TSTP Solution File: MGT045+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT045+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 : n015.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 : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT045+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % 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 : n015.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 06:50:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.39
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Take the following subset of the input axioms:
% 0.19/0.39 fof(assumption_6, axiom, ![X, T0, T]: (organization(X) => ((greater(external_ties(X, T), external_ties(X, T0)) => greater(position(X, T), position(X, T0))) & (external_ties(X, T)=external_ties(X, T0) => position(X, T)=position(X, T0))))).
% 0.19/0.39 fof(assumption_8, axiom, ![X2, T0_2, T2]: ((organization(X2) & greater(age(X2, T2), age(X2, T0_2))) => greater(external_ties(X2, T2), external_ties(X2, T0_2)))).
% 0.19/0.39 fof(lemma_4, conjecture, ![X2, T0_2, T2]: ((organization(X2) & greater(age(X2, T2), age(X2, T0_2))) => greater(position(X2, T2), position(X2, T0_2)))).
% 0.19/0.39
% 0.19/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.39 fresh(y, y, x1...xn) = u
% 0.19/0.39 C => fresh(s, t, x1...xn) = v
% 0.19/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.39 variables of u and v.
% 0.19/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.39 input problem has no model of domain size 1).
% 0.19/0.39
% 0.19/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.39
% 0.19/0.39 Axiom 1 (lemma_4_1): organization(x) = true2.
% 0.19/0.39 Axiom 2 (assumption_6_1): fresh9(X, X, Y, Z, W) = true2.
% 0.19/0.39 Axiom 3 (assumption_8): fresh7(X, X, Y, Z, W) = true2.
% 0.19/0.39 Axiom 4 (assumption_6_1): fresh10(X, X, Y, Z, W) = greater(position(Y, W), position(Y, Z)).
% 0.19/0.39 Axiom 5 (assumption_8): fresh8(X, X, Y, Z, W) = greater(external_ties(Y, W), external_ties(Y, Z)).
% 0.19/0.39 Axiom 6 (lemma_4): greater(age(x, t), age(x, t0)) = true2.
% 0.19/0.39 Axiom 7 (assumption_6_1): fresh10(organization(X), true2, X, Y, Z) = fresh9(greater(external_ties(X, Z), external_ties(X, Y)), true2, X, Y, Z).
% 0.19/0.39 Axiom 8 (assumption_8): fresh8(organization(X), true2, X, Y, Z) = fresh7(greater(age(X, Z), age(X, Y)), true2, X, Y, Z).
% 0.19/0.39
% 0.19/0.39 Goal 1 (lemma_4_2): greater(position(x, t), position(x, t0)) = true2.
% 0.19/0.39 Proof:
% 0.19/0.39 greater(position(x, t), position(x, t0))
% 0.19/0.39 = { by axiom 4 (assumption_6_1) R->L }
% 0.19/0.39 fresh10(true2, true2, x, t0, t)
% 0.19/0.39 = { by axiom 1 (lemma_4_1) R->L }
% 0.19/0.39 fresh10(organization(x), true2, x, t0, t)
% 0.19/0.39 = { by axiom 7 (assumption_6_1) }
% 0.19/0.39 fresh9(greater(external_ties(x, t), external_ties(x, t0)), true2, x, t0, t)
% 0.19/0.39 = { by axiom 5 (assumption_8) R->L }
% 0.19/0.39 fresh9(fresh8(true2, true2, x, t0, t), true2, x, t0, t)
% 0.19/0.39 = { by axiom 1 (lemma_4_1) R->L }
% 0.19/0.39 fresh9(fresh8(organization(x), true2, x, t0, t), true2, x, t0, t)
% 0.19/0.39 = { by axiom 8 (assumption_8) }
% 0.19/0.39 fresh9(fresh7(greater(age(x, t), age(x, t0)), true2, x, t0, t), true2, x, t0, t)
% 0.19/0.39 = { by axiom 6 (lemma_4) }
% 0.19/0.39 fresh9(fresh7(true2, true2, x, t0, t), true2, x, t0, t)
% 0.19/0.39 = { by axiom 3 (assumption_8) }
% 0.19/0.39 fresh9(true2, true2, x, t0, t)
% 0.19/0.39 = { by axiom 2 (assumption_6_1) }
% 0.19/0.39 true2
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Theorem (the conjecture is true).
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