TSTP Solution File: LAT037-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LAT037-1 : 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 : n020.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 06:27:13 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% 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
% 0.00/0.12 % Problem : LAT037-1 : 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
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 09:52:15 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
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% 0.20/0.40 % SZS status Unsatisfiable
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% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Take the following subset of the input axioms:
% 0.20/0.40 fof(commutativity_of_join, axiom, ![X, Y]: join(X, Y)=join(Y, X)).
% 0.20/0.40 fof(commutativity_of_meet, axiom, ![X2, Y2]: meet(X2, Y2)=meet(Y2, X2)).
% 0.20/0.40 fof(dist_meet, hypothesis, ![Z, X2, Y2]: meet(X2, join(Y2, Z))=join(meet(X2, Y2), meet(X2, Z))).
% 0.20/0.40 fof(lhs1, axiom, join(xx, yy)=n1).
% 0.20/0.40 fof(lhs2, axiom, join(xx, zz)=n1).
% 0.20/0.40 fof(lhs3, axiom, meet(xx, yy)=n0).
% 0.20/0.40 fof(lhs4, axiom, meet(xx, zz)=n0).
% 0.20/0.40 fof(rhs, negated_conjecture, yy!=zz).
% 0.20/0.40 fof(x_join_0, axiom, ![X2]: join(X2, n0)=X2).
% 0.20/0.40 fof(x_meet_1, axiom, ![X2]: meet(X2, n1)=X2).
% 0.20/0.40
% 0.20/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.40 fresh(y, y, x1...xn) = u
% 0.20/0.40 C => fresh(s, t, x1...xn) = v
% 0.20/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.40 variables of u and v.
% 0.20/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.40 input problem has no model of domain size 1).
% 0.20/0.40
% 0.20/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.40
% 0.20/0.40 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.20/0.40 Axiom 2 (x_join_0): join(X, n0) = X.
% 0.20/0.40 Axiom 3 (lhs1): join(xx, yy) = n1.
% 0.20/0.40 Axiom 4 (lhs2): join(xx, zz) = n1.
% 0.20/0.40 Axiom 5 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.20/0.40 Axiom 6 (x_meet_1): meet(X, n1) = X.
% 0.20/0.40 Axiom 7 (lhs3): meet(xx, yy) = n0.
% 0.20/0.40 Axiom 8 (lhs4): meet(xx, zz) = n0.
% 0.20/0.40 Axiom 9 (dist_meet): meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)).
% 0.20/0.40
% 0.20/0.40 Goal 1 (rhs): yy = zz.
% 0.20/0.40 Proof:
% 0.20/0.40 yy
% 0.20/0.40 = { by axiom 6 (x_meet_1) R->L }
% 0.20/0.40 meet(yy, n1)
% 0.20/0.40 = { by axiom 4 (lhs2) R->L }
% 0.20/0.40 meet(yy, join(xx, zz))
% 0.20/0.40 = { by axiom 1 (commutativity_of_join) }
% 0.20/0.40 meet(yy, join(zz, xx))
% 0.20/0.40 = { by axiom 9 (dist_meet) }
% 0.20/0.40 join(meet(yy, zz), meet(yy, xx))
% 0.20/0.40 = { by axiom 5 (commutativity_of_meet) R->L }
% 0.20/0.40 join(meet(yy, zz), meet(xx, yy))
% 0.20/0.40 = { by axiom 7 (lhs3) }
% 0.20/0.40 join(meet(yy, zz), n0)
% 0.20/0.40 = { by axiom 2 (x_join_0) }
% 0.20/0.40 meet(yy, zz)
% 0.20/0.40 = { by axiom 5 (commutativity_of_meet) R->L }
% 0.20/0.40 meet(zz, yy)
% 0.20/0.40 = { by axiom 2 (x_join_0) R->L }
% 0.20/0.40 join(meet(zz, yy), n0)
% 0.20/0.40 = { by axiom 8 (lhs4) R->L }
% 0.20/0.40 join(meet(zz, yy), meet(xx, zz))
% 0.20/0.40 = { by axiom 5 (commutativity_of_meet) }
% 0.20/0.40 join(meet(zz, yy), meet(zz, xx))
% 0.20/0.40 = { by axiom 9 (dist_meet) R->L }
% 0.20/0.40 meet(zz, join(yy, xx))
% 0.20/0.40 = { by axiom 1 (commutativity_of_join) R->L }
% 0.20/0.40 meet(zz, join(xx, yy))
% 0.20/0.40 = { by axiom 3 (lhs1) }
% 0.20/0.40 meet(zz, n1)
% 0.20/0.40 = { by axiom 6 (x_meet_1) }
% 0.20/0.40 zz
% 0.20/0.40 % SZS output end Proof
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% 0.20/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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