TSTP Solution File: MGT044-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : MGT044-1 : 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 : 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 09:17:12 EDT 2023
% Result : Unsatisfiable 0.22s 0.42s
% Output : Proof 0.22s
% 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 : MGT044-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 06:57:30 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.22/0.42 Command-line arguments: --no-flatten-goal
% 0.22/0.42
% 0.22/0.42 % SZS status Unsatisfiable
% 0.22/0.42
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 Take the following subset of the input axioms:
% 0.22/0.43 fof(assumption_5_32, axiom, ![B, C, A2]: (~organization(A2) | (~greater(stock_of_knowledge(A2, B), stock_of_knowledge(A2, C)) | (~smaller_or_equal(internal_friction(A2, B), internal_friction(A2, C)) | greater(capability(A2, B), capability(A2, C)))))).
% 0.22/0.43 fof(assumption_7_35, axiom, ![B2, C2, A2_2]: (~organization(A2_2) | (~greater(age(A2_2, B2), age(A2_2, C2)) | greater(stock_of_knowledge(A2_2, B2), stock_of_knowledge(A2_2, C2))))).
% 0.22/0.43 fof(assumption_9_36, axiom, ![B2, C2, A2_2]: (~organization(A2_2) | internal_friction(A2_2, B2)=internal_friction(A2_2, C2))).
% 0.22/0.43 fof(definition_smaller_or_equal_3, axiom, ![A, B2]: (A!=B2 | smaller_or_equal(A, B2))).
% 0.22/0.43 fof(lemma_3_37, negated_conjecture, organization(sk1)).
% 0.22/0.43 fof(lemma_3_38, negated_conjecture, greater(age(sk1, sk3), age(sk1, sk2))).
% 0.22/0.43 fof(lemma_3_39, negated_conjecture, ~greater(capability(sk1, sk3), capability(sk1, sk2))).
% 0.22/0.43
% 0.22/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.43 fresh(y, y, x1...xn) = u
% 0.22/0.43 C => fresh(s, t, x1...xn) = v
% 0.22/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.43 variables of u and v.
% 0.22/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.43 input problem has no model of domain size 1).
% 0.22/0.43
% 0.22/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.43
% 0.22/0.43 Axiom 1 (lemma_3_37): organization(sk1) = true2.
% 0.22/0.43 Axiom 2 (definition_smaller_or_equal_3): smaller_or_equal(X, X) = true2.
% 0.22/0.43 Axiom 3 (assumption_5_32): fresh18(X, X, Y, Z, W) = true2.
% 0.22/0.43 Axiom 4 (assumption_7_35): fresh8(X, X, Y, Z, W) = true2.
% 0.22/0.43 Axiom 5 (assumption_9_36): fresh7(X, X, Y, Z, W) = internal_friction(Y, W).
% 0.22/0.43 Axiom 6 (assumption_9_36): fresh7(organization(X), true2, X, Y, Z) = internal_friction(X, Y).
% 0.22/0.43 Axiom 7 (lemma_3_38): greater(age(sk1, sk3), age(sk1, sk2)) = true2.
% 0.22/0.43 Axiom 8 (assumption_7_35): fresh9(X, X, Y, Z, W) = greater(stock_of_knowledge(Y, Z), stock_of_knowledge(Y, W)).
% 0.22/0.43 Axiom 9 (assumption_5_32): fresh12(X, X, Y, Z, W) = greater(capability(Y, Z), capability(Y, W)).
% 0.22/0.43 Axiom 10 (assumption_5_32): fresh17(X, X, Y, Z, W) = fresh18(smaller_or_equal(internal_friction(Y, Z), internal_friction(Y, W)), true2, Y, Z, W).
% 0.22/0.43 Axiom 11 (assumption_5_32): fresh17(organization(X), true2, X, Y, Z) = fresh12(greater(stock_of_knowledge(X, Y), stock_of_knowledge(X, Z)), true2, X, Y, Z).
% 0.22/0.43 Axiom 12 (assumption_7_35): fresh9(organization(X), true2, X, Y, Z) = fresh8(greater(age(X, Y), age(X, Z)), true2, X, Y, Z).
% 0.22/0.43
% 0.22/0.43 Goal 1 (lemma_3_39): greater(capability(sk1, sk3), capability(sk1, sk2)) = true2.
% 0.22/0.43 Proof:
% 0.22/0.43 greater(capability(sk1, sk3), capability(sk1, sk2))
% 0.22/0.43 = { by axiom 9 (assumption_5_32) R->L }
% 0.22/0.43 fresh12(true2, true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 4 (assumption_7_35) R->L }
% 0.22/0.43 fresh12(fresh8(true2, true2, sk1, sk3, sk2), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 7 (lemma_3_38) R->L }
% 0.22/0.43 fresh12(fresh8(greater(age(sk1, sk3), age(sk1, sk2)), true2, sk1, sk3, sk2), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 12 (assumption_7_35) R->L }
% 0.22/0.43 fresh12(fresh9(organization(sk1), true2, sk1, sk3, sk2), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 1 (lemma_3_37) }
% 0.22/0.43 fresh12(fresh9(true2, true2, sk1, sk3, sk2), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 8 (assumption_7_35) }
% 0.22/0.43 fresh12(greater(stock_of_knowledge(sk1, sk3), stock_of_knowledge(sk1, sk2)), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 11 (assumption_5_32) R->L }
% 0.22/0.43 fresh17(organization(sk1), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 1 (lemma_3_37) }
% 0.22/0.43 fresh17(true2, true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 10 (assumption_5_32) }
% 0.22/0.43 fresh18(smaller_or_equal(internal_friction(sk1, sk3), internal_friction(sk1, sk2)), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 6 (assumption_9_36) R->L }
% 0.22/0.43 fresh18(smaller_or_equal(internal_friction(sk1, sk3), fresh7(organization(sk1), true2, sk1, sk2, sk3)), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 1 (lemma_3_37) }
% 0.22/0.43 fresh18(smaller_or_equal(internal_friction(sk1, sk3), fresh7(true2, true2, sk1, sk2, sk3)), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 5 (assumption_9_36) }
% 0.22/0.43 fresh18(smaller_or_equal(internal_friction(sk1, sk3), internal_friction(sk1, sk3)), true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 2 (definition_smaller_or_equal_3) }
% 0.22/0.43 fresh18(true2, true2, sk1, sk3, sk2)
% 0.22/0.43 = { by axiom 3 (assumption_5_32) }
% 0.22/0.43 true2
% 0.22/0.43 % SZS output end Proof
% 0.22/0.43
% 0.22/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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