TSTP Solution File: MGT049+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : MGT049+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 : n025.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 0.21s 0.42s
% 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
% 0.00/0.14 % Problem : MGT049+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
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 06:40:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.42 Command-line arguments: --no-flatten-goal
% 0.21/0.42
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 Take the following subset of the input axioms:
% 0.21/0.42 fof(assumption_11, axiom, ![X, T0, T]: (organization(X) => external_ties(X, T)=external_ties(X, T0))).
% 0.21/0.42 fof(assumption_6, axiom, ![X2, T0_2, T2]: (organization(X2) => ((greater(external_ties(X2, T2), external_ties(X2, T0_2)) => greater(position(X2, T2), position(X2, T0_2))) & (external_ties(X2, T2)=external_ties(X2, T0_2) => position(X2, T2)=position(X2, T0_2))))).
% 0.21/0.42 fof(lemma_6, conjecture, ![X2, T0_2, T2]: ((organization(X2) & greater(age(X2, T2), age(X2, T0_2))) => position(X2, T2)=position(X2, T0_2))).
% 0.21/0.42
% 0.21/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.42 fresh(y, y, x1...xn) = u
% 0.21/0.42 C => fresh(s, t, x1...xn) = v
% 0.21/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.42 variables of u and v.
% 0.21/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.42 input problem has no model of domain size 1).
% 0.21/0.42
% 0.21/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.42
% 0.21/0.42 Axiom 1 (lemma_6_1): organization(x) = true2.
% 0.21/0.42 Axiom 2 (assumption_6): fresh11(X, X, Y, Z, W) = position(Y, Z).
% 0.21/0.42 Axiom 3 (assumption_11): fresh10(X, X, Y, Z, W) = external_ties(Y, Z).
% 0.21/0.42 Axiom 4 (assumption_6): fresh9(X, X, Y, Z, W) = position(Y, W).
% 0.21/0.42 Axiom 5 (assumption_11): fresh10(organization(X), true2, X, Y, Z) = external_ties(X, Z).
% 0.21/0.42 Axiom 6 (assumption_6): fresh9(organization(X), true2, X, Y, Z) = fresh11(external_ties(X, Z), external_ties(X, Y), X, Y, Z).
% 0.21/0.42
% 0.21/0.42 Goal 1 (lemma_6_2): position(x, t) = position(x, t0).
% 0.21/0.42 Proof:
% 0.21/0.42 position(x, t)
% 0.21/0.42 = { by axiom 2 (assumption_6) R->L }
% 0.21/0.42 fresh11(external_ties(x, t), external_ties(x, t), x, t, t0)
% 0.21/0.42 = { by axiom 3 (assumption_11) R->L }
% 0.21/0.42 fresh11(fresh10(true2, true2, x, t, t0), external_ties(x, t), x, t, t0)
% 0.21/0.42 = { by axiom 1 (lemma_6_1) R->L }
% 0.21/0.42 fresh11(fresh10(organization(x), true2, x, t, t0), external_ties(x, t), x, t, t0)
% 0.21/0.42 = { by axiom 5 (assumption_11) }
% 0.21/0.42 fresh11(external_ties(x, t0), external_ties(x, t), x, t, t0)
% 0.21/0.42 = { by axiom 6 (assumption_6) R->L }
% 0.21/0.42 fresh9(organization(x), true2, x, t, t0)
% 0.21/0.42 = { by axiom 1 (lemma_6_1) }
% 0.21/0.42 fresh9(true2, true2, x, t, t0)
% 0.21/0.42 = { by axiom 4 (assumption_6) }
% 0.21/0.42 position(x, t0)
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Theorem (the conjecture is true).
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