Y, Z, W, V, U).
% 0.21/0.46 Axiom 21 (t2_FOL_5): fresh6(X, X, Y, Z, W, V, U) = fresh7(organization(Y, Z), true, Y, Z, W, V, U).
% 0.21/0.46 Axiom 22 (t1_FOL_4): fresh14(X, X, Y, Z, W, V, U, T) = fresh17(organization(Y, T), true, Y, Z, W, V, U, T).
% 0.21/0.46 Axiom 23 (t1_FOL_4): fresh13(X, X, Y, Z, W, V, U, T, S) = fresh15(organization(Z, W), true, Y, Z, W, U, T, S).
% 0.21/0.46 Axiom 24 (t2_FOL_5): fresh4(X, X, Y, Z, W, V, U) = fresh6(inertia(Y, V, Z), true, Y, Z, W, V, U).
% 0.21/0.46 Axiom 25 (t2_FOL_5): fresh4(greater(X, Y), true, Z, Y, X, W, V) = fresh5(inertia(Z, V, X), true, Z, Y, X, W, V).
% 0.21/0.46 Axiom 26 (t1_FOL_4): fresh12(X, X, Y, Z, W, V, U, T, S, X2) = fresh14(inertia(Y, V, X2), true, Y, Z, W, T, S, X2).
% 0.21/0.46 Axiom 27 (t1_FOL_4): fresh11(X, X, Y, Z, W, V, U, T, S, X2) = fresh13(inertia(Z, U, W), true, Y, Z, W, V, T, S, X2).
% 0.21/0.46 Axiom 28 (t1_FOL_4): 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).
% 0.21/0.46 Axiom 29 (t1_FOL_4): 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).
% 0.21/0.46
% 0.21/0.46 Lemma 30: inertia(sk2, sk1(sk5, sk2), sk5) = true.
% 0.21/0.46 Proof:
% 0.21/0.46 inertia(sk2, sk1(sk5, sk2), sk5)
% 0.21/0.46 = { by axiom 12 (mp5_3) R->L }
% 0.21/0.46 fresh(organization(sk2, sk5), true, sk2, sk5)
% 0.21/0.46 = { by axiom 2 (t3_FOL_6) }
% 0.21/0.46 fresh(true, true, sk2, sk5)
% 0.21/0.46 = { by axiom 7 (mp5_3) }
% 0.21/0.46 true
% 0.21/0.46
% 0.21/0.46 Lemma 31: inertia(sk2, sk1(sk6, sk2), sk6) = true.
% 0.21/0.46 Proof:
% 0.21/0.46 inertia(sk2, sk1(sk6, sk2), sk6)
% 0.21/0.46 = { by axiom 12 (mp5_3) R->L }
% 0.21/0.46 fresh(organization(sk2, sk6), true, sk2, sk6)
% 0.21/0.46 = { by axiom 3 (t3_FOL_7) }
% 0.21/0.46 fresh(true, true, sk2, sk6)
% 0.21/0.46 = { by axiom 7 (mp5_3) }
% 0.21/0.46 true
% 0.21/0.46
% 0.21/0.46 Goal 1 (t3_FOL_12): greater(sk4, sk3) = true.
% 0.21/0.46 Proof:
% 0.21/0.46 greater(sk4, sk3)
% 0.21/0.46 = { by axiom 13 (t1_FOL_4) R->L }
% 0.21/0.46 fresh16(true, true, sk2, sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 10 (mp4_2) R->L }
% 0.21/0.46 fresh16(fresh3(true, true, sk2, sk6), true, sk2, sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 6 (t3_FOL_8) R->L }
% 0.21/0.46 fresh16(fresh3(reorganization_free(sk2, sk5, sk6), true, sk2, sk6), true, sk2, sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 16 (mp4_2) }
% 0.21/0.46 fresh16(reorganization_free(sk2, sk6, sk6), true, sk2, sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 19 (t1_FOL_4) R->L }
% 0.21/0.46 fresh15(true, true, sk2, sk2, sk6, sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 3 (t3_FOL_7) R->L }
% 0.21/0.46 fresh15(organization(sk2, sk6), true, sk2, sk2, sk6, sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 23 (t1_FOL_4) R->L }
% 0.21/0.46 fresh13(true, true, sk2, sk2, sk6, sk1(sk5, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by lemma 31 R->L }
% 0.21/0.46 fresh13(inertia(sk2, sk1(sk6, sk2), sk6), true, sk2, sk2, sk6, sk1(sk5, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 27 (t1_FOL_4) R->L }
% 0.21/0.46 fresh11(true, true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 5 (t3_FOL_10) R->L }
% 0.21/0.46 fresh11(survival_chance(sk2, sk4, sk6), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 29 (t1_FOL_4) R->L }
% 0.21/0.46 fresh10(greater(sk1(sk6, sk2), sk1(sk5, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 15 (t2_FOL_5) R->L }
% 0.21/0.46 fresh10(fresh7(true, true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 2 (t3_FOL_6) R->L }
% 0.21/0.46 fresh10(fresh7(organization(sk2, sk5), true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 21 (t2_FOL_5) R->L }
% 0.21/0.46 fresh10(fresh6(true, true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by lemma 30 R->L }
% 0.21/0.46 fresh10(fresh6(inertia(sk2, sk1(sk5, sk2), sk5), true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 24 (t2_FOL_5) R->L }
% 0.21/0.46 fresh10(fresh4(true, true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 1 (t3_FOL_11) R->L }
% 0.21/0.46 fresh10(fresh4(greater(sk6, sk5), true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 25 (t2_FOL_5) }
% 0.21/0.46 fresh10(fresh5(inertia(sk2, sk1(sk6, sk2), sk6), true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by lemma 31 }
% 0.21/0.46 fresh10(fresh5(true, true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 20 (t2_FOL_5) }
% 0.21/0.46 fresh10(fresh8(organization(sk2, sk6), true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 3 (t3_FOL_7) }
% 0.21/0.46 fresh10(fresh8(true, true, sk2, sk5, sk6, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 14 (t2_FOL_5) }
% 0.21/0.46 fresh10(fresh9(reorganization_free(sk2, sk5, sk6), true, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 6 (t3_FOL_8) }
% 0.21/0.46 fresh10(fresh9(true, true, sk1(sk5, sk2), sk1(sk6, sk2)), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 9 (t2_FOL_5) }
% 0.21/0.46 fresh10(true, true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 28 (t1_FOL_4) }
% 0.21/0.46 fresh12(survival_chance(sk2, sk3, sk5), true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 4 (t3_FOL_9) }
% 0.21/0.46 fresh12(true, true, sk2, sk2, sk6, sk1(sk5, sk2), sk1(sk6, sk2), sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 26 (t1_FOL_4) }
% 0.21/0.46 fresh14(inertia(sk2, sk1(sk5, sk2), sk5), true, sk2, sk2, sk6, sk3, sk4, sk5)
% 0.21/0.46 = { by lemma 30 }
% 0.21/0.46 fresh14(true, true, sk2, sk2, sk6, sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 22 (t1_FOL_4) }
% 0.21/0.46 fresh17(organization(sk2, sk5), true, sk2, sk2, sk6, sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 2 (t3_FOL_6) }
% 0.21/0.46 fresh17(true, true, sk2, sk2, sk6, sk3, sk4, sk5)
% 0.21/0.46 = { by axiom 18 (t1_FOL_4) }
% 0.21/0.46 fresh18(reorganization_free(sk2, sk5, sk5), true, sk3, sk4)
% 0.21/0.46 = { by axiom 17 (mp4_1) R->L }
% 0.21/0.46 fresh18(fresh2(reorganization_free(sk2, sk5, sk6), true, sk2, sk5), true, sk3, sk4)
% 0.21/0.46 = { by axiom 6 (t3_FOL_8) }
% 0.21/0.46 fresh18(fresh2(true, true, sk2, sk5), true, sk3, sk4)
% 0.21/0.46 = { by axiom 11 (mp4_1) }
% 0.21/0.46 fresh18(true, true, sk3, sk4)
% 0.21/0.46 = { by axiom 8 (t1_FOL_4) }
% 0.21/0.46 true
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46
% 0.21/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------