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 : n023.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 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MGT045-1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 06:43:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.39 Command-line arguments: --no-flatten-goal
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% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 Take the following subset of the input axioms:
% 0.12/0.39 fof(assumption_6_30, axiom, ![B, C, A2]: (~organization(A2) | (~greater(external_ties(A2, B), external_ties(A2, C)) | greater(position(A2, B), position(A2, C))))).
% 0.12/0.39 fof(assumption_8_32, axiom, ![B2, C2, A2_2]: (~organization(A2_2) | (~greater(age(A2_2, B2), age(A2_2, C2)) | greater(external_ties(A2_2, B2), external_ties(A2_2, C2))))).
% 0.12/0.39 fof(lemma_4_33, negated_conjecture, organization(sk1)).
% 0.12/0.39 fof(lemma_4_34, negated_conjecture, greater(age(sk1, sk3), age(sk1, sk2))).
% 0.12/0.39 fof(lemma_4_35, negated_conjecture, ~greater(position(sk1, sk3), position(sk1, sk2))).
% 0.12/0.39
% 0.12/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.12/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.12/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.12/0.39 fresh(y, y, x1...xn) = u
% 0.12/0.39 C => fresh(s, t, x1...xn) = v
% 0.12/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.12/0.39 variables of u and v.
% 0.12/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.12/0.39 input problem has no model of domain size 1).
% 0.12/0.39
% 0.12/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.12/0.39
% 0.12/0.39 Axiom 1 (lemma_4_33): organization(sk1) = true2.
% 0.12/0.39 Axiom 2 (assumption_6_30): fresh12(X, X, Y, Z, W) = true2.
% 0.12/0.39 Axiom 3 (assumption_8_32): fresh7(X, X, Y, Z, W) = true2.
% 0.12/0.39 Axiom 4 (lemma_4_34): greater(age(sk1, sk3), age(sk1, sk2)) = true2.
% 0.12/0.39 Axiom 5 (assumption_8_32): fresh8(X, X, Y, Z, W) = greater(external_ties(Y, Z), external_ties(Y, W)).
% 0.12/0.39 Axiom 6 (assumption_6_30): fresh11(X, X, Y, Z, W) = greater(position(Y, Z), position(Y, W)).
% 0.12/0.39 Axiom 7 (assumption_6_30): fresh11(organization(X), true2, X, Y, Z) = fresh12(greater(external_ties(X, Y), external_ties(X, Z)), true2, X, Y, Z).
% 0.12/0.39 Axiom 8 (assumption_8_32): fresh8(organization(X), true2, X, Y, Z) = fresh7(greater(age(X, Y), age(X, Z)), true2, X, Y, Z).
% 0.12/0.39
% 0.12/0.39 Goal 1 (lemma_4_35): greater(position(sk1, sk3), position(sk1, sk2)) = true2.
% 0.12/0.39 Proof:
% 0.12/0.40 greater(position(sk1, sk3), position(sk1, sk2))
% 0.12/0.40 = { by axiom 6 (assumption_6_30) R->L }
% 0.12/0.40 fresh11(true2, true2, sk1, sk3, sk2)
% 0.12/0.40 = { by axiom 1 (lemma_4_33) R->L }
% 0.12/0.40 fresh11(organization(sk1), true2, sk1, sk3, sk2)
% 0.12/0.40 = { by axiom 7 (assumption_6_30) }
% 0.12/0.40 fresh12(greater(external_ties(sk1, sk3), external_ties(sk1, sk2)), true2, sk1, sk3, sk2)
% 0.12/0.40 = { by axiom 5 (assumption_8_32) R->L }
% 0.12/0.40 fresh12(fresh8(true2, true2, sk1, sk3, sk2), true2, sk1, sk3, sk2)
% 0.12/0.40 = { by axiom 1 (lemma_4_33) R->L }
% 0.12/0.40 fresh12(fresh8(organization(sk1), true2, sk1, sk3, sk2), true2, sk1, sk3, sk2)
% 0.12/0.40 = { by axiom 8 (assumption_8_32) }
% 0.12/0.40 fresh12(fresh7(greater(age(sk1, sk3), age(sk1, sk2)), true2, sk1, sk3, sk2), true2, sk1, sk3, sk2)
% 0.12/0.40 = { by axiom 4 (lemma_4_34) }
% 0.12/0.40 fresh12(fresh7(true2, true2, sk1, sk3, sk2), true2, sk1, sk3, sk2)
% 0.12/0.40 = { by axiom 3 (assumption_8_32) }
% 0.12/0.40 fresh12(true2, true2, sk1, sk3, sk2)
% 0.12/0.40 = { by axiom 2 (assumption_6_30) }
% 0.12/0.40 true2
% 0.12/0.40 % SZS output end Proof
% 0.12/0.40
% 0.12/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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