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 : n027.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 : Unsatisfiable 0.19s 0.40s
% 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 : MGT049-1 : 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 : n027.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
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 06:55:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
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% 0.19/0.40 % SZS status Unsatisfiable
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% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Take the following subset of the input axioms:
% 0.19/0.40 fof(assumption_11_32, axiom, ![B, C, A2]: (~organization(A2) | external_ties(A2, B)=external_ties(A2, C))).
% 0.19/0.40 fof(assumption_6_31, axiom, ![B2, C2, A2_2]: (~organization(A2_2) | (external_ties(A2_2, B2)!=external_ties(A2_2, C2) | position(A2_2, B2)=position(A2_2, C2)))).
% 0.19/0.40 fof(lemma_6_33, negated_conjecture, organization(sk1)).
% 0.19/0.40 fof(lemma_6_35, negated_conjecture, position(sk1, sk3)!=position(sk1, sk2)).
% 0.19/0.40
% 0.19/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.40 fresh(y, y, x1...xn) = u
% 0.19/0.40 C => fresh(s, t, x1...xn) = v
% 0.19/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.40 variables of u and v.
% 0.19/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.40 input problem has no model of domain size 1).
% 0.19/0.40
% 0.19/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.40
% 0.19/0.40 Axiom 1 (lemma_6_33): organization(sk1) = true2.
% 0.19/0.40 Axiom 2 (assumption_11_32): fresh10(X, X, Y, Z, W) = external_ties(Y, W).
% 0.19/0.40 Axiom 3 (assumption_6_31): fresh8(X, X, Y, Z, W) = position(Y, Z).
% 0.19/0.40 Axiom 4 (assumption_6_31): fresh7(X, X, Y, Z, W) = position(Y, W).
% 0.19/0.40 Axiom 5 (assumption_11_32): fresh10(organization(X), true2, X, Y, Z) = external_ties(X, Y).
% 0.19/0.40 Axiom 6 (assumption_6_31): fresh8(organization(X), true2, X, Y, Z) = fresh7(external_ties(X, Y), external_ties(X, Z), X, Y, Z).
% 0.19/0.40
% 0.19/0.40 Goal 1 (lemma_6_35): position(sk1, sk3) = position(sk1, sk2).
% 0.19/0.40 Proof:
% 0.19/0.40 position(sk1, sk3)
% 0.19/0.40 = { by axiom 4 (assumption_6_31) R->L }
% 0.19/0.40 fresh7(external_ties(sk1, sk3), external_ties(sk1, sk3), sk1, sk2, sk3)
% 0.19/0.40 = { by axiom 2 (assumption_11_32) R->L }
% 0.19/0.40 fresh7(fresh10(true2, true2, sk1, sk2, sk3), external_ties(sk1, sk3), sk1, sk2, sk3)
% 0.19/0.40 = { by axiom 1 (lemma_6_33) R->L }
% 0.19/0.40 fresh7(fresh10(organization(sk1), true2, sk1, sk2, sk3), external_ties(sk1, sk3), sk1, sk2, sk3)
% 0.19/0.40 = { by axiom 5 (assumption_11_32) }
% 0.19/0.40 fresh7(external_ties(sk1, sk2), external_ties(sk1, sk3), sk1, sk2, sk3)
% 0.19/0.40 = { by axiom 6 (assumption_6_31) R->L }
% 0.19/0.40 fresh8(organization(sk1), true2, sk1, sk2, sk3)
% 0.19/0.40 = { by axiom 1 (lemma_6_33) }
% 0.19/0.40 fresh8(true2, true2, sk1, sk2, sk3)
% 0.19/0.40 = { by axiom 3 (assumption_6_31) }
% 0.19/0.40 position(sk1, sk2)
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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