TSTP Solution File: LAT019-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT019-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n025.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 06:27:08 EDT 2023
% Result : Unsatisfiable 0.20s 0.50s
% 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
% 0.00/0.13 % Problem : LAT019-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 09:44:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.50
% 0.20/0.50 % SZS status Unsatisfiable
% 0.20/0.50
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 Axiom 1 (idempotence_of_meet): meet(X, X) = X.
% 0.20/0.51 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.20/0.51 Axiom 3 (idempotence_of_join): join(X, X) = X.
% 0.20/0.51 Axiom 4 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.20/0.51 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.20/0.51 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.20/0.51 Axiom 7 (distributivity_law): meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)).
% 0.20/0.51 Axiom 8 (quasi_lattice2): meet(join(X, meet(Y, Z)), join(X, Y)) = join(X, meet(Y, Z)).
% 0.20/0.51
% 0.20/0.51 Lemma 9: meet(X, join(Y, meet(X, Z))) = meet(X, join(Z, Y)).
% 0.20/0.51 Proof:
% 0.20/0.51 meet(X, join(Y, meet(X, Z)))
% 0.20/0.51 = { by axiom 4 (commutativity_of_join) R->L }
% 0.20/0.51 meet(X, join(meet(X, Z), Y))
% 0.20/0.51 = { by axiom 7 (distributivity_law) }
% 0.20/0.51 join(meet(X, meet(X, Z)), meet(X, Y))
% 0.20/0.51 = { by axiom 5 (associativity_of_meet) R->L }
% 0.20/0.51 join(meet(meet(X, X), Z), meet(X, Y))
% 0.20/0.51 = { by axiom 1 (idempotence_of_meet) }
% 0.20/0.51 join(meet(X, Z), meet(X, Y))
% 0.20/0.51 = { by axiom 7 (distributivity_law) R->L }
% 0.20/0.51 meet(X, join(Z, Y))
% 0.20/0.51
% 0.20/0.51 Lemma 10: join(meet(X, Y), meet(Z, Y)) = meet(Y, join(X, Z)).
% 0.20/0.51 Proof:
% 0.20/0.51 join(meet(X, Y), meet(Z, Y))
% 0.20/0.51 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.51 join(meet(X, Y), meet(Y, Z))
% 0.20/0.51 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.51 join(meet(Y, X), meet(Y, Z))
% 0.20/0.51 = { by axiom 7 (distributivity_law) R->L }
% 0.20/0.51 meet(Y, join(X, Z))
% 0.20/0.51
% 0.20/0.51 Lemma 11: meet(join(X, Y), join(Y, meet(Z, X))) = join(Y, meet(X, Z)).
% 0.20/0.51 Proof:
% 0.20/0.51 meet(join(X, Y), join(Y, meet(Z, X)))
% 0.20/0.51 = { by axiom 4 (commutativity_of_join) R->L }
% 0.20/0.51 meet(join(Y, X), join(Y, meet(Z, X)))
% 0.20/0.51 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.51 meet(join(Y, X), join(Y, meet(X, Z)))
% 0.20/0.51 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.51 meet(join(Y, meet(X, Z)), join(Y, X))
% 0.20/0.51 = { by axiom 8 (quasi_lattice2) }
% 0.20/0.51 join(Y, meet(X, Z))
% 0.20/0.51
% 0.20/0.51 Lemma 12: join(meet(X, Y), meet(Z, join(Y, Z))) = join(Z, meet(X, Y)).
% 0.20/0.51 Proof:
% 0.20/0.51 join(meet(X, Y), meet(Z, join(Y, Z)))
% 0.20/0.51 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.51 join(meet(Y, X), meet(Z, join(Y, Z)))
% 0.20/0.51 = { by axiom 4 (commutativity_of_join) R->L }
% 0.20/0.51 join(meet(Z, join(Y, Z)), meet(Y, X))
% 0.20/0.51 = { by lemma 11 R->L }
% 0.20/0.51 meet(join(Y, meet(Z, join(Y, Z))), join(meet(Z, join(Y, Z)), meet(X, Y)))
% 0.20/0.51 = { by axiom 4 (commutativity_of_join) }
% 0.20/0.51 meet(join(Y, meet(Z, join(Y, Z))), join(meet(X, Y), meet(Z, join(Y, Z))))
% 0.20/0.51 = { by axiom 4 (commutativity_of_join) R->L }
% 0.20/0.51 meet(join(Y, meet(Z, join(Z, Y))), join(meet(X, Y), meet(Z, join(Y, Z))))
% 0.20/0.51 = { by lemma 11 R->L }
% 0.20/0.51 meet(meet(join(Z, Y), join(Y, meet(join(Z, Y), Z))), join(meet(X, Y), meet(Z, join(Y, Z))))
% 0.20/0.51 = { by lemma 9 }
% 0.20/0.51 meet(meet(join(Z, Y), join(Z, Y)), join(meet(X, Y), meet(Z, join(Y, Z))))
% 0.20/0.51 = { by axiom 1 (idempotence_of_meet) }
% 0.20/0.51 meet(join(Z, Y), join(meet(X, Y), meet(Z, join(Y, Z))))
% 0.20/0.51 = { by axiom 4 (commutativity_of_join) }
% 0.20/0.51 meet(join(Y, Z), join(meet(X, Y), meet(Z, join(Y, Z))))
% 0.20/0.51 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.20/0.51 meet(join(Y, Z), join(meet(X, Y), meet(join(Y, Z), Z)))
% 0.20/0.51 = { by lemma 9 }
% 0.20/0.51 meet(join(Y, Z), join(Z, meet(X, Y)))
% 0.20/0.51 = { by lemma 11 }
% 0.20/0.51 join(Z, meet(Y, X))
% 0.20/0.51 = { by axiom 2 (commutativity_of_meet) }
% 0.20/0.51 join(Z, meet(X, Y))
% 0.20/0.51
% 0.20/0.51 Goal 1 (prove_distributivity_law_dual): join(a, meet(b, c)) = meet(join(a, b), join(a, c)).
% 0.20/0.51 Proof:
% 0.20/0.51 join(a, meet(b, c))
% 0.20/0.51 = { by lemma 12 R->L }
% 0.20/0.51 join(meet(b, c), meet(a, join(c, a)))
% 0.20/0.52 = { by axiom 4 (commutativity_of_join) }
% 0.20/0.52 join(meet(a, join(c, a)), meet(b, c))
% 0.20/0.52 = { by axiom 4 (commutativity_of_join) }
% 0.20/0.52 join(meet(a, join(a, c)), meet(b, c))
% 0.20/0.52 = { by axiom 7 (distributivity_law) }
% 0.20/0.52 join(join(meet(a, a), meet(a, c)), meet(b, c))
% 0.20/0.52 = { by axiom 1 (idempotence_of_meet) }
% 0.20/0.52 join(join(a, meet(a, c)), meet(b, c))
% 0.20/0.52 = { by axiom 6 (associativity_of_join) }
% 0.20/0.52 join(a, join(meet(a, c), meet(b, c)))
% 0.20/0.52 = { by axiom 4 (commutativity_of_join) }
% 0.20/0.52 join(a, join(meet(b, c), meet(a, c)))
% 0.20/0.52 = { by lemma 10 }
% 0.20/0.52 join(a, meet(c, join(b, a)))
% 0.20/0.52 = { by axiom 4 (commutativity_of_join) R->L }
% 0.20/0.52 join(a, meet(c, join(a, b)))
% 0.20/0.52 = { by lemma 12 R->L }
% 0.20/0.52 join(meet(c, join(a, b)), meet(a, join(join(a, b), a)))
% 0.20/0.52 = { by axiom 4 (commutativity_of_join) }
% 0.20/0.52 join(meet(c, join(a, b)), meet(a, join(a, join(a, b))))
% 0.20/0.52 = { by axiom 6 (associativity_of_join) R->L }
% 0.20/0.52 join(meet(c, join(a, b)), meet(a, join(join(a, a), b)))
% 0.20/0.52 = { by axiom 3 (idempotence_of_join) }
% 0.20/0.52 join(meet(c, join(a, b)), meet(a, join(a, b)))
% 0.20/0.52 = { by lemma 10 }
% 0.20/0.52 meet(join(a, b), join(c, a))
% 0.20/0.52 = { by axiom 4 (commutativity_of_join) }
% 0.20/0.52 meet(join(a, b), join(a, c))
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52
% 0.20/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
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