TSTP Solution File: LAT005-4 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT005-4 : TPTP v8.1.2. Released v1.1.0.
% 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 : n032.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 06:27:05 EDT 2023
% Result : Unsatisfiable 3.30s 0.78s
% Output : Proof 3.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LAT005-4 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Thu Aug 24 06:54:56 EDT 2023
% 0.09/0.27 % CPUTime :
% 3.30/0.78 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.30/0.78
% 3.30/0.78 % SZS status Unsatisfiable
% 3.30/0.79
% 3.97/0.85 % SZS output start Proof
% 3.97/0.85 Take the following subset of the input axioms:
% 3.97/0.85 fof(absorption1, axiom, ![X, Y]: meet(X, join(X, Y))=X).
% 3.97/0.85 fof(absorption2, axiom, ![X2, Y2]: join(X2, meet(X2, Y2))=X2).
% 3.97/0.85 fof(associativity_of_join, axiom, ![Z, X2, Y2]: join(join(X2, Y2), Z)=join(X2, join(Y2, Z))).
% 3.97/0.85 fof(associativity_of_meet, axiom, ![X2, Y2, Z2]: meet(meet(X2, Y2), Z2)=meet(X2, meet(Y2, Z2))).
% 3.97/0.85 fof(commutativity_of_join, axiom, ![X2, Y2]: join(X2, Y2)=join(Y2, X2)).
% 3.97/0.85 fof(commutativity_of_meet, axiom, ![X2, Y2]: meet(X2, Y2)=meet(Y2, X2)).
% 3.97/0.85 fof(define_a2, negated_conjecture, join(r1, meet(b, r2))=a2).
% 3.97/0.85 fof(define_b2, negated_conjecture, join(r1, meet(a, r2))=b2).
% 3.97/0.85 fof(idempotence_of_meet, axiom, ![X2]: meet(X2, X2)=X2).
% 3.97/0.85 fof(modular, axiom, ![X2, Y2, Z2]: (meet(X2, Z2)!=X2 | meet(Z2, join(X2, Y2))=join(X2, meet(Y2, Z2)))).
% 3.97/0.85 fof(prove_SAMs_lemma, negated_conjecture, meet(a2, b2)!=r1).
% 3.97/0.85 fof(r1_complement_join_a_b_2, negated_conjecture, meet(r1, join(a, b))=n0).
% 3.97/0.85 fof(r2_complement_meet_a_b_2, negated_conjecture, meet(r2, meet(a, b))=n0).
% 3.97/0.85 fof(x_join_0, axiom, ![X2]: join(X2, n0)=X2).
% 3.97/0.85 fof(x_meet_0, axiom, ![X2]: meet(X2, n0)=n0).
% 3.97/0.85
% 3.97/0.85 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.97/0.85 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.97/0.85 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.97/0.85 fresh(y, y, x1...xn) = u
% 3.97/0.85 C => fresh(s, t, x1...xn) = v
% 3.97/0.85 where fresh is a fresh function symbol and x1..xn are the free
% 3.97/0.85 variables of u and v.
% 3.97/0.85 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.97/0.85 input problem has no model of domain size 1).
% 3.97/0.85
% 3.97/0.85 The encoding turns the above axioms into the following unit equations and goals:
% 3.97/0.85
% 3.97/0.85 Axiom 1 (idempotence_of_meet): meet(X, X) = X.
% 3.97/0.85 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 3.97/0.85 Axiom 3 (x_meet_0): meet(X, n0) = n0.
% 3.97/0.85 Axiom 4 (commutativity_of_join): join(X, Y) = join(Y, X).
% 3.97/0.85 Axiom 5 (x_join_0): join(X, n0) = X.
% 3.97/0.85 Axiom 6 (absorption1): meet(X, join(X, Y)) = X.
% 3.97/0.85 Axiom 7 (r1_complement_join_a_b_2): meet(r1, join(a, b)) = n0.
% 3.97/0.85 Axiom 8 (r2_complement_meet_a_b_2): meet(r2, meet(a, b)) = n0.
% 3.97/0.85 Axiom 9 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 3.97/0.85 Axiom 10 (absorption2): join(X, meet(X, Y)) = X.
% 3.97/0.85 Axiom 11 (define_b2): join(r1, meet(a, r2)) = b2.
% 3.97/0.85 Axiom 12 (define_a2): join(r1, meet(b, r2)) = a2.
% 3.97/0.85 Axiom 13 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 3.97/0.85 Axiom 14 (modular): fresh(X, X, Y, Z, W) = join(Y, meet(W, Z)).
% 3.97/0.85 Axiom 15 (modular): fresh(meet(X, Y), X, X, Y, Z) = meet(Y, join(X, Z)).
% 3.97/0.85
% 3.97/0.85 Lemma 16: meet(r1, b2) = r1.
% 3.97/0.85 Proof:
% 3.97/0.85 meet(r1, b2)
% 3.97/0.85 = { by axiom 11 (define_b2) R->L }
% 3.97/0.85 meet(r1, join(r1, meet(a, r2)))
% 3.97/0.85 = { by axiom 6 (absorption1) }
% 3.97/0.85 r1
% 3.97/0.85
% 3.97/0.85 Lemma 17: meet(X, meet(X, Y)) = meet(X, Y).
% 3.97/0.85 Proof:
% 3.97/0.85 meet(X, meet(X, Y))
% 3.97/0.85 = { by axiom 9 (associativity_of_meet) R->L }
% 3.97/0.85 meet(meet(X, X), Y)
% 3.97/0.85 = { by axiom 1 (idempotence_of_meet) }
% 3.97/0.85 meet(X, Y)
% 3.97/0.85
% 3.97/0.85 Lemma 18: meet(X, meet(Y, Z)) = meet(Y, meet(X, Z)).
% 3.97/0.85 Proof:
% 3.97/0.85 meet(X, meet(Y, Z))
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.85 meet(meet(Y, Z), X)
% 3.97/0.85 = { by axiom 9 (associativity_of_meet) }
% 3.97/0.85 meet(Y, meet(Z, X))
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.85 meet(Y, meet(X, Z))
% 3.97/0.85
% 3.97/0.85 Lemma 19: meet(X, join(Y, X)) = X.
% 3.97/0.85 Proof:
% 3.97/0.85 meet(X, join(Y, X))
% 3.97/0.85 = { by axiom 4 (commutativity_of_join) R->L }
% 3.97/0.85 meet(X, join(X, Y))
% 3.97/0.85 = { by axiom 6 (absorption1) }
% 3.97/0.85 X
% 3.97/0.85
% 3.97/0.85 Lemma 20: meet(Y, meet(Z, X)) = meet(X, meet(Y, Z)).
% 3.97/0.85 Proof:
% 3.97/0.85 meet(Y, meet(Z, X))
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.85 meet(meet(Z, X), Y)
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.85 meet(meet(X, Z), Y)
% 3.97/0.85 = { by axiom 9 (associativity_of_meet) }
% 3.97/0.85 meet(X, meet(Z, Y))
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.85 meet(X, meet(Y, Z))
% 3.97/0.85
% 3.97/0.85 Lemma 21: meet(Z, meet(Y, X)) = meet(X, meet(Y, Z)).
% 3.97/0.85 Proof:
% 3.97/0.85 meet(Z, meet(Y, X))
% 3.97/0.85 = { by lemma 20 }
% 3.97/0.85 meet(X, meet(Z, Y))
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.85 meet(X, meet(Y, Z))
% 3.97/0.85
% 3.97/0.85 Lemma 22: join(X, meet(Y, X)) = X.
% 3.97/0.85 Proof:
% 3.97/0.85 join(X, meet(Y, X))
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.85 join(X, meet(X, Y))
% 3.97/0.85 = { by axiom 10 (absorption2) }
% 3.97/0.85 X
% 3.97/0.85
% 3.97/0.85 Lemma 23: meet(Y, meet(Z, meet(W, X))) = meet(X, meet(Y, meet(Z, W))).
% 3.97/0.85 Proof:
% 3.97/0.85 meet(Y, meet(Z, meet(W, X)))
% 3.97/0.85 = { by axiom 9 (associativity_of_meet) R->L }
% 3.97/0.85 meet(meet(Y, Z), meet(W, X))
% 3.97/0.85 = { by lemma 20 }
% 3.97/0.85 meet(X, meet(meet(Y, Z), W))
% 3.97/0.85 = { by axiom 9 (associativity_of_meet) }
% 3.97/0.85 meet(X, meet(Y, meet(Z, W)))
% 3.97/0.85
% 3.97/0.85 Lemma 24: join(X, meet(Y, join(X, Z))) = meet(join(X, Z), join(X, Y)).
% 3.97/0.85 Proof:
% 3.97/0.85 join(X, meet(Y, join(X, Z)))
% 3.97/0.85 = { by axiom 14 (modular) R->L }
% 3.97/0.85 fresh(X, X, X, join(X, Z), Y)
% 3.97/0.85 = { by axiom 6 (absorption1) R->L }
% 3.97/0.85 fresh(meet(X, join(X, Z)), X, X, join(X, Z), Y)
% 3.97/0.85 = { by axiom 15 (modular) }
% 3.97/0.85 meet(join(X, Z), join(X, Y))
% 3.97/0.85
% 3.97/0.85 Lemma 25: meet(join(a, b), join(b, r1)) = b.
% 3.97/0.85 Proof:
% 3.97/0.85 meet(join(a, b), join(b, r1))
% 3.97/0.85 = { by axiom 4 (commutativity_of_join) R->L }
% 3.97/0.85 meet(join(b, a), join(b, r1))
% 3.97/0.85 = { by lemma 24 R->L }
% 3.97/0.85 join(b, meet(r1, join(b, a)))
% 3.97/0.85 = { by axiom 4 (commutativity_of_join) }
% 3.97/0.85 join(b, meet(r1, join(a, b)))
% 3.97/0.85 = { by axiom 7 (r1_complement_join_a_b_2) }
% 3.97/0.85 join(b, n0)
% 3.97/0.85 = { by axiom 5 (x_join_0) }
% 3.97/0.85 b
% 3.97/0.85
% 3.97/0.85 Lemma 26: meet(X, meet(Y, join(X, Z))) = meet(X, Y).
% 3.97/0.85 Proof:
% 3.97/0.85 meet(X, meet(Y, join(X, Z)))
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.85 meet(X, meet(join(X, Z), Y))
% 3.97/0.85 = { by axiom 9 (associativity_of_meet) R->L }
% 3.97/0.85 meet(meet(X, join(X, Z)), Y)
% 3.97/0.85 = { by axiom 6 (absorption1) }
% 3.97/0.85 meet(X, Y)
% 3.97/0.85
% 3.97/0.85 Lemma 27: join(X, join(Y, meet(X, Z))) = join(X, Y).
% 3.97/0.85 Proof:
% 3.97/0.85 join(X, join(Y, meet(X, Z)))
% 3.97/0.85 = { by axiom 4 (commutativity_of_join) R->L }
% 3.97/0.85 join(X, join(meet(X, Z), Y))
% 3.97/0.85 = { by axiom 13 (associativity_of_join) R->L }
% 3.97/0.85 join(join(X, meet(X, Z)), Y)
% 3.97/0.85 = { by axiom 10 (absorption2) }
% 3.97/0.85 join(X, Y)
% 3.97/0.85
% 3.97/0.85 Lemma 28: meet(a2, meet(X, join(b, r1))) = meet(X, a2).
% 3.97/0.85 Proof:
% 3.97/0.85 meet(a2, meet(X, join(b, r1)))
% 3.97/0.85 = { by lemma 27 R->L }
% 3.97/0.85 meet(a2, meet(X, join(b, join(r1, meet(b, r2)))))
% 3.97/0.85 = { by axiom 12 (define_a2) }
% 3.97/0.85 meet(a2, meet(X, join(b, a2)))
% 3.97/0.85 = { by lemma 18 R->L }
% 3.97/0.85 meet(X, meet(a2, join(b, a2)))
% 3.97/0.85 = { by lemma 19 }
% 3.97/0.85 meet(X, a2)
% 3.97/0.85
% 3.97/0.85 Lemma 29: join(meet(X, Y), meet(X, Z)) = meet(X, join(Z, meet(X, Y))).
% 3.97/0.85 Proof:
% 3.97/0.85 join(meet(X, Y), meet(X, Z))
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.85 join(meet(X, Y), meet(Z, X))
% 3.97/0.85 = { by axiom 14 (modular) R->L }
% 3.97/0.85 fresh(meet(X, Y), meet(X, Y), meet(X, Y), X, Z)
% 3.97/0.85 = { by lemma 17 R->L }
% 3.97/0.85 fresh(meet(X, meet(X, Y)), meet(X, Y), meet(X, Y), X, Z)
% 3.97/0.85 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.85 fresh(meet(meet(X, Y), X), meet(X, Y), meet(X, Y), X, Z)
% 3.97/0.85 = { by axiom 15 (modular) }
% 3.97/0.85 meet(X, join(meet(X, Y), Z))
% 3.97/0.85 = { by axiom 4 (commutativity_of_join) }
% 3.97/0.86 meet(X, join(Z, meet(X, Y)))
% 3.97/0.86
% 3.97/0.86 Lemma 30: meet(b, meet(a2, b2)) = meet(a, meet(a2, b2)).
% 3.97/0.86 Proof:
% 3.97/0.86 meet(b, meet(a2, b2))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 meet(meet(a2, b2), b)
% 3.97/0.86 = { by lemma 22 R->L }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(meet(a, meet(a2, b2)), b)))
% 3.97/0.86 = { by axiom 9 (associativity_of_meet) }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(a, meet(meet(a2, b2), b))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(a, meet(b, meet(a2, b2)))))
% 3.97/0.86 = { by lemma 23 }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(b2, meet(a, meet(b, a2)))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(b2, meet(a, meet(a2, b)))))
% 3.97/0.86 = { by lemma 18 R->L }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(b2, meet(a2, meet(a, b)))))
% 3.97/0.86 = { by lemma 25 R->L }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(b2, meet(a2, meet(a, meet(join(a, b), join(b, r1)))))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(b2, meet(a2, meet(a, meet(join(b, r1), join(a, b)))))))
% 3.97/0.86 = { by lemma 26 }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(b2, meet(a2, meet(a, join(b, r1))))))
% 3.97/0.86 = { by lemma 28 }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(b2, meet(a, a2))))
% 3.97/0.86 = { by lemma 20 R->L }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(a, meet(a2, b2))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 meet(meet(a2, b2), join(b, meet(meet(a2, b2), a)))
% 3.97/0.86 = { by lemma 29 R->L }
% 3.97/0.86 join(meet(meet(a2, b2), a), meet(meet(a2, b2), b))
% 3.97/0.86 = { by axiom 4 (commutativity_of_join) }
% 3.97/0.86 join(meet(meet(a2, b2), b), meet(meet(a2, b2), a))
% 3.97/0.86 = { by lemma 29 }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(meet(a2, b2), b)))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(b, meet(a2, b2))))
% 3.97/0.86 = { by lemma 20 }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(b2, meet(b, a2))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(b2, meet(a2, b))))
% 3.97/0.86 = { by lemma 25 R->L }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(b2, meet(a2, meet(join(a, b), join(b, r1))))))
% 3.97/0.86 = { by lemma 28 }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(b2, meet(join(a, b), a2))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(b2, meet(a2, join(a, b)))))
% 3.97/0.86 = { by lemma 21 R->L }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(join(a, b), meet(a2, b2))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(meet(a2, b2), join(a, b))))
% 3.97/0.86 = { by lemma 24 }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(a, meet(a2, b2))))
% 3.97/0.86 = { by lemma 22 R->L }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(a, join(meet(a2, b2), meet(r1, meet(a2, b2))))))
% 3.97/0.86 = { by lemma 20 }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(a, join(meet(a2, b2), meet(b2, meet(r1, a2))))))
% 3.97/0.86 = { by axiom 12 (define_a2) R->L }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(a, join(meet(a2, b2), meet(b2, meet(r1, join(r1, meet(b, r2))))))))
% 3.97/0.86 = { by axiom 6 (absorption1) }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(a, join(meet(a2, b2), meet(b2, r1)))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(a, join(meet(a2, b2), meet(r1, b2)))))
% 3.97/0.86 = { by lemma 16 }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(a, join(meet(a2, b2), r1))))
% 3.97/0.86 = { by axiom 4 (commutativity_of_join) }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(a, join(r1, meet(a2, b2)))))
% 3.97/0.86 = { by axiom 13 (associativity_of_join) R->L }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(join(a, r1), meet(a2, b2))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(join(a, r1), meet(b2, a2))))
% 3.97/0.86 = { by lemma 26 R->L }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(join(a, r1), meet(b2, meet(a2, join(b2, a))))))
% 3.97/0.86 = { by lemma 21 R->L }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(join(a, r1), meet(join(b2, a), meet(a2, b2)))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(join(a, r1), meet(meet(a2, b2), join(b2, a)))))
% 3.97/0.86 = { by axiom 4 (commutativity_of_join) }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(join(a, r1), meet(meet(a2, b2), join(a, b2)))))
% 3.97/0.86 = { by axiom 11 (define_b2) R->L }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(join(a, r1), meet(meet(a2, b2), join(a, join(r1, meet(a, r2)))))))
% 3.97/0.86 = { by lemma 27 }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(join(a, r1), meet(meet(a2, b2), join(a, r1)))))
% 3.97/0.86 = { by lemma 22 }
% 3.97/0.86 meet(meet(a2, b2), meet(join(a, b), join(a, r1)))
% 3.97/0.86 = { by lemma 24 R->L }
% 3.97/0.86 meet(meet(a2, b2), join(a, meet(r1, join(a, b))))
% 3.97/0.86 = { by axiom 7 (r1_complement_join_a_b_2) }
% 3.97/0.86 meet(meet(a2, b2), join(a, n0))
% 3.97/0.86 = { by axiom 5 (x_join_0) }
% 3.97/0.86 meet(meet(a2, b2), a)
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 meet(a, meet(a2, b2))
% 3.97/0.86
% 3.97/0.86 Goal 1 (prove_SAMs_lemma): meet(a2, b2) = r1.
% 3.97/0.86 Proof:
% 3.97/0.86 meet(a2, b2)
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 meet(b2, a2)
% 3.97/0.86 = { by axiom 12 (define_a2) R->L }
% 3.97/0.86 meet(b2, join(r1, meet(b, r2)))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 meet(b2, join(r1, meet(r2, b)))
% 3.97/0.86 = { by axiom 15 (modular) R->L }
% 3.97/0.86 fresh(meet(r1, b2), r1, r1, b2, meet(r2, b))
% 3.97/0.86 = { by lemma 16 }
% 3.97/0.86 fresh(r1, r1, r1, b2, meet(r2, b))
% 3.97/0.86 = { by axiom 14 (modular) }
% 3.97/0.86 join(r1, meet(meet(r2, b), b2))
% 3.97/0.86 = { by axiom 9 (associativity_of_meet) }
% 3.97/0.86 join(r1, meet(r2, meet(b, b2)))
% 3.97/0.86 = { by lemma 18 }
% 3.97/0.86 join(r1, meet(b, meet(r2, b2)))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 join(r1, meet(b, meet(b2, r2)))
% 3.97/0.86 = { by lemma 18 R->L }
% 3.97/0.86 join(r1, meet(b2, meet(b, r2)))
% 3.97/0.86 = { by lemma 19 R->L }
% 3.97/0.86 join(r1, meet(b2, meet(meet(b, r2), join(r1, meet(b, r2)))))
% 3.97/0.86 = { by axiom 12 (define_a2) }
% 3.97/0.86 join(r1, meet(b2, meet(meet(b, r2), a2)))
% 3.97/0.86 = { by axiom 9 (associativity_of_meet) }
% 3.97/0.86 join(r1, meet(b2, meet(b, meet(r2, a2))))
% 3.97/0.86 = { by lemma 23 R->L }
% 3.97/0.86 join(r1, meet(b, meet(r2, meet(a2, b2))))
% 3.97/0.86 = { by lemma 18 R->L }
% 3.97/0.86 join(r1, meet(r2, meet(b, meet(a2, b2))))
% 3.97/0.86 = { by lemma 30 }
% 3.97/0.86 join(r1, meet(r2, meet(a, meet(a2, b2))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 join(r1, meet(r2, meet(meet(a2, b2), a)))
% 3.97/0.86 = { by axiom 9 (associativity_of_meet) R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), a))
% 3.97/0.86 = { by lemma 17 R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(meet(r2, meet(a2, b2)), a)))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(a, meet(r2, meet(a2, b2)))))
% 3.97/0.86 = { by lemma 17 R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(a, meet(a, meet(r2, meet(a2, b2))))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(a, meet(a, meet(meet(a2, b2), r2)))))
% 3.97/0.86 = { by axiom 9 (associativity_of_meet) R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(a, meet(meet(a, meet(a2, b2)), r2))))
% 3.97/0.86 = { by lemma 30 R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(a, meet(meet(b, meet(a2, b2)), r2))))
% 3.97/0.86 = { by axiom 9 (associativity_of_meet) }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(a, meet(b, meet(meet(a2, b2), r2)))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(a, meet(b, meet(r2, meet(a2, b2))))))
% 3.97/0.86 = { by lemma 18 R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(a, meet(r2, meet(b, meet(a2, b2))))))
% 3.97/0.86 = { by lemma 18 R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(r2, meet(a, meet(b, meet(a2, b2))))))
% 3.97/0.86 = { by axiom 9 (associativity_of_meet) R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(r2, meet(meet(a, b), meet(a2, b2)))))
% 3.97/0.86 = { by axiom 9 (associativity_of_meet) R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(meet(r2, meet(a, b)), meet(a2, b2))))
% 3.97/0.86 = { by axiom 8 (r2_complement_meet_a_b_2) }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(n0, meet(a2, b2))))
% 3.97/0.86 = { by axiom 2 (commutativity_of_meet) R->L }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), meet(meet(a2, b2), n0)))
% 3.97/0.86 = { by axiom 3 (x_meet_0) }
% 3.97/0.86 join(r1, meet(meet(r2, meet(a2, b2)), n0))
% 3.97/0.86 = { by axiom 9 (associativity_of_meet) }
% 3.97/0.86 join(r1, meet(r2, meet(meet(a2, b2), n0)))
% 3.97/0.86 = { by axiom 3 (x_meet_0) }
% 3.97/0.86 join(r1, meet(r2, n0))
% 3.97/0.86 = { by axiom 3 (x_meet_0) }
% 3.97/0.86 join(r1, n0)
% 3.97/0.86 = { by axiom 5 (x_join_0) }
% 3.97/0.86 r1
% 3.97/0.86 % SZS output end Proof
% 3.97/0.86
% 3.97/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------