TSTP Solution File: LAT009-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT009-1 : 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 : n006.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 06:27:06 EDT 2023
% Result : Unsatisfiable 3.39s 0.83s
% Output : Proof 3.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT009-1 : 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
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 07:54:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.39/0.83 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 3.39/0.83
% 3.39/0.83 % SZS status Unsatisfiable
% 3.39/0.83
% 3.39/0.85 % SZS output start Proof
% 3.39/0.85 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 3.39/0.85 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 3.39/0.85 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 3.39/0.85 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 3.39/0.85 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 3.39/0.85 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 3.39/0.85 Axiom 7 (distributivity_dual): join(meet(join(meet(X, Y), Z), Y), meet(Z, X)) = meet(join(meet(join(X, Y), Z), Y), join(Z, X)).
% 3.39/0.85
% 3.39/0.85 Lemma 8: join(X, meet(Y, X)) = X.
% 3.39/0.85 Proof:
% 3.39/0.85 join(X, meet(Y, X))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, meet(X, Y))
% 3.39/0.85 = { by axiom 5 (absorption2) }
% 3.39/0.85 X
% 3.39/0.85
% 3.39/0.85 Lemma 9: meet(X, meet(Y, join(X, Z))) = meet(X, Y).
% 3.39/0.85 Proof:
% 3.39/0.85 meet(X, meet(Y, join(X, Z)))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 meet(X, meet(join(X, Z), Y))
% 3.39/0.85 = { by axiom 4 (associativity_of_meet) R->L }
% 3.39/0.85 meet(meet(X, join(X, Z)), Y)
% 3.39/0.85 = { by axiom 3 (absorption1) }
% 3.39/0.85 meet(X, Y)
% 3.39/0.85
% 3.39/0.85 Lemma 10: join(X, join(meet(Y, X), Z)) = join(X, Z).
% 3.39/0.85 Proof:
% 3.39/0.85 join(X, join(meet(Y, X), Z))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(X, join(Z, meet(Y, X)))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, join(Z, meet(X, Y)))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(X, join(meet(X, Y), Z))
% 3.39/0.85 = { by axiom 6 (associativity_of_join) R->L }
% 3.39/0.85 join(join(X, meet(X, Y)), Z)
% 3.39/0.85 = { by axiom 5 (absorption2) }
% 3.39/0.85 join(X, Z)
% 3.39/0.85
% 3.39/0.85 Lemma 11: join(X, join(Y, meet(Z, join(X, Y)))) = join(X, Y).
% 3.39/0.85 Proof:
% 3.39/0.85 join(X, join(Y, meet(Z, join(X, Y))))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, join(Y, meet(join(X, Y), Z)))
% 3.39/0.85 = { by axiom 6 (associativity_of_join) R->L }
% 3.39/0.85 join(join(X, Y), meet(join(X, Y), Z))
% 3.39/0.85 = { by axiom 5 (absorption2) }
% 3.39/0.85 join(X, Y)
% 3.39/0.85
% 3.39/0.85 Lemma 12: join(X, meet(join(Y, X), join(X, Z))) = meet(join(Y, X), join(X, Z)).
% 3.39/0.85 Proof:
% 3.39/0.85 join(X, meet(join(Y, X), join(X, Z)))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(X, meet(join(Y, X), join(Z, X)))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(X, meet(join(X, Y), join(Z, X)))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, meet(join(Z, X), join(X, Y)))
% 3.39/0.85 = { by axiom 3 (absorption1) R->L }
% 3.39/0.85 join(meet(X, join(X, Z)), meet(join(Z, X), join(X, Y)))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.39/0.85 join(meet(X, join(Z, X)), meet(join(Z, X), join(X, Y)))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(meet(join(Z, X), join(X, Y)), meet(X, join(Z, X)))
% 3.39/0.85 = { by lemma 9 R->L }
% 3.39/0.85 join(meet(join(Z, X), join(X, Y)), meet(X, meet(join(Z, X), join(X, Y))))
% 3.39/0.85 = { by lemma 8 }
% 3.39/0.85 meet(join(Z, X), join(X, Y))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) }
% 3.39/0.85 meet(join(X, Y), join(Z, X))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.39/0.85 meet(join(Y, X), join(Z, X))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.39/0.85 meet(join(Y, X), join(X, Z))
% 3.39/0.85
% 3.39/0.85 Lemma 13: join(X, meet(join(X, Y), Z)) = join(X, meet(Z, Y)).
% 3.39/0.85 Proof:
% 3.39/0.85 join(X, meet(join(X, Y), Z))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, meet(Z, join(X, Y)))
% 3.39/0.85 = { by lemma 9 R->L }
% 3.39/0.85 join(X, meet(Z, meet(join(X, Y), join(Z, meet(join(Y, Z), X)))))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(X, meet(Z, meet(join(X, Y), join(meet(join(Y, Z), X), Z))))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, meet(Z, meet(join(meet(join(Y, Z), X), Z), join(X, Y))))
% 3.39/0.85 = { by axiom 7 (distributivity_dual) R->L }
% 3.39/0.85 join(X, meet(Z, join(meet(join(meet(Y, Z), X), Z), meet(X, Y))))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.39/0.85 join(X, meet(Z, join(meet(X, Y), meet(join(meet(Y, Z), X), Z))))
% 3.39/0.85 = { by lemma 8 R->L }
% 3.39/0.85 join(X, join(meet(Z, join(meet(X, Y), meet(join(meet(Y, Z), X), Z))), meet(join(meet(Y, Z), X), meet(Z, join(meet(X, Y), meet(join(meet(Y, Z), X), Z))))))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(X, join(meet(Z, join(meet(X, Y), meet(join(meet(Y, Z), X), Z))), meet(join(meet(Y, Z), X), meet(Z, join(meet(join(meet(Y, Z), X), Z), meet(X, Y))))))
% 3.39/0.85 = { by axiom 4 (associativity_of_meet) R->L }
% 3.39/0.85 join(X, join(meet(Z, join(meet(X, Y), meet(join(meet(Y, Z), X), Z))), meet(meet(join(meet(Y, Z), X), Z), join(meet(join(meet(Y, Z), X), Z), meet(X, Y)))))
% 3.39/0.85 = { by axiom 3 (absorption1) }
% 3.39/0.85 join(X, join(meet(Z, join(meet(X, Y), meet(join(meet(Y, Z), X), Z))), meet(join(meet(Y, Z), X), Z)))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.39/0.85 join(X, join(meet(join(meet(Y, Z), X), Z), meet(Z, join(meet(X, Y), meet(join(meet(Y, Z), X), Z)))))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) }
% 3.39/0.85 join(X, join(meet(join(meet(Y, Z), X), Z), meet(Z, join(meet(X, Y), meet(Z, join(meet(Y, Z), X))))))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) }
% 3.39/0.85 join(X, join(meet(Z, join(meet(Y, Z), X)), meet(Z, join(meet(X, Y), meet(Z, join(meet(Y, Z), X))))))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) }
% 3.39/0.85 join(X, join(meet(Z, join(meet(Y, Z), X)), meet(Z, join(meet(Z, join(meet(Y, Z), X)), meet(X, Y)))))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, join(meet(Z, join(meet(Y, Z), X)), meet(Z, join(meet(Z, join(meet(Y, Z), X)), meet(Y, X)))))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(X, join(meet(Z, join(meet(Y, Z), X)), meet(Z, join(meet(Y, X), meet(Z, join(meet(Y, Z), X))))))
% 3.39/0.85 = { by lemma 10 R->L }
% 3.39/0.85 join(X, join(meet(Y, X), join(meet(Z, join(meet(Y, Z), X)), meet(Z, join(meet(Y, X), meet(Z, join(meet(Y, Z), X)))))))
% 3.39/0.85 = { by lemma 11 }
% 3.39/0.85 join(X, join(meet(Y, X), meet(Z, join(meet(Y, Z), X))))
% 3.39/0.85 = { by lemma 10 }
% 3.39/0.85 join(X, meet(Z, join(meet(Y, Z), X)))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(X, meet(Z, join(X, meet(Y, Z))))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, meet(Z, join(X, meet(Z, Y))))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, meet(join(X, meet(Z, Y)), Z))
% 3.39/0.85 = { by axiom 5 (absorption2) R->L }
% 3.39/0.85 join(X, meet(join(X, meet(Z, Y)), join(Z, meet(Z, Y))))
% 3.39/0.85 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.85 join(X, meet(join(X, meet(Z, Y)), join(meet(Z, Y), Z)))
% 3.39/0.85 = { by lemma 12 R->L }
% 3.39/0.85 join(X, join(meet(Z, Y), meet(join(X, meet(Z, Y)), join(meet(Z, Y), Z))))
% 3.39/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.85 join(X, join(meet(Z, Y), meet(join(meet(Z, Y), Z), join(X, meet(Z, Y)))))
% 3.39/0.85 = { by lemma 11 }
% 3.39/0.85 join(X, meet(Z, Y))
% 3.39/0.85
% 3.39/0.85 Goal 1 (prove_distributivity): join(a, meet(b, c)) = meet(join(a, b), join(a, c)).
% 3.39/0.86 Proof:
% 3.39/0.86 join(a, meet(b, c))
% 3.39/0.86 = { by axiom 1 (commutativity_of_meet) R->L }
% 3.39/0.86 join(a, meet(c, b))
% 3.39/0.86 = { by lemma 13 R->L }
% 3.39/0.86 join(a, meet(join(a, b), c))
% 3.39/0.86 = { by lemma 13 R->L }
% 3.39/0.86 join(a, meet(join(a, c), join(a, b)))
% 3.39/0.86 = { by axiom 2 (commutativity_of_join) }
% 3.39/0.86 join(a, meet(join(c, a), join(a, b)))
% 3.39/0.86 = { by lemma 12 }
% 3.39/0.86 meet(join(c, a), join(a, b))
% 3.39/0.86 = { by axiom 1 (commutativity_of_meet) }
% 3.39/0.86 meet(join(a, b), join(c, a))
% 3.39/0.86 = { by axiom 2 (commutativity_of_join) }
% 3.39/0.86 meet(join(b, a), join(c, a))
% 3.39/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.86 meet(join(b, a), join(a, c))
% 3.39/0.86 = { by axiom 2 (commutativity_of_join) R->L }
% 3.39/0.86 meet(join(a, b), join(a, c))
% 3.39/0.86 % SZS output end Proof
% 3.39/0.86
% 3.39/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
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