TSTP Solution File: MGT048+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT048+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 : n031.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 09:17:13 EDT 2023
% Result : Theorem 0.13s 0.41s
% 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
% 0.13/0.12 % Problem : MGT048+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.13 % 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 : n031.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 06:39:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.41 Command-line arguments: --no-flatten-goal
% 0.13/0.41
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41
% 0.13/0.42 % SZS output start Proof
% 0.13/0.42 Take the following subset of the input axioms:
% 0.13/0.42 fof(assumption_10, axiom, ![X, T0, T]: (organization(X) => stock_of_knowledge(X, T)=stock_of_knowledge(X, T0))).
% 0.13/0.42 fof(assumption_12, axiom, ![X2, T0_2, T2]: ((organization(X2) & greater(age(X2, T2), age(X2, T0_2))) => greater(internal_friction(X2, T2), internal_friction(X2, T0_2)))).
% 0.13/0.42 fof(assumption_5, axiom, ![X2, T0_2, T2]: (organization(X2) => (((greater(stock_of_knowledge(X2, T2), stock_of_knowledge(X2, T0_2)) & smaller_or_equal(internal_friction(X2, T2), internal_friction(X2, T0_2))) => greater(capability(X2, T2), capability(X2, T0_2))) & (((smaller_or_equal(stock_of_knowledge(X2, T2), stock_of_knowledge(X2, T0_2)) & greater(internal_friction(X2, T2), internal_friction(X2, T0_2))) => smaller(capability(X2, T2), capability(X2, T0_2))) & ((stock_of_knowledge(X2, T2)=stock_of_knowledge(X2, T0_2) & internal_friction(X2, T2)=internal_friction(X2, T0_2)) => capability(X2, T2)=capability(X2, T0_2)))))).
% 0.13/0.42 fof(definition_smaller_or_equal, axiom, ![Y, X2]: (smaller_or_equal(X2, Y) <=> (smaller(X2, Y) | X2=Y))).
% 0.13/0.42 fof(lemma_5, conjecture, ![X2, T0_2, T2]: ((organization(X2) & greater(age(X2, T2), age(X2, T0_2))) => smaller(capability(X2, T2), capability(X2, T0_2)))).
% 0.13/0.42
% 0.13/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.42 fresh(y, y, x1...xn) = u
% 0.13/0.42 C => fresh(s, t, x1...xn) = v
% 0.13/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.42 variables of u and v.
% 0.13/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.42 input problem has no model of domain size 1).
% 0.13/0.42
% 0.13/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.42
% 0.13/0.42 Axiom 1 (lemma_5_1): organization(x) = true2.
% 0.13/0.42 Axiom 2 (definition_smaller_or_equal): smaller_or_equal(X, X) = true2.
% 0.13/0.42 Axiom 3 (assumption_5_1): fresh16(X, X, Y, Z, W) = true2.
% 0.13/0.42 Axiom 4 (assumption_10): fresh11(X, X, Y, Z, W) = stock_of_knowledge(Y, Z).
% 0.13/0.42 Axiom 5 (assumption_12): fresh10(X, X, Y, Z, W) = true2.
% 0.13/0.42 Axiom 6 (assumption_10): fresh11(organization(X), true2, X, Y, Z) = stock_of_knowledge(X, Z).
% 0.13/0.42 Axiom 7 (assumption_5_1): fresh8(X, X, Y, Z, W) = smaller(capability(Y, W), capability(Y, Z)).
% 0.13/0.42 Axiom 8 (lemma_5): greater(age(x, t), age(x, t0)) = true2.
% 0.13/0.42 Axiom 9 (assumption_12): fresh12(X, X, Y, Z, W) = greater(internal_friction(Y, W), internal_friction(Y, Z)).
% 0.13/0.42 Axiom 10 (assumption_5_1): fresh15(X, X, Y, Z, W) = fresh16(smaller_or_equal(stock_of_knowledge(Y, W), stock_of_knowledge(Y, Z)), true2, Y, Z, W).
% 0.13/0.42 Axiom 11 (assumption_12): fresh12(organization(X), true2, X, Y, Z) = fresh10(greater(age(X, Z), age(X, Y)), true2, X, Y, Z).
% 0.13/0.42 Axiom 12 (assumption_5_1): fresh15(organization(X), true2, X, Y, Z) = fresh8(greater(internal_friction(X, Z), internal_friction(X, Y)), true2, X, Y, Z).
% 0.13/0.42
% 0.13/0.42 Goal 1 (lemma_5_2): smaller(capability(x, t), capability(x, t0)) = true2.
% 0.13/0.42 Proof:
% 0.13/0.42 smaller(capability(x, t), capability(x, t0))
% 0.13/0.42 = { by axiom 7 (assumption_5_1) R->L }
% 0.13/0.42 fresh8(true2, true2, x, t0, t)
% 0.13/0.42 = { by axiom 5 (assumption_12) R->L }
% 0.13/0.42 fresh8(fresh10(true2, true2, x, t0, t), true2, x, t0, t)
% 0.13/0.42 = { by axiom 8 (lemma_5) R->L }
% 0.13/0.42 fresh8(fresh10(greater(age(x, t), age(x, t0)), true2, x, t0, t), true2, x, t0, t)
% 0.13/0.42 = { by axiom 11 (assumption_12) R->L }
% 0.13/0.42 fresh8(fresh12(organization(x), true2, x, t0, t), true2, x, t0, t)
% 0.13/0.42 = { by axiom 1 (lemma_5_1) }
% 0.13/0.42 fresh8(fresh12(true2, true2, x, t0, t), true2, x, t0, t)
% 0.13/0.42 = { by axiom 9 (assumption_12) }
% 0.13/0.42 fresh8(greater(internal_friction(x, t), internal_friction(x, t0)), true2, x, t0, t)
% 0.13/0.42 = { by axiom 12 (assumption_5_1) R->L }
% 0.13/0.42 fresh15(organization(x), true2, x, t0, t)
% 0.13/0.42 = { by axiom 1 (lemma_5_1) }
% 0.13/0.42 fresh15(true2, true2, x, t0, t)
% 0.13/0.42 = { by axiom 10 (assumption_5_1) }
% 0.13/0.42 fresh16(smaller_or_equal(stock_of_knowledge(x, t), stock_of_knowledge(x, t0)), true2, x, t0, t)
% 0.20/0.42 = { by axiom 6 (assumption_10) R->L }
% 0.20/0.42 fresh16(smaller_or_equal(stock_of_knowledge(x, t), fresh11(organization(x), true2, x, t, t0)), true2, x, t0, t)
% 0.20/0.42 = { by axiom 1 (lemma_5_1) }
% 0.20/0.42 fresh16(smaller_or_equal(stock_of_knowledge(x, t), fresh11(true2, true2, x, t, t0)), true2, x, t0, t)
% 0.20/0.42 = { by axiom 4 (assumption_10) }
% 0.20/0.42 fresh16(smaller_or_equal(stock_of_knowledge(x, t), stock_of_knowledge(x, t)), true2, x, t0, t)
% 0.20/0.42 = { by axiom 2 (definition_smaller_or_equal) }
% 0.20/0.42 fresh16(true2, true2, x, t0, t)
% 0.20/0.42 = { by axiom 3 (assumption_5_1) }
% 0.20/0.42 true2
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Theorem (the conjecture is true).
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