TSTP Solution File: LAT225-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT225-1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n007.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 06:27:50 EDT 2023
% Result : Unsatisfiable 44.06s 5.97s
% Output : Proof 44.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT225-1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Aug 24 06:02:10 EDT 2023
% 0.11/0.34 % CPUTime :
% 44.06/5.97 Command-line arguments: --no-flatten-goal
% 44.06/5.97
% 44.06/5.97 % SZS status Unsatisfiable
% 44.06/5.97
% 44.30/5.99 % SZS output start Proof
% 44.30/5.99 Take the following subset of the input axioms:
% 44.30/5.99 fof(absorption1, axiom, ![X, Y]: meet(X, join(X, Y))=X).
% 44.30/5.99 fof(absorption2, axiom, ![X2, Y2]: join(X2, meet(X2, Y2))=X2).
% 44.30/5.99 fof(associativity_of_join, axiom, ![Z, X2, Y2]: join(join(X2, Y2), Z)=join(X2, join(Y2, Z))).
% 44.30/5.99 fof(associativity_of_meet, axiom, ![X2, Y2, Z2]: meet(meet(X2, Y2), Z2)=meet(X2, meet(Y2, Z2))).
% 44.30/5.99 fof(commutativity_of_join, axiom, ![X2, Y2]: join(X2, Y2)=join(Y2, X2)).
% 44.30/5.99 fof(commutativity_of_meet, axiom, ![X2, Y2]: meet(X2, Y2)=meet(Y2, X2)).
% 44.30/5.99 fof(complement_join, axiom, ![X2]: join(X2, complement(X2))=one).
% 44.30/5.99 fof(complement_meet, axiom, ![X2]: meet(X2, complement(X2))=zero).
% 44.30/5.99 fof(equation_H10, axiom, ![X2, Y2, Z2]: meet(X2, join(Y2, meet(X2, Z2)))=meet(X2, join(Y2, meet(Z2, join(X2, meet(Y2, Z2)))))).
% 44.30/5.99 fof(meet_join_complement, axiom, ![X2, Y2]: (meet(X2, Y2)!=zero | (join(X2, Y2)!=one | complement(X2)=Y2))).
% 44.30/5.99 fof(prove_distributivity, negated_conjecture, join(complement(b), complement(a))!=complement(a)).
% 44.30/5.99 fof(prove_distributivity_hypothesis, hypothesis, meet(b, a)=a).
% 44.30/5.99
% 44.30/5.99 Now clausify the problem and encode Horn clauses using encoding 3 of
% 44.30/5.99 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 44.30/5.99 We repeatedly replace C & s=t => u=v by the two clauses:
% 44.30/5.99 fresh(y, y, x1...xn) = u
% 44.30/5.99 C => fresh(s, t, x1...xn) = v
% 44.30/5.99 where fresh is a fresh function symbol and x1..xn are the free
% 44.30/5.99 variables of u and v.
% 44.30/5.99 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 44.30/5.99 input problem has no model of domain size 1).
% 44.30/5.99
% 44.30/5.99 The encoding turns the above axioms into the following unit equations and goals:
% 44.30/5.99
% 44.30/5.99 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 44.30/5.99 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 44.30/5.99 Axiom 3 (prove_distributivity_hypothesis): meet(b, a) = a.
% 44.30/5.99 Axiom 4 (complement_join): join(X, complement(X)) = one.
% 44.30/5.99 Axiom 5 (complement_meet): meet(X, complement(X)) = zero.
% 44.30/5.99 Axiom 6 (meet_join_complement): fresh(X, X, Y, Z) = Z.
% 44.30/5.99 Axiom 7 (meet_join_complement): fresh2(X, X, Y, Z) = complement(Y).
% 44.30/5.99 Axiom 8 (absorption2): join(X, meet(X, Y)) = X.
% 44.30/5.99 Axiom 9 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 44.30/5.99 Axiom 10 (absorption1): meet(X, join(X, Y)) = X.
% 44.30/5.99 Axiom 11 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 44.30/5.99 Axiom 12 (meet_join_complement): fresh2(join(X, Y), one, X, Y) = fresh(meet(X, Y), zero, X, Y).
% 44.30/5.99 Axiom 13 (equation_H10): meet(X, join(Y, meet(X, Z))) = meet(X, join(Y, meet(Z, join(X, meet(Y, Z))))).
% 44.30/5.99
% 44.30/5.99 Lemma 14: meet(X, one) = X.
% 44.30/5.99 Proof:
% 44.30/5.99 meet(X, one)
% 44.30/5.99 = { by axiom 4 (complement_join) R->L }
% 44.30/5.99 meet(X, join(X, complement(X)))
% 44.30/5.99 = { by axiom 10 (absorption1) }
% 44.30/5.99 X
% 44.30/5.99
% 44.30/5.99 Lemma 15: meet(one, X) = X.
% 44.30/5.99 Proof:
% 44.30/5.99 meet(one, X)
% 44.30/5.99 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.30/5.99 meet(X, one)
% 44.30/5.99 = { by lemma 14 }
% 44.30/5.99 X
% 44.30/5.99
% 44.30/5.99 Lemma 16: join(X, one) = one.
% 44.30/5.99 Proof:
% 44.30/5.99 join(X, one)
% 44.30/5.99 = { by axiom 1 (commutativity_of_join) R->L }
% 44.30/5.99 join(one, X)
% 44.30/5.99 = { by lemma 15 R->L }
% 44.30/5.99 join(one, meet(one, X))
% 44.30/5.99 = { by axiom 8 (absorption2) }
% 44.30/5.99 one
% 44.30/5.99
% 44.30/5.99 Lemma 17: join(X, meet(Y, X)) = X.
% 44.30/5.99 Proof:
% 44.30/5.99 join(X, meet(Y, X))
% 44.30/5.99 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.30/5.99 join(X, meet(X, Y))
% 44.30/5.99 = { by axiom 8 (absorption2) }
% 44.30/5.99 X
% 44.30/5.99
% 44.30/5.99 Goal 1 (prove_distributivity): join(complement(b), complement(a)) = complement(a).
% 44.30/5.99 Proof:
% 44.30/5.99 join(complement(b), complement(a))
% 44.30/5.99 = { by axiom 1 (commutativity_of_join) R->L }
% 44.30/5.99 join(complement(a), complement(b))
% 44.30/5.99 = { by axiom 7 (meet_join_complement) R->L }
% 44.30/5.99 join(complement(a), fresh2(one, one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/5.99 = { by lemma 16 R->L }
% 44.30/5.99 join(complement(a), fresh2(join(b, one), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/5.99 = { by axiom 4 (complement_join) R->L }
% 44.30/5.99 join(complement(a), fresh2(join(b, join(meet(b, complement(a)), complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/5.99 = { by axiom 9 (associativity_of_join) R->L }
% 44.30/5.99 join(complement(a), fresh2(join(join(b, meet(b, complement(a))), complement(meet(b, complement(a)))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 8 (absorption2) }
% 44.30/6.00 join(complement(a), fresh2(join(b, complement(meet(b, complement(a)))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by lemma 15 R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(one, complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by lemma 16 R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(join(b, one), complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 4 (complement_join) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(join(b, join(a, complement(a))), complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 9 (associativity_of_join) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(join(join(b, a), complement(a)), complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 3 (prove_distributivity_hypothesis) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(join(join(b, meet(b, a)), complement(a)), complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 8 (absorption2) }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(join(b, complement(a)), complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 1 (commutativity_of_join) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(join(complement(a), b), complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(complement(meet(b, complement(a))), join(complement(a), b))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 1 (commutativity_of_join) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(complement(meet(b, complement(a))), join(b, complement(a)))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by lemma 17 R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(a), meet(complement(meet(b, complement(a))), join(b, complement(a)))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(a), meet(join(b, complement(a)), complement(meet(b, complement(a))))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 11 (associativity_of_meet) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(meet(complement(a), join(b, complement(a))), complement(meet(b, complement(a)))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 2 (commutativity_of_meet) }
% 44.30/6.00 join(complement(a), fresh2(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(meet(b, complement(a))), meet(complement(a), join(b, complement(a)))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 1 (commutativity_of_join) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(meet(b, complement(a))), meet(complement(a), join(complement(a), b))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 10 (absorption1) }
% 44.30/6.00 join(complement(a), fresh2(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(meet(b, complement(a))), complement(a)))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 2 (commutativity_of_meet) }
% 44.30/6.00 join(complement(a), fresh2(join(b, join(meet(complement(meet(b, complement(a))), join(b, complement(a))), meet(complement(a), complement(meet(b, complement(a)))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 1 (commutativity_of_join) }
% 44.30/6.00 join(complement(a), fresh2(join(b, join(meet(complement(a), complement(meet(b, complement(a)))), meet(complement(meet(b, complement(a))), join(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 2 (commutativity_of_meet) }
% 44.30/6.00 join(complement(a), fresh2(join(b, join(meet(complement(a), complement(meet(b, complement(a)))), meet(join(b, complement(a)), complement(meet(b, complement(a)))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 9 (associativity_of_join) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(join(b, complement(a)), complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, complement(a)))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by lemma 14 R->L }
% 44.30/6.00 join(complement(a), fresh2(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), one)))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 4 (complement_join) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(meet(b, complement(a)), complement(meet(b, complement(a)))))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 1 (commutativity_of_join) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), join(complement(meet(b, complement(a))), meet(b, complement(a))))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 13 (equation_H10) R->L }
% 44.30/6.00 join(complement(a), fresh2(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(meet(b, complement(a))), complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 2 (commutativity_of_meet) }
% 44.30/6.00 join(complement(a), fresh2(join(join(b, meet(complement(a), complement(meet(b, complement(a))))), meet(complement(meet(b, complement(a))), join(b, meet(complement(a), complement(meet(b, complement(a))))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by lemma 17 }
% 44.30/6.00 join(complement(a), fresh2(join(b, meet(complement(a), complement(meet(b, complement(a))))), one, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 12 (meet_join_complement) }
% 44.30/6.00 join(complement(a), fresh(meet(b, meet(complement(a), complement(meet(b, complement(a))))), zero, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 11 (associativity_of_meet) R->L }
% 44.30/6.00 join(complement(a), fresh(meet(meet(b, complement(a)), complement(meet(b, complement(a)))), zero, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 5 (complement_meet) }
% 44.30/6.00 join(complement(a), fresh(zero, zero, b, meet(complement(a), complement(meet(b, complement(a))))))
% 44.30/6.00 = { by axiom 6 (meet_join_complement) }
% 44.30/6.00 join(complement(a), meet(complement(a), complement(meet(b, complement(a)))))
% 44.30/6.00 = { by axiom 8 (absorption2) }
% 44.30/6.00 complement(a)
% 44.30/6.00 % SZS output end Proof
% 44.30/6.00
% 44.30/6.00 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------